Showing papers in "Journal of the Optical Society of America in 1978"
TL;DR: In this article, the possibility of using Bragg reflection in a cylindrical fiber to obtain lossless confined propagation in a core with a lower refractive index than that of the cladding medium is proposed and analyzed.
Abstract: The possibility of using Bragg reflection in a cylindrical fiber to obtain lossless confined propagation in a core with a lower refractive index than that of the cladding medium is proposed and analyzed.
833 citations
TL;DR: In this article, a direct numerical integration of the wave equation is used to establish the validity of approximating the fundamental mode of graded-index fibers by a Gaussian function, and the fundamental modes of fibers, whose index profile can be expressed as a power law, are indeed very nearly Gaussian in shape.
Abstract: Direct numerical integration of the wave equation is used to establish the validity of approximating the fundamental mode of graded-index fibers by a Gaussian function. We show that the fundamental modes of fibers, whose index profile can be expressed as a power law, are indeed very nearly Gaussian in shape (that is probably also true for graded-index fibers with convex profiles other than a power law). Graphs and empirical analytical expressions are presented for the optimum Gaussian beam width parameter and for the propagation constant of the fundamental mode.
445 citations
TL;DR: In this article, it was shown that the probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion.
Abstract: In short-exposure imaging through turbulence, there is some probability that the image will be nearly diffraction limited because the instantaneous wave-front distortion over the aperture was negligible. A number of years ago in a rather brief paper, Hufnagel (1966) argued heuristically that the probability of getting a good image would decrease exponentially with aperture area. This paper undertakes a rigorous quantitative analysis of the probability. We find that the probability of obtaining a good short-exposure image is Prob ≈ 5.6 exp[−0.1557 (D/r0)2] (for D/r0 ≥ 3.5), where D is the aperture diameter and r0 is the coherence length of the distorted wave front, as defined by Fried (1967). A good image is taken to be one for which the squared wave-front distortion over the aperture is 1 rad2 or less. The analysis is based on the decomposition of the distorted wave front over the aperture, in an orthonormal series with randomly independent coefficients. The orthonormal functions used are the eigenfunctions of a Karhunen-Loeve integral equation. The integral equation is solved using a separation of variables into radial and azimuthal dependence. The azimuthal dependence was solved analytically and the radial, numerically. The first 569 radial eigenfunctions and eigenvalues were obtained. The probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion. It is equal to the probability that a randomly chosen point in the hyperspace will lie within a hypersphere of unit radius, the points in the hyperspace being randomly chosen in accordance with the product of independent Gaussian probability distribution—one distribution for each dimension. The variance of these distrbutions is directly proportional to the eigenvalues of the Karhunen-Loeve equation. This hyperspace integral (involving up to several hundred dimensions) has been evaluated using Monte Carlo techniques.
357 citations
TL;DR: In this article, the diffraction of light by deep rectangular-groove transmission phase gratings is treated by solving Maxwell's equations numerically, and results are given for the light diffracted into the zero order by gratings with grating constants d in the range λ < d < 5λ, aspect ratio b (= linewidth/d), 0 < b < 1, and grating depths a < 5 λ, assuming a refractive index n 0 = 1.
Abstract: The diffraction of light by deep rectangular-groove transmission phase gratings is treated by solving Maxwell’s equations numerically. Results are given for the light diffracted into the zero order by gratings with grating constants d in the range λ < d < 5λ, aspect ratio b (= linewidth/d), 0 < b < 1, and grating depths a < 5λ, assuming a refractive index n0 = 1.5. Such gratings are used in practice as a dye-free replacement for color filters. They offer a new way of storing pictorial information in small format for read out in conventional projectors.
322 citations
TL;DR: In this article, a simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the core, and the resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation.
Abstract: A simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the refractive index of the core. The method applies to waveguides of arbitrary refractive index profile, arbitrary number of propagating modes, and arbitrary cross section. The resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation. Examples include modes on waveguides with circular symmetry and waveguides with two preferred axes of symmetry, e.g., an elliptical core. Only a minute amount of eccentricity is necessary for the well-known LP modes to be stable on an elliptical core, while the circle modes couple power among themselves.
