Journal of the Optical Society of America A

Published by Optical Society of America
Online ISSN: 1520-8532
Publications
Article
Following the trend of increased integration in complementary metal oxide semiconductor (CMOS) image sensors, we have explored the potential of implementing light filters by using patterned metal layers placed on top of each pixel's photodetector. To demonstrate wavelength selectivity, we designed and prototyped integrated color pixels in a standard 0.18-microm CMOS technology. Transmittance of several one-dimensional (1D) and two-dimensional (2D) patterned metal layers was measured under various illumination conditions and found to exhibit wavelength selectivity in the visible range. We performed (a) wave optics simulations to predict the spectral responsivity of an uncovered reference pixel and (b) numerical electromagnetic simulations with a 2D finite-difference time-domain method to predict transmittances through 1D patterned metal layers. We found good agreement in both cases. Finally, we used simulations to predict the transmittance for more elaborate designs.
 
Article
It is a great challenge to create a needle-like field with properties of long beam length, narrow lateral width, uniformity, and high optical efficiency. Here we show a method that can realize these properties all at once. The key element is a 90° apex-angle concave conical mirror. By using this condenser along with a radially polarized incident beam of a specific field distribution, we numerically created a super slim, uniform, pure needle-like axially polarized field. This axially polarized field has a length of 50,000λ along the optical axis, and its lateral width still maintains a minimum 0.36λ size.
 
Article
A heuristic formalism is developed for efficiently determining the specular reflectivity spectrum of two-dimensionally textured planar waveguides. The formalism is based on a Green's function approach wherein the electric fields are assumed to vary little over the thickness of the textured part of the waveguide. Its accuracy, when the thickness of the textured region is much smaller than the wavelength of relevant radiation, is verified by comparison with a much less efficient, exact finite difference solution of Maxwell's equations. In addition to its numerical efficiency, the formalism provides an intuitive explanation of Fano-like features evident in the specular reflectivity spectrum when the incident radiation is phase matched to excite leaky electromagnetic modes attached to the waveguide. By associating various Fourier components of the scattered field with bare slab modes, the dispersion, unique polarization properties, and lifetimes of these Fano-like features are explained in terms of photonic eigenmodes that reveal the renormalization of the slab modes due to interaction with the two-dimensional grating. An application of the formalism, in the analysis of polarization-insensitive notch filters, is also discussed.
 
Article
We describe high-efficiency, high-dispersion reflection gratings fabricated in bulk fused silica illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. Based on the phenomenon of total internal reflection, gratings with optimized profile parameters exhibit diffraction efficiencies of more than 90% under TM- and TE-polarized incident lights for 101-nm spectral bandwidths (1520-1620 nm) and can reach an efficiency of greater than 97% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, without coating of dielectric film layers, and independent of tooth shape, this new kind of grating should be of great interest for DWDM application.
 
Article
The transmittance of thin films of Sc deposited by evaporation in ultrahigh vacuum conditions has been investigated in the 20-1000 eV spectral range. Transmittance measurements were performed in situ on Sc layers that were deposited over grids coated with a C support film. Transmittance measurements were used to obtain the extinction coefficient of Sc films at each individual photon energy investigated. These data, along with the data available in the literature for the rest of the spectrum, were used to obtain the refractive index of Sc by means of the Kramers-Krönig analysis. Sum-rule tests indicated an acceptable consistency of the data.
 
Article
Ellipsomicroscopy for surface imaging (EMSI) is a powerful new tool for studying spatiotemporal adsorbate pattern formation on catalyst surfaces. It is a surface-sensitive technique that is able to measure submonolayer coverage of adsorbates. The imaging of the sample's surface achieves a spatial sensitivity, making it possible to measure nonuniformity of adsorbate coverage. The image contrast, however, depends strongly on the setup of the instrument. The optimum setup can be calculated from the ellipsometric properties of the catalyst/adsorbate system and the intrinsic parameters of the EMSI instrument. Optimizing the setup of the EMSI instrument permitted enhancement of the image contrast over the previous setup. As a result, new features in CO oxidation on Pt(110) were discovered.
 
