Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1984"
TL;DR: In this article, a convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections, which has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation.
Abstract: A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.
5,329 citations
2,970 citations
Journal Article•
TL;DR: It is proposed that, for the task of object recognition, the visual system decomposes shapes into parts using a rule defining part boundaries rather than part shapes, that the rule exploits a uniformity of nature—transversality, and that parts with their descriptions and spatial relations provide a first index into a memory of shapes.
1,271 citations
1,131 citations
TL;DR: In this article, the backscattered intensity from a dense distribution of latex microspheres is measured near the retroreflection direction and it is shown that a sharp peak appears in the retro-reflective direction when the volume density is above 1%.
Abstract: The backscattered intensity from a dense distribution of latex microspheres is measured near the retroreflection direction. It is shown that a sharp peak appears in the retroreflection direction when the volume density is above 1%. The angular width of this peak is much smaller than (wavelength)/(particle size) and cannot be explained by Mie theory, double-passage effects, or radiative-transfer theory. When the particle size D is less than the wavelength λw, a small peak appears at the retroreflection direction. When D is 2–4 times greater than λw, the peak becomes large as the density increases. When D is many times greater than λw, the sharp peak at the retroreflection direction is superimposed upon the Mie-scattering pattern. The angular width of the peak is of the order of (a wavelength)/(a mean free path).
551 citations
TL;DR: Performance with complex patterns can be predicted by spatiotemporal Fourier analysis that results in the segregation and linear addition in the output for different temporal frequencies and several predictions that were confirmed experimentally and rejected several other models.
Abstract: We propose a model of direction-sensitive units in human vision. It is a modified and elaborated version of a model by Reichardt [
Z. Naturforsch. Teil B12,
447 (
1957)]. The model is applied to threshold experiments in which subjects view adjacent vertical bars with independently (typically sinusoidally), temporally modulated luminances. The subject must report whether the patterns moved to the left or to the right. According to the model, a basic motion-detecting unit consists of two subunits tuned to opposite directions. Each performs a spatial and temporal linear filtering of its input; outputs of the filters are multiplied, and the multiplied output is integrated (for a time that is long relative to the modulation period). The model’s output consists of the difference between the subunit outputs. Direction of movement is indicated by the sign of the model output. Mathematical analysis of the model yielded several predictions that were confirmed experimentally. Specifically, we found that (1) performance with complex patterns can be predicted by spatiotemporal Fourier analysis that results in the segregation and linear addition in the output for different temporal frequencies; (2) under special conditions, performance depends on the product of adjacent bar amplitudes, offering strong support for the multiplication principle; (3) performance is unaffected by addition of stationary patterns; and (4) addition of homogeneous flicker normally produces no effect but under special conditions reverses perceived direction. These and other results confirm our model and reject several other models, including Reichardt’s original model.
477 citations
TL;DR: In this paper, a 2 × 2 matrix method is applied to planar multilayer optical waveguides to satisfy substrate-to-cover field transfer equations that reduce to the equation 0 for bound modes and leaky waves.
Abstract: A standard 2 × 2 matrix method-used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γcm11 + γcγsm12 + m21 + γsm22 = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.
419 citations
TL;DR: In this article, it was shown that a negative contribution to the group-velocity dispersion always accompanies angular dispersion and structures, such as slabs and prisms, that use this contribution to provide adjustable group velocity dispersion.
Abstract: It is shown that a negative contribution to the group-velocity dispersion always accompanies angular dispersion. We describe structures, such as slabs and prisms, that use this contribution to provide adjustable group-velocity dispersion. We discuss, in particular, considerations regarding incorporation of these structures with a laser resonator. A description of possible submillimeter semiconductor devices is also given.
414 citations
TL;DR: Perceived velocity appears to be a weighted average of luminance and chrominance velocity information and when luminance contrast was held constant, increasing chrominance modulation caused further decreases in apparent velocity.
Abstract: Equiluminous red-green sine-wave gratings were drifted at a uniform rate in the bottom half of a 10-deg field. In the top half of the display was a sinusoidal-luminance grating of the same spatial frequency and 95% contrast that drifted in the opposite direction. Observers, while fixating a point in the display center, adjusted the speed of this upper comparison grating so that it appeared to match the velocity of the chromatic grating below. At low spatial frequencies, equiluminous gratings were appreciably slowed and sometimes stopped even though the individual bars of the grating could be easily resolved. The amount of slowing was proportionally greatest for gratings with slow drift rates. Blue-yellow sine-wave gratings showed similar effects. When luminance contrast was held constant, increasing chrominance modulation caused further decreases in apparent velocity, ruling out the possibility that the slowing was simply due to decreased luminance contrast. Perceived velocity appears to be a weighted average of luminance and chrominance velocity information.
