Showing papers in "Journal of the Optical Society of America in 1948"
TL;DR: In this paper, the Gurevic and Judd formulas were derived from the Kubelka-Munk differential equations, and they are exact under the same conditions as in this paper, that is, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal.
Abstract: The system of differential equations of Kubelka-Munk, -di=-(S+K)idx+Sjdx, dj=-(S+K)jdx+Sidx(i, j⋯ intensities of the light traveling inside a plane-parallel light-scattering specimen towards its unilluminated and its illuminated surface; x⋯ distance from the unilluminated surface S, K⋯ constants), has been derived from a simplified model of traveling of light in the material. Now, without simplifying assumptions the following exact system is derived: -di=-12(S+K)uidx+12Svjdx,dj=-12(S+K)vjdx+12Suidx,u≡∫0π/2(∂i/i∂φ)(dφ/cosφ), v≡∫0π/2(∂j/j∂φ)(dφ/cosφ), φ≡angle from normal of the light). Both systems become identical when u=v=2, that is, for instance, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal. Consequently, the different formulas Kubelka-Munk got by integration of their differential equations are exact when these conditions are fulfilled. The Gurevic and Judd formulas, although derived in another way by their authors, may be got from the Kubelka-Munk differential equations too. Consequently, they are exact under the same conditions. The integrated equations may be adapted for practical use by introducing hyperbolic functions and the secondary constants a=12(1/R∞+R∞) and b=12(1/R∞-R∞), (R∞≡reflectivity). Reflectance R, for instance, is then represented by the formula R=1-Rg(a-b ctghbSX)a+b ctghbSX-Rg(Rg≡reflectance of the backing, X=thickness of the specimen) and transmittance T by the formula T=ba sinhbSX+b coshbSX.In many practical cases the exact formulas may be replaced by appropriated approximations.
2,322 citations
TL;DR: Several conceivable methods for the formation of optical images by x-rays are considered, and a method employing concave mirrors is adopted as the most promising.
Abstract: Several conceivable methods for the formation of optical images by x-rays are considered, and a method employing concave mirrors is adopted as the most promising. A concave spherical mirror receiving radiation at grazing incidence (a necessary arrangement with x-rays) images a point into a line in accordance with a focal length f=Ri/2 where R is the radius of curvature and i the grazing angle. The image is subject to an aberration such that a ray reflected at the periphery of the mirror misses the focal point of central rays by a distance given approximately by S=1.5Mr2/R, where M is the magnification of the image and r is the radius of the mirror face. The theoretically possible resolving power is such as to resolve point objects separated by about 70A, a limit which is independent of the wave-length used. Point images of points and therefore extended images of extended objects may be produced by causing the radiation to reflect from two concave mirrors in series. Sample results are presented.
1,149 citations
TL;DR: It is argued that the phenomenon of dark adaptation can be ascribed only in small part to thePrimary photo-process and must be mainly controlled by a variable gain mechanism located between the primary photo- process and the nerve fibers carrying pulses to the brain.
Abstract: An absolute scale of performance is set up in terms of the performance of an ideal picture pickup device, that is, one limited only by random fluctuations in the primary photo process. Only one parameter, the quantum efficiency of the primary photo process, locates position on this scale. The characteristic equation for the performance of an ideal device has the form BC2α2=constantwhere B is the luminance of the scene, and C and α are respectively the threshold contrast and angular size of a test object in the scene. This ideal type of performance is shown to be satisfied by a simple experimental television pickup arrangement. By means of the arrangement, two parameters, storage time of the eye and threshold signal-to-noise ratio are determined to be 0.2 seconds and five respectively. Published data on the performance of the eye are compared with ideal performance. In the ranges of B(10−6 to 102 footlamberts), C(2 to 100 percent) and α(2′ to 100′), the performance of the eye may be matched by an ideal device having a quantum efficiency of 5 percent at low lights and 0.5 percent at high lights. This is of considerable technical importance in simplifying the analysis of problems involving comparisons of the performance of the eye and man-made devices. To the extent that independent measurements of the quantum efficiency of the eye confirm the values (0.5 percent to 5.0 percent), the performance of the eye is limited by fluctuations in the primary photo process. To the same extent, other mechanisms for describing the eye that do not take these fluctuations into account are ruled out. It is argued that the phenomenon of dark adaptation can be ascribed only in small part to the primary photo-process and must be mainly controlled by a variable gain mechanism located between the primary photo-process and the nerve fibers carrying pulses to the brain.
