Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1992"

Properties of a 4Pi confocal fluorescence microscope

Abstract: In a 4Pi confocal fluorescence microscope two opposing microscope objective lenses were used to illuminate a fluorescent object from both sides and to collect the fluorescence emissions on both sides. Constructive interference of either the illumination wave fronts in the common focus or the detection wave fronts in the common detector pinhole resulted in an axial resolution approximately four times higher than that in a confocal fluorescence microscope. A precise 4Pi confocal fluorescence microscope that uses simultaneous illumination was built. The full width at half-maximum of the depth discrimination was determined experimentally to be approximately 110 nm when lenses with a numerical aperture of 1.4, an excitation of 633 nm, and detection of approximately 725 nm were used.

Joint estimation of object and aberrations by using phase diversity

Abstract: The joint estimation of an object and the aberrations of an incoherent imaging system from multiple images incorporating phase diversity is investigated. Maximum-likelihood estimation is considered under additive Gaussian and Poisson noise models. Expressions for an aberration-only objective function that accommodates an arbitrary number of diversity images and its gradient are derived for the case of a Gaussian noise model. Expressions for the log-likelihood function and its gradient are presented for the case of Poisson noise. An expectation-maximization algorithm that enforces a nonnegativity constraint in a natural fashion is constructed for use in the Poisson noise case.

Linear models of surface and illuminant spectra

Abstract: We describe procedures for creating efficient spectral representations for color. The representations generalize conventional tristimulus representations, which are based on the peripheral encoding by the human eye. We use low-dimensional linear models to approximate the spectral properties of surfaces and illuminants with respect to a collection of sensing devices. We choose the linear-model basis functions by minimizing the error in approximating sensor responses for collections of surfaces and illuminants. These linear models offer some conceptual simplifications for applications such as printer calibration; they also perform substantially better than principal-components approximations for computer-graphics applications.

Effect of random background inhomogeneity on observer detection performance.

Abstract: Many psychophysical studies of the ability of the human observer to detect a signal superimposed upon a uniform background, where both the signal and the background are known exactly, have been reported in the literature. In such cases, the ideal or the Bayesian observer is often used as a mathematical model of human performance since it can be readily calculated and is a good predictor of human performance for the task at hand. If, however, the background is spatially inhomogeneous (lumpy), the ideal observer becomes nonlinear, and its performance becomes difficult to evaluate. Since inhomogeneous backgrounds are commonly encountered in many practical applications, we have investigated the effects of background inhomogeneities on human performance. The task was detection of a two-dimensional Gaussian signal superimposed upon an inhomogeneous background and imaged through a pinhole imaging system. Poisson noise corresponding to a certain exposure time and aperture size was added to the detected image. A six-point rating scale technique was used to measure human performance as a function of the strength of the nonuniformities (lumpiness) in the background, the amount of blur of the imaging system, and the amount of Poisson noise in the image. The results of this study were compared with earlier theoretical predictions by Myers et al. [ J. Opt. Soc. Am. A7, 1279 ( 1990)] for two observer models: the optimum linear discriminant, also known as the Hotelling observer, and a nonprewhitening matched filter. Although the efficiency of the human observer relative to the Hotelling observer was only approximately 10%, the variation in human performance with respect to varying aperture size and exposure time was well predicted by the Hotelling model. The nonprewhitening model, on the other hand, fails to predict human performance in lumpy backgrounds in this study. In particular, this model predicts that performance will saturate with increasing exposure time and drop precipitously with increasing lumpiness; neither effect is observed with human observers.

Design and assessment of symmetrical phase-shifting algorithms

Abstract: Conventional phase-shifting algorithms based on a least-squares estimate use N samples over an incomplete period of the sampled waveform We introduce a class of phase-shifting algorithms having N + 1 samples symmetrically disposed over one full period of the sampled waveform Fourier analysis techniques are used to derive these algorithms and modify them to improve their performance in the presence of phase-shift errors The algorithms can be used in phase measurement systems having periodic, but not necessarily sinusoidal, waveforms

Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach

Abstract: Previous research presented by the author and others into maximum-likelihood image restoration for incoherent imagery is extended to consider problems of blind deconvolution in which the impulse response of the system is assumed to be unknown. Potential applications that motivate this study are wide-field and confocal fluorescence microscopy, although applications in astronomy and infrared imaging are foreseen as well. The methodology incorporates the iterative expectation-maximization algorithm. Although the precise impulse response is assumed to be unknown, some prior knowledge about characteristics of the impulse response is used. In preliminary simulation studies that are presented, the circular symmetry and the band-limited nature of the impulse response are used as such. These simulations demonstrate the potential utility and present limitations of these methods.

