Daniel Malacara-Doblado

Centro de Investigaciones en Optica | CIO · Ingenieria Optica

The graphical representation of the surface level or topography of optical surfaces and wavefronts is a relatively simple problem if the optical surface is a simple and smooth one. However, the problem is not so simple if the surface has many bumps and valleys. Typically, mainly for common optical systems, elevation maps provide sufficient informat...

Placido disk methods for corneal topography use a target with concentric rings in order to obtain measurements of the corneal surface, codifying the topography from the deformations of the rings’ image. Knowing exactly how the corneal surface departs from a rotational symmetric shape is difficult by using Placido rings. This is due to the fact that...

In this chapter, some of the most important optical systems using lenses will be described [1–4]. However, telescopes and microscopes are not described here, since they are the subjects of other chapters in this book. Since optical instruments cannot be studied without a previous background on the definitions of pupils, principal ray and skew and m...

In this chapter we want to provide an overview of contemporary microscopy. For this purpose, we have mainly focused our attention on confocal microscopy, which exploits the idea of focusing the source and the imaging system at the same point of the sample, by adding a punctual scanning process. In visible light imaging systems, this method is funda...

Instead of measuring the wavefront deformations, Hartmann and Shack–Hartmann tests, we measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in t...

In a previous work, we introduced the concept of transversal aberrations { U , V } calculated at arbitrary Hartmann-plane distances z = r [Appl. Opt. 55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W , as well as the classical transversal aberrations { X , Y } c...

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z = f , where f is the radius of a reference sphere. The function W and the transversal aberrations...

When testing lenses with Hartmann methods, a wave aberration function $W$ is typically estimated. This $W$ represents the deviations of the wavefront surface $w$ with respect to an ideal wavefront $E$. In this test, the distance $r$ from the observation screen to the second lens surface is considered, and such as in the case of $W$, by considering...

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack–Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with...

In this paper we will review some of the many different practical arrangements that have been obtained to measure the transversal aberrations of optical systems based on the odd and vulnerable Hartmann test. There are many optical testing configurations that apparently are not related to the original Hartmann test. However, they are really the same...

In the previously published paper [Appl. Opt. 53, 7422 (2014)10.1364/AO.53.007422APOPAI1559-128X], we had an error in some equations as described below.

In optical design, many error functions can be used to generate an optical system with desired characteristics. These error functions are optimized by iterative algorithms. However, these error functions should be theoretically and mathematically differentiable to be optimized. In this paper, the differentiability of an error function is partially...

Instead of measuring the wavefront deformations, Hartmann and Shack–Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categorie...

Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. To study these irregular surfaces at the vertex, which have principal meridians with an angle different from 90°, we attempt to define so-called parastigmatic surfaces; these surfaces allow us to correct several classes of irregular astigmatism, with non...

Instead of measuring the wavefront deformations directly, Hartmann and Shack–Hartmann tests measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified...

Spectacle lenses are the most commonly used solution for refractive errors of the eye, such as myopia, hyperopia, presbyopia and astigmatism. To correct a refractive error, the spectacle lens needs to have the correct lens power and an appropriate distribution of power along the surface of the lens, to measure these characteristics several methods...

Hartmann and Shack-Hartmann, instead of measuring the wavefront deformations directly they measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods had been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified i...

In this work, we describe a new method for assessing the refractive correction error in power corrected ophthalmic lenses. The ideal power distribution map corresponding to the lens design to be measured is initially obtained. Then, using some known techniques, the real power distribution map of the lens under test is obtained. Finally, the differe...

The Fourier analysis of two-stage phase-shifting (TSPS) algorithms is growing in interest as a research topic, specifically, the algorithm’s insensitivity properties to various error sources. The main motivation of this paper is to propose TSPS algorithms that perform well in the face of detuning and harmonics for each of the two sets of interferog...

A data fitting model is proposed to estimate phases from its cosine and sine. The a priori assumption is that the phases to be reconstructed should be expressed by polynomials. The cosine and sine of the phases are obtained from interferograms with high fringe density by generalized phase-shifting techniques. The proposed method is employed for ph...

A simple phase estimation employing cubic and average interpolations to solve the oversampling problem in smooth modulated phase images is described. In the context of a general phase-shifting process, without phase-unwrapping, the modulated phase images are employed to recover wavefront shapes with high fringe density. The problem of the phase rec...

From generalized phase-shifting equations, we propose a simple linear system analysis for algorithms with equally and nonequally spaced phase shifts. The presence of a finite number of harmonic components in the fringes of the intensity patterns is taken into account to obtain algorithms insensitive to these harmonics. The insensitivity to detuning...

In this manuscript, some interesting properties for generalized or nonuniform phase-shifting algorithms are shown in the Fourier frequency space. A procedure to find algorithms with equal amplitudes for their sampling function transforms is described. We also consider in this procedure the finding of algorithms that are orthogonal for all possible...

