Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2003"

Hierarchical Bayesian inference in the visual cortex

Abstract: Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spatiotemporal filters that extract local features from a visual scene. The extracted information is then channeled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas.

Temporal coupled-mode theory for the Fano resonance in optical resonators

Abstract: We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.

Phase retrieval by iterated projections

Abstract: Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map when a particular choice is made for two of the parameters. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby the form of stagnation encountered by alternating projection schemes is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved.

Bayesian integration of visual and auditory signals for spatial localization

Abstract: Human observers localize events in the world by using sensory signals from multiple modalities. We evaluated two theories of spatial localization that predict how visual and auditory information are weighted when these signals specify different locations in space. According to one theory (visual capture), the signal that is typically most reliable dominates in a winner-take-all competition, whereas the other theory (maximumlikelihood estimation) proposes that perceptual judgments are based on a weighted average of the sensory signals in proportion to each signal’s relative reliability. Our results indicate that both theories are partially correct, in that relative signal reliability significantly altered judgments of spatial location, but these judgments were also characterized by an overall bias to rely on visual over auditory information. These results have important implications for the development of cue integration and for neural plasticity in the adult brain that enables humans to optimally integrate multimodal information. © 2003 Optical Society of America OCIS codes: 330.0330, 330.1400, 330.4060, 330.7320.

Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

Abstract: A novel method for simulating field propagation is presented. The method, based on the angular spectrum of plane waves and coordinate rotation in the Fourier domain, removes geometric limitations posed by conventional propagation calculation and enables us to calculate complex amplitudes of diffracted waves on a plane not parallel to the aperture. This method can be implemented by using the fast Fourier transformation twice and a spectrum interpolation. It features computation time that is comparable with that of standard calculation methods for diffraction or propagation between parallel planes. To demonstrate the method, numerical results as well as a general formulation are reported for a single-axis rotation.

Aberration correction by maximizing generalized sharpness metrics

Abstract: The technique of maximizing sharpness metrics has been used to estimate and compensate for aberrations with adaptive optics, to correct phase errors in synthetic-aperture radar, and to restore images. The largest class of sharpness metrics is the sum over a nonlinear point transformation of the image intensity. How the second derivative of the point nonlinearity varies with image intensity determines the effects of various metrics on the imagery. Some metrics emphasize making shadows darker, and other emphasize making bright points brighter. One can determine the image content needed to pick the best metric by computing the statistics of the image autocorrelation or of the Fourier magnitude, either of which is independent of the phase error. Computationally efficient, closed-form expressions for the gradient make possible efficient search algorithms to maximize sharpness.

Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence

Abstract: The spreading of partially coherent beams propagating through atmospheric turbulence is studied by use of the coherent-mode representation of the beams. Specifically, we consider partially coherent Gaussian Schell-model beams entering the atmosphere, and we examine the spreading of each coherent mode, represented by a Hermite-Gaussian function, on propagation. We find that in atmospheric turbulence the relative spreading of higher-order modes is smaller than that of lower-order modes, whereas the relative spreading of all order modes is the same as in free space. This modal behavior successfully explains why under certain circumstances partially coherent beams are less affected by atmospheric turbulence than are fully spatially coherent laser beams.

Catchment areas of panoramic snapshots in outdoor scenes

Abstract: We took panoramic snapshots in outdoor scenes at regular intervals in two- or three-dimensional grids covering 1 m2 or 1 m3 and determined how the root mean square pixel differences between each of the images and a reference image acquired at one of the locations in the grid develop over distance from the reference position We then asked whether the reference position can be pinpointed from a random starting position by moving the panoramic imaging device in such a way that the image differences relative to the reference image are minimized We find that on time scales of minutes to hours, outdoor locations are accurately defined by a clear, sharp minimum in a smooth three-dimensional (3D) volume of image differences (the 3D difference function) 3D difference functions depend on the spatial-frequency content of natural scenes and on the spatial layout of objects therein They become steeper in the vicinity of dominant objects Their shape and smoothness, however, are affected by changes in illumination and shadows The difference functions generated by rotation are similar in shape to those generated by translation, but their plateau values are higher Rotational difference functions change little with distance from the reference location Simple gradient descent methods are surprisingly successful in recovering a goal location, even if faced with transient changes in illumination Our results show that view-based homing with panoramic images is in principle feasible in natural environments and does not require the identification of individual landmarks We discuss the relevance of our findings to the study of robot and insect homing

Modeling global scene factors in attention.

