Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2001"

Material parameter estimation with terahertz time-domain spectroscopy

Abstract: Imaging systems based on terahertz (THz) time-domain spectroscopy offer a range of unique modalities owing to the broad bandwidth, subpicosecond duration, and phase-sensitive detection of the THz pulses. Furthermore, the possibility exists for combining spectroscopic characterization or identification with imaging because the radiation is broadband in nature. To achieve this, we require novel methods for real-time analysis of THz waveforms. This paper describes a robust algorithm for extracting material parameters from measured THz waveforms. Our algorithm simultaneously obtains both the thickness and the complex refractive index of an unknown sample under certain conditions. In contrast, most spectroscopic transmission measurements require knowledge of the sample's thickness for an accurate determination of its optical parameters. Our approach relies on a model-based estimation, a gradient descent search, and the total variation measure. We explore the limits of this technique and compare the results with literature data for optical parameters of several different materials.

Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization

Abstract: Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.

Monochromatic aberrations of the human eye in a large population.

Abstract: From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eye's aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann-Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eye's aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eye's wave aberration. Even though there appears to be a random variation in the eye's aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform.

Abstract: It is widely believed, in the areas of optics, image analysis, and visual perception, that the Hilbert transform does not extend naturally and isotropically beyond one dimension. In some areas of image analysis, this belief has restricted the application of the analytic signal concept to multiple dimensions. We show that, contrary to this view, there is a natural, isotropic, and elegant extension. We develop a novel two-dimensional transform in terms of two multiplicative operators: a spiral phase spectral (Fourier) operator and an orientational phase spatial operator. Combining the two operators results in a meaningful two-dimensional quadrature (or Hilbert) transform. The new transform is applied to the problem of closed fringe pattern demodulation in two dimensions, resulting in a direct solution. The new transform has connections with the Riesz transform of classical harmonic analysis. We consider these connections, as well as others such as the propagation of optical phase singularities and the reconstruction of geomagnetic fields.

On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object

Abstract: We present a theoretical analysis of the relationship between incoming radiance and irradiance. Specifically, we address the question of whether it is possible to compute the incident radiance from knowledge of the irradiance at all surface orientations. This is a fundamental question in computer vision and inverse radiative transfer. We show that the irradiance can be viewed as a simple convolution of the incident illumination, i.e., radiance and a clamped cosine transfer function. Estimating the radiance can then be seen as a deconvolution operation. We derive a simple closed-form formula for the irradiance in terms of spherical harmonic coefficients of the incident illumination and demonstrate that the odd-order modes of the lighting with order greater than 1 are completely annihilated. Therefore these components cannot be estimated from the irradiance, contradicting a theorem that is due to Preisendorfer. A practical realization of the radiance-from-irradiance problem is the estimation of the lighting from images of a homogeneous convex curved Lambertian surface of known geometry under distant illumination, since a Lambertian object reflects light equally in all directions proportional to the irradiance. We briefly discuss practical and physical considerations and describe a simple experimental test to verify our theoretical results.

Dynamics of the eye’s wave aberration

Abstract: It is well known that the eye’s optics exhibit temporal instability in the form of microfluctuations in focus; however, almost nothing is known of the temporal properties of the eye’s other aberrations. We constructed a real-time Hartmann–Shack (HS) wave-front sensor to measure these dynamics at frequencies as high as 60 Hz. To reduce spatial inhomogeneities in the short-exposure HS images, we used a low-coherence source and a scanning system. HS images were collected on three normal subjects with natural and paralyzed accommodation. Average temporal power spectra were computed for the wave-front rms, the Seidel aberrations, and each of 32 Zernike coefficients. The results indicate the presence of fluctuations in all of the eye’s aberration, not just defocus. Fluctuations in higher-order aberrations share similar spectra and bandwidths both within and between subjects, dropping at a rate of approximately 4 dB per octave in temporal frequency. The spectrum shape for higher-order aberrations is generally different from that for microfluctuations of accommodation. The origin of these measured fluctuations is not known, and both corneal/lenticular and retinal causes are considered. Under the assumption that they are purely corneal or lenticular, calculations suggest that a perfect adaptive optics system with a closed-loop bandwidth of 1–2 Hz could correct these aberrations well enough to achieve diffraction-limited imaging over a dilated pupil.

