Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1988"

Closed-form solution of absolute orientation using orthonormal matrices

Abstract: Finding the relationship between two coordinate systems by using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. The solution has applications in stereophotogrammetry and in robotics. We present here a closed-form solution to the least-squares problem for three or more points. Currently, various empirical, graphical, and numerical iterative methods are in use. Derivation of a closed-form solution can be simplified by using unit quaternions to represent rotation, as was shown in an earlier paper [ J. Opt. Soc. Am. A4, 629 ( 1987)]. Since orthonormal matrices are used more widely to represent rotation, we now present a solution in which 3 × 3 matrices are used. Our method requires the computation of the square root of a symmetric matrix. We compare the new result with that obtained by an alternative method in which orthonormality is not directly enforced. In this other method a best-fit linear transformation is found, and then the nearest orthonormal matrix is chosen for the rotation. We note that the best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points.

Age and visual search: expanding the useful field of view.

Abstract: The useful field of view is defined as the visual area in which information can be acquired within one eye fixation. We studied visual search within this context and found a reduction in the size of the field as a function of age. This loss, however, was recovered partially with practice. Standard acuity and perimetric tests of visual field, although diagnostic of disease, underestimate the degree of difficulty experienced by visually healthy older adults in everyday activities requiring the use of peripheral vision. To aid in predicting such performance, a model incorporating the effects of distractors and secondary task demands was developed.

Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception.

Abstract: To some degree, all current models of visual motion-perception mechanisms depend on the power of the visual signal in various spatiotemporal-frequency bands. Here we show how to construct counterexamples: visual stimuli that are consistently perceived as obviously moving in a fixed direction yet for which Fourier-domain power analysis yields no systematic motion components in any given direction. We provide a general theoretical framework for investigating non-Fourier motion-perception mechanisms; central are the concepts of drift-balanced and microbalanced random stimuli. A random stimulus S is drift balanced if its expected power in the frequency domain is symmetric with respect to temporal frequency, that is, if the expected power in S of every drifting sinusoidal component is equal to the expected power of the sinusoid of the same spatial frequency, drifting at the same rate in the opposite direction. Additionally, S is microbalanced if the result WS of windowing S by any space-time-separable function W is drift balanced. We prove that (i) any space-time-separable random (or nonrandom) stimulus is microbalanced; (ii) any linear combination of pairwise independent microbalanced (respectively, drift-balanced) random stimuli is microbalanced and drift balanced if the expectation of each component is uniformly zero; (iii) the convolution of independent microbalanced and drift-balanced random stimuli is microbalanced and drift balanced; (iv) the product of independent microbalanced random stimuli is microbalanced; and (v) the expected response of any Reichardt detector to any microbalanced random stimulus is zero at every instant in time. Examples are provided of classes of microbalanced random stimuli that display consistent and compelling motion in one direction. All the results and examples from the domain of motion perception are transposable to the space-domain problem of detecting orientation in a texture pattern.

Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation

Abstract: We present a theoretical description of the scattering of a Gaussian beam by a spherical, homogeneous, and isotropic particle. This theory handles particles with arbitrary size and nature having any location relative to the Gaussian beam. The formulation is based on the Bromwich method and closely follows Kerker’s formulation for plane-wave scattering. It provides expressions for the scattered intensities, the phase angle, the cross sections, and the radiation pressure.

Iterative Fourier-transform algorithm applied to computer holography

Abstract: In the generation of computer-generated holograms the phase is in many applications a free parameter that can be manipulated to achieve a high diffraction efficiency, a small space–bandwidth product, and a speckle-free reconstruction. An iterative algorithm to determine such phase distributions is described. Experimental verifications are given.

Electromagnetic wave propagation through a dielectric–chiral interface and through a chiral slab

Abstract: The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of parallel- and perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = ∊E + iγB and H = iγE + (1/μ)B. The constants ∊, μ, and γ are real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. The conditions are obtained for the total internal reflection of the incident wave from the interface and for the existence of the Brewster angle. The effects of the chirality on the polarization and the intensity of the reflected wave from the chiral half-space are discussed and illustrated by using the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence.

Integration of depth modules: stereo and shading

Abstract: We studied the integration of image disparities, edge information, and shading in the three-dimensional perception of complex yet well-controlled images generated with a computer-graphics system. The images showed end-on views of flat- and smooth-shaded ellipsoids, i.e., images with and without intensity discontinuities (edges). A map of perceived depth was measured by adjusting a small stereo depth probe interactively to the perceived surface. Our data show that disparate shading (even in the absence of disparate edges) yields a vivid stereoscopic depth perception. The perceived depth is significantly reduced if the disparities are completely removed (shape-from-shading). If edge information is available, it overrides both shape-from-shading and disparate shading. Degradations of depth perception corresponded to a reduced depth rather than to an increased scatter in the depth measurement. The results are compared with computer-vision algorithms for both single cues and their integration for three-dimensional vision.