Abstract: Models of visual attention have focused predominantly on bottom-up approaches that ignored structured contextual and scene information. I propose a model of contextual cueing for attention guidance based on the global scene configuration. It is shown that the statistics of low-level features across the whole image can be used to prime the presence or absence of objects in the scene and to predict their location, scale, and appearance before exploring the image. In this scheme, visual context information can become available early in the visual processing chain, which allows modulation of the saliency of image regions and provides an efficient shortcut for object detection and recognition.

Statistical decision theory and the selection of rapid, goal-directed movements

Abstract: We present two experiments that test the range of applicability of a movement planning model (MEGaMove) based on statistical decision theory. Subjects attempted to earn money by rapidly touching a green target region on a computer screen while avoiding nearby red penalty regions. In two experiments we varied the magnitudes of penalties, the degree of overlap of target and penalty regions, and the number of penalty regions. Overall, subjects acted so as to maximize gain in a wide variety of stimulus configurations, in good agreement with predictions of the model.

Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions.

Abstract: A detailed study of time-averaged electromagnetic forces on subwavelength-sized particles is presented. An analytical decomposition of the force into gradient and scattering-plus-absorption components is carried out, on the basis of which the attractive or repulsive behavior of the force is explained. Small metallic particles are shown to experience both kinds of forces; which kind also depends on the excitation of surface plasmons. Resonances give rise to enhancements of both the scattering and the absorption forces, but the gradient force can become negligible. Also, close to resonant wavelengths, the gradient force can be maximum, while both the scattering and the absorption forces remain large. Comparisons of analytic results with rigorous calculations allow the establishment of ranges of validity of the dipolar approximation for these forces.

Hybrid projection–reflection method for phase retrieval

Abstract: The phase-retrieval problem, fundamental in applied physics and engineering, addresses the question of how to determine the phase of a complex-valued function from modulus data and additional a priori information. Recently we identified two important methods for phase retrieval, namely, Fienup's basic input-output and hybrid input-output (HIO) algorithms, with classical convex projection methods and suggested that further connections between convex optimization and phase retrieval should be explored. Following up on this work, we introduce a new projection-based method, termed the hybrid projection-reflection (HPR) algorithm, for solving phase-retrieval problems featuring nonnegativity constraints in the object domain. Motivated by properties of the HPR algorithm for convex constraints, we recommend an error measure studied by Fienup more than 20 years ago. This error measure, which has received little attention in the literature, lends itself to an easily implementable stopping criterion. In numerical experiments we found the HPR algorithm to be a competitive alternative to the HIO algorithm and the stopping criterion to be reliable and robust.

Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity

Abstract: Temporal frame-to-frame noise in multipattern structured light projection can significantly corrupt depth measurement repeatability. We present a rigorous stochastic analysis of phase-measuring-profilometry temporal noise as a function of the pattern parameters and the reconstruction coefficients. The analysis is used to optimize the two-frequency phase measurement technique. In phase-measuring profilometry, a sequence of phase-shifted sine-wave patterns is projected onto a surface. In two-frequency phase measurement, two sets of pattern sequences are used. The first, low-frequency set establishes a nonambiguous depth estimate, and the second, high-frequency set is unwrapped, based on the low-frequency estimate, to obtain an accurate depth estimate. If the second frequency is too low, then depth error is caused directly by temporal noise in the phase measurement. If the second frequency is too high, temporal noise triggers ambiguous unwrapping, resulting in depth measurement error. We present a solution for finding the second frequency, where intensity noise variance is at its minimum.

