Merit function regression method for efficient alignment control of two-mirror optical systems

TLDR

Precision alignment of high‑performance, wide‑field optical systems is generally difficult and laborious. The study introduces a merit function regression method that promises higher efficiency and accuracy than the conventional sensitivity table approach for optical alignment. The method employs an actively damped least‑squares algorithm to minimize a Zernike‑coefficient merit function that quantifies the difference between designed and misaligned wavefronts. In a 900‑mm Cassegrain collimator experiment, the method reduced the mean rms wave‑front error from 0.283 λ to 0.194 λ and the field‑dependent error from ±0.2 λ to ±0.014 λ in two alignment actions, outperforming the conventional sensitivity table method.

Abstract

The precision alignment of high-performance, wide-field optical systems is generally a difficult and often laborious process. We report a new merit function regression method that has the potential to bring to such an optical alignment process higher efficiency and accuracy than the conventional sensitivity table method. The technique uses actively damped least square algorithm to minimize the Zernike coefficient-based merit function representing the difference between the designed and misaligned optical wave fronts. The application of this method for the alignment experiment of a Cassegrain type collimator of 900mm in diameter resulted in a reduction of the mean system rms wave-front error from 0.283 lambda to 0.194 lambda;, and in the field dependent wave-front error difference from +/-0.2 lambda to +/-0.014 lambda in just two alignment actions. These results demonstrate a much better performance than that of the conventional sensitivity table method simulated for the same steps of experimental alignment.