Article

Normal-eye Zernike coefficients and root-mean-square wavefront errors

January 2007
Journal of Cataract and Refractive Surgery 32(12):2064-74

DOI:10.1016/j.jcrs.2006.07.022

Source
PubMed

Authors:

Marshall B. Ketchum University

To compare aberrometry measurements from multiple sites and compute mean Zernike coefficients and root-mean-square (RMS) values for the entire data pool to serve as a reference set for normal, healthy adult eyes. Northeastern State University, Tahlequah, Oklahoma, USA. Data were collected from 10 laboratories that measured higher-order aberrations (HOAs) in normal, healthy adult eyes using Shack-Hartmann aberrometry (2560 eyes of 1433 subjects). Signed Zernike coefficients were scaled to pupil diameters of 6.0 mm, 5.0 mm, 4.0 mm, and 3.0 mm and corrected to a common wavelength of 550 nm. The mean signed and absolute Zernike coefficients across data sets were compared. Then, the following were computed: overall mean values for signed and absolute Zernike coefficients; polar Zernike magnitudes and RMS values for coma-like aberrations (Z(3)(+/-1) and Z(5)(+/-1) combined); spherical-like aberrations (Z(4)(0) and Z(6)(0) combined); and 3rd-, 4th-, 5th-, and 6th-order, and higher-order aberrations (orders 3 to 6). The different data sets showed good agreement for Zernike coefficients values across most higher-order modes, with greater variability for Z(4)(0) and Z(3)(-1). The most prominent modes and their mean absolute values (6.0-mm pupil) were, respectively, Z(3)(-1) and 0.14 microm, Z(4)(0) and 0.13 microm, and Z(3)(-3) and 0.11 microm. The mean total higher-order RMS was 0.33 microm. There was a general consensus for the magnitude of HOAs expected in normal adult human eyes. At least 90% of the sample had aberrations less than double the mean values reported here. These values can serve as a set of reference norms.

Low Degree / High Degree polynomial decomposition in a large population of healthy normal eyes and how it compares to the Zernike polynomials: an observational study

Preprint

Full-text available

Aug 2022

Purpose: To evaluate and compare the ocular aberrations in healthy normal eyes with Zernike versus Low Degree/High Degree (LD/HD) coefficients using OPD-Scan III wavefront sampling. Methods: Retrospective case series. Ocular wavefront acquisition using automated skiascopy was performed in mesopic conditions on refractive surgery candidates. Root Mean Square (RMS) values were computed for 6 mm pupils and aberration data from the 1st to the 6th order were exported. A Principal Component Analysis was performed to investigate which of the two classifications explained better the variance of the wave aberrations for their respective higher order wavefront components. Results: Data from 3827 eyes of 2110 patients were analyzed. Z1⁻¹ (horizontal tilt) and Z1¹ (vertical tilt) modes had a mean absolute RMS of 0.299 +/- 0.233 μm and 0.242 +/- 0.194 μm. G1⁻¹ and G1¹ had a mean absolute RMS of 0.051 +/- 0.044 μm and 0.045 +/- 0.039 μm. Total Zernike coma (Z3⁻¹, Z3¹, Z5⁻¹ and Z5¹) had a mean absolute RMS of 0.168 +/- 0.089 μm. Total LD/HD coma (G3⁻¹, G3¹, G5⁻¹ and G5¹) had a mean absolute RMS of 0.488 +/- 0.261 μm. Zernike Spherical Aberration (SA = Z4⁰) had a mean absolute RMS of 0.093 +/- 0.070 μm while LD/HD SA (Z4⁰) had a mean absolute RMS of 0.642 +/- 0.481 μm. PCA demonstrated that the LD/HD classification provided a new set of basis functions that better fitted the variance of HOAs, compared with the Zernike classification. Conclusion: This study standardizes Zernike and LD/HD based wavefront reconstructions using the OPD-Scan III in mesopic conditions. LD/HD classifications appear to offer a more efficient description of the eye’s aberrations. The main differences of both classifications are expanded upon.

Adaptive optics for high-resolution imaging

Article

Full-text available

Oct 2021

Adaptive optics (AO) is a technique that corrects for optical aberrations. It was originally proposed to correct for the blurring effect of atmospheric turbulence on images in ground-based telescopes and was instrumental in the work that resulted in the Nobel prize-winning discovery of a supermassive compact object at the centre of our galaxy. When AO is used to correct for the eye’s imperfect optics, retinal changes at the cellular level can be detected, allowing us to study the operation of the visual system and to assess ocular health in the microscopic domain. By correcting for sample-induced blur in microscopy, AO has pushed the boundaries of imaging in thick tissue specimens, such as when observing neuronal processes in the brain. In this primer, we focus on the application of AO for high-resolution imaging in astronomy, vision science and microscopy. We begin with an overview of the general principles of AO and its main components, which include methods to measure the aberrations, devices for aberration correction, and how these components are linked in operation. We present results and applications from each field along with reproducibility considerations and limitations. Finally, we discuss future directions. This Primer provides an overview of the general principles of adaptive optics and explores the different ways in which adaptive optics can correct optical aberrations for high-resolution imaging in the fields of astronomy, vision science and microscopy.

Advancing Digital Workflows for Refractive Error Measurements

Article

Full-text available

Jul 2020

Advancements in clinical measurement of refractive errors should lead to faster and more reliable measurements of such errors. The study investigated different aspects of advancements and the agreement of the spherocylindrical prescriptions obtained with an objective method of measurement (“Aberrometry” (AR)) and two methods of subjective refinements (“Wavefront Refraction” (WR) and “Standard Refraction” (StdR)). One hundred adults aged 20–78 years participated in the course of the study. Bland–Altman analysis of the right eye measurement of the spherocylindrical refractive error (M) identified mean differences (±95% limits of agreement) between the different types of measurements of +0.36 D (±0.76 D) for WR vs. AR (t-test: p < 0.001), +0.35 D (± 0.84 D) for StdR vs. AR (t-test: p < 0.001), and 0.0 D (± 0.65 D) for StdR vs. WR (t-test: p < 0.001). Monocular visual acuity was 0.0 logMAR in 96% of the tested eyes, when refractive errors were corrected with measurements from AR, indicating that only small differences between the different types of prescriptions are present.

Study of accommodation dynamics and defocus fluctuations in the human eye (Title in Spanish: Estudio de la dinámica de la acomodación y las fluctuaciones del desenfoque en el ojo humano)

Thesis

Full-text available

Mar 2023

Vahid Pourreza Ghoushchi

The quality of the retinal image is the first, physical limiting factor of visual quality. Defocus is the most common source of blur leading to retinal image quality loss. It depends on the interrelationship between the eye's axial length, optical power, and distance to the object. Until it is lost with age, the eye has the ability to modify its optical power (i.e., to accommodate) to produce focused retinal images. Although this process is not instantaneous, accommodation is a fast and fairly accurate mechanism in most young subjects, that results in a clear vision. However, it has been suggested that myopia onset and/or progression may be related to alterations in the accommodative process that could upset the emmetropization process. On the other hand, even when steadily looking at an object at a fixed distance, the optical power of the eye fluctuates more or less randomly. It is unclear if this fluctuation is an undesired inability of the eye to keep a constant focus or may serve a purpose in the accommodative process. In any case, from an optical point of view, fast fluctuations of defocus would be expected to produce some kind of blurring in the retinal images. In those circumstances, a short integration time may allow the visual system to select the best focused position in the sequence to maximize visual quality. In this context, this thesis studies the effects of changes in focus, both discrete and progressive, aiming to discern how the visual system copes with them. Two separate experiments were carried out with an open-view Hartmann-Shack sensor measuring refraction and high-order aberrations in real time. First, the dynamics of the accommodative response was analyzed in realistic binocular viewing conditions, both for emmetropic subjects and myopes, when the fixation abruptly changed from far to near. In a second experiment, we studied the effect on contrast sensitivity of fast oscillations of defocus with different magnitudes and temporal frequencies, generated with a tunable lens attached to the system. During the accommodation mechanism, convergence of the eyeballs and miosis of the pupils accompany the change in optical power of the crystalline lens. There is extensive literature on these processes but relatively few studies simultaneously measuring all three of them in binocular vision. To the best of our knowledge, this is the first study of their combined dynamics in real time under realistic viewing conditions. Furthermore, it was performed in both myopic and emmetropic young individuals. Eighteen young subjects participated in the first experiment, with an average refractive error of -2.3 D and a range from -7.5 D to 0 D. Cylinder was below 2 D in all cases. Excluding refractive errors, no subject had a history of visual problems and all of them reached 20/20 VA or better in both eyes. They were corrected during the measurements. The near stimulus, located at 2.8 D, and far target, at 0.36 D, were both black-on-white Maltese crosses with 1.3° width. Each subject underwent 3 cycles of 6 target switching (far-near-far-near-far-near). The data was analyzed with a threshold method consisting of calculating the initial and final states for each studied variable and considering the central 80% of the variation. Several far-to-near response parameters were calculated, including accommodation speed and amplitude, convergence speed and amplitude, pupil miosis speed, and amplitude, high-order aberration RMS, spherical aberration, lag of accommodation, and duration of accommodation, convergence, and pupil miosis. Correlation analysis between refractive error and accommodation speed and of these two variables with various far-to-near response parameters was performed. The correlation analysis of refraction (spherical equivalent, SE) with accommodation dynamics parameters suggests that myopia mildly affects or is affected by accommodation. The lag of accommodation was found to be linked to refractive error (R = -0.57, p = 0.01). Moreover, the correlation between miosis speed and refractive error also had a p-value below 0.05 (R = -0.49, p = 0.04). In other words, myopes may tend to have less precise accommodation and slower pupil constriction. The correlation coefficients between SE and the rest of accommodation-related parameters were small, with p-values well above 0.05. A substantial, low-p-value correlation was found between accommodation speed and convergence speed (R = 0.48, p = 0.04). To the best of our knowledge, this finding has not been previously reported. Furthermore, the correlation was stronger between accommodation speed and convergence duration (R = 0.57, p = 0.01), which may reflect the differences in the dynamics of these two processes. In addition, there may be a correlation between accommodation speed and miosis amplitude since the p-value was below 0.05 (R = 0.47, p = 0.049). These analyses showed that slower accommodation might be a function of slow convergence and more evident pupil miosis. For the second part of the thesis, a faster HS sensor with a refresh rate of 60 Hz and higher sensitivity to 1050 nm IR light was developed. This sensor was employed to characterize an optically tunable lens both in the typical static mode and, for the first time to our knowledge, in dynamic mode. After calibration, the tunable lens was used to apply defocus oscillations during contrast sensitivity measurements. Different amplitudes and frequencies were induced in 5 young emmetropes with 20/20 or better VA and no previous history of visual troubles. The visual stimulus was a 12 c/deg Gabor patch of 1º angular diameter located at 3 m. It was tilted 10 degrees left or right and a two-choice forced-choice protocol was used to determine the contrast threshold for each oscillation condition. The measurements were carried out in monocular mode, and the subjects viewed the stimulus through the tunable lens with their right eye. The sinusoidal waves induced included combinations of 3 temporal frequencies, 5, 15, and 25 Hz, and 8 peak-to-valley defocus values, ranging from 0.15 to 3 D, presented in fully random order. To the best of our knowledge, the effect of this kind of fast fluctuations of defocus on visual quality has not been previously studied. Visual performance, in the form of contrast threshold, was found resilient to induced defocus oscillations. The data showed that only for fast, large variations (25 Hz, ± 1.5 D), there was a noticeable reduction in contrast sensitivity. This indicates that for the eye to clearly perceive visual stimuli, the retinal image only needs to be in focus for a short time. A quantitative model was developed for predicting the deterioration in retinal image quality due to periodic defocus fluctuations. For the amplitudes and frequencies of oscillation used in the experiment, the average PSF was calculated for several integration times and the loss in the ensuing MTF was computed. Comparison between experimental results and simulated data suggests that the eye may be integrating defocus blur at 10 to 20 ms intervals. El proceso de la visión que finaliza con la sensación de ver algo, es decir, con la percepción de un estímulo visual, comienza con la formación de la imagen del mundo sobre la retina. Esto hace que, aunque pueden surgir múltiples complicaciones a distintos niveles que empeoren la calidad visual, la calidad de la imagen retiniana impone un primer límite físico a nuestra capacidad de distinguir detalles y extraer información de lo que vemos. El desenfoque es la causa más importante y a la vez más común de emborronamiento de la imagen en la retina. Esta borrosidad reduce la calidad de imagen, disminuyendo su resolución y contraste y haciendo que se pierdan detalles. La nitidez de la imagen depende de la interrelación entre la longitud axial del ojo, su potencia óptica y la distancia al objeto. Hasta que se vuelve rígido con la edad, el ojo es capaz de modificar la forma del cristalino para ajustar su potencia óptica, un proceso que se denomina acomodación. De esta forma el sistema visual puede enfocar sobre la retina las imágenes de objetos situados a distintas distancias. Aunque este proceso no es instantáneo, la acomodación es un mecanismo rápido y bastante preciso en la mayoría de los sujetos jóvenes, que da como resultado una visión clara del mundo tridimensional. Sin embargo, se ha sugerido que la aparición y/o progresión de la miopía podría estar relacionada con alteraciones en el proceso acomodativo que podrían alterar el proceso de emetropización. Por otro lado, incluso cuando se mira fijamente un objeto a una distancia determinada, la potencia óptica del ojo fluctúa de forma más o menos aleatoria. No está claro si esta inestabilidad es un resultado no deseado de la incapacidad del ojo para mantener un enfoque constante o puede ser parte integrante del proceso de acomodación con un propósito concreto, por ejemplo, aumentando la velocidad de respuesta. Sea como fuere, considerando el fenómeno desde un punto de vista óptico, sería de esperar que la imagen retiniana sufriera algún tipo de degradación al verse sometida a una fluctuación de foco, perdiendo nitidez. En esas circunstancias, un tiempo de integración corto podría permitir que el sistema visual percibiera una secuencia instantáneas con distintos niveles de emborronamiento, y que empleara la más nítida para extraer información sobre el objeto, maximizando la calidad visual. En este contexto, esta tesis estudia los efectos de distintos tipos de variaciones de enfoque, tanto discretas como progresivas, con el objetivo de analizar cómo son manejados por el sistema visual. Para ello se llevaron a cabo dos experimentos separados empleando un sensor Hartmann-Shack (HS) de campo abierto, que mide tanto la refracción como las aberraciones de alto orden de ambos ojos en tiempo real. En primer lugar, se analizó la dinámica de la respuesta acomodativa en condiciones realistas de visión binocular, tanto en sujetos emétropes como miopes, cuando cambiaban su fijación abruptamente de un objeto lejano a otro cercano. Posteriormente, en un segundo experimento estudiamos el efecto sobre la sensibilidad al contraste de oscilaciones rápidas de desenfoque con diferentes amplitudes y frecuencias temporales, generadas con una lente sintonizable acoplada al sistema para este propósito. En el primer experimento, se midió la dinámica en tiempo real de las tres componentes de la respuesta acomodativa binocular (acomodación, convergencia y miosis pupilar) en emétropes y sujetos con distintos grados de miopía. El mecanismo de acomodación no solo conlleva el cambio de potencia óptica del cristalino sino que además incluye una rotación coordinada de los globos oculares para hacer que las líneas de mirada converjan sobre el objeto observado y una reducción del tamaño (miosis) de las pupilas. Existe una extensa literatura sobre estos procesos y sus combinaciones, pero relativamente pocos estudios los miden simultáneamente en visión binocular. Hasta donde sabemos, este es el primer estudio de la dinámica combinada de las tres componentes de la respuesta acomodativa se mide de forma precisa, en tiempo real y en condiciones realistas de observación. Además, se realizaron medidas tanto en miopes como emétropes, con el objeto de analizar las posibles diferencias de comportamiento entre ellos. En el estudio participaron 18 sujetos jóvenes, con un error refractivo promedio de -2.3 D en un rango de 0 D a -7.5 D, todos ellos con valores de cilindro por debajo de 2 D. Con su mejor corrección, que portaron durante las medidas en caso necesario, todos los sujetos alcanzaron una agudeza visual decimal por encima de la unidad y ninguno presentó antecedentes de enfermedades oculares o problemas visuales. Tanto el estímulo cercano, ubicado a 2.8 D, como el lejano, a 0.36 D, consistieron en cruces de Malta negras sobre un fondo blanco, con una anchura angular de 1.3° en ambos casos. Cada sujeto se sometió a 3 ciclos de 6 cambios de distancia de fijación (lejos-cerca-lejos-cerca-lejos-cerca). Para el análisis de datos se empleó un método de umbralización consistente determinar los instantes en los que se alcanza el 10% y se supera el 90% del rango de variación entre los estados inicial y final para cada variable estudiada. A partir de los datos experimentales se calcularon varios parámetros relacionados con el cambio de fijación de lejos a cerca, incluyendo las amplitudes de acomodación, convergencia y miosis pupilar, las duraciones de estos tres procesos y sus velocidades medias, el retraso acomodativo, el RMS total de las aberraciones de alto orden y la magnitud de la aberración esférica, y se analizaron los coeficientes de correlación de todas estas variables con el error refractivo y con la velocidad de acomodación. El análisis de correlación de la refracción (en forma de equivalente esférico) con los parámetros dinámicos de la respuesta acomodativa sugiere que la miopía afecta levemente o se ve afectada por la acomodación. Se encontró una relación de proporcionalidad entre el retraso acomodativo y el error refractivo (R = -0.57, p = 0.01), así como una correlación apreciable entre la velocidad de constricción pupilar y la refracción del sujeto (R = -0.49, p = 0.04), en ambos casos con valores de p por debajo de 0.05. En otras palabras, la acomodación en los miopes parece tender a ser menos precisa y la contracción de su pupila a ser más lenta. Los coeficientes de correlación entre el equivalente esférico y el resto de parámetros relacionados con la respuesta acomodativa fueron en general pequeños, con valores de p muy por encima de 0.05. Por otro lado, se encontró una correlación sustancial, con valor de p bajo, entre la velocidad de acomodación y la velocidad de convergencia (R = 0.48, p = 0.04), una asociación que no hemos encontrado mencionada en la literatura previa. Y todavía más fuerte fue la correlación la velocidad de acomodación y la duración de la convergencia (R = 0.57, p = 0.01), lo que puede reflejar las diferencias entre las dinámicas de estos dos procesos. Además, parece haber una correlación entre la velocidad de acomodación y la amplitud de la miosis pupilar, ya que el valor de p fue inferior a 0.05 (R = 0.47, p = 0.049). En resumen, el análisis de correlación de la velocidad de acomodación sugiere que una acomodación lenta puede estar asociada a una convergencia lente y a una constricción pupilar más evidente. Para la segunda parte de esta tesis se construyó un sensor HS más rápido, con una frecuencia de actualización de 60 Hz, y con mayor sensibilidad a la luz infrarroja de 1050 nm de longitud de onda. Este sensor se empleó para caracterizar una lente sintonizable, no solo para la producción en modo estático de valores fijos de desenfoque sino también, por primera vez que sepamos, en modo dinámico para la generación de variaciones sinusoidales de desenfoque. Después de la calibración, la lente sintonizable se utilizó para provocar oscilaciones periódicas de desenfoque, de distintas amplitudes y frecuencias, a 5 jóvenes emétropes mientras realizaban una tarea de sensibilidad al contraste. Todos los sujetos alcanzaron agudeza visual unidad o mejor y carecían de antecedentes de problemas visuales. El estímulo visual fue un test de Gabor de 1º de diámetro angular y una frecuencia espacial de 12 c/grado, ubicado a 3 m de distancia del observador. Las franjas se inclinaron aleatoriamente 10º hacia la izquierda o la derecha de la vertical y se utilizó un protocolo de elección forzada de dos opciones para determinar el umbral de contraste para cada condición de oscilación. Las medidas se tomaron monocularmente con el ojo derecho. En total se estudiaron 24 casos de fluctuación sinusoidal de desenfoque presentados en orden aleatorio, correspondientes a las combinaciones de 3 frecuencias temporales (5, 15 y 25 Hz) y 8 valores de pico-valle de desenfoque entre un mínimo de 0,15 D y 3 D de máximo. No se ha encontrado literatura previa analizando el efecto de este tipo de fluctuaciones rápidas de desenfoque en la calidad visual. Los resultados de este estudio indican que la calidad visual, cuantificada mediante el umbral de contraste, es resistente a las oscilaciones de desenfoque inducidas. Solo se encontró una reducción notable de la sensibilidad al contraste para las variaciones más grandes y rápidas (25 Hz, ± 1,5 D) consideradas. Este hecho se puede tomar como una indicación de que el ojo humano solo necesita que la imagen retiniana esté enfocada durante un periodo corto de tiempo para poder percibir claramente los estímulos visuales. Como complemento a las medidas experimentales, en la última sección de esta tesis se desarrolló un modelo cuantitativo para predecir el deterioro en la calidad de imagen retiniana que puede producir una fluctuación periódica de desenfoque. Para las amplitudes y frecuencias de oscilación utilizadas en el experimento, se calculó la PSF promedio para varios tiempos de integración. A partir de ellas se evaluó la MTF compuesta para 12 c/grado y se comparó con la MTF limitada por difracción a dicha frecuencia, con el objeto de determinar la pérdida de modulación inducida por las variaciones de enfoque. La comparación entre los resultados experimentales y los datos simulados sugiere que el ojo puede estar integrando el emborronamiento causado por desenfoque en intervalos de 10 a 20 ms, y que una instantánea más o menos enfocada en una secuencia muy emborronada resulta suficiente para que el sistema visual extraiga información relevante para percibir el estímulo.

