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