The system must also be space-invariant; photographic film always meets this condition.
In noncoherent systems, of course, the light distributions to be recorded are already expressed as intensity functions.
An alternative method is to use a two-step process with a gamma product of two. Unfortunately, at high spatial frequencies an MTF for the second step of the process must also be considered.
A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
R. L. Lamberts, J. Opt. Soc. Am. 49, 425 (1959).
L. O. Hendeberg, Arkiv Fysik 16, 457 (1960).
R. L. Lamberts, J. Opt. Soc. Am. 51, 982 (1961).
F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).
J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
F. Grum, Phot. Sci. Engr. 7, 96 (1963).
E. N. Leith, Phot. Sci. Engr. 6, 75 (1962).
R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).
Equation (6) is an approximation to the actual amplitude function, obtained by truncating a binomial expansion after the first two terms. This approximation clarifies the mathematical treatment without affecting its validity. As is explained in the next section, the effects of this approximation can be avoided during the reduction of the data to final form. (See also Fig. 8 and the relevant text.)
The MTF is sometimes dependent on exposure (see Lamberts cited in Ref. 5). In our experiments, the average density of the film was approximately 0.4. Measurements of the MTF at higher exposures showed that the MTF varied by less than 10%, possibly because the signals we recorded had small modulation.
E. N. Leith et al., Appl. Opt. 5, 1303 (1966).
A. L. Ingalls, Phot. Sci. Engr. 4, 135 (1960).
J. H. Altman, Phot. Sci. Engr. 10, 156 (1966).
Modulation Transfer Data for kodak Films, Kodak Pamphlet No. P-49, East man Kodak (Company, Rochester, N. Y., 1962.
H. Frieser, Phot. Sci. Engr. 4, 324 (1960).
A. Vander Lugt, Proc. IEEE 54, 1059 (1966).
Reference 20, p. 1062.