Corneal Physiology: Corneal Form and Function

Chapter

Apr 2022

Modulation of cortical activity by spherical blur and its correlation with retinal defocus

Article

Full-text available

Jul 2023

Cortical activity, as recorded via electroencephalography, has been linked to the refractive error of an individual. It is however unclear which optical metric modulates this response. Here, we measured simultaneously the brain activity and the retinal defocus of a visual stimulus perceived through several values of spherical blur. We found that, contrary to the existing literature on the topic, the cortical response as a function of the overcorrections follows a sigmoidal shape rather than the classical bell shape, with the inflection point corresponding to the subjective refraction and to the stimulus being in focus on the retina. However, surprisingly, the amplitude of the cortical response does not seem to be a good indicator of how much the stimulus is in or out of focus on the retina. Nonetheless, the defocus is not equivalent to the retinal image quality, nor is an absolute predictor of the visual performance of an individual. Simulations of the retinal image quality seem to be a powerful tool to predict the modulation of the cortical response with the refractive error.

Wavefront-Guided Contact Lens Corrections – Increasing Choice for the Individual with Keratoconus: Proceedings of the International Forum on Scleral Lens Research

Article

Full-text available

Apr 2018

If one were to ask an individual with keratoconus what need they hope to meet with an optical correction, the response would be as varied as the number of individuals diagnosed with the disease. Keratoconus impacts individual patients in myriad ways, and different aspects (or dimensions) of the correction are important to each individual patient. From our work in the laboratory, several recurring, and at times competing, dimensions have come to the forefront. For example, visual and optical performance may be of the utmost importance for one patient, while comfort and an ability to wear the lenses for the majority of waking hours may be paramount for another. Given that no single correction can meet the needs of every individual with keratoconus (just as no single correction can meet the needs of the typical population) a pressing need in regards to optical correction for the individual with keratoconus can be summarized in two words: increased choice.

Higher order aberrations and visual function in a young Asian population of high myopes

Article

Full-text available

Apr 2023

Purpose: To examine the associations between higher order aberrations (HOAs), visual performance, demographics, and ocular characteristics in a young Asian population with high myopia. Methods: This was a retrospective review of military pre-enlistees conducted between March 2014 to September 2018. Visual acuity and contrast sensitivity were tested under photopic, mesopic and simulated night conditions. Ocular, corneal and internal HOAs were measured with a Hartmann-Shack wavefront aberrometer (KR-1W, Topcon Co., Tokyo, Japan). Results: 522 eyes of 263 consecutive subjects with severe high myopia (defined as spherical equivalent refraction [SER] ≤ -10.00D) in at least one eye, and high myopia (SER ≤ -6.00D) in the fellow eye, [mean (SD) SER -11.85 (2.03D)] were analysed. The mean (SD) age of subjects was 18.5 (1.6) years. Chinese eyes had significantly greater internal total HOA root-mean-square (RMS) compared to Malay eyes [mean difference (SD) 0.0246 (0.007) μm, p < 0.001). More negative SER was associated with greater ocular total HOA (p = 0.038), primary coma (p = 0.003) and tetrafoil (p = 0.025) RMS, as well as more positive ocular (p = 0.003) and internal primary spherical aberration (p = 0.009). Greater ocular total HOAs was associated with reduced visual acuity in simulated night conditions and low contrast, decreased contrast sensitivity under mesopic and simulated night conditions (all p < 0.05). Conclusions: Greater HOAs were associated with Chinese ethnicity and more negative SER in a young Asian population with high myopia. Greater HOAs were associated with poorer visual performance in low luminance and reduced contrast conditions.

Characterization and prediction of the clinical result with a specific model of mini-scleral contact lens in corneas with keratoconus

Article

Full-text available

Oct 2022

Background: To investigate which factors are correlated with the visual improvement achieved with a specific model of scleral contact lens (SCL) in keratoconus (KC) eyes and to define a model to predict such improvement according to the pre-fitting data. In addition, the changes occurred with the fitting of a specific model of SCL during a period of 3 months in corneas with KC have been investigated. Methods: Longitudinal retrospective study including 30 eyes of 18 patients (age, 14-65 years) with KC fitted with the SCL ICD16.50 (Paragon Vision Sciences). Visual, refractive, corneal tomographic and ocular aberrometric changes were evaluated during a 3-month follow-up. Likewise, the characterization of the post-lens meniscus was performed by optical coherence tomography (OCT) with the measurement of central, nasal and temporal vaults. Results: The visual acuity increased significantly from a mean pre-fitting value with spectacles of 0.23 ± 0.07 logarithm of minimal angle of resolution (logMAR) to a mean value of 0.10 ± 0.04 logMAR after 1 month of SCL wear (P < 0.001). An improvement of 1 or more lines of visual acuity with the SCL occurred in 62.1% of the eyes. A significant decrease in central, nasal, and temporal vault was observed after 1 month of SCL wear (P ≤ 0.046). Likewise, there was a significant difference between nasal and temporal vaults during the first month of SCL use (P = 0.008). Furthermore, a significant reduction of ocular high order (P = 0.028) and primary coma root mean square (P = 0.018) was found with the SCL. A predicting linear equation of the change in visual acuity achievable with the SCL was obtained (P < 0.001, R2 = 0.878) considering the pre-fitting spectacle corrected distance visual acuity, and the power and sagittal lens of SCL. Conclusions: The scleral contact lens evaluated provides an efficacious visual rehabilitation in KC due to the improvement of visual acuity and the correction of low and high-order ocular aberrations. This visual acuity improvement can be predicted from some pre-fitting variables.

Improvement of Neural Contrast Sensitivity after Long-term Adaptation in Pseudophakic Eyes

Article

Full-text available

Jul 2022

An adaptive optics (AO) system was used to investigate the effect of long-term neural adaptation to the habitual optical profile on neural contrast sensitivity in pseudophakic eyes after the correction of all aberrations, defocus, and astigmatism. Pseudophakic eyes were assessed at 4 and 8 months postoperatively for changes in visual performance. Visual benefit was observed in all eyes at all spatial frequencies after AO correction. The average visual benefit across spatial frequencies was higher in the pseudophakic group (3.31) at 4 months postoperatively compared to the normal group (2.41). The average contrast sensitivity after AO correction in the pseudophakic group improved by a factor of 1.73 between 4 and 8 months postoperatively. Contrast sensitivity in pseudophakic eyes was poorer, which could be attributed to long-term adaptation to the habitual optical profiles before the cataract surgery, in conjunction with age-related vision loss. Improved visual performance in pseudophakic eyes suggests that the aged neural system can be re-adapted for altered ocular optics.

