Showing papers in "Journal of the Optical Society of America in 1983"

Deterministic phase retrieval: a Green’s function solution

Abstract: Equations for the propagation of phase and irradiance are derived, and a Green’s function solution for the phase in terms of irradiance and perimeter phase values is given A measurement scheme is discussed, and the results of a numerical simulation are given Both circular and slit pupils are considered An appendix discusses the local validity of the parabolic-wave equation based on the factorized Helmholtz equation approach to the Rayleigh–Sommerfeld and Fresnel diffraction theories Expressions for the diffracted-wave field in the near-field region are given

Electromagnetic scattering by magnetic spheres

Abstract: A number of unusual electromagnetic scattering effects for magnetic spheres are described. When ∊ = μ, the backscatter gain is zero; the scattered radiation is polarized in the same sense as the incident radiation. In the small-particle (or long-wavelength) limit, conditions are described for zero forward scatter, for complete polarization of scattered radiation in other directions, and for asymmetry of forward scatter to backscatter. The special case in the small-particle limit of m = 1, i.e., μ = 1/∊, provides interesting special instances of complete polarization and forward-scatter-to-backscatter asymmetry.

Degenerate four-wave mixing in semiconductor-doped glasses

Abstract: We report degenerate four-wave mixing (DFWM) of visible radiation in borosilicate glasses doped with crystallites of the mixed semiconductor CdSxSe1−x. These semiconductor-doped glasses—available commercially in the form of colored glass filters—exhibit third-order nonlinearities of ~10−9–10−8 esu for DFWM with short (~10-nsec) laser pulses at various visible wavelengths. Our studies on the temporal decay of the transient gratings indicate that the nonlinearity is not thermal in origin but may be attributed to the generation of a short-lived electron–hole plasma. In contrast with DFWM experiments in other semiconductors invoking gratings of optically generated carriers (or other mobile particles), we report unique diffusion-independent decay of the gratings in these glasses; this is deduced from the dependence of the intensity and polarization of the DFWM signal on the polarization combinations of the input beams. Finally, we report detailed data on the aberration-correction properties of these isotropic glasses.

Discrete Hartley transform

Abstract: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable. The inverse DHT is identical with the direct transform, and so it is not necessary to keep track of the +i and −i versions as with the DFT. Also, the DHT has real rather than complex values and thus does not require provision for complex arithmetic or separately managed storage for real and imaginary parts. Nevertheless, the DFT is directly obtainable from the DHT by a simple additive operation. In most image-processing applications the convolution of two data sequences f1 and f2 is given by DHT of [(DHT of f1) × (DHT of f2)], which is a rather simpler algorithm than the DFT permits, especially if images are. to be manipulated in two dimensions. It permits faster computing. Since the speed of the fast Fourier transform depends on the number of multiplications, and since one complex multiplication equals four real multiplications, a fast Hartley transform also promises to speed up Fourier-transform calculations. The name discrete Hartley transform is proposed because the DHT bears the same relation to an integral transform described by Hartley [ HartleyR. V. L., Proc. IRE30, 144 ( 1942)] as the DFT bears to the Fourier transform.

State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem

Abstract: We present new high-resolution methods for the problem of retrieving sinusoidal processes from noisy measurements. The approach taken is by use of the so-called principal-components method, which is a singular-value-decomposition-based approximate modeling method. The low-rank property and the algebraic structure of both the data matrix and the covariance matrix (under noise-free conditions) form the basis of exact modeling methods. In a noisy environment, however, the rank property is often perturbed, and singular-value decomposition is used to obtain a low-rank approximant in factored form. The underlying algebraic structure of these factors leads naturally to least-squares estimates of the state-space parameters of the sinusoidal process. This forms the basis of the Toeplitz approximation method, which offers a robust Pisarenko-like spectral estimate from the covariance sequence. Furthermore, the principle of Pisarenko’s method is extended to harmonic retrieval directly from time-series data, which leads to a direct-data approximation method. Our simulation results indicate that favorable resolution capability (compared with existing methods) can be achieved by the above methods. The application of these principles to two-dimensional signals is also discussed.