890 citations
TL;DR: In this paper, the properties of matrices, denoted by N, which refer not to the complete element, but only to a given infinitesimal path length within the element, were examined.
Abstract: The preceding papers of this series have examined the properties of an optical calculus which represented each of the separate elements of an optical system by means of a single matrix M. This paper is concerned with the properties of matrices, denoted by N, which refer not to the complete element, but only to a given infinitesimal path length within the element.If M is the matrix of the optical element up to the point z, where z is measured along the light path, then the N-matrix at the point z is defined by (A)N≡(dM/dz)M-1.Thus one may write symbolically, (B)N=dlogM/dz,and (C)M=M0 exp(∫Ndz).A general introduction is contained in Part I. The definition and general properties of the N-matrices are treated in Part II. Part III contains a detailed discussion of the important special case in which the optical medium is homogeneous, so that N is independent of z; Part III contains in Eq. (3.26) the explicit relation which corresponds to the symbolic relation (C). Part IV describes a systematic method, based on the N-matrices, by which the optical properties of the system at each point may be described uniquely and quantitatively as a combination of a certain amount of linear birefringence, a certain amount of circular dichroism, etc.; the method of resolution is indicated in Table I. Part V treats the properties of the inhomogeneous crystal which is obtained by twisting a homogeneous crystal about an axis parallel to the light path.
542 citations
TL;DR: A set of band pass filters for the 2400–3800A region of the ultraviolet is developed, which have a half-width of 200A and a maximum transmission of 30 percent, on the average.
Abstract: The problems involved in the development of ultraviolet transmission filters are discussed and criteria of stability, efficiency, and ease of preparation are applied to the materials suggested by previous workers. By the selection of the most suitable previous filters and the introduction of several new filters, a set of band pass filters for the 2400–3800A region of the ultraviolet is developed. These have a half-width of 200A and a maximum transmission of 30 percent, on the average. Quantitative spectrophotometric data are given for all components and filter combinations used. Suggestions are made for the further development of these tools.
263 citations
TL;DR: A detailed survey of the present-day knowledge of optical compensators is given in this article, with a reference made to the sensitivity and accuracy of the compensators and their applications.
Abstract: A detailed survey is given of the present-day knowledge of optical compensators. The compensators discussed are those of Babinet, Soleil, Rayleigh, De Forest Palmer, Brace, Szivessy, Senarmont, and Richartz. Each instrument is described, the theory developed, the method of use for the measurement of small phase differences given, and reference made to the sensitivity and accuracy.
157 citations
TL;DR: In this paper, the optical properties of gold smokes deposited on cellulose nitrate films under different experimental conditions have been studied and the conditions of pressure of the inert atmosphere, purity of the gas, rate of evaporation, and the distance between source and deposition surface giving the highest infra-red absorption per unit mass have been found.
Abstract: The optical properties of gold smokes deposited on cellulose nitrate films under different experimental conditions have been studied. The conditions of pressure of the inert atmosphere, purity of the gas, rate of evaporation, and the distance between source and deposition surface giving the highest infra-red absorption per unit mass have been found. The thermal mass required for high infra-red absorption is small compared to the thermal masses of other receivers used for infra-red measurements. The gold “blacks” turn yellow and have lower infra-red absorption when heated above 110°C.Gold “blacks” with very high infra-red transmission (3–15μ) and low transmission at shorter wave-lengths are prepared when oxygen is present in the “inert” atmosphere.The particle size and particle distribution of the gold smokes deposited under different experimental conditions have been investigated with the electron microscope at high resolution.
133 citations
TL;DR: In this article, the authors derived equations which describe the manner in which the apparent contrast of any object depends upon the distance of the observer, and applied these equations to the case of a homogeneous standard atmosphere; they may be applied to many kinds of nonstandard atmospheric conditions.
