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S. Y. Kung, K. S. Arun, D. V. Bhaskar Rao
Journal of the Optical Society of America, Volume 73, pp 1799-1811; https://doi.org/10.1364/josa.73.001799

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.
R. N. Bracewell
Journal of the Optical Society of America, Volume 73, pp 1832-1835; https://doi.org/10.1364/josa.73.001832

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 iniage-processing applications the convolution of two data sequences f1 and f2 is given by DHT of [(DHT of fl) times; (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 [R. V. L. Hartley, Proc. IRE 30,144 (1942)] as the DFT bears to the Fourier transform.
Yasuo Kuga, , Adam P. Bruckner
Journal of the Optical Society of America, Volume 73, pp 1812-1815; https://doi.org/10.1364/josa.73.001812

Abstract:
We present an experimental study of the pulse shape, delay, and spread of an optical pulse transmitted through a medium containing uniform latex microspheres using a mode-locked Nd:glass laser with a 20-psec pulse width. The delay of the arrival time of the peak intensity and the half-power pulse width for three different particle sizes are shown for an optical distance of up to 45.
Walter Tape
Journal of the Optical Society of America, Volume 73, pp 1641-1645; https://doi.org/10.1364/josa.73.001641

Abstract:
During low-level halo displays, ice crystals in the atmosphere at ground level were collected and studied. I discuss the crystals in connection with the halos present at the time of collection.
Craig F. Bohren
Journal of the Optical Society of America, Volume 73, pp 1646-1652; https://doi.org/10.1364/josa.73.001646

Abstract:
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.
P. L. Marston, J. L. Johnson, S. P. Love, B. L. Brim
Journal of the Optical Society of America, Volume 73, pp 1658-1664; https://doi.org/10.1364/josa.73.001658

Abstract:
A novel effect in the scattering of white light from bubbles consists of colored bands that appear near the critical scattering angle. The bands were photographed in the far-zone scattering from a cylindrical bubble in glass. Their existence is associated with the coarse structure present in the exact scattered intensity. A digital Butterworth filter was developed to remove (from computed intensities) fine structures that are lost when the optical bandwidth is large. The colors are found to be due to the combined effects of interference and diffraction (near the critical scattering angle) and dispersion of the refractive index. Coarse structures were previously modeled in the monochromatic scattering from spherical air bubbles in water. Colors are also to be expected in the appearance of clouds of bubbles in water. Such colors were reported [C. Pulfrich, Ann. Phys. Chem. (Leipzig) 33, 209 (1888)]. Some implications for the optical measurement of bubble size and surface quality are noted.
, Nathan Marcuvitz
Journal of the Optical Society of America, Volume 73, pp 1714-1718; https://doi.org/10.1364/josa.73.001714

Abstract:
A beam incident upon a slightly lossy layered dielectric structure at special (phase-matched) angles displays abnormal absorption and lateral beam shift on reflection. The amplitude of the reflected beam can be calculated either by a conventional transform technique or by a quasi-particle method. Different wave-number (k) expansions of the reflection coefficient may be employed for calculation of reflected beam properties. The convergence of these expansions is limited by the presence of poles and zeros and by the rapidity of dispersion in k of the reflection coefficient. The series expansions used in the quasi-particle method are not limited by the zeros and converge better for far fields than for fields on the reflecting surface; moreover, they permit faster numerical calculation of beam properties.
Jerry Nowakowski, Marek Elbaum
Journal of the Optical Society of America, Volume 73, pp 1744-1758; https://doi.org/10.1364/josa.73.001744

Abstract:
Expressions for the minimum number of photons required to measure the position of a light pattern on a noncoherent detector array with a desired accuracy are obtained from the Cramér–Rao lower bounds. The dependence of the Cramér–Rao bound on the shape, on the statistical properties of the intensity, on spatial sampling by the detector array, and on the array area is examined quantitatively. Examples of linear and nonlinear algorithms for measuring the pattern position with accuracies approaching the Cramér–Rao bound are presented. The analysis is carried out for photon statistics modeled as conditional Poisson processes.
Philip L. Marston
Journal of the Optical Society of America, Volume 73, pp 1816-1818; https://doi.org/10.1364/josa.73.001816