Multifocal contact lens myopia control: central and peripheral retinal image quality

Article

Full-text available

May 2022

Gerald Westheimer

Clinical relevance: That myopic defocus, even if restricted to the peripheral retina, inhibits eye growth in young monkey eyes has motivated the therapy of myopia control through multifocal contact lens wear in children. Background: To understand how eye-length regulating mechanisms are triggered by light requires knowledge of retinal light spread. That is largely lacking for the multifocal contact lenses used in the therapy because empirical methods identifying just the defocus in dioptres are inadequate. Methods: "Through-focus" diffraction computations in contact lens/eye models with typical normal eye parameters, including polychromatic light, the chromatic aberrations and an M-cone phototransduction layer, offer estimates of retinal image spread for a range of viewing distances. Results: Point- and edge-spread distributions of activation of phototransduction in the central retina show that the addition of multifocal zones produces some veiling for in-focus viewing and substantial improvement of image quality for near targets in the unaccommodated eye. These effects are much reduced in the retinal periphery. Conclusion: Whatever therapeutic value there is in prescribing multifocal contact lenses for myopia control, it is not particularly dependent on the precise configuration of the multifocal zones, nor can it be ascribed to changes in image quality specific to the retinal periphery; its origin is more likely less blur for near targets, reducing the stimulus to accommodation.

Numerical Study of Customized Artificial Cornea Shape by Hydrogel Biomaterials on Imaging and Wavefront Aberration

Article

Full-text available

Dec 2021

The blindness caused by cornea diseases has exacerbated many patients all over the world. The disadvantages of using donor corneas may cause challenges to recovering eye sight. Developing artificial corneas with biocompatibility may provide another option to recover blindness. The techniques of making individual artificial corneas that fit the biometric parameters for each person can be used to help these patients effectively. In this study, artificial corneas with different shapes (spherical, aspherical, and biconic shapes) are designed and they could be made by two different hydrogel polymers that form an interpenetrating polymer network for their excellent mechanical strength. Two designed cases for the artificial corneas are considered in the simulations: to optimize the artificial cornea for patients who still wear glasses and to assume that the patient does not wear glasses after transplanting with the optimized artificial cornea. The results show that the artificial corneas can efficiently decrease the imaging blur. Increasing asphericity of the current designed artificial corneas can be helpful for the imaging corrections. The differences in the optical performance of the optimized artificial corneas by using different materials are small. It is found that the optimized artificial cornea can reduce the high order aberrations for the second case.

Effects of Orthokeratology on Axial Length Elongation in Anisometropes

Article

Full-text available

Jul 2021

Introduction: This study aimed to investigate the therapeutic effects of overnight orthokeratology (OK) lenses on anisometropes. Methods: We enrolled 178 anisometropes from August 2015 to August 2017. We then divided these patients into 2 parts depending on them wearing either monocular or binocular OK lenses. In part one, 47 monocular myopic subjects (25 males and 22 females) were treated with OK lenses in the myopic eyes only. We also labeled the myopic eyes as the OK group and the contralateral nonmyopic eyes as the control group. The initial average wearing age of the subjects was 12.35 ± 2.37 years (8-16 years). The mean follow-up duration was 15.43 ± 4.88 months (7-25 months). The average spherical equivalent refraction (SER) was -2.31 ± 1.16 diopter (D) in the OK group and 0.15 ± 0.49 D in the control group (p < 0.001). In part 2, 131 binocular myopic anisometropes (56 males and 75 females) were involved in the study. The eyes with more severe myopia were assigned to the G group and the contralateral eyes to the L group. The initial average wearing age of the subjects was 12.92 ± 2.60 years ( 8-16 years). The mean follow-up duration was 17.83 ± 5.02 months (7-26 months). The average SER was -4.79 ± 1.90 D in the G group and -3.14 ± 1.88 D in the L group (p < 0.001). We calculated the axial length (AL) difference and AL elongation as our primary outcome measures. Results: In part one, the AL elongation in the OK group (0.21 ± 0.09 mm) was significantly lower than that in the control group (0.70 ± 0.17 mm) at 24 months (p < 0.001). Meanwhile, the AL difference exhibited a decrease of 0.50 ± 0.29 mm from a baseline of 1.08 ± 0.35 to 0.58 ± 0.25 mm at 24 months (F = 24.539, p < 0.001). In part 2, the AL had increased by 0.17 ± 0.13 mm in the G group and 0.24 ± 0.18 mm in the L group after 24-month follow-up, respectively (p < 0.001). While the AL difference decreased from 0.55 ± 0.11 mm at the baseline, to 0.48 ± 0.08 mm at 24 months, eliciting a decrement in AL difference of 0.07 ± 0.09 mm (F = 3.884, p = 0.030). Conclusions: OK lenses can slow down AL growth in anisometropes and has a greater effect on reducing AL elongation in the more severely affected myopic eyes of anisometropic patients.

One-year Effect of Wearing Orthokeratology Lenses on the Myopia Progression

Preprint

Full-text available

Feb 2021

Background: To Investigate the efficacy of overnight orthokeratology (Ortho-k) for myopia control and the relationship between axial length (AL) changes and different baseline factors. Methods: This is a retrospective study of 675 myopic patients (Affiliated Eye Hospital of Shandong University of TCM) who received Ortho-k correction between August 2015 and July 2017. These subjects were followed up at least for 12 months. Genders, age, parental refractive status, manifest refractions, cycloplegic refractions, uncorrected and best-corrected visual acuities, power vector of astigmatism, corneal curvature, age at initiation of Ortho-k wear (year), intraocular pressuren (IOP), anterior chamber depth (ACD), pupil size (PL), corneal diameter (CD) and AL were obtained for analysis. Correlation and multivariate logistic regression analyses were used to screen for the factors that can improve treatment outcome. Results: The baseline 675 patients’ AL of was 25.12±1.00 mm, and after 12 months of treatment, the AL was 25.30±0.94 mm, and the axial elongation was 0.18±0.22 mm. Univariate analysis of the right-eye independent variable of 675 patients showed a statistically significant association between age at initiation of Ortho-k wear, spherical equivalent refractive (SER), and changes in AL. Regression analysis results show that age at initiation of Ortho-k wear and SER are independent factors with effects on the treatment outcome. Conclusion: Ortho-k was effective in slowing myopia progression over a one-year follow-up period. Age at initiation of Ortho-k wear, and SER were found to be associated with increased change of AL during follow-up.

Optical Aberrations of Guinea Pig Eyes

Article

Full-text available

Aug 2020

Purpose: The guinea pig is widely used in studies of refractive error development and myopia which often involve experimental optical manipulations. The study described here investigated the optical quality of the guinea pig eye, for which there are limited data, despite its fundamental importance to understanding visually guided eye growth. Methods: The ocular aberrations of eight adolescent New Zealand pigmented guinea pigs (6-11 weeks old) were measured after cycloplegia using a custom-built Shack-Hartmann aberrometer and fit with a Zernike polynomial function to the 10th order (65 terms). The optical quality of their eyes was assessed in terms of individual Zernike coefficients, and data were further analyzed to derive root-mean-square (RMS) wavefront errors, modulation transfer functions (MTFs), point spread functions (PSFs), Strehl ratios, and depth of focus. A 4-mm pupil was used in all computations. The derived data are compared with equivalent data from normal young adult human eyes. Results: The guinea pigs exhibited low hyperopia and a small amount of positive spherical aberration, with other aberration terms decreasing with increasing order. Their average depth of focus, estimated from through-focus modulation, was 3.75 diopters. The RMS wavefront error of the guinea pig eye was found to be larger than that of the human eye for the same pupil size, reflecting a higher degree of aberrations, although the PSF (area) on the retina was smaller and sharper due to its shorter focal length. The radial average best-focus MTF derived for the guinea pig eye showed good performance at very low spatial frequencies, with a steeper decline with increasing frequency than for the human eye, dropping below 0.3 at 9 cpd. When converted to linear units (cycles/mm), the guinea pig eye had a higher spatial frequency cutoff and a slight contrast advantage for low spatial frequencies compared to the human eye. Conclusions: The optical quality of the guinea pig eye is far superior to their reported behavioral visual acuity. This implies a neuroanatomical limit to their vision, which contrasts with the close match of optical and neural limits to spatial resolution in human eyes. The significance for eye growth regulation of the relative optical advantages exhibited by guinea pig eyes, when optical quality is expressed in linear rather than angular retinal units, warrants further consideration.

Simulating the actual imaging in the individual eye: a novel approach to calculating spectacle lenses

Conference Paper

Jul 2020

Effects of chalazion on corneal astigmatism and wave-front aberrations in Egyptian patients

Article

Full-text available

Jan 2020

Aim This study investigated the correlation between chalazion, regarding its size, site and location, and different types of refractive errors, as well as high-order aberrations in Egyptian patients. Patients and methods This is a cross-sectional study which compared 53 eyes from 48 patients having eyelid chalazion with 43 eyes of age-matched control group. Chalazion was classified according to size, site, and location. Refraction was done using an autorefractokeratometer. Corneal topography and aberrations were done using a Scheimpflug topographer. Results The third-order aberration (coma Z31) and fourth-order aberration (secondary astigmatism Z42) were higher in the chalazion group compared with the control group (P=0.035 and 0.035, respectively). Lower lid chalazia showed higher Esafoil aberration Z66 than both upper lid and control group (P=0.015 and 0.001, respectively). In addition, the large-sized chalazion group showed a significant increase in Esafoil aberration Z66 than the small-sized group and the control group (P=0.004 and 0.003, respectively). No difference was observed between the chalazion group and the control group regarding autorefractokeratometer data or topographic data. Conclusion Although the presence of chalazion may not be associated with changes in refraction or corneal astigmatism, it still can cause increase in some high-order aberrations and hence, in the quality of vision. Besides, it is a threat as a source of infection before any surgical procedure. Therefore, it is important to exclude and treat any chalazion before proceeding with any refractive surgery especially wave-front-guided and wave-front-optimized corneal refractive procedures.

4D exploration of the retina for Adaptive Optics-assisted Laser Photocoagulation

Thesis

Sep 2018

Pedro Mecê

Retinal laser photocoagulation is commonly used to treat Diabetic Macular Edema. However, it is impossible with current laser systems to prevent some degree of damage to healthy neighboring tissues, due to the lack of control of the 3D confinement and position of the laser impact. These limitations are mostly caused by ocular aberrations and the constant eye movement. Adaptive Optics (AO) is a technology used since 1997 which enables ocular aberrations compensation in real-time, providing images of the retina with an unbeaten resolution. Laser photocoagulation systems could benefit from the AO capacity to control the 3D confinement of the therapeutic laser and to generate high- resolution retinal images that could be used to guide the surgeon and to control the 3D position of the laser impact in the retina. However, a great effort still has to be made to meet laser photocoagulation requirements. This thesis consists of the design and realization of the first 3D high-resolution AO-assisted Laser Photocoagulation system. For this end, we first present a high spatiotemporal resolution characterization of the 3D PSF evolution within the eye, enabling the design of a high-performance AO system, adapted to a therapeutic application, i.e. 3D control of the laser confinement. Then, I used the high-resolution retinal imaging system ECURoeil to validate these results and develop new methods enabling the 4D exploration of the retina (volume + temporal evolution) in real-time, for 3D control of the laser impact position. Finally, all the developments have been brought together in the CLOVIS3D bench, a compact instrument to perform clinically the first therapeutic application of Adaptive Optics.

Comparison of Corneal Wavefront-optimized and Wavefront-guided Alcohol-assisted Photorefractive Keratectomy Using Schwind Amaris 750S Laser for Myopia

Article

Full-text available

Jun 2020

Purpose: To compare the visual outcomes and corneal aberrations between wavefront-optimized (WFO) and corneal wavefront-guided (WFG) photorefractive keratectomy (PRK) in low to moderate myopia. Methods: Twenty-seven eyes treated with WFO and 29 eyes treated with WFG PRK using a Schwind Amaris 750S Excimer laser were included after 6 months of postoperative follow-up. Uncorrected distance visual acuity, corrected distance visual acuity, refractive errors, corneal higher-order aberrations (HOA) and corneal thickness obtained using a Scheimpflug system, and central ablation depth and volume were evaluated during the preoperative period and again at the postoperative 6-month visits. Results: Postoperatively, uncorrected distance visual acuity, corrected distance visual acuity, manifest spherical equivalent, and refractive astigmatism were improved in both groups, and there was no statistically significant difference between the two groups. There was no significant difference in safety, efficacy, or predictability of the refractive outcome. Postoperative total corneal HOA root mean square (RMS), coma RMS, and spherical aberration were significantly increased in both groups. Among these, only spherical aberration showed a significant difference between the two groups, with greater increase in the WFO group at 6 months postoperatively. The changes in corneal HOA RMS and spherical aberration were smaller in the WFG group, and this benefit was marked in eyes with high HOA RMS (≥0.4 μm) and spherical aberration (≥0.2 μm). Even though ablation volume in the WFG group was much larger than that of the WFO group, there was no significant difference in postoperative central and peripheral corneal thickness between the two groups. Conclusions: Both WFO and WFG PRK using a Schwind Amaris 750S laser for low to moderate myopia were safe and effective at improving visual and refractive outcomes. However, WFG PRK induced fewer spherical aberrations than WFO PRK and may be more advantageous for eyes with high HOA root mean square or spherical aberration.

Visual function of high-performance judokas

Article

Full-text available

Jan 2020

Descriptive case series of visual function of high performance judokas.

Image quality eigenfunctions for the human eye

Article

Nov 2019

This work presents a compact statistical model of the retinal image quality in a large population of human eyes following two objectives. The first was to develop a general modal representation of the optical transfer function (OTF) in terms of orthogonal functions and construct a basis composed of cross-correlations between pairs of complex Zernike polynomials. That basis was not orthogonal and highly redundant, requiring the application of singular value decomposition (SVD) to obtain an orthogonal basis with a significantly lower dimensionality. The first mode is the OTF of the perfect system, and hence the modal representation, is highly compact for well-corrected optical systems, and vice-versa. The second objective is to apply this modal representation to the OTFs of a large population of human eyes for a pupil diameter of 5 mm. This permits an initial strong data compression. Next, principal component analysis (PCA) is applied to obtain further data compression, leading to a compact statistical model of the initial population. In this model each OTF is approximated by the sum of the population mean plus a linear combination of orthogonal eigenfunctions (eigen-OTF) accounting for a selected percentage (90%) of the population variance. This type of models can be useful for Monte Carlo simulations among other applications.

