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128 THREE-DIMENSIONAL MOTION PICTURES Practical studio lighting conditions and emulsion speeds require the use of relatively large aperture lenses, between //2 and //3. This means that the apex of the cone of light forming a point image on the film embraces a rather large angle, and when not focused on the film casts thereon a circle of diffused light of appreciable size, a size also proportionate to the distance of the apex of the cone from the film. In order, therefore, that there may be a reasonable depth of focus and sharpness of image, the focal length of the lens must be short. This necessity is not avoided by using larger film. The average focal length used for general purposes is 50-mm. or 2 inches. Shorter focal lengths are fre quently used, for instance 1% inches; but the ability of most lenses to cover a 1-inch field at a 20 degree semi* angular opening with sufficient sharpness is partly due to the absolute decrease in the dimensions of the mar ginal imagery errors. A 2-inch lens covering a 1-inch field has a semiangular opening of 14 degrees. A discus sion of the characteristics of the images formed by such lenses will serve to set forth the conditions under which motion picture lenses operate. It has not been an easy problem to design lenses that will give satisfactory results under the conditions obtain ing in motion picture photography. W. Merte discusses briefly the difficulties with which the designer of such objectives is faced. One of the methods of approach to the problem is to modify the Petzval objective so as to flatten its field. As is well known,, this objective in its original form has a large aperture and an unusually sharp central definition for a lens of such simple con struction. The definition, however, rapidly falls off and is unsatisfactory even for short focal lengths at the mar gin of a field subtending a greater semiangular opening than about 7 degrees,, requiring thus a 4-inch lens to