7
such techniques will require more knowledge of the
adjacency and other non-linear effects that occur in
photographic emulsions during the development process*
Derivation of MTF's from Images
The techniques of microdensitometry and computation
which have increasingly come into use with the wider
interest in MTF's have made it possible to estimate the
operating performance of photographic systems by analysis
of aerial negatives without need of resolution targets in
the picture, provided that the scene contains an edge,
i*e. a luminance step equivalent to a step function. The
image of the edge is traced with a raicrodensitometer and
converted into a graph of effective exposure via the H and
D curve of the emulsion. The first derivative of this
graph is the spread function during exposure, and when
Fourier transformed this yields the MTF. Comparison of
this with the laboratory measured MTF, or the calculated
MTF for the system shows the extent to which the performance
may have been degraded by flight conditions. The method
is not highly accurate but can be very valuable when no
other quantitative method of assessing practical perfor
mance of an aerial camera is available. (68) (69)
Discussion
The foregoing examples have indicated something of
the scope and power of transfer function methods in photo-
optical image analysis. In most of the cases discussed the
MTF did not have to be known with great accuracy. In lens
design, for example, one of the final objectives is to
predict resolving power. Since resolving power cannot be
measured, without special precautions, with a precision
greater than - 10^, and there are inevitable differences
between design and the performance of the manufactured lens,
extreme accuracy in the calculation is not called for.
Again, since residual image movement can only be estimated
on a statistical basis, its equivalent MTF for system design
cannot realistically be assumed to an accuracy better than,
say, 1C$. Similar considerations prevail throughout system
design; an accuracy of 1C$ at any point on the MTF pro
vides an adequate working tool for most purposes. While our
knowledge of the significance of small variations of the MTF
at different spatial frequencies is by no means complete,
enough is known to make estimates in specific cases, and as
a rough general rule it might be suggested that variations
of less than 5% are not significant. Thus considering meas
urement of the MTF of a lens, sin accuracy of - 5% might be
considered good enough for data to be used in designing a
system, especially if the specification is written in terms
of resolving power, which must be experimentally determined
for each unit produced. However, higher standards of