Abstract: A veil of atmospheric haze reduces the visibility of all distant objects by decreasing their apparent contrast. In this paper equations are derived which describe the manner in which the apparent contrast of any object depends upon the distance of the observer. The treatment is not limited to horizontal paths of sight, but applies also to the apparent contrast of objects on the ground as seen from the air, and to the apparent contrast of objects aloft as viewed from the ground. The equations are not limited to the case of a homogeneous standard atmosphere; they may be applied to many kinds of non-standard atmospheric conditions. For every path of sight there exists a luminance level which will be transmitted unchanged. The apparent luminance of any receding object approaches this equilibrium level. For many paths of sight the equilibrium luminance is matched by the luminance of some portion of the horizon sky.
103 citations
TL;DR: It is shown that the solutions of the problem by the consideration of the electromagnetic disturbance in each medium, and by the summation of multiple beams, lead to the same result.
Abstract: By consideration of the formulae for the reflection and transmission of up to three films, it has been possible to form a generalization for an arbitrary number of films. This generalization is stated as a simple rule whereby the expressions for the reflected and transmitted amplitudes can be readily formed in terms of the Fresnel coefficients of the various boundaries. The generalization is proved by induction. It is also shown that the solutions of the problem by the consideration of the electromagnetic disturbance in each medium, and by the summation of multiple beams, lead to the same result.
94 citations
TL;DR: It is found that the chromaticity coordinates of the achromatic spot can be predicted by interpolation between the coordinates of a “white point,” which is independent of the state of adaptation, and those of the background.
Abstract: The tristimulus values of a small (foveal) spot which appears achromatic to an eye which is adapted to a uniform chromatic background have been found experimentally. Various colors have been used for the background, and a considerable range of luminances has been employed for both the background and the spot. It is found that the chromaticity coordinates of the achromatic spot can be predicted by interpolation between the coordinates of a “white point,” which is independent of the state of adaptation, and those of the background. An empirical interpolation formula, which expresses the effect of adaptation as a function of the tristimulus values of the background and the achromatic spot, is presented.
87 citations
TL;DR: A transmission polarizer for the near infra-red is described, which is small and compact and can be mounted on a spectrometer without alteration of the existing optical system and employs a pile of self-supporting selenium films.
Abstract: A transmission polarizer for the near infra-red is described, which is small and compact and can be mounted on a spectrometer without alteration of the existing optical system. It employs a pile of self-supporting selenium films, each approximately 4 microns thick. The advantages which such a polarizer possesses over other forms are pointed out, and the factors affecting the design of the pile are briefly discussed. The method of preparing the Se films is described in detail. The percentage polarization, measured by crossing two similar piles, is better than 94 percent with 5 films, and better than 98 percent with 6 films in each pile, over the spectral region 2–14 μ; the maximum transmission is 47 percent of the incident radiation.No absorption bands of selenium could be detected between 1 and 14 μ using a much thicker layer (52 microns).
TL;DR: Polarization interference filters as mentioned in this paper have a pass band ranging from a fraction of an angstrom to several hundred angstroms in width and can be shifted to any desired region of the spectrum.
Abstract: Polarization interference filters are described which can have a pass band ranging from a fraction of an angstrom to several hundred angstroms in width. The pass band can be shifted to any desired region of the spectrum. These tunable filters are based on the fixed filters discussed by Lyot and Evans. The transmission band is formed by the superposition of the polarized channel spectra, produced by x-cut plates of quartz or other birefringent media placed between parallel polarizers. The birefringent plates have thicknesses in the ratio 1:2:4 etc. The tuning is accomplished by changing the retardation of successive elements so that transmission maxima in the various channel spectra coincide at the desired wave-length. The retardation change can be made mechanically, for example, by stretching supplemental plastic sheets in series with the filter elements, or can be made electrically by using Kerr cells or crystals with high electro-optic coefficients, such as ammonium dihydrogen phosphate. The additional retardation never has to exceed a full wave at the wave-length of peak transmission. The measured transmission of an experimental filter is shown. The electrical tuning method is particularly adapted to cathode-ray oscillograph presentation of spectra. The filter also has possible application in color reproduction and colorimetry. With a pass band of a half-angstrom line of sight motion of solar prominences could be determined by the use of the Doppler shift of the prominence radiation.
