Showing papers in "Journal of the Optical Society of America in 1976"

Zernike polynomials and atmospheric turbulence

Abstract: This paper discusses some general properties of Zernike polynomials, such as their Fourier transforms, integral representations, and derivatives. A Zernike representation of the Kolmogoroff spectrum of turbulence is given that provides a complete analytical description of the number of independent corrections required in a wave-front compensation system.

Some fundamental properties of speckle

Abstract: A speckle pattern formed in polarized monochromatic light may be regarded as resulting from a classical random walk in the complex plane. The resulting irradiance fluctuations obey negative exponential statistics, with ratio of standard deviation to mean (i.e., contrast) of unity. Reduction of this contrast, or smoothing of the speckle, requires diversity in polarization, space, frequency, or time. Addition of M uncorrelated speckle patterns on an intensity basis can reduce the contrast by 1/√M. However, addition of speckle patterns on a complex amplitude basis provides no reduction of contrast. The distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view.

Approximate relativistic corrections to atomic radial wave functions

Abstract: The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of rm is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations.

Curvature loss formula for optical fibers

Abstract: The loss formula for optical fibers with constant radius of curvature of their axes is derived by expressing the field outside of the fiber in terms of a superposition of cylindrical outgoing waves. The expansion coefficients are determined by matching the superposition field to the field of the fiber along a cylindrical surface that is tangential to the outer perimeter of the curved fiber. This method is a direct extension of my derivation of the curvature-loss formula for slab guides.

Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration

Abstract: We show how the processes of visual detection and of temporal and spatial summation may be analyzed in terms of parallel luminance (achromatic) and opponent-color systems; a test flash is detected if it exceeds the threshold of either system. The spectral sensitivity of the luminance system may be determined by a flicker method, and has a single broad peak near 555 nm; the spectral sensitivity of the opponent-color system corresponds to the color recognition threshold, and has three peaks at about 440, 530, and 600 nm (on a white background). The temporal and spatial integration of the opponent-color system are generally greater than for the luminance system; further, a white background selectively depresses the sensitivity of the luminance system relative to the opponent-color system. Thus relatively large (1 degree) and long (200 msec) spectral test flashes on a white background are detected by the opponent-color system except near 570 nm; the contribution of the luminance system becomes more prominent if the size or duration of the test flash is reduced, or if the white background is extinguished. The present analysis is discussed in relation to Stiles' model of independent eta mechanisms.

Local structure of movement parallax of the plane

Abstract: The movement parallax field due to the translation of an observer relative to a plane surface is studied in an infinitesimal neighborhood of a visual direction. The parallax field is decomposed into elementary transformations: a translation, a rigid rotation, a similarity, and a deformation. A topologically invariant classification based on critical-point analysis is also obtained. It is shown that the field is either that of a node or that of a saddle point. Numerical results for a general case are offered as illustration. We discuss the relevance of the local, as opposed to the global structure of the parallax field for visual perception and the visual space sense.

Geometrical transformations in optics

Abstract: Geometrical image modifications such as coordinate transformations and local translation, inversion, reflection, stretching which require space-variant optical coherent systems are provided by introducing phase filters having a predetermined phase function into optical coherent systems in such a manner that the local phase variations influence light from local object areas. In one embodiment, the object distribution is multiplied by the phase function so that its spectrum at the frequency plane constitutes the desired transformation. In a second embodiment, the aforementioned concept is applied to produce a transformation in an image plane. The phase filters, in a preferred embodiment, comprise computer generated holograms.

Spectral coherence and the concept of cross-spectral purity

Abstract: A new measure of correlations in optical fields, introduced in recent investigations on radiometry with partially coherent sources, is studied and applied to the analysis of interference experiments. This measure, which we call the complex degree of spectral coherence, or the spectral correlation coefficient, characterizes the correlations that exist between the spectral components at a given frequency in the light oscillations at two points in a stationary optical field. A relation between this degree of correlation and the usual degree of coherence is obtained and the role that the complex degree of spectral coherence plays in the spectral structure of a two-beam interference pattern is examined. It is also shown that the complex degree of spectral coherence provides a clear insight into the physical significance of cross-spectral purity. When the optical field at two points is cross-spectrally pure, the absolute value of the complex degree of spectral coherence at these points is found to be the same for every frequency component of the light. This fact is reflected in the visibility of the spectral components of the interference fringes formed by light from these points.

New apodizing functions for Fourier spectrometry

Abstract: A new class of apodizing functions suitable for Fourier spectrometry (and similar applications) is introduced. From this class, three specific functions are discussed in detail, and the resulting instrumental line shapes are compared to numerous others proposed for the same purpose.

Field deformation and loss caused by curvature of optical fibers

Abstract: Curvature loss formulas of optical fibers usually ignore the effect of field deformation caused by the curved axis of the fiber. Contrary to naive intuition, this field deformation may substantially decrease the radiation losses of modes with low mode number. Losses of modes with high mode numbers are, however, increased. We present a theoretical evaluation of curvature losses of the modes of a step-index fiber with a bent axis incorporating the influence of field deformation on the loss coefficient. The limitations of the simple loss formula in case of a sharply bent overmoded waveguide are pointed out.

