ME | 
   
produce a type of phase shift in which the light and dark bars 
of a periodic target appear to change places. This is equivalent 
to negative lobes on the MTF, but in apparatus without a phase 
reference all MTF values are shown positive. Phase reversal in 
this sense can also be produced by image movement. 
4.1.1.4 Significant Amounts of Phase Shift 
  
Phase shift may be expressed as cycles of the sinewave 
frequency, or in the equivalent angular measure of degrees or radians. 
The magnitude and importance of phase shift depends on the shape 
of the actual spread function and the imaging application; no general 
relationships exist. To illustrate the orders of magnitude involved, 
Fig. 2 shows the MIF and PTF corresponding to a particular asymmetric 
spread function, and the effect on the intensity-profile of one 
bar of a squarewave at 10 cycles per mm. The example was taken 
at random from published measurements and relates to an actual 
photographic lens, but is not intended to be "typical"; very different 
slopes and shapes for the PTF are possible. 
Fig 2.1 shows the slope and shape of the PTF corresponding 
to the asymmetry of the spread function at the right. The phase 
shift is zero at zero spatial frequency and reaches one quarter 
cycle when the MIF has fallen to 0.3 at about 33 cycles per mm. 
In Fig. 2.2 the fundamental has been omitted for clarity. Only 
the third harmonic of 10 cycles per mm remains at significant 
strength. The resultant profiles are drawn for two conditions, 
(a) when there has been no phase shift, and (b) when the phase 
at 30 cycles per mm has been shifted in accordance with the PTF 
in 2.1. Evidently, the phase shift converts the rounded-off square- 
wave into an asymmetrically peaked waveform, but the difference 
would probably have little practical significance, especially when 
the image is further degraded by the emulsion MTF. This does not 
disagree with the opinion sometimes expressed, that phase shift 
has no practical significance until it exceeds one quarter cycle 
at the highest frequency of interest (In this case, three times 
the frequency of the basic squarewave.) Similar arguments could 
be applied to the sinewave syntheses of other real objects. 
4.2 Comparative MTF Lens and Camera Studies 
The Chairman of Commission I Werking Group on Image Geometry, 
Ziemann, made available to the OTF/MT7 Working Group the same two 
Zeiss and Wild reseau cameras which they were using in compartive 
geometry studies.  MTF data for the lenses was thus obtained by 
Rosenbruch in West Germany, Hakkarainen of Finland, and Martin in 
the USA. All used different equipment of different design (Rosenbruch 
used Eros II, Martin used Tropel, Hakkarainen used a goniometer with 
Squarewave targets) and derived both axial and off-axis values 
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