TL;DR: In this article, the effects of particle size, layer thickness, and optical constants of the materials are discussed, as well as the effect of particle number, particle size and layer thickness on the optical properties of dry films of zinc sulfide powders.
Abstract: Infra-red transmission measurements on dry films of quartz and zinc sulfide powders are presented. The effects of particle size, layer thickness, and the optical constants of the materials are discussed.
TL;DR: The corner-cube interferometer is analyzed geometrically and analytically andEquations are obtained describing the fringe patterns when one prism is used far off its axis, and also when both are used near their axis.
Abstract: The corner-cube interferometer is analyzed geometrically and analytically. When the prisms are used near their axis, the instrument is found to behave essentially like an interferometer using triple sets of front-surface mirrors. Equations are obtained describing the fringe patterns when one prism is used far off its axis, and also when both are used near their axis. These fringe patterns are discussed and illustrated.
TL;DR: An optical system for eliminating scattered light and providing means for a visual photometric comparison between the sky and the sun has been constructed and tested and explained in sufficient detail to permit the design of similar instruments for a wide range of applications.
Abstract: Measurement of the brightness of the sky near the sun is difficult because instrumental scattered light originating in the solar disk is usually many times brighter than light from the sky. An optical system for eliminating this scattered light and providing means for a visual photometric comparison between the sky and the sun has been constructed and tested. The principles of the instrument are explained in sufficient detail to permit the design of similar instruments for a wide range of applications.
TL;DR: Using this method, the depolarization factors of some highly polarized lines have been measured with a photoelectric spectrograph and were found to be considerably below previously accepted values.
Abstract: The errors arising in the measurement of the depolarization factor of highly polarized Raman lines are discussed. Particular attention is given to the error introduced by the convergence of the incident light. It is shown that the ratio of the intensity of the parallel component of the scattered light when incident light is polarized along the direction of observation of the sample to the intensity of the parallel component when the incident light is polarized perpendicular to this, gives a value of the depolarization factor ρs that is very nearly free from convergence errors. ρs is related to the depolarization factor in unpolarized light ρs by ρn=2ρs/(1+ρs). Using this method, the depolarization factors of some highly polarized lines have been measured with a photoelectric spectrograph. They were found to be considerably below previously accepted values. The depolarization factor ρn for the most highly polarized lines of carbon tetrachloride and benzene were found to be 0.013 and 0.038, respectively. It is shown that the depolarization factor is not constant across the width of the line for many Raman lines.
TL;DR: The method here used to measure coefficients of reflection depends on the variation of brightness within a spherical integrator when a section of the surface is removed or added, and comparison of results indicates the consistency of results.
Abstract: Both magnesium carbonate and magnesium oxide are used in laboratories as reflectors of visible radiation and a knowledge of their spectral characteristics is desirable. The method here used to measure coefficients of reflection depends on the variation of brightness within a spherical integrator when a section of the surface is removed or added. The photometry was done with a Macbeth instrument and interference filters were used to get six zones in the spectrum. The centroids were computed for low levels of luminosity. By taking photometric readings with three part-spheres of different degrees of completeness, the coefficients can be computed for three different combinations, and comparison of results indicates the consistency of results. The average coefficient of magnesium carbonate was found to be about 0.983, while that of the oxide was about 0.991, and both have a slight selectivity in favor of the red end of the spectrum.
TL;DR: In this article, it was shown that visual acuity, measured with the lines passing diagonally through the visual field at an angle of 45 degrees to the horizontal, is between 10 and 20 percent lower than that measured by the parallel lines passing vertically or horizontally through a visual field.
Abstract: Visual acuity has been measured in terms of the reciprocal of the angle in minutes subtended by the individual lines in a parallel-line test object at the limit of perception of the lines. Both clear and opaque lines in this test object were of equal width. It was found that the limit of perception of the lines in such a test object depends upon the orientation of the lines. Visual acuity, measured with the lines passing diagonally through the visual field at an angle of 45 degrees to the horizontal, is between 10 and 20 percent lower than that measured with the parallel lines passing vertically or horizontally through the visual field.
TL;DR: Xerography provides a unique and simplified process of graphic reproduction, particularly in printing and duplicating, and has a number of potential applications in graphic arts and related fields.
