Showing papers in "Journal of the Optical Society of America in 1979"

Chromaticity diagram showing cone excitation by stimuli of equal luminance.

Abstract: In a space where Cartesian coordinates represent the excitations of the three cone types involved in color vision, a plane of constant luminance provides a chromaticity diagram in which excitation of each cone type (at constant luminance) is represented by a linear scale (horizontal or vertical), and in which the center-of-gravity rule applies with weights proportional to luminance.

Motion and vision. II. Stabilized spatio-temporal threshold surface.

Abstract: The stabilized contrast-sensitivity function measured at a constant retinal velocity is tuned to a particular spatial frequency, which is inversely related to the velocity chosen The Fourier transforms of these constant-velocity passbands have the same form as retinal receptive fields of various sizes At low velocities, in the range of the natural drift motions of the eye, the stabilized contrast-sensitivity function matches the normal, unstablized result At higher velocities (corresponding to motions of objects in the environment), this curve maintains the same shape but shifts toward lower spatial frequencies The constant-velocity passband is displaced across the spatio-temporal frequency domain in a manner that is almost symmetric about the constant-velocity plane at v = 2 deg/s Interpolating these diagonal profiles by a suitable analytic expression, we construct the spatio-temporal threshold surface for stabilized vision, and display its properties in terms of the usual frequency parameters; eg, at low spatial frequencies, the temporal response becomes nearly independent of spatial frequency, while at low temporal frequencies, the spatial response becomes independent of temporal frequency

Electromagnetic propagation in birefringent layered media

Abstract: The propagation of electromagnetic radiation in birefringent layered media is considered. A general formulation of the plane-wave propagation in an arbitrarily birefringent layered medium is presented. The concepts of dynamical matrix and propagation matrix are introduced. A 4 × 4 transfer matrix method is used to relate the field amplitudes in different layers. Our general theory is then applied to the special case of periodic birefringent layered media, especially the Solc birefringent layered media [ I. Solc , Cesk. Casopis Fẏs.3, 366 ( 1953);Cesk. Casopis Fẏs.10, 16 ( 1960)]. The unit cell translation operator is derived. The band structures as well as the Bloch waves are obtained by diagonalizing the translation operator. Coupled mode theory is extended to the case of birefringent periodic perturbation to explain the exchange Bragg scattering. A general mode dispersion relation for guided waves is also obtained in terms of the transfer matrix elements.

Wigner distribution function and its application to first-order optics

Abstract: The Wigner distribution function of optical signals and systems has been introduced. The concept of such functions is not restricted to deterministic signals, but can be applied to partially coherent light as well. Although derived from Fourier optics, the description of signals and systems by means of Wigner distribution functions can be interpreted directly in terms of geometrical optics: (i) for quadratic-phase signals (and, if complex rays are allowed to appear, for Gaussian signals, too), it leads immediately to the curvature matrix of the signal; (ii) for Luneburg’s first-order system, it directly yields the ray transformation matrix of the system; (iii) for the propagation of quadratic-phase signals through first-order systems, it results in the well-known bilinear transformation of the signal’s curvature matrix. The zeroth-, first-, and second-order moments of the Wigner distribution function have been interpreted in terms of the energy, the center of gravity, and the effective width of the signal, respectively. The propagation of these moments through first-order systems has been derived. Since a Gaussian signal is completely described by its three lowest-order moments, the propagation of such a signal through first-order systems is known as well.

Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation

Abstract: We have derived analytic expressions for the angular distribution of light emitted by an atomic system, e.g., a fluorescent molecule, located in a dielectric medium 1 at distance z0 from the interface to a different dielectric medium 2. The theory is rigorously valid for electric and magnetic dipole transitions with arbitrary orientation of the dipole transition moment. (In Paper II [ J. Opt. Soc. Am.57, 1615– 1619 ( 1977)], only the special case of dipoles oriented perpendicular to the interface had been treated.) The radiation patterns of dipoles located on the interface (z0 = 0) and oriented parallel to it, and ensembles of such dipoles radiating incoherently with randomly oriented dipole moments were examined in particular. They differ greatly from the corresponding well-known dipole radiation patterns in an unbounded medium 1, due to the wide-angle interferences of emitted plane waves, and radiation from evanescent waves in the dipole’s near field into medium 2, if this is denser than medium 1.

