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An analytic expression for the field dependence of FRINGE Zernike polynomial coefficients in optical systems that are rotationally nonsymmetric

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces. From here, over time, they have come to be used as a sparsely sampled representation of the state of alignment of assembled optical systems both during and at the conclusion of the alignment process. We previously developed the field dependence that analytically interconnects the coefficients of the Zernike polynomial (which has to-date been characterized only by its aperture dependence) as a more complete representation of an aligned, rotationally symmetric optical system. Here, we extend this analytic expression for the RMS wavefront error to encompass the prediction of the performance of a misaligned optical system by expressing the field dependence within the framework of nodal aberration theory. This significant expansion to this valuable polynomial provides an important new tool for characterizing high performance optical systems throughout the optical design, fabrication, assembly, and interim and acceptance test process.