Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1996"

Interpretation of Mueller matrices based on polar decomposition

Abstract: We present an algorithm that decomposes a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by a depolarizer. Those factors are unique except for singular Mueller matrices. Based on this decomposition, the diattenuation and the retardance of a Mueller matrix can be defined and computed. Thus this algorithm is useful for performing data reduction upon experimentally determined Mueller matrices.

Use of Fourier series in the analysis of discontinuous periodic structures

Abstract: The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A13, 1019 ( 1996)], which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper. The new formulation converges faster because it uniformly satisfies the boundary conditions in the grating region, whereas the old formulations do so only nonuniformly. Mathematical theorems that govern the factorization of the Fourier coefficients of products of functions having jump discontinuities are given. The results of this paper are applicable to any numerical work that requires the Fourier analysis of products of discontinuous periodic functions.

Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings

Abstract: Two recursive and numerically stable matrix algorithms for modeling layered diffraction gratings, the S-matrix algorithm and the R-matrix algorithm, are systematically presented in a form that is independent of the underlying grating models, geometries, and mountings. Many implementation variants of the algorithms are also presented. Their physical interpretations are given, and their numerical stabilities and efficiencies are discussed in detail. The single most important criterion for achieving unconditional numerical stability with both algorithms is to avoid the exponentially growing functions in every step of the matrix recursion. From the viewpoint of numerical efficiency, the S-matrix algorithm is generally preferred to the R-matrix algorithm, but exceptional cases are noted.

Highly improved convergence of the coupled-wave method for TM polarization

Abstract: The coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am.73, 451 ( 1983)] is known to be slowly converging, especially for TM polarization of metallic lamellar gratings. The slow convergence rate has been analyzed in detail by Li and Haggans [ J. Opt. Soc. Am. A10, 1184 ( 1993)], who made clear that special care must be taken when coupled-wave methods are used for TM polarization. By reformulating the eigenproblem of the coupled-wave method, we provide numerical evidence and argue that highly improved convergence rates similar to the TE polarization case can be obtained. The discussion includes both nonconical and conical mountings.

Calculation of the T matrix and the scattering matrix for ensembles of spheres

Abstract: We present a method for determination of the random-orientation polarimetric scattering properties of an arbitrary, nonsymmetric cluster of spheres. The method is based on calculation of the cluster T matrix, from which the orientation-averaged scattering matrix and total cross sections can be analytically obtained. An efficient numerical method is developed for the T-matrix calculation, which is faster and requires less computer memory than the alternative approach based on matrix inversion. The method also allows calculation of the random orientation scattering properties of a cluster in a fraction of the time required for numerical quadrature. Numerical results for the random orientation scattering matrix are presented for sphere ensembles in the form of densely packed clusters and linear chains.

Efficient nonlinear algorithm for envelope detection in white light interferometry

Abstract: A compact and efficient algorithm for digital envelope detection in white light interferograms is derived from a well-known phase-shifting algorithm. The performance of the new algorithm is compared with that of other schemes currently used. Principal criteria considered are computational efficiency and accuracy in the presence of miscalibration. The new algorithm is shown to be near optimal in terms of computational efficiency and can be represented as a second-order nonlinear filter. In combination with a carefully designed peak detection method the algorithm exhibits exceptionally good performance on simulated interferograms.

Tilted fiber phase gratings

Abstract: A detailed theoretical treatment is presented of bound-mode to bound-mode Bragg reflection and bound-mode to radiation-mode coupling loss in a tilted optical-fiber phase grating. Numerical predictions of the effects of grating tilt on the spectral characteristics of such a grating are calculated. These predictions are compared with experimentally measured spectra of strong gratings written by ultraviolet irradiation of deuterium-sensitized fiber with grating tilt angles ranging from 0° to 15°. Good agreement is obtained between the theoretical predictions and the experimental results.

Space–bandwidth product of optical signals and systems

Abstract: The space–bandwidth product (SW) is fundamental for judging the performance of an optical system. Often the SW of a system is defined only as a pure number that counts the degrees of freedom of the system. We claim that a quasi-geometrical representation of the SW in the Wigner domain is more useful. We also represent the input signal as a SW in the Wigner domain. For perfect signal processing it is necessary that the system SW fully embrace the signal SW.

Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space

Abstract: The finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds. To account for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the direct discretization of the basic Maxwell equations. In the construction of the finite-difference scheme for the time-marching iteration for the near field the mean values of dielectric constants are defined and evaluated by the Maxwell–Garnett rule. In computing the scattered field in the radiation zone (far field) and the absorption cross section, we have applied a new algorithm involving the integration of the electric field over the volume inside the scatterer on the basis of electromagnetic principles. This algorithm removes the high-angular-resolution requirement in integrating the scattered energy for the computation of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by comparison with Mie scattering results for a number of size parameters and wavelengths. We demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20.