Abstract:
Expressions are derived from Mie theory for the cross-polarized and non-cross-polarized measurement configurations that are useful for the study of the optical glories of transparent spheres.
Kouichi Kamiuto
Journal of the Optical Society of America, Volume 73, pp 1819-1822; https://doi.org/10.1364/josa.73.001819

Abstract:
Computations of near-field scattering demonstrate that the value of the asymmetry factor increases with increasing distance from a sphere and is asymptotic to that in the far field. Further, it was found that the dimensionless distance from the sphere to the far field was given by the value of the size parameter.
D. S. Elliott, J. F. Ward
Journal of the Optical Society of America, Volume 73, pp 1836-1838; https://doi.org/10.1364/josa.73.001836

Abstract:
A novel two-wavelength one-path nonlinear interferometer is used to measure refractive-index dispersion for a number of molecular gases. Δn3ω, is measured directly, where Δn3ω = n3ω - nω with ω = 2πc/694 nm. Δn2ω was measured for these gases previously. For CH4, the results are consistent with conventional refractive-index data from the literature; for CHF3, CH3F, CF4, and SF6, these results improve refractive-index data for wavelengths shorter than 400 nm; and, for CH2F2, these results provide the only data on dispersion available to our knowledge.
Jacek Sochacki
Journal of the Optical Society of America, Volume 73, pp 1839-1839; https://doi.org/10.1364/josa.73.001839

Abstract:
Similarities between two papers on Luneburg lenses published previously are pointed out.
C. Bendjaballah, K. Hassan
Journal of the Optical Society of America, Volume 73, pp 1840-1843; https://doi.org/10.1364/josa.73.001840

Abstract:
Probabilities of detection of coherent optical signals in thermal background noise of a Lorentzian spectrum are calculated and compared for two cases: counting the number of photoelectrons within a fixed time T and measuring time intervals between photoelectrons within the same T. Although a comparison between the two methods is not always possible, it is shown that in some cases the counting method leads to better performance.
Christina A. Burbeck, D. Regan
Journal of the Optical Society of America, Volume 73, pp 1691-1694; https://doi.org/10.1364/josa.73.001691

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.
Michael T. Hyson, Bela Julesz, Derek H. Fender
Journal of the Optical Society of America, Volume 73, pp 1665-1673; https://doi.org/10.1364/josa.73.001665

Abstract:
Fender and Julesz [J. Opt. Soc. Am. 57, 819 (1967)] found that fused retinally stabilized binocular line targets could be misaligned on the two retinas in the temporalward direction by at least 30 min of arc without loss of fusion and stereopsis and that random-dot stereograms could be misaligned 2 deg before fusion was lost. To test these results in normal vision, we recorded eye motions of four observers while they viewed a random-dot stereogram that subtended about 10 deg. The observers misaligned overlaid vectograph stereo images by moving them apart in a temporalward direction until fusion was lost. They then returned the vectographs to the overlaid position. Throughout this cycle the observers reported at frequent intervals if they could perceive strong or weak depth, loss of depth, or loss of fusion. For some observers the image separation could be increased to 5 deg beyond parallel before fusion was lost. The visual axes diverged to follow the image centers and varied from overconverged to overdiverg d with respect to the image centers while the observers still reported depth and fusion. We call the difference between the image separation and eye vergence the yergence error. If a vergence error persisted for at least 10 sec without loss of the percepts of fusion and depth, we postulate that neutral remapping occurred that compensated for the retinal misalignment. We found that the average maximum neural remapping was 3.0 deg. The neural remapping was greater at loss of fusion than at regaining fusion. This phenomenon corresponds to the hysteresis measured by Fender and Julesz. We obtained an average hysteresis value of 2.6 deg with a maximum value of 4.1 deg. The average value is somewhat larger than the value reported by Fender and Julesz; this might result from our use of larger targets. We recorded many vergence saccades, in both the convergent and divergent directions, associated with scanning the target. Refusion occurred after the images were briefly aligned on the retinas by a pair of vergence sac ades. These saccades were initiated when the vergence error returned to the value that it had when fusion was lost, and the magnitude of the divergent saccade was such that the vergence error was reduced to zero. This may imply retention of the position of correspondence that spanned a period of nearly 1 min between loss and restoration of fusion.
Joseph Reader, Nicolo Acquista, David Cooper
Journal of the Optical Society of America, Volume 73, pp 1765-1770; https://doi.org/10.1364/josa.73.001765

