Showing papers in "Journal of the Optical Society of America in 1962"

Geometrical Theory of Diffraction

Abstract: The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.

Reconstructed Wavefronts and Communication Theory

Abstract: A two-step imaging process discovered by Gabor involves photographing the Fresnel diffraction pattern of an object and using this recorded pattern, called a hologram, to construct an image of this object. Here, the process is described from a communication-theory viewpoint. It is shown that construction of the hologram constitutes a sequence of three well-known operations: a modulation, a frequency dispersion, and a square-law detection. In the reconstruction process, the inverse-frequency-dispersion operation is carried out. The process as normally carried out results in a reconstruction in which the signal-to-noise ratio is unity. Techniques which correct this shortcoming are described and experimentally tested. Generalized holograms are discussed, in which the hologram is other than a Fresnel diffraction pattern.

Refraction and Dispersion of Synthetic Sapphire

Abstract: The refractive indices of synthetic sapphire (Al2O3) were measured at selected wavelengths and the values of index range from 1.834 at 0.265 μ in the ultraviolet to 1.586 at 5.58 μ in the infrared. A three-term Sellmeier dispersion equation of the form n2-1=∑iAiλ2λ2-λt2was fitted to the experimental data. Dispersive quantities were computed which estimate the optical performance to be expected from sapphire.

General ray-tracing procedure

Abstract: Computing formulas are presented for tracing skew rays through optical systems containing cylindrical and toric surfaces of arbitrary orientation and position. Particular attention is given to the treatment of diffraction gratings and a vector form of the diffraction law is suggested.

Vision during Voluntary Saccadic Eye Movements

Abstract: Vision seems to be a continuous process even though eye movements occupy a portion of the time spent in reading or inspecting objects in the field of view. This observation has led to the supposition that a “blanking out” of vision occurs with saccadic eye movements. Some workers attribute this effect to the rapid motion of the image on the retina. Others have suggested a central inhibition, possibly related to the physiological mechanisms of attention. The present research compared vision during saccades with vision during fixation by means of three representative psychophysical tasks. Each stimulus pattern was presented to the fovea in the form of an instantaneous flash that was delivered before, during, or after an eye movement. The flash lasted only 20 μsec, so that retinal blur due to movement was reduced to a negligible amount. The time of the stimulus flash was signaled on a continuously moving film on which the eye movements were recorded by a corneal reflection technique. Detection thresholds for dot patterns and recognition thresholds for words were found to be about 0.5 log unit higher during saccades than during steady fixation. Similar differences, though smaller and less consistent, were found in the minimum angles for the resolution of gratings. It is concluded that vision is not “blanked out” during eye movements, but that it is significantly depressed even under conditions that minimize blur due to movement of the retinal image, and that assure foveal stimulation.

Determination of the Properties of Films on Silicon by the Method of Ellipsometry

Abstract: The use of exact reflection theory to interpret data allows the application of ellipsometry to the determination of the thicknesses and optical constants of surface films without the thickness limitations of approximate theory. Ellipsometer measurements as a function of the thicknesses and optical constants of a variety of different films on silicon substantiate the predictions of exact theory and yield the properties of the films.

Calibration of Spectrofluorimeters for Measuring Corrected Emission Spectra

Abstract: A rhodamine B quantum counter and a thermopile were used to calibrate a grating monochromator and photomultiplier for the measurement of corrected emission spectra from 240 to 600 mμ. The calibration was checked over a limited wavelength range with a standard tungsten lamp. Fluorescence spectra determined with the instrument agree well with previously reported spectra.

