Showing papers in "Journal of the Optical Society of America in 1972"
TL;DR: An iterative method of restoring degraded images was developed by treating images, point spread functions, and degraded images as probability-frequency functions and by applying Bayes’s theorem.
Abstract: An iterative method of restoring degraded images was developed by treating images, point spread functions, and degraded images as probability-frequency functions and by applying Bayes’s theorem. The method functions effectively in the presence of noise and is adaptable to computer operation.
3,869 citations
TL;DR: A 4×4-matrix technique was introduced by Teitler and Henvis as discussed by the authors to solve the problem of reflection and transmission by cholesteric liquid crystals and other liquid crystals with continuously varying but planar ordering.
Abstract: A 4×4-matrix technique was recently introduced by Teitler and Henvis for finding propagation and reflection by stratified anisotropic media. It is more general than the 2×2-matrix technique developed by Jones and by Abeles and is applicable to problems involving media of low optical symmetry. A little later, we developed a 4×4 differential-matrix technique in order to solve the problem of reflection and transmission by cholesteric liquid crystals and other liquid crystals with continuously varying but planar ordering. Our technique is mathematically equivalent to that of Teitler and Henvis, but we used a somewhat different approach. We start with a 6×6-matrix representation of Maxwell’s equations that can include Faraday rotation and optical activity. From this, we derive expressions for 16 differential-matrix elements so that a wide variety of specific problems can be attacked without repeating a large amount of tedious algebra. The 4×4-matrix technique is particularly well suited for solving complicated reflection and transmission problems on a computer. It also serves as an illuminating alternative way to rederive closed solutions to a number of less-complicated classical problems. Teitler and Henvis described a method of solving some of these problems, briefly in their paper. We give solutions to several such problems and add a solution to the Oseen–DeVries optical model of a cholesteric liquid crystal, to illustrate the power and simplicity of the 4×4-matrix technique.
1,787 citations
TL;DR: In this paper, a set of coupled-mode equations is derived to describe mode propagation in uniform and slightly nonuniform cylindrical optical-fiber systems, and the coupling between fibers of an array made up of n identical fibers each at the vertex of a polygon and one at the center, which is not necessarily the same as its n neighbors, is determined.
Abstract: A set of coupled-mode equations is derived to describe mode propagation in uniform and slightly nonuniform cylindrical optical-fiber systems. The coupling between fibers of an array made up of n identical fibers each at the vertex of a polygon and one at the center, which is not necessarily the same as its n neighbors, is determined. Examples of this array are two fibers, three fibers in a row, and a hexagonal array with a fiber in the center. Very simple expressions for the coupling coefficients are presented. Mode coupling on a lossy fiber is investigated and a simple expression for the loss of a HE11 mode is given.
695 citations
TL;DR: A communication-theory model for the process of image formation is used and it is found that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited.
Abstract: Given M sampled image values of an incoherent object, what can be deduced as the most likely object? Using a communication-theory model for the process of image formation, we find that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited. The derivation is an adaptation to optics of a formulation by Jaynes for unbiased estimates of positive probability functions. The restoring formula is tested, via computer simulation, upon noisy images of objects consisting of random impulses. These are found to be well restored, with resolution often exceeding the Rayleigh limit and with a complete absence of spurious detail. The proviso is that the noise in each image input must not exceed about 40% of the signal image. The restoring method is applied to experimental data consisting of line spectra. Results are consistent with those of the computer simulations.
673 citations
TL;DR: The experiments demonstrate that a grating is masked only by noise whose spatial frequencies are similar to the grating frequency, and provide further indication of the existence of channels in the visual system that are selectively tuned to different spatial frequencies.
