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the midpoint of the squarewave the third, seventh, etc., harmonics 
subtract from the fundamental, whereas the fifth, ninth, etc., 
add to it. In general, the amplitude of the sinewaves is less 
in the image than in the object, the increasing attenuation as 
a function of spatial frequency being expressed by the MTF.  Depen- 
ding on the extent to which the harmonics are attenuated, the edges 
of the imaged squarewave are more or less rounded off, and eventually 
a pure sinewave is left. If the PTF remains zero over the whole 
frequency range, the rounding-off is symmetrical. If the PTF is 
finite but increases linearly with frequency, the rounding off 
is still symmetrical but the image moves as a whole with reference 
to a fixed coordinate, which could be, for example, the Gaussian 
image position. This movement is photogrammetric "distortion." 
The linear phase shift means that all component frequencies are 
moved laterally by a number of cycles proportional to frequency, 
hence there is no relative phase shift. A large distortion corresponds 
to a steeper slope on the linear PTF, and vice versa. In principle, 
a large distortion can co-exist with a symmetrical spread function, 
the symmetry of the latter accounting for the zero relative phase 
shift between frequencies. If the spread function is unsymmetrical, 
due for example to comatic aberration, then the PTF will exhibit 
non-linearity of a kind and degree depending on the spread function 
shape. Thus, in the squarewave image, the rounding-off could be 
accompanied by an unsymmetrical effect due to the relative phase 
shift between the fundamental and harmonic frequencies. 
An unsymmetrical spread function can co-exist with photogrammetric 
distortion, which is equivalent to saying that the PTF has linear 
and non-linear components; the linear part, which in the present 
sense is irrelevant, can be moved by subtraction, leaving the non- 
linearity which distorts the image shape as distinct from its position. 
The subtraction is equivalent to making a change of coordinate 
origin relative to the actual image. 
In general, the shape of an image cannot be significantly 
distorted by an unsymmetrical spread function unless it is small 
enough that its outlines are already significantly blurred. In 
OTF terms, the nonlinearity of the PTF cannot be very important 
unless the MIF has already fallen significantly. In photogrammetric 
images, the sinewave components of the optical image are further 
attenuated by the MTF of the emulsion, whose spread function is 
inherently symmetrical (no phase shift). Thus, any unsymmetrical 
blurring due to the lens will be less evident in the photographic 
image. 
The MIF alone is a good guide to the definition of a lens, 
though it is incomplete, and for sophisticated image calculations 
the PTF also is required. The PTF alone conveys no useful informa- 
tion for aerial photography or photogrammetry. Since the PTF is 
more difficult to measure than the MTF, the common practice of 
reporting the MIF alone is justified. 
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