285 citations
TL;DR: In this paper, an accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation, and the model is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length.
Abstract: Recent experiments reveal the high-wave-number form of the power spectrum of temperature fluctuations in turbulent flow. It is precisely this high-wave-number portion of the temperature spectrum that strongly affects optical propagation in the atmosphere. An accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation. An outstanding feature of the model and the observed temperature spectrum is a “bump” at high wave numbers. The accurate model of the temperature spectrum is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length. These results are compared with the predictions of Tatarskii’s spectrum. The bump in the temperature spectrum produces a corresponding bump in the temperature structure function, the variance of log intensity, and the structure function of phase. The accurate model is also used to determine the shape of the structure function of aerosol concentration fluctuations; it is found that this structure function varies as the logarithm of the separation distance for small separations.
256 citations
TL;DR: In this article, the relationship between the state of coherence of a source and the directionality of the light that the source generates is discussed. But the authors do not discuss the relationship of the two properties.
Abstract: Recent researches have revealed that there exists an intimate connection between radiometry and the theory of partial coherence. In this paper a review is presented of some of these developments. After a brief discussion of various models for energy transport in optical fields and of some of the basic concepts of the classical theory of optical coherence, the following topics are discussed: the foundations of radiometry, the coherence properties of Lambertian sources, and the relationship between the state of coherence of a source and the directionality of the light that the source generates. Some very recent work is also described which reveals that certain sources that are spatially highly incoherent in a global sense will generate light that is just as directional as a laser beam.
253 citations
TL;DR: In this article, the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the stokes vector.
Abstract: We extend the scope of the Mueller calculus to parallel that established by Jones for his calculus. We find that the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the Stokes vector. We determine the differential matrix m for eight basic types of optical behavior, find its form for the most general anisotropic nondepolarizing medium, and determine its relationship to the complex 2 × 2 differential Jones matrix. We solve the Stokes-vector differential equation for light propagation in homogeneous nondepolarizating media with arbitrary absorptive and refractive anisotropy. In the process, we solve the differential-matrix and Mueller-matrix eigenvalue equations. To illustrate the case of inhomogeneous anisotropic media, we consider the propagation of partially polarized light along the helical axis of a cholesteric or twisted-nematic liquid crystal. As an example of depolarizing media, we consider light propagation through a medium that tends to equalize the preference of the state of polarization to the right and left circular states.
239 citations
TL;DR: In this paper, a new optical technique for measuring the refractive-index structure parameter Cn2 was described, using relatively large incoherent transmitting and receiving optics, the scintillometer maintains its calibration and path-weighting function throughout the range of observed refractive turbulence values, even to the case of saturated scintillation.
Abstract: This paper describes a new optical technique for measuring the refractive-index structure parameter Cn2. By using relatively large incoherent transmitting and receiving optics, the scintillometer maintains its calibration and path-weighting function throughout the range of observed refractive turbulence values, even to the case of saturated scintillation.
237 citations
TL;DR: In this article, a new method of evaluating the MTF of a Kolmogorov turbulence phase aberration Zernike modal compensating system using an approximation of the correlation of the residual phase aberrations and the compensating phase distribution is described.
Abstract: A new method of evaluating the MTF of a Kolmogorov turbulence phase aberration Zernike modal compensating system using an approximation of the correlation of the residual phase aberration and the compensating phase distribution is described. This approach enables the extension of our previous results to cases including high-order terms in the compensating phase function. The Karhunen-Loeve expansion is discussed along with its relation to the Zernike polynomial expansion. Calculation of the optical resolution, or correlation quality, and the relative structure content, shows the Karhunen-Loeve expansion to be noticeably better than the Zernike expansion when terms through third and fifth order are included in the compensating phase distribution.
192 citations
IBM1
TL;DR: In this paper, the use of an ellipsometer having the configuration PCSC'A to determine the Mueller matrix of a linear optical system S, using imperfect compensators C and C′ and linear polarizer P and analyzer A, is described.