Spherical Aberration of Astigmatic Corneas in a Cataract Population

Article

Aug 2023
J REFRACT SURG

Purpose: To study the distribution of spherical aberration (SA) in astigmatic corneas in a cataract population and the relationship between magnitude of corneal astigmatism and fourth-order corneal SA. Methods: Data routinely collected using a Scheimpflug camera (Pentacam; Oculus Optikgeräte GmbH) were retrospectively analyzed. Patients with a minimum age of 60 years were included. Total corneal SA (from anterior and posterior corneal surface) was obtained for a 6-mm cor-neal area aligned with the pupil center. Exclusion criteria were insufficient measurement quality, total deviation index (Belin/Ambrósio Deviation) greater than 1.60, and corneal thickness at the thinnest point of less than 490 μm. One eye per patient was chosen randomly. Eyes were divided into low (≤ 1.00 diopters [D]), moderate (> 1.00 to ≤ 2.00 D), and high (> 2.00 D) astigmatism groups according to the Scheimpflug measurements. Results: A total of 528 eyes were included in this analysis. Low astigmatism was found in 129 patients, moderate astigmatism in 265 patients, and high astigmatism in 134 patients. Mean astigmatism was 0.68 ± 0.24, 1.45 ± 0.28, and 2.91 ± 0.95 D in the low, moderate, and high astigmatism groups, respectively. Mean corneal SA in patients with moderate and high astigmatism was higher than in the low astigmatism group. The difference reached the significance level for the comparison of low and high astigmatism groups (P = .023). The fourth-order SA increased gradually with the magnitude of astigmatism with a slope of 0.015. Conclusions: SA was significantly larger in the cataract population with high corneal astigmatism. The increase of positive sign SA with the magnitude of astigmatism suggests that patients with moderate to high astigmatism may benefit more from intraocular lenses with negative sign SA correction. [J Refract Surg. 2023;39(8):532-538.].

Radial keratotomy and cataract surgery: A quest for emmetropia

Article

Aug 2023
J CATARACT REFR SURG

A 75-year-old man with an ocular history of 8-cut radial keratotomy (RK) in both eyes presented for cataract surgery evaluation. He was previously correctable in spectacles in years prior despite his irregular corneas to 20/25 in the right eye and 20/30 in the left eye. He recently noticed a change in his overall visual function with significant nighttime glare and difficulty reading despite spectacle correction. Of note, he was unable to tolerate contact lenses and was resistant to refitting despite additional encouragement. Cataract surgery was delayed for many years, given he was correctable in spectacles and the concern of uncovering a highly aberrated cornea after removing his cataracts (Figures 1 and 2 JOURNAL/jcrs/04.03/02158034-202308000-00021/figure1/v/2023-07-21T030437Z/r/image-tiff JOURNAL/jcrs/04.03/02158034-202308000-00021/figure2/v/2023-07-21T030437Z/r/image-tiff ). Of note, the patient was interested in returning to the spectacle independence he enjoyed in the past. Ocular examination revealed a corrected distance visual acuity (CDVA) of 20/30 in the right eye and 20/60 in the left eye, with a manifest refraction of +4.50 −0.50 × 177 in the right eye and +5.75 −1.75 × 14 in the left eye. Glare testing was 20/50 in the right eye and 20/100 in the left eye, with retinal acuity meter testing of 20/25 in each eye. Pupils, confrontation visual fields, and intraocular pressures were normal. Pertinent slitlamp examination revealed corneal findings of 8-cut RK with nasal-gaping arcuate incisions in both eyes and lens findings of 2+ nuclear sclerosis with 2+ cortical changes in the right eye and 3+ nuclear sclerosis with 3+ cortical changes in the left eye. Cup-to-disc ratios of the optic nerves measured 0.5 with temporal sloping in the right eye and 0.6 with temporal sloping in the left eye. The dilated fundus examination was unremarkable. What intraocular lens (IOL) options would you offer this patient and how would you counsel regarding realistic expectations? What additional diagnostic testing would be helpful in your assessment? How would you calculate the IOLs?

Monochromatic ocular high-order aberrations in children and adolescents

Article

May 2023
OPHTHAL PHYSL OPT

Purpose: To investigate the prevalence and repeatability of high-order aberrations (HOAs) from non-cyclopleged eyes in 1515 children and adolescents 2.5-18 years of age. Methods: The Leipzig Research Centre for Civilization Diseases (LIFE)-Child study is a population-based, prospective, observational single-centre study that investigates the development of children and adolescents in Germany. Wavefront measurements were repeated three times in each eye of 1515 healthy subjects. Results were described by 36 Zernike coefficients for a 5 mm reference pupil diameter. Short-term repeatability is given for each coefficient. The impact on vision is described by the root mean squared (RMS) value of the HOA Zernike coefficients. Results: High-order aberrations were dominated by five contributions. For 1004 right eyes: spherical aberration (c12 = 0.06 ± 0.07 μm), coma (c7 = 0.03 ± 0.09 μm, c8 = 0.03 ± 0.06 μm) and trefoil (c6 = -0.01 ± 0.07 μm, c9 = 0.008 ± 0.06 μm). The RMS value was 0.18 ± 0.06 μm. Modes higher than fourth order do not contribute clinically to the aberrations. HOAs show no clinically significant dependency with age. Instead, HOA values agree well with previous results on aberrations in adult eyes. Spherical aberration was highly correlated between the two eyes. Repeatability was worst for coma, 0.033 μm, due to variability in the alignment of the pupil centre. The left eye showed, on average, a 0.08 mm larger pupil diameter than the right eye (p < 0.02). Conclusions: Across the age span from 2.5 to 18 years, we see the same distribution of HOA as for adults. We established that only five Zernike coefficients, spherical aberration, coma and trefoil were of clinical significance in healthy eyes. A high correlation between the two eyes for spherical aberration suggests a common blueprint for each eye in any one subject.

Wavefront-Guided Laser In Situ Keratomileusis

Chapter

Jun 2016

Jens Bühren

Optics of the Human Eye

Book

Feb 2023

David A. Atchison

Comatic Aberrations

Chapter

Jun 2016

Jens Bühren

Corneal Physiology: Corneal Form and Function

Chapter

Aug 2021

The cornea forms the anterior meniscus-shaped transparent portion of the ocular globe; it serves as the principal refractive element in the eye, while maintaining a highly impermeable barrier between the eye and the environment. The cornea is avascular, meeting its oxygen requirements largely from the atmosphere by diffusion across the tear film and epithelium; conversely, it derives most of its additional nutritional requirements from the aqueous humor arising from across the corneal endothelium. The epithelium of the cornea provides the major barrier to tear-borne pathogens, while the corneal endothelium is principally responsible for maintaining the hydration and clarity of the corneal stroma. As the highest refractive power in the optics of the eye, subtle variations in corneal curvature lead to higher order aberrations that can be assessed with corneal topography. Measured with instruments that analyze reflected patterns from the tear film, variations of the Placido disk permit the most sensitive assessments of corneal optical properties. These data form the basis for the color-coded contour map display of corneal curvature, permitting clinical diagnosis of a wide variety of corneal pathologies as well as evaluation and development of refractive surgical procedures. Adjunct slit-based methodologies provide tomographic curvature data of both corneal surfaces and three-dimensional corneal pachymetry. Several artificial intelligence-based approaches have used topography and tomography variables for the automatic detection and interpretation of corneal shape anomalies.

Motion adaptation improves acuity (but perceived size doesn't matter)

Article

Full-text available

Oct 2022
J VISION

Recognition acuity-the minimum size of a high-contrast object that allows us to recognize it-is limited by optical and neural elements of the eye and by processing within the visual cortex. The perceived size of objects can be changed by motion-adaptation. Viewing receding or looming motion makes subsequently viewed stimuli appear to grow or shrink, respectively. It has been reported that resulting changes in perceived size impact recognition acuity. We set out to determine if such acuity changes are reliable and what drives this phenomenon. We measured the effect of adaptation to receding and looming motion on acuity for crowded tumbling-T stimuli (). We quantified the role of crowding, individuals' susceptibility to motion-adaptation, and potentially confounding effects of pupil size and eye movements. Adaptation to receding motion made targets appear larger and improved acuity (-0.037 logMAR). Although adaptation to looming motion made targets appear smaller, it induced not the expected decrease in acuity but a modest acuity improvement (-0.018 logMAR). Further, each observer's magnitude of acuity change was not correlated with their individual perceived-size change following adaptation. Finally, we found no evidence that adaptation-induced acuity gains were related to crowding, fixation stability, or pupil size. Adaptation to motion modestly enhances visual acuity, but unintuitively, this is dissociated from perceived size. Ruling out fixation and pupillary behavior, we suggest that motion adaptation may improve acuity via incidental effects on sensitivity-akin to those arising from blur adaptation-which shift sensitivity to higher spatial frequency-tuned channels.

Wavefront aberrometry repeatability and agreement—A comparison between Pentacam AXL Wave, iTrace and OPD‐Scan III

Article

Sep 2022

Introduction: To compare intrasession agreement and repeatability of wavefront aberration measurements from three different aberrometers obtained using Hartmann-Shack, ray tracing and automated retinoscopy methods, as well as their interdevice agreement. Methods: Three consecutive measurements were obtained using the Pentacam AXL Wave, the iTrace and the OPD-Scan III in 47 eyes of 47 patients. Wavefront refractions, root mean square of total aberrations (RMS total), RMS of higher-order aberrations (HOA) and second-, third- and fourth-order HOAs were exported for 4-mm pupils. Wavefront refractions were converted into vector components: M, J0 and J45 . Intrasession agreement and repeatability were evaluated using intraclass correlation coefficients (ICCs) and repeatability coefficients (RCs); interdevice agreement was assessed using the Bland-Altman method. Results: The intrasession agreement and repeatability of RMS HOA were comparable between the three devices; both the Pentacam AXL Wave and the OPD-Scan III had better intrasession agreement and repeatability for the RMS total than the iTrace (p ≤ 0.02). Intrasession repeatability for the majority of second- and third-order aberrations was better on the Pentacam AXL Wave than on the iTrace (p ≤ 0.01) and OPD-Scan III (p ≤ 0.04), although their agreement and repeatability in spherical aberration were comparable (p ≥ 0.24). Significant systematic differences and proportional bias were detected for almost all refraction power vectors and Zernike coefficients among the three devices. Conclusions: In this study, all three devices provided good-to-excellent agreement for aberration measurements. Most of the individual Zernike's components were not exchangeable between different aberrometers. Their relative intrasession performance in agreement and repeatability varied significantly across different ocular aberration parameters.

Compact Models of Presbyopia Accommodative Errors for Wearable Adaptive-Optics Vision Correction Devices

Article

Full-text available

Jan 2022

Subjective accommodation refractive error models are essential for implementing adaptive vision correction devices that utilize varifocal optics. This article describes compact empirical models of subjective accommodative refractive errors in subjects with advanced presbyopia. The models are based on measurements of subjective refractive errors from fifteen presbyopes over the age of 45 using commercially available focus-tunable eyeglasses under three different illumination conditions over a 3.08D accommodation stimulus range. The resulting average residual root-mean-squared (RMS) error values for the best fitting 8-parameter model was 0.25D compared to an average RMS error of 0.4D for the conventional DDF and HHG models. The RMS error for the best-fitting model is below the average refractive error of the human eye.

Simulation of Keratoconic Optical Aberrations and Correction with an Adaptive Optics System

Thesis

Jul 2021

Nikolaos Kourasmenakis

Aberration analysis and compensate method of BP neural network and sparrow search algorithm in deep ultraviolet lithography

Article

Jun 2022

Mass production can be planned by utilizing the multiple patterning technology of 193 nm immersion scanners at the 7 nm technology node. In deep ultraviolet lithography, imaging performance is significantly affected by distortions of projection optics. For 7 nm immersion lithography layer patterns, distortions of the projection optics must be tightly controlled. This paper proposes an optimization method to determine the distribution of Zernike aberration coefficients. First, we build aberration prediction models using the backpropagation (BP) neural network. Then, we propose an aberration optimization method based on the sparrow search algorithm (SSA), using the common indicators of the lithography process window, depth of focus, mask error enhancement factor, and image log slope as the objective function. Some sets of optimized aberration distributions are obtained using the SSA optimization method. Finally, we compare the results of the SSA optimization algorithm with those obtained by rigorous computational simulations. The aberration combination distribution optimized by the SSA method is much more significant than the value under the zero aberration (ideal conditions), a nonoptimal distribution in deep ultraviolet lithography image simulation. Furthermore, the results indicate that the aberration optimization method has a high prediction accuracy.

Changes in Corneal Aberrations with Axial Rotation of Toric Soft Contact Lenses

Article

Sep 2021

Correction of Ocular Aberrations with Prismatic Rigid Gas-permeable Contact Lenses in Keratoconic Eyes

Article

Sep 2021

Significance: A base-down prism was incorporated on the anterior surface of rigid-gas-permeable (RGP) contact lenses to explore potential effects on the residual ocular aberrations after contact lens fitting in keratoconic eyes. Purpose: To evaluate the correction of ocular aberrations with corneal prismatic RGP contact lenses in keratoconic eyes and their impact on visual function. Methods: A cross-sectional and randomized study was performed. Seventeen eyes of 17 keratoconus patients (34.6 ± 11.1 years) were evaluated. Two designs (standard and prismatic) of a corneal RGP contact lens (KAKC) were fitted to the same eye of each patient in erandom order: a standard rigid-gas-permeable contact lens as control and a prismatic RGP contact lens with a base-down prism of 1.6 prism diopters. Ocular aberrations were measured for a pupil diameter of 3 mm with and without both contact lenses, while high-contrast distance visual acuity, low-contrast distance visual acuity, and contrast sensitivity were measured under photopic and mesopic conditions. Results: Both contact lenses improved oblique primary astigmatism, defocus, vertical coma, coma-like, and RMS higher-order aberrations compared with the unaided eyes (P < .05). Besides, the prismatic RGP contact lenses offered lower values of vertical coma and RMS higher-order aberrations than the standard rigid-gas-permeable contact lenses (P < .05). Both designs (standard and prismatic) produced a positive vertical coma of lower magnitude than the negative vertical coma of the unaided eyes. On the other hand, the improvement achieved in all visual function variables was the same for both contact lens designs (P ≥ .05). Conclusions: The prismatic RGP contact lenses corrected higher levels of higher-order aberrations compared with the standard rigid-gas-permeable contact lenses. However, both contact lens designs with the same refractive power were equally efficient at improving visual function.

