We modeled discrimination thresholds for object colors under different lighting environments [J. Opt. Soc. Am. 35, B244 (2018)]. First, we built models based on chromatic statistics, testing 60 models in total. Second, we trained convolutional neural networks (CNNs), using 160,280 images labeled by either the ground-truth or human responses. No single chromatic statistics model was sufficient to describe human discrimination thresholds across conditions, while human-response-trained CNNs nearly perfectly predicted human thresholds. Guided by region-of-interest analysis of the network, we modified the chromatic statistics models to use only the lower regions of the objects, which substantially improved performance.
We reported on stereovisual localization of a labeled target versus three-dimensional (3D) position and orientation with a resolution of a few micrometers [Opt. Express 18, 24152 (2010)]. A pseudo-periodic pattern (PPP) is fixed on the target, whose center is identified with subpixel accuracy in both stereo images. This subpixel position definition is fed into the geometrical model of the stereovision system and, thus, leads to subvoxel resolution in the 3D target positioning. This paper reports on improvements and specialization of the method for addressing the measurement of 3D translations: (a) The use of an encrypted PPP wider than the field of observation of the cameras has two beneficial effects. First, the allowed lateral target displacements are wider than the field of view of each camera, thus extending the workspace volume. Second, the 3D position is always derived from the same zone located at the center of the camera sensor chip. A simplified geometrical model is thus sufficient, and the effects of the lens distortions lead to a different kind of calibration issues. (b) By considering only translations, the pattern directions remain stationary in the recorded images. Two-dimensional Fourier transforms are then replaced by single dimension ones, thus reducing the computation time. (c) The choice of a higher magnification lens allows the achievement of submicrometer resolution in target position determination. This level of performance makes the method attractive in various automated applications requiring microstage position control and sensing. This approach may, for instance, fulfill the requirements for the coarse positioning of specimens in front of nanotechnology instruments that are equipped with their own high-accuracy but short-excursion-range translation stages.
Intensity fluctuations of partially polarized light with Gaussian statistics are investigated using a field decomposition approach. These developments provide an enlightening interpretation of the Hanbury Brown-Twiss effect of partially polarized Gaussian light. In particular, the behavior of the intensity fluctuation correlations can be interpreted as resulting from the mixing of two incoherent lights between themselves.
An angular spectrum representation is applied for a description of statistical properties of arbitrary beamlike fields propagating through atmospheric turbulence. The Rytov theory is used for the characterization of the perturbation of the field by the atmosphere. In particular, we derive expressions for the cross-spectral density of a coherent and a partially coherent beam of arbitrary type in the case when the power spectrum of atmospheric fluctuations is described by the von Karman model. We illustrate the method by applying it to the propagation of several model beams through the atmosphere.
Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.
The axial resolution of fluorescence microscopes can be considerably improved by superposing two illumination beams and by adding coherently the two wavefronts emitted by the luminescent sample. This solution has been implemented in 4Pi microscopes. Theoretical and experimental results have shown that a considerable improvement of the axial resolution can be obtained with these microscopes. However, the lateral resolution remains limited by diffraction. We propose a configuration of a 4Pi microscope in which the lateral displacement of the source modifies the collection efficiency function (CEF). Numerical calculations based on an approximate scalar theory and on exact vector-wave-optics results of the field distribution of the electromagnetic field in image space show that the lateral extent of the CEF can be reduced by a factor greater than 2 with respect to the diffraction limit. We show that, with this solution, the resolution in the transverse plane of 4Pi type B and 4Pi type C microscopes can be improved significantly.
The problem of reconstructing dielectric permittivity from scattered field data is dealt with for scalar two-dimensional geometry at a fixed frequency by use of a linearized approximation about a chosen reference permittivity profile. To investigate the capabilities and limits of linear inversion algorithms, we analyze the class of retrievable profiles with reference to some canonical geometries for which either analytical or numerical details can be worked through easily. The tool for such an analysis consists of the singular-value decomposition of the relevant scattering operators. For a constant reference permittivity function, the different behavior of linear inversion algorithms with respect to either radial or angular variations of the permittivity profiles is pointed out. In the last-named case the general situation of a multiview radiation is accounted for, and, unlike for the Born approximation, profiles that cannot be reconstructed by linear inversion comprise slowly varying functions. Moreover, the effect of an angularly varying reference profile is examined for a thin circular shell, permitting the possibility of reconstruction of rapidly varying angular profiles by linear inversion. Numerical results of linear inversions that confirm the predictions are shown. (C) 1999 Optical Society of America [S0740-3232(99)00607-9].
