7.0 CORRELATION OF MIF MEASUREMENTS AND CALCULATIONS 
7.1 Measurement. The most recent study of correlation of Measurements 
following those reported by Brockl, and Hopkins and Dutton* is reported 
by Marchant, Ironside, Attryde and Williams83 Nine European laboratories 
correlated in this study in which sixteen separate sets of measurements 
were made (from 1969 to 1973) using six distinct techniques. A simple 
6" £/5.6 wide-field lens were used in which all glass elements were 
carefully cemented into the cells and extreme care was used in mounting 
the lens on the optical bench. Tests were made on axis and at 10°, 
20°, 30°, and 40° for radial and tangential lines. The data showed 
spreads of + 0.14. Investigations followed on the major sources of 
errors: (1) normalization, (2) focus setting, (3) spatial frequency 
calibration, (4) tilt, and possible combinations of these. SIRA 
carried out a standard regression analysis and after discussion with 
the laboratory concerned, was able to correct that data such that the 
spread of MIF values was greatly reduced, never exceeding +0.07 and 
usually amounting to less than +0.03. ER 
One of the informative tests conducted showed the variation of 
MTF with focus at 0?, 20?, 30?, and 40? on the radial and tangential 
lines for various frequencies approaching the cut-off. 
This report provides practical guidance in analyzing the 
precision requirements of optical benches used in MTF analysis. 
7.2 Calculations. Hopkins and Dutton reported” on the wide spread 
of data from various designers who computed MTF for a prescribed lens 
formula. McDonald now reports more favorably on a later test 
conducted via the SIRA Group on Image Assessment and involving the 
intercomparison of several different and independent OTF calculations 
programs. 
In the ten different programs all agreed on axis and eight were 
in good agreement at 20°. At 30°, seven were within +0.05 and at 40° 
there was little agreement. An investigation to track down the cause 
of disagreement at large field angles followed, and while not yet 
complete, it is generally concluded that methods and programs do 
differ. A number of pitfalls exist but raytracing, including 
polynomial fitting and pupil shape, and evaluation of reduced spacial 
frequency appear to be common stumbling blocks. 
In both measurement and calculation of OTF, the spread of 
results is significant at the larger field angles, with the possibility 
of improving measurements appearing more direct and more achievable 
than the calculations. Since the equations used in calculations are 
not always exact, since programs differ and assumptions are made, it 
would appear necessary to evaluate the effect of these differences 
before further progress can be expected. When agreement on measured 
values are obtained, the results might be considered as "absolute" 
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