Atmospheric optical communication with a Gaussian Schell beam.

Abstract: We consider a wireless optical communication link in which the laser source is a Gaussian Schell beam. The effects of atmospheric turbulence strength and degree of source spatial coherence on aperture averaging and average bit error rate are examined. To accomplish this, we have derived analytic expressions for the spatial covariance of irradiance fluctuations and log-intensity variance for a Gaussian beam of any degree of coherence in the weak fluctuation regime. When spatial coherence of the transmitted source beam is reduced, intensity fluctuations (scintillations) decrease, leading to a significant reduction in the bit error rate of the optical communication link. We have also identified an enhanced aperture-averaging effect that occurs in tightly focused coherent Gaussian beams and in collimated and slightly divergent partially coherent beams. The expressions derived provide a useful design tool for selecting the optimal transmitter beam size, receiver aperture size, beam spatial coherence, transmitter focusing, etc., for the anticipated atmospheric channel conditions.

Kalman filtering for adaptive nonuniformity correction in infrared focal-plane arrays.

Abstract: A novel statistical approach is undertaken for the adaptive estimation of the gain and bias nonuniformity in infrared focal-plane array sensors from scene data. The gain and the bias of each detector are regarded as random state variables modeled by a discrete-time Gauss–Markov process. The proposed Gauss–Markov framework provides a mechanism for capturing the slow and random drift in the fixed-pattern noise as the operational conditions of the sensor vary in time. With a temporal stochastic model for each detector’s gain and bias at hand, a Kalman filter is derived that uses scene data, comprising the detector’s readout values sampled over a short period of time, to optimally update the detector’s gain and bias estimates as these parameters drift. The proposed technique relies on a certain spatiotemporal diversity condition in the data, which is satisfied when all detectors see approximately the same range of temperatures within the periods between successive estimation epochs. The performance of the proposed technique is thoroughly studied, and its utility in mitigating fixed-pattern noise is demonstrated with both real infrared and simulated imagery.

Propagating modes in gain-guided optical fibers.

Abstract: Optical fibers in which gain-guiding effects are significant or even dominant compared with conventional index guiding may become of practical interest for future high-power single-mode fiber lasers. I derive the propagation characteristics of symmetrical slab waveguides and cylindrical optical fibers having arbitrary amounts of mixed gain and index guiding, assuming a single uniform transverse profile for both the gain and the refractive-index steps. Optical fibers of this type are best characterized by using a complex-valued v-squared parameter in place of the real-valued v parameter commonly used to describe conventional index-guided optical fibers.

Validating the use of channels to estimate the ideal linear observer

Abstract: Image quality can be objectively defined according to how well an observer can perform a task of practical interest given the image. We review a practical model observer for the signal-detection task. The ideal observer for this task is a function of the image probability distributions, which are multidimensional and complicated. This observer is often too difficult to derive or estimate. An alternative to the ideal observer is the ideal linear observer, which can still be unmanageable. Our alternative is the ideal linear observer constrained to a small set of channels: the channelized-Hotelling observer.

Optical aberrations of intraocular lenses measured in vivo and in vitro.

Abstract: Corneal and ocular aberrations were measured in a group of eyes before and after cataract surgery with spherical intraocular lens (IOL) implantation by use of well-tested techniques developed in our laboratory. By subtraction of corneal from total aberration maps, we also estimated the optical quality of the intraocular lens in vivo. We found that aberrations in pseudophakic eyes are not significantly different from aberrations in eyes before cataract surgery or from previously reported aberrations in healthy eyes of the same age. However, aberrations in pseudophakic eyes are significantly higher than in young eyes. We found a slight increase of corneal aberrations after surgery. The aberrations of the IOL and the lack of balance of the corneal spherical aberrations by the spherical aberrations of the intraocular lens also degraded the optical quality in pseudophakic eyes. We also measured the aberrations of the IOL in vitro, using an eye cell model, and simulated the aberrations of the IOL on the basis of the IOL's physical parameters. We found a good agreement among in vivo, in vitro, and simulated measures of spherical aberration: Unlike the spherical aberration of the young crystalline lens, which tends to be negative, the spherical aberration of the IOL is positive and increases with lens power. Computer simulations and in vitro measurements show that tilts and decentrations might be contributors to the increased third-order aberrations in vivo in comparison with in vitro measurements.

Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond.

Abstract: We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell’s equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.

Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging.

Abstract: We deduce the signal-to-noise ratio for fluorescence lifetime imaging when using frequency-domain methods. We assume mono-exponential decay and quantum-noise-limited performance. The results are compared with Monte Carlo simulations with good agreement. We also compare our results with previous investigations of time-domain methods for fluorescence lifetime imaging. For a given number of detected photons, we find that frequency-domain and time-domain methods are equally good. The correct choice of detection technique and its parameters is important for obtaining good results.

Bubbles: a unifying framework for low-level statistical properties of natural image sequences

Abstract: Recently, different models of the statistical structure of natural images have been proposed. These models predict properties of biological visual systems and can be used as priors in Bayesian inference. The fundamental model is independent component analysis, which can be estimated by maximization of the sparsenesses of linear filter outputs. This leads to the emergence of principal simple cell properties. Alternatively, simple cell properties are obtained by maximizing the temporal coherence in natural image sequences. Taking account of the basic dependencies of linear filter outputs permit modeling of complex cells and topographic organization as well. We propose a unifying framework for these statistical properties, based on the concept of spatiotemporal activity “bubbles.” A bubble means here an activation of simple cells (linear filters) that is contiguous both in space (the cortical surface) and in time.

Note on the S-matrix propagation algorithm

Abstract: A set of full-matrix recursion formulas for the W→S variant of the S-matrix algorithm is derived, which includes the recent results of some other authors as a subset. In addition, a special type of symmetry that is often found in the structure of coefficient matrices (W matrices) that appear in boundary-matching conditions is identified and fully exploited for the purpose of increasing computation efficiency. Two tables of floating-point operation (flop) counts for both the new W→S variant and the old W→t→S variant of the S-matrix algorithm are given. Comparisons of flop counts show that in performing S-matrix recursions in the absence of the symmetry, it is more efficient to go directly from W matrices to S matrices. In the presence of the symmetry, however, using t matrices is equally and sometimes more advantageous, provided that the symmetry is utilized.

Integrated color pixels in 0.18-microm complementary metal oxide semiconductor technology.

Abstract: Following the trend of increased integration in complementary metal oxide semiconductor (CMOS) image sensors, we have explored the potential of implementing light filters by using patterned metal layers placed on top of each pixel’s photodetector. To demonstrate wavelength selectivity, we designed and prototyped integrated color pixels in a standard 0.18-µm CMOS technology. Transmittance of several one-dimensional (1D) and two-dimensional (2D) patterned metal layers was measured under various illumination conditions and found to exhibit wavelength selectivity in the visible range. We performed (a) wave optics simulations to predict the spectral responsivity of an uncovered reference pixel and (b) numerical electromagnetic simulations with a 2D finite-difference time-domain method to predict transmittances through 1D patterned metal layers. We found good agreement in both cases. Finally, we used simulations to predict the transmittance for more elaborate designs.

Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues

Abstract: Two efficient Monte Carlo models are described, facilitating predictions of complete time-resolved fluorescence spectra from a light-scattering and light-absorbing medium. These are compared with a third, conventional fluorescence Monte Carlo model in terms of accuracy, signal-to-noise statistics, and simulation time. The improved computation efficiency is achieved by means of a convolution technique, justified by the symmetry of the problem. Furthermore, the reciprocity principle for photon paths, employed in one of the accelerated models, is shown to simplify the computations of the distribution of the emitted fluorescence drastically. A so-called white Monte Carlo approach is finally suggested for efficient simulations of one excitation wavelength combined with a wide range of emission wavelengths. The fluorescence is simulated in a purely scattering medium, and the absorption properties are instead taken into account analytically afterward. This approach is applicable to the conventional model as well as to the two accelerated models. Essentially the same absolute values for the fluorescence integrated over the emitting surface and time are obtained for the three models within the accuracy of the simulations. The time-resolved and spatially resolved fluorescence exhibits a slight overestimation at short delay times close to the source corresponding to approximately two grid elements for the accelerated models, as a result of the discretization and the convolution. The improved efficiency is most prominent for the reverse-emission accelerated model, for which the simulation time can be reduced by up to two orders of magnitude.

Coherent-mode decomposition of partially polarized, partially coherent sources.

Abstract: It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

Circularly polarized beams and vortex generation in uniaxial media.

Abstract: We deduce the expressions for the two circularly polarized components of a paraxial beam propagating along the optical axis of a uniaxial crystal. We find that each of them is the sum of two contributions, the first being a free field and the second describing the interaction with the opposite component. Moreover, we expand both components as a superposition of vortices of any order, thus obtaining a complete physical picture of the interaction dynamics. Consequently, we argue that a left-hand circularly polarized incoming beam, endowed with a circular symmetric profile, gives rise, inside the crystal, to a right-hand circularly polarized vortex of order 2. The efficiency of this vortex generation is investigated by means of a power exchange analysis. The Gaussian case is fully discussed, showing the relevant features of the vortex generation.

Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams

Abstract: Two forms of the transverse energy circulation within plane-polarized paraxial light beams are specified: one inherent in wave-front singularities (optical vortices) and the other peculiar to astigmatism and asymmetry of beams with a smooth wave front. As quantitative measures of these energy flow components, the concepts of vortex and asymmetry parts of a beam's orbital angular momentum are introduced and their definitions are proposed on the basis of beam intensity moments. The properties and physical meaning of these concepts are analyzed, and their use for the study of transformations of optical vortices is demonstrated.

Multidistortion-invariant image recognition with radial harmonic Fourier moments

Abstract: We propose radial harmonic Fourier moments, which are shifting, scaling, rotation, and intensity invariant Compared with Chebyshev–Fourier moments, the new moments have superior performance near the origin and better ability to describe small images in terms of image-reconstruction errors and noise sensitivity A multidistortion-invariant pattern-recognition experiment was performed with radial harmonic Fourier moments

Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques.

Abstract: The ideal observer sets an upper limit on the performance of an observer on a detection or classification task. The performance of the ideal observer can be used to optimize hardware components of imaging systems and also to determine another observer’s relative performance in comparison with the best possible observer. The ideal observer employs complete knowledge of the statistics of the imaging system, including the noise and object variability. Thus computing the ideal observer for images (large-dimensional vectors) is burdensome without severely restricting the randomness in the imaging system, e.g., assuming a flat object. We present a method for computing the ideal-observer test statistic and performance by using Markov-chain Monte Carlo techniques when we have a well-characterized imaging system, knowledge of the noise statistics, and a stochastic object model. We demonstrate the method by comparing three different parallel-hole collimator imaging systems in simulation.

Action spectrum for photophobia.

Abstract: Thresholds for photophobia (light-induced discomfort) were determined at wavelengths from 440 to 640 nm for three subjects. Photophobia was assessed by means of electromyography, which was used to measure subjects' level of squinting. After correction for absorption by macular pigment and the ocular media, subjects' functions displayed a trend of increasing sensitivity with decreasing wavelength. We propose that the corrected function is indicative of increased sensitivity to potential retinal damage by short-wavelength light. It is therefore suggested that photophobia serves a function of biological protection. Results also suggest that photophobia is significantly mitigated by macular pigment in the short wavelengths.