Properties of speckle integrated with a finite aperture and logarithmically transformed

Abstract: When image plane speckle intensity integrated over a finite aperture is submitted to a logarithmic transformation, the noise becomes additive and signal independent. The first- and second-order moments of the probability distribution are derived. It is found that the logarithm of speckle noise approaches a normal distribution much faster than speckle intensity. The properties of speckle noise are different from those of film-grain noise; for example, neither Nutting’s law nor Selwyn’s law is satisfied by speckle.

Effects of luminance and stimulus distance on accommodation and visual resolution.

Abstract: Measurements of accommodation and visual resolution were obtained at a number of luminance levels and stimulus distances. With reductions in luminance the eye approached a “fixed-focus” condition of accommodation for intermediate distances, resulting in successively larger errors in accommodation for both near and far stimuli. The visual resolution values were initially affected by both the luminance and distance of the stimulus. Subsequent measurements of resolution, following the correction of accommodative errors, were found to be independent of the stimulus distance. The findings are discussed with regard to the problems of “night myopia” and variations in visual resolution with stimulus distance.

High-resolution methane ν 3 -band spectra using a stabilized tunable difference-frequency laser system*

Abstract: Techniques are described for drift compensation and scan calibration of a visible-to-infrared difference-frequency converter enabling high-resolution molecular spectra to be recorded with a precision and reproducibility of 5 × 10−4 cm−1. The capabilities of the spectrometer are illustrated by scans of the tetrahedral fine structure in the ν3 band of methane under low pressure, Doppler-limited and atmospheric pressure, collision-broadened conditions.

Speckle reduction in synthetic-aperture radars

Abstract: Airborne synthetic-aperture radar (SAR) systems employ coherent techniques to generate images of terrain in the microwave region of the spectrum The high degree of coherence required by radar system considerations results in the presence of radar speckle when diffuse scatterers are imaged It is possible to introduce frequency and/or angle diversity in such a manner that multiple uncorrelated images of the terrain may be generated and then summed incoherently to reduce the speckle When system bandwidth and/or viewing angle is severely constrained, then a compromise must be made between image resolution and speckle reduction Visual examination of controlled samples of radar imagery shows that speckle is reduced noticeably when incoherent summation of uncorrelated images is provided via use of diversity Some examples of radar images with varying degrees of diversity are presented in the paper and are compared qualitatively

Very long optical paths in air

Abstract: Two different multiple traversal optical systems are described; one gives the longest paths, the other the best compensation for vibration and misalignment problems. In the first, seven mirrors in a near confocal arrangement permit a large aperture beam of light to pass through a restricted volume for a discrete and very large number of times. A rectangular array of images corresponding to different numbers of passes appears on four mirrors at one end of the system. At the other end, three mirrors form the array and illuminate each image in it from one or more different directions. The possible numbers of passes are (4mn − 2)k + 2, where m and n are any integers representing, respectively, the number of columns and half the number of rows in the array. k is the number of different directions from which the array is illuminated. Geometrically, the beam may be isolated after thousands of passes; practically, the number is limited by reflection losses. In the second system the addition of four diagonal mirrors to a White cell converts the two lines of images on the single mirror to a rectangular array of images, almost squaring the maximum possible number of passes. With multiples of four rows of images in the array, the position of the output image is invariant to small errors in alignment of the mirrors.

Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section

Abstract: Resonances in partial waves an and bn are directly responsible for a ripple structure in the normalized extinction cross section. The distance Δx in the size parameter between two neighboring resonances is equal to a basic period of a ripple structure.

Interference with line-orientation sensitivity.

Abstract: Sensitivity for inclination detection of a foveally seen line is exceedingly high. It is shown that appropriately structured visual stimuli can interfere with the inclination detection threshold, presumably by inhibiting some neural signals before they are channeled to interact with others of their ensemble. The parameters of this inhibition, and by implication those of the sensitivity of the involved neural elements, are outlined: spatial location, time course, movement sensitivity, dichoptic nature, nonrecurrent characteristics, and position rather than orientation dependency.

Single-layer, gradient refractive index antireflection films effective from 0.35 to 2.5 μ

Abstract: Gradient refractive index antireflection films are produced by a chemical etch/leach process applied to glasses sensitized by a phase-separating heat treatment. The reflectance (two surfaces) is effectively reduced from ~ 8% to < 1/2% in the wavelength regime 0.35–2.5 μ. The broadband antireflection film consists of a single, porous, skeletal layer made up largely of silica. The optical properties of the film are shown to depend on the time, temperature parameters of the phase-separating heat treatment, as well as the time, temperature parameter of the film-forming etch/leach treatment. The properties of films produced under different process conditions are correlated in a fashion that suggests that progressively steeper refractive index gradients are obtained for samples phase separated and formed at higher temperatures. A number of applications for these films are suggested, including solar energy devices.

Phase retrieval from modulus data

Abstract: Phase retrieval implies extraction of the phase of a complex signal f from its modulus |f|. We give examples where an additional constraint is imposed: knowledge of the modulus of F, the Fourier transform of f. The retrieval is accomplished by computer processing of samples of |f| and |F|. The problems of noisy data and nonuniqueness are addressed.