Abstract: We describe the use of an ellipsometer having the configuration PCSC’A to determine the Mueller matrix of a linear optical system S, using imperfect compensators C and C′ and linear polarizer P and analyzer A. Two manual (16 intensity), one semiautomatic (rotating-compensator) and one fully automatic (dual rotating-compensator) methods are described. Real-time Fourier analysis (of both raw and reduced data) is used in the automatic methods to reduce random and systematic measurement errors. Calibration procedures given for each method permit Mueller matrix spectroscopy using (quasi-) achromatic retarders whose principal axes, as well as retardation and transmission ratios change slightly with wavelength.
TL;DR: In this paper, a new rigorous integral formalism for the theoretical study of dielectric coated gratings and grating couplers is presented, which applies in the resonance domain, where the wavelength of the incident field and the groove spacing are of the same order of magnitude.
Abstract: We present a new rigorous integral formalism for the theoretical study of dielectric coated gratings and grating couplers. It applies in the resonance domain, where the wavelength of the incident field and the groove spacing are of the same order of magnitude. The computed program issued from this theory extends the domain of application of the previous differential or integral theories. It can be used to investigate, with a very good accuracy, the properties of bare or dielectric coated gratings, for any groove shape and any polarization, in the entire visible, ultraviolet, and infrared regions. Various classical criteria are used to control the validity of the numerical results and comparisons are made with the numerical results obtained using the previous integral and differential formalisms. Two examples of applications are given. First, we show that the new possibilities of our program lead to a better agreement between theoretical results and experimental data. Second, a theoretical study of a certain type of grating coupler is given.
TL;DR: In this article, the diffraction by thin refractive-index gratings of arbitrary periodic shape is treated, and three analytical approaches are shown to be equivalent for all diffracted orders.
Abstract: Diffraction by thin refractive-index gratings of arbitrary periodic shape is treated. Three analytical approaches are indicated and are shown to be equivalent. Resultant expressions for the diffraction efficiencies are given for all diffracted orders.
TL;DR: In this article, the propagation and scattering characteristics of a short optical pulse in a dense distribution of scatterers were studied, and the integral and differential equations for the two-frequency mutual coherence function under the first-order smoothing approximation were obtained.
Abstract: This paper presents a theoretical study on propagation and scattering characteristics of a short optical pulse in a dense distribution of scatterers. Examples include pulse diffusion in whole blood and in a dense distribution of particulate matter in the atmosphere and the ocean. The parabolic equation technique is applicable to the forward-scatter region where the angular spread is confined within narrow forward angles. When the angular spread becomes comparable to the order of unit steradian, there is as much backscattering as forward scattering and diffusion phenomena take place. We start with the integral and differential equations for the two-frequency mutual coherence function under the first-order smoothing approximation, and a general diffusion equation and boundary conditions are obtained. As examples, we present solutions for diffusion of a pulse from a point source and a plane wave incident on a slab of scatterers.
TL;DR: Contrast detection thresholds for moving spatial sine wave gratings were obtained, at the fovea, and at eccentricities of 1°, 2°, 4°, 6°, and 8° on the nasal horizontal meridian, for two subjects as mentioned in this paper.
Abstract: Contrast detection thresholds for moving spatial sine wave gratings were obtained, at the fovea, and at eccentricities of 1°, 2°, 4°, 6°, and 8° on the nasal horizontal meridian, for two subjects. The target field subtended 30 × 30 minutes of arc. The spatial frequency range extended from 2 cpd up to the spatial resolution limit, the temporal frequency range from 0.1 Hz up to the CFF. Mean retinal illuminance was 10 trolands. We find for these conditions: (i) Contrast detection thresholds are higher, the higher the spatial and/or temporal frequency of the stimulus. (ii) Acuity appears to be independent of the temporal frequency, the CFF appears to be independent of the spatial frequency. (iii) The higher the eccentricity, the higher the contrast detection threshold for any drifting sine wave pattern. The threshold doubles roughly any 2°–3° for spatial frequencies of 2–20 cpd, except that the visual field for a given fineness of grating is blind beyond a certain critical eccentricity. This critical eccentricity is a monotonically decreasing function of the spatial frequency of the grating. These measurements do not support the hypothesis that coarse patterns are preferentially detected at extrafoveal sites in the visual field.
TL;DR: In this paper, a multimode planar optical waveguide of homogeneous refractive index can produce real one-dimensional self-images by interference of the waveguide modes, and the authors discuss the image formation, the linespread function, and its apodisation and optimization.