Plot of relative energy for scattering by a spherical droplet of water of radius r ˆ 200 μm as a function of scattering angle for monochromatic sources (from 400 to 700 nm in steps of 20 nm producing 16 curves), and their sum (arbitrarily scaled by 0.25 for plotting). Curves are pseudo-colored to specify wavelength and the resultant color of the mixture.
Pseudo-color representation of the spectra obtained as a function of scattering angle (within a rainbow) and droplet radius (between rainbows). 
Plots of the MacLeod-Boynton coordinates of spectra obtained by simulating scattering of light by spherical droplets of water, as occurs in natural rainbows. Each pseudo-colored symbol represents a particular combination of scattering angle and droplet size, according to the range represented in the Lee diagram of Fig. 2. Black lines are used to link points that share the same droplet size and are therefore characterized as within the same rainbow. (a) A projection onto the chromatic plane (Media 1). (b) An oblique projection, additionally showing the variation in (log) luminance (Media 1).
Plots of the CIELAB coordinates of spectra obtained by simulating scattering of light by spherical droplets of water, as occurs in natural rainbows. Each pseudo-colored symbol represents a particular combination of scattering angle and droplet size, according to the range represented in the Lee diagram of Fig. 2. Black lines are used to link points that share the same droplet size and are therefore characterized as within the same rainbow. The white-point is set to correspond to the daylight illuminant D65 at the maximum luminosity available within each rainbow. (a) A projection onto the chromatic plane (Media 2). (b) An oblique projection, additionally showing the variation in luminance (Media 2). (c) Analogous to (a), but including the spectral locus. (d) Analogous to (b) but including the spectral locus.
Article
We present a new analysis of Robert Grosseteste's account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste's De colore [see J. Opt. Soc. Am. A29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste's key terms.
 
(a) RGB color space; (b) a rotation of the RGB space, in which the achromatic axis ( R G B ) is vertically aligned; (c) achromatic axis and a chromatic plane, spanned by a red-green and a blue-yellow axis; (d) achromatic plane, showing variation in hue (azimuthally) and saturation (radially). 
Article
We present a new commentary on Robert Grosseteste's De colore, a short treatise that dates from the early 13th century, in which Grosseteste constructs a linguistic combinatorial account of color. In contrast to other commentaries (e.g., Kuehni & Schwarz, Color Ordered: A Survey of Color Order Systems from Antiquity to the Present, 2007, p. 36), we argue that the color space described by Grosseteste is explicitly three-dimensional. We seek the appropriate translation of Grosseteste's key terms, making reference both to Grosseteste's other works and the broader intellectual context of the 13th century, and to modern color spaces.
 
Article
We constructed an automated reflectometry system for accurate measurement of coherent reflectance curves of turbid samples and analyzed the presence of coherent and diffuse reflection near the specular reflection angle. An existing method has been validated to determine the complex refractive indices of turbid samples on the basis of nonlinear regression of the coherent reflectance curves by Fresnel's equations. The complex refractive indices of fresh porcine skin epidermis and dermis tissues and Intralipid solutions were determined at eight wavelengths: 325, 442, 532, 633, 850, 1064, 1310, and 1557 nm.
 
Article
The resolution of optical microscopy is limited by the numerical aperture and the wavelength of light. Many strategies for improving resolution such as 4Pi and I5M have focused on an increase of the numerical aperture. Other approaches have based resolution improvement in fluorescence microscopy on the establishment of a nonlinear relationship between local excitation light intensity in the sample and in the emitted light. However, despite their innovative character, current techniques such as stimulated emission depletion (STED) and ground-state depletion (GSD) microscopy require complex optical configurations and instrumentation to narrow the point-spread function. We develop the theory of nonlinear patterned excitation microscopy for achieving a substantial improvement in resolution by deliberate saturation of the fluorophore excited state. The postacquisition manipulation of the acquired data is computationally more complex than in STED or GSD, but the experimental requirements are simple. Simulations comparing saturated patterned excitation microscopy with linear patterned excitation microscopy (also referred to in the literature as structured illumination or harmonic excitation light microscopy) and ordinary widefield microscopy are presented and discussed. The effects of photon noise are included in the simulations.
 
Article
The optical constants of Yb films have been determined in the 23-1700 eV spectral range from transmittance measurements performed in situ on Yb films deposited by evaporation in ultrahigh vacuum conditions. Yb films were deposited over grids coated with a thin carbon film. Transmittance measurements were used to obtain the extinction coefficient of Yb films at each individual photon energy investigated. The energy range investigated encompasses Yb edges from M(4,5) to O(2,3). The current results, along with data in the literature, show that Yb has an interesting low-absorption band in the approximately 12-24 eV range, which may be useful for the development of transmittance filters and multilayer coatings. The current data along with literature data and extrapolations were used to obtain n, the real part of the complex refractive index, using a Kramers-Krönig analysis. The application of the sum rules showed a good consistency of the results.
 
Article
Foveal flicker contrast sensitivity was measured for healthy adults at temporal frequencies from 2.5 to 50 Hz. The first experiment compared two-interval forced-choice (2IFC) and yes-no detection (Y-N) testing procedures for younger (19-33-year-old) and older (67-73-year-old) observers. The 2IFC technique resulted in higher absolute estimates of sensitivity. However, within a method, relative differences were similar. Therefore the two methods gave similar estimates of temporal contrast-sensitivity change with age. Experiment 2 compared 89 observers from 18 through 77 years of age to explore the effect of the time course of aging on flicker sensitivity. The 2IFC procedure was used, and retinal illuminance changes with age were controlled. Significant overall losses in contrast sensitivity were found for the 45-54, 55-64, and 65-77-year-old age groups. Overall sensitivities for the 35-44-year-old group were comparable with or (not significantly) higher than those for the 18-24- and 25-34-year-old groups. The results suggested that (1) foveal temporal contrast sensitivity does not decline until after 44 years, (2) losses after 44 years are in amplitude but not in temporal resolution of the visual response, and (3) the mean rate of loss is approximately 0.78 decilog per decade after 44 years. These results are consistent with the existence of three phases of development of temporal contrast sensitivity over the life span. The results also emphasize the importance of including healthy-eyed age-matched controls in studies of flicker sensitivity in visual dysfunctions that affect mainly older adults.
 
