Quantitative analysis of transformed ray transferences of optical systems in a space of augmented Hamiltonian matrices*

Abstract

There is a need for methods for quantitative analysis of the first-order optical character of optical systems including the eye and components of the eye.  Because of their symplectic nature ray transferences
themselves are not closed under addition and multiplication by ascalar and, hence, are not amenable to conventional quantitative analysis such as the calculation of an arithmetic mean.  However transferences can be transformed into augmented Hamiltonian matrices which are amenable to such analysis.  This paper provides a general methodology and in particular shows how to calculate means and variance-covariances representing the first-order optical character of optical systems.  The systems may be astigmatic and may
have decentred elements.  An accompanying paper shows application to the cornea of the human eye with allowance for thickness.