Journal of the Society of Motion Picture Engineers (1930-1949)

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666 W. S. VAUGHN AND F. TUTTLE If certain prescribed conditions of the system preclude using the value of r derived from Equation 5 (as in the case of one-to-one magnification), we may resort to an approximation method for finding the radius for a circular image gate which will cut the image curve in three points, one on the axis and the other two symmetrically spaced with respect to the axis. Thus if we wish to make the top, center, and bottom of the image fall on a circular image gate we choose a radius of curvature such that l/z cord of image gate " Sin [180° 2 arc tan ('/'chOTd °f ™agegate\-| L \ sagitta or image gate / J where the chord of image gate is computed (see Fig. 3) as v/u times the chord of object gate, and the sagitta of the image gate is: f(u + sagitta of object gate) (« — / + sagitta of object gate) It should be mentioned that with any curved object gate there will be distortion in the image. The central portion of the picture will be vertically expanded or condensed relative to the top and bottom of the picture, depending on whether the picture is being enlarged or reduction printed.