Schematic of experimental configuration for porcine eye ablation experiments, including laser delivery system and emission collection optics. 
Comparison of ablation rates predicted by (1) the dynamic ablation model in the static limit, whereby species 3 and 4 have the same absorption cross sections as species 1, and (2) rates predicted by the static Beer-Lambert law. Dynamic model parameters: x = 20 nm, P = 0.8, 3 = 4 = 1 = 1.19 10 −17 cm 2 .
Comparison of peak photon density as a function of tissue depth as predicted by the dynamic ablation model and by the static Beer-Lambert blow-off model for absorption coefficients of 16,000 and 40,000 cm −1. A dashed horizontal line indicates the ablation threshold, and the ablation depths predicted by the models are shown. Dynamic model parameters: x = 20 nm, P = 0.8, 3 =4.5 10 −15 cm 2 , 4 =4.5 10 −24 cm 2 , F = 350 mJ/ cm 2 .
Photon density temporal profiles predicted by the dynamic ablation model at five tissue depths. The temporal profile of the incident laser pulse is also shown. Dynamic model parameters: x = 20 nm, P = 0.8, 3 =4.5 10 −15 cm 2 , 4 =4.5 10 −24 cm 2 , F = 350 mJ/ cm 2 .
Ablation rate as a function of laser fluence for ArF excimer laser ablation of corneal tissue, comparing reported experimental data 8,48-55 with values predicted by the dynamic ablation model (middle curve). Values predicted by the static BeerLambert law (upper and lower curves) are also included for absorption coefficients of 16,000 and 40,000 cm −1. Dynamic model parameters: x = 20 nm, P = 0.8, 3 =4.5 10 −15 cm 2 , 4 =4.5 10 −24 cm 2 .
Article
We detail the development and implementation of a global ablation model that incorporates a dynamically changing tissue absorption coefficient. Detailed spectroscopic measurements rule out plasma-shielding effects during the laser-tissue interaction and thereby support a photochemical mechanism. The model predicts ablation rate behavior that agrees well with a variety of experimental ablation rate data and that substantially deviates from a static Beer-Lambert model. The dynamic model predicts an enhancement in the tissue absorption coefficient of about 25%-50% as compared with the initial, static value. In addition, the model predicts an increase in the tissue ablation rate as corneal hydration increases, which may provide additional insight into variations in refractive surgery outcome.
 
Article
Most of the optical axes in modern systems are bent for optomechanical considerations. Antireflection (AR) coatings for polarized light at oblique incidence are widely used in optical surfaces like prisms or multiform lenses to suppress undesirable reflections. The optimal design and fabrication method for AR coatings with large-angle range (68°-74°) for a P-polarized 193 nm laser beam is discussed in detail. Experimental results showed that after coating, the reflection loss of a P-polarized laser beam at large angles of incidence on the optical surfaces is reduced dramatically, which could greatly improve the output efficiency of the optical components in the deep ultraviolet vacuum range.
 
Article
The diffraction computation of crossed gratings is very slow compared with that of line-space gratings of the same size when using a modal method such as rigorous coupled wave analysis (RCWA) or the Chandezon coordinate transformation method. It is well known that the main bottleneck in terms of computation speed is the solution of an eigenproblem for each RCWA slice or interface in the case of the C-method. Even if the crossed grating contains layers that are periodic only in one direction, usually the full 2D problem has to be solved for this layer in order to connect it to the full system solution. In this paper, a computation schema is presented that takes advantage of the 1D periodicity of layers inside a 2D multilayer grating. This results in a considerable acceleration of the formulation and solution of the eigenproblem for these layers. With this new computation schema the total time required for 1D layers in a 2D layer stack can be greatly reduced.
 
Article
We show that by using a one-dimensional anisotropic photonic structure, it is possible to realize optical wave polarization conversion by reflection and transmission processes. Thus a single incident S(P) polarized plane wave can produce a single reflected P(S) polarized wave and a single transmitted P(S) polarized wave. This polarization conversion property can be fulfilled with a simple finite superlattice (SL) constituted of anisotropic dielectric materials. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The transmission and reflection coefficients are calculated in the framework of the Green's function method. The amplitude and the polarization characteristics of reflected and transmitted waves are determined as functions of frequency, wave vector k(parallel) (parallel to the interface), and the orientations of the principal axes of the layers constituting the SL. Specific applications of these results are given for a SL consisting of alternating biaxial anisotropic layers NaNO(2)/SbSI sandwiched between two identical semi-infinite isotropic media.
 