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

Abstract: A new implementation of the coupled-wave method for TM polarization is proposed. We use a second-order differential operator established by Neviere together with a scattering-matrix approach. Thus we obtain for metallic gratings a convergence rate as quick as that in TE polarization.

Minimum Lp-norm two-dimensional phase unwrapping

Abstract: We develop an algorithm for the minimum Lp-norm solution to the two-dimensional phase unwrapping problem. Rather than its being a mathematically intractable problem, we show that the governing equations are equivalent to those that describe weighted least-squares phase unwrapping. The only exception is that the weights are data dependent. In addition, we show that the minimum Lp-norm solution is obtained by embedding the transform-based methods for unweighted and weighted least squares within a simple iterative structure. The data-dependent weights are generated within the algorithm and need not be supplied explicitly by the user. Interesting and useful solutions to many phase unwrapping problems can be obtained when p< 2. Specifically, the minimum L0-norm solution requires the solution phase gradients to equal the input data phase gradients in as many places as possible. This concept provides an interesting link to branch-cut unwrapping methods, where none existed previously.

Optical image reconstruction using frequency-domain data: simulations and experiments

Abstract: Optical image reconstruction in a heterogeneous turbid medium with the use of frequency-domain measurements is investigated in detail. A finite-element reconstruction algorithm for optical data based on a diffusion equation approximation is presented and confirmed by a series of simulations and experiments using phantoms having optical properties in the range of those expected for tissues. Simultaneous reconstruction of absorption and scattering coefficients is achieved both theoretically and experimentally. Images with different target locations and contrast levels between target and background are also successfully recovered. All reconstructed images from both simulated and experimental data are derived directly from absolute optical data in which no differential measurement scheme is used. Results from the use of simulated and measured data suggest that quantitative images can be produced in terms of absorption and scattering coefficient values and location, size, and shape of heterogeneities within a circular background region over a range of contrast levels. Further, the effects of modulation frequency are found to be relatively modest, although boundary conditions appear to be important factors.

Resonant scattering from two-dimensional gratings

Abstract: A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.

Imaging localized retinal dysfunction with the multifocal electroretinogram

Abstract: Conventional electroretinographic techniques do not permit efficient mapping of retinal responsiveness for the detection of small dysfunctional areas. This study explores the application of a new technique that makes such mapping possible. It utilizes a multifocal electroretinogram technique based on binary m sequences that simultaneously tests a large number of small retinal areas by multiplexing their responses onto a single signal derived from the human cornea. The focal responses are subsequently extracted for the derivation of high-resolution maps that characterize retinal responsiveness. The required recording times are short enough to make such testing feasible in the clinic. In this study we demonstrate the high sensitivity of the technique by mapping a small area that has been partially bleached by a strobe flash in a normal retina and by mapping dysfunctional areas in three patients with different, well-documented retinal pathologies. The results suggest that the multifocal electroretinogram has the potential to become a valuable clinical tool.

Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination

Abstract: In a previous paper [ J. Opt. Soc. Am. A12, 1932 ( 1995)] we presented a method for phase recovery with the transport-of-intensity equation by use of a series expansion. Here we develop a different method for the solution of this equation, which allows recovery of the phase in the case of nonuniform illumination. Though also based on the orthogonal series expansion, the new method does not require any separate boundary conditions and can be more easily adjusted for apertures of various shapes. The discussion is primarily for the case of a circular aperture and Zernike polynomials, but we also outline the solution for a rectangular aperture and Fourier harmonics. The latter example may have some substantial advantages, given the availability of the fast Fourier transform.

Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO 2

Abstract: For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [ R. M. A. Azzam N. M. Bashara , J. Opt. Soc. Am.62, 1521 ( 1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2 cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.

Propagation of axially symmetric flattened Gaussian beams

Abstract: Flattened Gaussian beams are characterized by a waist profile that passes in a continuous way from a nearly flat illuminated region to darkness. The steepness of the transition region is controlled by an integer parameter N representing the order of the beam. Being expressible as a sum of N Laguerre–Gauss modes, a flattened Gaussian beam turns out to be very simple to study as far as propagation is concerned. We investigate the main features of the field distribution pertaining to a flattened Gaussian beam throughout the space and present experimental results relating to the laboratory production of this type of beam.

Inner retinal contributions to the primate photopic fast flicker electroretinogram.

