Journal of the Society of Motion Picture and Television Engineers (1950-1954)

tive f number will be related to the f number by: (Effective f number for magnification m) = (f number) (1 + m) (10) 4.4 However, many lenses cannot be regarded as being "thin," and in such cases the Effective f number at a finite magnification will not* be equal to the infinity f number multiplied by (1 + m). However, the photographer knows from long experience that he should always multiply the marked f number of a lens by (1 + m) in order to determine the Effective f number at a finite magnification, m. Therefore, in order that this procedure can continue to be used, it is suggested that if a lens is designed to work at or near some particular finite magnification, m, the aperture markings should be engraved with the "Equivalent f number" defined by: Equivalent f number — {"Effective f number at magnification ml (11) I 1 +m J 5. Definition of T Number 5.1 When lenses are marked in accordance with the f system, differences of value in the factor f of equation (1 ) are completely ignored, with the consequence that for a given f-setting of the diaphragms, even though correctly marked, the exposures made with different lenses may vary greatly, this variation arising from a variation in the number of component elements of the different lenses and from the large differences in the values of transmittance that exist between coated and uncoated lenses. The T system defined in this section is a new system of diaphragm graduation designed to compensate for this variation. With the T system of graduation, the image illuminance in the center of the field is independent of the variations in lens structure enumerated above. * For example, an afocal lens of symmetrical construction can be used as a printer or copying lens at unit magnification. The Effective f number is then equal to the f number of the half system, but since the focal length of the whole lens is infinite, no meaning can be given to the f number of the whole system. For other examples see: R. Kingslake, "The effective aperture of a photographic objective," J. Opt. Soc. Am., vol.35, pp. 518-520(1945). Page 3 of 8 pages 5.2 For a lens used with a distant object, the T number is defined as the f number of an ideal lens having 100 percent transmittance and a circular aperture, which would give the same central-image illuminance as the actual lens at the specified stop opening. 5.3 Hence, for a lens with a circular aperture, following the argument of equation (8): (12) T number =JM£ V f and for a lens with an entrance pupil of any shape and area, A, the corresponding formula is: (13) T number = — 2V f A 5.4 In practice, however, it is expected that the normal procedure will be to re-engrave the diaphragm ring on the lens at a series of definite T numbers, rather than to measure the T number corresponding to each of the existing marked f numbers. 5.5 It may be remarked again that the T number is a photometrically determined quantity, whereas the f number is a geometrical quantity. Since the T numbers are determined photometrically, they automatically take account of the size and shape of the aperture, the actual focal length of the lens, the lens transmittance, and any internally reflected stray light which may happen to strike the film at the center of the field (such as in a flare spot). It is implicit in the T number system of aperture markings that every lens should be individually calibrated. 5.6 For a lens designed to be used at finite magnification, the engraved T number will correspond to the Equivalent f number defined by equation (11). 5.7 The procedure for measuring the T number of a lens is given in Section 13. 6. Standard Series of Aperture Markings 6.1 The diaphragm ring of a lens shall be marked at every whole stop on either system. A "whole stop" is taken to represent an interval of double or half the image illuminance, PH22.90-1953 February 1954 Journal of the SMPTE Vol. 62 177