Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1998"

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

Abstract: It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2× in each dimension (i.e., oversampling by 4× for 2D and 8× for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop.

Statistics of cone responses to natural images: implications for visual coding

Abstract: We gathered hyperspectral images of natural, foliage-dominated scenes and converted them to human cone quantal catches to characterize the second-order redundancy present within the retinal photoreceptor array under natural conditions. The data are expressed most simply in a logarithmic response space, wherein an orthogonal decorrelation robustly produces three principal axes, one corresponding to simple changes in radiance and two that are reminiscent of the blue–yellow and red–green chromatic-opponent mechanisms found in the primate visual system. Further inclusion of spatial stimulus dimensions demonstrates a complete spatial decorrelation of these three cone-space axes in natural cone responses.

Properties of photonic crystal fiber and the effective index model

Abstract: We report on the waveguiding properties of a new type of low-loss optical waveguide. The photonic crystal fiber can be engineered to support only the fundamental guided mode at every wavelength within the transparency window of silica. Experimentally, a robust single mode has been observed over a wavelength range from 337nm to beyond 1550nm (restricted only by available wavelength sources). By studying the number of guided modes for fibers with different parameters and the use of an effective index model we are able to quantify the requirements for monomode operation. The requirements are independent of the scale of the fiber for sufficiently short wavelengths. Further support for the predictions of the effective index model is given by the variation of the spot size with wavelength,

Analysis of resolution limitation of integral photography

Abstract: The resolution limitation of integral photography (IP) is analyzed. Estimating the resolution of IP measured at the viewpoint, we derive the optimum width of the aperture or lens. It is shown that the resolution of aperture-plate IP is lower than conventional two-dimensional displays, even with an optimum design. When the ideal lens is utilized, however, lens-array IP can provide a three-dimensional display that is free from any discontinuous change of images that occur with the observer’s movement and with the same resolution that conventional two-dimensional displays feature.

X-ray imaging with submicrometer resolution employing transparent luminescent screens

Abstract: Microimaging techniques with synchrotron radiation demand fast, on-line x-ray detectors with a spatial resolution in the micrometer or submicrometer range. For this task an x-ray detector based on a transparent, i.e., nonscattering, luminescent screen has been developed. Its performance is described experimentally and theoretically. The detector consists of an Y3Al5O12:Ce screen, microscope optics, and a low-noise CCD camera, operated at x-ray energies between 10 and 50 keV. Good image quality is achieved if the depth of focus of the optical system is matched to the x-ray absorption length or thickness of the scintillator. A spatial resolution of 0.8 µm fwhm (1000 line pairs/mm with 10% contrast) was measured by recording the interferogram of a boron fiber. First applications in phase contrast imaging and microtomography are shown.

Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction

Abstract: A new optimization technique, stochastic parallel-gradient descent, is applied for high-resolution adaptive wave-front correction. A performance criterion for parallel-perturbation-based algorithms is introduced and applied to optimize adaptive system architecture. We present numerical simulation results for an adaptive imaging system based on the stochastic parallel-perturbation technique, along with experimental results obtained for a white-light adaptive imaging system with 37 control channels. An adaptive system with a self-organized (adaptive) control channel hierarchy is introduced and analyzed.

Simulation of light emission from thin-film microcavities

Abstract: In light-emitting devices based on thin-film technology, light waves that are partially or totally reflected at interfaces between different materials interfere and influence the angular distribution of the emitted light. For an electrical dipole transition, the radiation pattern is equivalent to that of an electrical dipole antenna. New theoretical expressions are provided for the radiation, discriminating for polarization, emission angle, absorption, and transmission; and the numerical calculation of discrete modes, narrow modes, and evanescent waves near absorbing media is discussed.

Method of source terms for dipole emission modification in modes of arbitrary planar structures

Abstract: Modification of dipole emission that is due to its optical environment is calculated for planar layered structures. The layers are optically described by standard matrix techniques, and the dipole is included by using additive source terms for the electric field that depend on dipole orientation and wave polarization. These source terms also allow coupling through evanescent waves. We emphasize the applicability of this method to cases in which the power distribution into various modes is affected: dipole emission into guided modes and emission distribution into the various modes of structures that contain multilayer reflectors, such as microcavities.

Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions

Abstract: We continue the theme of previous papers [J. Opt. Soc. Am. A 7, 1266 (1990); 12, 834 (1995)] on objective (task-based) assessment of image quality. We concentrate on signal-detection tasks and figures of merit related to the ROC (receiver operating characteristic) curve. Many different expressions for the area under an ROC curve (AUC) are derived for an arbitrary discriminant function, with different assumptions on what information about the discriminant function is available. In particular, it is shown that AUC can be expressed by a principal-value integral that involves the characteristic functions of the discriminant. Then the discussion is specialized to the ideal observer, defined as one who uses the likelihood ratio (or some monotonic transformation of it, such as its logarithm) as the discriminant function. The properties of the ideal observer are examined from first principles. Several strong constraints on the moments of the likelihood ratio or the log likelihood are derived, and it is shown that the probability density functions for these test statistics are intimately related. In particular, some surprising results are presented for the case in which the log likelihood is normally distributed under one hypothesis. To unify these considerations, a new quantity called the likelihood-generating function is defined. It is shown that all moments of both the likelihood and the log likelihood under both hypotheses can be derived from this one function. Moreover, the AUC can be expressed, to an excellent approximation, in terms of the likelihood-generating function evaluated at the origin. This expression is the leading term in an asymptotic expansion of the AUC; it is exact whenever the likelihood-generating function behaves linearly near the origin. It is also shown that the likelihood-generating function at the origin sets a lower bound on the AUC in all cases.

Branch point problem in adaptive optics

Abstract: It is shown that when branch points are present in the phase of a turbulence-distorted optical field, the ability of an adaptive optics system that utilizes a least mean square error type of wave-front reconstructor to sense all of the turbulence-induced phase perturbations is limited. There is a portion of the turbulence-induced phase perturbation, which portion we refer to as the hidden phase, that such a least mean square error type of wave-front reconstructor will, in effect, ignore. It is shown that the presence of branch points indicates that the measured phase-difference vector field cannot be considered to be simply the gradient of some scalar potential—the phase function—but is in part also the curl of a vector potential function. A solution is developed for this vector potential, and from this a simple closed-form solution for the hidden phase is developed. Sample numerical results are presented showing the nature of the hidden phase. Suggestions are provided for a branch-point-tolerant wave-front reconstructor based on use of the closed-form solution for the hidden phase.

Color constancy in the nearly natural image. 2. achromatic loci

Abstract: Most empirical work on color constancy is based on simple laboratory models of natural viewing conditions. These typically consist of spots seen against uniform backgrounds or computer simulations of flat surfaces seen under spatially uniform illumination. In this study measurements were made under more natural viewing conditions. Observers used a projection colorimeter to adjust the appearance of a test patch until it appeared achromatic. Observers made such achromatic settings under a variety of illuminants and when the test surface was viewed against a number of different backgrounds. An analysis of the achromatic settings reveals that observers show good color constancy when the illumination is varied. Changing the background surface against which the test patch is seen, on the other hand, has a relatively small effect on the achromatic loci. The results thus indicate that constancy is not achieved by a simple comparison between the test surface and its local surround.

Differential absorption imaging with optical coherence tomography

Abstract: The spatial variation of the backscattering cross section is the primary source of contrast in present applications of optical coherence tomography (OCT). We introduce and analyze a technique for obtaining OCT images of the local concentration of an absorbing compound in biological tissues and other highly scattering media. A pair of light-emitting diodes, one emitting in a vibrational absorption band of the chemical compound of interest and the other emitting just outside this band, are used as sources at the input of the interferometer. The differential absorption of the probe beam is determined by Fourier transformation and ratiometric processing of the measured interference signals. The ability of the technique to distinguish lipid and water inclusions in a scattering material is demonstrated with an OCT system that uses a pair of light-emitting-diode sources with center wavelengths of 1.3 µm and 1.46 µm.

Use of image-based information in judgments of surface-reflectance properties.

Abstract: We examined how well we can recover surface-reflectance properties from shading patterns under changes in surface shape. The stimulus we used was a square surface modulated in depth by a low-pass-filtered random field and rendered by the Phong illumination model [Commun. ACM 18, 311 (1975)]. Two different surface images (target and match) were presented side by side, with either the viewing direction or the surface-normal direction rotating around the horizontal axis. The target shape was manipulated by changing the spatial spectrum, and the target reflectance was manipulated by changing the diffuse-reflection coefficient and the specular-reflection exponent (shininess) of the Phong model. The shape parameters of the match stimulus were fixed, but its reflectance parameters were under the control of subjects, who had to make the apparent reflectance of the two surfaces as similar as possible. The results showed that the constant error (difference between simulated and matched values) was large except when the two surfaces had the same shape parameters or when they differed only in scale. The pattern of the constant errors and response variabilities suggests that the judgments of the subjects were based on the similarity of the luminance histogram of the surface image. Our results demonstrate a limitation of surface-reflectance constancy for changes in shape and the importance of image-based information in reflectance judgments. The results are discussed in relation to previous studies that showed effects of spatial layout on surface-reflectance perception.

