# The use of optical aberration coefficients.

Ford, Peter Wilbraham,1929- (1962) The use of optical aberration coefficients. PhD thesis, University of Tasmania.

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## Abstract

An extensive theory of aberration coefficients of
symmetrical optical systems has been developed by Buchdahl in his
monograph "Optical Aberration Coefficients -(hereafter called M) and
3,•99. extended in subsequent papers, 2, The advantages resulting from
the use of these coefficients rest in two important properties.
Firstly, the one set of coefficients characterise systems of rays,
that is, they apply simultaneously to all rays that traverse the
optical system. Secondly the aberration coefficients are the suns
of corresponding coefficients computed for each surfaceof the system
(the contributions to the coefficients). This enables the action of
the system on all rays to be analysed surface by surface and it is
this that places a powerful tool in the hands of the designer.
Now, although there is only one set of coefficients for
each system, it is an infinite set. Obviously the calculation of
them all is impossible. So far, computing schemes have been designed
for the computation of all the third, fifth and seventh order
monochromatic coeff1cients 4, the coefficients of ninth5 and eleventh9
order spherical aberration, and several of the more important
chromatic coefficients (M Chapter XIII). Naturally, the aberrations
of a system are not completely described by only these coefficients.
The object of this thesis is to examine the effectiveness
of the first three orders of the monochromatic coefficients in the
description of the aberrations of optical systems. As well as
enabling a detailed analysis of a system, the coefficients and their
surface contributions are of considerable use in the differential
correction of a system following the initial design. The effectiveness
of the coefficients in this field is also examined here.
The work has been restricted to monochromatic coefficients,
since, after the initial design, the majority of design is carried out in monochromatic light. Also, the systems studied here have been restricted to those containing spherical surfaces only. The extension
of the work to aspherical surfaces is a matter of detail and not of
method; as mentioned in M Section 55, the only change is that the
"intrinsic" coefficients (Section 5, 6 of this thesis) contain
additional terms which depend on the "extra-axial" curvatures of the
aspheric surfaces. These additional terms in no way affect the
general theory or the application of the coefficients. The aberration
coefficients in no way indicate whether the system they represent is
aspheric or not. However, in the construction of computing schemes
for the coefficients, many simplifications can be introduced if only
spherical surfaces are being considered, resulting in comparatively
short schemes, e.g. compare M 81.3 with 84.23, 33, 44.

Item Type: Thesis - PhD Ford, Peter Wilbraham,1929- Aberration, Optics The Author Copyright 1962 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). Thesis (Ph.D.) - University of Tasmania, 1962 09 Dec 2014 01:11 11 Mar 2016 05:56 View statistics for this item