Robert L. Lamberts

Reversal bleaching for low flare light in holograms.

It has been shown that the principal cause of flare light in a bleached hologram is self-interference of light from an extended object. In most bleaching processes the surface relief image and variation of refractive index of the bleached emulsion combine to enhance the self-interference pattern at low spatial frequencies and thus to enhance the flare light. This paper describes a reversal bleach process for Kodak spectroscopic plates, Type 649-F, such that the relief image tends to cancel the effects of the index variation for low spatial frequencies. This makes it possible to achieve high diffraction efficiencies and signal-to-noise ratios. Data are given.

Measurement of Sine-Wave Response of a Photographic Emulsion*

A method for experimentally determining the sine-wave response of a photographic emulsion is described. It consists in determining the sine-wave response of a lens, using the lens to photograph a sinusoidal test object on the emulsion under test, determining the response of the lens-emulsion combination, and dividing out the response of the lens. Since sine-wave response is defined in terms of relative exposure in the emulsion, it should be substantially independent of development conditions and the exposure level when adjacency effects are absent. This expectation has been confirmed experimentally. It is also shown that the sine-wave response of a lens and the response of an emulsion can be combined to predict the characteristics of the lens-emulsion combination.

Relationship between the Sine-Wave Response and the Distribution of Energy in the Optical Image of a Line*

The method of obtaining the sine-wave response of a lens, both theoretically and experimentally, is described, and it is shown that the line spread-function can be derived from the sine-wave response alone if the spread function is symmetrical. If the spread-function is not symmetrical, it can be computed from the sine-wave response only when the phase function is also known, and an experimental method of obtaining this function is described. The mathematical procedure for the reciprocal inversion of the spread-function and the sine-wave response is confirmed experimentally.

Characterization of a Bleached Photographic Material

Experimental measurements show that the phase transmittance characteristics of a photographic material, caused by relief images and variations of refractive index, can be fairly reproducible if processing is properly controlled. To manipulate these characteristics, particularly those of bleached materials, it would be desirable to have data for the phase image corresponding to the density-log exposure curve and the MTF curve of the density image obtained by conventional processing. A method is described for obtaining both curves from measurements of optical path variation of sinusoidally exposed images. Components from both the relief image and the variation of refractive index can be determined. It is shown that such data for a bleached photographic material can be used to produce an optical path variation having an arbitrary profile.

Measurement and Analysis of the Distribution of Energy in Optical Images

It is pointed out that a theoretical relation exists between the distribution of energy in the image of an edge (edge trace) and the distribution in the image of a line (line spread-function). Experimental data are presented in support of this relation and the method of determining these distributions experimentally is outlined. It is also pointed out that, since the spot diagram of a lens represents the point spread-function, the line spread-function, needed for the foregoing procedure, can be found by mechanical summation of this diagram. An example is given to show that the edge trace of the finished lens can be thus predicted from the spot diagram.

Sine-Wave Response Techniques in Photographic Printing*

A single photographic emulsion serves as a linear device when analysis is made in terms of the exposure that the material receives. When sinusoidal patterns are printed, harmonics in terms of the transmittance of the negative are introduced in the print, but the odd and even harmonics tend to compensate each other so that the over-all error tends to be small even though the modulation of the sinusoidal pattern may be as large as 60% or 70%. The response function in terms of the exposure of the negative should therefore approximate the product of the sine-wave response functions of the two materials and should be little affected by processing conditions. Experimentally, these conclusions are found to hold very well when a contact print of good quality is made on positive film, even through as many as three successive printings. It is also found that such cascaded response functions can be used to predict the density distribution across an edge.

Comparison of Experimental and Theoretical Holographic Image Radiance

In a previous paper, several theoretical expressions were derived for calculating the ratio of the light flux in a holographic image of a uniform but extended source to that of a direct image of the source itself, account being taken of the sensitometric characteristics of the photographic material. The present paper is an experimental extension of this work. In particular, comparisons are made between theoretical curves and experimental data for variations of (1) the average density of the hologram, (2) the ratio of object-beam to reference-beam irradiances, and (3) the angular extent of the object. The performance of certain photographic developers is also discussed.

Effects of Some Photographic Characteristics on the Light Flux in a Holographic Image

The total light flux diffracted by a developed holographic plate is proportional to the variance of the spatial distribution of amplitude transmittance of the plate. This light forms the real and virtual holographic images and also the flare surrounding the reference beam. The variance of amplitude transmittance does not, in general, depend upon the size or form of the object, but only upon the total amount of light received from it, as this affects the beam-balance ratio. The sensitometric characteristics of the plate are taken into account by making use of three plots, namely, amplitude transmittance vs exposure, amplitude transmittance vs log exposure, and density vs log exposure. First-order expressions are derived for the ratio of the light flux diffracted by the hologram to that received from the object in terms of measurable parameters such as beam-balance ratio, average exposure, and gradient of the sensitometric curve. In like manner, we can calculate the ratio of the radiance of the holographic image to that of the original object.

Optical-Path Variation in a Photographic Emulsion

The variation of optical path length through the developed photographic image has been determined for Kodak Panatomic-X film by exposing with a spatial-frequency series of sinusoidal line patterns and scanning the developed images to determine the peak-to-peak variation of density and of optical path for each pattern. For the conditions studied, the ratio of the optical-path variation to the density difference in each pattern depended upon the average density of the pattern. A similar study was made to examine the relationship between the variation of optical path and the variation of silver per unit area on the film. Because the ratio of these showed little, if any, dependence upon the average density, it was concluded that a fairly linear relationship existed between optical path and the mass of silver in an area of the emulsion. Application of linear-systems theory proved to be successful in that the path variation associated with an isolated line exposure could be calculated from the sine-wave data by means of convolution and Fourier-transform techniques. By immersing the film sample in a liquid of known refractive index, it was possible to determine both the variation in optical path resulting from a variation in refractive index and that from the variations in thickness that constitute the relief image.

The Production and Use of Variable-Transmittance Sinusoidal Test Objects

Test objects that vary sinusoidally in transmittance have been made by photographing variable-width sinusoidal test objects with cylindrical optics and printing the negative in such a way that the over-all gamma of the negative-positive combination is approximately unity. A gray scale is included with the test-object array and serves to calibrate the various levels carried through the systems that are tested. Methods of use are described and a practical example is given.