Visual signal detection. IV: Observer inconsistency

Abstract: Historically, human signal-detection responses have been assumed to be governed by external determinants (nature of the signal, the noise, and the task) and internal determinants. Variability in the internal determinants is commonly attributed to internal noise (often vaguely defined). We present a variety of experimental results that demonstrate observer inconsistency in performing noise-limited visual detection and discrimination tasks with repeated presentation of images. Our results can be interpreted by using a model that includes an internal-noise component that is directly proportional to image noise. This so-called induced internal-noise component dominates when external noise is easily visible. We demonstrate that decision-variable fluctuations lead to this type of internal noise. Given this induced internal-noise proportionality (sigma i/sigma 0 = 0.75 +/- 0.1), the upper limit to human visual signal-detection efficiency is 64% +/- 6%. This limit is consistent with a variety of results presented in earlier papers in this series.

Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings

Abstract: The contrast dependence of simultaneous masking has been measured using isochromatic yellow–black luminance sinusoids and isoluminant red–green chrominance gratings. Masking functions for all four combinations of chromatic and luminance masks and tests are reported. In the two same-on-same conditions (luminance mask/luminance test and chromatic mask/chromatic test) these functions (increment threshold contrast versus mask contrast) have the typical dipper shape and are almost identical when test and mask contrasts are normalized to the unmasked contrast thresholds. The contrast dependence of the luminance mask/color test and color mask/luminance test functions are quite different. The luminance mask/color test shows facilitation over a broad range of both subthreshold and suprathreshold contrasts of the luminance mask. In the color mask/luminance test condition facilitation is never observed, but at suprathreshold contrasts a 2-cycle/degree (c/deg) chromatic grating masks a 2-c/deg luminance grating as strongly as does a luminance mask. The luminance mask/chromatic test results are invariant over the 0.25–2-c/deg spatial-frequency range, whereas the robust masking of luminance by color at 2 c/deg diminishes at lower spatial frequencies. The spatial-frequency selectivity of the luminance-facilitates-color interaction is much broader than facilitatory interactions in either the color–color or luminance–luminance conditions. Possible mechanisms of color–luminance interactions are considered. The lack of facilitation in the color mask/luminance test condition precludes a simple pedestal interpretation of this masking interaction. The data are, however, consistent with models that invoke inhibitory or more elaborate excitatory masking interactions.

Optical and photoreceptor immaturities limit the spatial and chromatic vision of human neonates.

Abstract: We examine the contributions of preneural mechanisms, i.e., the optics of the eye and the aperture, spacing, and efficiency of foveal cones, to poor spatial and chromatic vision in human neonates. We do so by comparing the performances of ideal observers incorporating the characteristics of the optics and the foveal cones of adults and neonates. Our analyses show that many, but not all, of the differences between neonatal and adult contrast sensitivities and grating acuities can be explained by age-related changes in these factors. The analyses also predict differing growth curves for vernier and grating acuities. Finally, we demonstrate that preneural mechanisms constrain chromatic discrimination in human neonates and that discrimination failures may reflect poor visual efficiency rather than immature chromatic mechanisms per se.

Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals

Abstract: We present a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media. It is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials. It is applied successfully to the modeling of total attenuated reflection in nematic liquid crystals with beyond-critical-angle incidence when the conventional transfer matrix methods normally fail.

Axial behavior of pupil-plane filters

Abstract: The relationship between the transverse and the on-axis behaviors of various pupil-plane filters is described. Expressions for general energy constraints associated with these filters are also derived. Transverse and axial diffraction properties of filters with quadratic radial transmittance are demonstrated experimentally.

Faster 4 × 4 matrix method for uniaxial inhomogeneous media

Abstract: An exact representation of the transfer matrix for stratified homogeneous uniaxial media is derived. It can be used to calculate optical quantities such as reflectance and transmittance by means of Berreman’s 4 × 4 matrix method, permitting calculations for thick homogeneous slabs such as polarizers in one single step without the commonly used truncated series expansion. When the dielectric tensor of an inhomogeneous medium varies continuously with the normal to the plane of stratification, the medium is divided into thin slabs. The transfer matrix of the whole medium is then obtained by multiplying the transfer matrices of all slabs. Treating each slab as homogeneous gives satisfactory results, as shown in an example of a periodic structure for which an analytic solution is known.

