Aberrations inherent in the design of a dioptric or catadioptric system vary proportionately as the design is scaled up or down, where the scaling factor is the focal length of the system. As the design of a dioptric or catadioptric imaging system of given fixed f-number (also called "relative aperture" or "focal ratio") is scaled up to provide a longer focal length for the system, the monochromatic and chromatic aberrations inherent in the design increase concomitantly as the focal length increases.
An optical imaging system having tolerable monochromatic and chromatic aberrations in a specified wavelength band for a given f-number and given focal length cannot generally be enlarged in scale to provide a longer focal length for the same f-number, while the same degree of correction for monochromatic and chromatic aberrations is maintained. An enlargement in the scale of the imaging system to provide a longer focal length for the same f-number would generally cause the aberrations inherent in the design of the system to increase to such an extent that re-optimization of the design would become necessary in order to reduce the monochromatic and chromatic aberrations to a tolerable level.
Refractive imaging systems having a relatively high degree of color correction at long focal lengths (i.e., at focal lengths longer than a few meters) could be designed using various combinations of optical materials for bringing two or more wavelengths to a common focus. However, until the method described in co-pending U.S. patent application Ser. No. 419,705 for selecting optical materials for designing color-corrected optical systems was discovered, very few pairs of optical materials were known that could be used for designing dioptric and catadioptric systems that are color-corrected at more than two wavelengths. Furthermore, residual chromatic aberrations (i.e., secondary and higher-order spectra) inherent in the designs of refractive imaging systems are usually intolerable at long focal lengths.