Abstract: A multimode planar optical waveguide of homogeneous refractive index can produce real one-dimensional self-images by interference of the waveguide modes. We discuss the image formation, the linespread function, and its apodisation and optimization. Under optimum conditions, the theoretical linear resolution can reach 0.25(W λf)1/2, where W is the slab thickness and λf is the wavelength in the slab material.
TL;DR: The measurements show that maximum RBC velocities in retinal arteries vary markedly during each cardiac cycle, and Doppler shift frequency spectra obtained from suspensions of polystyrene spheres and RBC's flowing through glass capillary tubes are used to illustrate the basic principles of the technique.
Abstract: We have measured Doppler shift frequency spectra (DSFS) of laser light scattered from red blood cells (RBC’s) flowing through individual human retinal vessels. Each spectrum exhibits a cutoff frequency which is directly related to the maximum RBC velocity at the measurement site. Meaningful DSFS can be measured in times as short as 0.1 s. DSFS obtained from suspensions of polystyrene spheres and RBC’s flowing through glass capillary tubes are used to illustrate the basic principles of the technique and to aid in the interpretation of the in vivo measurements. Our measurements show that maximum RBC velocities in retinal arteries vary markedly during each cardiac cycle.
TL;DR: In this article, an extended Rayleigh-Sommerfeld integral method is used to derive expressions for the mutual coherence function and radiation intensity derived from a planar, partially coherent source propagating through the atmosphere.
Abstract: An extended, Rayleigh-Sommerfeld integral method is used to derive expressions for the mutual coherence function and radiation intensity derived from a planar, partially coherent source propagating through the atmosphere. The derived results reduce to previous results for (i) coherent radiation propagation in the atmosphere and (ii) the relations relating the far-field intensity angular distribution and the source coherence for a partially coherent source in vacuo. A mathematical description of the predicted results in terms of the vacuum distribution and scattering functions (related to the Fourier-transformed two-source mutual coherence function) is permitted by this development. Analytical results are calculated for a homogeneous atmosphere and a source coherence that simulates a laser-illuminated rough surface. The effective far-field range is determined by the source size, wavelength, and source coherence length. The phase of the calculated mutual coherence function is determined by the field-point separation for off-axial propagation directions. Numerical results for the amplitude and phase coherence lengths are calculated and illustrated as a function of the source size, source coherence length, propagation angle, range, and refractive-index structure constant.
TL;DR: It is shown that a smaller area, measuring several just resolvable distances across, has to be stimulated before successive or simultaneous contrast detection is possible at all.
Abstract: Contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6°, 21°, and 50° on the nasal horizontal meridian. The targets subtended from 30 × 30 minutes of arc up to 16° × 16°. We have found that the contrast detection thresholds depend critically on the extent of the target field. If this extent is large enough peripheral detection thresholds are on a par with those measured at the fovea, only the sensitivity range is shifted to lower spatial frequencies. We show that if the just resolvable distance at any eccentricity is taken as a yardstick, and field width and spatial frequency are scaled accordingly, then the spatio-temporal contrast detection thresholds become identical over the whole visual field. It is shown that a smallest area, measuring several just resolvable distances across, has to be stimulated before successive or simultaneous contrast detection is possible at all. Detection performance improves if the stimulated area is enlarged up to diameters of at least 102 just resolvable distances. The just resolvable distance correlates well with mean interganglion cell distance, and with the cortical magnification factor.
TL;DR: In this article, the spectral distribution of Australian daylight falling on a horizontal plane over the wavelength range 280-2800 nm has been made at two locations in southeastern Australia, one set of measurements in an urban environment and the other in the country.
Abstract: Measurements of the spectral distribution of Australian daylight falling on a horizontal plane over the wavelength range 280–2800 nm have been made at two locations in southeastern Australia, one set of measurements in an urban environment and the other in the country. Each set has been subjected to characteristic vector analysis. The major differences between the results and those of northern hemisphere workers are a higher ultraviolet-to-visible ratio and a chromaticity locus slightly to the purple side of the full radiator locus.