Correction of the aberrations in the human eye with a liquid-crystal spatial light modulator: limits to performance

Abstract: We evaluated the performance of a liquid-crystal spatial light modulator for static correction of the aberrations in the human eye. By applying phase-retrieval techniques to pairs of double-pass images we first estimated the wave aberration of the eye to be corrected. Then we introduced the opposite phase map in the modulator, which was placed in a plane conjugated with the eye’s pupil, and we recorded double-pass images of a point source before and after correction of the aberrations. In a slightly aberrated artificial eye a clear improvement was obtained after correction, and, although diffraction-limited performance was not achieved, the results were close to the theoretical predictions. In the two living eyes that we studied some benefit also appeared in the correction, but the performance was worse than that expected. We evaluated possible explanations for the relatively poor performance that was obtained in the human eye: an incorrect estimate of the ocular aberration, the limited spatial resolution of the modulator, and the dynamic changes in the ocular aberrations. Based on the results in the artificial eye, the first problem was not considered to be a major source of error. However, we showed that the spatial resolution of the liquid-crystal spatial light modulator limits the maximum correction to be attained. In addition, the changes in the ocular optics over time also impose a limit in the performance of static corrections.

Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law

Abstract: A generalized bidirectional distribution function (BRDF) that relates the specific intensity of the scattered light from a semi-infinite medium to the specific intensity of the incident light is introduced in the framework of coherence theory. This derivation allows us to obtain from first principles several fundamental properties: First, it is established that the generalized BRDF takes the form of a nonlocal relation between the incident and the scattered specific intensities. This nonlocal structure allows us to account naturally for the lateral shift of a beam. Second, the generalized BRDF is the Fourier transform of the correlation function that describes the memory effect. Third, the Helmholtz principle for specific intensities is derived as a theorem from the reciprocity property of the scattering operator for wave fields. This result allows us to prove Kirchhoff’s law.

Color and luminance information in natural scenes

Abstract: The spatial filtering applied by the human visual system appears to be low pass for chromatic stimuli and band pass for luminance stimuli. Here we explore whether this observed difference in contrast sensitivity reflects a real difference in the components of chrominance and luminance in natural scenes. For this purpose a digital set of 29 hyperspectral images of natural scenes was acquired and its spatial frequency content analyzed in terms of chrominance and luminance defined according to existing models of the human cone responses and visual signal processing. The statistical 1/f amplitude spatial-frequency distribution is confirmed for a variety of chromatic conditions across the visible spectrum. Our analysis suggests that natural scenes are relatively rich in high-spatial-frequency chrominance information that does not appear to be transmitted by the human visual system. This result is unlikely to have arisen from errors in the original measurements. Several reasons may combine to explain a failure to transmit high-spatial-frequency chrominance: (a) its minor importance for primate visual tasks, (b) its removal by filtering applied to compensate for chromatic aberration of the eye's optics, and (c) a biological bottleneck blocking its transmission. In addition, we graphically compare the ratios of luminance to chrominance measured by our hyperspectral camera and those measured psychophysically over an equivalent spatial-frequency range.

Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms

Abstract: The advent of interferometric synthetic aperature radar for geophysical studies has resulted in the need for accurate, efficient methods of two-dimensional phase unwrapping. Inference of the lost integral number of cycles in phase measurements is critical for three-pass surface deformation studies as well as topographic mapping and can result in an order of magnitude increase in sensitivity for two-pass deformation analysis. While phase unwrapping algorithms have proliferated over the past ten years, two main approaches are currently in use. Each is most useful only for certain restricted applications. All these algorithms begin with the measured gradient of the phase field, which is subsequently integrated to recover the unwrapped phases. The earliest approaches in interferometric applications incorporated residue identification and cuts to limit the possible integration paths, while a second class using least-squares techniques was developed in the early 1990’s. We compare the approaches and find that the residue-cut algorithms are quite accurate but do not produce estimates in regions of moderate phase noise. The least-squares methods yield complete coverage but at the cost of distortion in the recovered phase field. A new synthesis approach, combining the cuts from the first class with a least-squares solution, offers greater spatial coverage with less distortion in many instances.