Generalization of the maggi-rubinowicz theory of the boundary diffraction wave part I

Abstract: As a first step towards a generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave, a new vector potential W(Q,P) is associated with any monochromatic scalar wavefield U(P). This potential has the property that the normal component of its curl, taken with respect to the coordinates of any point Q on a closed surface S surrounding a field point P, is equal to the integrand of the Helmholtz-Kirchhoff integral; that is, curlQW(Q,P)·n=14π{U(Q)∂∂n(exp(iks)s)−exp(iks)s∂∂nU(Q)}.where s is the distance QP and ∂/∂n denotes the differentiation along the inward unit normal n to S.Further it is shown that the vector potential always has singularities at some points Q on S and that the field at P may be rigorously expressed as the sum of disturbances propagated from these points alone.A closed expression for the vector potential associated with any given monochromatic wavefield that obeys the Sommerfeld radiation condition at infinity is derived and it is shown that in the special case when U is a spherical wave, this expression reduces to that found by G. A. Maggi and A. Rubinowicz in their researches on the boundary diffraction wave.

Absorption of light by turbid materials

Abstract: The transmission and absorption properties of turbid media have been examined with Kubelka and Munk’s theory of the optics of intensely scattering material. The equation for the optical density of such material as a function of thickness has been derived and examined experimentally. It is shown that the reflectivity and scattering coefficient can be determined absolutely without reference to a standard material from the optical-density measurements. The absorption spectra of pigments in scattering media and in clear solution have been compared. It is shown that light in passing through a turbid sample may traverse an optical path which is many times the sample thickness. The practical consequence of this increased path length is an intensification of the absorption bands of pigments in light-scattering media. The theoretical expression for this intensification has been derived and tested experimentally. Spectral effects due to the physical binding of pigment molecules to the scattering particles have also been examined.

Multiple scattering of waves and optical phenomena.

Abstract: Starting with the most elementary multiple scattering problem, a symmetrically excited pair of monopoles, we use both “successive-scattering” and “self-consistent” procedures to obtain the closed-form multiply scattered amplitude in terms of the singly scattered value. Then we represent the field for an arbitrary configuration of arbitrary scatterers in terms of the individual, multiply scattered amplitudes, and specify these in terms of singly scattered amplitudes by a system of self-consistent integral equations. Applications are made to fixed configurations (two scatterers, and the diffraction grating), and to random distributions (models for rough surfaces, and for random media). Simple explicit results in terms of isolated scatterer functions are derived, and some of their essential features are given in graphs: the coupling effects for two dielectric rods (intensity and phase) are graphed versus spacing for both polarizations; for the diffraction grating, when a surface wave is “near grazing,” the spectral orders show essential features of the anomalies measured by Wood, Strong, and Palmer; for a lossless rough surface, the graphs for both polarizations for the coherently reflected intensity and phase are analogous to those obtained for reflection from a lossy interface (the corresponding results for the incoherent scattering accounting for the loss from the “main beam”); and for a slab region containing a random distribution of nearly transparent large scatterers, we graph the macroscopic parameters, and the coherent and incoherent, forward-scattered intensities versus the fractional volume.

Method for computing the radial distribution of emitters in a cylindrical source

Abstract: A method for computing the distribution of emitters from the observed projected intensity profile is described. The method is applicable to optically thin volume sources with cylindrical symmetry. Unlike previous methods, this method yields results which are relatively insensitive to small random errors in the data.

Light distribution in the image formed by the living human eye.

Abstract: By photoelectric scanning, the light distribution was determined in the aerial ophthalmoscopic image of a thin light filament viewed by an observer with an homatropinized eye. Light distributions were obtained for various pupil sizes and degrees of defocusing. Measurements were also obtained with bar and grating objects.To compute the line-spread function on the fundus, correction was made for the double passage of the light through the optical system of the eye on the assumption that the spread in angular measure is the same in both directions. The results may be considered to depict distributions which are possibly broader, but certainly not narrower, than the real distributions in the retinal image. The line-spread function on the fundus was determined to have a half-width at half-height of one minute of arc for an eye in best focus with a 3-mm pupil, and this suggests that the point-spread function has half-width 0.66 min of arc as an upper estimate.

