(41C) non-Fourier techniques (second moment & statistical approach)
09-15-2019, 03:17 PM
Post: #1
 SlideRule Senior Member Posts: 903 Joined: Dec 2013
(41C) non-Fourier techniques (second moment & statistical approach)
An extract from Comparison of Methods of MTF-OTF Analysis for Optical Systems, Jean Claude Croteau, B.S. College Militaire Royal de St-Jean, M.S. Degree Thesis, NOV 1983, 65 pages

"ABSTRACT
A comparison study for the methods of obtaining the MTF of optical systems was performed. It is demonstrated that non-Fourier methods are as good predictors of the MTF as are the Fourier methods. A new technique based on the moment theorem is introduced and is found to be a good predictor. A computer algorithm has been written to perform all the necessary operations.

INTRODUCTION
The Optical Transfer Function (OTF) and the Modulation Transfer Function (MTF), are used for comparing the image quality of lenses. The MTF/OTF is a function of spatial frequency and can be derived from either the line spread function or the edge response function. Both will, however, contain some error term when obtained by experimentation. Each element of an experimental set-up can introduce error but the worst elements are: source fluctuation, non uniformity of the detector, amplifier noise and emulsion grain when an emulsion is involved.
The methods currently used to compute MTF or OTF all involve some degree of estimation and smoothing to minimize the experimental error, which results in some degree of degradation of the MTF. Whether smoothing is accomplished by convolution with an appropriate function, by regression analysis on a model, or by other schemes, the object is to extract from the data the best estimate of the true signal. Different techniques, however, may result in different estimates, and each may have advantages, depending on what the user is really looking for.

RECOMMENDATIONS
The primary recommendation for future work on this topic is that each technique be applied to experimentally obtained edge traces and that the results be compared with the manufacturer's computed MTF, based on the design parameters, so that we can get a better estimation of the accuracy of each technique.
The attention of the researcher should be concentrated on the "second moment technique" and the "statistical approach", as the two other non-Fourier techniques developed here, although simple in principle, are time-consuming…

APPENDIX A: MAIN PROGRAMS
MTF TECH
RANDOM NOISE GENERATOR/STATS
HP-41C: SECOND MOMENT
HP-41C: STATISTICAL APPROACH

HP-41C : SECOND MOMENT {pg. 63 progam listing}

HP-41C : STATISTICAL APPROACH {pg. 64 program listing}

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