Article
To support refinement of the ANSI Maximum Permissible Exposure safety limits, a series of experiments were conducted in vivo on Dutch Belted rabbit corneas to determine corneal minimum visible lesion thresholds for 2.0 microm continuous-wave laser irradiation. Single pulse radiant exposures were made at specified pulse durations of 0.1, 0.25, 0.5, 1.0, 2.0, and 4.0 s for spot 1/e(2) diameters of 1.17 mm and 4.02 mm. Threshold lesions were defined as the presence of a superficial surface whitening one hour after irradiation. Temperature measurements indicated that threshold peak temperatures were dependent on spot size and exposure duration. The exposure duration dependence of threshold average radiant exposure was described by an empirical power law equation: threshold radiant exposure[J/cm(2)]=a x exposure duration[s](b).
 
Article
After discussing the rationale and assumptions of the ANSI Z136.1-2000 Standard for protection of the human eye from laser exposure, we present the concise formulation of the exposure limits expressed as maximum permissible radiant exposure (in J/cm(2)) for light overfilling the pupil. We then translate the Standard to a form that is more practical for typical ophthalmic devices or in vision research situations, implementing the special qualifications of the Standard. The safety limits are then expressed as radiant power (watts) entering the pupil of the eye. Exposure by repetitive pulses is also addressed, as this is frequently employed in ophthalmic applications. Examples are given that will familiarize potential users with this format.
 
Article
In the context of color perception on modern wide-gamut displays with narrowband spectral primaries, we performed a theoretical analysis on various aspects of physiological observers proposed by CIE TC 1-36 (CIEPO06). We allowed certain physiological factors to vary, which was not considered in the CIEPO06 framework. For example, we analyzed that the long-wave-sensitive (LWS) or medium-wave-sensitive (MWS) peak wavelength shift in the photopigment absorption spectra, a factor not modeled in CIEPO06, contributed more toward observer variability than some of the factors considered in the model. Further, we compared the color-matching functions derived from the CIEPO06 model and the CIE 10° standard colorimetric observer to the average observer data from three distinct subgroups of Stiles-Burch observers, formed on the basis of observer ages (22-23 years, 27-29 years, and 49-50 years). The errors in predicting the x(λ) and y(λ) color-matching functions of the intragroup average observers in the long-wave range and in the medium-wave range, respectively, were generally more in the case of the CIEPO06 model compared to the 10° standard colorimetric observer and manifested in both spectral and chromaticity space. In contrast, the short-wave-sensitive z₁₀(λ) function of the 10° standard colorimetric observer performed poorly compared to the CIEPO06 model for all three subgroups. Finally, a constrained nonlinear optimization on the CIEPO06 model outputs showed that a peak wavelength shift of photopigment density alone could not improve the model prediction errors at higher wavelengths. As an alternative, two optimized weighting functions for each of the LWS and MWS cone photopigment densities led to significant improvement in the prediction of intra-age-group average data for both the 22-23 year and 49-50 year age groups. We hypothesize that the assumption in the CIEPO06 model that the peak optical density of visual pigments does not vary with age is false and is the source of these prediction errors at higher wavelengths. Correcting these errors in the model can lead to an improved age-dependent observer and can also help update the current CIE 10° standard colorimetric observer. Accordingly, it would reduce the discrepancies between color matches with broadband spectral primaries and color matches with narrowband spectral primaries.
 
Article
Some printing errors in the equations of our previous paper [J. Opt. Soc. Am. A24, 2963 (2007)] are corrected.
 
Article
We correct a mistake in the expression of the coupled power into an optical fiber that led to some erroneous conclusions in Opt. Lett. 34 , 2829 (2009) and J. Opt. Soc. Am. A 26 , 2452 (2009).
 
Article
Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.
 
First case of scanning lines.
Average Errors for the Estimations of Fig. 14, Presented as the Results in Table 1
Histograms of errors for the estimations of Fig. 14, arranged as in Fig. 11.
Maps of relative magnitude error for the estimations of Fig. 14, arranged as in Fig. 12.
Maps of absolute error in orientation, measured in degrees, for the estimations of Fig. 14, arranged as in Fig. 13.
Article
We consider the application of tomography to the reconstruction of two-dimensional vector fields. The most practical sensor configuration in such problems is the regular positioning along the boundary of the reconstruction domain. However, such a configuration does not result in uniform distribution in the Radon parameter space, which is a necessary requirement to achieve accurate reconstruction results. On the other hand, sampling the projection space uniformly imposes serious constraints on space or time. In this paper, we propose to place the sensors regularly along the boundary of the reconstruction domain and employ probabilistic weights with the purpose of compensating for the lack of uniformity in the distribution of projection space parameters. Simulation results demonstrate that, when the proposed probabilistic weights are employed, an average 27% decrease in the reconstruction error may be achieved, over the case that projection measurements are not weighed (e.g., in one case the error reduces from 3.7% to 2.6%). When compared with the case where actual uniform sampling of the projection space is employed, the proposed method achieves a 90 times reduction in the number of the required sensors or 180 times reduction in the total scanning time, with only 7% increase in the error with which the vector field is estimated.
 