Use of grating theories in integrated optics.

Abstract: Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.

Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability.

Abstract: We consider detection of a nodule signal profile in noisy images meant to roughly simulate the statistical properties of tomographic image reconstructions in nuclear medicine. The images have two sources of variability arising from quantum noise from the imaging process and anatomical variability in the ensemble of objects being imaged. Both of these sources of variability are simulated by a stationary Gaussian random process. Sample images from this process are generated by filtering white-noise images. Human-observer performance in several signal-known-exactly detection tasks is evaluated through psychophysical studies by using the two-alternative forced-choice method. The tasks considered investigate parameters of the images that influence both the signal profile and pixel-to-pixel correlations in the images. The effect of low-pass filtering is investigated as an approximation to regularization implemented by image-reconstruction algorithms. The relative magnitudes of the quantum and the anatomical variability are investigated as an approximation to the effects of exposure time. Finally, we study the effect of the anatomical correlations in the form of an anatomical slope as an approximation to the effects of different tissue types. Human-observer performance is compared with the performance of a number of model observers computed directly from the ensemble statistics of the images used in the experiments for the purpose of finding predictive models. The model observers investigated include a number of nonprewhitening observers, the Hotelling observer (which is equivalent to the ideal observer for these studies), and six implementations of channelized-Hotelling observers. The human observers demonstrate large effects across the experimental parameters investigated. In the regularization study, performance exhibits a mild peak at intermediate levels of regularization before degrading at higher levels. The exposure-time study shows that human observers are able to detect ever more subtle lesions at increased exposure times. The anatomical slope study shows that human-observer performance degrades as anatomical variability extends into higher spatial frequencies. Of the observers tested, the channelized-Hotelling observers best capture the features of the human data.

Three-systems theory of human visual motion perception: review and update

Abstract: Lu and Sperling [Vision Res. 35, 2697 (1995)] proposed that human visual motion perception is served by three separate motion systems: a first-order system that responds to moving luminance patterns, a second-order system that responds to moving modulations of feature types—stimuli in which the expected luminance is the same everywhere but an area of higher contrast or of flicker moves, and a third-order system that computes the motion of marked locations in a ‘‘salience map,’’ that is, a neural representation of visual space in which the locations of important visual features (‘‘figure’’) are marked and ‘‘ground’’ is unmarked. Subsequently, there have been some strongly confirmatory reports: different gain-control mechanisms for first- and second-order motion, selective impairment of first- versus second- and/or third-order motion by different brain injuries, and the classification of new third-order motions, e.g., isoluminant chromatic motion. Various procedures have successfully discriminated between second- and third-order motion (when first-order motion is excluded): dual tasks, second-order reversed phi, motion competition, and selective adaptation. Meanwhile, eight apparent contradictions to the three-systems theory have been proposed. A review and reanalysis here of the new evidence, pro and con, resolves the challenges and yields a more clearly defined and significantly strengthened theory. © 2001 Optical Society of America OCIS codes: 330.4150.

Macular pigment density measured by autofluorescence spectrometry: comparison with reflectometry and heterochromatic flicker photometry.

Abstract: We present a technique for estimating the density of the human macular pigment noninvasively that takes advantage of the autofluorescence of lipofuscin, which is normally present in the human retinal pigment epithelium. By measuring the intensity of fluorescence at 710 nm, where macular pigment has essentially zero absorption, and stimulating the fluorescence with two wavelengths, one well absorbed by macular pigment and the other minimally absorbed by macular pigment, we can make accurate single-pass measurements of the macular pigment density. We used the technique to measure macular pigment density in a group of 159 subjects with normal retinal status ranging in age between 15 and 80 years. Average macular pigment density was 0.48 ± 0.16 density unit (D.U.) for a 2°-diameter test field. We show that these estimates are highly correlated with reflectometric (mean: 0.23±0.07 D.U.) and psychophysical (mean: 0.37±0.26 D.U.; obtained by heterochromatic flicker photometry) estimates of macular pigment in the same subjects, despite the fact that systematic differences in the estimated density exist between techniques. Repeat measurements over both short- and long-time intervals indicate that the autofluorescence technique is reproducible: The mean absolute difference between estimates was less than 0.05 D.U., superior to the reproducibility obtained by reflectometry and flicker photometry. To understand the systematic differences between density estimates obtained from the different methods, we analyzed the underlying assumptions of each technique. Specifically, we looked at the effect of self-screening by visual pigment, the effect of changes in optical property of the deeper retinal layers, including the role of retinal pigmented epithelium melanin, and the role of secondary fluorophores and reflectors in the anterior layers of the retina.

Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations

Abstract: An ideal correcting method, such as a customized contact lens, laser refractive surgery, or adaptive optics, that corrects higher-order aberrations as well as defocus and astigmatism could improve vision The benefit achieved with this ideal method will be limited by decentration To estimate the significance of this potential limitation we studied the effect on image quality expected when an ideal correcting method translates or rotates with respect to the eye’s pupil Actual wave aberrations were obtained from ten human eyes for a 73-mm pupil with a Shack–Hartmann sensor We computed the residual aberrations that appear as a result of translation or rotation of an otherwise ideal correction The model is valid for adaptive optics, contact lenses, and phase plates, but it constitutes only a first approximation to the laser refractive surgery case where tissue removal occurs Calculations suggest that the typical decentrations will reduce only slightly the optical benefits expected from an ideal correcting method For typical decentrations the ideal correcting method offers a benefit in modulation 2–4 times higher (15–2 times in white light) than with a standard correction of defocus and astigmatism We obtained analytical expressions that show the impact of translation and rotation on individual Zernike terms These calculations also reveal which aberrations are most beneficial to correct We provided practical rules to implement a selective correction depending on the amount of decentration An experimental study was performed with an aberrated artificial eye corrected with an adaptive optics system, validating the theoretical predictions The results in a keratoconic subject, also corrected with adaptive optics, showed that important benefits are obtained despite decentrations in highly aberrated eyes

Color constancy at a pixel.

Abstract: In computational terms we can solve the color constancy problem if device red, green, and blue sensor responses, or RGB’s, for surfaces seen under an unknown illuminant can be mapped to corresponding RGB’s under a known reference light. In recent years almost all authors have argued that this three-dimensional problem is too hard. It is argued that because a bright light striking a dark surface results in the same physical spectra as those of a dim light incident on a light surface, the magnitude of RGB’s cannot be recovered. Consequently, modern color constancy algorithms attempt only to recover image chromaticities under the reference light: They solve a two-dimensional problem. While significant progress has been made toward achieving chromaticity constancy, recent work has shown that the most advanced algorithms are unable to render chromaticity stable enough so that it can be used as a cue for object recognition [ B. V. Funt K. Bernard L. Martin , in Proceedings of the Fifth European Conference on Computer Vision (European Vision Society, Springer-Verlag, Berlin, 1998), Vol. II, p. 445.] We take this reductionist approach a little further and look at the one-dimensional color constancy problem. We ask, Is there a single color coordinate, a function of image chromaticities, for which the color constancy problem can be solved? Our answer is an emphatic yes. We show that there exists a single invariant color coordinate, a function of R, G, and B, that depends only on surface reflectance. Two corollaries follow. First, given an RGB image of a scene viewed under any illuminant, we can trivially synthesize the same gray-scale image (we simply code the invariant coordinate as a gray scale). Second, this result implies that we can solve the one-dimensional color constancy problem at a pixel (in scenes with no color diversity whatsoever). We present experiments that show that invariant gray-scale histograms are a stable feature for object recognition. Indexing on invariant distributions supports almost perfect recognition for a dataset of 11 objects viewed under five colored lights. In contrast, object recognition based on chromaticity histograms (post-color constancy preprocessing) delivers much poorer recognition.

A class of partially coherent beams carrying optical vortices.

Abstract: A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.

Role of light intensification by cracks in optical breakdown on surfaces.

