Sensitivity-informed multi-objective adaptive weighting method for automatic alignment of freeform USTP systems

In catadioptric ultra-short-throw projection (USTP) systems, six-degree-of-freedom pose errors of the freeform mirror simultaneously affect geometric distortion and the modulation transfer function (MTF), causing significant coupling among multiple performance metrics during system alignment and leading to changes in the optimization objectives at different alignment stages. To address this problem, full-parameter six-degree-of-freedom scanning simulations were carried out to obtain the response laws of geometric distortion and MTF to pose perturbations. The results reveal that the dominant responses of these two metrics to pose errors undergo a stage-dependent shift as the error scale changes, and that stable mapping relationships exist between different distortion modes and specific subsets of degrees of freedom. On this basis, a physics-guided adaptive weight allocation and stage-wise optimization method is proposed. The above optical laws are explicitly incorporated into the weight evolution and optimization process, thereby establishing a physics-guided optimization framework for the automatic alignment of freeform USTP systems. Experimental results show that this method achieves stable convergence from coarse alignment to fine alignment. In 10 experiments with different initial conditions, the final mean MTF exceeded 70%, the alignment time for each run was about 10 min, and the dispersion of the results was significantly reduced. This work not only enables efficient automatic alignment of freeform USTP systems but also provides a reference for modeling the coupling between pose errors and image-quality degradation and for designing alignment strategies in related optical systems.