Article
We propose an advanced physical optics formulation for the accurate modeling of dielectric lenses used in quasi-optical systems of millimeter, submillimeter, and infrared wave applications. For comparison, we obtain an exact full-wave solution of a two-dimensional lens problem and use it as a benchmark for testing and validation of asymptotic models being considered.
 
Article
A nematic liquid crystal spatial light modulator used as a phase-modulating device and operating in the reflective mode is analyzed using three-dimensional modeling. Two configurations, which differ in their electrode placement relative to a fixed quarter-wave plate, are considered across a range of steering directions, with the grating conformal and in some cases oblique to the pixel grid. For each steering direction the sensitivity of the diffraction orders to the polarization state of the incident wavefront is studied. Optimal alignment of the liquid crystal is suggested to reduce this sensitivity.
 
Article
We report the measurement of a polarization-independent guided-mode resonant filter with a Q factor of approximately 2200 functioning near normal incidence in the near infrared (850 nm). Besides this remarkable performance, we provide a detailed optical and structural characterization of the component, which points out the origins of the limitation of the experimental performance. We conclude that the defaults in question can be corrected by improving the lithography process, and we are confident that even greater performance will be obtained in future realizations.
 
Article
We consider the application of tomography to the reconstruction of 2-D vector fields. The most convenient sensor configuration in such problems is the regular positioning along the domain boundary. However, the most accurate reconstructions are obtained by sampling uniformly the Radon parameter domain rather than the border of the reconstruction domain. This dictates a prohibitively large number of sensors and impractical sensor positioning. In this paper, we propose uniform placement of the sensors along the boundary of the reconstruction domain and interpolation of the measurements for the positions that correspond to uniform sampling in the Radon domain. We demonstrate that when the cubic spline interpolation method is used, a 60 times reduction in the number of sensors may be achieved with only about 10% increase in the error with which the vector field is estimated. The reconstruction error by using the same sensors and ignoring the necessity of uniform sampling in the Radon domain is in fact higher by about 30%. The effects of noise are also examined.
 
Article
We present an optofluidic sensor based on an elastomeric two-dimensional (2D) grating integrated inside a hemispherical fluid chamber. A laser beam is diffracted before (reflection) and after (transmission) going through the grating and liquid in the dome chamber. The sensing mechanism is investigated and simulated with a finite-difference time-domain-based electromagnetic method. For the experiment, by analyzing the size, power, and shape of the 2D diffraction patterns, we can retrieve multiple parameters of the liquid, including the refractive index, pressure, and opacity with high sensitivity. We demonstrate that the glucose concentration can be monitored when mixed in a different concentrated phosphate-buffered saline solution. The free-solution binding of bovine serum albumin (BSA) and anti-BSA IgG is detected with this optical sensor. This low-cost, multifunctional, and reliable optofluidic sensor has the potential to be used as a monitor of biofluid, such as blood in hemodialysis.
 
Article
A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators. The problem is formulated in terms of a uniquely solvable set of second-kind boundary integral equations and discretized by the Galerkin method with angular exponents as global test and trial functions. The log-singular term is extracted from one of the kernels, and closed-form expressions are derived for the main parts of all the integral operators. The resulting discrete scheme has a very high convergence rate. The method is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems.
 
Article
Analysis and optimization of diffraction effects in nanolithography through multilayered media with a fast and accurate field-theoretical approach is presented. The scattered field through an arbitrary two-dimensional (2D) mask pattern in multilayered media illuminated by a TM-polarized incident wave is determined by using an electric field integral equation formulation. In this formulation the electric field is represented in terms of complex images Green's functions. The method of moments is then employed to solve the resulting integral equation. In this way an accurate and computationally efficient approximate method is achieved. The accuracy of the proposed method is vindicated through comparison with direct numerical integration results. Moreover, the comparison is made between the results obtained by the proposed method and those obtained by the full-wave finite-element method. The ray tracing method is combined with the proposed method to describe the imaging process in the lithography. The simulated annealing algorithm is then employed to solve the inverse problem, i.e., to design an optimized mask pattern to improve the resolution. Two binary mask patterns under normal incident coherent illumination are designed by this method, where it is shown that the subresolution features improve the critical dimension significantly.
 