Many optical systems need to be evaluated but they cannot be disassembled to test the imaging lens separately. Then, they have to be tested in a retroreflecting configuration, frequently called double-pass. A typical example of this procedure is in the optical eye. In this manuscript we will describe the different possibilities that might exist whe...

In this work, we have developed a different algorithm than the classical one on phase-shifting interferometry. These algorithms typically use constant or homogeneous phase displacements and they can be quite accurate and insensitive to detuning, taking appropriate weight factors in the formula to recover the wrapped phase. However, these algorithms...

In this work we have developed a different algorithm to the classical one on phase-shifting interferometry. These algorithms typically use constant or homogeneous phase displacements and they can be quite accurate and insensitive to detuning, taking appropriate weight factors in the formula to recover the wrapped phase. However, these algorith...

A new, simple method to measure the effective focal length of a thick lens or lens system in the laboratory when a lens nodal bench is not readily available is described. Use is made of the Talbot autoimaging effect by placing the lens in a collimated light beam, with a Ronchi ruling in front of the lens and another in the refracted beam.

A wavefront aberration can be retrieved from a defocused image or a Hartmanngram by several different methods using diffraction theory and Fourier transforms. In this manuscript, we describe an alternate method for wavefront aberration determination from a defocused image or a Hartmanngram using a geometric l approximation. The main assumption is t...

The detuning phase shift error is a common systematic error observed in temporal phase shifting (TPS) algorithms. This error, generally due to miscalibration of the phase shifter, is solved by using a quadrature filter insensitive to this detuning error. To compare algorithms, this error is frequently analyzed numerically. However, in this work we...

The main purpose of this paper is to present a method to design tunable quadrature filters in phase shifting interferometry. The algorithm is obtained from a generalized Fourier transform of a symmetrical quadrature filter. This formalism allows us to represent the detuning phase shift error and bias modulation as geometrical conditions. Therefore,...

An astigmatic optical surface has two different orthogonal curvatures. There are a great number of them, but only a few are in common use in optical instruments. These are similar in shape but have some important differences to be considered. These differences must be taken into account during the design, fabrication, and testing of optical systems...

Introduction Some Practical Aspects Hartmann Test Using a Rectangular Screen Wavefront Retrieval Hartmann Test Using a Screen with Four Holes Hartmann Test of Ophthalmic Lenses Hartmann Test Using Nonrectangular Screens Hartmann–Shack Test Crossed Cylinder Test Testing with an Array of Light Sources or Printed Screens Michelson–Gardner–Bennett Test...

This article describes a simple Hartmann test data interpretation that can be used to evaluate the performance of ophthalmic lenses. Considering each spot of the Hartmann pattern such as a single test ray, using simple ray tracing analysis, it is possible to calculate the power values from the lens under test at the point corresponding with each sp...

In the classical Hartmann test the wave front is obtained by integration of the transverse aberrations, joining the sampled points by small straight segments, in the so-called Newton integration. This integration is performed along straight lines joining the holes on the Hartmann screen. We propose a modification of this procedure, considering the...

The classical method for wavefront retrieval from Hartmann test data by integration of the transverse aberrations using a linear approximation between the sampled points: In this work we report a method using splines that produces a more precise wavefront shape.

In the classical Hartmann test analysis, the transverse aberrations are represented by small straight segments joining two consecutive measured points in the pupil. In the analysis presented in this paper we propose the wavefront to be synthesized by many nonflat functions whose domains are the squares defined by the square unit cell defined by an...

In this paper, we will describe a method used to obtain the power error distribution map for a spherical well corrected ophthalmic lens. The proposed method uses a computer to perform a null test compensation to probe the real refractive correction state of the lens under test. The Hartman test is used to probe an ophthalmic lens and subtract the i...

This paper describes a simple Hartmann test data interpretation that can be used to evaluate the performance in spherical ophthalmic lenses. Considering each spot of the Hartmann pattern like a single ray, using traditional ray tracing analysis it is possible to calculate the value of the spherical power in the point corresponding with each spot. T...

The proper location of the eye with respect to a visual optical instruments is not a trivial problem. It depends on many practical factors not widely known. This paper describes some of the many factors that determine the best position for the pupil of the observer with respect to the optical system which is not necessarily the exit pupil of the sy...

Keystone distortion that occurs in overhead projectors when the projecting lens head is tilted upward to a high screen is commonly observed. Here we suggest a modification of the typical overhead projector to eliminate this distortion of the image.

Most of the optics measurements techniques used generate interferograms as a result. These give us information about the object's quality, surface, etc. Evaluating and knowing the heat gradient of an object, is a typical application of the interferograms analysis. We know that if we subject an object to heat, this will generate interferograms, in w...

There are many sources of possible errors in phase shifting algorithms. One of those errors that may greatly influence the results is the detuning of the sampling points. Here we will describe a procedure to make the frequency interval in which the detuning error is smaller than a certain tolerances, as large as possible.

