Abstract
D.Phil. (Optometry)
An important issue in the quantitative analysis of optical systems is,
for example, the question of how to calculate an average of a set of eyes. An
average that also has an optical character as a whole and is representative or central to the optical characters of the eyes within that set of eyes. In the
case of refraction, an average power is readily calculated as the arithmetic
average of several dioptric power matrices. The question then is: How does
one determine an average that represents the average optical character of a
set of eyes, completely to first order? The exponential-mean-log transference
has been proposed by Harris as the most promising solution to
the question of the average eye. For such an average to be useful, it is
necessary that the exponential-mean-log-transference satisfies conditions of
existence, uniqueness and symplecticity, The first-order optical nature of a
centred optical system (or eye) is completely characterized by the 4x4 ray
transference. The augmented ray transference can be represented as a 5x5
matrix and is usually partitioned into 2x2 and 2x 1 submatrices.
They are the
dilation A, disjugacy B, divergence C, divarication D, transverse
translation e and deflection 1t. These are the six fundamental first-orders
optical properties of the system. Other optical properties, called derived
properties, of the system can be obtained from them. Excluding decentred or
tilted elements, everything that can happen to a ray is described by a 4x4
system matrix. The transference, then, defines the four A, B, C and D
fundamental optical properties of the system…