(a) Principal optical scheme and (b) scheme of the DOE movement in the method. The DOE structure is shown schematically (without a structure of one DOE period). 
Barker code DOE: (a) photograph of the Barker code DOE, (b) photograph of the intensity of green collimated laser beam diffracted on the Barker code DOE, and (c) cross-section of the intensity distribution in diffracted order. 
Photograph of the green light beam intensity distribution projected on a screen (a) with and (b) without the moving Barker code DOE. 
Article
This paper reports the findings from an experimental evaluation of speckle suppression efficiency using a method based on a moving 2D Barker code diffractive optical element (DOE). The optical setup and the optical scheme parameters of the method are presented. A speckle contrast of ∼4.4-5.3% and speckle suppression coefficient (coefficient of speckle contrast reduction) of k>8 was obtained in experiments. However, the experimentally obtained speckle suppression coefficient was approximately 1.5 times smaller than the theoretical prediction. It is speculated that the discrepancy between the theoretical and the experimental data is due to an inexact match between the optical setup and the optimal optical parameters of the method. Analysis of the experimental data revealed that once the optical scheme is optimized, it will be possible to obtain a speckle suppression that is closer to the theoretical prediction.
 
Article
In his works on diffraction [Proc. R. Soc. London Ser. A204, 533 (1951)], E. Wolf introduced the Q2n function, which enters his expressions for the encircled energy. This quantity specifies the fraction of the total energy within various rings in receiving planes parallel to the geometrical focal plane. In addition to the Q2n function, another special function, called the Yn function, was used in his formulation, which had been introduced by H. H. Hopkins [Proc. Phys. Soc. London Sect. B62, 22 (1949)]. The purpose of this study is to generalize both the Q2n and Yn functions for evaluating the encircled energy in systems of focused truncated Gaussian beams by apertures of different Fresnel numbers and different levels of beam truncation. The generalized Q and Y functions are functions of more than one variable and are applicable to all nonnegative integers m; they may therefore be called the Qm and the Ym functions. Computed results are shown graphically in the form of contour lines of the encircled energy. Part II of this study [J. Opt. Soc. Am. A24, 2033 (2007)] contains an analysis of maximizing beam energy concentration on a target.
 
Article
The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.
 
Article
Stimulated emission depletion (STED) can achieve optical superresolution, with the optical diffraction limit broken by the suppression on the periphery of the fluorescent focal spot. Previously, it is generally experimentally accepted that there exists an inverse square root relationship with the STED power and the resolution, but with arbitrary coefficients in expression. In this paper, we have removed the arbitrary coefficients by exploring the relationship between the STED power and the achievable resolution from vector optical theory for the widely used 0-2π vortex phase modulation. Electromagnetic fields of the focal region of a high numerical aperture objective are calculated and approximated into polynomials of radius in the focal plane, and analytical expression of resolution as a function of the STED intensity has been derived. As a result, the resolution can be estimated directly from the measurement of the saturation power of the dye and the STED power applied in the region of high STED power.
 
Article
We presented theoretical and experimental demonstrations of the possibilities of performing time-resolved diffusing wave spectroscopy: We successfully registered field fluctuations for selected photon path lengths that can surpass 300 transport mean free paths. Such performance opens new possibilities for biomedical optics applications.
 
Article
Journal of the Optical Society of America A Editor-in-Chief, Franco Gori, announces the 30th Anniversary of the journal.
 
Article
Traditional microscopes have limitations in obtaining true 3D (three-dimensional) stereovision. Although some optical microscopes have been developed for 3D vision, many of them are complex, expensive, or limited to transparent samples. In this research, a freeform optical prism array was designed and fabricated to achieve 3D stereo imaging capability for microscope and machine vision applications. To form clear stereo images from multiple directions simultaneously, freeform optical surface design was applied to the prisms. In a ray tracing operation to determine the optical performance of the freeform prisms, Taylor series was used to calculate the surface shape. The virtual image spot diagrams were generated by using ray tracing methods for both the freeform prisms and the regular prisms. The results showed that all the light rays can be traced back to a single point for the freeform prism, and aberration was much smaller than that of the regular prism. The ray spots formed by the freeform prisms were adequate for image formation. Furthermore, the freeform prism array was fabricated by using a combined ultraprecision diamond turning and slow tool servo broaching process in a single, uninterrupted operation. The slow tool servo process ensured that the relative tolerance among prisms is guaranteed by the precision of the ultraprecision machine without the need for assembly. Finally 3D imaging tests were conducted to verify the freeform prism array's optical performance. The principle of the freeform prism array investigated in this research can be applied to microscopy, machine vision, robotic sensing, and many other areas.
 
Article
A method for distortion-tolerant recognition of objects in water using three-dimensional (3D) integral imaging with a neural network classification architecture is presented. Recognition algorithms are developed and experimental results are presented with rotation-variable 3D objects. To test the robustness of the system, objects are placed under a variety of water conditions, including variable Maalox-induced scattering levels and occlusion using pine needles. Neural networks have long been used for two-dimensional recognition and have recently been used for 3D digital holographic recognition. To the best of our knowledge, this is the first use of neural networks for passive 3D integral imaging and recognition of underwater objects.
 
