Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1991"

Affine structure from motion

Abstract: A mobile observer samples sequences of narrow-field projections of configurations in ambient space. The so-called structure-from-motion problem is to infer the structure of these spatial configurations from the sequence of projections. For rigid transformations, a unique metrical reconstruction is known to be possible from three orthographic views of four points. However, human observers seem able to obtain much shape information from a mere pair of views, as is evident in the case of binocular stereo. Moreover, human observers seem to find little use for the information provided by additional views, even though some improvement certainly occurs. The rigidity requirement in its strict form is also relaxed. We indicate how solutions of the structure-from-motion problem can be stratified in such a way that one explicitly knows at which stages various a priori assumptions enter and specific geometrical expertise is required. An affine stage is identified at which only smooth deformation is assumed (thus no rigidity constraint is involved) and no metrical concepts are required. This stage allows one to find the spatial configuration (modulo an affinity) from two views. The addition of metrical methods allows one to find shape from two views, modulo a relief transformation (depth scaling and shear). The addition of a third view then merely serves to settle the calibration. Results of a numerical experiment are discussed.

Production and uses of diffractionless beams

Abstract: It is proposed to obtain intense optical fields, whose form shows little change in size over long paths, through the use of either conical lenses or spherical lenses showing spherical aberration together with a single projecting lens. The conical lens is shown to produce fields whose transverse structure is given by a zero-order Bessel function J0, while the spherical aberrating lens produces (real or virtual) J0-like transverse structures, provided that the central portion of the aberrating lens is occluded. In all cases projection gives a J0 real-image optical structure. Intensity, size of the transverse structure, and range considerations are developed, and some aspects of optimization are discussed. A negative aberrating lens gives a long range of nearly constant size in the image field, and a universal expression is presented to describe the image size as a function of image distance for this case. Projection with an aberrating projection lens is shown to improve the constancy of the final J0 pattern size dramatically. Typical photographic results are included for beams generated by using a low-power He–Ne laser. Brief considerations of practical uses of diffractionless beams are presented.

Light scattering by randomly oriented axially symmetric particles

Abstract: Light scattering by ensembles of independently scattering, randomly oriented, axially symmetric particles is considered. The elements of the scattering matrices are expanded in (combinations of) generalized spherical functions; this is advantageous in computations of both single and multiple light scattering. Waterman’s T-matrix approach is used to develop a rigorous analytical method to compute the corresponding expansion coefficients. The main advantage of this method is that the expansion coefficients are expressed directly in some basic quantities that depend on only the shape, morphology, and composition of the scattering axially symmetric particle; these quantities are the elements of the T matrix calculated with respect to the coordinate system with the z axis along the axis of particle symmetry. Thus the expansion coefficients are calculated without computing beforehand the elements of the scattering matrix for a large set of particle orientations and scattering angles, which minimizes the numerical calculations. Like the T-matrix approach itself, the method can be used in computations for homogeneous and composite isotropic particles of sizes not too large compared with a wavelength. Computational aspects of the method are discussed in detail, and some illustrative numerical results are reported for randomly oriented homogeneous dielectric spheroids and Chebyshev particles. Results of timing tests are presented; it is found that the method described is much faster than the commonly used method of numerical angle integrations.

Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy.

Abstract: Oil-immersion microscope objective lenses have been designed and optimized for the study of thin, two-dimensional object sections that are mounted immediately below the coverslip in a medium that is index matched to the immersion oil. It has been demonstrated both experimentally and through geometrical- and physical-optics theory that, when the microscope is not used with the correct coverslip or immersion oil, when the detector is not located at the optimal plane in image space, or when the object does not satisfy specific conditions, aberration will degrade both the contrast and the resolution of the image. In biology the most severe aberration is introduced when an oil-immersion objective lens is used to study thick specimens, such as living cells and tissues, whose refractive indices are significantly different from that of the immersion oil. We present a model of the three-dimensional imaging properties of a fluorescence light microscope subject to such aberration and compare the imaging properties predicted by the model with those measured experimentally. The model can be used to understand and compensate for aberration introduced to a microscope system under nondesign optical conditions so that both confocal laser scanning microscopy and optical serial sectioning microscopy can be optimized.

Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces

Abstract: Surface-relief structures having the form of an array of modified pyramids (having curved rather than flat triangular shown to produce an index-matching layer that will reduce surface reflection by several orders of sides) are Such structures are equivalent to a quintic (fifth-order polynomial) gradient-index layer, which has magnitude. been shown to be near optimum for reducing reflection at dielectric interfaces.