Abstract:
Spectra of the copperlike ions Ru15+, Rh16+, Pd17+, Ag18+, Cd19+, In20+, and Sn21+ were observed with a laser-produced plasma and a 10.7-m grazing-incidence spectrograph. Wavelengths, energy levels, and ionization energies were determined for each of these ions. The wavelengths are compared with relativistic Hartree–Fock calculations.
Alistair B. Fraser
Journal of the Optical Society of America, Volume 73, pp 1626-1628; https://doi.org/10.1364/josa.73.001626

Abstract:
Although the spectra of drop radii in rain showers are broad, the supernumerary bows are caused by only those drops with radii of about 0.25 mm. The angle of minimum deviation, the rainbow angle, is a function of drop size, being large for big drops, owing to drop distortion, and large for small drops, owing to interference. Between these extremes, there is a minimum rainbow angle. The drops that cause it give rise to the supernumerary bows.
Y Ejima, S Takahashi
Published: 1 December 1983
Journal of the Optical Society of America, Volume 73

The publisher has not yet granted permission to display this abstract.
Craig F. Bohren, Alistair B. Fraser, William H. Mach
Journal of the Optical Society of America, Volume 73; https://doi.org/10.1364/josa.73.001621

R. F. Cybulski, M. P. Silverman
Journal of the Optical Society of America, Volume 73, pp 1732-1738; https://doi.org/10.1364/josa.73.001732

Abstract:
We investigate the reflection of plane waves of s and p polarization from the interface between a homogeneous transparent medium and an amplifying medium with a gain profile decreasing exponentially with depth of penetration. For angles of incidence less than critical angle, the reflectance curves are essentially the same as those deduced from the usual Fresnel formulas for two transparent media. In the vicinity of critical angle, the reflection coefficients are virtually the same for both polarizations and are greater than unity. Beyond critical angle, the reflectances fall toward unity as grazing incidence is approached. Both the reflectance and the far-field transmittance peak in the immediate vicinity of critical angle. For angles less than critical angle, the transmittance can be 2 orders of magnitude greater than the reflectance. Certain values of gain parameters and incident angle lead to singularities in the theoretical reflectance. At these points the usual neglect of the effect of the transmitted wa ve on the population inversion is no longer valid.
Jeffrey T. Ives, Peter W. Barber, Richard A. Normann
Journal of the Optical Society of America, Volume 73, pp 1725-1731; https://doi.org/10.1364/josa.73.001725

Abstract:
Cone oil droplets are highly retractile, optically dense spheres located in front of the cone outer segment. Because of their refractile strength, absorbance, and size, these spherical oil droplets have a pronounced influence on the light reaching the photopigment. We used electromagnetic scattering theory to interrelate these factors, and we calculated the light energy distribution around cone oil droplets modeled as isolated spheres. The necessary electromagnetic parameters were determined from anatomical and optical measurements in the turtle retina. Cone and oil-droplet dimensions were determined with a light microscope. The index-of-refraction values for the red, yellow, orange, and clear oil droplets were measured to be 1.69, 1.55, 1.51, and 1.48, respectively, by the technique of immersion matching. The application of the electromagnetic scattering theory suggests that oil droplets significantly increase cone sensitivity. Cone action spectra predicted by this analysis show that the largest increases o ccur around the absorption maximum of each cone's photopigment.
W. A. Van De Grind, A. J. Van Doorn, J. J. Koenderink
Journal of the Optical Society of America, Volume 73, pp 1674-1683; https://doi.org/10.1364/josa.73.001674

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.
H. Xu
Journal of the Optical Society of America, Volume 73, pp 1709-1713; https://doi.org/10.1364/josa.73.001709

