ON THE EVALUATION OF STRONGLY ENLARGED PHOTOGRAPHS

摘要

The accuracy of the evaluation of a photographic plate is limited by its grain structure. One approximates the value for the light density at a given point by the average light density in a small area (the "test are") surrounding the point. This paper establishes confidence limits for evaluation procedures of this kind. It is assumed that the grains on the photographic plate arise in independent random processes controlled by the local density of the light flux. In the evaluation procedure one counts the number of grains in the test area. Generalizing the method one attaches a weight factor to each grain depending upon the grain position within the test area and then determines the sum of the weight factors for the grains found in the test area. By such a procedure one can determine quantities related to the light density, e.g. the density gradient; one can also scan for patterns of a special kind, e. g. a sudden jump of the light density. For measurements of this kind probability theory predicts the expected value and the variance in terms of the light density and the chosen weight function. There are two kinds of errors in the measurement process: errors due to the non-vanishing size of the test area, and errors due to the randomness inherent in the process of grain generation. The variance due to errors of both kinds must be minimized. The treatment of these questions is shown in a number of examples of increasing complexity. Moreover, this report investigates the probability of making an error if one tries to discriminate between two known light densities on the basis of grain counts, and it also examines a step-wise method for carrying out such counts.