Generalized phase-shifting interferometry

Abstract: We describe a generalized phase-shifting interferometry for which the reference phases are directly evaluated at each time that the interference fringe data are read. The reference phases are obtained from the additional straight fringes on the interfering plane by the fast-Fourier-transform method. According to error estimation, the repeatabilities in the measurements of optical surfaces are λ/500 rms, when the generalized algorithm with eight data acquisitions is used.

Peripheral spatial vision: limits imposed by optics, photoreceptors, and receptor pooling.

Abstract: We examined the contribution of optical and photoreceptor properties as well as receptor pooling to eccentricity-dependent variations in spatial vision by comparing the performance of ideal observers with that of human observers. We measured contrast sensitivity functions in human observers and calculated such functions in ideal observers for retinal eccentricities of 0-40 deg. Comparisons of human and ideal performance in a variety of tasks reveal that many aspects of the variation in spatial vision with eccentricity can be understood from an analysis of the discrimination information available at the retinal ganglion cells.

Simultaneous color constancy: papers with diverse Munsell values

Abstract: Arend and Reeves [J. Opt. Soc. Am. A 3, 1743 (1986)] described measurements of color constancy in computer simulations of arrays of colored papers of equal Munsell value under 4000-, 6500-, and 10,000-K daylight illuminants. We report an extension of those experiments to chromatic arrays spanning a wide range of Munsell values. The computer-simulated scene included a standard array of Munsell papers under 6500-K illumination and a test array, an identical array of the same papers under 4000 or 10,000 K. Observers adjusted a patch in the test array in order to match the corresponding patch in the standard array by one of two criteria. They either matched hue and saturation or they made surface-color matches, in which the test patch was made to "look as if it were cut from the same pice of paper as the standard patch." The test and the standard patches were surrounded by a single color (annulus display) or by many colors (Mondrian display). The data agreed with those of our previous equal-value experiment. The paper matches were often approximately color constant. The hue-saturation matches were in the correct direction for constancy but were always closer to a chromaticity match (no constancy) than to the chromaticity required for hue-saturation constancy.

Light scattering from a sphere on or near an interface.

Abstract: The light-scattering problem of a sphere on or near a plane surface is solved by using an extension of the Mie theory. The approach taken is to solve the boundary conditions at the sphere and at the surface simultaneously and to develop the scattering amplitude and Mueller scattering matrices. This is performed by projecting the fields in the half-space region not including the sphere multiplied by an appropriate Fresnel reflection coefficient onto the half-space region including the sphere. An assumption is that the scattered fields from the sphere, reflecting off the surface and interacting with the sphere, are incident upon the surface at near-normal incidence. The exact solution is asymptotically approached when either the sphere is a large distance from the surface or the refractive index of the surface approaches infinity.

Parametric characterization of general partially coherent beams propagating through ABCD optical systems

Abstract: Within the formalism of the Wigner distribution function, a new parameter is proposed, which characterizes arbitrary tridimensional partially coherent beams and is invariant through ABCD optical systems. The relationship between such a parameter and the bidimensional concept of beam quality is analyzed. An absolute lower bound that the new parameter can reach is also shown.

Light scattering from random rough dielectric surfaces

Abstract: A theoretical and numerical study is made of the scattering of light and other electromagnetic waves from rough surfaces separating vacuum from a dielectric. The extinction theorem, both above and below the surface, is used to obtain the boundary values of the field and its normal derivative. Then we calculate the angular distribution of the ensemble average of intensity of the reflected and transmitted fields. The scattering equations are solved numerically by generating one-dimensional surface profiles through a Monte Carlo method. The effect of roughness σ and correlation distance T on the aforementioned angular distribution, as well as on the reflectance, is analyzed. Enhanced backscattering and new transmission effects are observed, also depending on the permittivity. The ratio σ/T is large in all cases studied, and thus no analytical approximation, such as the Kirchhoff approximation (KA) and small perturbation methods, could a priori be expected to hold. We find, however, that the range of validity of the KA can be much broader than that previously found in perfect conductors.

Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications

Abstract: The solution of the scalar wave equation in the parabolic approximation is considered through the finite-difference and the Fourier-transform (i.e., beam propagation method) techniques. Examples are taken from the field of integrated optics and include propagation in straight, tapered, Y-branched, and coupled waveguides. A comparison of numerical results obtained by the two methods is presented, and a comparison with other analytical or numerical methods is also given. In the numerous cases studied it is shown that the finite-difference method yields a large, order-of-magnitude range improvement in accuracy or computational speed when compared with the Fourier-transform method.