The design of phase-shifting algorithms (PSA’s) has been carried out with diverse strategies by different authors. A generalized algebraic approach is employed to obtain a family of detuning-insensitive PSA’s; their behavior against a linear phase error is analyzed from a geometric point of view. The obtained results are compared with the condition...

The simplest two qualitative geometrical tools to evaluate lenses and mirrors are the Ronchi and Hartmann tests. They only require a knife or a ruling and a point light source. Frequently, the main desired characteristic of a test is not high sensitivity and precision, but speed and simplicity. The test proposed in this paper does not require any a...

The angle measurement method described here measures the difference in arrival time to a detector of a light beam reflected by a surface being measured and a reference ray. This measurement is made by alternately detecting both rays with a photodetector at the focal plane of a lens and electronically obtaining their arrival time difference. With th...

We employ the Fourier-transform graphic representation of a set of antisymmetrical and symmetrical sampling reference harmonics to obtain new symmetrical phase-shifting algorithms tailored to specific characteristics. As an example, a new detuning-insensitive seven-point algorithm, with a third signal harmonic insensitivity and which is detuning in...

Here, we propose a method using the fringe projection method to measure the surface of a diffuse or ground surface with a rotationally symmetric shape in a qualitative manner, by means of a null test. When in a visual observation the fringes are straight, equidistant and parallel, the surface has its correct shape.

A family of detuning insensitive algorithms with an odd number of points and a maximum of seven is developed here following a simple algebraic approach. Detuning insensitive algorithms are quite useful because the phase error due to any possible phase shifter miscalibration can be substantially reduced. A method to evaluate the second order detunin...

The wavefront shape can be obtained from lateral shear interferograms even if the lateral shear is large. Many procedures have been devised in the past to achieve this purpose. However, all of them have serious practical restrictions. A method is reported here using a digital analysis of the interferogram in the Fourier space. An alternative iterat...

If a flat wavefront illuminates a lens and we measure the curvature of the refracted wavefront, the focal length of this lens can be determined. Different alternatives to measure the convergence or divergence power of a wavefront using fringes projected by a Ronchi ruling placed in contact with the lens are described. The Talbot autoimaging phenome...

A theory of phase-detecting algorithms based on Fourier theory was described by Freischlad and Koliopoulos (1990). We present an application of this theory to a discrete sampling. It is shown that Greivenkamp (1984) results for a least-squares fitting of the sampling points can be obtained from this Fourier theory. We also present a new graphical v...

Axially astigmatic surfaces have different curvatures in or-thogonal diameters. Toroidal and spherocylindrical optical surfaces are two mathematically different special cases of axially astigmatic surfaces as noted by Menchaca and Malacara (1986), but they are almost identi-cal in the vicinity of the optical axis. The difference between these two s...

An instrument to measure the convergence or divergence power of a wavefront using moire fringes or software synchronous detection is described. This instrument could be used to measure the dioptrical power of ophthalmic lenses. The working principle could also be applied to measure angles with high sensitivity.

A least squares procedure to fit irradiance measurements ofa digitalized interferogram data to a sinusoidal function has been described in the literature by Greivenkamp. On the other hand, a general theory of phase stepping algorithms based on Fourier theory has been described by Freischlad and Kouliopoulos. In this paper it is shown that Greivenka...

Another way to explain the autoimaging effect is to consider it as the Fresnel diffraction field obtained with the Huygens-Fresnel model using Young spherical waves generated by each transparent point in the ruling. This model has been used by Latimer and Crouse (1993) and later commented by Szwaykowski (1993). Here we present another analysis more...

Toroidal and sphero-cylindrical optical surfaces are two different kinds of surfaces (Menchaca and Malacara, 1986), but they are almost identical in the vicinity of the optical axis. The separation between these two surfaces increases when the distance to the optical axis increases. In this work the separation between these two surfaces outside of...

There are some optical arrangements closely resembling interferometric configurations. These, however, do not produce fringe patterns. An important characteristic of this device is that they do not have two different outputs with complementary patterns, but only one. Two of these configurations are described.

A very elegant theory for the autoimaging of diffraction objects has been developed some years ago where the concept of the Montgomery rings arouse. Using the concept of the Montgomery ring we may obtain a large variety of structures that produce autoimages. Many of these structures are periodic and well known, but some others are not periodic and...

A Shack-Fizeau interferometer has been designed and constructed to test concave conical telescope mirrors. Many interesting practical problems and results were found on the way. Some of these problems are, for example, the design of each optical element and the imaging of the interference pattern on the detector, etc. Here, we describe the design p...

It is well known that in Talbot imaging the so called autoimages are reproduced with unit magnification with a constant axial separation known as Raleigh's distance. When the incident wavefront is not flat but spherical, the autoimages are reproduced with magnification. The purpose of this paper is to show that in this second case the images are al...