Optical misalignment sensing and image reconstruction using phase diversity

Abstract: A segmented-aperture telescope such as the Multiple-Mirror Telescope will suffer from phase errors unless the segments are aligned to within a small fraction of a wavelength. Such a coherent alignment of the segments is difficult to achieve in real time. An alternative is to record the images degraded by phase errors and to restore them after detection by using phase-retrieval techniques. In this paper we describe the use of Gonsalves’s phase-diversity method (which was previously used to combat atmospheric turbulence) to correct imagery blurred by a misaligned segmented-aperture telescope. Two images are recorded simultaneously: the usual degraded image in the focal plane and a second degraded image in an out-of-focus plane. An iterative gradient-search algorithm finds the phase error of the telescope that is consistent with both degraded images. We refer to this technique as the method of multiple-plane measurements with iterative reconstruction. The final image is obtained by a Wiener–Helstrom filtering of the degraded image using the retrieved phase errors. The results of reconstruction experiments performed with simulated data including the effects of noise are shown for the case of random piston phase errors on each of six segments.

Birefringence of the human foveal area assessed in vivo with Mueller-matrix ellipsometry

Abstract: We have assessed retinal birefringence in the foveal and parafoveal regions by applying Mueller matrix ellipsometry on the human eye in vivo. Basically, a light beam passed the ocular media twice and was scattered at the fundus intermediately. Keeping the entry and exit positions on the cornea constant and varying the retinal location along a circle around the foveal center enabled us to separate the corneal and retinal components of the measured retardation. We conclude that the retina within the outer margin of the parafovea behaves as a uniaxial crystal, with its slow axis radially oriented from the fovea and a retardation of about 16 deg (to 70 deg in the corneal center). We believe that Henle’s fiber layer causes retardation in this specific configuration of entrance and exit beams. The outer segments of the photoreceptors, although birefringent, have their optic axes aligned with these beams.

Least-squares phase estimation from the phase difference

Abstract: The purpose of this paper is to clarify the relationship between the isolated zero points in modulus distribution and the least-squares phase estimation from the phase difference. The concepts of phase and phase difference are reaffirmed. In addition, a necessary condition that makes the least-squares phase estimation feasible is derived by applying the concept of complete observability in estimation theory to the measurement of the phase difference. The occurrence of isolated zero points causes the conventional least-squares phase estimation to fail because the phase difference defined by this concept does not satisfy the necessary condition when isolated zero points occur. This condition also generates a new type of least-squares phase estimation that is feasible for phase retrieval even if zero points exist. One algorithm for realizing this new type of least-squares phase estimation is proposed, and its effectiveness is verified by using computer simulations. Two types of phase unwrapping are also presented: one is the exponential function type; the other results from the proposed least-squares phase-estimation algorithm.

Two-dimensional curvature operators

Abstract: Most computer vision systems use one-dimensional operators to calculate the curvature of boundaries or image contours. However, the more sophisticated biological systems use two-dimensional operators. Here we analyze how curvature can be computed by using two-dimensional operators and show the relation of this approach to the one-dimensional methods currently in use.

Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media

Abstract: Several aspects of electromagnetic wave propagation and scattering in isotropic chiral media (D = ∊E + β∊▽ × E, B = μH + βμ▽× H) are explored here. All four field vectors, E, H, D, and B, satisfy the same governing differential equation, which reduces to the vector Helmholtz equation when β = 0. Vector and scalar potentials have been postulated. Conservation of energy and momentum are examined. Some properties, consequences, and computationally attractive forms of the applicable infinite-medium Green’s function have been explored. Finally, the mathematical expression of Huygens’s principle, as applicable to chiral media, has also been derived and employed to set up a scattering formalism and to establish the forward plane-wave-scattering amplitude theorems. Several of the results given that pertain to the field equations and Green’s dyadic are available for constitutive equations other than those mentioned above; these results, along with some others, have been given now for the above-mentioned constitutive equations. The derivations of Huygens’s principle and other developments described here have not been given earlier, to our knowledge, for any pertinent set of constitutive equations. With advances in polymer science, the formalisms developed here may be useful in the utilization of artificial chiral dielectrics at suboptical and microwave frequencies; application to vision research is also anticipated.

Knox–Thompson and triple-correlation imaging through atmospheric turbulence

Abstract: A comparative study is made of the Knox–Thompson and triple-correlation techniques as applied to image restoration. Both photon-noise-degraded imaging and atmospheric-turbulence-degraded imaging are considered. The signal-to-noise ratios of the methods are studied analytically and with the aid of computer simulations. The ability to retain diffraction-limited information on imaging through turbulence is considered in terms of phase-closure relationships. On the basis of this work it is found that the two image-restoration techniques are effectively equivalent.