Non-line-of-sight single-scatter propagation model

Abstract: A propagation model that describes the temporal characteristics of singly scattered radiation in a homogeneous scattering and absorbing medium is presented. The model generalizes previous results in the area and is used to analyze the angular spectrum of singly scattered energy as well as the impulse-response durations and path losses of short-range non-line-of-sight optical communication systems. It is shown that the angular response starts to drop off significantly at an off-axis angle equal to the receiver half-field of view. It is also shown that lower path losses correspond to longer impulse responses so that a lower available bandwidth is indicated. These results are based on numerical examples motivated by the operation of non-line-of-sight communications links in the middle-ultraviolet wave band.

Color appearance in the peripheral retina: effects of stimulus size

Abstract: Hue and saturation scaling were used to measure the appearance of spectral lights as a function of stimulus size for nine loci across the horizontal retinal meridian. At a given locus, each hue (R, Y, G, and B) grew as a function of stimulus size up to some asymptotic value. The parameter values of Michaelis–Menten growth functions fitted to the hue data were used to derive the sizes of the so-called perceptive fields of the hue mechanisms. The fields for all mechanisms increased with eccentricity, and this increase was greater on the temporal than on the nasal retina. By increasing stimulus size it was possible to achieve fovealike color vision to eccentricities of 20 deg. However, even the largest stimuli failed to produce fully saturated hues at 40 deg. The retinal size scales of the four hue mechanisms were not the same; those for R and B were similar, and these mechanisms had the smallest perceptive fields everywhere. The perceptive fields of the hue mechanisms at all loci were larger than anatomical estimates of the sizes of retinal receptive fields.

Image formation in a fiber-optical confocal scanning microscope

Abstract: Theoretical studies on image formation in a confocal scanning microscope with optical fibers as the transmission medium are reported. Theoretical analyses show that this new kind of microscope can be considered a coherent imaging system, even for finite fiber spot size. Based on these studies the coherent transfer functions in both in-focus and defocused cases are derived and calculated. The axial coherent transfer functions are also obtained, and, furthermore, the optical-sectioning property of the microscope system is investigated with the consideration of the image formation of a perfect-reflection planar object and a point object.

Error-diffusion algorithm with edge enhancement

Abstract: Error diffusion is a popular algorithm for the binarization of continuous-tone images. A modification of the error-diffusion algorithm is shown that introduces an input-dependent threshold into the process. This modification establishes a fast and efficient way to increase or decrease edge enhancement in the algorithm.

Propagation invariance and self-imaging in variable-coherence optics

Abstract: The concept of propagation invariance in partially coherent optics is introduced. Explicit expressions are given for the cross-spectral density and the angular correlation function (cross-angular spectrum) characterizing a class of fields that are propagation invariant in the sense that their correlation properties in the space-frequency domain are exactly the same in every transverse plane. The so-called diffraction-free beams are shown to be members of this new, wider class of wave fields, which itself is a subset of a generalized class of partially coherent self-imaging fields. The existence of partially coherent propagation-invariant fields with a sharp correlation peak is verified experimentally by considering radiation from a planar J0 Bessel-correlated source.

Comparison of the propagation characteristics of Bessel, Bessel–Gauss, and Gaussian beams diffracted by a circular aperture

Abstract: We use the scalar Kirchhoff–Huygens diffraction integral to obtain analytic expressions for both axial and transverse intensity distributions, assuming normal incidence on a circular aperture for four types of incident field: (1) plane wave, (2) Bessel beam, (3) Gaussian beam, and (4) Bessel–Gauss beam. We use the Fresnel approximation to obtain the axial intensity as a function of distance from the aperture. We consider both Fresnel and Fraunhofer diffraction for the case of the transverse intensity distributions. For the axial case, we find that the Bessel–Gauss beam performs worse than the Bessel beam, in terms both of the magnitude of intensity and of its ability to extend a distance from the aperture. In the transverse case, we find that the Bessel–Gauss beam performance in terms of remaining nearly diffraction free over a given distance is highly dependent on the relationship among the aperture radius, the beam waist parameter, and the transverse wave number.

Model for color vision and light adaptation.

