Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1989"

High-resolution image recovery from image-plane arrays, using convex projections.

Abstract: We consider the problem of reconstructing remotely obtained images from image-plane detector arrays. Although the individual detectors may be larger than the blur spot of the imaging optics, high-resolution reconstructions can be obtained by scanning or rotating the image with respect to the detector. As an alternative to matrix inversion or least-squares estimation [Appl. Opt. 26, 3615 (1987)], the method of convex projections is proposed. We show that readily obtained prior knowledge can be used to obtain good-quality imagery with reduced data. The effect of noise on the reconstruction process is considered.

Realization of general nondiffracting beams with computer-generated holograms

Abstract: A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.

Characteristic spectra of Munsell colors

Abstract: The 1257 reflectance spectra of the chips in the Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976) were measured with a rapid acousto-optic spectrophotometer. Measured spectra were sampled from 400 to 700 nm at 5-nm intervals. The correlation matrix of this sample set was formed, and the characteristic vectors of this matrix were computed. It is shown, contradictory to earlier recommendations [ Psychon. Sci.1, 369 ( 1964)], that as many as eight characteristic spectra are needed to achieve good representation for all spectra.

Nondiffracting optical fields: some remarks on their analysis and synthesis

Abstract: Recently Durnin pointed out the existence of nondiffracting beams that propagate in free space with their energy confined around their axis but that experience no spread or divergence [ J. Opt. Soc. Am. A4, 651 ( 1987)]. This Communication provides an alternative way of interpreting these results. The approach is based on the McCutchen theorem from which the necessary conditions for a nondiffracting field are derived. This description may be useful in suggesting several different means of synthesizing such fields and in providing a convenient way of estimating their practical limitations. Some examples, inspired by known techniques studied for depth of field enhancement, are briefly mentioned.

Computational structure of a biological motion-detection system as revealed by local detector analysis in the fly's nervous system.

Abstract: The computations performed by individual movement detectors are analyzed by intracellularly recording from an identified direction-selective motion-sensitive interneuron in the fly's brain and by comparing these results with model predictions based on movement detectors of the correlation type. Three main conclusions were drawn with respect to the movement-detection system of the fly: (1) The essential nonlinear interaction between the two movement-detector input channels can be characterized formally by a mathematically almost perfect multiplication process. (2) Even at high contrasts no significant nonlinearities seem to distort the time course of the movement-detector input signals. (3) The movement detectors of the fly are not perfectly antisymmetrical; i.e., they respond with different time courses and amplitudes to motion in their preferred and null directions. As a consequence of this property, the motion detectors can respond to some degree to stationary patterns whose brightness is modulated in time. Moreover, the direction selectivity, i.e., the relative difference of the responses to motion in the preferred and null directions, depends on the contrast and on the spatial-frequency content of the stimulus pattern.

Standard surface-reflectance model and illuminant estimation

Abstract: In the standard reflectance model for inhomogeneous materials it is assumed that light is reflected by two independent mechanisms. One component is reflected at the interface of the material and air. Light reflected by this mechanism does not interact with surface colorant, and its spectral composition is assumed to equal that of the incident light. The second component is reflected after entering and interacting with the subsurface structure of the material. This interaction substantially changes the spectral composition of the reflected light. We adopt a vector analysis technique for testing the standard reflectance model. Further, we develop a computational method to determine the components of the observed spectra, and we obtain an estimate of the illuminant without using a reference white standard. Finally, we evaluate the accuracy of the standard model and the feasibility of the illuminant spectral estimation by using several test objectives.

Transient and steady-state response properties of movement detectors

Abstract: The transient and steady-state responses of movement detectors are studied at various pattern contrasts (i) by intracellularly recording from an identified movement-sensitive interneuron in the fly's brain and (ii) by comparing these results with computer simulations of an array of movement detectors of the correlation type. At the onset of stimulus motion, the membrane potential oscillates with a frequency corresponding to the temporal frequency of the stimulus pattern before it settles at its steady-state level. Both the transient and the steady-state response amplitudes show a characteristic contrast dependence. As is shown by computer modeling, the transient behavior that we found in the experiments reflects an intrinsic property of the general scheme of movement detectors of the correlation type. To account for the contrast dependence, however, this general scheme has to be elaborated by (i) a subtraction stage, which eliminates the background light intensity from the detector input signal, and (ii) saturation characteristics in both branches of each movement-detector subunit.