Abstract:
A new measure called color-rendering capacity is developed, by applying some of the concepts used in communication engineering, to describe another aspect of the color-rendering properties of illumination, i.e., the maximum possible number of different colors that can be displayed by a given illumination. It is a relative measure expressed as a dimensionless parameter between zero and unity, depending only on the spectral power distribution of the illumination. The computer program involved in calculating this parameter and calculated examples for several different light-source types are presented. By reference to this parameter, the prediction for four different fluorescent lamps about the extent to which a lamp can make an average chromatic environment appear colorful and bright is in general agreement with the existing observation. Another potential use of this parameter, in collaboration with the luminous efficacy, as a relevant indicator of the visual efficiency of illumination is also discussed.
, Martial Ducloy
Journal of the Optical Society of America, Volume 73, pp 1844-1845; https://doi.org/10.1364/josa.73.001844

Abstract:
Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.
W. Livingston
Journal of the Optical Society of America, Volume 73, pp 1653-1657; https://doi.org/10.1364/josa.73.001653

Abstract:
Wood's 1910 study of the UV landscape by photography [R. W. Wood, Photog. J. 50, 329 (1910)] is resumed. Through a narrow-band filter at 320 nm we find uniform skies even under broken clouds, a Rayleigh veiling that attenuates distant detail, an absence of shadows, and a low reflectivity for most natural substances (except snow). Rainbows broaden by a factor of more than 2 when the UV is included. The fact that glass is opaque at 320 nm causes cities to be dark at night in this wavelength, with astronomical consequences. The aphakic human eye (i.e., the eye after removal of its crystalline lens for a cataract condition) proves to have a practical sensitivity at 320 nm so that the aphakic observer can verify the unique character of the UV scene.
Waldemar H. Lehn
Journal of the Optical Society of America, Volume 73, pp 1622-1625; https://doi.org/10.1364/josa.73.001622

Abstract:
Information derived from the superior mirage is used to compute the average vertical temperature profile in the atmosphere between the observer and a known object. The image is described by a plot of ray-elevation angle at the eye against elevation at which that ray intersects the object. The computational algorithm, based on the tracing of rays that have at most one vertex, iteratively adjusts the temperature profile until the observed image characteristics are reproduced. An example based on an observation made on the Beaufort Sea illustrates the process.
M. P. Silverman, R. F. Cybulski
Journal of the Optical Society of America, Volume 73, pp 1739-1743; https://doi.org/10.1364/josa.73.001739

Abstract:
We have measured as a function of incident angle, for a range of critical angles between 880° and 89° and of characteristic gain depths between 41 and 96 probe wavelengths, the single-pass reflectance of a He–Ne probe beam reflected from a transverse optically pumped solution of rhodamine B. In contrast to previously reported experiments, no anomalously high reflectances were observed. The theoretical formulas for the exponentially nonuniform- gain model reproduce well the observed reflectance curves including the locations, slopes, and heights of the amplification maximum in the vicinity of critical angle. Peak amplifications of 200–300% were predicted and observed for the given experimental conditions.
M. Piché, P. A. Bélanger,
Journal of the Optical Society of America, Volume 73, pp 1825-1827; https://doi.org/10.1364/josa.73.001825

Abstract:
The directional behavior of power losses in aberrated multiaperture optical resonators with one or two phase-conjugate mirrors is investigated through integral equations and the reciprocity theorem. In a resonator with one phasecohjugate mirror, the losses of the mode traveling from the conventional mirror to the phase-conjugate mirror are shown to be larger than the losses of the counterpropagating mode. In a resonator with two phase-conjugate mirrors, the losses along each direction are found to be equal.
Erwin Delano
Journal of the Optical Society of America, Volume 73, pp 1828-1831; https://doi.org/10.1364/josa.73.001828

Abstract:
A discussion of the effect on the primary monochromatic aberrations of moving the stop or the object for a system of axially symmetric curved Fresnel surfaces is presented. Mathematical expressions, which are generalizations of similar results for non-Fresnel systems, for the changes in the aberrations are derived.
Erratum
Robert M. Boynton, John J. Wisowaty
Journal of the Optical Society of America, Volume 73, pp 1846-1846; https://doi.org/10.1364/josa.73.001846

Abstract:
Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.
Hayao Kubo, Ryo Nagata
Journal of the Optical Society of America, Volume 73, pp 1719-1724; https://doi.org/10.1364/josa.73.001719

