‚The phase of the image transform is far more important 
than the modulus according to Shack because an image in which 
the modulus is drastically altered is still recognizable, whereas 
corresponding phase changes completely destroy recognizability. 
Many instruments measure only the modulus, it being a matter of 
great practical convenience if phase can be neglected. Shack shows 
that under general circumstances the phase must be considered and, 
if significant, some method found of incorporating it into a 
specification of image quality. 
It is principally in the area of image evaluation that 
the question of the significance of the phase-transfer function 
must be faced. Both the spread function and the transfer function 
are determined by the complex, fundamental pupil function. The 
modulus of the pupil function is determined by the geometry and 
transmission of the pupil, whereas the phase is determined by the 
aberrations. 
The phase transfer function is shown as depending on the 
location of the origin in the description of the spread function. 
If the spread function is asymmetric and the peak of the asymmetric 
blur is used as the origin (as would be natural in measuring photo- 
grammetric images), very little harm would be done in evaluating 
the MIF, but the asymmetry itself would introduce an error in location 
of the object. 
One must be careful in dealing with the modulus alone, 
however, even though the spread function may be symmetrical. This 
is true if the nature of the spread function is such that its Fourier 
transform, although purely real, has strong negative components. 
There are situations in which the inverse transform of the modulus 
does not correspond well to the true spread function showing the 
modulus to be overly optimistic. Shack concludes that for nonco- 
herent image-forming systems, the quality of the image in terms 
of the spread function is adequately judged by the modulus of the 
transfer function as long as the phase-transfer function referred 
to the peak (not the centroid) of the spread function, is well within 
a quarter cycle over the range of significant values of the modulus. 
5.9.3.2 Scale Matching Analysis (SMA) 
Schowengerdt and Slater (Optical Sciences Center) report 
that measurements of the operational imaging performance of 
optical systems can be used to determine variations from design 
predictions, to study temporal factors affecting the optical systems. 
One quantitative descriptor of optical system performance is the 
Optical Transfer Function (OTF). The OTF of downward-looking aerial 
and orbital optical systems can be determined from the images they 
produce of special ground targets, existing man-made structures, 
or naturally occurring edge-like features. 
23