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We report a novel calculation model for dense spot pattern multi-pass cells consisting of two common identical spherical mirrors. A modified ABCD matrix without the paraxial approximation was developed to describe the ray propagation between two spherical mirrors and the reflection on the mirror surfaces. The intrinsic aberration from the spherical curvature creates a set of intricate variants with respect to a standard Herriot circle spot pattern. A series of detailed numerical simulations are implemented to verify that the input and output beams remain the same and, hence, retrace the same ray pattern. The set of exotic spot patterns obtained with a high fill factor improves the utilization efficiency of the mirror surfaces and produces a longer total optical path length with a low mirror cost.
Cui et al. (Fri,) studied this question.