Digital halftoning technique using a blue-noise mask

Abstract: A novel digital halftoning technique, by which the halftoning is achieved by a pixelwise comparison of the gray-scale image to an array (halftone screen), the blue-noise mask, is presented. This mask is designed so that the halftone image has blue-noise (high-frequency) characteristics in the frequency domain. The algorithm for the construction of the blue-noise mask and an algorithm for the construction of binary patterns with the same first-order but different second-order statistics are presented. Two psychovisual tests in which human subjects rated halftone patterns and images according to various criteria are also described.

Full-spectrum cone sensitivity functions for X-chromosome-linked anomalous trichromats.

Abstract: We derived the cone fundamentals for X-chromosome-linked anomalous trichromats for the wavelength range of 400–700 nm. Pigment templates were constructed from the cone fundamentals of normal trichromats after correction for ocular media absorption. The resultant retinal-level sensitivities had small irregularities in the short-wavelength region that were smoothed. The pigment templates, expressed as quantal sensitivities, were then shifted on a frequency abscissa to solve for the λmax of the pigments of anomalous trichromats needed to predict average anomaloscope matching data. We found that the protanomalous M- and L′-cone pigments are separated by 10 nm and the deuteranomalous M′- and L-cone pigments are separated by 6 nm (rounded to the nearest nanometer), where M and L indicate middle- and long-wavelength sensitive, respectively. The triads of peak wavelengths for the corneal energy-based sensitivities were as follows: normal: 440, 543, and 566 nm; protanomalous: 440, 543, and 553 nm; and deuteranomalous: 440, 560, and 566 nm.

Asymmetric color matching: how color appearance depends on the illuminant.

Abstract: We report the results of matching experiments designed to study the color appearance of objects rendered under different simulated illuminants on a CRT monitor. Subjects set asymmetric color matches between a standard object and a test object that were rendered under illuminants with different spectral power distributions. For any illuminant change, we found that the mapping between the cone coordinates of matching standard and test objects was well approximated by a diagonal linear transformation. In this sense, our results are consistent with von Kries's hypothesis [Handb. Physiol. Menschen 3, 109 (1905) [in Sources of Color Vision, D. L. MacAdam, ed. (MIT Press, Cambridge, Mass., 1970)]] that adaptation simply changes the relative sensitivity of the different cone classes. In addition, we examined the dependence of the diagonal transformation on the illuminant change. For the range of illuminants tested, we found that the change in the diagonal elements of the linear transformation was a linear function of the illuminant change.

Model for the computation of self-motion in biological systems.

Abstract: I present a method by which direction- and speed-tuned cells, such as those commonly found in the middle temporal area of the primate brain, can be used to analyze the patterns of retinal image motion that are generated during observer movement through the environment. For pure translation, the retinal image motion is radial in nature and expands out from a point that corresponds to the direction of heading. This heading direction can be found by the use of translation detectors that act as templates for the radial image motion. Each translation detector sums the outputs of direction- and speed-tuned motion sensors arranged such that their preferred direction of motion lies along the radial direction out from the detector center. The most active detector signifies the heading direction. Rotation detectors can be constructed in a similar fashion to detect areas of uniform image speed and direction in the motion field produced by observer rotation. A model consisting of both detector types can determine the heading direction independently of any rotational motion of the observer. The model can achieve this from the outputs of the two-dimensional motion sensors directly and does not assume the existence of accurate estimates of image speed and direction. It is robust to the aperture problem and is biologically realistic. The basic elements of the model have been shown to exist in the primate visual cortex.

Contrast detection in luminance and chromatic noise.