Relation between the angular dependence of scattering and the statistical properties of optical surfaces

Abstract: A relation from vector scattering theory has been used to predict the angular distribution of scattered light from optical surfaces as a function of the wavelength, optical constants of the material, and spectral density function. For calculations of one-dimensional (two-dimensional) scattering, the spectral density function of the surface roughness is obtained from the Fourier transform (Hankel transform) of the autocovariance function, which in turn is determined from surface-profile data. Measured statistics presented for various types of optical surfaces indicate that there are three basic components of surface structure: long-range waviness, short-range random roughness, and periodicity; one or more of which may be present on a given surface. Averaged and unaveraged surface-profile data for the same surface are shown to be consistent. Experimental data are presented that yield an exponential autocovariance function, and give a reasonably good fit to a Poisson distribution of zero crossings. Finally, angular scattering values calculated using measured surface statistics with vector scattering theory are compared to scattering values measured on the same surface. The shapes of the measured and calculated curves are similar, but the magnitudes are not. However, the rms surface roughnesses calculated from total integrated scattering measurements are in excellent agreement with values measured directly on these same surfaces.

Optical beam propagation for a partially coherent source in the turbulent atmosphere

Abstract: The extended Huygens-Fresnel principle is used to formulate general expressions of the mutual intensity function for a finite optical source with partial spatial coherence propagating in the weakly turbulent atmosphere. Formulations are developed for both the focused and collimated Gaussian beam. Generalized criterion for the effective far-field range is defined in terms of the source aperture, optical wave number, source coherence, and characteristic length associated with the atmospheric turbulence. Beam spread and lateral coherence length in the near and far field are investigated for a combination of parameter variations and the physical implications discussed. Finally, analytic results are calculated and plotted to illustrate the functional behavior of relevant physical parameters.

Matrix formulation of the reconstruction of phase values from phase differences

Abstract: Methods in speckle imaging and adapative optics, as well as a new technique in digital image restoration, require the calculation of the Fourier phase spectrum from measurements of the differences on a two-dimensional grid of the phase spectrum. The calculation of phases from phase differences has been analyzed in the literature and relaxation mechanisms for computing the phase have been derived by least-squares analysis. In the following paper we formulate the phase reconstruction problem in terms of a vector-matrix multiplication, and we then show that previous solution methods are equivalent to this general description. We also analyze the errors in reconstruction and reconcile previously published error results based on simulations with an analytical error expression derived from Parseval’s theorem. Finally, we comment upon the rate of convergence of phase reconstructions, and discuss numerical analysis literature which indicates that the methods previously published for phase reconstruction can be made to converge much faster.

Spatial frequency masking in human vision: binocular interactions.

Abstract: Binocular contrast interactions in human vision were studied psychophysically. Thresholds were obtained for sinewave grating stimulation of the right eye in the presence of simultaneous masking gratings presented to the right eye (monocular masking) or left eye (dichoptic masking). In the first experiment, thresholds were measured at 0.25, 1.0, 4.0, and 16.0 cycle per degree (cpd) as a function of the contrast of masking gratings of identical frequency and phase. Thresholds rose nonmonotonically with masking contrast. At medium and high contrast levels, dichoptic masking was more effective in elevating contrast thresholds than monocular masking, and approached Weber’s Law behavior. In the second experiment, spatial frequency tuning functions were obtained for test gratings at five spatial frequencies, by measuring threshold elevation as a function of the spatial frequency of constant-contrast masking gratings. At 1.0, 4.0, and 16.0 cpd, the tuning functions peaked at the test frequencies. The dichoptic tuning functions had a bandwidth of about 1 octave between half-maximum points, narrower than the ± 1 octave bandwidths of the monocular tuning functions. At 0.125 and 0.25 cpd, the tuning functions were broader and exhibited a shift in peak masking to frequencies above the test frequencies.