Three-dimensional vector coupled-wave analysis of planar-grating diffraction

Abstract: Diffraction by an arbitrarily oriented planar grating with slanted fringes is analyzed using rigorous three-dimensional vector coupled-wave analysis. The method applies to any sinusoidal or nonsinusoidal amplitude and/or phase grating, any plane-wave angle of incidence, and any linear polarization. In the resulting (conical) diffraction, it is shown that coupling exists between all space-harmonic vector fields inside the grating (corresponding to diffracted orders outside the grating). Therefore the TE and TM components of an incident wave are each coupled to all the TE and TM components of all the forward- and backward-diffracted waves. For a general Bragg angle of incidence, it is shown that the diffraction efficiency can approach 100% for a lossless grating if either the incident electric field or the magnetic field is perpendicular to the grating vector. Maximum coupling between incident and diffracted waves is shown to occur when the incident electric field is perpendicular to the grating vector. In general, the diffracted waves are shown to be elliptically polarized. The three-dimensional vector coupled-wave analysis presented is shown to reduce to ordinary rigorous coupled-wave theory when the grating vector lies in the plane of incidence.

Spatiotemporal variation of chromatic and achromatic contrast thresholds

Abstract: Moving the retinal image of a sinusoidal grating at a constant velocity (compensated for eye movements) provides controlled spatial and temporal frequencies at every point in the stimulus field. Using this controlled-velocity technique, we have measured the detection threshold for isoluminance, red/green gratings as a function of their spatial and temporal frequencies. The chromatic contrast-threshold surface obtained in this way is analogous to the achromatic contrast-threshold surface measured previously, but the results are quite different. For very low temporal frequencies (below 0.2 Hz), the chromatic sensitivity decreases steadily with decreasing temporal frequency. Below 0.01 Hz, chromatic patterns disappear completely even at maximum contrast (although achromatic or homochromatic patterns do not). In the region above 0.2 Hz, both achromatic and chromatic thesholds can be explained by the same receptive-field-like model. When the center and the surround components of this model are additively combined, they form the chromatic threshold surface; when the sign of either component is reversed, they form the achromatic one.

Optimal wave-front correction using slope measurements

Abstract: In adaptive optical systems that compensate for random wave-front disturbances, a wave front is measured and corrections are made to bring it to the desired shape For most systems of this type, the local wave-front slope is first measured, the wave front is next reconstructed from the slope, and a correction is then fitted to the reconstructed wave front Here a more realistic model of the wave-front measurements is used than in the previous literature, and wave-front estimation and correction are analyzed as a unified process rather than being treated as separate and independent processes The optimum control law is derived for an arbitrary array of slope sensors and an arbitrary array of correctors Application of this law is shown to produce improved results with noisy measurements The residual error is shown to depend directly on the density of the slope measurements, but the sensitivity to the precise location of the measurements that was indicated in the earlier literature is not observed

Rigorous coupled-wave analysis of grating diffraction— E-mode polarization and losses

Abstract: Rigorous coupled-wave theory of diffraction by dielectric gratings is extended to cover E-mode polarization and losses. Unlike in the H-mode-polarization case, it is shown that, in the E-mode case, direct coupling exists between all diffracted orders rather than just between adjacent orders.

Optical logic array processor using shadowgrams

Abstract: On the basis of a lensless shadow-casting technique, a new, simple method of optically implementing digital logic gates has been developed. These gates are capable of performing a complete set of logical operations on a large array of binary variables in parallel, i.e., the pattern logics. A light-emitting diode (LED) array is used as an incoherent light source in the lensless shadow-casting system. Sixteen possible functions of two binary variables are simply realizable with these gates in parallel by controlling the switching modes of the LED’s. Experimental results demonstrate the feasibility of various gate arrays, such as AND, OR, NOR, XOR, and NAND. As an example of application of the proposed method, we construct an optical logic array processor that can implement parallel operations of addition or subtraction for two binary variables without considering the carry mechanism. Use of the light-modulated LED array means that the proposed method can be applied to combinational circuits.

