Sensitivity Analysis of a Two‐Lens System for Positioning Feedback

Abstract

AbstractPrecise alignment of optical components is crucial for the assembly of optical system. Misaligned components (due to positioning tolerances) lead to a distorted wavefront that deviates from a desired wavefront given by an initial nominal design. Inferring the current poses of optical components solely from detector measurements is a difficult but necessary task in order to calculate corrections for feedback control without using external measurement devices. In this paper, we aim at deducing lens poses of a two‐lens system solely from wavefront measurements. The wavefront can be decomposed into a finite sequence of polynomials which are weighted by coefficients. Since pose deviations directly lead to deviations in the wavefront (and therefore in the wavefront coefficients), a sensitivity matrix can be established. The choice of lens poses and wavefront coefficients determines the sensitivity matrix which is often ill‐conditioned and may potentially suffer from rank loss. We conduct a sensitivity analysis and show how the sensitivity matrix can be utilized to generate a linear estimate of the optical component poses. This estimate can then be used to close the feedback loop. Validation is conducted by simulating an optical system consisting of a laser, two bi‐convex lenses, and a wavefront sensor.