Abstract: The primate electroretinogram (ERG) recorded at the cornea in response to fast flickering light is thought to reflect primarily the cone photoreceptor potential. We investigated the origin of the photopic 33-Hz corneal flicker ERG to square-wave and photostrobe flashes by recording in the monkey before and after blocking postsynaptic responses with intravitreal injections of 2-amino-4-phosphonobutyric acid and/or cis-2,3-piperidiendicarboxylic acid or sodium aspartate. Blocking postsynaptic ON or OFF responses produced effects on the timing and the waveform of the 33-Hz flicker ERG similar to changes in the b and the d waves in the corneal single-flash ERG. When all the ERG waves of postsynaptic origin in the flash ERG were abolished the flicker response was greatly suppressed, suggesting the postsynaptic cells producing the b and the d waves make major contributions to the photopic fast flicker ERG.

Multichannel vision system for estimating surface and illumination functions

Abstract: This paper describes a set of experimental measurements and theoretical calculations designed to recover both the surface-spectral reflectance function and the illuminant spectral-power distribution from the image data. A multichannel vision system comprising six color channels was created with the use of a monochrome CCD camera and color filters. The spectral sensitivity of each color channel is calibrated, and the dynamic range of the camera is extended for sensing a wide range of intensity levels. Three algorithms and the corresponding results are introduced. First, a method of choosing the appropriate dimension of the linear model dimensions is introduced. Second, the illuminant parameters are estimated from the sensor measurements made at multiple points within separate objects. Third, the sensor responses are corrected for highlight and shading variations. The body reflectance parameters, unique to each surface, are recovered from these corrected values. Experimental results with a small number of test surfaces and a simple illumination geometry demonstrate that the illuminant spectrum and the surface-spectral reflectance functions can be recovered to within typical deviations of 1% and 4%, respectively.

Wave fields in three dimensions: analysis and synthesis

Abstract: Distributions of wave fields in three-dimensional domains are analyzed, synthesized, and generated experimentally. Fundamental limits are discussed and sampling conditions are derived for their generation, with use of a single diffractive element. A general design procedure, based on optimization algorithms, is developed and implemented. Experimental results show that special three-dimensional light distributions can be achieved with low-information-content elements in on-axis configurations.

Laser Doppler and time-varying speckle: a reconciliation

Abstract: The techniques of laser Doppler and time-varying speckle can both be used to measure velocities. The two techniques have developed separately, and there has been little interchange of ideas between them. The essential equivalence of the two techniques for measuring line-of-sight velocities is demonstrated, and ways in which the two techniques might learn from each other are suggested.

b wave of the scotopic (rod) electroretinogram as a measure of the activity of human on-bipolar cells

Abstract: The beta wave of the human electroretinogram (ERG) is widely believed to reflect the activation of on-bipolar cells. However, the shape of the beta wave is also influenced by the activity of other cell types. To assess how the activity of on-bipolar cells is reflected in the human ERG, rod ERG's were recorded in the dark and on the steady fields. Derived P2 responses were obtained by computer subtraction of the receptor contribution to the ERG. The light-adapted derived P2 was shown to have properties similar to those predicted from previous studies of on-bipolar activity. This was also true of the dark-adapted derived P2 if a small (less than 10%) contribution from a negative potential was taken into consideration. The derived P2, and under certain conditions the beta wave, can be used to study rod on-bipolar activity.

Lossless laser beam shaping

Abstract: The Fresnel approximation is used in the design of a lens that turns a beam with one intensity distribution into a beam with a different distribution at the focal plane of a Fourier transform lens. In general, this cannot be done exactly, so one must be satisfied with approximate solutions to this problem. It is shown that the difficulty of this problem depends on a parameter β that is a dimensionless measure of how well the geometrical optics approximation holds. An analytical method is given for determining the lens when β is large. The sensitivity of this solution to various imperfections in the system alignment is also analyzed.

Occlusion edge blur: a cue to relative visual depth

Abstract: We studied whether the blur/sharpness of an occlusion boundary between a sharply focused surface and a blurred surface is used as a relative depth cue. Observers judged relative depth in pairs of images that differed only in the blurriness of the common boundary between two adjoining texture regions, one blurred and one sharply focused. Two experiments were conducted; in both, observers consistently used the blur of the boundary as a cue to relative depth. However, the strength of the cue, relative to other cues, varied across observers. The occlusion edge blur cue can resolve the near/far ambiguity inherent in depth-from-focus computations.