Abstract: A multizone color model is described. It has nonlinear receptor gain control, two postreceptor opponent-colors processing stages, and neural compression late in the visual pathway. It is assumed that gain control can be activated by receptor responses from a test light itself (self-adaptation) and (or) by receptor responses from other adapting fields. Apparent brightnesses and visual discriminations are mediated by the first processing stage, and apparent hues and saturations are mediated by the second stage. The model accounts for a wide range of data, including nonlinear hue shifts in the color solid, various apparent brightness effects, visual discriminations for achromatic and chromatic lights under various adaptation conditions, and effects of chromatic adaptation on color appearances.

Spatial summation properties of directionally selective mechanisms in human vision.

Abstract: Our goal in this paper was to measure psychophysically the receptive-field size of motion units in human vision. To this aim, length and width spatial summation functions were measured for drifting (8-Hz) sinusoidal gratings of spatial frequencies 0.1, 1.0, and 10.0 cycles per degree (c/deg) with two threshold criteria: direction discrimination and simple detection. For each spatial frequency, contrast sensitivity for detection of the direction of drift increased with increasing stimulus size (length or width), at first rapidly (slope ≥ 1.0) and then more gradually (slope 0.29). For most stimuli, the detection and direction-discrimination contrast thresholds were nearly the same. However, for stimuli severely curtailed in width, significantly more contrast was required for direction discrimination than for detection. These results were predicted with a summation model, which incorporated three-dimensional (space–space–time) linear input filters, and probability summation over space and among different filter types. The fit of the model gave an estimate of both the receptive-field length and width of motion-detector units in human vision. At each spatial frequency, the estimates of receptive-field width and length were similar, indicating that the receptive fields of motion-detector units are as long as they are wide at all spatial scales. Receptive-field size varied from approximately 0.12 cycle at 0.1 c/deg to 0.52 cycle at 10.0 c/deg.

Analysis of dielectric gratings of arbitrary profiles and thicknesses

Abstract: An efficient and stable eigenmode method is presented for the analysis of dielectric gratings of arbitrary profiles and thicknesses. The solution is expanded in terms of multiple sets of modes. The method differs from the usual eigenmode methods in that mode couplings are achieved through an iterative one-way wave multiple reflection series requiring only matrix–vector multiplications. The solution is computationally simple, has a physical interpretation, and remains stable for gratings of any thickness. Numerical results agree well with those of previous methods.

Diffusers in digital holography

Abstract: In Fourier and Fresnel holography diffuse illumination is used to smooth the power spectrum of the object wave. A speckle pattern will then disturb the diffraction pattern. We present methods to calculate appropriate diffusers in digital holography that do not introduce speckle. The considerations include deterministic object-independent as well as iteratively calculated object-dependent diffusers. Object-independent diffusers are suited for initial phases to avoid stagnation of the iterative procedure.

Relative orientation revisited

Abstract: Relative orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences among five or more ray pairs. It is one of four core problems in photogrammetry and is of central importance in binocular stereo as well as in long-range motion vision. While five ray correspondences are sufficient to yield a finite number of solutions, more than five correspondences are used in practice to ensure an accurate solution with least-squares methods. Most iterative schemes for minimizing the sum of the squares of weighted errors require a good guess as a starting value. The author has previously published a method that results in the best solution without requiring an initial guess [ J. Opt. Soc. Am. A4, 629 ( 1987)] An even simpler method is presented here that utilizes the representation of rotations by unit quaternions.

Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence

Abstract: Phase distortions in optical systems induced by atmospheric turbulence are investigated with the use of Zernike polynomial decompositions. An analytic solution for the variances of the Zernike coefficients is found for the case of Kolmogorov turbulence with a finite outer-scale length. It is shown that the effect of finite outer scale is to attenuate low-order Zernike components, even when the outer-scale length is much larger than the optical aperture. Effects are investigated for constant outer-scale size and for height-dependent outer scales. It is found that seeing effects on large telescopes are dependent more on the magnitude of the outer scale than on the shape of the outer-scale vertical profile.

Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars

Abstract: The laser power requirement for an adaptive-astronomical telescope using laser guide stars is determined largely by the effects of turbulence-induced anisoplanatism. Owing to the relatively low altitude of laser guide stars and the small size of the isoplanatic angle at visible wavelengths, multiple guide stars are required for correcting large telescope apertures. The laser power requirements are proportional to the required number of guide stars. Using an analysis technique that takes into account the realistic characteristics of the wave-front sensor and deformable mirror, as well as the spherical nature of the wave front from the laser guide star, we present computational results that show how the imaging performance of a laser-guided adaptive telescope varies as a function of the number and height of the guide stars. The results are presented as a function of the isoplanatic angle θIP as defined by Fried [ J. Opt. Soc. Am.72, 52 ( 1982)]. A new parameter, the characteristic diameter of the largest telescope requiring a single guide star, is also introduced. This parameter is designated DIP and is related to the height of the guided star zg and the isoplanatic angle θIP by DIP = 2zgθIP. The effects of anisoplanatism on the design of a 2-m-diameter adaptive telescope using laser guide stars created in the mesospheric Na layer is considered. Using a Hufnagel Cn2 model, an isoplanatic angle of θIP = 1.64 arcsec (calculated for a value of ro = 20 cm), and zg = 92 km (the nominal height of the mesospheric Na layer), we find that three Na guide stars are required in order to achieve a rms wave-front error of approximately λ/10 across the telescope aperture.

