Sufficient conditions for the avoidance of spectral dispersion in optical prisms

Prisms are common optical elements consisting of only flat boundary surfaces. Two conditions need to be fulfilled to avoid chromatic aberration for a prism, namely, no mutual image tilt and no mutual image shift for different wavelengths. Mutual image tilt occurs when the unit directional vector of the exit ray varies as a function of the prism's refractive index, resulting in spectral dispersion. In a previous study by the present group [Appl. Opt. 45, 3951 (2006)], it was shown that when the rays enter and exit a prism perpendicularly, image reorientation is achieved without spectral dispersion. The present study derives a further sufficient condition to avoid spectral dispersion caused by refraction. The condition explains the ability of Dove prisms and solid glass corner cubes to produce the required image orientation even when the entrance and exit rays are not normal to the respective boundary surfaces. In general, the proposed condition provides a useful analytical guideline for avoiding spectral dispersion in a wide variety of optical systems.