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Abstract

The aberration theory of Buchdahl is extended to allow greater
utilisation of it in optical image assessment and automatic design programs.
Expressions are presented for the calculation of the derivatives of the
seventh order aberration coefficients as well as for the determination of
effects on the derivatives of OT coefficients due to pupil shifts arising
from parameter changes. Where details of the theory for various
constructional parameters differ attention has been confined to axial
curvature derivatives. The wavefront retardation expansion has been
checked for convergence and the results show general agreement with the
convergence properties found by other authors for transverse aberration
expansions. A series of transformations, valid over the region of
convergence of the retardation expansion, is introduced to reduce the
exit pupil periphery defined on a reference sphere to a circle. It is
shown that, under these transformations, the form of the retardation
expansion remains constant and only the coefficients need be altered.
These changes are independent of the field angle but depend on the
f-number of the system.
A new set of assessment functions, derived from the real and imaginary
parts of the optical transfer function,is introduced. It is shown that,
in the geometrical limit, these approximate a set of functions defined in
terms of the spot diagram distribution. Theoretical and numerical
comparisons of these and some other assessment functions are presented.
These show that, in general, there is agreement on the ordering of
correction states when different criteria are used. However some
differences in ranking do arise and these are discussed. It is found
that, with a modification to allow for products of two negative quantities,
a function based on the variance, V(r), of the aberration difference
function provides an extremely versatile assessment quantity. The
usefulness of this new quantity is shown, both theoretically and
numerically, to extend far beyond the conditions under which V(r)
provides a valid approximation to the modulation transfer function.
Predictions of the location of optimum image planes using the various
criteria are examined, and it is shown that by choosing different
fractional spatial frequencies, r, at which to evaluate V(r), most
of these predictions can be obtained using minimization of the variance
V(r).
Finally all the assessment functions introduced are used to
examine two different processes of automatic optical design based on
reduction of transverse aberrations. The first of these is a primitive
design program, developed by the writer, which uses derivatives of the
spot diagram assessment quantities introduced earlier. The second method,
due to Cruickshank, reduces selected aberration coefficients to
prescribed residuals determined by the designer on the basis of past
experience and the requirements of the user. The results from this work
indicate that the choice of assessment function is not critical in
attaining an optimum region of parameter space, but the actual optimum
point is dependent on the choice of assessment function. The usefulness
of the modified function based on V(r) is again illustrated numerically.

Item Type:	Thesis - PhD
Authors/Creators:	Woodruff, Christopher James
Keywords:	Optical pattern recognition, Imaging systems
Copyright Holders:	The Author
Copyright Information:	Copyright 1975 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).
Additional Information:	Thesis (Ph.D.)--University of Tasmania, 1975. Includes bibliographical references
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