TL;DR: Stereoscopic acuity in the human fovea remains unimpaired with retinal image motions of up to 2 deg/s, and the presence during a short exposure of some stimulus components lying outside this zone leads to an overall reduction of stereoscope acuity.
Abstract: Stereoscopic acuity in the human fovea remains unimpaired with retinal image motions of up to 2 deg/s. These findings apply to lateral motion of the test target alone, and to simultaneous lateral motion of both test and comparison targets. For good stereoscopic acuity, depth motion can be tolerated only so long as the configuration does not move outside the disparity zone for optimal stereoscopic acuity, within 2–3 arc min of either side of the fixation plane. The presence during a short exposure of some stimulus components lying outside this zone leads to an overall reduction of stereoscopic acuity, either by dilution through summation, or by active inhibition of the best achievable depth resolution.
TL;DR: In this paper, contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6°, 12°, 21°, 32°, and 50° on the nasal horizontal meridian.
Abstract: Contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6°, 12°, 21°, 32°, and 50° on the nasal horizontal meridian. The field subtended 4° × 4°. Spatial frequencies ranged from 0.25 cpd up to the resolution limit, temporal frequencies from 0.1 Hz up to the CFF. Mean retinal illuminance was 10 trolands. We find for these conditions: (i) For any eccentricity there exists a unique combination of spatial frequency and velocity for which the threshold is a minimum. (Extremes are 2 cpd and 2° s−1 at the fovea, and 0.5 cpd and 12° s−1 at an eccentricity of 50°. (ii) Acuity depends little on velocity, the CFF only little on spatial frequency. (iii) The higher the eccentricity, the higher the threshold for any drifting sine wave pattern. Except for this the qualitative threshold behavior as a function of spatial and temporal frequency is identical at the fovea and at eccentricities up to 50°. The thresholds double every 12° for spatial frequencies of 0.25–2 cpd. For a given spatial frequency the visual field is blind beyond a certain critical eccentricity. This critical eccentricity is a monotonically decreasing function of spatial frequency.
TL;DR: The monocular, steady-state response to targets under various colors of illumination is investigated and it is shown that the ocular longitudinal chromatic aberration increases slightly with accommodation.
Abstract: Previous studies of the effects of color on the accommodation response are reviewed. The monocular, steady-state response to targets under various colors of illumination is investigated. It is shown that trained observers change their level of accommodation, when viewing a target at a constant distance, to compensate for the varying ocular longitudinal chromatic aberration as the color of the target is changed. Untrained subjects, however, may initially show inconsistent responses. Results in white and greeen are closely comparable. Dynamic aspects of these effects are illustrated and it is shown that the ocular longitudinal chromatic aberration increases slightly with accommodation. The results are related to current ideas on the accommodative system.
TL;DR: The method provides a simple and intuitive means for determing the effect of twisting on the linear birefringence and dichroic absorption of the medium, particularly when the light is initially linearly polarized.
Abstract: The propagation of light through a slowly twisting anisotropic medium is described by a coupled-mode theory; expressions are derived for the electric field for the case of a birefringent dichroic medium with a constant rate of twist. The method provides a simple and intuitive means for determing the effect of twisting on the linear birefringence and dichroic absorption of the medium, particularly when the light is initially linearly polarized. The theory is well suited to the analysis of light absorption in twisting insect photoreceptors, such as found in bees and ants. We provide full expressions and useful approximations for polarization sensitivity and the initial direction of polarization to give maximum absorption for several types of photoreceptors.
TL;DR: In this article, a description of the properties of plane diffraction gratings used in conical diffraction is given and a formula for computing the direction of the diffracted orders is given.
Abstract: A description is given of the properties of plane diffraction gratings used in conical diffraction. Formulas are given for computing the direction of the diffracted orders. Experiments were performed to investigate the behavior of gratings used on conical diffraction mountings. Comparisons made with classical diffraction mountings show a significant increase in the efficiency of the -1 order. An empirical formula to predict the efficiencies of gratings used in conical diffraction mountings has been verified by the measurements.
TL;DR: In this article, the Rydberg spectra of ten lanthanides have been studied using stepwise laser excitation and ionization methods, and the authors derived accurate ionization limits from observed photoionization thresholds.
