Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1997"

Supernormal vision and high-resolution retinal imaging through adaptive optics

Abstract: Even when corrected with the best spectacles or contact lenses, normal human eyes still suffer from monochromatic aberrations that blur vision when the pupil is large. We have successfully corrected these aberrations using adaptive optics, providing normal eyes with supernormal optical quality. Contrast sensitivity to fine spatial patterns was increased when observers viewed stimuli through adaptive optics. The eye's aberrations also limit the resolution of images of the retina, a limit that has existed since the invention of the ophthalmoscope. We have constructed a fundus camera equipped with adaptive optics that provides unprecedented resolution, allowing the imaging of microscopic structures the size of single cells in the living human retina.

New formulation of the Fourier modal method for crossed surface-relief gratings

Abstract: A new formulation of the Fourier modal method (FMM) that applies the correct rules of Fourier factorization for crossed surface-relief gratings is presented. The new formulation adopts a general nonrectangular Cartesian coordinate system, which gives the FMM greater generality and in some cases the ability to save computer memory and computation time. By numerical examples, the new FMM is shown to converge much faster than the old FMM. In particular, the FMM is used to produce well-converged numerical results for metallic crossed gratings. In addition, two matrix truncation schemes, the parallelogramic truncation and a new circular truncation, are considered. Numerical experiments show that the former is superior.

Discriminant analysis for recognition of human face images

Abstract: In this paper the discriminatory power of various human facial features is studied and a new scheme for Automatic Face Recognition (AFR) is proposed. Using Linear Discriminant Analysis (LDA) of different aspects of human faces in spatial domain, we first evaluate the significance of visual information in different parts/features of the face for identifying the human subject. The LDA of faces also provides us with a small set of features that carry the most relevant information for classification purposes. The features are obtained through eigenvector analysis of scatter matrices with the objective of maximizing between-class and minimizing within-class variations. The result is an efficient projection-based feature extraction and classification scheme for AFR. Soft decisions made based on each of the projections are combined, using probabilistic or evidential approaches to multisource data analysis. For medium-sized databases of human faces, good classification accuracy is achieved using very low-dimensional feature vectors.

Aberrations and retinal image quality of the normal human eye.

Abstract: We have constructed a wave-front sensor to measure the irregular as well as the classical aberrations of the eye, providing a more complete description of the eye's aberrations than has previously been possible. We show that the wave-front sensor provides repeatable and accurate measurements of the eye's wave aberration. The modulation transfer function of the eye computed from the wave-front sensor is in fair, though not complete, agreement with that obtained under similar conditions on the same observers by use of the double-pass and the interferometric techniques. Irregular aberrations, i.e., those beyond defocus, astigmatism, coma, and spherical aberration, do not have a large effect on retinal image quality in normal eyes when the pupil is small (3 mm). However, they play a substantial role when the pupil is large (7.3-mm), reducing visual performance and the resolution of images of the living retina. Although the pattern of aberrations varies from subject to subject, aberrations, including irregular ones, are correlated in left and right eyes of the same subject, indicating that they are not random defects.

Anatomically accurate, finite model eye for optical modeling

Abstract: There is a need for a schematic eye that models vision accurately under various conditions such as refractive surgical procedures, contact lens and spectacle wear, and near vision. Here we propose a new model eye close to anatomical, biometric, and optical realities. This is a finite model with four aspheric refracting surfaces and a gradient-index lens. It has an equivalent power of 60.35 D and an axial length of 23.95 mm. The new model eye provides spherical aberration values within the limits of empirical results and predicts chromatic aberration for wavelengths between 380 and 750 nm. It provides a model for calculating optical transfer functions and predicting optical performance of the eye.

Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation

Abstract: The diffusion of correlation is used to detect, localize, and characterize dynamical and optical spatial inhomogeneities in turbid media and is accurately modeled by a correlation diffusion equation. We demonstrate experimentally and with Monte Carlo simulations that the transport of correlation can be viewed as a correlation wave {analogous to a diffuse photon-density wave [Phys. Today48, 34 (1995)]} that propagates spherically outward from sources and scatters from macroscopic spatial variations in dynamical and/or optical properties. We demonstrate the utility of inverse scattering algorithms for reconstructing images of the spatially varying dynamical properties of turbid media. The biomedical applicability of this diffuse correlation probe is illustrated in studies of the depth of burned tissues.

Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium

Abstract: Improved solutions of the diffusion equation for time-resolved and steady-state spatially resolved reflectance are investigated for the determination of the optical coefficients of semi-infinite turbid media such as tissue. These solutions are derived for different boundary conditions at the turbid-medium-air interface and are compared with Monte Carlo simulations. Relative reflectance data are fitted in the time domain, whereas relative and absolute reflectance are investigated in the steady-state domain. It is shown that the error in deriving the optical coefficients is, especially for steady-state spatially resolved reflectance, considerably smaller for the solutions under study than for the commonly used solutions. Analysis of experimental measurements of absolute steady-state spatially resolved reflectance confirms these results.

Bayesian color constancy.

Abstract: The problem of color constancy may be solved if we can recover the physical properties of illuminants and surfaces from photosensor responses. We consider this problem within the framework of Bayesian decision theory. First, we model the relation among illuminants, surfaces, and photosensor responses. Second, we construct prior distributions that describe the probability that particular illuminants and surfaces exist in the world. Given a set of photosensor responses, we can then use Bayes’s rule to compute the posterior distribution for the illuminants and the surfaces in the scene. There are two widely used methods for obtaining a single best estimate from a posterior distribution. These are maximum a posteriori (MAP) and minimum mean-squared-error (MMSE) estimation. We argue that neither is appropriate for perception problems. We describe a new estimator, which we call the maximum local mass (MLM) estimate, that integrates local probability density. The new method uses an optimality criterion that is appropriate for perception tasks: It finds the most probable approximately correct answer. For the case of low observation noise, we provide an efficient approximation. We develop the MLM estimator for the color-constancy problem in which flat matte surfaces are uniformly illuminated. In simulations we show that the MLM method performs better than the MAP estimator and better than a number of standard color-constancy algorithms. We note conditions under which even the optimal estimator produces poor estimates: when the spectral properties of the surfaces in the scene are biased. © 1997 Optical Society of America [S0740-3232(97)01607-4]

Model of visual contrast gain control and pattern masking

Abstract: We have implemented a model of contrast gain and control in human vision that incorporates a number of key features, including a contrast sensitivity function, multiple oriented bandpass channels, accelerating nonlinearities, and a devisive inhibitory gain control pool. The parameters of this model have been optimized through a fit to the recent data that describe masking of a Gabor function by cosine and Gabor masks [J. M. Foley, "Human luminance pattern mechanisms: masking experiments require a new model," J. Opt. Soc. Am. A 11, 1710 (1994)]. The model achieves a good fit to the data. We also demonstrate how the concept of recruitment may accommodate a variant of this model in which excitatory and inhibitory paths have a common accelerating nonlinearity, but which include multiple channels tuned to different levels of contrast.

Two-dimensional phase unwrapping with minimum weighted discontinuity

Abstract: Given an interferometric phase image of a surface profile, the task of two-dimensional phase unwrapping is to reconstruct the profile by adding multiples of 2π to the image. Discontinuities in the unwrapped phase must be restricted to areas of noise and true discontinuity in the profile. Such areas can often be identified by their low quality. This suggests that the unwrapped phase should be chosen to minimize a weighted sum of discontinuity magnitudes. An algorithm is presented that computes such an unwrapped phase from any initial guess. The elementary operation of the algorithm is to partition the image into two connected regions, then raise the unwrapped phase by 2π in one of the regions, reducing the weighted sum; this is done repeatedly until no suitable partitions exist. The operations are found by creating paths that follow discontinuity curves and extending them to form complete partitions. The algorithm terminates when no path can be extended. The behavior of the algorithm and the benefits of weighting are illustrated with an example.