Abstract:
An investigation is made of the vectorial and geometrical representation of the polarization of light propagating through a weakly inhomogeneous absorbing anisotropic and optically active medium. When the approximations of geometrical optics are used, Maxwell's equations lead to the equation ∂G/∂x3 = (i/2)(Ω + iT)G, governing the behavior of polarized light propagating along the X3 axis in the medium, where X3 is the propagation distance along a light path, G is the complex amplitude of the electric vector, the vectors Ω = (0, Ω1, Ω2, Ω3) and T= (T0, T1, T2, T3), whose basis vectors are the unit matrix and the Pauli spin matrices, represent the optical properties of the medium. The two successive transformations of the resulting equation by the Stokes vector and the normalized polarization vector s yield a simple vector equation ∂s/∂x3 = Ω × s + (T˚ × s) × s, where Ω = (Ω1, Ω2, Ω3) and T˚ = (T1, T2, T3) are defined as the birefringent vector and the dichroic vector, respectively, representing the birefrin ence and the dichroism of the absorbing medium. The component Ω1, (or T1) shows the linear birefringence (or the dichroism) along the x1 and x2 axes, Ω2 (or T2) shows the linear birefringence (or dichroism) along the bisectors of the x1 and X2 axes, and Ω3 (or T3) shows the circular birefringence (or dichroism). The vector equation can represent clearly the geometrical behavior of the polarization of light in the inhomogeneous absorbing medium with the help of the Poincaré sphere.
D Regan, K I Beverley
Published: 1 December 1983
Journal of the Optical Society of America, Volume 73

The publisher has not yet granted permission to display this abstract.
J. Saijonmaa, D. Yevick
Journal of the Optical Society of America, Volume 73, pp 1785-1791; https://doi.org/10.1364/josa.73.001785

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 stepindex monomode fiber losses can be used to predict the losses of graded-index monomode fibers.
J. C. Charmet, P. G. De Gennes
Journal of the Optical Society of America, Volume 73, pp 1777-1784; https://doi.org/10.1364/josa.73.001777

Abstract:
The reflectances of inhomogeneous layers are usually calculated by numerical solution of Maxwell’s equations. This requires a specific model for the layer structure. We are interested here in the inverse problem: finding the refractive-index profile n(z) from ellipsometric data (ψ and Δ). We have calculated the reflectances explicitly in a first Born approximation [i.e., to first order in n(z) − n0, where n0 is the index of the pure liquid]. The effect of the reflecting wall at z = 0 is incorporated exactly. Finally, we express ψ and Δ in terms of the Fourier transform of the profile Γ(2q), where q is the normal component of the incident wave vector. The equation Γ(2q) = Γ′ + iΓ″ is complex; one can construct Γ′(2q) and Γ″(2q) in terms of the experimental ψ and Δ for all the accessible span of q vectors. For thick diffuse layers of thickness e ≫ λ/4π, this should allow for a complete reconstruction of the profile. For thin layers, e ≪ λ/4π, what are really measured are the moments Γ0 and Γ1 (of orders 0 and 1) of the index profile. To illustrate these methods, we discuss two specific examples of a slowly decreasing index profile: (1) wall effects in critical binary mixtures and (2) polymer adsorption from a good solvent.
Howard C. Howland, , Janette Atkinson, Bradford Howland
Journal of the Optical Society of America, Volume 73, pp 1701-1708; https://doi.org/10.1364/josa.73.001701

Abstract:
Analysis of the optics of photorefractively computed ray tracing shows that, for short camera-to-subject distances, the function relating image size to defocus of the eye is not symmetrical for errors of focus in front of and behind the camera. This asymmetry is exploited in the new method of isotropic photorefraction, in which the supplementary cylinder lenses of the original orthogonal photorefractors are replaced by defocusing of the camera lens itself. By comparing photographs taken with the camera focused in front of and behind the subject, the sign of the eyes’ defocus (myopic or hyperopic relative to the camera) can be determined. The axis of any astigmatism is readily apparent as the direction in which the photorefractive images are elongated. The method is well adapted for the refractive screening of infants and young children.
, Shigeko Takahashi
Journal of the Optical Society of America, Volume 73, pp 1695-1700; https://doi.org/10.1364/josa.73.001695