Modal wave-front estimation from phase derivative measurements

Abstract: Modal estimation of wave-front phase from phase derivatives is discussed. It is shown that it is desirable to minimize the number of modes estimated and the number of measurements used to maintain the quality of the estimates of low-order modes. It is also shown that mode cross coupling occurs when one tries to estimate modes higher than astigmatism.

Gaussian beam propagation beyond the paraxial approximation

Abstract: The propagation of a Gaussian beam in a homogeneous, isotropic, local, linear, and nonmagnetic dielectric medium is studied using the angular spectrum representation for the electric field. The electric field associated with the Gaussian beam inside the dielectric medium consists of the paraxial result and higher-order non-Gaussian correction terms. It is shown that the second-order correction term satisfies an equation consistent with the recent work of Lax, Louisell, and McKnight. Numerical results showing the corrections to the paraxial approximation are presented.

Diffraction theory of laser read-out systems for optical video discs

Abstract: The form of discs considered has λ/4-deep pits along the track, the spacings and lengths of which are modulated. A laser beam is focused on the track by means of a high-aperture objective, and the light which is scattered back through the objective is detected. The diffraction theory of this system is treated, both for simple periodic and for more complicated forms of disc. Formulas are obtained for the fundamental and harmonics of the read-out signal. The influences of focus error and aberrations are studied, for certain cases of which numerical results are given. Also treated are cross-talk between adjacent tracks and intermodulation between the pit-spacing frequencies and those of the length modulation of the pits.

Opponent chromatic mechanisms: Relation to photopigments and hue naming

Abstract: Opponent chromatic response functions were determined for monochromatic, equal-luminance stimuli from 400 to 700 nm for three observers using a hue cancellation procedure. The same observers scaled the hue of the stimuli using the terms red, green, yellow, and blue. The results showed that the hue scaling was accurately predicted from the cancellation functions using the model of Hurvich and Jameson. Theoretical curves were generated to fit the chromatic response functions with a linear combination of three cone photopigments. The theoretical photopigments were based on an iodopsin nomogram with λmax at a = 435, β = 530, and γ = 562 nm. An estimate of the density of each observer’s preretinal optic media was obtained in order to relate the photopigment absorption spectra to the psychophysical data. Good linear fits were obtained for each observer’s red-green curve, but not for the yellow-blue curves. A nonlinear model with an expansive exponent was used to fit the yellow-blue response functions with the three theoretical photopigments.

Motion and vision. I. Stabilized images of stationary gratings

Abstract: To demonstrate that eye movements have profound effects on the sine-wave contrast threshold, the author uses a new method of stabilizing the retinal image, in which the Purkinje reflections from the eye move the stimulus pattern displayed on a CRT screen. Calibration of this compensatory motion is very critical; a gain error greater than 1% may produce significant destabilization. Under optimum conditions, image stabilization elevates the subject’s contrast threshold by a factor of about 20; it also produces after-images with resolution greater than 12 c/deg. These results compare favorably with those obtained by other methods.

Bandwidths of orientation channels in human vision

Abstract: The ability of observers to discriminate between stimuli differing in orientation was measured using low contrast, foveally viewed stimuli. Detection and discrimination performance were measured simultaneously. A model is presented which permits bandwidths of orientation-tuned mechanisms to be estimated from the data. In a group of five observers, half-amplitude bandwidths varied from 10° to 20°.

K distributions in atmospheric propagation of laser light

Abstract: Experimental results are presented which suggest that the probability distribution of fluctuations in the intensity of laser light propagating through atmospheric turbulence are reasonably well described by K distributions in the intermediate range of propagation path lengths, L ≃ 600 m, β0≃1–2, where the mean square fluctuation 〈I2〉 /〈I〉2 can be as high as five.

