Pupil aberrations in Offner spectrometers.

The light path function (LPF) of an Offner spectrometer is presented. The evaluation of the LPF of this spectrometer enables its imaging properties to be studied for arbitrary object and image positions, while avoiding the more complicated analysis of intermediate images generated by the diffraction grating, which is often involved. A power series expansion of the LPF on the grating coordinates directly determines pupil aberrations of the generated spectrum and facilitates the search for configurations with small low-order aberrations. This analysis not only confirms the possibility of reducing low-order aberrations in Rowland-type mounts, namely astigmatism and coma, as predicted in previous studies, but also proves that all third-order terms in the series expansion of the aberration function can be canceled at the image of the design point and for the corresponding design wavelength, when the design point is located on a plane orthogonal to the optical axis. Furthermore, fourth-order terms are computed and shown to represent the most relevant contribution to image blurring. Third- and fourth-order aberrations are also evaluated for Rowland mounts with the design point located outside the aforementioned plane. The study described in this manuscript is not restricted to small angles of incidence, and, therefore, it goes beyond Seidel and Buchdahl aberrations.