Strehl ratio for primary aberrations in terms of their aberration variance

Abstract: The Strehl ratio for imaging systems with circular and annular pupils aberrated by primary aberrations is considered in terms of the variance σΦ2 of the phase aberration across the pupil. Classical as well as balanced (Zernike) aberrations are considered. By comparing the actual numerical results with the approximate ones, we find that exp(−σΦ2) gives a better approximation for the Strehl ratio than does the Marechal formula. Whereas the Marechal formula underestimates the Strehl ratio, exp(−σΦ2) generally overestimates it, especially for annular pupils with a large obscuration.

Light-distribution on the retina of a wide-angle theoretical eye

Abstract: In a theoretical eye with spherical and aspheric surfaces, the retinal illumination is calculated if a Ganzfeld luminance field is used. The resulting retinal light distribution is nearly homogeneous over the whole retina. The homogeneity is not much influenced by the size of the optical surfaces. The corresponding retinal area and the luminous flux entering the eye are calculated as functions of the size of the visual field. The values of the length of the light path through the crystalline lens and of the angle of incidence on the retina are described as functions of the angle in the visual field.

Wave-front dislocations: topological limitations for adaptive systems with phase conjugation

Abstract: The density of wave-front dislocations for optical fields as a function of radiation parameters is investigated both theoretically and experimentally. A field with dislocations cannot be conjugated by means of flexible adaptive mirrors.

Iterative convolution backprojection algorithms for image reconstruction from limited data

Abstract: Image-reconstruction algorithms implemented on existing computerized tomography (CT) scanners require the collection of line integrals that are evenly spaced over 360 deg. In many practical situations, some of the line integrals are inaccurately measured or are not measured at all. In these limited-data situations, conventional algorithms produce images with severe streak artifacts. Recently, several other image-reconstruction algorithms were suggested, each tailored to a specific type of limited-data problem. These algorithms make minimal use of a priori knowledge about the image; only one has been demonstrated with real x-ray data. We present a new operator framework that treats all types of limited-data image-reconstruction problems in a unified way. From this framework we derive iterative convolution backprojection algorithms that make no restrictions on the location of missing line integrals. All available a priori information is incorporated by constraint operators. The algorithm has been implemented on a commercial CT scanner. We present examples of images reconstructed from real x-ray data in two limited-data situations and demonstrate the use of additional a priori information to reduce streak artifacts further.

Bayesian approach to limited-angle reconstruction in computed tomography

Abstract: An arbitrary source function cannot be determined fully from projection data that are limited in number and range of viewing angle. There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. It is demonstrated that these artifacts may be reduced by a Bayesian maximum a posteriori (MAP) reconstruction method that permits the use of significant a priori information. Since normal distributions are assumed for the a priori and measurement-error probability densities, the MAP reconstruction method presented here is equivalent to the minimum-variance linear estimator with nonstationary mean and covariance ensemble characterizations. A more comprehensive Bayesian approach is suggested in which the ensemble mean and covariance specifications are adjusted on the basis of the measurements.

Theory of a self-pumped phase conjugator with two coupled interaction regions

Abstract: We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.

Beam propagation in uniaxial anisotropic media

Abstract: Paraxial wave equations are derived for the propagation of beams in uniform uniaxial anisotropic media. The equations are generalized to the case of nonuniform media with weakly varying refractive indices. An ordinary wave beam is governed by a standard paraxial equation, whereas an extraordinary wave beam is governed by a paraxial wave equation, which involves both a displacement relative to the position of an ordinary wave beam and a rescaling of one transverse coordinate. The solution to the latter equation for a propagating Gaussian beam displays a distortion of both shape and phase front. Numerical results for diffraction by a uniformly illuminated circular aperture in a calcite medium display various anomalies ascribable to a loss of circular symmetry.