Using color for geometry-insensitive segmentation

Abstract: Physical models indicate that, in general, reflectance is a complicated function of wavelength and geometry. An analysis of general reflectance models, however, shows that approximate reflectance models exist that preserve much of the structure of the more-detailed models. In particular, I show from general models that Shafer’s dichromatic reflection model [ Color Res. Appl.10, 210 ( 1985)] is a reasonable approximation for a large class of inhomogeneous dielectrics. I also show that a unichromatic reflection model is a useful approximation for metals. The approximate color-reflectance model is the basis for two algorithms that use color information. The first algorithm uses normalized color to classify surfaces according to material composition and is insensitive to geometrical variation in the scene. The second algorithm is used to identify metal and dielectric materials from their images. Experimental results are presented.

Frequency shifts of spectral lines produced by scattering from spatially random media

Abstract: Scattering of polychromatic light by a medium whose dielectric susceptibility is a random function of position is considered within the accuracy of the first Born approximation. It is shown, in particular, that if the two-point spatial correlation function of the dielectric susceptibility has Gaussian form and the spectrum of the incident light has a Gaussian profile, the spectrum of the scattered light may be shifted toward the shorter or the longer wavelengths, depending on the angle of scattering. The results are analogous to those derived recently in connection with radiation from partially coherent sources [ Nature (London)326, 363 ( 1987)].

Certain computational aspects of vector diffraction problems

Abstract: Fourier decomposition of a given amplitude distribution into plane waves and the subsequent superposition of these waves after propagation is a powerful yet simple approach to diffraction problems. Many vector diffraction problems can be formulated in this way, and the classical results are usually the consequence of a stationary-phase approximation to the resulting integrals. For situations in which the approximation does not apply, a factorization technique is developed that substantially reduces the required computational resources. Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.

Electromagnetic scattering from very rough random surfaces and deep reflection gratings

Abstract: A theoretical study of electromagnetic wave scattering from deep perfectly conducting one-dimensional random rough surfaces and reflection gratings is performed by means of the extinction theorem. The scattering equations are solved numerically (instead of being solved by the usual analytical procedures, which are valid only for slight corrugations). This permits us to obtain an exhaustive collection of results for the mean scattered intensity as a function of polarization and surface parameters. In particular, Lambertian scattering and enhanced backscattering are predicted for random surfaces. Also, the range of validity of the Kirchhoff approximation is established for random surfaces whose correlation length is comparable with or smaller than the wavelength. Concerning gratings, generalizations of the blaze for large angles of incidence, large periods, and arbitrary shapes are obtained. Finally, it is shown that the blaze of the antispecular order for gratings is at the root of the enhanced backscattering for random surfaces.

Complex-source pulsed-beam fields

Abstract: Pulsed beams (PB’s) are time-dependent wave fields that are confined in beamlike fashion in transverse planes perpendicular to the propagation axis, whereas confinement along the axis is due to temporal windowing. Because they have these properties, pulsed beams are useful wave objects for generating and synthesizing highly focused transient fields. The PB problem is addressed here within the context of fundamental Green’s-function propagators for the time-dependent field equations. In a departure from known results in the frequency domain, by which beam solutions can be generated from point-source solutions by displacing the source coordinate location into a complex coordinate space, the complex extension is applied here as well to the source initiation time. This procedure converts the conventional causal impulsive-source Green’s-function propagator into a noncausal PB propagator, which must be defined as an analytic signal because, owing to causality, the analytic continuation into the complex domain cannot be performed by direct substitution. This being done, PB’s can be manipulated as conventional Green’s functions. Some previous results obtained by similar methods are viewed here from a sharper perspective, and new results, both analytical and numerical, are presented that grant basic insight into the PB behavior, including the ability to excite these fields by finite-causal-aperture-source distributions. Besides the basic (analytic Green’s-function) PB, examples include PB’s with frequency spectra of special interest. Particular attention is paid to the PB synthesis of focus-wave modes, which are source-free solutions of the time-dependent wave equation, and to the compact PB formulation of wave fields synthesized by focus-wave-mode spectral superposition.

Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence

Abstract: First a rigorous formulation is presented for the scattering of a uniform plane wave by an infinite dielectric grating waveguide, under the most general condition of oblique incidence. The results are then applied to the analysis of the guidance of waves by the dielectric grating waveguide. By using a simple coordinate rotation, the TE and TM Floquet mode functions determined previously for the special case of principal-plane incidence are combined to treat the general case of oblique incidence. In terms of the coupling between the known Floquet mode functions of both polarizations, the general case of oblique incidence is formulated in an exact fashion, as a three-dimensional boundary-value problem, so that the hybrid nature of waves supported by the structure can be investigated rigorously.

