The concept of the average eye

Abstract

For most quantitative studies one needs to calculate an average. In the case of refraction an average is readily computed as the arithmetic average of dioptric power matrices. Refraction, however, is only one aspect of the first-order optical  character  of  an  eye.  The  question  is: How does one determine an average that rep-resents the average optical character of a set of eyes  completely  to  first  order? The  exponen-tial-mean-log  transference  has  been  proposed recently  but  it  is  not  without  its  difficulties.  There  are  four  matrices,  naturally  related  to the  transference  and  called  the  characteristics or characteristic matrices, whose mathematical features suggest that they may provide alterna-tive  solutions  to  the  problem  of  the  average eye. Accordingly the purpose of this paper is to propose averages based on these characteristics, to  examine  their  nature  and  to  calculate  and compare them in the case of a particular sample of 30 eyes. The eyes may be stigmatic or astig-matic and component elements may be centred or  decentred.  None  turns  out  to  be  a  perfect average. One of the four averages (that based on one of the two mixed characteristics) is proba-bly of little or no use in the context of eyes. The other three, particularly the point-characteristic average, seem to be potentially useful.