Abstract: We measured detection thresholds for a vertically oriented 1.2-cycle-per-degree sine-wave grating embedded in spatiotemporal broadband noise. Noise and signal were modulated in different directions in color space around an equal-energy white point. When signal and noise were modulated in the same direction, we observed a linear relationship between noise spectral density and signal energy at threshold. The slope of this function was the same whether the modulation was along a luminance axis or a red-green axis. If the signal was on one axis and the noise was on the other, no masking was observed. These results support the notion of two independent and equally efficient mechanisms tuned to these directions. We then measured threshold elevations for masks with both chromatic and luminance components. When signal and noise were modulated along the same line (for example, bright red and dark green), thresholds were elevated. When we inverted the phase of the chromatic component of the noise relative to the luminance component (bright green and dark red), the masking effect disappeared, even though the amount of noise in the putative luminance and chromatic mechanisms was exactly the same as before. This implies that detection performance is limited by mechanisms sensitive to both luminance and chromatic contrast signals. We characterized these mechanisms by their spectral tuning curves.

Synthetic aperture holography: a novel approach to three-dimensional displays

Abstract: We describe an electro-optic apparatus capable of displaying a computer-generated hologram in real time. The computer-generated hologram is calculated by a supercomputer, read from a fast frame buffer, and transmitted to a wide-bandwidth acousto-optic modulator. Coherent light is modulated by the acousto-optic modulator and optically processed to produce a three-dimensional image with horizontal parallax. We evaluate different display geometries and their effect on the optical parameters of the system. We then show how the display resolution can be increased by simultaneously writing three acoustic columns on a single crystal and optically multiplexing the resulting holograms. We finally describe some improvements that follow from the analysis.

Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series

Abstract: The contributions of complex rays and the secondary radiation shed by surface waves to scattering by a dielectric sphere are calculated in the context of the Debye series expansion of the Mie scattering amplitudes. Also, the contributions of geometrical rays are reviewed and compared with the Debye series. Interference effects between surface waves, complex waves, and geometrical waves are calculated, and the possibility of observing these interference effects is discussed. Experimental data supporting the observation of a surface wave-geometrical pattern is presented.

Reading speed with a pixelized vision system.

Abstract: A visual prosthesis based on electrical stimulation of the visual cortex with an array of penetrating electrodes is expected to produce pixelized visual images consisting of punctate spots of light (phosphenes). We measured reading speed in subjects viewing text with optically simulated phosphene fields in order to obtain estimates of the following design parameters for such an electrode array: pixel number, pixel spacing, and visual-field size. Comparisons were made between scanning the text with eye movements and scanning the text with head movements. The results indicate that a 25 × 25 array of pixels representing four letters of text projected on a visual field of 1.7° is sufficient to provide reading rates near 170 words/min with scrolled text and near foveal 100 words/min with fixed text.

Imaging through scattering media with holography

Abstract: Various holographic methods for imaging through scattering media such as biological tissue are described. The methods utilize light of either reduced spatial coherence or reduced temporal coherence.

Cross-talk-limited storage capacity of volume holographic memory

Abstract: We consider the storage density limited by the cross talk between stored pages during readout. We review some earlier work done in this area and present new theoretical work that characterizes the storage capacity limitations due to the cross talk. The results show that because of the presence of degeneracy noise, storage capacity does not benefit from expanding the reference points from one dimension to two dimensions. An optimum configuration that fully utilizes storage capacity and completely eliminates degeneracy noise is given for an angularly multiplexed volume holographic memory system.

Scanning-tunneling optical microscopy: a theoretical macroscopic approach

Abstract: A theoretical model for calculating the images obtained in scanning-tunneling optical microscopy is proposed. We calculate the intensity detected by a small spherical tip above a regular glass lattice illuminated in total internal reflection. The model is based on a macroscopic approach. We show that the resolution is limited neither by the wavelength nor by the decay length of the evanescent wave but that it is determined by the tip–sample distance and by the signal-to-noise ratio. We also discuss the quality of the images. In general, the intensity profile does not reproduce the sample profile. We analyzed two kinds of filtering that can deform the true profile. We also show that for a small sample period a strong signal is obtained only in TM polarization.

Color constancy : surface color from changing illumination

Abstract: Viewing the lights reflected by a set of three or more surfaces, a trichromatic visual system can recover three color-constant descriptors of reflectance per surface if the color of the surfaces’ illuminant changes. This holds true for a broad range of models that relate photoreceptor, surface, and illuminant spectral properties. Changing illumination, which creates the problem of color constancy, affords its solution.