Abstract: Vertical sinusoidal gratings were viewed in masking noise consisting of vertical stripes spread along the horizontal direction. Masking functions were obtained while varying the grating frequency relative to various one-octave-wide bands of noise. These functions closely resemble curves derived from previous experiments on adaptation to gratings. Masking was also measured as a function of the width of a band of noise centered on the grating frequency. Masking increased as the band was widened up to approximately ±1 octave; masking did not increase further when the band was widened beyond this range. The results demonstrate that a grating is masked only by noise whose spatial frequencies are similar to the grating frequency. The experiments provide further indication of the existence of channels in the visual system that are selectively tuned to different spatial frequencies.
401 citations
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TL;DR: In this article, a two-term Sellmeier formula was proposed to fit the resulting infrared data as well as the data selected by Edlen in the visible and ultraviolet (UV) wavelengths.
Abstract: New measurements of the infrared dispersion of air are reported. They agree with series I of the 1962 data of Peck and Khanna, but lie below Edlen’s 1966 formula. A two-term Sellmeier formula suffices to fit the resulting infrared (ir) data as well as the data selected by Edlen in the visible and ultraviolet (uv), being valid down to nearly 0.23 μm. Other possible Sellmeier fits are discussed, including extension to 0.185 μm.
382 citations
TL;DR: Four methods of heterochromatic photometry were employed, using the same four observers in each case, and the minimally distinct-border method (MDB) is shown to yield results that are linear and obey Abney’s law.
Abstract: Four methods of heterochromatic photometry were employed, using the same four observers in each case. These were (i) two types of direct heterochromatic photometry (direct comparison with white, and step by step), (ii) flicker photometry, and (iii) the minimally distinct-border method (MDB). The MDB method is shown to yield results that are linear and obey Abney’s law. Flicker and MDB methods generate relative luminous-efficiency functions that agree well with each other and also with the CIE standard observer as modified by Judd; the methods of direct heterochromatic photometry yield data that agree fairly well with each other, whereas they differ greatly from the data obtained by flicker or MDB. Luminous efficiency as measured by the direct methods seems to receive a contribution from two sources, (a) achromatic signals of the photopic visual system, which exclusively determine the MDB setting, and (b) chromatic signals of the visual system, which produce extra brightness, the amount of which is related to the saturation of the stimulus used.
278 citations
TL;DR: In this article, the authors derived the third-order and chromatic aberrations of the zone plate and showed that the image may be diffraction limited only if the illumination is relatively monochromatic.
Abstract: The zone plate is an optical device that depends on interference, not reflection or refraction, for its image-forming properties. Although the irradiance at the focus is only 110 that of a lens with the same aperture, a zone plate with 100 or more zones is capable of resolution equal to that of the lens. Zone plates can be used in spectral regions where conventional optics are unavailable and for special applications in the visible spectrum. This paper derives the third-order and chromatic aberrations of the zone plate. The image may be diffraction limited only if the illumination is relatively monochromatic. Like the pinhole camera, the zone plate turns out not to suffer from linear distortion, even at very wide fields.
179 citations
TL;DR: Threshold amounts of light variation needed to see flicker and to see a flickering line, as functions of frequency of variation, are significantly different.
Abstract: Threshold amounts of light variation needed to see flicker and to see a flickering line, as functions of frequency of variation, are significantly different. Sensitivity to flicker increases between 0.4 and approximately 10 Hz, and shows a subsequent decrease at higher frequencies; sensitivity to spatial contrast decreases gradually between 3 and 30 Hz.
170 citations
TL;DR: In this paper, the electromagnetic field associated with a generalized beam is analyzed theoretically, where the beam may take on an irradiance cross section described by a gaussian function with arbitrary elliptical symmetry.
Abstract: The electromagnetic field associated with a generalized beam is analyzed theoretically, where the beam may take on an irradiance cross section described by a gaussian function with arbitrary elliptical symmetry. For this analysis, the field is represented by an expansion into an angular spectrum of plane waves. Expressions for the field components throughout a medium that is free of sources are found by use of an asymptotic approximation that is common in gaussian-beam analysis. In addition, more-precise expressions for these components are found, which are valid outside the neighborhood of focus. Near focus, gaussian beams may have only approximately gaussian cross sections, and in this region the behavior of beams without circular symmetry is greatly complicated. The effects of noncircular symmetry are discussed in some detail, and a method for correcting a beam to produce circular symmetry is described.
