Frequency spectra of absolute optical instruments

We analyse frequency spectra of absolute optical instruments and show that they have very specific properties: the eigenfrequencies form tight groups that are almost equidistantly spaced. We prove this by theoretical analysis and demonstrate by numerically calculated spectra of various examples of absolute instruments. We also show that in rotationally and spherically symmetric absolute instruments a source, its image and the centre of the device must lie on a straight line. (paper)