Article
The success of the model-based infrared reflectrometry (MBIR) technique relies heavily on accurate modeling and fast calculation of the infrared metrology process, which continues to be a challenge, especially for three-dimensional (3D) trench structures. In this paper, we present a simplified formulation for effective medium approximation (EMA), determined by a fitting-based method for the modeling of 3D trench structures. Intensive investigations have been performed with an emphasis on the generality of the fitting-determined (FD)-EMA formulation in terms of trench depth, trench pitch, and incidence angle so that its application is not limited to a particular configuration. Simulations conducted on a taper trench structure have further verified the proposed FD-EMA and demonstrated that the MBIR metrology with the FD-EMA-based model achieves an accuracy one order higher than that of the conventional zeroth-order EMA-based model.
 
Article
Optical coherence tomography (OCT) has proven to be a useful tool for investigating internal structures in ceramic tapes, and the technique is expected to be important for roll-to-roll manufacturing. However, because of high scattering in ceramic materials, noise and speckles deteriorate the image quality, which makes automated quantitative measurements of internal interfaces difficult. To overcome this difficulty we present in this paper an innovative image analysis approach based on volumetric OCT data. The engine in the analysis is a 3D image processing and analysis algorithm. It is dedicated to boundary segmentation and dimensional measurement in volumetric OCT images, and offers high accuracy, efficiency, robustness, subpixel resolution, and a fully automated operation. The method relies on the correlation property of a physical interface and effectively eliminates pixels caused by noise and speckles. The remaining pixels being stored are the ones confirmed to be related to the target interfaces. Segmentation of tilted and curved internal interfaces separated by ∼10 μm in the Z direction is demonstrated. The algorithm also extracts full-field top-view intensity maps of the target interfaces for high-accuracy measurements in the X and Y directions. The methodology developed here may also be adopted in other similar 3D imaging and measurement technologies, e.g., ultrasound imaging, and for various materials.
 
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A conformal cubical transformation-based metamaterial invisibility cloak is presented and verified, in the near and the far field, by a rigorous full-wave numerical technique based on a higher-order, large-domain finite element method, employing large anisotropic, continuously inhomogeneous generalized hexahedral finite elements, with no need for discretization of the permittivity and permeability profiles of the cloak. The analysis requires about 30 times fewer unknowns than with commercial software. To our knowledge, this is the first conformal cubical cloak and the first full-wave computational characterization of such a structure with sharp edges. The presented methodology can also be used in development of conformal, transformation-based perfectly matched layers.
 
Illustration of a digit recognition task from a digital hologram: (a) a simulation of a 400×400-pixels hologram of digits located at different distances (pixel size: 20 µm, fill-factor: 0.7, laser wavelength: 0.532 µm, depth range: [0.55 0.85] m); (b) Fresnel reconstruction of the volume displaying both infocus and out-of-focus images of the digits which makes digit recognition from the reconstructed volume a difficult task. Direct recognition of the diffraction patterns using the approach described in the paper avoids dealing with these numerous image artifacts.  
First 100 singular values of the dictionary in descending order. The dictionary of digits (in green) contains 300 centered patterns for digits placed at different depth positions with the application parameters in Sec. 4.A. The dictionary of spherical particles (in red) consists of the diffraction models for spherical objects changing depth and radius with the application parameters in Sec. 4.B. The Fresnel dictionary (in blue) corresponds to Fresnel functions with changing depth values. The dictionary of rotated digits (in mustard) contains 900 centered patterns (10 (digits)×90 (angle samples) ). In the case of spherical objects, 5 first modes can approximate the dictionary accurately. The vanishing rate of the singular values of the Fresnel dictionary is very low which implies that it is not possible to deduce an accurate low rank approximation of Fresnel dictionary.  
(a): Experimental hologram of droplets from LMFA Lyon used in Sec. 4.C, (b): same experimental hologram cleaned from the in-field particles using the 5 first modes. The magnitude of the residuals is high due to the signature of the out-of-field particles placed close to the borders.
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Pattern recognition methods can be used in the context of digital holography to perform the task of object detection, classification, and position extraction directly from the hologram rather than from the reconstructed optical field. These approaches may exploit the differences between the holographic signatures of objects coming from distinct object classes and/or different depth positions. Direct matching of diffraction patterns, however, becomes computationally intractable with increasing variability of objects due to the very high dimensionality of the dictionary of all reference diffraction patterns. We show that most of the diffraction pattern variability can be captured in a lower dimensional space. Good performance for object recognition and localization is demonstrated at a reduced computational cost using a low-dimensional dictionary. The principle of the method is illustrated on a digit recognition problem and on a video of experimental holograms of particles.
 
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We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.
 
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In tomography algorithms, the complex amplitude scattering matrix corresponds to the input parameter. When considering 3D targets, the scattering matrix now contains vectorial information. Thus, this scattering matrix might be calculated with various polarization projections. Moreover, when dealing with experimental data, we are almost every time faced with truncated data. We focus here on the impact of selecting parts of the amplitude scattering matrix elements versus others and in particular on the influence of the polarization choices on the imaging results. In order to better apprehend the physical content associated to each polarization term, the study is conducted with a simple vectorial-induced current reconstruction algorithm allowing reconstruction of qualitative maps of the scene. This algorithm is applied on scaled models of aggregates combined with experimental scattered fields acquired in the microwave frequency range.
 
