Roberto V. F. Lopes

Misalignment parameters estimation in refractive optical systems

High image quality and complex, refractive optical systems, as those used in remote sensing applications, are, in general, very difficult to be manufactured with the required performance. This can be charged to the high sensitivity of such systems to the fabrication tolerances, mainly concerning the relative alignment of the optical components with respect to each other. When the system does not achieve the expected quality, the puzzle is to identify where the problems lies. This is even worsened when the number of optical elements becomes high. Due to these facts, some misalignment characterization and estimation techniques based on Bayesian estimators and wavefront measurements have been proposed in the literature. This paper is the result of a deep study and investigation of these techniques, with emphasis on an application to an intentionally simple system for the sake of illustration that highlights conceptual issues that could be extended to more realistic, complex optical systems. With this purpose, the sensitivity of the wavefront Zernike coefficients to the misalignment parameters, its use in a parameter estimator design that includes nonlinear terms, the study of the system observability, and a statistical analysis of the estimator performance considering the observation noise are addressed in details. Numerical simulation results for the simple system are shown. We also present insights on how to apply the technique to the alignment of a 11-lens optical system used in the Brazilian remote sensing camera MUX, that will fly on-board the upcoming Sino-Brazilian satellites CBERS 3&4.