Comparing the CamBlobs2 contrast sensitivity test to the near Pelli‐Robson contrast sensitivity test in normally‐sighted young adults

Article

Aug 2021

Purpose Contrast sensitivity (CS) has been proposed as a potential method for patients to assess their vision at home. The CamBlobs2 contrast sensitivity test is meant to be performed easily in the clinic or at home. The purpose of this study was to determine the intra-visit coefficient of repeatability of the CamBlobs2 compared with the near Pelli-Robson test, and the limits of agreement between these two tests on normally-sighted subjects. Methods Twenty-two normally-sighted subjects (mean age 28 ± 4 years) completed two trials of the near Pelli-Robson and CamBlobs2 contrast sensitivity tests within a single visit. Tests were performed monocularly on each eye in random order. Pelli-Robson tests were scored as 0.05 logCS for each letter read correctly after deducting the first triplet. CamBlob2 tests were scored as the highest line where two or fewer blobs were marked correctly. The coefficient of repeatability was determined as 1.96 times the standard deviation of the difference between the two measurements using the same type of chart on the same eye. The limits of agreement between the two tests were evaluated using Bland-Altman analysis. Results The mean difference between intra-visit measurements for both the near Pelli-Robson and CamBlobs2 was less than 0.05 logCS and the coefficient of repeatability was within ±0.20 log CS for both left and right eyes. The mean ± standard deviation differences between near Pelli-Robson and CamBlobs2 scores was −0.08 ± 0.08 (limits of agreement: −0.24 to 0.09) for right eyes and −0.05 ± 0.10 (limits of agreement: −0.23 to 0.14) logCS for left eyes based on average measurements. Conclusions The intra-visit repeatability of CamBlobs2 was consistent with the near Pelli-Robson contrast sensitivity test (±0.20 logCS). With a 0.05 correction, the CamBlobs2 scores showed excellent agreement with the near Pelli-Robson contrast sensitivity test.

Correcting Presbyopia With Autofocusing Liquid-Lens Eyeglasses

Article

Jul 2021

Objective: Presbyopia, an age-related ocular disorder, is characterized by the loss in the accommodative abilities of the human eye. Conventional methods of correcting presbyopia divide the field of view, thereby resulting in significant vision impairment. We demonstrate the design, assembly and evaluation of autofocusing eyeglasses for restoration of accommodation without dividing the field of view. Methods: The adaptive optics eyeglasses comprise of two variable-focus liquid lenses, a time-of-flight range sensor and low-power, dual microprocessor control electronics, housed within an ergonomic frame. Subject-specific accommodation deficiency models were utilized to demonstrate high-fidelity accommodative correction. The abilities of this system to reduce accommodation deficiency, its power consumption, response time, optical performance and MTF were evaluated. Results: Average corrected accommodation deficiencies for 5 subjects ranged from -0.021 D to 0.016 D. Each accommodation correction calculation was performed in ~67 ms which consumed 4.86 mJ of energy. The optical resolution of the system was 10.5 cycles/degree, and featured a restorative accommodative range of 4.3 D. This system was capable of running for up to 19 hours between charge cycles and weighed ~132 g. Conclusion: The design, assembly and performance of an autofocusing eyeglasses system to restore accommodation in presbyopes has been demonstrated. Significance: The new autofocusing eyeglasses system presented in this article has the potential to restore pre-presbyopic levels of accommodation in subjects diagnosed with presbyopia.

Lags and leads of accommodation in humans: Fact or fiction?

Article

Full-text available

Mar 2021
J VISION

The focusing response of the human eye - accommodation - exhibits errors known as lags and leads. Lags occur when the stimulus is near and the eye appears to focus farther than the stimulus. Leads occur with far stimuli where the eye appears to focus nearer than the stimulus. We used objective and subjective measures simultaneously to determine where the eye is best focused. The objective measures were made with a wavefront sensor and an autorefractor, both of which analyze light reflected from the retina. These measures exhibited typical accommodative errors, mostly lags. The subjective measure was visual acuity, which of course depends not only on the eye's optics but also on photoreception and neural processing of the retinal image. The subjective measure revealed much smaller errors. Acuity was maximized at or very close to the distance of the accommodative stimulus. Thus, accommodation is accurate in terms of maximizing visual performance.

Predicting factors for progression of the myopia in the MiSight assessment study Spain (MASS)

Article

Full-text available

Mar 2021

Purpose To investigate which baseline factors are predictive for success in controlling myopia progression in a group of children wearing MiSight Contact Lens (CLs). Methods Myopic patients (n = 41) fitted with MiSight CLs and followed up two years were included in this study. Bivariate analysis, a logistic regression analysis (LG) and a decision tree (DT) approach were used to screen for the factors influencing the success of the treatment. To assess the response, axial length (AL) changes were considered as main variable. Patients were classified based on a specific range of change of axial length at the end of each year of treatment as “responders” (R) (AL change <0.11 mm/per year) and “non-responders” (NR) (AL change ≥0.11 mm/per year). Results Of a total of forty-one Caucasian patients treated with MiSight CLs, 21 and 16 were considered responders in the first and the second year of follow-up, respectively. LG analysis showed that the only factor associated with smaller axial length growth was more time spent outdoors (p = 0.0079) in the first year of treatment. The decision tree analysis showed that in the responding group spending more than 3 and 4 h outdoors per week was associated with the best response in the first year and in the second year of treatment respectively. Conclusions The LR and the DT approach of this pilot study identifies time spent outdoors as a main factor in controlling axial eye growth in children treated with MiSight CLs.

Higher Order Aberrations: Differences Among Populations from Various Demographics

Chapter

Feb 2021

Gaurav Prakash

The understanding of the role of higher order aberrations of the visual system has explained multiple optical phenomena to the researchers and clinicians alike. Many disorders are better understood now due to application of wavefront optics in ophthalmology. In this chapter, we first summarize the current basic understanding of higher order aberrations and then review the literature on the differences in the normative data from various demographic populations in the higher order aberrations noted. A pooled analysis of the data suggested that in most of the demographic databases, at a 6-mm wavefront diameter, the adult human eye tends to have anywhere between 0.3 and 0.4 μm of higher order aberrations root mean square (HOARMS). However, there were variations noted in sub-analysis of the Zernike modes between different populations. The role of normative data for a given population is that of a guideline. It gives base information on which individual wavefront profile of an eye can be evaluated for the differences between normal and abnormal.

Correcting Presbyopia with Autofocusing Liquid-Lens Eyeglasses

Preprint

Full-text available

Jan 2021

Presbyopia, an age-related ocular disorder, is characterized by the loss in the accommodative abilities of the human ocular system and afflicts more than 1.8 billion people world-wide. Conventional methods of correcting presbyopia fragment the field of vision, inherently resulting in significant vision impairment. We demonstrate the development, assembly and evaluation of autofocusing eyeglasses for restoration of accommodation without vision field loss. The adaptive optics eyeglasses consist of two variable-focus piezoelectric liquid lenses, a time-of-flight range sensor and low-power, dual microprocessor control electronics housed within an ergonomic frame. Patient-specific accommodation deficiency models were utilized to demonstrate a high-fidelity accommodative correction. Each accommodation correction calculation was performed in ~67 ms requiring 4.86 mJ of energy. The optical resolution of the system was 10.5 cycles/degree, featuring a restorative accommodative range of 4.3 D. This system can run for up to 19 hours between charge cycles and weighs ~132 g, allowing comfortable restoration of accommodative function

A Randomized Trial of Objective Spectacle Prescriptions for Adults with Down Syndrome: Baseline Data and Methods

Article

Jan 2021

Significance: It is difficult to determine the most efficacious refractive correction for individuals with Down syndrome using routine clinical techniques. New objective methods that optimize spectacle corrections for this population may reduce limitations on daily living by improving visual quality. Purpose: This article describes the methods and baseline characteristics of study participants in a National Eye Institute-sponsored clinical trial to evaluate objectively derived spectacle corrections in adults with Down syndrome. Intersession repeatability of the primary outcome measure (distance visual acuity) is also reported. Methods: Adults with Down syndrome were enrolled into a nine-visit study to compare clinically derived spectacle corrections and two different objective spectacle corrections derived from wavefront aberration data. Spectacle corrections were randomized and dispensed for 2 months each. Distance visual acuity was measured with a Bailey-Lovie-style chart. Intersession repeatability of acuity was established by performing difference versus mean analysis from binocular acuity measures obtained through habitual corrections at visits 1 and 2. Results: Thirty adults (mean ± standard deviation age, 29 ± 10 years) with a large range of refractive errors were enrolled. Presenting visual acuity at visit 1 was reduced (right eye, 0.47 ± 0.20 logMAR; left eye, 0.42 ± 0.17 logMAR). The mean difference between visits 1 and 2 was 0.02 ± 0.06 logMAR, with a coefficient of repeatability (1.96 × within-subject standard deviation) of 0.12 logMAR. Conclusions: This study seeks to investigate new strategies to determine optical corrections that may reduce commonly observed visual deficits in individuals with Down syndrome. The good intersession repeatability of acuity found in this study (six letters) indicates that, despite the presence of reduced acuity, adults with Down syndrome performed the outcome measure for this clinical trial reliably.

The visual image quality after small-incision lenticule extraction (SMILE) compared to spectacles and contact lenses

Article

Nov 2020
J CATARACT REFR SURG

Purpose: To assess the influence of small-incision lenticule extraction (SMILE) for high myopia on the visual image quality assessed by the logarithm of the Visual Strehl Ratio (logVSX), and put this into a clinical context by pairwise comparing the logVSX of postoperative eyes with those of myopic controls wearing spectacles and/or contact lenses. Setting: University Hospital DESIGN:: Prospective & cross-sectional clinical study METHODS:: Patients with a myopic spherical equivalent of at least 6 diopters treated with SMILE aimed at emmetropia and correspondingly myopic controls corrected with spectacles and/or contact lenses were included. The logVSX calculation was divided into habitual logVSX based on the wavefront aberration measurement directly, and optimal logVSX calculated in a theoretical through-focus experiment to obtain the best-achievable logVSX. Results: 117 eyes of 61 patients and 64 eyes of 34 myopic controls were included. SMILE did not affect the habitual logVSX, but worsened the optimal logVSX (P<0.001). The postoperative habitual logVSX was significantly worse compared to contact lenses (P=0.002). The postoperative optimal logVSX was significantly worse compared to both spectacles (P<0.01) and contact lenses (P=0.003). There was no difference in habitual or optimal logVSX between spectacles and contact lenses. Conclusions: SMILE for high myopia does not affect the habitual logVSX but decreases the optimal logVSX slightly. The postoperative habitual logVSX is worse than for contact lenses but not spectacles, and the postoperative optimal logVSX is worse than for both contact lenses and spectacles. There is no difference in either habitual or optimal logVSX between spectacles and contact lenses.

Pupillodynamics and corneal spherical aberrations in a set of Indian cataract patients and its implications for aberrometric customisation of intraocular lenses PMID: *****

Article

Full-text available

Nov 2020

Purpose: Assessment of pupil diameter in various light conditions and the corresponding corneal spherical aberrations in a cohort of Indian eyes with bilateral senile cataracts and the possible use of this data in aberrometric customization of intraocular lenses (IOLs). Methods: In this prospective observational study done at a tertiary eye care centre in India, the selected patients were subjected to measurement of their pupil diameters in scotopic, mesopic, and photopic conditions as well as the corresponding corneal spherical aberrations, using the Sirius Topographer (Costruzione Strumenti Oftalmici, Florence, Italy). Shapiro-Wilk test, Independent t-test, ANOVA with Bonferroni correction on post-hoc testing were used for statistical analysis. Results: 104 eyes of 52 patients were enrolled for the study. The mean age was 53 ± 11.88 years. The mean scotopic, mesopic, and photopic pupil sizes were 4.37 mm (4.11-4.63 mm), 3.92 mm (3.71 mm-4.15 mm), and 3.37 mm (3.18-3.67 mm), respectively. There was a statistically significant difference (P = <0.001) in the mean corneal spherical aberration measured at the 6 mm zone (0.23 ± 0.02 microns) and at the 4 mm zone (0.06 ± 0.01 microns). Conclusion: The mean corneal spherical aberration corresponding to the average mesopic pupil size of our patient population was substantially lower than that of the scotopic pupil size and also less than the amount corrected by most of the negative aspheric IOLs. This perhaps indicates the need for customising IOLs based on the spherical aberrations of cornea at the zone corresponding to the mesopic pupil diameter for optimal residual total postoperative spherical aberrations.

The Impact of Misaligned Wavefront-guided Correction in a Scleral Lens for the Highly Aberrated Eye

Article

Sep 2020
OPTOMETRY VISION SCI

Significance: To achieve maximum visual benefit, wavefront-guided scleral lens corrections (WGCs) are aligned with the underlying wavefront error of each individual eye. This requirement adds complexity to the fitting process. With a view toward simplification in lens fitting, this study quantified the consequences of placing WGCs at two pre-defined locations. Purpose: This study aimed to quantify performance reduction accompanying the placement of the WGC at two locations: (1) the average decentered location (ADL; average decentration observed across individuals wearing scleral lenses) and (2) the geometric center (GC) of the lens. Methods: Deidentified residual aberration and lens translation data from 36 conventional scleral lens-wearing eyes with corneal ectasia were used to simulate WGC correction in silico. The WGCs were decentered from the eye-specific pupil position to both the ADL and GC locations. The impact of these misalignments was assessed in terms of change (from the aligned, eye-specific pupil position) in higher-order root mean square (HORMS) wavefront error, change in log of the visual Strehl ratio (logVSX), and predicted change in logMAR visual acuity (VA). Results: As expected, HORMS increased, logVSX decreased, and predicted VA was poorer at both ADL and GC compared with the aligned condition (P < .001). Thirty-four of 36 eyes had greater residual HORMS, and 33 of 36 eyes had worse logVSX values at the GC than at the ADL. In clinical terms, 19 of 36 eyes at the ADL and 35 of 36 eyes at the GC had a predicted loss in VA of three letters or greater. Conclusions: The placement of the WGC at either ADL or GC is predicted to lead to a noticeable reduction in VA for more than half of the eyes studied, suggesting the simplification of the fitting process is not worth the cost in performance.