Complex angular momentum theory of the rainbow and the glory

Abstract: A survey is given of the applications of complex angular momentum theory to Mie scattering, with special emphasis on the recent treatments of the rainbow and the glory. The theory yields uniform asymptotic expansions of the scattering amplitudes for rainbows of arbitrary order, for size parameters ≳ 50, in close agreement with the exact results. The Airy theory fails for parallel polarization in the primary bow and for both polarizations in higher-order rainbows. The theory provides for the first time a complete physical explanation of the glory. It leads to the identification of the dominant contributions to the glory and to asymptotic expressions for them. They include a surface-wave contribution, whose relevance was first conjectured by van de Hulst, and the effect of complex rays in the shadow of the tenth-order rainbow. Good agreement with the exact results is obtained. Physical effects that play an important role include axial focusing, cross polarization, orbiting, the interplay of various damping effects, and geometrical resonances associated with closed or almost closed orbits. All significant features of the glory pattern found in recent numerical studies are reproduced.

Bound, odd-parity J = 1 spectra of the alkaline earths: Ca, Sr, and Ba

Abstract: We have used multiphoton excitation via selected intermediate states to observe and identify triplet Rydberg series of the type msnp3P0 up to high n in Ca, Sr, and Ba. Previous efforts have failed to identify these series beyond n = 7. We present details of our experimental method, give tables of the newly determined energy levels, and describe their analysis by multi-channel quantum defect theory (MQDT). For the most part, the msnp3P0 series in Ca and Sr can be described by a nearly constant quantum defect δ with δCa = 19.7 and δSr = 2.90. The 6s n p3P0 series in Ba is more heavily affected by the configuration interaction, but to a reasonable approximation has δBa ≈ 3.81. For all three elements, we find that the msnp¹P10 series are much more strongly perturbed than the ³P10 series. Most of this paper treats Ba. In addition to the 3P0 states, 3F2 and 1G4 states are measured and tabulated. Further results in Ba include new and/or revised values for some ¹P10 states a revised ionization limit, evidence for an energy-dependent configuration interaction, and an MQDT prediction of the photoabsorption cross section at the ionization limit. This prediction agrees with the most recent experimental cross section. The MQDT analysis of Ba is described in great detail to make it useful as a guide to the reader who wishes to become a user of MQDT.

Bandpass Channels, Zero-Crossings, and Early Visual Information Processing

Abstract: Under appropriate conditions zero-crossings of a bandpass signal are very rich in information. The authors examine here the relevance of this result to the early stages of visual information processing, where zero-crossings in the output of independent spatial-frequency-tuned channels may contain sufficient information for much of the subsequent processing.

Geometrical vector flux and some new nonimaging concentrators

Abstract: The geometrical vector flux, a quantity related to measures of illumination, is defined; some of its properties are explained and used to develop new forms of nonimaging concentrators.

Distribution of absorption centers within irradiated spheres

Abstract: This paper presents the distribution of absorption centers within an absorbing sphere under monochromatic, parallel illumination. Results for the equatorial plane are represented by topographical perspective views for size parameters a, up to 5, and for refractive indices up to m = 3.0−0.1i. The main features of the topography become increasingly structured with increasing magnitude of the size parameter and the real part of the refractive index. Although the imaginary part of the refractive index strongly influences the magnitude of the absorption, it does not influence the shape of the topography as long as the imaginary part is less than the real part of the refractive index. Results are also presented for m = 1.95−0.66i corresponding to carbon. The source function, which is depicted for the first time in this paper, must be the starting point for any theory of radiation pressure on small absorbing particles, for photophoresis, or for other phenomena concerned with the temperature distribution within irradiated particles.

Bimorph piezoelectric flexible mirror

Abstract: We describe a flexible mirror constructed from plates of glass and lead zirconium titanate (PZT) piezoelectric ceramic glued together. It is activated by a series of electrodes on the reverse side. An equation of state is derived, giving the surface profile as a function of the electrode voltages, and the experimental behavior of the mirror is illustrated.