We study Wigner phase-space distributions W (x, p) in position (x) and momentum (p) for light undergoing multiple small-angle scattering in a turbid medium. Smoothed Wigner phase-space distributions are measured by using a heterodyne technique that achieves position and momentum resolution determined by the width and the diffraction angle of the local oscillator beam. The sample consists of 5.7-micron-radius polystyrene spheres suspended in a water-glycerol mixture. The momentum distribution of the transmitted light is found to contain a ballistic peak, a narrow diffractive pedestal, and a broad background. The narrow diffractive pedestal is found to decay more slowly than the ballistic peak as the concentration of scatterers is increased. The data are in excellent agreement with a simple theoretical model that explains the behavior of the narrow pedestal by including multiple diffractive scattering and treating large-angle scattering as a loss.
A monochromatic analysis of the RX nonimaging concentrators as imaging optical systems is presented (R stands for refractive, X for reflective). All of them have rotational symmetry and an image-side numerical aperture of 1.46 with the use of an index of refraction n' = 1.5, which means a half-rim angle of illumination of 77 deg. This is equivalent to 95% of the theoretical limit of concentration. For an object-side focal length of f = 17.1 mm (i.e., an entry aperture diameter of 50 mm) and a wavelength lambda = 950 nm, the RX has an equivalent passband above 32 mm(-1) in a field of view of +/-3.2 deg and above 19 mm(-1) in a field of view of +/-4.8 deg. This feature of RX concentrators allows one to use the same RX with receivers/emitters very different from the one of the design presented (in size and contour shape) with no loss of nonimaging quality. Moreover, the combination of simplicity, compactness, imaging capability, and high concentration makes the RX an exceptionally good optical device for high-sensitivity focal plane array applications. (C) 1997 Optical Society of America.
Recently the combination of the Gerchberg–Saxton (GS) algorithm and a fractional Fourier transform was proposed to implement beam shaping in the fractional Fourier domain [ Zalevsky , Opt. Lett.21, 842 (1996)]. We generalize this idea to deal with the problem of phase retrieval from two intensity measurements in a fractional Fourier transform system. The relevant equations for determining the unknown phases are derived, based on the general theory of amplitude–phase retrieval in an optical system. The unitarity condition of the fractional Fourier transform in a practical optical system with finite aperture is discussed. For different fractional orders P, the phase retrieval of several typical model images is studied in detail. A comparison of the GS and our algorithms is given, based on numerical simulations. It follows that our algorithm can offer the desired phase in all cases considered. However, the GS algorithm may fail when the transform system is nonunitary.
The system under consideration consists of a piece of thin diffractive element (the Fresnel zone plate) and a uniform, converging spherical wave that is incident on the diffractive element. The center of curvature of the incident spherical wave and the primary focus of the zone plate are the two foci of the system. The point of absolute maximum intensity switches from the former to the latter when the Fresnel number of the system decreases to a sufficiently low level. Both a mathematical formulation and a physical interpretation of this effect are presented. (C) 1997 Optical Society of America.
Although the spectra of drop radii in rainshowers are very broad, the supernumerary bows are caused by only those drops with radii of about one-fourth millimeter.
The direct analysis in the time domain of the fluctuations of a signal propagating in a fiber-optic link in the presence of an imperfect connector makes it possible to formalize in a simple manner the description of its statistical properties. This permits, in particular, the clarification of the role played by the various time scales involved in the problem (coherence time of the fiber-exciting source, fiber modal delay, detector response time, etc.) in evaluating the statistical averages. The formalism includes in a straightforward way the case of simultaneous excitation of the fiber by more than one source. This last circumstance is expedient for checking the beneficial effect on modal noise derived from exciting the fiber with N laser sources.
