Aberration analysis of a concentric imaging spectrometer with a convex grating

We analyze the ray-optical aberrations in a concentric imaging spectrometer composed of one convex grating and two concave mirrors of different radii. We assume that the system is generally not telecentric. First we derive aberration functions of Seidel and Buchdahl types for a bundle of rays converging to dispersed Gaussian images. Next we discuss the conditions in which the third and fifth-order ray aberrations are balanced. Finally we show that a concentric imaging spectrometer for use with a CCD detector can be optimized effectively in the neighborhood of a stigmatic condition. The stigmatic condition derived here can be useful in rapidly creating an initial design of a concentric imaging spectrometer with minimal aberrations.