Abstract: The intensity distribution of an initially plane light wave incident on planar and conical surface cracks is calculated numerically by using a wave propagation computer code. The results show that light intensity enhancements caused by interference of internal reflections at the crack and the surface are very sensitive to the light polarization, the beam angle of incidence, and the crack geometry (e.g., crack width and orientation with the surface). The light intensity enhancement factor (LIEF) can locally reach 2 orders of magnitude for conical cracks of ideal shape. The electric field direction relative to the crack surfaces determines the light intensity profile around the crack. For normal-incidence illumination on the output surface, total internal reflection at the crack and the surface can occur and leads to higher LIEFs. For identical geometry and illumination conditions, a crack located on the entrance surface of an optic generates electric field enhancements that are weaker than those on the exit surface. As cracks on polished surfaces are randomly oriented, the probability for large intensity enhancements to occur is high. The model is able to predict quantitatively the magnitude of surface laser-induced damage threshold drop and damage propagation enhancement in dielectric materials that are due to cracks.

Optical trapping of dielectric particles in arbitrary fields.

Abstract: We present a new method to calculate trapping forces of dielectric particles with diameters D < or = lambda in arbitrary electromagnetic, time-invariant fields. The two components of the optical force, the gradient force and the scattering force, are determined separately. Both the arbitrary incident field and the scatterer are represented by plane-wave spectra. The scattering force is determined by means of the momentum transfer in either single- or double-scattering processes. Therefore the second-order Born series is evaluated and solved in the frequency domain by Ewald constructions. Numerical results of our two-force-component approach and an established calculation method are compared and show satisfying agreement. Our procedure is applied to investigate axial trapping by focused waves experiencing effects of aperture illumination and refractive-index mismatch.

Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media.

Abstract: We establish the most general differential equations that are satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived by use of the recently published fast-Fourier-factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classic isotropic gratings arises as a particular case of the derived equations; the case of anisotropic classic gratings was published elsewhere. The equations can be resolved either through classic differential theory or through the modal method for particular groove profiles. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two-dimensional arbitrarily shaped periodic surfaces, appear as particular cases of the theory, as do three-dimensional photonic crystals. The method can be extended to nonperiodic media through the use of a Fourier transform.

Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics.

Abstract: Paraxial Gaussian beams (GB’s) are collimated wave objects that have found wide application in optical system analysis and design. A GB propagates in physical space according to well-established quasi-geometric-optical rules that can accommodate weakly inhomogeneous media as well as reflection from and transmission through curved interfaces and thin-lens configurations. We examine the GB concept from a broad perspective in the frequency domain (FD) and the short-pulse time domain (TD) and within as well as arbitrarily beyond the paraxial constraint. For the formal analysis, which is followed by physics-matched high-frequency asymptotics, we use a (space–time)–(wavenumber–frequency) phase-space format to discuss the exact complex-source-point method and the associated asymptotic beam tracking by means of complex rays, the TD pulsed-beam (PB) ultrawideband wave-packet counterpart of the FD GB, GB’s and PB’s as basis functions for representing arbitrary fields, GB and PB diffraction, and FD–TD radiation from extended continuous aperture distributions in which the GB and the PB bases, installed through windowed transforms, yield numerically compact physics-matched a priori localization in the plane-wave-based nonwindowed spectral representations.

Optimal wave-front reconstruction strategies for multiconjugate adaptive optics.

Abstract: We propose an optimal approach for the phase reconstruction in a large field of view (FOV) for multiconjugate adaptive optics. This optimal approach is based on a minimum-mean-square-error estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the Cn2 profile in order to optimally estimate the correction wave front to be applied to each deformable mirror (DM). This optimal approach also accounts for the fact that the number of DMs will always be smaller than the number of turbulent layers, since the Cn2 profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consists of a full tomographic reconstruction of the turbulence volume followed by a projection onto the DMs accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions [model-approximation (MA) approach], which might be a crude approximation, is also considered for comparison. This MA approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and MA approaches is proposed. It is shown that the optimal approach provides very good performance even with a small number of DMs (typically, one or two). For instance, good Strehl ratios (greater than 20%) are obtained for a 4-m telescope on a 150-arc sec×150-arc sec FOV by using only three guide stars and two DMs.

Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform.

Abstract: Utilizing the asymptotic method of stationary phase, I derive expressions for the Fourier transform of a two-dimensional fringe pattern. The method assumes that both the amplitude and the phase of the fringe pattern are well-behaved differentiable functions. Applying the limits in two distinct ways, I show, first, that the spiral phase (or vortex) transform approaches the ideal quadrature transform asymptotically and, second, that the approximation errors increase with the relative curvature of the fringes. The results confirm the validity of the recently proposed spiral phase transform method for the direct demodulation of closed fringe patterns.