Sine-Wave Response of the Visual System. II. Sine-Wave and Square-Wave Contrast Sensitivity*†

Abstract: Part I of this series described a method which yielded the sine-wave response of the complete visual system by assuming that the Mach phenomenon is the result of a convolution, in the optical sense, of the object luminance distribution with the effective spread-function of the visual system This second paper is concerned with measuring the response of the visual system to sine-wave and square-wave spatial distributions using the threshold criterion of contrast sensitivity Particular emphasis is placed on the low spatial frequencies, a region which is believed to be critically important in the mechanism of visual contrast phenomena Results strongly imply interaction of two basic mechanisms in the visual system These mechanisms may be characterized individually as a low-pass filter component (optical) and a high-pass filter component (neural, chemical, electrical, etc)

Transmission Filters in the Far-Infrared Region

Abstract: Transmission filters in the far-infrared region from 25 to 300 μ which cut off short-wave radiation are obtained from polyethylene sheet containing powders of reststrahlen crystals. The cut-off wavelength of these filters can be shifted with choice of restrahlen crystals. By using finer powder size and/or thinner polyethylene sheet, the steepness of the transmittance curve can be increased. These filters are very economical and convenient to use in far-infrared spectrometers.

Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses

Abstract: The senior author’s interpolation formula for computing the dispersion of glass has been appropriately modified and applied to infrared materials. Indices of refraction for 14 optical materials that are suitable for practical refracting systems have been fitted by the modified formula and have been tabulated at increments of 0.5 μ for the useful transmittance range of each material. The method of applying the dispersion formula is discussed and is illustrated by the design of two three-element superachromats corrected for the region of 2.0–5.0 μ.

Light Distribution in Human Retinal Images

Abstract: The image-forming properties of the human optical system have been examined with the aid of a photoelectric ophthalmoscope. The light distributions in images of bright vertical lines formed by a double passage through the eye optics were measured. On the assumption that the eye optics are reversible, the light distributions on the retina were computed by means of Fourier transforms. The results are also expressed in terms of the spatial frequency response functions for the eye. The effects of pupil size were examined. The best imagery was obtained with a 5-mm pupil. The results confirmed the earlier measurements on human eyes reported by Flamant. The more recent experiments on animal material by DeMott do not seem to be relevant to living human eyes.

Regenerative Circulatory Multiple-Beam Interferometry for the Study of Light-Propagation Effects

Abstract: Novel circulatory and regenerative multiple-beam interferometry methods making use of optical maser oscillations of extreme monochromaticity based on stimulated emission present interesting possibilities for investigating with high-precision various effects of motion and of fields on the propagation of light. These methods inherently permit increasing considerably the accuracy of the historical relativistic experiments of Michelson, Sagnac, and others, and have also potential applications to studies of other radiation propagation effects in magnetic, electric, and gravitational fields, and in moving refractive media, and to the modulation of coherent radiation. These propagation effects can produce frequency splits of the optical-maser oscillations, and the frequencies of the resulting optical beats are a measure for those effects; frequency measurements can be accomplished with high accuracy by using primary frequency standards, e.g., atomic clocks. Contrary to the many proposed applications of optical masers which are directed towards utilizing the high-spatial coherence of the wave fields, the present subject is thus primarily concerned with the narrow-frequency bandwidths possible with these novel radiation sources. The high accuracies possible with the new interferometric methods described should lead to quantitative results which up to now were either impossible to achieve, or only by experiments on very large scales.

Mathematical Resolution of Overlapping Spectral Lines

Abstract: This paper presents two methods for decomposing into individual components an observed spectrum composed of a number of overlapping spectral lines, each having the same known shape. The first method of solution described is for lines all of the same half-width and is based on properties of the Fourier transform of even functions. The second method presented is an iterative least-squares procedure for lines of different half-widths and for which a computer program is available.