Symmetries that simplify the design of spot array phase gratings

Abstract: The design of advanced diffraction gratings that produce spot arrays is highly influenced by the computational capabilities that are available to the designer. This is due to the increased pattern complexity that is required for larger spot arrays or higher efficiencies. Symmetries that lead to a significant reduction in the design complexity can be incorporated into the grating pattern. In addition, a translational symmetry leads to the highly desired result of even-numbered spot arrays. We examine the symmetries that can be applied to both general-and discrete-level design parameterization.

Enhanced backscattering of polarized light from discrete random media : calculations in exactly the backscattering direction

Abstract: Enhanced backscattering of polarized light by disordered media composed of independently scattering particles of arbitrary size and shape is studied theoretically Rigorous relations between the cyclical and the ladder parts of the backscattering matrix in exactly the backscattering direction are derived for three commonly used representations of polarization, and the corresponding polarization backscattering enhancement factors are introduced The ladder part of the Stokes-backscattering matrix is calculated by solving Chandrasekhar’s vector radiative transfer equation [ Radiative Transfer ( Clarendon, London, 1950)] The general properties of the enhancement factors are studied, and the results of numerical computations are reported for finite and semi-infinite homogeneous slabs composed of spherical and randomly oriented nonspherical particles It is shown that the enhancement factors depend strongly on the direction of light incidence, the optical thickness of the medium, the true absorption, and the particle size and shape

Two integrating spheres with an intervening scattering sample

Abstract: Two integrating spheres placed so that the exit port of one and the entry port of the other are adjacent, with only a sample intervening, will permit the simultaneous determination of the reflectance and the transmittance of the sample. Such a geometry permits measurements to be made as the sample undergoes some external stimulation, such as heat, pressure, or a chemical change. To determine the sample reflectance and the transmittance from the measured values of irradiance within each sphere requires the calculation of the exchange of light through the sample between the spheres. First the power collected by a detector situated in the wall of an integrating sphere is calculated as a function of the area and the reflectance of the wall, the holes, the sample, and the detector for both diffuse and collimated light incident upon the sample and for a sample located at either the exit port (reflectance) or the entry port (transmittance) of the sphere. Next, by using the single-sphere equations, we calculate the effect of the multiple exchange of light between two integrating spheres arranged so that the sample is placed between them. In all the cases of two integrating spheres the power detected is greater than or equal to that for the single sphere and depends on both the reflection and the transmission properties of the sample. Additionally, the effect of a baffle placed between the sample and the detector or of a nonisotropic detector is to reduce the power detected.

Modeling the power of the aging human eye.

Abstract: A hypothesis is presented that may explain why the aging eye does not become myopic with age. The power of the eye lens is predicted with a modeling approach to determine how the form of the refractive-index gradient within the lens can change to maintain a constant power in spite of age-related curvature increase. Methods used include published age-dependent data on the optical parameters of the eye, a mathematical model of the lens based on elliptical isoindicial contours, and a refractive-index profile that can be expressed as a power series in the distance from the lens center. The kinds of change in profile required to prevent the eye from becoming myopic as its lens grows are shown.

Blind deconvolution of speckle images

Abstract: A technique for deconvolving an image from both a single convolution and an ensemble of differently blurred images is presented. The method is more robust than the earlier blind deconvolution algorithms proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and Davey et al. [ Opt. Commun.69, 353 ( 1989)]. The performance of the algorithm in the presence of noise is evaluated. It is also demonstrated how the algorithm can be modified to utilize the much greater amount of information contained in an ensemble of differently blurred pictures of an image. Reconstructions using both computer simulations and infrared astronomical speckle data are presented. The speckle reconstructions are compared with those obtained by both Fourier phase retrieval and bispectral estimation.

Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams

Abstract: The propagation characteristics of a beam generated by driving an aperture with an ultrashort, hence ultrawide-bandwidth, space–time Gaussian pulse are considered. It is shown analytically with an approximate form of the solution that the beam intensity and the beam energy have different diffraction lengths and rates of beam spread in the far field. These beam properties are also discussed for a derivative receiver system. The analytical results are supported with numerical simulations of the exact pulsed-beam solution.