Temperature dependence of absorptance in laser damage of metallic mirrors: I. Melting

Abstract: Naval Weapons Center damage thresholds for ultraclean metals (45 J/cm2, 100 ns, 10.6 μm, Cu) are a milestone in laser-damage studies, being reproducible, with no isolated-spot damage, and showing the first excellent agreement (∼ 15%) with a first-principles theory (developed here) for any metal or transparent material. An exact premelting temperature result for the case of optical absorptance A = Ai + A1Ts indicates that the surface-temperature rise Ts reduces the theoretical threshold (Itp)m for raising Ts to the melting temperature Tm by a factor of 3.6 to 1.6, typically. Raising Ts to Tm is a good damage criterion for 100-ns pulses, but not for single subnanosecond pulses. The previous scaling Itp∼tp1/2/A is invalid in general, but Itp∼tp1/2 is valid for (Itp)m even with A = Ai + A1Ts. Approximating a Gaussian I(t) pulse by a square pulse makes (Itp)m 17% too small in the constant-A approximation.

Estimation of spatial power spectra in speckle interferometry

Abstract: Calculations of the signal-to-noise ratio (SNR) of estimates of the power spectra of spatially varying random processes, such as stellar speckle patterns, usually include realizations that contain less than two detected photons. It is shown in this paper that if these cases are excluded from the analysis procedure either implicitly or explicitly, then under the usual definition of SNR, the overall SNR of an estimate can increase by up to a factor of N¯−1/2, where N¯≪1 is the average number of detected photons per realization.

Modes of dielectric waveguides of arbitrary cross sectional shape

Abstract: A technique is presented for determining the modal propagation properties of a homogeneous cylindrical dielectric waveguide of arbitrary cross sectional shape and index n1 embedded in a medium of index n2. Both the weakly guiding case in which n1 ≈ n2 and the general case of arbitrary index difference are discussed theoretically. In both cases the approach is to derive integral representations for appropriate components of E and B. These satisfy the appropriate Helmholtz equations inside and outside the guide and also guarantee that the boundary conditions are satisfied. On expansion of the components in certain sets of basis functions, the representations become a set of linear equations. The vanishing of the determinant of this set yields the propagation constants of the various modes. Numerical results are given for weakly guiding fibers of various shapes. Among these are rectangles and ellipses, which make comparisons with previous work possible.

Quantitative surface topography determination by Nomarski reflection microscopy. I. Theory

Abstract: The Nomarksi differential interference contrast microscope is examined as a tool for determination of metallic mirror surface topography. This discussion includes the development of an optical model for the Nomarski system, an examination of the key results of the model’s application to sloped sample surfaces, and recommended procedures for implementation. The functional relationship is developed between image intensity and the component of surface slope along the Nomarski shear direction, the fixed parameters in the Nimarksi system, and the adjustable phase shifts related to Nomarski prism position. Equations are also developed to allow the determination of surface slope from relative image intensity when sample reflectively is uniform and slopes are small.

The Rayleigh hypothesis in the theory of reflection by a grating

Abstract: In this paper, the Rayleigh hypothesis in the theory of reflection by a grating is investigated analytically. Conditions are derived under which the Rayleigh hypothesis is rigorously valid. A procedure is presented that enables the validity of the Rayleigh hypothesis to be checked for a grating whose profile can be described by an analytic function. As examples, we consider some grating profiles described by a finite Fourier series. Numerical results are then presented.

The Mandelbaum Effect: Evidence for an accommodative bias toward intermediate viewing distances

Abstract: Previous research has shown that ocular accommodation tends to correspond to an intermediate distance, the dark focus, in the absence of effective stimulation. The present experiments measured accommodative responses in the presence of two adequate, monocular stimuli superimposed optically at different distances. In Experiment I, observers attempted to maintain a matrix of letters in clear focus as a superimposed mesh screen was varied in distance. In experiment II, observers were instructed to focus the "easier" of two similar grating patterns that were presented over a range of distances with a constant separation of two diopters. The results of both experiments showed an accomodative response bias toward target distances near the observers' dark focus of accommodation. The implications of these findings for the theoretical resting state of accomodation and for practical problems of visual performance are discussed.

Sampling theorems in polar coordinates

Abstract: We investigate the problem of representing an arbitrary class of real functions f(·) in terms of their sampled values along the radius r and at equal angular increments of the azimuthal angle θ. Two different bandwidth constraints on f(r,θ) are considered: Fourier and Hankel. The end result is two theorems which enable images to be reconstructed from their samples. The theorems have potential application in image storage, image encoding, and computer-aided tomography.