ABSTRACT
This chapter explains finite raytracing through toric surfaces, diffraction gratings and hologram lenses and mirrors. One can depart from axial symmetry the possibilities are endless. Alternatively one might say that finite raytracing through any kind of surface is covered in principle that provides an appropriate modifications to the algorithms for transfer and for finding the normal to the next surface are made; this, however, is not strictly true since diffractive optical elements. For example diffraction gratings and hologram lenses, are components through which rays have to be traced and they require an extension of Snell's law to take a ray through them. It would be possible to treat the problem of raytracing through diffraction gratings as a special case of raytracing through holographic optical elements, particularly since many diffraction gratings are now made interferometrically, that is as, in effect, holographic optical elements. Holographic optical elements are sometimes made on non-plane substrates.
