An algorithm of separating rigid-body linear displacement from FEA data of optical imaging system

Optical imaging system always appears an asymmetric displacement under finite element analysis (FEA) for the asymmetry of the loads and the optomechanical structure, although the system is designed by an axisymmetric way. The asymmetric displacement can generate a misalignment, between "the (0,0) field" of the aberration analysis and "the central field" through the optical axis, and decline the accuracy of objective function of an optimization design. An algorithm is presented to separate the rigid-body linear displacement, which has no influence on the imaging quality, from the FEA data. Actually the linear displacement of system is a special region around the (0,0) field on the image surface rather than a displacement such as any single optical element. In the algorithm, the region with the same value of optical modulation transfer function (MTF) calculated by the optical ray tracing tools is defined as a domain D(x,y), where the (x,y) is a set or subset of (x ₀,y₀) and MTF(x₀,y₀) is equal to MTF(0,0). The nodal displacements can add or subtract a certain value while the modified central point on or in the region in an optimal design of optical system under any static, dynamic and vibratory loads. And an example is demonstrated that the nodal displacement processed by the algorithm is more suitable to optimize the imaging system suffered from the static and vibration conditions than the original FEA data.