157 citations
TL;DR: The area of the gamut, in a uniform chromaticity-scale diagram of the chromaticities of a standard array of object colors, is taken to be a measure of color-discrimination capability of an illuminant.
Abstract: The area of the gamut, in a uniform chromaticity-scale diagram of the chromaticities of a standard array of object colors, is taken to be a measure of color-discrimination capability of an illuminant. The 1960 CIE u, v chromaticity diagram, and the eight test colors of the interim method for computing a color-rendering index, are used for demonstration. Correlation with long-standing subjective evaluations of color rendering of eight commercial lamps is shown. Artificial illuminants excel daylight and the equal-energy spectrum in the gamut of chromaticities of illuminated samples.
TL;DR: In this paper, it is confirmed that absorption proceeds at a rate proportional to the second-order product of the complex field amplitude, whether the light field is homogeneous or evanescent, and that the emission process follows a reciprocity principle.
Abstract: Experiments have been carried out to investigate the excitation of molecules by evanescent light, and the emission of evanescent light in the fluorescence of excited molecules. It is confirmed that the absorption proceeds at a rate proportional to the second-order (normally ordered) product of the complex field amplitude, whether the light field is homogeneous or evanescent, and that the emission process follows a reciprocity principle.
TL;DR: In this paper, the change of refractive index of the sample caused by the temperature change due to absorption of light was measured with an interferometer, and the lowest values were obtained for carbon tetrachloride, chloroform, and bromobenzene.
Abstract: Measurements have been made of the absorptivity of 31 low-loss liquids by a new technique. The change of refractive index of the sample caused by the temperature change due to absorption of light was measured with an interferometer. Absorptivity values as small as 10−5 cm−1 have been measured. The lowest values were obtained for carbon tetrachloride, chloroform, and bromobenzene. The absorptivity of heavy water is <5×10−5 cm−1, 1/60 that of ordinary water at the same wavelength. Measurements were made at 6328 A.
TL;DR: In this article, the problem of designing a reflector to distribute the illumination of a nonisotropic point source on a plane aperture according to a pre-assigned pattern is analyzed.
Abstract: The problem of designing a reflector to distribute the illumination of a nonisotropic point source on a plane aperture according to a pre-assigned pattern is analyzed. An integral equation and equivalent partial differential equation are derived. The form of the latter reveals this reflector-design problem to be a singular elliptic Monge–Ampere boundary-value problem.
TL;DR: In this paper, the characteristic resonance-line spectrum in the Kr i isoelectronic sequence, consisting of the five transitions to the 4p6 1S0 ground state from levels with J = 1, was observed from Rb ii to Mo vii.
Abstract: The characteristic resonance-line spectrum in the Kr i isoelectronic sequence, consisting of the five transitions to the 4p6 1S0 ground state from levels with J = 1 in the 4p54d and 5s configurations has been observed from Rb ii to Mo vii. The observations were made with sliding sparks, on the 10.6-m normal-incidence spectrograph at NBS and the 5-m grazing-incidence spectrograph in Lund. A number of transitions from higher levels of the type 4p5nd, 4p5ns, and 4s4p65p were also observed. Isoelectronic comparisons are given for all observed levels. The ionization energies in electron volts are Rb ii 27.285Y iv 60.60Nb vi 102.06Sr iii 42.87Zr v 80.36Mo vii 125.66.Anomalous relative intensities observed for the 4p54d transitions are found to be caused by excitation conditions within the light source.
TL;DR: In this article, the angular correlation function of a stationary optical field is introduced, which characterizes the correlation that exists between the complex amplitudes of any two plane waves in the angular spectrum description of the statistical ensemble that represents the field.
