Sufficient conditions for prisms to produce orthogonal image orientation functions without spectral dispersion

One of the main functions of a prism is to produce an image orientation function without spectral dispersion. The present study extends the work previously reported in [JOSAA 33(7), 2016, pp. 1257-1266] to analyze the sufficient conditions for a prism to produce two particular image orientation functions (Phi(2) and Phi(5)) without spectral dispersion. It is shown that there exist two sufficient conditions under which spectral dispersion can be avoided: (1) the rays enter and exit the prism perpendicularly, or (2) the prism comprises two halves which are mirror images of one another. The present findings provide a useful basis for the design of prisms without spectral dispersion.