Robert N. Wolfe

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.

The Relation of Definition to Sharpness and Resolving Power in a Photographic System

Definition, as the term is used in the present paper, is the quality aspect of photographs that is associated with the clarity of detail. Resolving power is used in its customary sense, and sharpness is defined as the impression received by an observer viewing well-resolved elements of detail; its objective correlate is acutance, which has been defined quantitatively elsewhere. A series of negatives was made of a scene, the lens being moved longitudinally between exposures to vary the resolving power and the acutance in the negatives. A corresponding set of negatives was made of resolving power and acutance test objects. Positive transparencies were made from both sets of negatives. The transparencies of the scene were judged for definition, and numerical values were assigned by statistical methods. Neither acutance nor resolving power correlated well with definition except when the resolving power exceeded the limit set by the eye, in which case acutance correlated fairly well. A practical correlate of definition is proposed which consists of acutance multiplied by an exponential function of resolving power.

Psychometric Evaluation of the Sharpness of Photographic Reproductions

Psychometric methods were used to evaluate the relative sharpness of a number of photographic reproductions in which sharpness was the only significant variable. Since sharpness is an observer’s subjective impression of an aspect of picture definition, the methods for deriving sharpness values involve introspective processes and methods of quantifying these subjective impressions. Although no physical measurements of any aspect of the stimulus are involved in deriving sharpness values by the psychometric method, repeated evaluations showed that the scale values obtained are a reliable indication of the sharpness attribute of a photographic reproduction. Three methods of quantifying the judgment data were used, and the sharpness ratings obtained from all three were in good agreement with one another. Projected transparencies gave. substantially the same results as paper enlargements. Attempts to correlate the sharpness ratings with physical measurements of some aspect of the developed image were not entirely successful; neither resolving power nor simple density relationships across an abrupt boundary between light and dark areas resulted in satisfactory correlations with sharpness ratings.

Determination of the Modulation Transfer Function of Photographic Emulsions from Physical Measurements

The modulation transfer function (MTF) of a photographic layer is customarily determined by means of photographic photometry. It is difficult to obtain the true function because of the interference of adjacency effects. De Belder, et al. have recently presented a method of obtaining the MTF from physical measurements of the layer. This method, which utilizes the random-walk technique, simulates the physical processes involved and requires data concerning several physically measurable parameters, including the absorption and scattering coefficients. Data for these coefficients, which De Belder lacked, have been obtained from measurement of the volume reflectance and volume transmittance of the layers by the technique developed by Wolfe, DePalma, and Saunders. The coefficients were calculated by using the Schuster, Kubelka–Munk two-flux, radiative-transfer theory. After the necessary parameters had been measured for several fine-grain silver bromide photographic layers varying in thickness from 3 to 33 μ, the MTF of each of these layers was calculated. These values were compared with the MTF of the layers measured by photographic photometry, when they were developed under conditions giving minimal adjacency effects.Good agreement was obtained between the results of these two methods; the calculated physical values, however, were consistently somewhat higher than the photographic values. At least part of this lack of agreement is caused by halation in the photographic layers from the base-air interfaces.

The Spatial Photographic Recording of Fine Interference Phenomena

Interference bands as close together as 0.4μ were recorded with the Kodak Type 548 Spectroscopic Plates. The penetration of these bands into the emulsion layer was detected by microscopic examination of a vertical section of the photographic record. The photographic record of such bands, the spacing between which depends only upon the angular tilt of a Lloyd mirror and the wave-length of the radiant energy being used, should prove useful as a stage micrometer. Since these photographic records behave as diffraction gratings, the spacing between the band images was checked by measuring the diffraction angle, using radiant energy having a wave-length shorter than the spacing.

Irradiance Distribution in a Lloyd Mirror Interference Pattern

The Lloyd mirror interference pattern reappears and disappears in a periodic manner at distances from the mirror edge greater than the distance to the initial point of disappearance. In certain cases bright lines appear where, according to the textbook theory, which assumes spectrally homogeneous radiation and a slit source of infinitesimal width, dark lines should appear. A photograph of such a pattern is shown, measured values of the relative irradiance as a function of distance from the mirror edge are presented, and a theoretical determination which accounts for certain features of this variation of irradiance with distance is outlined.If we let IR=relative irradiance at a distance P from edge of mirror, θ=angular tilt of mirror, α=angular subtense of slit, ν0=wave number of radiation, ν1=width of wave band, and ω=2πν0, then IR=2ωα(ν1/ν0)-(1/P)Si[Pω(1+12(ν1/ν0)(2θ+α)]+ (1/P)Si[Pω(1-12(ν1/ν0)(2θ+α)]+ (1/P)Si[Pω(1+12(ν1/ν0)(2θ-α)]- (1/P)Si[Pω(1-12(ν1/ν0)(2θ-α)].If spectrally homogeneous radiation is assumed, then IR1=0.50−0.50 cos4πPθν0(sin2πPν0α/2πPν0α).

A Method for the Measurement of the Energy Distribution in Optical Images

A method has been developed for measuring the energy distribution across optical images of a line source. This method is completely photographic. It makes use of a line source and a neutral colloidal carbon wedge having a linear increase in density with distance. The energy distribution across edge diffraction patterns can be measured by a slight variation of this method.

Measurement of Volume Reflectance and Volume Transmittance of Turbid Media

A description is given of an integrating-sphere-type instrument for measuring volume reflectance and volume transmittance of a thin plane-parallel slab of gelatin having scattering particles embedded within it when uniformly diffuse radiation is incident on the slab. Fresnel surface reflections are eliminated by immersing the slab of gelatin in a liquid matching the refractive index of gelatin. The liquid consists of a mixture of 73% bromobenzene and 27% Nujol Extra Heavy Mineral Oil. The theory of the instrument is outlined.

Width of the Human Visual Spread Function as Determined Psychometrically

The response of the human visual system to an optical image is assumed to be linearly related to the logarithm of the spread function of the photographic system projected onto the retina combined with the spread function of the visual system. From psychophysical data derived from viewing (at different distances) a series of pictures generated with different spread functions, an estimate is obtained of the variance of the spread function of the visual system. The square root of this variance ranges from 3 μ to 8 μ, depending on the techniques used and on the training of the judges. Although the residual errors in this determination are small, they show systematic trends, indicating that definition depends on other factors than the composite variance.

Detail Rendition by Photographic Systems as a Function of Exposure Time

Photographs were made using several photographic systems, all having entrance pupils of the same diameter. Each of five lenses, varying in focal length from 212 to 33 in., was used with five different kinds of photographic film. The lenses were the best that could be obtained for the purpose of this experiment. The films varied from a fast aerial film to a fine-grain film designed for document reproduction, but all were developed to a gamma of approximately 1.5. The test object was a transparency of a farm scene. An enlarged positive transparency was made from each negative to such a scale that the image of the scene had the same size in each one. It was found that the films of moderate and high speed recorded practically the same amount of detail for a given exposure time but that the document-copying films recorded much less.