Abstract: In the first part of this paper, the concept of the angular correlation function of a stationary optical field is introduced. This function characterizes the correlation that exists between the complex amplitudes of any two plane waves in the angular spectrum description of the statistical ensemble that represents the field. Relations between this function and the more commonly known correlation functions are derived. In particular, it is shown that the angular correlation function is essentially the four-dimensional spatial Fourier transform of the cross-spectral density function of the source. The angular correlation function is shown to characterize completely the second-order coherence properties of the far field. An expression for the intensity distribution in the far zone of a field generated by a source of any state of coherence is deduced. Some generalizations of the far-zone form of the Van Cittert–Zernike theorem are also obtained.
TL;DR: In this paper, the Ne i resonance line λ743 has been accurately measured in the fifth order of the NBS 10.7m vacuum spectrograph against Ar ii Ritz standards in the same order; the measured wavelength is 743.71955±0.0002 A.
Abstract: The Ne i resonance line λ743 has been accurately measured in the fifth order of the NBS 10.7-m vacuum spectrograph against Ar ii Ritz standards in the same order; the measured wavelength is 743.71955±0.0002 A. This gives for the lowest excited level, 2p5(P2112°)3s[112]2° (1s5 in Paschen’s notation), the value 134 041.84±0.04 cm−1 relative to the ground level. This result was used to calculate all of the observed 2p5nl levels relative to the ground level, by use of Ne i observations published during the last two decades and the dispersion formula for air adopted after the publication of Atomic Energy Levels (NBS 1949). The 2p5 P2112° ionization energy is 173 929.75±0.06 cm−1. From the level system, 46 lines in the vacuum ultraviolet (vuv) between 743 and 576 A have been calculated according to the combination principle; these should be accurate to ±0.0002 A or better between 743 and 580 A and to about ±0.0003 A for the few lines below 580 A.
TL;DR: In this article, the radiance of an initially narrow collimated beam propagating in the ocean is investigated with the aid of the small-angle scattering theory of electron scattering, and the resulting expression for N is calculated approximately and compared both with experiments and numerical calculations.
Abstract: The radiance N, resulting from an initially narrow collimated beam, propagating in the ocean, is investigated with the aid of the small-angle-scattering theory of electron scattering The resulting expression for N is calculated approximately and compared both with experiments and numerical calculations Various properties of the approximate expression for N are explored; an observer, located off the axis of the beam at an axial distance z from the source, who attempts to determine the direction to the source by seeking the maximum of N with respect to ray direction, would sight a point on the beam axis at a distance z/3 from the source
TL;DR: In this paper, the Kubelka-Munk hyperbolic equation for reflectance and transmittance of a turbid, isotropically scattering medium has been found formally identical with the solution for reflected and transmitted fluxes of Chandrasekhar's radiative-transfer equation for highly scattering media.
Abstract: The Kubelka–Munk hyperbolic equations for reflectance and transmittance of a turbid, isotropically scattering medium have been found formally identical with the solution for reflected and transmitted fluxes of Chandrasekhar’s radiative-transfer equation for isotropically highly scattering media. The absorption and scattering coefficients of the two theories have been related through numerical coefficients. The Kubelka–Munk absorption coefficient is nearly proportional to the true absorption coefficient in the range of reflectance values between 0.6 and 1 but deviations from proportionality up to a factor of 2 occur for lower reflectance values.
TL;DR: In this paper, the authors derived the approximate equations of the arbitrary-order coherence functions, which are equivalent to those recently obtained by several authors using different methods, for the Gaussian medium and for the nongaussian medium.
Abstract: The complete statistical description of the waves in a random medium can be obtained from the characteristic functional or the cumulant functional of the wave function. The basic equations of these functionals are found first for the gaussian medium and then for the nongaussian medium. As an application of those equations, the approximate equations of the arbitrary-order coherence functions are derived, which are found to be equivalent to those recently obtained by several authors using different methods. The operational method is introduced to solve the equation of the νth-order moment of the irradiance, and an exact solution is obtained for the particular correlation function of the medium, assuming the gaussian form of the incident wave. The irradiance probability-density function is obtained without approximation by the use of the νth-order moment of irradiance for this particular medium, and is found to be exactly the Rice–Nakagami distribution with respect to the log irradiance. This distribution approaches the log-normal distribution in the outside domain of the wave beam, and is also checked in several points. Finally, the operator representation of the physical variables is introduced, and it is shown that the various equations, e.g., the wave equation and the energy-conservation equation, in the statistical system of the wave plus the random medium can be represented by the same equations as the corresponding equations in the deterministic medium. The discussion is also extended on the basis of DeWolf’s result for the irradiance-distribution function.
