Proximity factor in image size magnification for optical instruments in general

A general expression is derived for the proximity factor in near image size magnification for an arbitrary instrument in front of an arbitrary eye. The proximity factor is a 2 x 2 matrix. The instrument and eye may be astigmatic and have decentred elements. The image on the retina may be blurred or not. The analysis is exact within the limitations of linear optics. The general results are specialized for the case of a stigmatic instrument and a stigmatic eye. The results are applied to the case of a thick, possibly bitoric, spectacle lens. The Appendix treats two numerical examples.