Optical tomographic imaging of dynamic features of dense-scattering media

Abstract: Methods used in optical tomography have thus far proven to produce images of complex target media (e.g., tissue) having, at best, relatively modest spatial resolution. This presents a challenge in differentiating artifact from true features. Further complicating such efforts is the expectation that the optical properties of tissue for any individual are largely unknown and are likely to be quite variable due to the occurrence of natural vascular rhythms whose amplitudes are sensitive to a host of autonomic stimuli that are easily induced. We recognize, however, that rather than frustrating efforts to validate the accuracy of image features, the time-varying properties of the vasculature can be exploited to aid in such efforts, owing to the known structure-dependent frequency response of the vasculature and to the fact that hemoglobin is a principal contrast feature of the vasculature at near-infrared wavelengths. To accomplish this, it is necessary to generate a time series of image data. In this report we have tested the hypothesis that through analysis of time-series data, independent contrast features can be derived that serve to validate, at least qualitatively, the accuracy of imaging data, in effect establishing a self-referencing scheme. A significant finding is the observation that analysis of such data can produce high-contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data. Given the central role of hemoglobin in tissue function, this finding suggests that a wealth of new features associated with vascular dynamics can be identified from the analysis of time-series image data.

Accuracy of velocity estimation by Reichardt correlators.

Abstract: Although a great deal of experimental evidence supports the notion of a Reichardt correlator as a mechanism for biological motion detection, the correlator does not signal true image velocity. This study examines the accuracy with which realistic Reichardt correlators can provide velocity estimates in an organism’s natural visual environment. The predictable statistics of natural images imply a consistent correspondence between mean correlator response and velocity, allowing the otherwise ambiguous Reichardt correlator to act as a practical velocity estimator. Analysis and simulations suggest that processes commonly found in visual systems, such as prefiltering, response compression, integration, and adaptation, improve the reliability of velocity estimation and expand the range of velocities coded. Experimental recordings confirm our predictions of correlator response to broadband images.

Primate retina imaging with polarization-sensitive optical coherence tomography

Abstract: Polarization-sensitive optical coherence tomography (PSOCT) is applied to determine the depth-resolved polarization state of light backreflected from the eye. The birefringence of the retinal nerve fiber layer (RNFL) was observed and measured from PSOCT images recorded postmortem in a Rhesus monkey. An image-processing algorithm was developed to identify birefringent regions in acquired PSOCT retinal images and automatically determine the thickness of the RNFL. Values of the RNFL thickness determined from histology and PSOCT were compared. PSOCT may provide a new method to determine RNFL thickness and birefringence for glaucoma diagnostics.

Ideal cue combination for localizing texture-defined edges

Abstract: Many visual tasks can be carried out by using several sources of information. The most accurate estimates of scene properties require the observer to utilize all available information and to combine the information sources in an optimal manner. Two experiments are described that required the observers to judge the relative locations of two texture-defined edges (a vernier task). The edges were signaled by a change across the edge of two texture properties [either frequency and orientation (Experiment 1) or contrast and orientation (Experiment 2)]. The reliability of each cue was controlled by varying the distance over which the change (in frequency, orientation, or contrast) occurred—a kind of “texture blur.” In some conditions, the position of the edge signaled by one cue was shifted relative to the other (“perturbation analysis”). An ideal-observer model, previously used in studies of depth perception and color constancy, was fitted to the data. Although the fit can be rejected relative to some more elaborate models, especially given the large quantity of data, this model does account for most trends in the data. A second, suboptimal model that switches between the available cues from trial to trial does a poor job of accounting for the data.

Information limit on the spatial integration of local orientation signals.

Abstract: Channel-based models of human spatial vision require that the output of spatial filters be pooled across space. This pooling yields global estimates of local feature attributes such as orientation that are useful in situations in which that attribute may be locally variable, as is the case for visual texture. The spatial characteristics of orientation summation are considered in the study. By assessing the effect of orientation variability on observers' ability to estimate the mean orientation of spatially unstructured textures, one can determine both the internal noise on each orientation sample and the number of samples being pooled. By a combination of fixing and covarying the size of textured regions and the number of elements constituting them, one can then assess the effects of the texture's size, density, and numerosity (the number of elements present) on the internal noise and the sampling density. Results indicate that internal noise shows a primary dependence on texture density but that, counterintuitively, subjects rely on a sample size approximately equal to a fixed power of the number of samples present, regardless of their spatial arrangement. Orientation pooling is entirely flexible with respect to the position of input features.

