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Proposed American Standard
Aperture Calibration of Motion Picture Lenses
PH22.90
p. 2 of 10 pp.
whence
— 2
(4)
2.5 For an aplanatic lens, we may now replace sin 6 by D'/2f, and the image illuminance equation (1) becomes
E TT t B (D'/202 whence by equation (4), we find
E = t BA/f2 (5)
3. Definition of t Number
3.1 For a lens of the type assumed, having a circular aperture, which is perfectly corrected for spherical aberration and satisfies the sine condition, and which is also assumed to form an image in air of a very distant object, the f number of the lens is defined by the equation
f number =-L=
D 2 sin 00 (6)
where 00 is the semiangle of the cone subtended by the circular exit pupil of the lens at the point where the lens axis intersects the plane of the image of the assumed distant object, and the entrance pupil has a diameter D.
3.2 If the entrance pupil is not circular, this relation becomes
/number— — = — /— u\
D' 2V A (7)
following the reasoning of Section 2.4.
3.3 If the aperture is circular, but the lens does not satisfy the sine condition, then f/D will not be equal to l/(2sin$). In such a case, the f number of the lens is to be defined by l/(2 sin B) rather than by the ratio f/D. This value is chosen because both the image illuminance and the depth of field of the lens depend directly on sin 0. In such a lens, then, the marked f number will not be equal to the simple ratio of the focal length to the diameter of the entrance pupil.
3.4 The procedure for measuring the f number of a lens with a distant object is given in Section 11.
3.5 In terms of f number, equation (1) giving the image illuminance becomes
E TT t B/4(f number)2
(8)
4. Effective and Equivalent f Number of a Lens Used at Finite Magnification
4.1 If a lens with a circular aperture is used to form an image at a finite magnification m, the image illuminance will, as always, be given by equation (1).
NOT APPROVED
340
October 1952 Journal of the SMPTE Vol. 59