;r technique is valuable and
earch and system design, but
images, not on their Fourier
ists us in aerial photography
¡tail size. The general desire
is expressed by the common
the transfer function at some
lality of an image whose size
ncy. A “ frequency ” is of
»attern without beginning or
?w frequency any more than
:y ; on the contrary, a small
transformed into frequency
actions directly from transfer
intly to frequencies, and not
onal space, a small object is
Ld for the shapes of aerial
' consideration. We could
til size was the smallest of
ng bar width in image scale
o study image quality. Our
• image might be reduced to
^ than a perfect image, and
i presence can only just be
te on the bar with transfer
into its frequency spectrum,
vledge of its width and the
hows part of the theoretical
and 1/10 millimetre wide,
i that narrow lines have a
a. Remembering that the
to infinity it will now be
ing as a theoretically perfect
r wide, for its spectrum will
cut-off point of any optical
• the normal photographic
ressively towards the higher
3bes of the spectrum must
nd in practice the cut-off or
f occur well below the first-
the spectra for bar-widths
100
s PE« M.M.
ous Line Widths with
ïns and Plus X Aerecon
of 1/10, 1/20, 1/40, 1/80 and 1/120 millimetres, with a transfer
function representing a typical f/5-6 photogrammetric lens
in combination with Plus X Aerecon film. For clarity the
spectra have not been drawn beyond the first zeros ; a high
proportion of the total energy is of course contained in this
part of the spectrum. This transfer function will retain most
of the content of the spectrum for bars down to 1/40 millimetre
wide, though at reduced intensity for frequencies higher than
say 20 lines per millimetre. Only about half the spectrum
content of a 1/120 millimetre bar is passed, but clearly some
energy will always get through, no matter how narrow the bar
may become. Whether the image will be detectable or not
must depend on its initial contrast and the emulsion grain
threshold for single lines, about which little is known at
present. Our general conclusion must be that there is no
sharp cut-off size for isolated lines, from which it follows that
resolving-power, which does have a theoretical and practical
cut-off value, is a poor guide to the size of isolated detail
which can be detected. Directly, it is no guide to the quality
of definition on isolated details, but insofar as it is a guide
to the system bandwidth it can be interpreted to give indirect
information about definition. It will also be clear that a
transfer function which drops rapidly to a low modulation
transfer but continues with a long run-out at this level can
weaken those spectral components which carry most of the
energy ; thus the line contrast will be poor although the
system may have a high resolving-power, at least on a high
contrast target.
The high-contrast resolving-power of the lens-film combina
tion shown in Figure 6 would be about 40 lines per millimetre,
yet the frequency analysis suggests that bars narrower than
1/80 millimetre might be recorded. In fact it is well known
that aerial photographs often record lines, e.g., white road
markers, power cables, which are very much narrower than
the bars in the smallest resolved pattern of a resolving-power
test. Thus the sine-wave analysis technique gives insight
into a practical effect which has been known for a long time
and which has led some photographers to conclude that
resolving-power is a poor guide to definition. Resolving-
power however is just one way of evaluating image quality,
which if properly understood and applied can give useful
information.
This discussion of the spectrum for the relatively simple
case of the single line may have emphasized that the basic
problem is to find the best way of intergrating the transfer
function, whether we wish to grade systems in general or to
match them to particular tasks. The difficulty is to settle
the upper limit of the integration. In television this is fixed
by the electronic bandwidth, which imposes a definite upper
frequency beyond which the lens transfer function is of no
interest. In photography, however, we have no such con
venient limit. The object spectra in which we may be
interested do not cut off sharply but dwindle away gradually
and we do not yet know how to weight the upper frequencies.
(It need hardly be pointed out that we should not, as is some
times thought, preferentially weight them because we are
interested in small objects.) The emulsion transfer function
falls away gradually ; any lens may be used with any emul
sion, and any system may be used on any scene. Much work
remains to be done in assessing the significance of numerous
physical and subjective factors which affect the choice of an
integration method, and any decision will inevitably be, to
some extent, an arbitrary one. One of the major problems
is the non-linearity of the photographic process, which
complicates the task of interpreting small changes of transfer
function shape into corresponding changes of subjective image
quality and of assessing the importance of the regions of
very low modulation transfer. This task is already difficult
even in a linear system. It is perhaps significant that tele
vision engineers found it insoluble many years ago and
substituted the transmission of standard pulse shapes for
sine-wave analysis of certain parts of their systems. 4
Lewis and Hauser 3 suggest a single-bar target for photo
graphic use as the analogy of the television pulse ; the bar
contrast is measured as a function of its width and image
quality is assumed to be related to the bar width at which
contrast has fallen to some fraction, say 80 per cent, of its
maximum value. This assumption remains to be proved for
aerial photography, but it is eminently reasonable. Certainly
any defect of image quality, such as lens aberrations (sym
metrical or unsymmetrical), image movement, or spreading
of light within the emulsion, will reduce image contrast as
a function of reciprocal size, and the bar target will show
this by an automatic integration without the complications
of sine-wave analysis, i.e., Fourier transformation, operation
with the transfer function, inverse transformation, and
interpretation of the resulting intensity distribution. We
cannot say that the loss of contrast is an exact measure of
definition, since we cannot specify definition in exact terms,
but sine-wave analysis has to face the same problem after
its more complex manipulations.
Compared to resolving-power, the single bar test suffers
from needing a microdensitometer, but more complex
instrumentation must always be the price of better
information. At least this removes the subjective uncer
tainties of resolving-power measurement. Moreover,
expressing definition in terms of a degradation at the upper
end of the quality scale has certain advantages over specifying
it near the lower end, as is done in resolving-power. (As we
have seen, this characteristic of resolving-power has a mis
leading aspect in that it is used to estimate the smallest object
sizes which can be seen.)
Compared to the transfer function approach, the single bar
test does not offer the convenience of easy cascading of
system component performances and it does not fit so easily
into other calculations. However, it is always possible to
calculate single bar response from transfer functions, and it
may be found that calculation of the bar response at the end
of a system development is a good compromise. For direct
evaluation of a given system, the bar test is much easier than
measurement of transfer functions and the effort to interpret
them in terms which can be directly appreciated.
The Present Situation and Future Possibilities
As time goes on it becomes more apparent that there can
be no single image evaluation technique or criterion suitable
for all applications. The complexity of the situation calls
for emphasis on different aspects according to the require
ment, which may be basic research, testing system perform
ance, evaluating the quality of a negative, or estimating the
performance required for some new task. All of these are
interconnected, but all do not require the same approach.
The perpetual problem is to devise physical tests which will
substitute as perfectly as possible for the labour of taking and
judging photographs. We try to obtain good correlation
between the physical tests and the subjective quality of the
corresponding photography, by studying the underlying
fundamentals and checking our physical scales against real
images, but a universally perfect correlation will never be
possible. In the limit, no test is representative except for its
own conditions.
The emphasis on Fourier techniques during the last
7