Estimating Cn 2 over snow and sea ice from meteorological data

Abstract: Because turbulent fluctuations in the atmospheric refractive index (n) at a wavelength λ are related to fluctuations in the temperature (t) and the humidity (q) by n = A(λ, P, T, Q)t + B(λ, P, T, Q)q it is possible to estimate the refractive-index structure parameter Cn2 from meteorological quantities. I describe and evaluate two such estimation procedures,one based on the velocity, temperature and humidity scales u*, t*, and q*and a second based on the routine meteorological quantities Uh, Ts − Th and Qs − Qh. The subscript h here denotes the wind speed (Uh), temperature (Th), or humidity (Qh) at a reference height h; the subscript s indicates the surface value. I also develop analytical expressions for the coefficients A and B as functions of λ, the atmospheric pressure (P), and the temperature and the humidity in four wavelength regions: visible (including near infrared), an infrared window, near millimeter, and radio. In a sensitivity analysis of the two estimation procedures, the core of the paper, I demonstrate that the accuracy of the Cn2 estimate is a strong function of the Bowen ratio (Bo). At two Bo values within the interval [−10, 10], one dependent on λ and the other dependent on meteorological conditions, the uncertainty in the Cn2 estimate becomes infinite.

Enhanced backscattering through a deep random phase screen

Abstract: The distribution of intensity scattered by a plane mirror placed in the Fresnel region behind a smoothly varying deep random phase screen is calculated for arbitrary angles of incidence of the illuminating beam. It is found that enhancement occurs in the backward direction because of the coherent addition of doubly scattered waves, as in particle-scattering systems, and also as a result of statistical geometrical-optics effects. These effects are largest when reflection takes place near the focusing plane of the phase screen and lead to an enhancement factor proportional to the logarithm of the phase variance introduced by the screen. The coherence and higher-order statistical properties of the scattered wave are briefly examined.

Compound optical-fiber-based resonators

Abstract: The relative merits of three designs of compound optical-fiber-based resonators for application to line narrowing in fiber lasers and demultiplexing in optical-communications systems are discussed. The three resonator designs are a set of concatenated rings, a three-reflector resonator with loop mirrors, and a fiber Fox–Smith interferometer.

General analysis and optimization of the four- detector photopolarimeter

Abstract: The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, ψi, Δi,) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A ≠ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on the detectors are required, and a thin dielectric (e.g., thermal oxide) layer would suffice. The differential reflection phase shift Δ is unrestricted for the first and third detectors and has optimum values of ±90° for the second. The optimum rotation angles of the POI are ±45° and ±135°. The optimum values of the surface parameter ψ are 27.37°, 22.5° or 67.5°, and 0 or 90° for the first, second, and third reflections, respectively. The following topics are also considered: (1) the partition of energy among detectors, (2) the effect of tilting the last detector, (3) operation of the FDP over a broadband spectral range, (4) choice of the light-beam path, and (5) calibration.

Analysis of the development of spatial contrast sensitivity in monkey and human infants

Abstract: The development of spatial contrast sensitivity in human and monkey infants reveals changes in the properties of underlying contrast-detection mechanisms in the visual system. A reanalysis of published data shows that the development of the spatial contrast sensitivity function can be described satisfactorily by the simultaneous vertical and horizontal scaling of a template function whose shape on a log–log axis does not change during development. Because individuals differ in the point to which contrast sensitivity has developed at any particular time, the use of group-averaged data as a basis for estimating the course of the developmental process has two undesirable results. First, it provides estimates of spatial contrast sensitivity during development that do not reflect any individual’s sensitivity. Second, it incorrectly suggests that the shape of the spatial contrast sensitivity function changes during development.

Age-related changes in the central visual field for short-wavelength-sensitive pathways.

