Alignment method for cascaded microlens arrays based on centroid registration of focal spot array images

Cascaded microlens arrays (MLAs) provide a compact approach for beam redistribution and homogenization, but their performance is highly sensitive to residual relative pose errors between adjacent arrays. This paper presents an image-based residual pose estimation method for fine alignment of cascaded MLAs after mechanical prealignment. Mechanically constrained degrees of freedom, including axial spacing and transverse tilts, are separated from in-plane misalignments observable in the image. Under collimated paraxial incidence, focal spot centroid shifts are converted into equivalent array plane displacements using a chief ray proportional model. Residual lateral decentering and rotation about the optical axis are then recovered by robust registration of the focal spot centroid field. Geometric and Huber robust weighting are introduced to improve pose estimation stability in the presence of weak spots, local defects, and erroneous centroid extraction. Simulations demonstrate robust parameter recovery under centroid perturbations and quantify the correspondence-preserving operating range and residual tilt sensitivity. Under a prescribed uncertainty budget, a 10,000-trial parameter-level Monte Carlo analysis yielded a median of two corrections to enter the 5 μ m residual region. Experimentally, closed-loop alignment reduced the complete-array residual metric from 48.55 μ m to 4.75 μ m. A representative downstream beam homogenization simulation further indicates that reducing the residual relative pose improves target plane irradiance uniformity.