4.1.1.2 Illustrations: The following may assist visualization. 
Fig. 1 shows pairs of cosine and sine area masks, as used 
in certain OTF-measuring techniques, An enlarged image of the 
line spread function is centered on the upper member of a pair, 
at the peak, as in Fig. 1.1; this being the cosine mask, the lower 
becomes the sine. For simplicity, only one frequency is shown; 
to visualize other frequencies, imagine the spread function scaled 
appropriately, all the masks being kept in phase. Fig. 1.2 repre- 
sents a very low frequency, at which the spread function, indicated 
in profile above, is equivalent to a very narrow line lying wholly 
at the peak of the cosine mask. In making an OTF measurement, 
there are two reference levels for the light transmitted through ( e 
the masks. Through the upper mask, in Fig. 1.1, all the light 
in the spread function is transmitted; on the scale at the left, 
this is shown as 1.0. If the spread function were so broad (spatial 
frequency sufficiently increased) that the whole aperture area 
was uniformly filled with light, the transmission would fall to 
0.5, which would correspond to zero MIF. But in Fig. 1.1, the 
transmission through the sine mask is 0.5; the transmission through 
a phase-shifted mask being 0.5, the PTF is called zero. In Fig. 
1.2 the spread function is broader but still symmetrical. (It 
could be the first spread function analyzed by a mask of higher 
spatial frequency). The total light in the spread function being 
constant, it cannot become broader without a drop in the peak inten- 
sity. Evidently the cosine transmission is now less than 1.0, 
part of the light being cut off by opaque areas of the mask, and 
this is indicated on the cosine scale at the left. The sine trans- 
mission is still 0.5 (PTF zero) because of the symmetry of the 
spread function. In Fig. 1.3, an unsymmetrical spread function, 
supposed to contain the same total light as before is shown with 
its peak at the peak of the cosine mask. The cosine transmission ( 0 
is again less than 1.0, but the sine transmission is now greater S 
than 0.5 because of the asymmetry of the spread function. The 
response through the phase-shifted mask being greater than 0.5, 
the PTF has a finite value. The apparent relative phase shift 
will clearly depend upon the location of the spread function rela- 
tive to the masks. It is convenient to center the spread function 
at the peak of a cosine mask at a very low frequency, when its 
effective width is negligible, and to take the phase shift as zero 
at zero or near-zero frequency. 
4.1.1.3 Other Examples of Phase Shift 
  
The PTF specifically relates to the relative phase shift 
between different spatial frequencies produced by asymmetric spread 
functions. It should not be confused with other types of phase 
shift which can occur in photo-optical systems. For example, gross 
out-of-focus for a lens with a symmetrical spread function can