Technical note: dimensionless ray transference

The ray transference matrix completely characterises the first-order optical nature of an optical system including the eye. It is in terms of the transference that quantitative analyses (for example, calculation of an average eye) can be performed. However, the fact that the entries of the transference do not have the same physical dimensions precludes the calculation of the usual scalar value (a Frobenius norm for example) for a change or difference between two optical systems. The purpose of this note is to show how to use the wavelength of the light as a natural unit of length to define a dimensionless transference and so make it possible to calculate a meaningful norm. In most practical applications, some components of the dimensionless transference may dominate unreasonably in the resulting norm in which case suitably weighted norms may be more appropriate. In an appendix, some of the issues are illustrated by application to a lens.