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It will be noticed that even for a perfectly corrected lens 
the MTF starts falling from zero frequency upwards, hence 
perfect imagery of the object spectrum is never possible. 
This contrasts with electronic transfer systems, which 
commonly have a flat transfer function over their entire 
working range. 
Numerous techniques have been developed for measuring 
MTF’s, but discussion of them is outside the scope of this 
Figure 3. Representative Lens and Emulsion 
Transfer Functions 
article. It should be mentioned, however, that actual 
sinusoidal targets are not always used ; other methods 
include the harmonic analysis of the image of a very narrow 
line, and calculation from the shape of the wavefront of the 
light emerging from a lens. When applied to a given lens 
these apparently very different methods give concordant 
results, strengthening belief in the reality of the transfer 
function and the value of the Fourier approach. Flowever, 
it must be appreciated that the instrumental problems are 
much more severe than in the measurement of resolving- 
power, very precise specification of all relevant physical 
factors is essential, and the familiar problems of working 
off-axis and averaging across the field are even more difficult 
to solve. The precise transfer function obtained for a given 
lens at a given point in its field naturally depends upon the 
colour and spectral bandwidth of the light used and on the 
focal plane selected. 
Application of the Transfer Function 
Transforming the image as we see it into its spatial fre 
quency spectrum, and measuring transfer functions, are fairly 
elaborate procedures requiring experimental and computing 
facilities not universally available ; we may well inquire what 
is gained by such an artificial approach. The complication is 
partially justified by the theoretical insight it affords. Fourier 
analysis is a tool of general scientific importance which has 
contributed to progress in many fields, e.g., physical optics, 
electrical engineering, and tidal research. By extending it to 
photography, or by studying the possibilities of doing so, 
what is apparently an extreme artificiality might be justified 
by using a terminology common to science in general, possibly 
leading to greater understanding by suggestive analogies. To 
a certain extent this has proved true. A more practical 
advantage lies in the ability to combine any number of 
transfer functions by simple multiplication. In aerial 
photography the image may become blurred or degraded at 
numerous stages, e.g., in the optical imagery, by image move 
ment and so on. At each of these stages an ideal point object 
gives rise to a more or less blurred image, the “ spread 
function.” To estimate the overall performance we must 
combine these individual blurs, which can only be done with 
full accuracy by the difficult mathematical process of convolu 
tion. Moreover, in certain important cases the spread 
function cannot be measured directly but is derived by 
Fourier transformation from the transfer function. Some 
stages, such as the aircraft window or atmospheric turbulence, 
cannot be assigned a general transfer function, but for any 
particular conditions an effective transfer function can be 
calculated. Then by multiplying all the functions together, 
ordinate by ordinate, the overall transfer function of the 
system is obtained. An example is given in Figure 4. The 
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A - PAN X EMULSION 
B - f/5*0 6" LENS 
C - 25 MICRONS MOVEMENT 
D - A * B * C 
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M.M. 
SPATIAL FREdUENCY CYCLES PER 
Figure 4. Cascading of Transfer Functions 
transfer functions for a typical 6-inch photogrammetric lens, 
for Panatomic X Aerographic emulsion, and for 25 microns 
of uniform image movement, are shown separately and 
combined. The diagram gives information about the system 
as a whole and the contribution of each component, clearly 
displayed for all points in the frequency passband. By using 
logarithmic scales the multiplication is simplified, slide-rule 
methods can be used, and the procedure becomes very useful 
to the designer, who can see where weaknesses lie, rapidly 
change parameters, and converge his system towards the 
optimum balance. This is apparently a great advance on 
resolving-power, which gives information about just one 
point on the frequency scale and can only be combined with 
other resolving-power figures by arbitrary reciprocal formulae. 
However, it is not enough to obtain an overall transfer 
function for the system. By itself this tells us nothing about 
the image quality we can obtain, since it is merely a statement 
of relative modulation transfer. We cannot even rank 
systems by their transfer functions alone ; to say that one is 
better than another we must specify the purpose for which it 
is better, and this requires a knowledge of the input spectrum 
on which it is to operate. It cannot be said too often that 
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