358 citations
TL;DR: In this article, a model for spatial-frequency discrimination analogous to line-element models for color discrimination is presented and shown to provide a reasonable fit to the available data, based on the predicted responses of six spatialfrequency-tuned mechanisms, whose sensitivity curves have been estimated in previously published masking experiments.
Abstract: Recent data from several laboratories have shown that spatial-frequency discrimination is not a smooth function of frequency but rather exhibits alternate peaks and troughs. A model for spatial-frequency discrimination analogous to line-element models for color discrimination is presented here and shown to provide a reasonable fit to the available data. This model is based on the predicted responses of six spatial-frequency-tuned mechanisms, whose sensitivity curves have been estimated in previously published masking experiments. In order to fit the data it is necessary to pool responses from units centered under the stimulus as well as from spatially neighboring units. Thus it appears that the visual system utilizes both spatial and spatial-frequency information in discrimination tasks.
284 citations
TL;DR: An algorithm known as generalized projections, which can be used to handle the restoration-from-magnitude (RFM) as well as other nonconvex constraints, is described and its properties are discussed.
Abstract: The method of projections onto convex sets can be used to solve many problems in image restoration, e.g., restoration from phase, spectral extrapolation, and signal recovery in computer-aided tomography. However, image-restoration problems involving nonconvex constraints cannot be handled by the method of projection onto convex sets in a fashion that ensures convergence. The restoration-from-magnitude (RFM) problem is such a case. To handle the RFM as well as other nonconvex constraints, we describe an algorithm known as generalized projections and discuss its properties. When sets are nonconvex, it is possible for the algorithm to exhibit pathological behavior that is never manifest in convex projections. We introduce an error criterion called the summed-distance error (SDE) and show under what circumstances the SDE is a monotonically decreasing function of the number of iterations. Near-optimum performance of the algorithm is achieved by relaxation parameters. Comparisons with other RFM methods are furnished for synthetic imagery.
TL;DR: In this paper, the half-amplitude half-bandwidths (θ 1/2) of Cartesian-separable receptive fields that may underlie orientation selectivity were obtained.
Abstract: Orientation tuning curves were measured at 10 spatial frequencies ranging from 0.5 to 11.3 cycles per degree (cpd) using a masking paradigm. The stimuli were spatially localized test patterns of 1.0 octave bandwidth superimposed upon cosine grating masks. By using a model that corrects for the nonlinearity inherent in the masking process, we obtain the half-amplitude half-bandwidths (θ1/2) of Cartesian-separable receptive fields that may underlie orientation selectivity. Additional experiments show that the data are not compatible with separability in polar coordinates (spatial frequency and orientation). The orientation half-bandwidths have been found to decrease somewhat with increasing spatial frequency, going from about 30° at 0.5 cpd to 15° at 11.3 cpd, for both sustained and transient forms of temporal modulation. Similar bandwidths are obtained from data where the test is oriented along 45°. These bandwidth estimates are shown to be consistent with subthreshold summation data as well as physiological data from monkey striate cortex.
TL;DR: The subjective crossedcylinder aberroscope method of Howland and Howland as discussed by the authors has been modified by the addition of a beam splitter and a camera to permit direct photographic recording of the distorted retinal image of the aberronscope grid.
Abstract: The subjective crossed-cylinder aberroscope method of Howland and Howland [J. Opt. Soc. Am. 67, 1508 (1977)] has been modified by the addition of a beam splitter and a camera to permit direct photographic recording of the distorted retinal image of the aberroscope grid. The ocular aberration can then be deduced from direct measurements of the grid distortion. Preliminary results on 11 subjects confirm earlier findings that comalike, third-order aberrations are more important than spherical or other fourth-order aberrations in degrading the retinal image and for the average subject, the diffraction-limited pupil size is approximately 3 mm. This new objective method for measuring wave aberration yields significantly less variance in population estimates of the coefficients of the wave-aberration polynomial than that of the previous subjective method.
TL;DR: In this article, qualitative and quantitative arguments are presented that elucidate the modifications that the whole three-dimensional structure of the diffracted field undergoes as the Fresnel number is gradually decreased, and contours of equal intensity in the focal region are presented for systems of selected Fresnel numbers, which focus uniform waves.