Resolution: a survey

Abstract: In applied science, resolution has always been, and still is, an important issue. Since it is not unambiguously defined, it is interpreted in many ways. In this paper, which reviews the concept of optical resolution, a number of these interpretations are discussed. A discussion of resolution has to be preceded by a discussion of what is actually understood by an ‘‘optical image.’’ In a remarkable paper, Ronchi1 distinguished ethereal images, calculated images, and detected images. The term ethereal image was introduced only to represent the physical nature of the imaging phenomenon. As is customary in science in general, attempts have been made to give a mathematical representation of this phenomenon, both geometrically and algebraically. According to Ronchi, the images that have thus been calculated are mere mathematical constructions and should therefore be called calculated images. In the past, many approaches to the concept of resolution concerned these calculated images. This resulted in the so-called classical resolution criteria, such as Rayleigh’s criterion and the associated reciprocal bandwidth of the image. These criteria provide resolution limits that are determined solely by the calculated shape of the point-spread function associated with the imaging aperture and the wavelength of the light. From now on, they will be called classical resolution limits. Calculated images are by their very nature exactly describable by a mathematical model and thus noise free. Such images do not occur in practice. Therefore Ronchi stated that the resolution of detected images is much more important than the classical resolution, since it provides practical information about the imaging system employed. Hence one should consider primarily the resolution of detected images instead of that of calculated images. This means a necessary introduction of some new quantities of interest, such as the energy of the source and the sensitivity properties of the detector. Since Ronchi’s paper, further research on resolution— concerning detected images instead of calculated ones— has shown that in the end, resolution is limited by systematic and random errors resulting in an inadequacy of the description of the observations by the mathematical model chosen. This important conclusion was independently drawn by many researchers who were approaching the concept of resolution from different points of view, which will be discussed in the subsequent sections.

Computerized simulation of color appearance for dichromats

Abstract: We propose an algorithm that transforms a digitized color image so as to simulate for normal observers the appearance of the image for people who have dichromatic forms of color blindness. The dichromat's color confusions are deduced from colorimetry, and the residual hues in the transformed image are derived from the reports of unilateral dichromats described in the literature. We represent color stimuli as vectors in a three-dimensional LMS space, and the simulation algorithm is expressed in terms of transformations of this space. The algorithm replaces each stimulus by its projection onto a reduced stimulus surface. This surface is defined by a neutral axis and by the LMS locations of those monochromatic stimuli that are perceived as the same hue by normal trichromats and a given type of dichromat. These monochromatic stimuli were a yellow of 575 nm and a blue of 475 nm for the protan and deutan simulations, and a red of 660 nm and a blue–green of 485 nm for the tritan simulation. The operation of the algorithm is demonstrated with a mosaic of square color patches. A protanope and a deuteranope accepted the match between the original and the appropriate image, confirming that the reduction is colorimetrically accurate. Although we can never be certain of another's sensations, the simulation provides a means of quantifying and illustrating the residual color information available to dichromats in any digitized image.

Reflection and transmission guided-mode resonance filters

Abstract: New reflection and transmission optical filters based on guided-mode resonances in multilayer waveguide gratings are characterized and compared with homogeneous thin-film filters. These guided-mode resonance filters are implemented by integration of diffraction gratings into classical thin-film multilayers to produce high-efficiency filter response and arbitrarily low sidebands extended over a large spectral range. Compared with homogeneous thin-film reflection filters, guided-mode resonance reflection filters require significantly fewer layers for a narrow linewidth and a high peak response to be obtained. The single-grating transmission filters presented have a narrower linewidth than Fabry–Perot filters with an equal number of layers and similar materials while maintaining high peak transmittance and low sidebands.