Abstract: Photoionization and Rydberg spectra of ten lanthanides have been studied using stepwise laser excitation and ionization methods. These spectra were obtained from several different laser populated excited states in each case. Accurate ionization limits were derived from observed photoionization thresholds. Except for praseodymium, the observation of one or more long Rydberg progressions allowed more accurate limits to be determined. The Rydberg convergence values in eV are: Ce, 5.5387(4); Nd, 5.5250(6); Sm, 5.6437(6); Eu, 5.6704(3); Gd, 6.1502(6); Tb, 5.8639(6); Dy, 5.9390(6); Ho, 6.0216(6), and Er 6.1077(10). For praseodymium a threshold value of 5.464(+12-2) was obtained. When plotted against N, the lanthanide ionization limits normalized to correspond to ionization from the lowest level of fNs2 to the lowest level of fNs form two straight lines connected at the half-filled shell.
TL;DR: The spectrum of optical refractive-index fluctuations caused by temperature or salinity fluctuations in turbulent water is much different from the refractive index spectrum of temperature or humidity fluctuations in air as discussed by the authors.
Abstract: The spectrum of optical refractive-index fluctuations caused by temperature or salinity fluctuations in turbulent water is much different from the refractive-index spectrum of temperature or humidity fluctuations in air. This occurs because the ratio of kinematic viscosity to diffusivity is much greater for temperature and salinity fluctuations in water than for temperature and humidity fluctuations in air. In turbulent water the temperature and salinity spectra have viscous-convective ranges that extend roughly one and two decades in wave number, respectively. The consequences of these viscous-convective ranges for optical propagation in water are examined. It is found that the variance of log intensity, as a function of Fresnel-zone size, rises far above its large Fresnel-zone-size asymptotic form, and the covariance function of log-amplitude is relatively narrow when the viscous-convective range dominates its shape. If the viscous-convective range dominates the shape of the structure function of phase, then the structure function is proportional to the spacing and is less sensitive to outer scale effects than for propagation in air. Likewise, the lateral coherence length has a new asymptotic form arising from a viscous-convective range and is also less sensitive to outer scale effects than for propagation in air.
TL;DR: The change in the voltage between the electrodes of a gas discharge plasma when illuminated at wavelengths corresponding to allowed transitions in the gas atoms has been measured for cesium, uranium, argon, neon, hydrogen, and mercury plasmas.
Abstract: The change in the voltage between the electrodes of a gas discharge plasma when illuminated at wavelengths corresponding to allowed transitions in the gas atoms has been measured for cesium, uranium, argon, neon, hydrogen, and mercury plasmas. Using this effect, high signal-to-noise absorption spectra were obtained with a mechanically scanned cw Rh6G dye laser. Magnitude, polarity, and saturation of the induced voltage charges were determined; a 30% decrease in the operating voltage of a cesium discharge tube was the largest effect observed.
TL;DR: It is argued that both electrophysiological and psychophysical evidence indicates that Weber behavior starts whenever some small fixed number of quantum absorptions occur within an area of 1 mean interganglion cell distance across.
Abstract: Contrast detection thresholds for moving sine wave gratings were obtained at the fovea and at eccentricities of 6°, 21°, and 50° on the nasal horizontal meridian. The targets subtended from 30 × 30 minutes of arc up to 16° × 16°. Mean retinal illuminance was varied between 10 and 0.01 trolands. The transition from the de Vries–Rose to the Weber region occurs in the far peripheral visual field at a 2–3 decades lower illuminance level than at the fovea. The spatio-temporal contrast detection thresholds become comparable over the whole visual field if the mean distance between retinal ganglion cells is taken as a yardstick, and field width, spatial frequency, and quantum density are scaled accordingly. This means that at scotopic illuminance levels coarse or medium gratings are preferentially detected at other than foveal locations. (The fine gratings cannot be resolved at all at such levels.) It is argued that both electrophysiological and psychophysical evidence indicates that Weber behavior starts whenever some small fixed number of quantum absorptions occur within an area of 1 mean interganglion cell distance across. Or, equivalently, if a fixed small number of “neural quanta” enters a 100 × 100 μm2 area of the visual cortex.