Analysis of anisotropic dielectric gratings

Abstract: A method for analyzing slanted anisotropic gratings is presented. The propagation of electromagnetic waves in the periodic anisotropic media is described by coupled-wave equations in a unified matrix form expressing the coupling of the space harmonics in the grating region. The solution of the equations is reduced to an eigenvalue problem of this coupling matrix. Through introduction of the concepts of transmission and boundary matrices, the diffraction properties of general slanted gratings are obtained rigorously by systematic matrix calculations that are easily implemented on a computer. The calculated results indicate that not only TE–TE or TM–TM but also TE–TM diffractions take place in general slanted gratings.

Simultaneous masking interactions between chromatic and luminance gratings

Abstract: Simultaneous masking using test and mask gratings composed of isochromatic luminance variations and isoluminant chromatic variations was studied. Masking of chromatic gratings by chromatic gratings shows less spatial-frequency specificity than does masking of luminance gratings by luminance gratings. Luminance gratings mask chromatic gratings of identical space-average luminance and chromaticity little and only when the spatial frequencies of the test and mask gratings are similar. Chromatic gratings, however, profoundly mask luminance gratings with a degree of spatial-frequency specificity akin to that of luminance-luminance masking. The insensitivity of the luminance-color masking results to the relative phase of the chromatic and luminance gratings indicates that the observed asymmetry is not due to local interactions.

Rayleigh backscattering theory for single-mode optical fibers

Abstract: The theory of backscattering in single-mode optical fibers is described through use of a correlation function for the refractive-index fluctuation in the fiber. A simple formula for the backscattered power is derived using two correlation functions for the Booker–Gordon and Gaussian models. The zeroth-order approximation of the formula, in which the correlation length is much smaller than the spot size of the waveguide mode, coincides with Brinkmeyer’s model. The backscattered power at the input end of single-mode fiber is compared with that for multimode fiber. It is also shown that the backscattered power level at the input end is lower by approximately 55 dB than the input power level.

Scattering of laser beams and the optical potential well for a homogeneous sphere

Abstract: A theory is developed for the scattering of a fundamental-mode laser beam by a homogeneous sphere located in the beam passage. The expression for the incident laser beam is obtained by using the complex-source-point method, and the light-field distributions inside and outside the sphere are given. The formulas for the energies scattered and absorbed by the sphere and for the radiation pressure exerted on the sphere are derived, and their qualitative features are discussed. Results of numerical calculation of the radiation pressure and their physical interpretations are presented. All the analytical formalism is generalized for immediate treatment of the scattering of higher-order Hermite–Gaussian-mode laser beams by a homogeneous sphere.

Loss calculation and design of arbitrarily curved integrated-optic waveguides

Abstract: Radiation losses in arbitrarily curved integrated-optic waveguides are computed numerically by means of the beam-propagation method. From the results obtained, design rules for bends and S-shaped curves connecting two straight waveguides are derived.

Detection of coherent movement in peripherally viewed random-dot patterns.

Abstract: We studied the detection of coherent motion in stroboscopically moving random-dot patterns for foveal vision and at eccentricities of 6, 12, 24, and 48 deg in the temporal visual field. Threshold signal-to-noise ratios (SNR’s) were determined as a function of velocity for a range of stimulus sizes. It was found that the motion-detection performance is roughly invariant throughout the temporal visual field, provided that the stimuli are scaled according to the cortical magnification factor to obtain equivalent cortical sizes and velocities at all eccentricities. The maximum field velocity compatible with the percept of coherent motion increased about linearly with the width of the square stimuli. At this high-velocity threshold any pixel crossed the field in five to nine equal steps with a constant total crossing time of 50–90 msec, regardless of stimulus size or eccentricity. The lowest SNR values were reached at the optimal or tuning velocity V0. They approached the amazingly low values of 0.04–0.05 for large stimuli and at all eccentricities. Regardless of stimulus size, the parameter V0 increased about linearly with eccentricity from roughly 1 deg sec−1 at the fovea to some 8 deg sec−1 at 48 deg in the temporal visual field.

Spatial-frequency discrimination and detection: comparison of postadaptation thresholds

Abstract: 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.

