Computer-aided alignment method using rms WFE value as an optimization criterion

Several computer-aided alignment (CAA) methods have been developed for the alignment of multi-element optical systems. Most of the methods use singular value decomposition or non-linear optimization to calculate the amount of misalignment. However, when we do the alignment of the optical system, we frequently encounter at least two problems; one is the solution stalled in local minima that fails to align the system within requirement and the other is the field imbalance of the system. We presume this is due to the lack of boundary conditions imposed during the optimization. In order to overcome these problems, we propose a new CAA method using rms wavefront error (WFE) value as an additional boundary condition in optimization. This boundary condition of target rms WFE helps to get around the local minima and field imbalance while guaranteeing the system performance. We applied this method to the alignment of the optical system consisting of three mirrors and four lenses. By only single trial of alignment, we obtained the rms WFE of less than lambda/20 (lambda=3390 nm) at all fields and field difference less than lambda/200 in off-axis field. Therefore, it is clear that our new method is very effective and accurate, compared to the conventional CAA algorithm.