Abstract: A new process of graphic reproduction and photography has been developed. The basic process, known as xerography, is dry, direct positive-to-positive, rapid, and has a number of potential applications in graphic arts and related fields. As a photographic process, xerography employs a re-usable plate consisting of a thin layer of a photo-conductive material on an electrically conductive base. The plate is sensitized by electrostatic charging immediately before use. After exposure, the image is developed by dusting the plate with a micronized powder. Prints are made by transferring and fixing the powder image to paper or other materials. The plate can be used many times to produce additional images. Xerography also provides a unique and simplified process of graphic reproduction, particularly in printing and duplicating.
TL;DR: The demonstration of an optimum level of illumination makes highly questionable the current practice of recommending “minimum” levels of illumination for industrial jobs, since deterioration of performance and increase in fatigue may result when the optimal level is exceeded.
Abstract: The purpose of this study was to investigate the relation of the level of illumination intensity to performance and fatigue in visual work. The question of illumination requirements is of considerable importance from the point of view of physiological optics, industrial physiology, and public health. Yet a large part of the research done in the past leaves much to be desired in regard to general approach and specific testing techniques as well as experimental analysis and statistical evaluation. In the present series six illumination levels (2, 5, 15, 50, 100, and 300 footcandles) were studied in repeated experiments in six normal subjects. The work task involved recognition of fine details (letters) and reproduced the essential features of a conveyor inspection operation. In addition to the studying of various criteria of work performance and their change in the course of 2 hours of work, a large battery of visual tests was applied before and after the work so as to characterize the degree of fatigue. Varied illumination affected the performance more than the functional criteria of fatigue. Only one function, the recognition time for stimuli of threshold size, showed a decreasing degree of fatigue up to 300 ft.-c, all other variables, including performance, which changed with a changing level of illumination showed an optimum at 100 ft.-c. The demonstration of an optimum level of illumination makes highly questionable the current practice of recommending “minimum” levels of illumination for industrial jobs, since deterioration of performance and increase in fatigue may result when the optimal level is exceeded. The optimum of 100 ft.-c for the present strenuous visual task is at or below the minimum which should be recommended on the basis of the code of the Illuminating Engineering Society.
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TL;DR: The purpose of this paper is to identify the principal factors involved in the visibility of an object, to indicate how each factor affects the range of visibility, and to supply charts which, by combining these factors, enable the limiting range to be found under any set of prevailing conditions.
Abstract: For thousands of years, thousands of mariners have sighted thousands of ships, and have made appropriate entries in their logs. Even so, this mass of miscellaneous information is of little use in predicting the range at which a specified object will be just visible under a new set of circumstances. The purpose of this paper is to identify the principal factors involved in the visibility of an object, to indicate how each factor affects the range of visibility, and to supply charts which, by combining these factors, enable the limiting range to be found under any set of prevailing conditions. (This paragraph has been lifted, almost verbatim, from some material prepared during the war by Professor Arthur C. Hardy, then Chief of the Camouflage Section (16.3) of the NDRC.)
TL;DR: In this paper, the effect of the intensity of the exciting radiation on the efficiency of zinc-sulphide phosphors activated with silver an d containing varying amounts of cobalt below 4·10−4 percent has been studied at temperatures between −180° and 100°C.
Abstract: The effect of the intensity of the exciting radiation on the efficiency of zinc-sulphide phosphors activated with silver an d containing varying amounts of cobalt below 4·10−4 percent has been studied at temperatures between −180° and 100°C. The results are in agreement with the theory of hole migration and show that the rate of recombination of electrons with ionized killing centers is much faster than that of electrons with ionized silver centers. From the change of intensity dependence with temperature between 0 and 100°C the distance between the activator level and the full band was found to be 0.37 ev. To explain an anomalous result at low temperatures with high Co concentrations, it is suggested that shallow electron traps are present in the zinc-sulphide lattice.
TL;DR: Frequency-of-seeing curves have been obtained for targets having various image perimeters at background brightnesses of 2950 and 17.5 foot-lamberts, respectively, indicating that in order to detect the target, at least one of the cones along the boundary must absorb at least 4 quanta.