Clinical utility of irx3 in keratoconus

Article

Sep 2020
CLIN EXP OPTOM

Clinical relevance: Diagnosis and monitoring of keratoconus is increasingly being conducted with the aid of imaging equipment such as corneal aberrometry. There is a need to also know the confidence with which ocular aberration measurements can be made. Background: To assess the repeatability of lower- and higher-order aberration measurements in patients with keratoconus using the irx3 wavefront aberrometer (Imagine Eyes, Orsay, France) and evaluate correlations with corneal curvature. Methods: The irx3 wavefront aberrometer was used to measure bilateral lower- and higher-order ocular aberrations on 33 participants with keratoconus. Three measurements were taken from each eye to determine the repeatability of lower-order aberrations (quantified as sphere and cylinder in dioptres) and higher-order aberration co-efficients (up to eighth order in micrometres), coma, trefoil and total higher-order aberration root mean square (in micrometres). Corneal curvature was measured using the Pentacam HR system (OCULUS, Wetzlar, Germany). Results: Repeat measurements for lower-order aberrations resulted in larger co-efficients of repeatability than higher-order aberrations. Similarly, larger co-efficients of repeatability between repeated measures across all Zernike co-efficients were observed in eyes with severe keratoconus (that is, corneal curvature > 52 D) compared to eyes with flatter corneas. The difference between repeated measures tended to be significant for the lower-order aberrations regardless of corneal curvature. The highest correlations with corneal curvature for right and left eyes respectively, were identified for total higher-order aberration root mean square (r = 0.92, p < 0.001 and r = 0.91, p < 0.001), followed closely by coma (r = -0.93, p < 0.001 and r = -0.86, p < 0.001) and the Z (3, -1) co-efficient (r = -0.92, p < 0.001 and r = -0.86, p < 0.001 for right and left eyes, respectively). Conclusions: Lower-order aberrations tended to be less repeatable, indicating that instrument variability must be considered when monitoring progression. Total higher-order aberration root mean square and third-order aberrations, in particular the vertical coma Z (3, -1) co-efficient, demonstrated a stronger correlation with corneal curvature than the lower-order aberrations.

Optimal pupil size in older adults for retinal imaging

Conference Paper

May 2020

Visual interaction of 2nd to 5th order Zernike aberration terms with vertical coma

Article

Aug 2020

Purpose In order to better understand the optical consequence of residual aberrations during conventional rigid contact lens wear in keratoconus, this study aimed to quantify the visual interaction between positive vertical coma (C(3, −1)) and other individual 2nd to 5th radial order Zernike aberration terms. Methods The experiment proceeded in two parts. First, two levels of C(3, −1) (target term) were simulated. Individual Zernike aberration terms from the 2nd to 5th radial orders (test terms) were combined in 0.05‐µm steps a) from −2.00 µm to +2.00 µm with +1.00 µm of C(3, −1) and b) from −1.00 µm to +1.00 µm with +0.50 µm of C(3, −1). The resulting combinations were used to calculate the logarithm of the visual Strehl ratio (logVSX) and predict the relative beneficial or deleterious impact of the interaction. Second, for test terms where an interaction was predicted to provide more than a 0.25 logVSX benefit compared to C(3, −1) alone, high contrast logMAR acuity charts were constructed (simulating the manner in which the test + target term combinations would impact the retinal image of the chart), and randomly read by three well‐corrected, typically‐sighted individuals through a 3.0‐mm diameter artificial pupil. Results When combined with positive C(3, −1), C(3, −3), C(4, −4), C(5, −5), C(5, −3), and C(5, −1) exhibited better visual image quality compared with C(3, −1) alone. Ratios of the test terms to target term providing maximal benefit remained constant for both +0.50 µm and +1.00 µm of C(3, −1). C(3, −3) and C(5, −1) had the largest predicted beneficial effect, with the maximal effect for +1.00 µm of C(3, −1) occurring with +0.35 µm of C(5, −1) and −1.00 µm of C(3, −3). When individuals read letter charts convolved with the point spread function derived from C(3, −1) combined with C(3, −3) and C(3, −1) combined with C(5, −1), the maximal beneficial effect was 0.27 logMAR (13.5 letters) for C(3, −3) and 0.36 logMAR (18 letters) for C(5, −1). Conclusions While most interactions reduced visual image quality, combinations of C(3, −3) (vertical trefoil) and C(5, −1) (vertical secondary coma) provided a clinically relevant beneficial effect in the presence of C(3, −1) (vertical coma) which was demonstrated in both through‐focus simulation and chart reading tests. Future work will examine whether these effects persist in the presence of the entire spectrum of residual aberrations seen in the eyes of individuals with keratoconus.

Comparative Analysis on Refractive Errors and High-Order Aberrations according to Changes in Pupil Size before and after Presbyopia

Article

Jun 2020

Study of spatial thermal distribution of gold nanourchins in saline by combined transverse probe beam deflection and beam wavefront sensor: biomedical implications

Article

Full-text available

Nov 2019
APPL PHYS B-LASERS O

Mohammad E. Khosroshahi

Combined probe beam deflection (PBD) and wavefront sensor (WFS) technique are used to investigate the thermal distribution of gold nanourchins (GNU) in physiological saline (PS) using a low-power continuous NIR diode laser. Three different samples were prepared for the experiment: (S1) 0.5 mg/mL GNU only, (S2) 0.5 mL PS and 0.3 mL GNU, and (S3) 0.5 mL PS and 0.1 mL GNU. The laser transmission initially increases linearly as S3 > S2 > S1, but reaches a plateau and remains constant. The probe beam response in an adjective statistics process exhibited a stochastic behaviour at different positions and constant power in x- and y-directions. The beam view profiles showed a non-uniform intensity distribution and the addition of PS dramatically caused a blue shift indicating its cooling effect, S1 (20) warmer > S1(10) medium > S2 (20) cooler. S1 (10), S1 (20), and S2 (20) correspond to the samples irradiated with the laser power (mW) shown in the bracket. The peak-to-valley (PV) and root-mean-square (RMS) values demonstrated a non-linear intensity distribution during the scanning process. The greater PV values in deeper positions may well due to agglomeration, hence the sedimentation process. The Zernike coefficients with high absolute values represent the aberrations that cause the greatest distortion of the wavefront and found in the order of S2(20) > S1(10) > S1(20). This is consistent with PV wavefront slope and spatial period aberration relation. The opto-thermal coefficients were obtained as S2 (− 7.86 × 10⁻⁴⁾ > S3: 0.5 mL PS and 0.1 ml GNU (− 6.3 × 10⁻⁴), respectively.

Effect of aging in retinal image quality

Article

Full-text available

Aug 1993
J Opt Soc Am

The retinal image quality characterized by the modulation-transfer function of the eye was measured for two groups of subjects aged in the late twenties and mid sixties, respectively. In both groups, we obtained modulation transfer functions by using a double-pass method under the same experimental conditions: 4-mm artificial pupil, paralyzed accommodation, and objective control of the refractive state and centering. Results showed lower values of modulation in the retinal image for older subjects compared with the younger subjects. The modulation transfer function ratio is similar to that previously found for contrast-sensitivity measurements with subjects in the same age groups. These results suggest that a significant fraction of the loss in spatial vision with age has an optical origin. Apart from the well-known increase in intraocular scattering, there also appears to be an increment in ocular aberration that causes an additional reduction in the contrast of retinal images.

Average Optical Performance of the Human Eye as a Function of Age in a Normal Population

Article

Full-text available

Feb 1999
INVEST OPHTH VIS SCI

To determine the average optical performance of the human eye, in terms of the modulation transfer function (MTF), as a function of age. An apparatus was constructed to measure the ocular MTF, based on the recording of images of a green, 543-nm laser-point source after reflection in the retina and double pass through the ocular media. MTFs were computed from the average of three 4-second-exposure double-pass images recorded by a slow-scan, cooled charge-coupled device camera. The ocular MTF was measured for three artificial pupil diameters (3 mm, 4 mm, and 6 mm) with paralyzed accommodation under the best refractive correction in 20 subjects for each of three age categories: young subjects aged 20 to 30 years, middle-aged subjects aged 40 to 50 years, and older subjects aged 60 to 70 years. The selected subjects passed an ophthalmologic examination, excluding subjects with any form of ocular or retinal disease, spherical or cylindrical refractive errors exceeding 2 D, and corrected visual acuity lower than 1 (0.8 in the older age group). The average MTF was determined for each age group and pupil diameter. A two-parameter analytical expression was proposed to represent the average MTF in each age group for every pupil diameter. The ocular MTFs declined as age increased from young to older groups. The SD of the MTF results within age groups was lower than the differences between the mean for each group. The average optical performance of the human eye progressively declines with age. These MTF results can serve as a reference for determining mean ocular optics according to age.

Report From the VSIA Taskforce on Standards for Reporting Optical Aberrations of the Eye

Article

Full-text available

Sep 2000

The human eye's monochromatic aberrations in a large population

Article

Full-text available

Sep 2001

From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eye's aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann-Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eye's aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eye's wave aberration. Even though there appears to be a random variation in the eye's aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

Contribution of cornea and internal surfaces to the change of ocular aberration with age

Article

Full-text available

Feb 2002

We studied the age dependence of the relative contributions of the aberrations of the cornea and the internal ocular surfaces to the total aberrations of the eye. We measured the wave-front aberration of the eye with a Hartmann-Shack sensor and the aberrations of the anterior corneal surface from the elevation data provided by a corneal topography system. The aberrations of the internal surfaces were obtained by direct subtraction of the ocular and corneal wave-front data. Measurements were obtained for normal healthy subjects with ages ranging from 20 to 70 years. The magnitude of the RMS wave-front aberration (excluding defocus and astigmatism) of the eye increases more than threefold within the age range considered. However, the aberrations of the anterior corneal surface increase only slightly with age. In most of the younger subjects, total ocular aberrations are lower than corneal aberrations, while in the older subjects the reverse condition occurs. Astigmatism, coma, and spherical aberration of the cornea are larger than in the complete eye in younger subjects, whereas the contrary is true for the older subjects. The internal ocular surfaces compensate, at least in part, for the aberrations associated with the cornea in most younger subjects, but this compensation is not present in the older subjects. These results suggest that the degradation of the ocular optics with age can be explained largely by the loss of the balance between the aberrations of the corneal and the internal surfaces.

A New Method for Describing the Aberrations of the Eye Using Zernike Polynomials

Article

Full-text available

Feb 2003

Charles E Campbell

The standard Zernike polynomial functions are reformulated in a way so that the number of functions (or terms) needed to describe an arbitrary wavefront surface to a given Zernike radial order is reduced by a factor of approximately two, and the terms are described in a fashion quite similar to that used to describe common sphero-cylindrical errors of the eye. A wavefront is represented using these terms by assigning a pair of values, a magnitude and an axis, to all terms that are radially symmetric so that the individual aberrations are presented in a way similar to the way common astigmatism is currently given in terms of cylinder power and axis. The root mean square of these magnitudes gives the root mean square wavefront error just as does the root mean square of the standard Zernike coefficients. Formulas are given to convert standard Zernike coefficients to the magnitude and axis values.

Matrix method to find a new set of Zernike coeffcients from an original set when the aperture radius is changed

Article

Full-text available

Mar 2003

Charles E Campbell

A matrix method is developed that allows a new set of Zernike coefficients that describe a surface or wave front appropriate for a new aperture size to be found from an original set of Zernike coefficients that describe the same surface or wave front but use a different aperture size. The new set of coefficients, arranged as elements of a vector, is formed by multiplying the original set of coefficients, also arranged as elements of a vector, by a conversion matrix formed from powers of the ratio of the new to the original aperture and elements of a matrix that forms the weighting coefficients of the radial Zernike polynomial functions. In developing the method, a new matrix method for expressing Zernike polynomial functions is introduced and used. An algorithm is given for creating the conversion matrix along with computer code to implement the algorithm.

Monochromatic Aberrations as a Function of Age, from Childhood to Advanced Age

Article

Full-text available

Dec 2003
INVEST OPHTH VIS SCI

To describe monochromatic optical aberrations of the eye as a function of age. One hundred fourteen subjects with a spherical equivalent within +/-3.50 D from emmetropia, corrected visual acuity of 20/40 or better, and normal findings in an ophthalmic examination were enrolled. The mean age was 43.2 +/- 24.5 years (range, 5.7-82.3). Monochromatic optical aberrations were measured with a Hartmann-Shack wavefront sensor after pharmacological dilation and cycloplegia. For a 5-mm pupil and for third- to seventh-, third-, fourth-, and fifth- to seventh-order aberrations, as well as for coma and spherical aberrations, the root mean square (RMS) error as a function of age was modeled by a second-order polynomial regression. It decreased progressively through childhood, adolescence, and early adulthood; reached a minimum level during the fourth decade of life, then increased progressively with age, to age 82. For a 5-mm pupil, the mean modulation transfer function (MTF) was reduced in both the child-teenage (5-20 years; n = 29) and the elderly (61-82 years; n = 37) groups versus the middle-aged adult group (41-60 years; n = 24; P < 0.05). In young adults (21-40 years; n = 23) and elderly subjects, the MTF curves were very close and almost superimposed at spatial frequencies higher than 38 cyc/deg. Aberrations of the whole eye were objectively measured from early childhood to an advanced age, and the relationship between monochromatic aberrations and age has been shown to fit a quadratic model. The results suggest that the definition of emmetropization should be broadened to include the reduction of higher order aberrations.

Variability of wavefront aberration measurements in small pupil sizes using a clinical Shack-Hartmann aberrometer

Article

Full-text available

Feb 2004
BMC Ophthalmol

Recently, instruments for the measurement of wavefront aberration in the living human eye have been widely available for clinical applications. Despite the extensive background experience on wavefront sensing for research purposes, the information derived from such instrumentation in a clinical setting should not be considered a priori precise. We report on the variability of such an instrument at two different pupil sizes. A clinical aberrometer (COAS Wavefront Scienses, Ltd) based on the Shack-Hartmann principle was employed in this study. Fifty consecutive measurements were performed on each right eye of four subjects. We compared the variance of individual Zernike expansion coefficients as determined by the aberrometer with the variance of coefficients calculated using a mathematical method for scaling the expansion coefficients to reconstruct wavefront aberration for a reduced-size pupil. Wavefront aberration exhibits a marked variance of the order of 0.45 microns near the edge of the pupil whereas the central part appears to be measured more consistently. Dispersion of Zernike expansion coefficients was lower when calculated by the scaling method for a pupil diameter of 3 mm as compared to the one introduced when only the central 3 mm of the Shack - Hartmann image was evaluated. Signal-to-noise ratio was lower for higher order aberrations than for low order coefficients corresponding to the sphero-cylindrical error. For each subject a number of Zernike expansion coefficients was below noise level and should not be considered trustworthy. Wavefront aberration data used in clinical care should not be extracted from a single measurement, which represents only a static snapshot of a dynamically changing aberration pattern. This observation must be taken into account in order to prevent ambiguous conclusions in clinical practice and especially in refractive surgery.