Diffraction by a circular aperture as a model for three-dimensional optical microscopy

Abstract: Existing formulations of the three-dimensional (3-D) diffraction pattern of spherical waves that is produced by a circular aperture are reviewed in the context of 3-D serial-sectioning microscopy. A new formulation for off-axis focal points is introduced that has the desirable properties of increased accuracy for larger field angles, invariance to shifts of the focal point about spheres of constant radius when the detection point is on the sphere for both intensity and amplitude fields, and invariance to shifts in three transformed coordinates for intensity fields. Finally, calculated intensity fields for both on-axis and off-axis focal points are included to illustrate the proposal that the classical 3-D diffraction patterns that have been used as analytical models in 3-D serial-sectioning fluorescence microscopy may not be accurate enough for this application.

Loss characteristics of circular hollow waveguides for incoherent infrared light

Abstract: A simple and convenient method was proposed for the calculation of transmission loss in a circular hollow waveguide. The method is based on a simple ray theory and is applicable to multimode transmission of incoherent light. In order to confirm the validity of the method, spectral losses of various kinds of hollow waveguide were measured and compared with the theoretical values. For a silica waveguide, good coincidence was obtained between calculated and measured values, whereas, for metallic waveguides, surface irregularities must be taken into account for prediction of optical losses.

Temporal properties of information extraction in reading studied by a text-mask replacement technique

Abstract: A text was replaced with a visual mask for a fixed duration every time the reader made a saccade. The threshold duration was measured when the mask was presented at the beginning of a saccade or a fixation, or at a certain delay after the onset of a fixation. The effect of the mask on reading time, as well as on the subjective legibility of the text, was also investigated. It was shown that saccadic suppression exists in reading; subjects are not affected by a mask as long as it is inserted during the saccade. The visual sensitivity is recovered only partially at the initial part of fixation and is recovered fully approximately 70 msec after the beginning of the fixation. The visual information can be extracted during a later part of the fixation period as efficiently as or even more efficiently than during the early part of the fixation.

Performance analysis of adaptive-optics systems using laser guide stars and slope sensors.

Abstract: Many current wave-front-reconstruction systems use localized phase-slope measurements to estimate wave fronts distorted by atmospheric turbulence. Analytical expressions giving the performance of this class of adaptive-optics system are derived. Performance measures include the mean-square residual phase error across the aperture, the optical transfer function, the point-spread function, and the Strehl ratio. Numerical examples show that the mean-square residual error and the Strehl ratio are sensitive to variations of the photon noise in the wave-front sensor and to variations in the sensor spacing and the actuator spacing. The Strehl ratio degrades rapidly as the diameters of the individual slope sensors are made larger than the Fried seeing-cell diameter r0 and when the sensor signal levels fall below 100 counts per slope measurement. On the other hand, the resolution of the optical system is relatively unaffected by moderate changes in the photon noise or the densities of sensors and actuators. The diameter of the individual slope sensors can be as much as 1.5 times r0 without significant degradation in angular resolution. These performance measures are particularly important in the design of adaptive telescopes used for imaging in astronomy. For adaptive telescopes using laser guide stars, these measures can be used to determine the key design parameters for the laser.

Mechanisms of contour curvature discrimination

Abstract: Visual processing of contour curvature was investigated by measuring increment thresholds for curvatures from 0.31 to 25.4 deg−1. Curvature discrimination was assessed for three classes of stimuli: simple curved contours, high-frequency bandpass-filtered contours, and low-pass-filtered contours. High-frequency bandpass filtering had no effect on discrimination at low curvatures and only a modest effect at high curvatures. In contrast, low-pass filtering caused substantial threshold elevations at all curvatures. Thus the data lead to the surprising conclusion that high-spatial-frequency, orientation-selective mechanisms dominate curvature processing over the entire range of curvatures tested, a conclusion at odds with previous suggestions that large, low-spatial-frequency filters are involved in analyzing low curvatures. The data are explained accurately by a two-process model for curvature extraction: at high curvatures the local-processing model proposed by Wilson [ J. Opt. Soc. Am. A.2, 1191 ( 1985)] fits the data well, whereas at low curvatures orientations are compared at points displaced a fixed distance along the tangent to the curve.