Abstract: It was recently shown that, when a converging spherical wave is focused in a diffraction-limited system of sufficiently low Fresnel numbers, the point of maximum intensity does not coincide with the geometrical focus but is located closer to the exit pupil. In the present paper both qualitative and quantitative arguments are presented that elucidate the modifications that the whole three-dimensional structure of the diffracted field undergoes as the Fresnel number is gradually decreased. Contours of equal intensity in the focal region are presented for systems of selected Fresnel numbers, which focus uniform waves.
TL;DR: In this article, a second-order multiple-scattering theory of discrete particles is proposed to explain the angular width of backscattering from a random distribution of discrete scatterers.
Abstract: A recent laboratory-controlled optical experiment demonstrates that a sharp peak of small but finite angular width is exhibited in backscattering from a random distribution of discrete scatterers. In this paper the phenomenon is explained by using a second-order multiple-scattering theory of discrete particles. The theory gives an angular width of the order of the attenuation rate divided by the wave number and is in agreement with experimental observations. The relations of the present results to past theories on backscattering enhancements are also discussed.
TL;DR: The effect of signal-location uncertainty on the detectability of simple visual signals in uncorrelated image noise is measured and is consistent with the view that humans can act as suboptimal maximum a posteriori probability observers.
Abstract: We have measured the effect of signal-location uncertainty on the detectability of simple visual signals in uncorrelated image noise. An M-alternative forced-choice signal-location identification technique was used with values of M ranging from 2 to 1800. We find high statistical efficiency (50% for aperiodic signals), and results from one value of M can be used to predict all others. The results are consistent with the view that humans can act as suboptimal maximum a posteriori probability observers.
TL;DR: In this article, an ideal detector for the discrimination of arbitrary stimuli in the two-alternative forced-choice paradigm was derived for the discriminative recognition task, where the ideal detector's performance is limited only by quantal fluctuations, the optics of the eye, and the size and spacing of the receptors in the retinal mosaic.
Abstract: An ideal detector is derived for the discrimination of arbitrary stimuli in the two-alternative forced-choice paradigm. The ideal detector's performance is assumed to be limited only by quantal fluctuations, the optics of the eye, and the size and spacing of the receptors in the retinal mosaic. Detailed predictions are presented for two-point acuity and hyperacuity tasks. The ideal detector's two-point resolution, over a wide range of luminances, is approximately 10 times worse than its two-point vernier acuity or separation discrimination. Furthermore, twopoint resolution is shown to vary in proportion to the -1/4 power of spot intensity, but vernier acuity and separation discrimination vary in proportion to the -1/2 power of spot intensity. It is shown that this ideal detector can be implemented by the use of appropriately shaped receptive fields. The derivation provides a simple way to determine the shapes of these optimal receptive fields for arbitrary stimuli. The sensitivities of real (human) and ideal detectors are compared. Under many circumstances, the eye is capable of resolving changes in position that are nearly an order of magnitude smaller than the 0.5-min diameter of a foveal photoreceptor. For example, observers can reliably detect an 8-10-sec instantaneous displacement of a short line or bar,' a 2-4-sec
TL;DR: In this article, Sine-wave contrast thresholds were measured at four retinal eccentricities: 0°, 3°, 6°, 12° and 12°, and the results were in good agreement with unstabilized single-meridian data from other laboratories.
Abstract: Spatiotemporal sine-wave contrast thresholds were measured at four retinal eccentricities: 0°, 3°, 6°, and 12°. Threshold functions of spatial frequency were determined for each eccentricity at two selected temporal frequencies, and functions of temporal frequency at two selected spatial frequencies. Fixation was controlled by stabilizing the retinal image. The stimulus patterns were circular cosine targets confined to annular zones, so that stimulation occurred in all meridians simultaneously. In spite of these unusual conditions, our results were in good agreement with unstabilized, single-meridian data from other laboratories. The spatial-frequency functions obtained at both high and low flicker rates scaled with eccentricity in the same way. For the bandpass functions obtained at 0.5 Hz, the reciprocal of the peak spatial frequency varied linearly with eccentricity. Measured with spatial patterns chosen in accord with this scaling relation, both sets of temporal-frequency functions were essentially independent of eccentricity. Threshold functions at constant velocity were also consistent with the same scaling relation.
TL;DR: In this paper, the authors used the symbolic programming language reduce to verify the convergence and accuracy of the numerical Bessel function routines required in these computations, and used a standard zero-finding routine to find the zeros of the scattering coefficient denominators, and a separate zero-counting routine in conjunction with the search routine to ensure that all poles within a given region of the complex plane were found.