Hyperfine Structure and Intercombination Line Intensities in the Spectra of Magnesium, Zinc, Cadmium, and Mercury*

Abstract: The transition probabilities of the lines 1S0–3P0 and 1S0–3P2 of the s2–sp arrays in Mg i, Zn i, Cd i, and Hg i, which arise by the interactions of the nuclear moments with the electrons, are computed for each odd isotope individually and for the naturally occurring isotopic mixture. The individual hyperfine structure component transition probabilities are given for the 1S0–3P2 lines. Part of the intensity of the lines arises from the interaction of 3P0 or 3P2 with 3P1 and part from the interaction of 3P0 or 3P2 with 1P1, the former being more important for 1S0–3P0 and the latter for 1S0–3P2. Spin-spin and spin-other-orbit interactions in Mg i are calculated for the 3s3p3P term and compared with observations.

Latency and duration of eye movements in the horizontal plane.

Abstract: The electrical method of eye movement recording (EOG) was used to study the reactions of the eyes when subjects attempted to fixate as quickly as possible on light stimuli appearing at various points along the horizontal plane. Each eye was recorded separately, allowing an assessment of the degree of independence of the eyes when reacting in this way. In addition to the data concerning latency of ocular reactions and the duration of eye movements, information regarding the relative speed of movements from periphery to center as compared to movements from center to periphery was obtained. It was also found that the two eyes tend to act independently in regard to latency and speed of movement when moving toward peripheral stimuli.

Head-mounted eye-marker camera.

Abstract: Many visual problems require a better understanding of where people look in a given situation. Most of these questions can be answered by using a simple head-mounted optical device. This consists of a small movie camera and a periscope that transmits a spot of light reflected from the eye. As the subject moves his head and eyes, the equipment photographs the changing scene. In the camera the image of the scene is instantaneously marked with a spot that indicates the position of the line of sight. The effects of eye movements can be distinguished from those of head movements. (1) Immediate recordings can therefore be taken; (2) the subject can turn his head; (3) the scene can be rapidly changing all the time.

Carbon Arc as a Radiation Standard

Abstract: The value of a carbon arc with properly chosen graphite electrodes and operating conditions as a reproducible high-temperature source of radiation has been recognized for a long time. Many studies both in this country and abroad have shown that the crater of the positive electrode has a brightness temperature at wavelengths near 6500 A which falls very close to 3800°K, with a deviation of probably less than ±20°K. However, a number of scattered observations have shown small effects of operating conditions such as current, angular arrangement of electrodes, and size and composition of electrodes. New studies of these variables, including measurements of spectral and total radiance, have clearly defined operating conditions under which the crater radiates like a blackbody at 3800°K over the entire wavelength range 3000°–42 000 A except for molecular radiation at specific wavelengths.

Infrared spectrum of hydrogen fluoride: line positions and line shapes. Part II. Treatment of data and results

Abstract: The spectrometer and experimental methods described in a companion paper were used to measure the center frequencies of some absorption lines in the HF fundamental and first-overtone bands and to measure the pressure-broadened shapes of some lines in the fundamental. The centers of both bands were calculated, and strongly J-dependent, pressure-induced line center shifts were measured for the fundamental. A method for correcting the measured shape of a spectral line for the effects of instrumental broadening in order to obtain the “true shape” is explained. It was possible to obtain the true shape of lines whose pressure broadened half-width was as small (0.03 cm−1) as several times the Doppler half-width.It was found that the true line shape could be represented quite satisfactorily by a modified form of the Lorentz expression, i.e., α=α0(Δν)2[|ν−ν0|η+(Δν)2]−1. For spectral lines whose half-width at one-half the maximum percent absorptance was less than 2.25 cm−1, η=2 gave good agreement between the true shape and that predicted by the Lorentz expression. If this width was greater than 3 cm−1 then η=1.85 allowed the best fit to the true line shape. No pressure dependence of η could be measured in the range of pressures used (0–5 atm).