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Among the most popular approaches used for simulating plasmonic systems, the discrete dipole approximation suffers from poorly scaling volume discretization and limited near-field accuracy. We demonstrate that transformation to a surface integral formulation improves scalability and convergence and provides a flexible geometric approximation allowing, e.g., to investigate the influence of fabrication accuracy. The occurring integrals can be solved quasi-analytically, permitting even rapidly changing fields to be determined arbitrarily close to a scatterer. This insight into the extreme near-field behavior is useful for modeling closely packed particle ensembles and to study "hot spots" in plasmonic nanostructures used for plasmon-enhanced Raman scattering.
 
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An airborne sensor measures the radiance spectrum, which is dependent on the spectral reflectance of the ground material, the orientation of the material surface, and the atmospheric and illumination conditions. We present an algorithm to estimate the surface spectral reflectance, given the sensor radiance spectrum corresponding to a single pixel. The algorithm uses a nonlinear physics-based image formation model. A low-dimensional linear subspace model is used for the reflectance spectra. The solar radiance, sky radiance, and path-scattered radiance are dependent on the environmental conditions and viewing geometry, and this interdependence is considered by using a coupled-subspace model for these spectra. The algorithm uses the Levenberg-Marquardt method to estimate the subspace model parameters. We have applied the algorithm to a large set of synthetic and real data.
 
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Photon counting techniques have been introduced with integral imaging for three-dimensional (3D) imaging applications. The previous reports in this area assumed a priori knowledge of exact sensor positions for 3D image reconstruction, which may be difficult to satisfy in certain applications. In this paper, we extend the photon counting 3D imaging system to situations where sensor positions are unknown. To estimate sensor positions in photon counting integral imaging, scene details of photon counting images are needed for image correspondences matching. Therefore, an iterative method based on the total variation maximum a posteriori expectation maximization (MAP-EM) algorithm is used to restore photon counting images. Experimental results are presented to show the feasibility of the method. To the best of our knowledge, this is the first report on 3D photon counting integral imaging with unknown sensor positions.
 
(Color online) Effect of the periodization on the radial coordinate of a bent structure, with PMLs. Periodization on the z axis is not represented here.
AFMM convergence of the ratio of integrals I, as defined by Eq. (18), versus the number of spatial harmonics S r and S z , for a bending radius r 0 of 0.5 μm (I 41;41 ˆ 0.18612), 1 μm (I 41;41 ˆ 0.57017), and 2 μm (I 41;41 ˆ 0.75410).
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This paper deals with a full vectorial generalization of the aperiodic Fourier modal method (AFMM) in cylindrical coordinates. The goal is to predict some key characteristics such as the bending losses of waveguides having an arbitrary distribution of the transverse refractive index. After a description of the method, we compare the results of the cylindrical coordinates AFMM with simulations by the finite-difference time-domain (FDTD) method performed on an S-bend structure made by a 500 nm × 200 nm silicon core (n=3.48) in silica (n=1.44) at a wavelength λ=1550 nm, the bending radius varying from 0.5 up to 2 μm. The FDTD and AFMM results show differences comparable to the variations obtained by changing the parameters of the FDTD simulations.
 
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A simple roadmap is established for the construction of the smallest three-dimensional (3D) isotropic focal spots. It is achieved in a 4Pi configuration by imposing a restriction/condition of equal transverse and longitudinal spot sizes to determine the position of an annular aperture and then optimize its size. The calculations were performed for cylindrically symmetric radial, azimuthal, and circular polarizations for the cases of in-phase and out-of-phase counter-propagating beams as well as when a vortex was added to the beams. A diffraction-limited bright 3D isotropic spot containing solely longitudinal or transverse electric field components is obtained, while the 3D dark spot can be formed from one of two complementary combinations, each containing both transverse and longitudinal field components.
 
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Integral imaging (II) is an important 3D imaging technology. To reconstruct 3D information of the viewed objects, modeling and calibrating the optical pickup process of II are necessary. This work focuses on the modeling and calibration of an II system consisting of a lenslet array, an imaging lens, and a charge-coupled device camera. Most existing work on such systems assumes a pinhole array model (PAM). In this work, we explore a generic camera model that accommodates more generality. This model is an empirical model based on measurements, and we constructed a setup for its calibration. Experimental results show a significant difference between the generic camera model and the PAM. Images of planar patterns and 3D objects were computationally reconstructed with the generic camera model. Compared with the images reconstructed using the PAM, the images present higher fidelity and preserve more high spatial frequency components. To the best of our knowledge, this is the first attempt in applying a generic camera model to an II system.
 
Top-cited authors
Berthold K. P. Horn
  • Massachusetts Institute of Technology
L. C. Davis
James Kress
  • Kressworks Foundation
Lee Feldkamp
  • Ford Research and Engineering,Dearborn, USA
James R. Fienup
  • University of Rochester