Non-axial optical design of a multi-pass spectral absorption cell: algorithms.

A 3×3 matrix-based algorithm is, to our knowledge, first proposed for designing a multi-pass optical absorption cell with higher precision. Compared to previous publications based on the traditional 2×2 matrix, the proposed algorithm can effectively avoid paraxial approximation and directional astigmatism simultaneously by defining matrix elements with five key parameters. To demonstrate its applicability, various numerical simulations were investigated theoretically and verified with experimental results; a good agreement was also obtained by comparing with commercial TracePro software. Beam transmission trajectories related to different total optical paths were achieved and demonstrated by adjusting the values of the initial position, the incident angle, and the cavity length. Moreover, the simulation indicates that the accumulated optical path error ratio due to non-axial propagation of light and spherical aberration decreases significantly with the increase in reflection numbers.