Abstract: The natural resonant frequencies and poles associated with the electromagnetic modes of a dielectric sphere with a relative index of refraction of 1.4 have been calculated for size parameters ranging from 1 to 50. Determining pole locations in the complex plane entailed the computation of spherical Bessel functions for large complex arguments. The symbolic programming language reduce was used to provide independent verifications of the convergence and accuracy of the numerical Bessel function routines required in these computations. To determine pole locations, we used a standard zero-finding routine to find the zeros of the scattering coefficient denominators. In addition, we used a separate zero-counting routine in conjunction with the search routine to ensure that all poles within a given region of the complex plane were found. The real parts of the calculated poles agree with the location of peaks in the resonance spectrum (calculated for real frequency excitation), whereas the imaginary parts are related to the widths of these peaks. The intensity inside the sphere, averaged over all spherical angles, was computed as a function of radius. When the particle is excited at resonance, the internal intensity exhibits a sharp peak near, but not on, the surface. The intensity was found to be the strongest when the particle is driven at resonant frequencies whose poles have small imaginary components in the complex plane.
TL;DR: This work compared the visual detection of such camouflaged objects with the detection of objects whose boundaries were defined by luminance contrast, finding that the effect of eccentricity on threshold is less for large objects than for small objects.
Abstract: Some naturally camouflaged objects are invisible unless they move; their boundaries are then defined by motion contrast between object and background. We compared the visual detection of such camouflaged objects with the detection of objects whose boundaries were defined by luminance contrast. The summation field area is 0.16 deg2 , and the summation time constant is 750 msec for parafoveally viewed objects whose boundaries are defined by motion contrast; these values are, respectively, about 5 and 12 times larger than the corresponding values for objects defined by luminance contrast. The log detection threshold is proportional to the eccentricity for a camouflaged object of constant area. The effect of eccentricity on threshold is less for large objects than for small objects. The log summation field diameter for detecting camouflaged objects is roughly proportional to the eccentricity, increasing to about 20 deg at 32-deg eccentricity. In contrast to the 100:1 increase of summation area for detecting camouflaged objects, the temporal summation time constant changes by only 40% between eccentricities of 0 and 16 deg.
TL;DR: In this paper, a method to obtain an estimate of Fried's seeing parameter r0 from time series of an arbitrarily shaped, resolved structure that exhibits degradation resulting from atmospheric turbulence is presented.
Abstract: A method to obtain an estimate of Fried’s seeing parameter r0 from time series of an arbitrarily shaped, resolved structure that exhibits degradation resulting from atmospheric turbulence is presented. The basic idea is to evaluate the ratio of the observed squared modulus of the average Fourier transform and the observed average power spectrum. The theory of the method is developed, and the influence of noise on the ratio is discussed. The method has been applied to five consecutive time series of observations of solar granulation under different seeing conditions. The power spectra, which are reconstructed with appropriate theoretical modulation transfer functions, converge.
TL;DR: A pulse-density coding technique is presented that efficiently uses the capabilities of binary raster-scan devices and an active sequential procedure based on hard clipping and error correction is implemented.
Abstract: Computer-generated holograms suffer from a limited space–bandwidth product. A pulse-density coding technique is presented that efficiently uses the capabilities of binary raster-scan devices. An active sequential procedure to generate the pulse-density modulation based on hard clipping and error correction is implemented.
TL;DR: Experimental evidence that humans use phase information for detection and discrimination of visual signals (static sine waves) when sufficient a priori information is made available is presented.
Abstract: We present experimental evidence that humans use phase information for detection and discrimination of visual signals (static sine waves) when sufficient a priori information is made available. Under these conditions human performance exceeds that of the best-possible phase-insensitive detector. There is a marked reduction in performance when signal-phase information is not given to the observer.
TL;DR: In this paper, an analysis of transverse laser resonator modes is presented, based on a recently developed coherence theory in the space-frequency domain, where the modes are introduced by means of solutions of an integral equation that expresses a steady-state condition for a second-order correlation function of the field across a mirror of the laser cavity.
Abstract: An analysis of transverse laser resonator modes is presented, based on a recently developed coherence theory in the space-frequency domain. The modes are introduced by means of solutions of an integral equation that expresses a steady-state condition for a second-order correlation function of the field across a mirror of the laser cavity. All solutions of this integral equation are found to be expressible as quadratic forms involving the Fox–Li modes of the conventional theory. If there is no degeneracy, each mode is shown to be necessarily completely spatially coherent, at each frequency, within the framework of second-order correlation theory. It is also shown that, if several transverse modes are excited, the output cannot be completely spatially coherent.
TL;DR: In this paper, the current distribution that focuses the electromagnetic energy into a small spot in the dielectric medium, such as in hyperthermia applications, has been studied and the variation of spot size and focal point electric-field intensity as functions of polarization, scanning, and the permittivity of the half-space.