Theory of high-NA imaging in homogeneous thin films

Abstract: A description is given of a modeling technique that is used to explore three-dimensional image distributions formed by high numerical aperture (NA > 0.6) lenses in homogeneous, isotropic, linear, and source-free thin films. The approach is based on a plane-wave decomposition in the exit pupil. Factors that are due to polarization, aberration, object transmittance, propagation, and phase terms are associated with each plane-wave component. These are combined with a modified thin-film matrix technique in a derivation of the total field amplitude at each point in the film by a coherent vector sum over all plane waves. One then calculates the image distribution by squaring the electric-field amplitude. The model is used to show how asymmetries present in the polarized image change with the influence of a thin film. Extensions of the model to magneto-optic thin films are discussed.

Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loève functions

Abstract: Modal wave-front reconstruction by use of Zernike polynomials and Karhunen–Loeve functions from average slope measurements with circular and annular apertures is discussed because of its practical applications in astronomy. A new error source, referred to as the remaining error, is formulated theoretically and evaluated numerically. The total reconstruction error is found to be the sum of the uncompensated wave-front residual error, the measurement error, and the remaining error. Numerical calculation shows that modal wave-front reconstruction with atmospheric Karhunen–Loeve functions results in a smaller residual error than with Zernike polynomials.

Cone–rod receptor spaces with illustrations that use CRT phosphor and light-emitting-diode spectra

Abstract: The purpose of the study is to characterize the excitation of the three cone types and the rods in a colorimetric system. Two representations of photoreceptor activity are developed. In the first, rod activity is characterized within a cone colorimetric system that is based on three known physical primaries. Examples are given that use color CRT phosphor spectra. We illustrate how this representation can be used to evaluate the range of chromaticities over which rod signals may intrude into color-monitor-based investigations of cone function. In the second representation, mixtures of four physical primary lights are used to manipulate the four receptor excitations independently. This method allows specification of sets of lights that isolate or silence up to three receptor classes or any combination of receptor classes. Examples are given that use spectra from four light-emitting diodes. This approach opens a field of research in which rod input to various retinal pathways can be evaluated.

Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms

Abstract: We have obtained two- and three-dimensional detection threshold contours in cone contrast space for sinusoidal gratings for three subjects at three spatiotemporal conditions (1 cycle/degree (c/deg), 0 Hz; 0.125 c/deg, 0 Hz; 1 c/deg, 24 Hz). These conditions were chosen to favor the response of each of the three postreceptoral mechanisms in turn. Contours were obtained from measurements in as many as 60 axes in (L, M, S) cone contrast space and were fitted by superellipses. Our technique permitted us to improve on earlier estimates of the cone weightings to the mechanisms. We found that the red–green mechanism has an input cone weighting of L−M with a 2% S-cone input; the luminance mechanism has a weighting of kL + M, where k varies between 3 and 5 at the high-temporal condition, with a 5% S-cone input in opposition to L- and M-cones; and the blue–yellow mechanism consists of S inputs in closely balanced opposition to L and M inputs. These cone weights were found to be consistent among our three subjects.

Electroretinogram flicker photometry and its applications.

Abstract: The electroretinogram (ERG) has been a traditional tool for the measurement and the analysis of spectral sensitivity. With the appropriate choices of stimulus and measurement conditions, the ERG permits a noninvasive examination of photopigment complement and provides the means for studying the combination of spectral signals at various locations throughout the retina. There are a number of practical problems associated with making spectral measurements with the ERG. One approach to minimizing these problems is to exploit the advantages of a flicker-photometric procedure. We summarize a method used to conduct ERG flicker photometry and illustrate a range of problems to which this technique can be successfully applied.

Visual signal detection in structured backgrounds I. Effect of number of possible spatial locations and signal contrast

Abstract: Several studies have investigated the effect of signal location uncertainty on the detectability of simple visual signals in uncorrelated Gaussian noise with a deterministic background. For this case, human performance in locating a signal in a forced-choice experiment has been successfully predicted for 2–1800 alternative locations with the use of signal detection theory and the usual assumption that the observer’s internal response is Gaussian distributed. Gaussian uncorrelated noise is far from realistic medical image noise, which includes not only fluctuations in intensity of quantum origin but also other anatomical objects lying in the x-ray path (structured backgrounds). Our goal is to determine whether signal detection theory with the Gaussian assumption is adequate for the case of structured backgrounds, or whether other more complex models need to be developed to predict human performance as a function of the number of possible signal locations in structured backgrounds. We present experimental data suggesting that an assumed Gaussian internal response accurately predicts the decrease in observer performance as the number of alternative locations is increased. The one exception is a lower-than-predicted performance for the detection of low-contrast signals for two alternative locations. Performance as measured by the index of detectability d′ is also found to be linear with signal contrast. Together these findings extend the applicability of signal detection theory with Gaussian internal response functions to the case of complex structured backgrounds.