Reconstruction of rough-surface profiles with the Kirchhoff approximation

Abstract: An inversion algorithm, based on the Kirchhoff approximation, for the reconstruction of a rough-surface profile from measurements of the scattered field is described. It is shown that the data can be related to the surface profile through a Fourier-transform relationship by a specific choice of data and so lead to a simple fast-Fourier-transform-based procedure. The algorithm is illustrated through the use of numerical results.

Phase-space beam summation for time-harmonic radiation from large apertures

Abstract: Analytical modeling of high-frequency time-harmonic and transient radiation from extended aperture sources and of propagation of the resulting fields through perturbing environments is facilitated by simultaneous use of configurational (space-time) and spectral (wave number–frequency) information for suitably defined synthesizing wave objects. Such a bilateral approach can be embodied within a configuration-spectrum phase space. The present investigation deals with radiation from extended aperture sources, with emphasis on alternative uses of the phase space at high frequencies, on promising wave objects as basis elements for field synthesis, and on extraction of physical information from exact wave solutions by asymptotic methods. Of special interest are beam-type wave objects that exhibit localization in the phase space because localized wave fields have favorable propagation characteristics in complex external environments. In this paper, alternative phase-space parameterizations are applied to time-harmonic plane aperture distributions and to the corresponding fields radiated into a homogeneous half-space. The parameterizations include nonwindowed continuum versions, in which localization occurs asymptotically through constructive interference; windowed continuum versions, in which localization is embedded inherently; and windowed discretized versions, in which the basis elements are situated on a self-consistent configuration–wave number lattice. By analysis and illustrative examples, it is shown how these alternative formulations are interrelated, how the localization around well-defined regions in the phase space takes place in each formulation, and how these localization properties, through the beam propagators, influence the synthesis of the radiation field. Transient phenomena will be addressed in separate publications.

Performance limits of stationary Fourier spectrometers

Abstract: Theoretical performance limits of stationary Fourier spectrometers without mechanical scanning are analyzed and compared with the performance of a scanning Fourier spectrometer. Spectrometers employing uncollimated light are most favorable. In amplitude-splitting interferometers the reduction in fringe visibility brought about by the extended source can be avoided and leads to high optical throughput in the corresponding spectrometer. In a stationary wave-front-splittirig interferometer, realized without a beam splitter, the fringe contrast depends on the size of the source. The use of a slit source increases the optical throughput of source-size-limited spectrometers.

Scattering by a small object close to an interface. I. Exact-image theory formulation

Abstract: Exact-image theory is applied to the problem of electromagnetic wave scattering from a small dielectric object above an interface separating two isotropic and homogeneous media. The object is assumed to be electrically small and far enough from the interface so that its internal field can be assumed to be uniform. The approach is applicable to any scatter that can be represented by an electric dipole.

Acceleration of maximum-likelihood image restoration for fluorescence microscopy and other noncoherent imagery

Abstract: Maximum-likelihood image restoration for noncoherent imagery, which is based on the generic expectation maximization (EM) algorithm of Dempster et al. [ J. R. Stat. Soc. B39, 1 ( 1977)], is an iterative method whose convergence can be slow. We discuss an accelerative version of this algorithm. The EM algorithm is interpreted as a hill-climbing technique in which each iteration takes a step up the likelihood functional. The basic principle of the acceleration technique presented is to provide larger steps in the same vector direction and to find some optimal step size. This basic line-search principle is adapted from the research of Kaufman [ IEEE Trans. Med. Imag.MI-6, 37 ( 1987)]. Modifications to her original acceleration algorithm are introduced, which involve extensions in considering truncated data and an alternative way of implementing the search for an optimal step size. Log-likelihood calculations and reconstructed images from simulations show the execution time’s being shortened from the nonaccelerated algorithm by approximately a factor of 7.