Table 1. Resolving-power, cycles per millimetre 
High 
Contrast 
Low Contrast 
Pan X 
Tri X 
Pan X 
Tri X 
Axis ... 
49 
26 
29 
14 
Edge 
47 
23 
27 
11 
Axis/Edge .. 
1-04 
1-14 
107 
1-27 
Now it clearly would make little difference, in ranking 
these two cases, whether we used high or low contrast 
resolving power, Tri X or Panatomic X emulsion. This is 
indeed obvious even from a glance at the graph. Yet the 
transfer functions, at frequencies much lower than the 
resolving powers, show a great difference in modulation 
transfer, which must somehow be evidenced in the quality of 
definition. How such differences can affect image quality is 
discussed in the next section. In general the relative merit of 
systems as judged by their resolving power will depend on 
the shape of their transfer functions, the position of the 
emulsion thresholds, and the target contrast. A low target 
contrast is often valuable because it forces the comparison 
into the low frequency region, where some systems have a 
relatively poor transfer of modulation over a fairly wide 
bandwidth, thus emphasising deficiencies which would not be 
revealed by a high contrast test. In Figure 5 it is not the 
difference of modulation transfer at any one frequency 
which matters (we cannot interpret directly from resolving 
power or spatial frequency to image quality at reciprocal 
size) but the generally poor transfer over a substantial part 
of the spectrum. In practice resolving-power usually ranks 
systems in their correct order, because transfer functions 
often have rather similar shapes, but its fundamental limita 
tions must always be borne in mind. 
We have implicitly assumed the use of sine-wave thresholds 
in this account, but resolving-power is commonly measured 
on bar targets ; can these be fitted into the model? A bar 
target, like any other sharp-edged pattern, has a complex 
spectrum, and the image contrast as a function of frequency 
changes in different ways for different transfer functions. 
It is possible to calculate “ response functions ” for bar 
targets, assuming conditions such as a perfect lens or specific 
amounts of aberration, but there is no generally applicable 
relationship between the sine-wave and bar target responses. 
In general the bar response is greater than the sine-wave 
response at a given frequency, but the difference depends on 
the state of correction of the lens and on the frequency. 
Also, it is not evident which kind of threshold should be 
used, since for a rigorously correct approach the threshold 
would have to be determined with the same transfer function 
as the one for which the resolution is being predicted, which 
is absurd. Resolving-power prediction is in fact an emprical 
technique and will not bear rigorous examination. Never 
theless, it is still a useful tool if its limitations are recognized, 
and enables the designer to estimate performance within say 
plus or minus 10 per cent, which is helpful in choosing 
between alternative systems. 
Definition and the Transfer Function 
One of the apparent advantages of the transfer function 
is that it reveals the system performance over its whole 
frequency range, but so far we have only tied it down to 
image quality at one frequency, the resolving-power. How 
can we make better use of the total information provided by 
the function? Resolving-power as such has little or no 
significance for aerial photography ; it persists because of 
the inertia of established custom and because it is simple and 
convenient in use. Spatial frequencies as such have no 
significance at all ; the Fourier technique is valuable and 
sometimes indispensable for research and system design, but 
in the end our eyes operate on images, not on their Fourier 
transforms. What really interests us in aerial photography 
is definition as a function of detail size. The general desire 
for information in such terms is expressed by the common 
mistake of taking the value of the transfer function at some 
frequency as an index of the quality of an image whose size 
is the reciprocal of the frequency. A “ frequency ” is of 
course a repetitive sinusoidal pattern without beginning or 
end. A large object is not a low frequency any more than 
a small object is a high frequency ; on the contrary, a small 
object is a wide bandwidth if transformed into frequency 
terms. If we wish to make deductions directly from transfer 
functions we must keep consistently to frequencies, and not 
confuse them with sizes. 
In our simplified one-dimensional space, a small object is 
a narrow bar, which can stand for the shapes of aerial 
photography, in a preliminary consideration. We could 
assume that some ground detail size was the smallest of 
interest and use the corresponding bar width in image scale 
as a critical dimension at which to study image quality. Our 
interest in the quality of the bar image might be reduced to 
two cases ; when it is just worse than a perfect image, and 
when it is so degraded that its presence can only just be 
detected. Before we can operate on the bar with transfer 
functions we must transform it into its frequency spectrum, 
which is easily done from knowledge of its width and the 
sin x/x relationship. Figure 2 shows part of the theoretical 
spectrum for lines 1 millimetre and 1/10 millimetre wide, 
illustrating the general principle that narrow lines have a 
wide bandwidth and vice versa. Remembering that the 
spectrum theoretically extends to infinity it will now be 
apparent that there is no such thing as a theoretically perfect 
reproduction of any bar, however wide, for its spectrum will 
always extend beyond the finite cut-off point of any optical 
system. Transfer functions, for the normal photographic 
case of incoherent light, fall progressively towards the higher 
frequencies, so that the outer lobes of the spectrum must 
always suffer some attenuation, and in practice the cut-off or 
the drop to a very low value may occur well below the first- 
zero frequency. Figure 6 shows the spectra for bar-widths 
FREQUENCY CYCLES PER M.M. 
Figure 6. Spectra for Various Line Widths with 
Transfer Function for f/5.6 Lens and Plus X Aerecon 
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