On transmission and recovery of three-dimensional image information in optical waveguides*

Abstract: The paper considers two questions. The first one is: Is it possible to transmit three-dimensional pictorial information through transparent glass (or other dielectric) fibers? We find that due to modal dispersion, pictorial information is invariably "smeared" in transmission. The second question is: Given nature's reluctance to transmit pictures through fibers, is there anything we can do about it? We suggest that the answer is yes and point to a class of solutions involving nonlinear optical mixing.

Energy levels of neutral atomic uranium (Ui)

Abstract: High-resolution grating and Fourier transform spectroscopy measurements, using hollow-cathode and electrodeless discharge lamp sources, have resulted in a list of 92000 lines of Ui and Uii. The wave-number accuracy is about 0.003 cm−1. With this list and new Zeeman structure, isotope-shift, and 233U hyperfine-structure spectrograms, we have found 500 new Ui levels. We now know 1240 even levels between 7020 and 42000 cm−1 and 360 odd levels up to 38000 cm−1. All levels expected to lie below 10000 cm−1 have been found. Levels of five odd configurations (f3ds2, f3d2s, f4sp, f3ds8s, f4dp) and seven even configurations (f4s2, f2d2s2, f3s2p, f3dsp, f4ds, f3d2p, f3ds8p) are now known.

A new restoring algorithm for the preferential enhancement of edge gradients

Abstract: We present here a new restoring algorithm that is based on use of a “median-window filter.” This is intrinsically a nonlinear operation that, when cyclically used with any linear restoring algorithm, can typically enhance edge gradients by a factor of 5:1 with nearly a complete absence of Gibbs oscillation.

Color-tolerance data and the tentative CIE 1976 L*a*b* formula

Abstract: In response to a general request of CIE Technical Committee TC 1.3 for evaluation of the proposed small-color-difference formula, tentative CIE 1976 L*a*b*, unit color-difference contours generated by this formula have been calculated and compared to cross sections in the chromaticity diagram of ellipsoids fitted nearly optimally to relevant visual color-tolerance data.

Power spectra requirements for wave-front-compensative systems*

Abstract: The phase degradation of an optical wave front distorted by turbulence in the propagation medium may be corrected in a piecewise-linear fashion by using an array of small circular mirrors. An option in the correction scheme is to compensate for overall tilt separately. We have evaluated power spectra and variances of the piston and tilt motions of the mirror segments as well as the motion of the overall tilt corrector. The form of the spectra for any propagation medium is an aperture integral of the product of the phase-difference power spectrum, describing the medium, and a generalized transfer function, representing the aperture and its segments. In the case of low-power atmospheric propagation, the necessary propagation results are linear in turbulence strength; hence the path may be sectioned into a large number of thin slices. A set of standard curves is found to represent a generalized slice, and the differential contributions may be summed to represent any propagation path. The standard curves, further modeled in terms of power-law dependencies, are practical for use on a desk calculator.

Real-time measurement of surface roughness by correlation of speckle patterns

Abstract: In a previous article we have shown that the two speckle patterns produced from the same rough surface illuminated by two coherent plane waves under two different angles of incidence are correlated. The correlation depends on the surface roughness. In this paper a method is described where the rough surface is illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-time measurement of the surface roughness in the range of large roughness (σ > λ). The theoretical calculations have been performed for a normally distributed surface. The experimental results are in good agreement with theory. We describe the optical arrangement of an instrument based on this principle.

Raman-scattering cross sections for water vapor

Abstract: We present cross sections for Raman scattering from water vapor excited at the four argon-laser wavelengths 476.5, 488.0, 496.5, and 514.5 nm. These cross sections, for the strong vibrational band centered at a shift near 3654 cm−1, are approximately 2.5 times larger than the corresponding N2Q-branch cross sections, and follow closely the expected (1/λR)4 dependence, where λR is the Raman scattering wavelength. We also report observations of the room-temperature depolarization and spectral profile of the band, and the overall spectral distribution of the scattering from 470 to 630 nm, for incident light at 488 nm. The latter observation indicates the absence of any other strong vibrational Raman-active modes.

Sums of independent lognormally distributed random variables

Abstract: The probability-density function of the sum of lognormally distributed random variables is studied by a method that involves the calculation of the Fourier transform of the characteristic function; this method is exact. When the number of terms in the sum is large, we employ an asymptotic series in N−1, where N is the number of terms, developed by Cramer. This method is employed in order to show that the permanence of the lognormal probability-density function is a consequence of the fact that the skewness coefficient of the lognormal variables is nonzero. Finally, a simplified proof, by use of the Carleman criterion, is presented to show that the lognormal is not uniquely determined by its moments.

Effect of field size on red - green color mixture equations

Abstract: Red-green color mixture equations were measured in 10 color-normal observers for fields of view varying from 30' to 10 degrees. The G/R mixture decreases continuously as field size is increased. The data are consistent with the interpretation that the cone visual photopigments decrease exponentially in effective optical density as the field size is increased.