Abstract: Given a time-harmonic electric-current distribution over a finite planar aperture situated in front of a dielectric half-space, the transmitted field in the dielectric half-space is calculated by the plane-wave-spectrum technique. We concentrate on the current distribution that focuses the electromagnetic energy into a small spot in the dielectric medium, such as in hyperthermia applications. Numerical results are given to illustrate the variation of spot size and of focal-point electric-field intensity as functions of polarization, scanning, and the permittivity of the half-space. We find that (1) the maximum electric-field intensity is not at the focal point but rather at a point closer to the aperture; for a small aperture, this focal shift may be more than one wavelength; (2) when the dielectric half-space is introduced, the 3-dB spot size changes according to the ratio of the wavelength in the half-space to that in the original aperture medium; and (3) the electric-field intensity at the focal point is greatest when the permittivity of the half-space is less than that of the aperture medium, not when the two media are electrically matched.
TL;DR: These results agree quantitatively with the predictions (some of which were made without knowledge of the experimental results) of a line-element model for spatial-frequency discrimination.
Abstract: Recent data have shown that spatial-frequency adaptation has little effect on spatial-frequency discrimination at the adapting frequency, but there is a substantial elevation of discrimination thresholds at frequencies about one octave higher than the adapting frequency. It has also been shown that adaptation produces elevations in grating-orientation discrimination at orientations displaced by ±12.0–15.0 deg from the adapting orientation. In this paper, we show that these results agree quantitatively with the predictions (some of which were made without knowledge of the experimental results) of a line-element model for spatial-frequency discrimination. Spatial-frequency bandwidths of the visual mechanisms were previously obtained from masking data. For the orientation-discrimination predictions, the line-element model was generalized to incorporate orientation bandwidths for the spatial mechanisms, again estimated from masking data.
TL;DR: In this paper, the directional reflectance distributions of radiant flux from homogeneous vegetation canopies with greater than 90 percent ground cover were analyzed with a radiative transfer model, assuming that the leaves consist of small finite planes with Lambertian properties.
Abstract: The directional-reflectance distributions of radiant flux from homogeneous vegetation canopies with greater than 90 percent ground cover are analyzed with a radiative-transfer model. The model assumes that the leaves consist of small finite planes with Lambertian properties. Four theoretical canopies with different leaf-orientation distributions were studied: erectophile, spherical, planophile, and heliotropic canopies. The directional-reflectance distributions from the model closely resemble reflectance distributions measured in the field. The physical scattering mechanisms operating in the model explain the variations observed in the reflectance distributions as a function of leaf-orientation distribution, solar zenith angle, and leaf transmittance and reflectance. The simulated reflectance distribution show unique characteristics for each canopy. The basic understanding of the physical scattering properties of the different canopy geometries gained in this study provide a basis for developing techniques to infer leaf-orientation distributions of vegetation canopies from directional remote-sensing measurements.
TL;DR: The 4 × 4 matrix formalisms developed by Berreman and Yeh as mentioned in this paper for the description of the ellipsometric properties of planar multilayer anisotropic media are compared.
Abstract: The 4 × 4 matrix formalisms developed respectively by Berreman [ D. W. Berreman , J. Opt. Soc. Am.62, 502 ( 1972)] and by Yeh [P. Yeh , J. Opt. Soc. Am.69, 742 ( 1979)] for the description of the ellipsometric properties of planar multilayer anisotropic media are compared. Features of both are used to provide a framework that is applicable to the calculation of ellipsometric properties of, e.g., stratified media that incorporate magnetic materials.
TL;DR: The corneal electroretinogram was used to investigate the spectral sensitivities of cones in 12 dichromatic squirrel monkeys whose color-vision capacities were established in behavioral tests, and the spectral-sensitivity functions obtained are similar to previous estimates of cone spectral sensitivity in dichromatics squirrel monkeys derived from direct microspectrophotometric measurements.
Abstract: The corneal electroretinogram (ERG) was used to investigate the spectral sensitivities of cones in 12 dichromatic squirrel monkeys (Saimiri sciureus) whose color-vision capacities were established in behavioral tests. Three different varieties of dichromacy were represented among these animals. A flicker-photometric procedure was used in which the ERG response to a rapidly flickering monochromatic test light was compared with the response elicited by a similarly flickering reference light. The spectral-sensitivity functions obtained by the use of this technique are similar to previous estimates of cone spectral sensitivity in dichromatic squirrel monkeys derived from direct microspectrophotometric measurements.