Model of optical coherence tomography of heterogeneous tissue

Abstract: A comprehensive model of optical coherence tomography (OCT) is described that includes the interference effects that produce speckle in images of dense heterogeneous tissue. It is based on the extended Huygens–Fresnel formulation of beam propagation in a turbulent atmosphere, adapted to the analysis of OCT. Incorporated in the model is a fractal description of the size distribution of scatterers in tissue. We demonstrate its application in the simulation of images of tissue volumes containing high-contrast targets embedded in a mixture of two sizes of particles. The simulated images show the degradation of image quality caused by speckle noise, along with the benefits of employing a light source with a short coherence time and an objective lens with a high numerical aperture. Based on model results, an estimate of the maximum probing depth is given in terms of the design variables of an OCT scanner and the optical properties of the tissue.

Individual variations in the spatial profile of human macular pigment

Abstract: Individual variations in the spatial profile of macular pigment (MP) density were measured for 32 subjects. Peak density of MP measured with a 460-nm, 12-arcmin stimulus averaged 0.58, standard deviation (SD) = 0.26, with a range of 0.175 to 1.39. To assess the symmetry of the MP distribution, MP density was measured on the horizontal and vertical meridians at ±1 deg eccentricity. The density varied by no more than 16% at these four locations, indicating a basically symmetric distribution. Based on a linear interpolation between measured locations, the width of the spatial distribution of MP at half the maximal density averaged 1.03 deg, SD=0.38, with a range of 0.25 to 1.9 deg. The average spatial profile of MP density across subjects was fitted with both an exponential and a Gaussian function. An exponential decay with eccentricity explained more variance in the data than did a Gaussian function. Assuming an exponential decay with eccentricity, once MP density has been measured in the center of the retina (denoted A), MP density at more eccentric locations (X, deg) can be predicted with a standardized equation (MP=A×10-0.42x). For individual cases, small deviations from an exponential function suggest the existence of minor flanking peaks or shoulders for 40% of the subjects. We also examined the temporal stability of the MP profile of four subjects over a time span of 4–14 months and for a single spatial location for ten subjects over a time span of 1–16 years. These longitudinal data show that differences in MP density among subjects are maintained over time, if dietary patterns are stable.

Acousto-optic tomography with multiply scattered light

Abstract: We have investigated the modulation of the optical field transmitted through a colloid of polystyrene spheres by a narrow quasi-cw ultrasound beam. Measurements of the scale dependence of the heterodyne modulation signal at the acoustic frequency are obtained for samples that are up to 140 scattering lengths thick. A calculation of the modulation signal predicts the possibility of tomographic imaging, which is confirmed experimentally.

Color constancy in the nearly natural image. I. Asymmetric matches

Abstract: Most empirical work on color constancy is based on simple laboratory models of natural viewing conditions. These typically consist of spots seen against uniform backgrounds or computer simulations of flat surfaces seen under spatially uniform illumination. We report measurements made under more natural viewing conditions. The experiments were conducted in a room where the illumination was under computer control. Observers used a projection colorimeter to set asymmetric color matches across a spatial illumination gradient. Observers' matches can be described by either of two simple models. One model posits gain control in one-specific pathways. This diagonal model may be linked to ideas about the action of early visual mechanisms. The other model posits that the observer estimates and corrects for changes in illumination but does so imperfectly. This equivalent illuminant model provides a link between human performance and computational models of color constancy.

List-mode likelihood

Abstract: As photon-counting imaging systems become more complex, there is a trend toward measuring more attributes of each individual event. In various imaging systems the attributes can include several position variables, time variables, and energies. If more than about four attributes are measured for each event, it is not practical to record the data in an image matrix. Instead it is more efficient to use a simple list where every attribute is stored for every event. It is the purpose of this paper to discuss the concept of likelihood for such list-mode data. We present expressions for list-mode likelihood with an arbitrary number of attributes per photon and for both preset counts and preset time. Maximization of this likelihood can lead to a practical reconstruction algorithm with list-mode data, but that aspect is covered in a separate paper [IEEE Trans. Med. Imaging (to be published)]. An expression for lesion detectability for list-mode data is also derived and compared with the corresponding expression for conventional binned data.

Fractal character of the neural spike train in the visual system of the cat.