Standards for reporting the optical aberrations of eyes-OSA Technical Digest

Article

Jan 2000

Mathematical Treatment of Ocular Aberrations: a User's Guide

Article

Feb 2000

We explain the nature of optical aberrations and how they may be represented mathematically. We describe the use of Zernike polynomials in a way that will aid understanding and provide potential tools for manipulating the wavefront aberration expressions given in this form.

Validation of a clinical aberrometer

Article

Dec 2002
J VISION

Purpose: To test the accuracy, tolerance and repeatability of the COAS aberrometer (Wavefront Sciences, Inc.) with model eyes and normal human eyes. Methods: Model eyes were constructed from six PMMA, single-surface lenses with known characteristics. Accuracy was evaluated by comparing theoretical predictions with measured spherical aberration, coma, defocus, and astigmatism. Tolerance to axial and lateral misalignment was measured by controlled displacements of the model eye relative to the aberrometer. Repeatability was tested with measurements taken within seconds or across several days on the same model eye. The same tolerance and repeatability experiments were then repeated on human eyes. Results: Accuracy of spherical aberration and coma agreed closely with theoretical predictions (e.g. for all six aspheric models, the mean difference between predicted and measured Z4\0 was 0.006 microns). Defocus and astigmatism were accurately measured (e.g. measured defocus was within +/- 0.25 diopters over a +/-3 D range of refractive error). Axial displacements over the range +/- 2.5 cm had little effect on measurements for myopic and emmetropic model eyes. Also, lateral displacements over the range +/-1.5 mm did not produce significant coma. The standard deviations of repeated measurements of higher order RMS were less than 1% of the mean over seconds and less than 8% over days for model eyes. Tolerance to small lateral displacements was also observed for human eyes. Rotational (fixation) errors over a 3° range increased measurement variability, but not enough to fully account for long-term variations in human eyes. Conclusion: The COAS aberrometer can measure 2nd, 3rd, and 4th order aberrations accurately and repeatably on model eyes. Variability in human eye measurements is mostly due to fixational error and other physiological factors, rather than instrument fluctuations or errors of alignment.

Scaling pseudo-Zernike expansion coefficients to different pupil sizes

Article

Aug 2011
OPT LETT

Jim Schwiegerling

Orthogonal polynomials are routinely used to represent complex surfaces over a specified domain. In optics, Zernike polynomials have found wide application in optical testing, wavefront sensing, and aberration theory. This set is orthogonal over the continuous unit circle matching the typical shape of optical components and pupils. A variety of techniques has been developed to scale Zernike expansion coefficients to concentric circular subregions to mimic, for example, stopping down the aperture size of an optical system. Here, similar techniques are used to rescale the expansion coefficients to new pupil sizes for a related orthogonal set: the pseudo-Zernike polynomials.

The Chromatic Eye – a New Reduced-Eye Model of Ocular Chromatic Aberration in Humans

Article

Jul 1992

New measurements of the chromatic difference of focus of the human eye were obtained with a two-color, vernier-alignment technique. The results were used to redefine the variation of refractive index of the reduced eye over the visible spectrum. The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration. The resulting chromatic-eye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.

Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor

Article

Oct 1998

The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack-Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of approximately lambda/2 and approximately lambda/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack-Hartmann wave-front sensor for measuring the optical quality of the human eye.

Effect of aging on the monochromatic aberrations of the human eye

Article

Oct 1999

We measured the contrast sensitivity (CS) of a group of older subjects through natural pupils and compared the results with those from a group of younger subjects. We also measured each subject's monochromatic ocular wave-front aberrations using a crossed-cylinder aberroscope and calculated their modulation transfer functions (MTF's) and root-mean-squared (RMS) wave-front aberrations for fixed pupil diameters of 4 mm and 6 mm and for a natural pupil diameter. The CS at a natural pupil diameter and the MTF computed for a fixed pupil diameter were found to be significantly poorer for the older group than for the younger group. However, the older group showed very similar MTF's and significantly smaller RMS wave-front aberrations compared with the younger group at their natural pupil diameters, owing to the effects of age-related miosis. These results suggest that although monochromatic ocular wave-front aberrations for a given pupil size increase with age, the reduction in CS with age is not due to this increase.

Comparing Laser Ray Tracing, Spatially Resolved Refractometer And Hartmann-Shack Sensor To Measure The Ocular Wave Aberration

Article

Apr 2001

To compare quantitatively three techniques to measure the optical aberrations of the human eye: laser ray tracing (LRT), the Hartmann-Shack wavefront sensor (H-S), and the spatially resolved refractometer (SRR). LRT and H-S are objective imaging techniques, whereas SRR is psychophysical. Wave aberrations were measured in two normal subjects with all three techniques implemented in two different laboratories. We compared the experimental variability of the results obtained with each technique with the overall variability across the three methods. For the two subjects measured (RMS wavefront error 0.5 microm and 0.9 microm, respectively), we found a close agreement; the average standard deviation of the Zernike coefficients within a given method was 0.07 microm, whereas the average global standard deviation across techniques was 0.09 microm, which is only slightly higher. There is a close match between the Zernike coefficients obtained by LRT, H-S, and SRR. Thus, all three techniques provide similar information concerning wave aberration when applied to normal human eyes. However, the methods are operationally different, and each has advantages and disadvantages depending on the particular application.

Article

Jun 2001
INVEST OPHTH VIS SCI

To investigate the relations between age and the optical aberrations of the whole eye. The eye's optical quality, as measured by the modulation transfer function (MTF), degrades with age, but the MTF does not provide a means to assess the contributions of individual aberrations, such as coma, spherical aberration, and other higher order aberrations to changes in optical quality. The method used in this study provides measures of individual aberrations and overall optical quality. Wave aberrations in 38 subjects were measured psychophysically using a spatially resolved refractometer. Data were fit with Zernike polynomials up to the seventh order to provide estimates of 35 individual aberration terms. MTFs and root mean square (RMS) wavefront errors were calculated. Subjects ranged in age from 22.9 to 64.5 years, with spherical equivalent corrections ranging from +0.5 to -6.0 D. Overall RMS wavefront error (excluding tilts, astigmatism, and defocus) was significantly positively correlated with age (r = 0.33, P = 0.042). RMS error for the highest order aberrations measured (fifth through seventh order) showed a strong positive correlation with age (r = 0.57, P = 0.0002). Image quality, as quantified by the MTF, also degraded with age. Wave aberrations of the eye increase with age. This increase is consistent with the loss of contrast sensitivity with age observed by other investigators.

Wave-front aberrations in the eye of myopic and emmetropic school children and young adults

Article

May 2002
VISION RES

Wavefront aberrations were measured using a psychophysical ray-tracing technique in both eyes of 316 emmetropic and moderately myopic school children and young adults. Myopic subjects were found to have greater mean root mean square (RMS) value of wavefront aberrations than emmetropic subjects. Emmetropic adults had the smallest mean RMS, which remained smaller than the values for myopic adults and children and for emmetropic children both when second order Zernike aberrations (astigmatism) and third order Zernike aberrations were removed. Twenty percent of myopic adults had RMS values greater than values for all of the emmetropic adults, with significantly greater values for Zernike aberrations from second to seventh orders. High amounts of wavefront aberrations, which degrade the retinal image, may play a role in the development of myopia.

Ocular wave-front aberration statistics in a normal young population

Article

Jul 2002
VISION RES

Monochromatic ocular aberrations in 108 eyes of a normal young population (n=59) were studied. The wave-front aberration were obtained under natural conditions using a near-infrared Shack-Hartmann wave-front sensor. For this population and a 5 mm pupil, more than 99% of the root-mean square wave-front error is contained in the first four orders of a Zernike expansion and about 91% corresponds only to the second order. Comparison of wave-fronts aberrations from right and left eye in 35 subjects, showed a good correlation between most of the second- and third-order terms and a slight (but not clear) tendency for mirror symmetry between eyes.

A statistical model of the aberration structure of normal, well-corrected eyes

Article

Oct 2002

A statistical model of the wavefront aberration function of the normal, well-corrected eye was constructed based on normative data from 200 eyes which show that, apart from spherical aberration, the higher-order aberrations of the human eye tend to be randomly distributed about a mean value of zero. The vector of Zernike aberration coefficients describing the aberration function for any individual eye was modelled as a multivariate, Gaussian, random variable with known mean, variance and covariance. The model was verified by analysing the statistical properties of 1000 virtual eyes generated by the model. Potential applications of the model include computer simulation of individual variation in aberration structure, retinal image quality, visual performance, benefit of novel designs of ophthalmic lenses, or outcome of refractive surgery.

Scaling Zernike expansion coefficients to different pupil sizes

Article

Nov 2002

Jim Schwiegerling

Recent developments in technologies to correct aberrations in the eye have fostered extensive research in wave-front sensing of the eye, resulting in many reports of Zernike expansions of wave-front errors of the eye. For different reports of Zernike expansions, to be compared, the same pupil diameter is required. Since no standard pupil size has been established for reporting these results, a technique for converting Zernike expansion coefficients from one pupil size to another is needed. This investigation derives relationships between the Zernike expansion coefficients for two different pupil sizes.

Statistical variation of aberration structure and image quality in a normal population

Article

Jan 2003

A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

Measurement of Refractive Errors in Young Myopes Using the COAS Shack-Hartmann Aberrometer

Article

Feb 2003

To evaluate the Complete Ophthalmic Analysis System (COAS; WaveFront Science) for accuracy, repeatability, and instrument myopia when measuring myopic refractive errors. We measured the refractive errors of 20 myopic subjects (+0.25 to -10 D sphere; 0 to -1.75 D cylinder) with a COAS, a phoropter, and a Nidek ARK-2000 autorefractor. Measurements were made for right and left eyes, with and without cycloplegia, and data were analyzed for large and small pupils. We used the phoropter refraction as our estimate of the true refractive error, so accuracy was defined as the difference between phoropter refraction and that of the COAS and autorefractor. Differences and means were computed using power vectors, and accuracy was summarized in terms of mean vector and mean spherocylindrical power errors. To assess repeatability, we computed the mean vector deviation for each of five measurements from the mean power vector and computed a coefficient of repeatability. Instrument myopia was defined as the difference between cycloplegic and noncycloplegic refractions for the same eyes. Without cycloplegia, both the COAS and autorefractor had mean power vector errors of 0.3 to 0.4 D. Cycloplegia improved autorefractor accuracy by 0.1 D, but COAS accuracy remained the same. For large pupils, COAS accuracy was best when Zernike mode Z4(0) (primary spherical aberration) was included in the computation of sphere power. COAS repeatability was slightly better than autorefraction repeatability. Mean instrument myopia for the COAS was not significantly different from zero. When measuring myopes, COAS accuracy, repeatability, and instrument myopia were similar to those of the autorefractor. Error margins for both were better than the accuracy of subjective refraction. We conclude that in addition to its capability to measure higher-order aberrations, the COAS can be used as a reliable, accurate autorefractor.

Validation of a Clinical Shack-Hartmann Aberrometer

Article

Aug 2003

To validate the accuracy, tolerance, and repeatability of the complete ophthalmic analysis system aberrometer (COAS, Wavefront Sciences Inc.) with model eyes and normal human eyes. Model eyes were constructed from six polymethyl methacrylate, single-surface lenses with known characteristics. Accuracy of second-order aberrations was verified by measuring defocus and astigmatism induced by series of spherical and cylindrical trial lenses. Accuracy of higher-order aberrations was evaluated by comparing ray-tracing predictions with measured spherical aberration and coma of the aspheric model eyes. Tolerance to axial and lateral misalignment was measured by controlled displacements of the model eye relative to the aberrometer. Repeatability was tested on the same model eyes with repeated measurements taken within 1 s or within half an hour with realignment between each trial. Analyses were based on a 5-mm pupil diameter. Defocus and astigmatism were accurately measured within the working range of the instrument automatic focus adjustment (e.g., measured defocus was within +/-0.25 diopters over a -6.50 to +3.00 D range of refractive error). Accuracy of spherical aberration and coma agreed closely with theoretical predictions (e.g., for all six aspheric models, the mean absolute difference between predicted and measured Z(4)0 was 0.007 microm). Axial displacements over the range +/-2.5 mm had little effect on measurements for myopic and emmetropic model eyes. Also, lateral displacements over the range +/-1.5 mm did not produce significant coma. The standard deviations of repeated measurements of higher-order root mean square on model eyes were <1% of the mean with repeated measures within 1 s and 10% of the mean for five individual measurements with realignment in between each. Tolerance to small lateral displacements was also observed for human eyes. The complete ophthalmic analysis system aberrometer can measure second-, third-, and fourth-order aberrations accurately and repeatedly on model eyes.

Ocular high-order aberrations in individuals screened for refractive surgery

Article

Oct 2003

To explore the distribution of ocular higher-order aberrations (HOAs, 3rd to 6th orders) in the population, evaluate the symmetry of ocular aberrations between right and left eyes in each subject using a Hartmann-Shack wavefront sensor, and study the differences in aberration as a function of age. Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. Ocular HOAs were examined across a 6.0 mm pupil in 532 eyes of 306 subjects (mean age 41 years +/- 10 [SD] [range 20 to 71 years]; mean WaveScan spherical equivalent -3.39 +/- 2.84 diopters [D] [range -11.56 to 7.60 D]) using the WaveScan system (Visx, Inc.). Zernike coefficients and root-mean-square (RMS) values of HOAs, spherical aberration (SA, Z(4)(0) and Z(6)(0)), and coma (Z(3)(-1), Z(3)(1), Z(5)(-1), and Z(5)(1)) were analyzed. Correlation analysis was performed to assess the association between ocular HOAs and age and investigate the aberration symmetry between right and left eyes. For individual terms, the highest mean absolute values were for 4th-order SA (Z(4)(0)), 3rd-order coma, and trefoil terms. The mean RMS values of HOA, SA, and coma were 0.305 +/- 0.095 microm, 0.128 +/- 0.074 microm, and 0.170 +/- 0.089 microm, respectively. Moderate to high correlations were found between the right and left eyes for HOA, SA, and coma (Pearson correlation coefficient = 0.601, 0.776, and 0.511, respectively; all P<.001). Thirteen of the 22 Zernike terms (59%) were significantly correlated across eyes (Bonferroni correction, P'<.05/22). Higher-order aberrations, SA, and coma were weakly correlated with age (r = 0.317, 0.273, and 0.176, respectively; all P<.002). Wavefront aberrations varied widely among subjects and increased slightly with age. A moderate to high degree of mirror symmetry existed between right and left eyes.