Experimental Doppler-limited spectra of the ν 2 bands of H 2 16 O, H 2 17 O, H 2 18 O, and HDO by Fourier-transform spectroscopy: secondary wave-number standards between 1066 and 2296 cm −1

Abstract: More than 2000 absolute wave numbers of 7 vibrational bands of H216O, H217O, H218O, and HDO (natural abundance) measured with a Fourier interferometer between 1066 and 2296 cm−1 are provided, with the greatest uncertainty about 50 × 10−6 cm−1 (1.5 MHz). These experimental values extracted from 12 different absorption spectra reveal a much greater consistency and are consequently given in inverse centimeters to the sixth decimal place. The spectral range covered corresponds to a large zone for which experimental accurate data were almost nonexistent. The precise knowledge of these strong atmospheric ν2 bands is of interest for astronomical studies. It will also improve with complementary recent similar work on N2O, the calibration of diode lasers, and Fourier-transform and classical spectrometers and will facilitate the coincidence search with laser radiation. For convenience, the wave numbers of the lines and their absolute uncertainty are given with their rotational and vibrational assignments and their experimental half-widths and intensities.

Comparison of calculated and measured performance of diffused channel-waveguide couplers

Abstract: Diffused channel-waveguide couplers were fabricated on z-cut y-propagating LiNbO3 crystals by the indiffusion of titanium. Both mode spot sizes and coupling lengths were measured. The fields and coupling lengths were computed for both TM and TE polarizations from fabrication conditions. Good agreement was obtained between the measured and computed mode spot sizes and coupling lengths. It is concluded that the calculation method could aid in the design of such couplers.

Beam-propagation analysis of loss in bent optical waveguides and fibers

Abstract: We demonstrate that the beam-propagation method can be used to calculate accurately both the pure bending loss and the transition loss of bent single-mode optical waveguides and fibers. Our results allow us to establish the accuracy of several commonly used theories of bending loss and to investigate the degree to which theories of step-index monomode fiber losses can be used to predict the losses of graded-index monomode fibers.

Scattering from arbitrarily oriented dielectric disks in the physical optics regime

Abstract: A solution has been developed for electromagnetic-wave scattering from a dielectric disk of arbitrary shape and orientation The solution is obtained by approximating the fields inside the disk with the fields induced inside an identically oriented dielectric slab having the same thickness and dielectric constant The fields inside the disk excite conduction and polarization currents, which are in turn used to calculate the fields scattered from the disk This computation has been executed for observers in the far field of the disk for arbitrarily polarized incident waves, and the solution has been expressed in the form of a dyadic scattering amplitude The results apply when the minimum dimension of the disk’s cross section is large compared with both wavelength and disk thickness, although the thickness need not be small compared with wavelength Examples of the dependence of the scattering amplitude on frequency, relative dielectric constant, and disk orientation are presented for disks of circular cross section

Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere

Abstract: Using a Gaussian weighting function for the receiver aperture, we obtain a closed-form representation for the receiver-aperture averaging effect for the intensity fluctuation of a beam wave in the turbulent atmosphere. It is shown that, unlike for the plane-wave case, the power scintillations do not always decrease when the receiver aperture is increased. The reasons are that (1) the intensity fluctuations on the axis for a coherent beam-wave source are smaller than these off the axis and (2) the averaging effect cannot show up when the total beam is within a coherent patch (i.e., the coherence length is larger than the beamwidth).

Independence of orientation and size in spatial discriminations

Abstract: This study of form vision explores the relationships between orientation and spatial frequency in suprathreshold discrimination tasks. Orientation discrimination thresholds for sine-wave gratings were 0.3–0.5 deg, much less than the roughly 10–24-deg orientational bandwidth of channels; spatial-frequency discrimination thresholds were 3–7%, much less than the roughly 1.2-octave spatial-frequency bandwidth of channels. We find that spatial-frequency discrimination between two gratings was as acute when the two gratings were orthogonal as when they were parallel. Orientation discrimination between two gratings was as acute when the two gratings had the same spatial frequencies as when they had different spatial frequencies. Thus orientation and spatial frequency are independent dimensions at the discrimination stage of spatial information processing.