Abstract: The sensitivity of short-wavelength-sensitive (SWS) cone pathways throughout the central 30-deg visual field was determined in both eyes of 62 normal volunteers between the ages of 20 and 72 years. We found an average SWS cone pathway sensitivity decrease with age of ~0.15 log unit per decade. The sensitivity reduction was approximately linear, with a slightly larger decrease beyond the age of 50 years. The age-related SWS cone pathway sensitivity reductions also became larger as a function of increasing stimulus eccentricity. Measurements of ocular-media absorption characteristics in each eye revealed that 30–40% of the age-related sensitivity loss could be attributed to reductions in transmission of short-wavelength light by the ocular media. After corrections for preretinal media transmission loss, the decrease in the sensitivity of SWS cone pathways with age was ~0.09 log unit per decade. This age-related loss is greater than age-related sensitivity decreases in the middle-wavelength-sensitive and/or long-wavelength-sensitive cones (appoximately 0.06 to 0.07 log unit per decade). In the age group older than 60 years, there was an inverse relationship between media-corrected SWS cone pathway sensitivity and media absorption characteristics (i.e., media-corrected SWS cone pathway sensitivity was higher in eyes with lower media transmission of short wavelengths). This relationship was not so evident for younger subjects. A similar inverse relationship between transmission loss in the ocular media and SWS cone pathway sensitivity was found between left and right eyes of the same individual. These findings raise the possibility that reductions in short-wavelength transmission by the ocular media may have a long-term protective effect against light-induced damage to SWS cone pathways.

Imaging of Gaussian Schell-model sources

Abstract: Imaging of Gaussian Schell-model sources by general lossless systems is analyzed with an extended ray-transfermatrix method. Algebraic expressions are derived for the location, size, and coherence area of the image waist and for the depth of focus and the far-field diffraction angle. These results are shown to provide a continuous transformation between laser-beam optics and geometrical optics. They also lead naturally to several equivalence and invariance relations pertaining to isotropic and anisotropic Gaussian Schell-model sources. As an application, the importance of effects due to partial spatial coherence in beam focusing is examined.

Maximum-likelihood image restoration adapted for noncoherent optical imaging

Abstract: Noncoherent optical-imaging systems are identified as potential applications for the maximum-likelihood image-restoration methods that are currently being studied for various modalities of nuclear-medicine imaging. An analogy between the quantum-photon measurements of such an optical system and that of a gamma camera allow for this new application. Results of a computer simulation are presented that support its feasibility. One important property revealed by this simulation is that the maximum-likelihood method demonstrates the ability to extrapolate the Fourier spectrum of a band-limited signal. This ability can be partially understood in that this algorithm, similar to some of the other spectral-extrapolation algorithms, constrains the solution to nonnegative values. This observation has implications on the potential of superresolution, the restoration of images from a defocused optical system, and three-dimensional imaging with a microscope.

Short-wavelength-sensitive-cone sensitivity loss with aging: a protective role for macular pigment?

Abstract: The hypothesis was tested that the yellow macular pigment protects the human fovea from retinal neural damage caused by visible-light exposure over a lifetime. The sensitivities of the short-wavelength-sensitive-cone (S-cone) pathways and a long-wavelength-sensitive pathway were assessed across the central retina in a young group (average age, 23 years) and an older group (average age, 67 years) of normal healthy observers. No statistically significant difference was found at any retinal locations between the groups for the measures of long-wavelength sensitivity. However, the older group showed a significant differential loss of S-cone sensitivity across the retina compared with the younger group, with more loss of sensitivity at nonfoveal locations than at the fovea. This differential loss across the retina cannot be accounted for by yellowing of the crystalline lens, since lens effects are present equally at all retinal eccentricities. This result supports the hypothesis that the macular pigment protects the foveal area from light damage.

Factors underlying individual differences in the color matches of normal observers.

Abstract: We have used a factor analysis of the Stiles–Burch [ Opt. Acta6, 1 ( 1959)] 10° field color matches to examine the basis of individual differences in the color matches made by observers with normal color vision. The differences in the matches are primarily due to interobserver variations in the macular-pigment density [with a standard deviation (σ) of 0.12 at 460 nm]; the lens-pigment density (σ = 0.18 at 400 nm); the spectral position of the long-wavelength-sensitive (σ = 50.3 cm−1), medium-wavelength sensitive (σ = 31.9 cm−1), and short-wavelength-sensitive (σ = 45.3 cm−1) photopigments; the covarying densities of the three photopigments (σ = 0.045); and the degree of rod intrusion. Variations in the different factors appear to be uncorrelated. Comparable estimates of the sources and range of interobserver differences in color matching were obtained from a similar analysis of the Stiles–Burch 2° color matches [ Opt. Acta2, 168 ( 1955)].

Spatial contrast sensitivity: effects of age, test–retest, and psychophysical method

Abstract: Two different psychophysical methods were used to test the spatial contrast sensitivity in normal subjects from five age groups. The method of adjustment showed a decline in sensitivity with increasing age at all spatial frequencies, while the forced-choice procedure showed an age-related decline predominantly at high spatial frequencies. It is suggested that a neural component is responsible for this decline.