Rotational and Vibrational Constants of the HCl 35 and DCl 35 Molecules

Abstract: The 1–0, 2–0, 3–0, 4–0, and 5–0 bands of HCl35 and the 1–0 and 2–0 bands of DCl35 have been measured with high precision. A critical analysis has been made to determine the rotational and vibrational constants of these molecules. It is necessary to use a polynomial in m of the sixth degree to satisfactorily represent the frequencies of the band lines in the case of the most precisely measured bands. B0 for HCl35 has been found to have a value of 10.440254±0.000010 cm−1. B0 for DCl35 was found to be 5.392261±0.000010 cm−1. When the B0 obtained for DCl35 is combined with the microwave measurement of B0 by Cowan and Gordy the value obtained for the velocity of light c=299 793.1±0.65 km/sec. The observed rotational and vibrational constants (Ylj) have been used to calculate the potential constants of HCl35 by making use of Dunham’s theory of a rotating vibrator. It is shown that HCl35 is not a pure rotating vibrator since the observed and calculated values of Y02~De are in disagreement by about 1 part in 1000 which is approximately 10 times the experimental error. By making use of the molecular constants for HCl35 and DCl35 and the accurately known atomic masses it is deduced that the ground level Be is perturbed by the upper electronic levels by 1 part in 8000. The sign of the perturbation is to increase Be over its unperturbed value. The sign of the perturbation is such that it may be presumed the HCl molecule has a positive magnetic moment. It was calculated that μJ=+0.2 and +0.1 nuclear magnetons, respectively, for HCl35 and DCl35.

Ruby Optical Maser as a Raman Source

Abstract: The successful use of the ruby optical maser for excitation of Raman spectra is described. The conditions of the experiment are discussed, and the utility of the ruby maser for this purpose is evaluated.

Polarization Properties of Corner Reflectors and Cavities

Abstract: The polarization properties of single-corner reflectors and of certain types of cavities using corner reflectors are investigated and described. States of polarization are found which remain invariant under transmission. Particular attention is given to the lossless case of total internal reflection.

Solution of the Luneberg Apodization Problems

Abstract: Detailed solutions are given to the Luneberg apodization problems set by Luneberg. All problems are in the context of Fraunhofer diffraction and only aberration-free systems are studied. The first problem is to determine the pupil function (amplitude distribution over the exit pupil) which maximizes the central illuminance subject to the condition that the total energy passing through the aperture be constant. The second problem is to determine the pupil function which maximizes the central illuminance while decreasing the radius of the first zero of the diffraction pattern a prespecified amount. The third problem is to find a pupil function which maximizes the total flux through a prespecified circle (for a circular aperture) or narrow rectangle (for a slit aperture). The methods used are the calculus of variations leading to Fredholm integral equations for the desired pupil functions. Both circular and slit apertures are studied.

Visual Responses to Time-Dependent Stimuli.* III. Individual Variations†

Abstract: Eight normal and two dichromatic observers are tested for amplitude sensitivity to sinusoidally flickering white light at various photopic adaptation levels. The mean response curve of the color-normal observers is in good agreement with the theoretical model of the visual system proposed in Part II. In addition, certain individual curves show three smaller peaks of sensitivity in the frequency ranges of 4–7, 10–15, and 20–30 cps. Their stability with varying adaptation level indicates that these subpeaks occur in the initial, photoreactive stage of system, according to the proposed model. Thus they may be associated with the linear mechanism of color discrimination. Abnormal amplitude-sensitivity curves obtained with one deuteranope and one protanope lend further weight to this hypothesis.

Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. I. Coherent Illumination

Abstract: A resolution criterion due to Sparrow is studied. Unlike the well-known Rayleigh resolution criterion, the Sparrow resolution criterion is dependent upon the coherence properties of the incident light. The extreme limits of complete coherence and complete incoherence are investigated. An apodization scheme for increasing the coherent Sparrow resolution limit is formulated via the calculus of variations. The determination of the required pupil function (amplitude distribution over the exit pupil) necessitates the solution of an inhomogeneous Fredholm integral equation. Both slit and circular aperture are studied in detail.