Abstract: We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGC's) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The continuing statistics reveal 1/f-type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted form one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids

Abstract: We present a new use of dynamic light scattering that permits the determination of the viscoelastic behavior of a complex fluid. By describing the motion of a scattering particle in a viscoelastic medium in terms of a generalized Langevin equation with a memory function, we relate the time evolution of its mean-square displacement to the frequency-dependent storage and loss moduli of the medium. The utility of this technique is illustrated through the application of diffusing-wave spectroscopy to probe the viscoelastic behavior of two complex fluids. The properties of a concentrated suspension of colloidal particles interacting as hard spheres are shown to be strongly influenced by the incipient colloidal glass transition, which leads to an extended range of frequencies over which they behave like an elastic solid. Similar elasticity is observed in a compressed emulsion, resulting in this case from the additional interfacial energy of the deformed droplets. In both cases diffusing-wave spectroscopy is used to measure the frequency dependence of the storage and loss moduli, and these results are compared with those from mechanical measurements. Besides providing a purely optical method for measuring mechanical properties, this technique provides new insight into the origin of the viscoelastic behavior.

Improved formulation of the coupled-wave method for two-dimensional gratings

Abstract: A new formulation of the coupled-wave method for two-dimensional gratings is proposed. It is based on mathematical and physical results recently obtained for one-dimensional gratings. Numerical evidence obtained for many different diffraction problems, including dielectric, metallic, volume, and surface-relief gratings, shows that the new formulation outperforms the conventional one in terms of convergence rates. The specific case of gratings with very small thickness, for which opposite conclusions on the convergence performance are obtained, is studied and explained. The methodology can be applied to other numerical techniques that rely on Fourier expansions of the electromagnetic fields and on grating parameters such as the permittivity and the permeability.

Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities

Abstract: We use a rigorous method for diffraction by a finite set of parallel cylinders to study the influence of defects in a photonic crystal. The method allows us to give an accurate description of all the characteristics of the electromagnetic field (near-field map, scattered field, and energy flow). The localized resonant modes can also be computed. We show some of their symmetry properties and the influence of coupling between two neighboring defects. Finally, an example is given, which shows that a slight local change in the crystal period can be used for the realization of devices that radiate energy in a very narrow angular range.

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts

Abstract: In phase-shifting interferometry spatial nonuniformity of the phase shift gives a significant error in the evaluated phase when the phase shift is nonlinear. However, current error-compensating algorithms can counteract the spatial nonuniformity only in linear miscalibrations of the phase shift. We describe an error-expansion method to construct phase-shifting algorithms that can compensate for nonlinear and spatially nonuniform phase shifts. The condition for eliminating the effect of nonlinear and spatially nonuniform phase shifts is given as a set of linear equations of the sampling amplitudes. As examples, three new algorithms (six-sample, eight-sample, and nine-sample algorithms) are given to show the method of compensation for a quadratic and spatially nonuniform phase shift.

Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter

Abstract: Polarizing beam splitters that use the anisotropic spectral reflectivity (ASR) characteristic of high-spatial-frequency multilayer binary gratings have been designed, fabricated, and characterized. Using the ASR effect with rigorous coupled-wave analysis, we design an optical element that is transparent for TM polarization and reflective for TE polarization at an arbitrary incidence angle and operational wavelength. The experiments with the fabricated element demonstrate a high efficiency (97), with polarization extinction ratios higher than 220:1 at a wavelength of 1.523 m over a 20 angular bandwidth by means of the ASR characteristics of the device. These ASR devices combine many useful characteristics, such as compactness, low insertion loss, high efficiency, and broad angular and spectral bandwidth operations.

Visual signal detectability with two noise components: anomalous masking effects.

