Arthur C. Hardy

The Correction of Slit-Width Errors

The original purpose of this investigation was to explore the possibility of providing a spectrophotometer with automatic means for correcting the error that results when a continuous source is used with a monochromator having slits of finite width. In connection therewith, it was necessary to make what appears to be the first rigorous analysis of slit-width errors. The results of this analysis can be applied to the experimental determination of any functional relationship when the size of the “probe” is significant.

Color Correction in Color Printing1

In a three-color print, the color of any area that is large in comparison with the size of the dots of the structured image can be regarded as an additive mixture of eight colors: the unprinted paper stock; the cyan, magenta, and yellow of the individual ink dots; the red, green, and blue that result when ink dots overlap in pairs; and the black that results when all three ink dots overlap. Since the extent of overlapping is determined by the sizes of the dots, the color of the additive mixture can be expressed by three equations. The straightforward attack on the problem of color reproduction is to solve these fundamental equations for the required dot sizes on the assumption that, in every area, the tristimulus values of the reproduction should be equal to those of the original. This has not been accomplished hitherto, because it involves solving three simultaneous equations of third degree, each containing eight terms. However, a relatively simple electronic equation-solving network has been constructed which solves these equations with ample precision in 0.001 second. By using this network in connection with a scanning machine of the type described in the preceding paper, full color correction is achieved. A corresponding set of equations can be written for the additive mixture produced in four-color printing, wherein the fourth color is black. Since the three equations now contain four unknowns, an additional condition must be imposed. From the standpoint of the printing requirements, it is desirable that at least one of the color dots be absent, or of some predetermined minimal size, in every region of the reproduction. An extension of the principles embodied in the electronic network mentioned above imposes this condition and yields a continuous solution to the three fourth-degree equations.

In Defense of Beer’s Law

To state that a substance fails to obey Beer’s Law is an injustice, since it is the investigator who has failed to make proper use of the Law. If the substance becomes a mixture of substances when in solution, Beer’s Law must be applied to each component of the mixture. It does not seem to be generally realized that this can often be done, even when none of the components of the mixture can be isolated in the pure state.

A Photoelectric Method for Preparing Printing Plates1

Whenever the subject being reproduced has a regular pattern, the conventional type of halftone screen, because of its regular structure, may produce an objectionable beat pattern, called moire. In multicolor printing, the regular patterns of the several structured images produce complex beat patterns whose effects are minimized, but not eliminated, through proper choice of screen angles. This paper describes a procedure in which a continuous-tone image is scanned; and the resulting photo-tube signal is used to actuate a light valve in such a manner as to produce a structured image containing dots that are, in effect, distributed at random. It is shown that this procedure avoids both the distortions in tone reproduction and the moire patterns associated with the conventional use of halftone screens.

Colorimetry by Abridged Spectrophotometry

It seems to be generally conceded that the results obtained with a photoelectric colorimeter are significant only when the spectral characteristics of the sample and standard are similar. When this is the case, the selected ordinate method of integrating spectrophotometric data can be greatly abridged, a single selected ordinate being adequate under many circumstances. This means that an abridged spectrophotometer can be used for the dual purpose of production control and, when necessary, the determination of tristimulus values.

Graininess in Motion Picture Negatives and Positives

An instrument which measures the graininess of a photographic material is described. It is shown by the aid of photomicrographs that the readings of the instrument represent the true graininess as understood by the photographer. The instrument has been used in an investigation of the various steps in the preparation of a motion picture positive to determine the conditions for minimum graininess in the finished print. The exposure of the negative is found to have considerable influence on the graininess of the print, developing conditions being relatively unimportant. An explanation of the excessive graininess which sometimes occurs is given.

A New Non-Intermittent Sensitometer

A new non-intermittent sensitometer has been constructed which consists of two sector wheels rotating about the same axis at different angular speeds. During the exposure, the larger disk makes only one revolution. In this interval, the small disk makes many revolutions but the large wheel covers the photographic material except for one revolution of the small wheel.With the ordinary sector wheel sensitometer, the exposure range is rarely more than 256 to 1 because of the difficulty of cutting the wheel. It is shown that by using two sector wheels, the exposure range may easily be increased to 16,384 to 1. An extension of this principle to three disks would not involve any serious mechanical difficulties and would increase the exposure range to more than one million to one.

An Electronic Method for Solving Simultaneous Equations1

In connection with the requirements of color correction discussed in the preceding paper, we found that a set of n simultaneous equations can be solved by using each of the n error signals to control one of the independent variables. Stability of this equation-solving network can be achieved by the proper interconnection. In applying this procedure to the equations for color correction, it was necessary to find the sum of eight terms, each of which is the product of either three or four independent variables. It was found that these individual products could be computed by making use of the fact that, if n events have probabilities of occurrence a, b, ⋯n, respectively, the probability of their simultaneous occurrence is the product of their individual probabilities abc ⋯n. By generating rectangular waves of irrationally related frequencies whose positive pulse widths are proportional to the values of the unknown variables, and applying these signals to the grid of a vacuum tube in such a manner that its plate current flows only when all of the signals have positive values simultaneously, the average value of the plate current is proportional to the required product. When controlled in this way, eight vacuum tubes with their plates connected in parallel deliver an average current that is proportional to the required sum.