Vectorial theory of propagation in uniaxially anisotropic media.

Abstract: We describe propagation in a uniaxially anisotropic medium by relying on a suitable plane-wave angular-spectrum representation of the electromagnetic field. We obtain paraxial expressions for both ordinary and extraordinary components that satisfy two decoupled parabolic equations. As an application, we obtain, for a particular input beam (a quasi-Gaussian beam), analytical results that allow us to identify some relevant features of propagation in uniaxial crystals.

Color and spectral analysis of daylight in southern Europe.

Abstract: We have analyzed the colorimetric and spectral characteristics of 2600 daylight spectra (global spectral irradiances on a horizontal surface) measured for all sky states during a 2-year period at Granada, Spain. We describe in detail the chromaticity coordinates, correlated color temperatures (CCT), luminous efficacies, and relative UV and IR contents of Granada daylight. The chromaticity coordinates of Granada daylight lie far above the CIE locus at high CCTs (>9,000 K), and a CCT of 5,700 K best typifies this daylight. Our principal-components analysis shows that Granada daylight spectra can be adequately represented by using six-dimensional linear models in the visible, whereas seven-dimensional models are required if we include the UV or near-IR. Yet on average only three-dimensional models are needed to reconstruct spectra that are colorimetrically indistinguishable from the original spectra.

Physics-based approach to color image enhancement in poor visibility conditions

Abstract: Degradation of images by the atmosphere is a familiar problem. For example, when terrain is imaged from a forward-looking airborne camera, the atmosphere degradation causes a loss in both contrast and color information. Enhancement of such images is a difficult task because of the complexity in restoring both the luminance and the chrominance while maintaining good color fidelity. One particular problem is the fact that the level of contrast loss depends strongly on wavelength. A novel method is presented for the enhancement of color images. This method is based on the underlying physics of the degradation process, and the parameters required for enhancement are estimated from the image itself.

Steady-state reflectance spectroscopy in the P 3 approximation

Abstract: The Green’s function of the steady-state radiative-transport equation is derived in the P3 approximation for isotropic sources It is demonstrated that the P3 approximation models the radiance in highly absorbing media or close to sources more accurately than does diffusion theory Boundary conditions consistent with the P3 approximation are also developed for semi-infinite media bounded by a nonscattering medium Expressions for the reflectance remitted from media interrogated by a normally incident pencil beam are derived and fitted to simulated and experimental reflectance data from media having optical properties typical of biological tissue The reconstructed optical properties are accurate to within ±10% in absorption and scattering for source–detector separations as small as 043 mm and albedos as low as 059 Methods for simplifying these expressions given some a priori knowledge of the scattering phase function are discussed

Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms

Abstract: An algorithm for phase demodulation of a single interferogram that may contain closed fringes is presented. This algorithm uses the regularized phase-tracker system as a robust phase estimator, together with a new scanning technique that estimates the phase that initially follows the bright zones of the interferogram. The combination of these two elements constitutes a powerful new method, the fringe-follower regularized phase tracker, that makes it possible to correctly demodulate complex, single-image interferograms for which traditional methods fail.

Chromatic structure of natural scenes

Abstract: We applied independent component analysis (ICA) to hyperspectral images in order to learn an efficient representation of color in natural scenes. In the spectra of single pixels, the algorithm found basis functions that had broadband spectra and basis functions that were similar to natural reflectance spectra. When applied to small image patches, the algorithm found some basis functions that were achromatic and others with overall chromatic variation along lines in color space, indicating color opponency. The directions of opponency were not strictly orthogonal. Comparison with principal-component analysis on the basis of statistical measures such as average mutual information, kurtosis, and entropy, shows that the ICA transformation results in much sparser coefficients and gives higher coding efficiency. Our findings suggest that nonorthogonal opponent encoding of photoreceptor signals leads to higher coding efficiency and that ICA may be used to reveal the underlying statistical properties of color information in natural scenes.