British Kinematography (1953)

ns BRITISH KINKMAIOCiRAPHY Vol. 22, No. 4 From his theory it can be deduced that on the log Input-Brightness/log Resolving-Power graphs of Figs. 6-10, a constant degree of visibility (corresponding to a given probability of seeing the test object) at a given contrast will correspond to a straight line at a fixed slope on the graph. The position of this line will depend on (a) the degree of randomness (noise) in the system, (b) the contrast of the test object used, and (c) the visibility criterion. The higher the noise content of the signal, the lower the contrast of the test object, or the more certain the visibility criterion used (the higher the probability of seeing the test object), the lower will be the resolving power attainable at any given value of brightness, i.e. the further to the right on the graph will the limit line lie. It is shown in the previous publication that with this approach, a tolerably good explanation can be given of the behaviour of the three dimensional surface resulting from a constant visibility criterion and viewing distance plotted in terms of the three axes Brightness, Resolution and Contrast. The principle of this method of approach is illustrated in Fig. 17 which shows two hypothetical constant visibility curves resulting from two positions of the " noise " limit line, corresponding to a low and a high noise content in the signal, other conditions being unchanged. It should be noted that this diagram applies to a given value of contrast and is therefore effectively a two-dimensional cross section of the three dimensional diagram referred to, perpendicular to the contrast axis. Fig. 17 shows that there are four limit lines to the constant visibility curve for a given value of contrast (these of course become four limit surfaces to the constant visibility surface when contrast is also allowed to vary). These limits are the maximum and minimum input brightness determined by the knee and toe of the S-shaped transfer characteristic, the maximum resolution set by the size of the resolving element used in the system, and the noise limit already mentioned. In cinematography the maximum input brightness corresponds to clear film on the positive. In a television camera tube it corresponds to the maximum potential which the target will sustain. Similarly the minimum input brightness corresponds to unexposed negative coupled with the limit set to tone perception by the background graininess of the positive emulsion ; in television it corresponds to the " standing noise " present in the camera tube when no light is falling on it. The maximum resolution limit* is set by the average grain size in the case of a photographic emulsion and by the size of the scanning aperture in a television tube. Fig. 17 shows the interaction of these limits on the constant visibility curve. In particular it shows the effect of low and high noise content, the other three limits remaining constant. ■ Remembering that the same type of change in the visibility curve would be expected from a lower contrast test object, or a higher degree of visibility as from a higher noise limit, it will be seen by inspection that the experimental curves of Figs. 6-10 are entirely in accord with this conception. From this it will be seen that if a high contrast test object is used with a low visibility criterion (N/J for example), the resulting curve will tend to be like " a " in Fig. 17. This curve is relatively unaffected by the noise limit which is overshadowed by the minimum input brightness limit and the maximum resolution limit. The curve does, however, closely approach the maximum resolving power of the system, but at a brightness less than the highlight brightness B. If a low contrast test object is used and/or a high visibility criterion (V/C for example), then the visibility curve will be more like " b " in Fig. 17. This does not approach the limit of resolution, but is almost entirely controlled by the noise limit in the lower brightness range. For determining the limiting resolution it is therefore preferable to use a high contrast test object and a limiting visibility criterion — which of course has been common practice. On the other hand for determining the fundamental limitation due to true randomness (noise, grain) in the system, * Note that in this connection the effect of optical elements are considered to be sufficiently perfect to be neglected.