A population study on changes in wave aberrations with accomodation

Article

May 2004
J VISION

Wave aberrations were measured with a Shack-Hartmann wavefront sensor (SHWS) in the right eye of a large young adult population when accommodative demands of 0, 3, and 6 D were presented to the tested eye through a Badal system. Three SHWS images were recorded at each accommodative demand and wave aberrations were computed over a 5-mm pupil (through 6th order Zernike polynomials). The accommodative response was calculated from the Zernike defocus over the central 3-mm diameter zone. Among all individual Zernike terms, spherical aberration showed the greatest change with accommodation. The change of spherical aberration was always negative, and was proportional to the change in accommodative response. Coma and astigmatism also changed with accommodation, but the direction of the change was variable. Despite the large inter-subject variability, the population average of the root mean square for all aberrations (excluding defocus) remained constant for accommodative levels up to 3.0 D. Even though aberrations change with accommodation, the magnitude of the aberration change remains less than the magnitude of the uncorrected aberrations, even at high accommodative levels. Therefore, a typical eye will benefit over the entire accommodative range (0-6 D) if aberrations are corrected for distance viewing.

Article

Jun 2004
AM J OPHTHALMOL

To investigate age-related changes in ocular and corneal higher-order wavefront aberrations and elucidate relative contributions of the cornea and the lens in the age-related changes. Observational case series. Corneal and ocular higher-order wavefront aberrations in the central 6 mm diameter were measured with videokeratography and the Hartmann-Shack wavefront aberrometer in 75 normal eyes of 75 patients with a mean age of 43.5 +/- 11.7 years (range, 18-69 years). Higher-order wavefront aberrations were calculated with Zernike polynomials up to sixth order. From the Zernike coefficients, we calculated root mean square (RMS) of coma and spherical aberration. To examine age-related changes of the polarity of spherical aberration, the changes of the Zernike coefficient Z(4)(0) was also investigated. Both corneal (r =.307, P =.007) and ocular (r =.334, P =.0033) coma RMS showed positive correlations with age. There was a positive correlation between corneal and ocular coma RMS (r =.468, P <.0001). The RMS of corneal spherical aberration did not change with aging (r =.153, P =.1895), whereas the RMS of ocular spherical aberration had a positive correlation with aging (r =.308, P =.0068). These results suggest that the ocular coma increases with age, mainly because of the increase in the corneal coma, and the ocular spherical aberration increases with age, mainly because of the increase in the spherical aberration in the internal optics.

Article

Dec 2004
AM J OPHTHALMOL

Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers

Article

Nov 2004

To compare the accuracy and verify the reliability of different commercial and experimental prototypes of aberrometers using a small group of normal subjects with low myopia. Three different devices were used to measure the wavefront aberration of five normal myopic eyes: 1) Zywave--commercial aberrometer based on a Hartmann-Shack wavefront sensor; 2) Tracey--commercial system based on the laser ray tracing principle; and 3) an experimental laboratory laser ray tracing instrument working at two different wavelengths (532 and 786 nm). A series of five measurements were taken for each subject. Pupil diameter and alignment were controlled. All wave aberration maps were reduced to a common 6.5-mm pupil diameter, and then the mean and standard deviation were computed for the series, as well as the global average and standard deviation for each subject. Despite several important differences among devices and sessions, the results obtained with the different devices were equivalent. The main difference found between aberrometers was due to the longitudinal chromatic aberration caused by the use of different wavelengths. The signal-to-noise ratio estimated from the raw data was moderate, 12, but could be improved by a factor of 2 by discarding those measurements with a higher deviation from the mean and averaging the remaining data, which was the approach implemented in the Zywave instrument. The aberrometers tested were reliable in normal eyes with low myopia. Aberrometry is a robust but noisy technique. Accuracy is limited by noise and other sources of variability, including the size and alignment of the pupil. These conclusions might not apply to eyes with large aberrations.

Ocular higher-order aberrations in eyes with supernormal vision

Article

Mar 2005
AM J OPHTHALMOL

To quantify ocular higher-order aberrations (HOAs) in eyes with supernormal vision, that is, natural uncorrected visual acuity (UCVA) > or = 20/15, to analyze the correlation between ocular HOAs and age in these eyes, and to investigate the correlation of HOAs between right and left eyes. Observational case series. Ocular HOAs were examined across a naturally dilated pupil with a diameter > or = 6.0 mm in 70 eyes of 35 subjects with > or = 20/15 UCVA (mean age 24.3 years +/- 7.7 [SD]) using the Nidek OPD scan wavefront aberrometer. Root-mean-square (RMS) values of HOA, total spherical aberration (TSA), total coma (TC), and total trefoil (TT) were analyzed. Correlation analysis was performed to assess the association between ocular HOAs and age and the correlation of HOAs between right and left eyes. Mean RMS values were 0.334 +/- 0.192 microm for HOA, 0.110 +/- 0.077 microm for TSA, 0.136 +/- 0.081 microm for TC, and 0.268 +/- 0.220 microm for TT. There were no significant differences in the mean values of HOA, TSA, TC, and TT between right and left eyes. The Pearson correlation coefficient between right and left eyes for TSA was 0.764 (P<.0001). No significant correlation was found between right and left eyes for HOA, TC, and TT. No significant correlation was found between each of the ocular aberrations and age. The amount of ocular HOAs in eyes with natural supernormal vision is not negligible, and is comparable to the reported amount of HOAs in myopic eyes.

Ocular higher-order aberrations in myopia and skiascopic wavefront repeatability

Article

Jun 2005

To study the distribution of ocular higher-order aberrations (HOAs) in a myopic population and to assess the repeatability of HOA measurements determined by a commercially available skiascopic wavefront sensor. Department of Ophthalmology, Assaf Harofeh Medical Center, Zerifin, Israel. Ocular HOAs were examined 3 times across a 6.0 mm naturally dilated pupil in 61 eyes using the Optical Path Difference (OPD)-scan wavefront aberrometer. Root-mean-square (RMS) values of HOAs, total spherical aberration (TSA), total coma (TC), and total trefoil (TT) were analyzed. Correlation analysis was performed to assess the aberration symmetry between right and left eyes. The repeatability of the OPD-scan measurements was assessed by calculating Pearson r correlation coefficients between each pair of measurements and the interclass correlation coefficients between the 3 measurements of each score. The mean RMS values of HOAs, TSA, TC, and TT were 0.347 microm +/- 0.252 (SD), 0.120 +/- 0.174 microm, 0.165 +/- 0.168 microm, and 0.252 +/- 0.157 microm, respectively. The HOAs, TSA, TC, and TT changed slightly and not significantly with increasing refractive error (all P>.05). The RMS level of HOAs and TTR of the 3rd measurement was significantly different from the 1st and 2nd measurements (P<.05), with overall low correlation between the 3 measurements for the HOAs, TSA, TC, and TT. The ocular wavefront aberrations varied greatly from subject to subject. Ocular HOAs were not correlated with refractive error. The repeatability of HOAs measurements with the OPD-aberrometry was low.

Wavefront Analysis in Normal Refractive Surgery Candidates

Article

Nov 2004

To quantify the higher order aberrations of refractive surgery candidates and compare the wavefront-determined refractions with manifest refractions refined with a +/- 0.25 Jackson cross cylinder. Results of 226 consecutive patients (418 eyes) were analyzed with the WaveScan WavePrint system (VISX, Santa Clara, Calif). Only patients with normal eyes without previous surgery were included. The mean spherical equivalent refraction determined with wavefront analysis was -3.40 +/- 3.14 diopters (D) (range: -10.72 to +5.41 D). The largest amount of higher order aberrations was detected with : a 6-mm pupil diameter (coma 0.14 +/- 0.08 microm; trefoil 0.10 +/- 0.07 microm; spherical aberrations 0.09 +/- 0.07 microm). The mean root-mean-square of higher order aberrations and total aberrations were 0.23 +/- 0.11 microm and 4.00 +/- 2.45 microm, respectively. No statistically significant correlation was noted between higher order aberrations and gender (P = 0.7) or between higher order aberration and refractive level (P > .59). The mean differences in spherical equivalent refraction, sphere, and cylinder between WaveScan measurements and manifest refraction were 0.36 +/- 0.41 D, 0.40 +/- 0.44 D, and 0.28 +/- 0.32 D, respectively. This study provides reference values for higher order aberrations in normal refractive surgery candidates. Wavefront analysis also proved to be a valuable tool for objectively measuring preoperative refractive error.

Higher-order aberrations from the internal optics of the eye

Article

Aug 2005

To analyze the distribution of human higher-order wavefront aberrations (3rd- to 6th-order) from the internal optics (WA(internal)) and the variations with age and to evaluate the degree of compensation that the internal optics provide for anterior corneal aberrations (WA(cornea)). Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. With assumption of a simple model for the eye, the WA(internal) were obtained by direct subtraction of the WA(cornea) from the ocular aberrations (WA(eye)). The WA(eye) were measured using the WaveScan system (Visx, Inc.), and the WA(cornea) were computed from the topographic data (Humphrey Atlas) using the CTView program (Sarver and Associates, Inc.). In 144 eyes of 114 normal patients (age 20 to 69 years), WA(internal) were calculated for a 6.0 mm pupil and a compensation factor (CF) was computed, with positive values representing compensation of WA(cornea) by WA(internal) and negative values indicating that the internal surfaces add aberrations to those of the cornea. There was wide individual variation in WA(internal). The mean coefficient for 4th-order spherical aberration (Z(4)(0)) was -0.145 microm +/-0.094 (SD) (95% confidence interval [CI], -0.160 to -0.130 microm); 95.1% of eyes had negative values. The mean root-mean-square value for HOAs was 0.334 +/- 0.096 microm (95% CI, 0.319 to 0.350 microm). Moderate to high correlations were found between the right and left eyes in HOAs, 4th-order and 6th-order spherical aberration coefficients (Z(4)(0) and Z(6)(0)). With increasing age, the HOAs did not change, whereas the negative coefficients for Z(4)(0) tended to become less negative. Only the term Z(4)(0) had a CF significantly correlated with increasing age (r=-0.338, P<.05 with Bonferroni correction). WA(internal) varied widely among patients, and a moderate to high degree of mirror symmetry existed between the right and left eyes. Internal surfaces compensated at least partially for the HOA and Z(4)(0) in most eyes, and this compensation decreased only mildly with increasing age.

Evaluation of a clinical aberrometer for lower-order accuracy and repeatability, higher-order repeatability, and instrument myopia

Article

Sep 2005
Optometry

Refractive surgery has stimulated the development of aberrometers, which are instruments that measure higher-order aberrations. The purpose of this study was to test one clinical aberrometer, the Complete Ophthalmic Analysis System (COAS), for its accuracy, repeatability, and instrument myopia for measuring sphere and astigmatism and its repeatability for measuring higher-order aberrations. Aberrations of 56 normal eyes (28 subjects) were measured with and without cycloplegia using a COAS, a conventional autorefractor and by subjective refraction. We evaluated lower-order accuracy (sphere and astigmatism) of the COAS and autorefractor by comparing that data with that of subjective refraction. We also tested COAS lower- and higher-order repeatability for 5 measurements taken in less than 1 minute. We evaluated instrument myopia by comparing cycloplegic and noncycloplegic measurements of the same eye. Data were analyzed for a 5.0-mm-diameter pupil. Mean COAS spherical error was between -0.1 and +0.4 diopters (D), depending on cycloplegia and the kind of sphere power computation selected. Cylinder power errors were less than 0.1 D. COAS repeatability coefficients were better than 0.25 D, and instrument myopia was less than 0.4 D. These were comparable with those of autorefraction. Higher-order repeatability was sufficient to allow reliable measurement of normal third-order aberrations and spherical aberration. Accuracy, repeatability, and instrument myopia of the COAS are similar to those of a conventional autorefractor. Accuracy and repeatability are also similar to those of subjective refraction. Like an autorefractor, the COAS provides instantaneous, objective measurements of sphere and astigmatism, but it also measures higher-order aberrations. We found that it is capable of reliably measuring problematic higher-order aberrations and is therefore a valuable asset for modern clinical eye care.

Monochromatic aberrations as afunctionofage,fromchildhoodtoadvancedage

5438-544

I Brunette
Jm Bueno
M Parent

Brunette I, Bueno JM, Parent M, et al. Monochromatic aberrations as afunctionofage,fromchildhoodtoadvancedage.InvestOphthalmol Vis Sci 2003; 44:5438–544

Wavefront analysis in normal refractive surgery candidates

Jan 2005
J REFRACT SURG
332-338

M V Netto
Jr
T T Shen
S E Wilson

Netto MV, Ambró sio R Jr, Shen TT, Wilson SE. Wavefront analysis in normal refractive surgery candidates. J Refract Surg 2005; 21:332-338

Effect of aging on the monochromatic aberrations of the human eye

Jan 1999
2069-2078

Ri Calver
Mj Cox
Db Elliot

Calver RI, Cox MJ, Elliot DB. Effect of aging on the monochromatic aberrations of the human eye. J Opt Soc Am A Opt Image Vis Sci 1999; 16:2069-2078

Jan 2006

Zernike
Rms
Errors

ZERNIKE COEFFICIENTS AND RMS WAVEFRONT ERRORS IN NORMAL EYES J CATARACT REFRACT SURG -VOL 32, DECEMBER 2006

Normal-eye Zernike coefficients and root-mean-square wavefront errors

Abstract

No full-text available

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