Speckle-free reconstruction in digital holography

Abstract: Generally, speckles impair the reconstruction of digital and optical holograms of diffusely scattering objects. With the help of an iterative method, it is possible to introduce diffusers in digital holography that do not suffer from this disadvantage. Optically obtained speckle-free reconstructions of digital holograms are presented.

Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements

Abstract: The first three columns of the instrument matrix A of the four-detector photopolarimeter (FDP) are determined by Fourier analysis of the output current vector I(P) as a function of the azimuth angle P of the incident linearly polarized light. Therefore 12 of the 16 elements of A are measured free of the imperfections of the (absent) quarter-wave retarder (QWR). The effect of angular beam deviation by the polarizer is compensated for by taking the average, (1/2) [I(P) + I(P + 180°)], of the FDP output at 180°-apart, optically equivalent, angular positions of the polarizer. The remaining fourth column of A is determined by the FDP’s response to the right- and left-handed circular polarization states. Because these states are impossible to generate with an imperfect QWR, a novel procedure is developed. In particular, the response of the FDP to the unattainable right- or left-handed circular polarization state is found by taking the average of the responses of the FDP to an elliptical near-circular state and that state rotated in azimuth by 90°. This calibration scheme is applied to measure A of our prototype FDP of four Si detectors at λ = 632.8 nm. A is determined, in external and internal reference frames, free of imperfections in the polarizing optical elements. The FDP, with its uncontaminated A matrix, is used subsequently to evaluate the imperfections of the QWR with the help of an appropriate model.

Motions in orthogonal directions are mutually suppressive

Abstract: Models of motion-sensing units that are local or nearly local in their measurements suffer from a problem that the actual meaning of a unit’s firing is ambiguous. In order for this ambiguity to be resolved, the outputs of many units must be combined and compared. In the experiments described here the predictions of one such model of this process were tested. The effect of vertical motion was measured for patterns moving horizontally. It was found that there was a strong suppression from the vertical motion that could not be accounted for by the simple addition of noise to the motion signal. Further, this suppressive effect was found to be asymmetric in time, in that motions occurring for as much as 300 msec after the vertical motion were affected. whereas those almost immediately before the motion were unaffected. I suggest that such results are predicted by a cooperative–competitive network of interactions between local motion measurements.

Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium)

Abstract: The uniform asymptotic description of electromagnetic pulse propagation in a single-resonance Lorentz medium is presented. The modern asymptotic theory used here relies on Olver’s saddle-point method [ Stud. Appl. Math. Rev.12, 228 ( 1970)] together with the uniform asymptotic theory of Handelsman and Bleistein [ Arch. Ration. Mech. Anal.35, 267 ( 1969)] when two saddle points are at infinity (for the Sommerfeld precursor), the uniform asymptotic theory of Chester et al. [ Proc. Cambridge Philos. Soc.53, 599 ( 1957)] for two neighboring saddle points (for the Brillouin precursor), and the uniform asymptotic theory of Bleistein [ Commun. Pure Appl. Math.19, 353 ( 1966)] for a saddle point and nearby pole singularity (for the signal arrival). Together with the recently derived approximations for the dynamical saddle-point evolution, which are accurate over the entire space–time domain of interest, the resultant asymptotic expressions provide a complete, uniformly valid description of the entire dynamic field evolution in the mature dispersion limit. Specific examples of the delta-function pulse and the unit-step-function-modulated signal are considered.

Short-rise-time microwave pulse propagation through dispersive biological media

Abstract: Numerical research is reported on the propagation of short microwave pulses into living, biological materials. These materials are dispersive, and data on the dielectric constant and conductivity for these materials follow a Debye model. A Fourier-series calculation is presented that predicts the occurrence of Brillouin precursors when the incident pulses have sufficiently short rise times. These transients are attenuated with increasing propagation distance but are attenuated more slowly than the carrier frequency of the pulse, which is attenuated exponentially with distance. An analysis of the numerical error resulting from truncation of the Fourier series is given. Upper-bound estimates of truncation error show good series convergence.

Structure from two orthographic views of rigid motion.

Abstract: We study the inference of rigid three-dimensional interpretations for the structure and motion of four or more moving points from but two orthographic views of the points. We develop an algorithm to determine whether image data are compatible with a rigid interpretation. As a corollary of this result we find that the measure of false targets (roughly, nonrigid objects that appear rigid) is zero. We find that if the two views have at least one rigid interpretation, then in fact there is a canonical one-parameter family of rigid interpretations; we show how to compute this family, and we describe precisely how the rigid interpretations vary within it. Since only two views are used, this analysis is relevant also to stereo vision.