TL;DR: In this paper, the pulsed Raman technique utilizing a Q-switched frequency-doubled Nd:YAG laser and a pulse-activated nanosecond photon counting detection system has been used to reduce the fluorescence background in Raman spectra.
Abstract: The pulsed Raman technique utilizing a Q-switched frequency-doubled Nd:YAG laser and a pulse-activated nanosecond photon-counting detection system has been used to reduce the fluorescence background in Raman spectra when the fluorescence-pump lifetime is much shorter than the duration of the laser output pulse. A fluorescence discrimination factor shows the improvement of the Raman signal-to-noise ratio obtained with pulsed Raman over cw Raman. Dark-current-limited operation can be virtually eliminated using the pulsed Raman technique. When applied to a sample of Mn-doped ZnSe using an uncooled 1P28 photomultiplier and about 10 mW of average laser power at 532 nm, a 60-count/s fluorescence peak of 125-μs lifetime, observed with a 200-μs detection interval, was reduced by a factor of ≳60 with a 1-μs detection interval. The computed factor is 63.
TL;DR: In this paper, the authors measured the normal-incidence spectral reflectance of water at 5, 27, and 70 C in the spectral region between 5000 and 350 per cm and determined the optical constants n sub r and n sub i by Kramers-Kronig methods.
Abstract: Measurement of the normal-incidence spectral reflectance of water at 5, 27, and 70 C in the spectral region between 5000 and 350 per cm. From the measured values of spectral reflectance the optical constants n sub r and n sub i are determined by Kramers-Kronig methods. The band strengths and bandwidths have been determined for the absorption bands near 3400, 1640, and 600 per cm at each temperature. A similar study of deuterium oxide at 27 C has been conducted for purposes of comparison.
TL;DR: In this article, an interferometric method for measuring the electro-optic (EO) coefficients has been proposed, which consists of the relative determination of the coefficient of a sample using a Mach-Zehnder interferometer, by compensating the phase shift due to the EO effect of the sample with that of a standard material.
Abstract: An interferometric method for measuring the electro-optic (EO) coefficients has been proposed. The method consists of the relative determination of the coefficient of a sample using a Mach–Zehnder interferometer, by compensating the phase shift due to the EO effect of the sample with that of a standard material. The technique offers a simple and highly sensitive measuring method for the EO coefficient. Values of the coefficients for typical EO crystals have been measured and are found to be in agreement with the previous data and with those obtained by another interferometric method proposed by Fujii and Sakudo.
TL;DR: In this paper, a series of balloon flights in southeastern New Mexico was obtained on microthermal atmospheric turbulence structure from the surface to altitudes of 12 to 15 km and the beginning of the tropopause region.
Abstract: During a series of balloon flights in southeastern New Mexico new data was obtained on microthermal atmospheric turbulence structure from the surface to altitudes of 12 to 15 km and the beginning of the tropopause region. It was possible to compute the temperature structure coefficient and the refractive-index-structure coefficient. The major significance of the data is the thermal evidence for turbulence and the strength of this effect in the upper-altitude regions.
TL;DR: In this article, a first-order, second-degree, ordinary differential equation (Riccati's equation) was used to specify the ellipse of polarization of light passing through an anisotropic medium, and the solution χ(z,χ0) represents a trajectory in the complex plane which is traversed as the distance z is increased, starting from an initial polarization χ0 at z = 0.