Abstract:
Detection thresholds of sinusoidal gratings in the simultaneous presence of high-contrast peripheral masking stimuli partially overlapping the test gratings were determined as a function of the separation between the center of the test grating and the peripheral stimulus by a two-alternative forced-choice method. The results showed that the threshold-elevating effect of simultaneously present peripheral masking stimuli depends on how much of the test grating is left unexposed. An additional experiment, in which the detection thresholds in the absence of the peripheral stimulus were determined as a function of the number of cycles of the test grating, enabled us to show that the threshold-elevating effect is somewhat higher than the effect of simply cutting the test grating down in size. The threshold-elevating effects caused by high-contrast peripheral masking stimuli can be explained in terms of a lateral inhibition and a probability summation across space, taking into account the nonuniform sensitivity across the visual field.
D. Regan, K. I. Beverley
Journal of the Optical Society of America, Volume 73, pp 1684-1690; https://doi.org/10.1364/josa.73.001684

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 discriminati n is determined by the relative activities of multiple overlapping spatial-frequency channels or sizetuned 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.
D. E. Aspnes, H. Arwin
Journal of the Optical Society of America, Volume 73, pp 1759-1764; https://doi.org/10.1364/josa.73.001759

Abstract:
We describe a method for accurately determining critical point parameters from optical spectra in which digital filtering in real (energy) and reciprocal (Fourier-coefficient) space is treated on an equivalent basis. Experimental and theoretical line shapes are also filtered in parallel, thereby eliminating systematic errors that can arise in the standard approach in which only the data are processed. Real-space filtering is done using false data to isolate individual or groups of critical points in complicated spectra, to provide a more accurate representation of the data in reciprocal space, and to minimize the effects of end-point discontinuities and truncation errors on the Fourier coefficients calculated from these spectra. Reciprocal-space filtering is done by numerically differentiating the data to maximize the amplitudes of the Fourier coefficients carrying the critical point information, followed by truncating low- and high-order coefficients to minimize artifacts that are due to baseline effects and noise. The optimum order of differentiation (not necessarily integral) is determined from the coefficients themselves. We show that a least-squares regression (LSR) analysis of a restricted interval of equally weighted points in reciprocal space is equivalent to the LSR analysis of all data points equally weighted in real space, making LSR particularly useful for analyzing higher-derivative spectra, where the real-space line shapes rapidly approach zero outside the central structure. For a specific example discussed here, maximum accuracy is obtained if the data are analyzed in the form of a third derivative, as was previously concluded empirically from numerical processing in real space.
G. P. Können
Journal of the Optical Society of America, Volume 73, pp 1629-1640; https://doi.org/10.1364/josa.73.001629

Abstract:
By using Taylor expansions, simple expressions are obtained for the deflection of light by ice crystals. With these simplified formulas, the intensity distributions of halos as a function of scattering angle are calculated analytically near the halo angle. It is found that the intensity distributions of halos depend on the number of degrees of freedom of the generating set of crystals. The differences in the purity of the colors of various types of halo are explained subsequently on the basis of their intensity distributions. An analytical description of the shape of the halo or of the halocaustic near the halo angle is obtained also. On the basis of the obtained intensity distributions, the polarization of refraction halos as a function of scattering angle is calculated, in which both contributions (birefringence of ice and polarization by refraction) are taken into account. It is found that the polarization of parhelia and tangent arcs shows a strong maximum near the inner edge of the halo over an angular ange of 0.1°, followed by a similar maximum of reversed polarization at 0.5° from the first one. The 22° halo shows a less strong maximum near its edge over an angular range of 0.5°. Halos at 46° from the sun also show a strong polarization near their inner edges, but the direction of the polarization is perpendicular to the polarization of the 22° halo edges. The possibility for detecting ice crystals on Venus by polarimetry near the halo angle is discussed briefly.
Nori Shibata, Katsunari Okamoto, Kazunori Suzuki, Yukinori Ishida
Journal of the Optical Society of America, Volume 73, pp 1792-1798; https://doi.org/10.1364/josa.73.001792

Abstract:
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.
Edward P. Wallner
Journal of the Optical Society of America, Volume 73, pp 1771-1776; https://doi.org/10.1364/josa.73.001771

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.
David Casasent
Journal of the Optical Society of America, Volume 73; https://doi.org/10.1364/josa.73.001847

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