Diffraction by a circular aperture: a generalization of Fresnel diffraction theory

Abstract: A generalization of the Fresnel approximation in diffraction theory is proposed. The phase term in the diffraction integral is approximated by a paraboloidal variation, not by a binomial expansion but rather by a matching at the critical points in asymptotic evaluation of the integral. The method provides a correction to the optical coordinates of the Fresnel diffraction theory that extends its region of validity. It is applied to diffraction by a circular aperture of a plane wave or focused beam, including effects caused by a large numerical aperture, finite Fresnel number, off-axis illumination, and the presence of aberrations. The method may also be used with other geometries: It is readily applied to cylindrical focusing.

Control of volume holograms

Abstract: The mismatch in the number of degrees of freedom supported by volume holograms and the boundary fields that control them limits the dynamic range of recorded holograms. For holograms controlled by using fractal sampling grids, the maximum dynamic range falls inversely with the minimum number of exposures needed to record the hologram, the rank of the hologram. In adaptive holography, feedback between coupled holograms prevents the dynamic range from decreasing faster than the fundamental limit. If the control problem is overcome, the maximum dynamic range that a hologram can support falls inversely with the square root of the rank. In principle, holograms in which the dynamic range falls inversely with the square root of the rank can be recorded by using cross-spectrally coherent polychromatic pulses.

Tomographic reconstruction from optical scattered intensities

Abstract: A generalized tomographic reconstruction procedure is described for determining the complex-valuedindex-of-refraction distribution of a semitransparent, three-dimensional inhomogeneous object from observations of the far-field intensity patterns generated by the object in a sequence of scattering experiments. The inversion procedure is based on the wave equation governing the scattered optical field and fully accounts for the diffraction and propagation effects associated with the interaction of the incident wave with the object and the subsequent free-space propagation of the scattered wave to the wave zone (far field). The reconstruction of the object’s index-of-refraction distribution is performed digitally directly from the far-field intensity of the scattered wave and does not require direct measurement or retrieval of the phase of the scattered field. An optical scattering experiment is reported in which the cross-sectional profile of the index-of-refraction distribution of an optical fiber is reconstructed from the measured intensity of the diffraction pattern of the fiber by using the described inversion procedure.

Nondiffracting beam from a spatially filtered Fabry-Perot resonator

Abstract: An experiment was performed in which a single ring from a Fabry–Perot transmission fringe pattern was used to create a nondiffracting beam. The transverse and axial intensity distributions of this beam were measured and found to be in good agreement with previously existing and newly derived theoretical expressions. The diffraction-free range was found from calculation to be proportional to the cavity finesse and length, and the central-spot radius of the beam was theoretically shown to be proportional to the square root of the wavelength and cavity length.

Interference of diffusive light waves.

Abstract: We examine interference effects resulting from the superposition of photon-density waves produced by coherently modulated light incident upon a turbid medium Photon-diffusion theory is used to derive expressions for the ac magnitude and phase of the aggregate diffusive wave produced in full- and half-space volumes by two sources Using a frequency-domain spectrometer operating at 410 MHz, we verify interference patterns predicted by the model in scattering samples having optical properties similar to those of skin tissue Potential imaging applications of interfering diffusive waves are discussed in the context of the theoretical and experimental results

Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections.

Abstract: The inverse problem involving the determination of a three-dimensional biological structure from images obtained by means of optical-sectioning microscopy is ill posed. Although the linear least-squares solution can be obtained rapidly by inverse filtering, we show here that it is unstable because of the inversion of small eigenvalues of the microscope's point-spread-function operator. We have regularized the problem by application of the linear-precision-gauge formalism of Joyce and Root [J. Opt. Soc. Am. A 1, 149 (1984)]. In our method the solution is regularized by being constrained to lie in a subspace spanned by the eigenvectors corresponding to a selected number of large eigenvalues. The trade-off between the variance and the regularization error determines the number of eigenvalues inverted in the estimation. The resulting linear method is a one-step algorithm that yields, in a few seconds, solutions that are optimal in the mean-square sense when the correct number of eigenvalues are inverted. Results from sensitivity studies show that the proposed method is robust to noise and to underestimation of the width of the point-spread function. The method proposed here is particularly useful for applications in which processing speed is critical, such as studies of living specimens and time-lapse analyses. For these applications existing iterative methods are impractical without expensive and/or specially designed hardware.