Hermite–Sinusoidal-Gaussian Beams in Complex Optical Systems

Abstract: Sinusoidal-Gaussian beams have recently been obtained as exact solutions of the paraxial wave equation for propagation in complex optical systems. Another useful set of beam solutions for Cartesian coordinate systems is based on Hermite–Gaussian functions. A generalization of these solution sets is developed here. The new solutions are referred to as Hermite–sinusoidal-Gaussian beams, because they are in the form of a product of Hermite-polynomial functions of either complex or real argument, sinusoidal functions of complex argument, and Gaussian functions of complex argument. These beams are valid for propagation through systems that can be represented in terms of complex beam matrices, and the previous beam solution sets are special cases of these more general results. Propagation characteristics and applications of these beams are discussed, including their use as a basis set for propagation of arbitrary electromagnetic beams.

Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach

Abstract: A fast and accurate numerical method for free-space beam propagation between arbitrarily oriented planes is developed. The only approximation made in the development of the method was that the vector nature of light was ignored. The method is based on evaluating the Rayleigh–Sommerfeld diffraction integral by use of the fast Fourier transform with a special transformation to handle tilts and offsets of planes. The fundamental aspects of a software package based on the developed method are presented. A numerical example realized with the software package is presented to establish the validity of the method.

Direct method for restoration of motion-blurred images

Abstract: We deal with the problem of restoration of images blurred by relative motion between the camera and the object of interest. This problem is common when the imaging system is in moving vehicles or held by human hands, and in robot vision. For correct restoration of the degraded image, it is useful to know the point-spread function (PSF) of the blurring system. We propose a straightforward method to restore motion-blurred images given only the blurred image itself. The method first identifies the PSF of the blur and then uses it to restore the blurred image. The blur identification here is based on the concept that image characteristics along the direction of motion are affected mostly by the blur and are different from the characteristics in other directions. By filtering the blurred image, we emphasize the PSF correlation properties at the expense of those of the original image. Experimental results for image restoration are presented for both synthetic and real motion blur.

Monochromatic aberrations and point-spread functions of the human eye across the visual field

Abstract: The monochromatic aberrations of the human eye along the temporal meridian are studied by a novel laser ray-tracing method. It consists of delivering a narrow laser pencil into the eye through a given point on the pupil and recording the aerial image of the retinal spot with a CCD camera. The relative displacement of this image is proportional to the geometrical aberration of the ray (laser pencil) at the retina. We scanned the pupils of four observers in steps of 1 mm (effective diameter, 6.7 mm) and for five field angles (0 degree, 5 degrees, 10 degrees, 20 degrees, and 40 degrees). In addition, the aerial image for each chief ray is a low-pass-filtered version of the retinal point-spread function corresponding to a fully dilated pupil. The resulting spot diagrams, displaying the distribution of ray aberrations, are highly correlated with these point-spread functions. We have estimated the wave-front error by fitting Zernike polynomials (up to the fifth order). Despite the large variation found among observers, the overall rms wave-front error is relatively homogeneous. At the fovea, the average rms value was 1.49 microns when the second-order terms (defocus and astigmatism) were considered; this was reduced to 0.45 micron when the second-order terms were ignored. The rms values increase slowly, in a roughly linear fashion with eccentricity, such that at 40 degrees they are approximately double. These results are consistent with previous findings on the off-axis optical quality of the eye.

Measurement of the wave-front aberration of the eye by a fast psychophysical procedure

Abstract: We used a fast psychophysical procedure to determine the wave-front aberrations of the human eye in vivo. We measured the angular deviation of light rays entering the eye at different pupillary locations by aligning an image of a point source entering the pupil at different locations to the image of a fixation cross entering the pupil at a fixed location. We fitted the data to a Zernike series to reconstruct the wave-front aberrations of the pupil. With this technique the repeatability of the measurement of the individual coefficients was 0.019 µm. The standard deviation of the overall wave-height estimation across the pupil is less than 0.3 µm. Since this technique does not require the administration of pharmacological agents to dilate the pupil, we were able to measure the changes in the aberrations of the eye during accommodation. We found that administration of even a mild dilating agent causes a change in the aberration structure of the eye.