Abstract: Frequency-of-seeing curves have been obtained for targets having various image perimeters at background brightnesses of 2950 and 17.5 foot-lamberts, respectively. A description of the data has been obtained on the basis of the assumption that the absorption of a light quantum by a foveal cone is a random event which is subject to the laws of chance. On this basis the data indicate that the detection of a target takes place across the image boundary; that in order to detect the target, at least one of the cones along the boundary must absorb at least 4 quanta, and that this critical number of quanta is the same for each of the two background brightnesses investigated. At the higher brightnesses, this critical number of quanta absorbed from the target is about equal to the random fluctuation to be expected in the number absorbed from the background during the critical time of one exposure.
TL;DR: In this paper, it was shown from extensive threshold measurements with flashes for foveal and peripheral vision that a red cone in the periphery probably gives rise to a light impression when two quanta are absorbed in it within a time τ.
Abstract: With the aid of the three methods for the determination of the number of absorbed quanta necessary for light perception described in previous papers, it is found from extensive threshold measurements with flashes for foveal and peripheral vision that a “red cone” in the periphery probably gives rise to a light impression when two quanta are absorbed in it within a time τ.For the foveal cone systems a light impression is caused for every wave-length by the absorption of two quanta within a time τ and within an angular distance of 2–4 minutes. The different kinds of receptors proved to be capable of reacting in mutual dependence on each other, and the conclusion is drawn that all receptors send a nerve impulse to the nerve connection when one quantum is absorbed.A light impression will occur when a second quantum is absorbed after the first absorption within τ sec. within a receptor within a distance D of the first receptor.Experiments on the visual acuity demonstrate that for all wave-lengths, for foveal as well as for peripheral vision, the dependence of the visual acuity on the intensity agrees with the two-quanta theory.
TL;DR: A method of high accuracy applicable to various prisms in infra-red spectrometry has been used to calibrate NaCl and KBr prisms and permits a tabulated calibration without the necessity of drawing calibration curves.
Abstract: A method of high accuracy applicable to various prisms in infra-red spectrometry has been used to calibrate NaCl and KBr prisms. The method requires only a small number of experimental bands, is practically independent of resolving power, provides an extensive wave-length range, and permits a tabulated calibration without the necessity of drawing calibration curves. The procedure is described in detail with an example.
TL;DR: Tests with the 100-hue series of Munsell papers and with a spectrometer showed that perception of red and green is entirely lacking, and it is possible to obtain reliable information as to the colors actually perceived by the deuteranopic right eye.
Abstract: Studies are reported of a subject with deuteranopia of the right eye and mild deuteranomaly of the left. On the Nagel anomaloscope this subject, using the right eye, matched both spectral red and spectral green to yellow. The left eye did not differ from normal on this test. Selected pseudo-isochromatic charts and the Farnsworth-Munsell 100-hue test, however, revealed, in the left eye, definite color deficiency of the deutan type. Scores on the color threshold tester indicated a marked defect in the right eye, slight in the left.Because of the relatively slight abnormality of the left eye it is possible to obtain reliable information as to the colors actually perceived by the deuteranopic right eye. Tests with the 100-hue series of Munsell papers and with a spectrometer showed that perception of red and green is entirely lacking. The Munsell papers were described as browns, grays, and blues. In the spectrum the range from 501 to 505 millimicrons was reported as white; longer wave-lengths were reported as yellow, shorter ones, as blue. The only regions of the spectrum identical in appearance to the two eyes were those wave-lengths chosen by the deuteranomalous left eye as unitary blue (451–453) and unitary yellow (584).
TL;DR: Of the 25 superconducting bolometers studied in detail the 9 most sensitive had figures of merit ranging from 14.0 to 1.3, and compared with other infra-red detectors described in the literature on the basis of reference conditions suggested by Jones.
Abstract: Columbium nitride superconducting bolometers have been studied for sensitivity when irradiated with a wide band of modulated infra-red radiation of about 0.1 microwatt/mm2 intensity. The bolometer response was amplified by means of a matching input transformer and wide-band amplifier. Time constants for different bolometers ranging from 0.7 to 17.0 milliseconds were observed. Comparisons are given between these superconducting bolometers and other infra-red detectors described in the literature on the basis of reference conditions suggested by Jones (reference 1). Of the 25 superconducting bolometers studied in detail the 9 most sensitive had figures of merit ranging from 14.0 to 1.3.