Optical Magnification Matrix: Near Objects and Strongly Oblique Incidence

Abstract

The result is a generalization of any of the formerly known results for the magnification matrix in the paraxial case. The treatment is complete in the sense that it covers any situation that can be encountered when light propagates through an optical system with a finite number of refracting surfaces to an eye. In particular, the oblique case is treated exactly even if the chief ray lies beyond the domain in which the transference theory of linear optics could be applied.

Lateral magnification matrix from the dioptric power matrix formalism in the paraxial case

“…Keating was the first who calculated image size magnification for an astigmatic spectacle lens . After that, much work has been done for the generalization of the lateral magnification change when looking through optical instruments in general, and, specifically, considering spectacle or contact lenses . But it was Harris a couple of years ago who illustrated us with a comprehensive interpretation of the generalized magnification matrix .…”

“…Moreover, in the presence of astigmatism, this definition is much more complicated and involves optical changes in both object shape and orientation that are not usually described as conventional scalar magnification but as anamorphic distortion, astigmatic or meridional magnification, and torsion, and is complicated further by blur. As a consequence, much work has been reported on the description of a generalized magnification matrix concerning the change in magnification produced when correcting the refractive error using spectacle lenses or when looking through an arbitrary optical instrument which is usually adapted to spectacle or contact lenses …”

Derivation of analytical refraction, propagation and reflection equations for higher order aberrations of wavefronts

“…Especially in spectacle lens optics local features of a wavefront are very important, because the aperture stop is not stationary as in technical optics. Also magnification and anamorphotic distortion previously have been calculated locally [32,33,34].…”