Mathematical properties of the two-dimensional motion field: from singular points to motion parameters

Abstract: The motion field, that is, the two-dimensional vector field associated with the velocity of points on the image plane, can be seen as the flow vector of the solution to a planar system of differential equations. Therefore the theory of planar dynamical systems can be used to understand qualitative and quantitative properties of motion. In this paper it is shown that singular points of the motion field, which are the points where the field vanishes, and the time evolution of their local structure capture essential features of three-dimensional motion that make it possible to distinguish translation, rotation, and general motion and also make possible the computation of the relevant motion parameters. Singular points of the motion field are the perspective projection onto the image plane of the intersection between a curve called the characteristic curve, which depends on only motion parameters, and the surface of the moving object. In most cases, singular points of the motion field are left unchanged in location and spatial structure by small perturbations affecting the vector field. Therefore a description of motion based on singular points can be used even when the motion field of an image sequence has not been estimated with high accuracy.

Restoration of piecewise constant images by mean-field annealing

Abstract: An algorithm is described that removes the noise from images without causing blurring or other distortions of edges. The problem of noise removal is posed as a restoration of an uncorrupted image, given additive noise. The restoration problem is solved by using a new minimization strategy called mean-field annealing (MFA). An a priori statistical model of the image is chosen that drives the minimization toward solutions that are locally homogeneous. The strategy for MFA is derived, and the resulting algorithm is discussed. Applications of the algorithm to both synthetic images and real images are presented.

Spatial modifications of Gaussian beams diffracted by reflection gratings

Abstract: By using an angular spectral representation, we show that the fields of Gaussian beams scattered by reflection gratings differ markedly from those predicted by geometrical considerations. We find that, in general, each diffracted beam exhibits a lateral displacement, a focal shift, and an angular deflection; in addition, the size of the beam width is enlarged or reduced. The beam changes are largest if the incidence angle is phase matched to a leaky wave that may be supported by the grating. This phase condition is identical to that for which Wood’s anomalies of the resonant variety occur if plane waves, instead of bounded beams, are incident. By evaluating the spatial modifications of beams diffracted at a canonic grating structure consisting of a sinusoidal reactance plane, we show that the magnitudes of the beam effects can be considerably large. We also examine the special case of blazed diffracted orders and find that their corresponding beams are not extinguished completely but appear with reduced intensity and strong profile distortion.

Two processes control variations in flicker sensitivity over the life span

Abstract: Flicker thresholds were measured in an automated paradigm at several temporal frequencies for the critical fusion frequency in more than 1000 observers of ages 5-75 years. The results can be described by two processes. The first process was a uniform increase in sensitivity at all frequencies, at a rate that would double sensitivity every 10 years, up to the age of 16 years. In the second process the data indicated that after the age of 16 years the visual response showed gradual slowing but little sensitivity decrease for the remainder of the life span.

Signal reconstruction from multiple correlations: frequency- and time-domain approaches

Abstract: One-dimensional (1-D) ultrashort laser signals cannot be recorded directly, although it is possible to detect their multiple correlations. The reconstruction of 1-D deterministic sampled signals from their multiple correlations is studied. A computationally efficient, fast-Fourier-transform-based, frequency-domain algorithm is described for simultaneously reconstructing the amplitude and the phase of a finite-duration signal. It is shown that, by modeling the Fourier transform of a discrete sequence as a pole-zero rational function, unique (modulo time shifts) signal recovery is possible from any multiple correlation of order greater than 2. The resulting time-domain algorithm uses all the nonredundant 1-D slices of a multiple-correlation sequence and applies to one- or two-sided, finite- or infinite-duration signals. The signal parameters are obtained in closed form by using a set of linear equations. Noise effects are studied theoretically and experimentally through simulated data. Both frequency-and time-domain algorithms are applicable to modeling and interpolation of raster-scanned images.

Analysis of signal and noise propagation for several imaging mechanisms

Abstract: The utility of multivariate moment-generating functions for analyzing the influence of stochastic amplifying and scattering mechanisms on the transfer of signal and noise through multistage imaging systems was shown in a previous study [ J. Opt. Soc. Am. A4, 895 ( 1987)]. Here we extend that study to include cases in which the amplification or scattering parameters are themselves stochastic variables. Each of these cases is illustrated by a physical example drawn from the study of radiographic screen–film imaging. For stationary, photon-limited inputs, expressions for the noise power spectrum and the detective quantum efficiency are derived for each case.