Abstract: We measured human observers' detectability of aperiodic signals in noise with two components (white and low-pass Gaussian). The white-noise component ensured that the signal detection task was always noise limited rather than contrast limited (i.e., image noise was always much larger than observer internal noise). The low-pass component can be considered to be a statistically defined background. Contrast threshold elevation was not linearly related to the rms background contrast. Our results gave power-law exponents near 0.6, similar to that found for deterministic masking. The Fisher-Hotelling linear discriminant model assessed by Rolland and Barrett [J. Opt. Soc. Am. A 9, 649 (1992)] and the modified nonprewhitening matched filter model suggested by Burgess [J. Opt. Soc. Am. A 11, 1237 (1994)] for describing signal detection in statistically defined backgrounds did not fit our more precise data. We show that it is not possible to find any nonprewhitening model that can fit our data. We investigated modified Fisher-Hotelling models by using spatial-frequency channels, as suggested by Myers and Barrett [J. Opt. Soc. Am. A 4, 2447 (1987)]. Two of these models did give good fits to our data, which suggests that we may be able to do partial prewhitening of image noise.

Resonant grating–waveguide structures for visible and near-infrared radiation

Abstract: A new ray picture model based on the multiple interference of light waves in dielectric resonant grating–waveguide structures is presented. The model clearly elucidates the phase relationship between the incident plane wave and the waves diffracted from the resonant grating structure that is responsible for the interference of these waves. As a result of this interference process the incident wave can be totally reflected at a certain wavelength and orientation angle. The model is used to describe and analyze this resonance behavior of the grating–waveguide structures as a function of wavelength and incidence angle. The analysis is verified experimentally with semiconductor (InGaAsP/InP) structures at wavelengths of 1.55 μm and also with dielectric (silicon nitride/SiO2) structures at wavelengths of 0.6 μm. All of the structures were formed by electron beam lithography and chemical vapor deposition. The measured results reveal that subnanometer resonance bandwidths and finesses as large as 6000 can be achieved at contrast ratios of 50 with relatively compact structures.

Error-reduction methods for shape measurement by temporal phase unwrapping

Abstract: Temporal phase unwrapping is a method of analyzing fringe patterns in which the fringe phase at each pixel is measured and unwrapped as a function of time t. We propose two methods for improving th ...

Estimation of the adaptive optics long-exposure point-spread function using control loop data

Abstract: Astronomical images obtained with adaptive optics systems can be enhanced by using image restoration techniques. However, this usually requires an accurate knowledge of the system point-spread function (PSF) which is variable in time. We present a method to estimate the PSF related to each image, using data from the adaptive optics control computer, namely, the wave-front sensor measurements and the commands to the deformable mirror, accumulated in synchronization with the acquisition. This method requires no extra observing time and has been successfully tested on PUEO, the Canada–France–Hawaii Telescope adaptive optics system. With this system, accurate PSF estimations could be achieved for guide stars of magnitude 13 or brighter.

Diffractive superresolution elements

Abstract: Superresolution phase-only pupil filters designed to utilize the degrees of freedom made available by diffractive optics technology are investigated theoretically. These so-called diffractive superresolution elements improve the quality of the superresolved diffraction pattern from the point of view of Strehl ratio, reduction of the spot size, control of the sidelobe effects, optimization procedures, and fabrication tolerances. The performance of these elements is studied, and the nature of the solutions obtainable with binary and multiple-phase structures is analyzed. Design considerations and solutions for applications such as confocal scanning microscopy and optical data storage are presented. Optimization of the degrees of freedom to satisfy desired constraints is discussed and compared with other methods.

Lateral interactions in peripherally viewed texture arrays

Abstract: A horizontal array of vertically oriented Gabor elements was used to examine lateral masking in the near periphery (1.9°–5.7° eccentricity). Thresholds were assessed for detecting changes in the contrast, the spatial frequency, and the orientation of the central element within the array. The presence of surround elements induced marked threshold elevations that increased in strength as interelement spacing decreased and as retinal eccentricity increased. A model incorporating spatial summation by complex cells and reciprocal inhibition between simple and complex cells is shown to provide a quantitative fit to the data. This model suggests that complex cells analyze highly redundant textures, whereas simple cells function predominantly in the presence of isolated contours.