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

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June, 1930] CURVED GATES IN OPTICAL PRINTERS 665 bola, or ellipse, and hence a value of r was sought which would make the gate a circle, that is, make the coefficients of x2 and y2 in (2) equal. This value is: u0(u0 U0 V0 •(4) 2(u0 /) 2 This value not only makes the image curve a circle, but a circle of FIG. 2. Special solution for a 2 : 1 reduction printer. exactly the same size as the object circle. For any magnification we may express r as a function of / and m (magnification) as follows: , r -•/,/(» -i) (5) Thus for a print with a 2:1 reduction ratio (see Fig. 2) r = V2/(3/2) = 3/4/ From (5) we see, however, that it is impossible to make use of this special solution for printing at one-to-one magnification, for in that case m = 1 and the radius becomes zero. —I — AV FIG. 3. Illustration of method of computing best circle for image gate.