Correction of astigmatism and coma using analytic theory of aberrations in imaging spectrometer based on concentric off-axis dual reflector system

A specific imaging spectrometer based on a concentric off-axis dual reflector system is proposed, free of astigmatism and coma. The described imaging spectrometer consists of four spherical mirrors and a plane grating. The analytic theory of aberrations and the optical path-length concept are used to derive the astigmatism elimination and coma removal. It is shown that the astigmatism in these imaging spectrometers is eliminated by characterizing three angles, and the coma is corrected when unequal mirror radii are configured in collimating and condensing optics. The developed aberration principle is verified by comparing the performance of the astigmatism-eliminated spectrometer with the spectrometer which has neither astigmatism nor coma.