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March, 1930] OPTICS OF MOTION PICTURE PROJECTORS 311
that could be expected of an ideal optical system and a source of intrinsic brightness B. It is as futile to attempt to produce more illumination than is indicated by equation (2) as it is to attempt to build a perpetual motion machine, and for the same reason. Obviously, it makes no difference how far the diffusing glass is placed behind the gate, provided the gate appears filled with light from every point of the projection lens.
When 6' is small, as it is in this case, equation (3) below gives substantially the same result.
,., _ Brightness of Source X Effective Area of Projection Lens . .
xi — . . (^oj
Square of Distance from Lens to Screen
The units of E will be lumens per square foot (or foot-candles) when the brightness of the source is expressed in candles per square foot and the area of the projection lens and its distance from the screen are measured in square feet and feet, respectively. Equations (2) and (3) apply only to the center of the screen or better to the point where the optical axis intersectst he screen. It has been shown1 that the illumination decreases toward the edge of the screen as the fourth power of the distance from the projection lens. For example, the illumination at the edge of the screen can be determined by multiplying the illumination at the center by the fourth power of the ratio of the respective distances of the two points in question from the projection lens. As the screen is usually small, this decrease in illumination toward the edge of the screen is not serious. As a practical matter, a slight reduction in illumination toward the edge is desirable because of the contrast between the edge of the screen and the black border surrounding it. In fact, it has been found experimentally that an absolutely uniform illumination of the screen makes it appear too bright at the edges due to this contrast effect.
THE EFFECT OF APERTURES
Before attempting to include the light source and condenser, let us consider briefly the effect of apertures on the performance of the optical system. Fig. 1 shows two apertures, one being the gate and the other the rim or effective stop of the projection lens. Since the gate is imaged on the screen, it is known in optical theory as a field stop and limits only the area of the picture without having any effect on the screen illumination. If a metal mask containing a small hole were inserted at the gate, the size of the picture would be reduced