We found that inspecting a sine-wave grating elevated threshold for spatial-frequency discrimination as it does for contrast detection, but discrimination threshold was maximally elevated at about twice the adapting frequency, where detection threshold was little affected; and detection threshold was maximally elevated at the adapting frequency, where discrimination threshold was not elevated at all. Orientation tuning was roughly similar for contrast and for discrimination threshold elevations; elevations fell by half at between 7 and 17 deg from the adapting orientation. We compared our findings with the predictions of three models of discrimination: (1) The data are inconsistent with the idea that the most strongly stimulated channels are the most important channels for discrimination. (2) With an additional assumption, the Hirsch-Hylton scaled-lattice model could account for our finding that discrimination threshold elevations are asymmetric. (3) With no additional assumptions, the idea that discrimination is determined by the relative activities of multiple overlapping spatial-frequency channels or size-tuned neurons can account for our finding that discrimination thresholds are asymmetric. We propose a physiologically based discrimination model: Asymmetrically tuned cortical cells feed a ratio-tuned neural mechanism whose properties are formally analogous to those of ratio-tuned neurons that have recently been found in cat visual cortex. The linear relation between firing frequency and contrast can explain why discrimination threshold is substantially independent of contrast.
The propagation properties of strip waveguides are analyzed by a mode-matching technique. Mode coupling, which causes leakage effects, is taken into account in the analysis. The numerical results for the attenuation constants of the first three leaky modes are presented as a function of the strip width. The numerical results obtained by the present method are compared with other theoretical and experimental results. It is found that the higherorder leaky modes have varied and interesting properties, as does the fundamental leaky mode.
The problem of interreflections for Lambertian surfaces of arbitrary shape and with varying reflectance is of interest for many practical applications. We present a general method to approach this problem. We define photometric modes that are uncoupled in the sense that each mode may be assigned a (pseudo) reflectance and that interreflections among modes vanish. Then the problem is formally identical with that of a convex body, in which interreflections are of no importance. The photometric modes depend on the shape of the body. In many practical cases one or a few modes dominate, and the reflected radiance depends more on the shape of the body (the dominant mode) than on the precise irradiance distribution. A few examples are treated explicitly. The redistribution of radiation described by the modes is treated by means of the net vector flux and the space density of radiation. Knowledge of these fields for the dominant mode yields considerable intuitive insight in the physical situation and provides the means to estimate the effects of painting part of the surface or of the introduction of screens.
Phase-conjugate lasers with saturable gain medium are analyzed, taking into account the saturation of the reflectivity of the phase-conjugate mirror that is due to pump depletion. It is shown that the behavior of the laser is determined by the extent to which the reflectivity is saturated as compared with the saturation of the gain medium. For weakly saturated phase-conjugate mirrors, the intensities and gain are not much different from those in conventional lasers. For strongly saturated mirrors, the laser behaves more like a single-pass amplifier with output intensity proportional to the pump intensity of the phase-conjugate mirror.
Snow presents more than just a uniformly white face. Beneath its surface a vivid blueness, the purity of which exceeds that of the bluest sky, may be seen. This subnivean blue light results from preferential absorption of red light by ice; multiple scattering by ice grains, which is not spectrally selective, merely serves to increase the path length that photons travel before reaching a given depth. Although snow is usually white on reflection, bubbly ice, which can be found in frozen waterfalls and icebergs, may not be. To a first approximation, bubbly ice is equivalent to snow with an effective grain size that increases with decreasing bubble volume fraction. Ice grains in snow are too small to give it a spectrally selective albedo, but the much larger effective grain sizes of bubbly ice can give it bluish-green hues of low purity on reflection.
Polarization-mode properties of elliptical-core fibers and stress-applied single polarization fibers are clarified theoretically and experimentally. Normalized frequency dependence of modal birefringence and polarization-mode dispersion is measured, and the results are found to be in good agreement with the calculated results. It is revealed that the stress distribution over core and cladding has a strong influence on the polarization properties for the single-mode fibers examined here.
The equation that describes the tangential focal conditions for a curved grating is found to be a natural solution for the position of the plane of stationarity in laser refraction. It is also found that the imaging equation of the macroscopic surface treated as a mirror is a particular solution when (1) the observation is in the specular direction or (2) the incidence and observation directions are close to the normal to the surface. When speckle is viewed in this way, some errors in previous research on speckle motion are brought to light.