High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms

Abstract: We derive closed-form expressions for the effective index of subwavelength gratings up to the fourth and the second order for TE and TM polarization, respectively. These expressions are valid for arbitrary grating structures and are a generalization of previous results obtained for lamellar gratings with one groove per period (a structure often called a two-component layered medium). The effective-medium-theory predictions are carefully validated with exact electromagnetic theories for slanted and unslanted sinusoidally modulated volume gratings and for classical mounting. It is shown that, even for large period-to-wavelength ratios near the cutoff value, the form birefringence is accurately predicted at any angle of incidence.

Production and propagation of Hermite–sinusoidal-Gaussian laser beams

Abstract: Hermite–sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite–Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite–Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.

Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams

Abstract: The x-polarized and y-polarized beam modes of simple confining circularly symmetric spherical-mirror laser resonators may be represented with Laguerre–Gaussian functions. The corresponding r- and ϕ-polarized beam-mode profiles are found to be represented by a different Laguerre–Gaussian mode set. Though similar in name, these cylindrically polarized modes are fundamentally different from their rectangularly polarized counterparts. For example, the fundamental x-polarized mode is Gaussian, which has a maximum at the center of the beam, while the fundamental ϕ-polarized mode has a null at the beam center. The complete propagation characteristics of several types of azimuthally polarized Laguerre–Gaussian beams through optical systems representable by complex ABCD matrices are obtained. Cylindrically polarized Laguerre–Gaussian beams may be produced by inserting the appropriate Brewster window into a simple confining circularly symmetric laser resonator.

Infrared optical constants of CO and CO 2 thin icy films

Abstract: We derived the optical constants (n, k) of carbon monoxide (CO) and carbon dioxide (CO2) cryofilms (T=12 K) in the 4400–400-cm-1 (2.27–25-µm) infrared spectral range. Icy films were accreted on a silicon substrate inclined at an angle of 45 deg with respect to the infrared beam of the spectrometer. Transmittance spectra were taken at different thicknesses (0.05–3 µm) with the electric vector parallel (p polarized) and perpendicular (s polarized) to the incidence plane. Optical constants were derived, with a nonlinear least-squares method, in a way such that they satisfy the Kramers–Kronig relation and give the best agreement with the transmittance spectra at oblique incidence for p and s polarizations measured at different thicknesses. We showed that this procedure can clearly separate the contribution of n and k to the spectrum. This is essential for deriving optical constants of ices where strong transitions occur. The optical constants derived can be found at the website http://www.ct.astro.it/lasp/optico.html.

Influence of a perturbation in a double phase-encoding system

Abstract: We consider the recently proposed double phase-encoding system [Opt. Lett.20, 767 (1995)]. We study the robustness of the decoding process, that is, the way in which a perturbation of the coded image modifies the decoded image. We demonstrate that the amplitude signal-to-noise ratio (SNR) in the decoded image is strictly (and not only statistically) equal to the SNR in the coded image for different kinds of coded-image perturbations. In optical implementations the intensity of the decoded image is measured at the output of the decoding system. We show that there exists a simple relation between the intensity SNR of the decoded image and the amplitude SNR of the coded image and that this relation is quasi-independent of the nature of the coded-image perturbation. The results presented could provide a simple and efficient way of determining the precision level of the components of the optical decoding system necessary to reach a predefined quality level of the decoded image.

Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor

Abstract: The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack–Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of ∼λ/2 and ∼λ/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack–Hartmann wave-front sensor for measuring the optical quality of the human eye.

Anisotropies in visual motion perception: a fresh look.

Abstract: We measured motion-detection and motion-discrimination performance for different directions of motion, using stochastic motion sequences. Random-dot cinematograms containing 200 dots in a circular aperture were used as stimuli in a two-interval forced-choice procedure. In the motion-detection experiment, observers judged which of two intervals contained weak coherent motion, the other internal containing random motion only. In the direction-discrimination experiment, observers viewed a standard direction of motion followed by comparison motion in a slightly different direction. Observers indicated whether the comparison was clockwise or counterclockwise, relative to the standard. Twelve directions of motion were tested in the detection task and five standard directions (three cardinal directions and two oblique directions) in the discrimination task. Detection thresholds were invariant with direction of motion, but direction-discrimination thresholds were significantly higher for motion in oblique directions, even at low-coherence levels. Results from control conditions ruled out monitor artifacts and indicate that the oblique effect is relative to retinal coordinates. These results have broad implications for computational and physiological models of motion perception.

Reciprocity of evanescent electromagnetic waves

Abstract: We derive reciprocity relations for the generalized reflection and transmission coefficients of vector wave fields containing evanescent components. This is done by using Lorentz’s reciprocity theorem with sources at finite distance from the scatterer.