Abstract: When a single complex variable χ is used to specify the ellipse of polarization of light passing through an anisotropic medium, a first-order, second-degree, ordinary differential equation (Riccati’s equation) governs the evolution of χ with distance along the direction of propagation. In this differential equation the properties of the medium are represented by the elements nij of its N-matrix, which was first introduced by Jones. Its solution χ(z,χ0) represents a trajectory in the complex plane which is traversed as the distance z is increased, starting from an initial polarization χ0 at z = 0. A stereographic projection onto a tangent sphere produces the corresponding trajectory in the more-familiar Poincare-sphere representation. The function χ(z,χ0) has been determined for propagation along (i) an arbitrary direction in a homogeneous anisotropic medium, and (ii) the helical axis of a cholesteric liquid crystal. The solution in the first case provides a unified law that leads to all the rules for the use of the Poincare sphere. For axial propagation in a cholesteric liquid crystal, it is found that two orthogonal polarizations are privileged in that the axes of their ellipses are forced to remain in alignment with the principal axes of birefringence of the molecular planes. The general solution (that satisfies the conditions of propagation) shows that the ellipse of polarization never repeats itself. As to the two parameters of the ellipse, the ellipticity is shown to be periodic with periodicity shorter than the pitch of the helical structure and the azimuth is aperiodic.
TL;DR: In this article, the fourth moment of a scalar wave propagating in a random medium is investigated, starting with a partial differential equation obtained by various authors in a multiple-scattering approximation, and then presenting numerical results for a two-dimensional plane wave.
Abstract: The fourth statistical moment of a scalar wave propagating in a random medium is investigated. Starting with a partial differential equation obtained by various authors in a multiple-scattering approximation, we discuss the general properties of the fourth moment of an initially plane wave and then present numerical results for a two-dimensional plane wave. Results are presented for the variance and covariance of irradiance scintillations. Both results are shown to agree well with experiment. In particular, the variance exhibits the experimentally observed saturation phenomenon, and the covariance results indicate that the correlation length for irradiance scintillations is not proportional to (λz)12 in the saturation region and that the aperture-averaging effect is less than that predicted by results based on the Born or Rytov approximations.
TL;DR: In this paper, the beamfoil spectrum of nitrogen has been studied between 300 and 1250 A at beam energies of 0.5-2 MeV. Some newly observed lines have been identified and the lifetimes of some excited levels of N ii, N iii, N iv, and N v have been measured.
Abstract: The beam-foil spectrum of nitrogen has been studied between 300 and 1250 A at beam energies of 0.5–2 MeV. Some newly observed lines have been identified and the lifetimes of some excited levels of N ii, N iii, N iv, and N v have been measured.
TL;DR: For sinusoidal modulations of disparity between 1/2 to 2 deg of disparity, most depth response functions exhibit a lowfrequency decrease that is not observed with square-wave modulations as discussed by the authors.
Abstract: Depth sensations cannot be elicited by modulations of disparity that are more rapid than about 6 Hz, regardless of the modulation amplitude. Vergence tracking also fails at similar modulation rates, suggesting that this portion of the oculomotor system is limited by the behavior of disparity detectors. For sinusoidal modulations of disparity between 1/2 to 2 deg of disparity, most depth-response functions exhibit a low-frequency decrease that is not observed with square-wave modulations of disparity.
TL;DR: In this article, the polarization states of light incident on and emerging from an optical system are represented by complex numbers χ¯ and ξ¯, respectively, in two different planes.
Abstract: The polarization states of light incident on and emerging from an optical system are represented by complex numbers χ¯ and ξ¯, respectively, in two different planes. In this representation, the input–output transfer function ξ¯=f(χ¯) is a conformal bilinear transformation with coefficients given by the elements of the system’s Jones matrix. From the known properties of the bilinear transformation, important conclusions can be reached on the response of optical systems to incident light of all possible polarization forms. In addition, the analysis appears to have considerable potential in the synthesis of systems to effect a prescribed polarization transfer. As an example, the ellipsometer is analyzed by use of some of the ideas developed.