Optimal parameter solution for optical design of testing large-aperture off-axis aspheric mirror with computer-generated holograms

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Large-aperture aspheric mirror is usually transferred to the test axis by rotating and translating when measured by a computer-generated hologram(CGH). This paper focused on the optimal design of CGH, minimizing the line density of CGH, in testing off-axis aspheric mirror with large aperture, off-axis amount and asphericity. The analytics formula of the transferred aspheric is used for deriving the phase function of CGH by geometric computing. And the precision of optical path difference(OPD) is proved reaching nanometer level for aspheric mirror with large asphericity by zemax. The defocus and tilt-carrier amount are two parameters to be optimized for filtering the unwanted orders brought out by CGHs. A merit function consists of the line densities at lower and upper boundaries of CGH to describe the etching difficulty of CGH is proposed. The propagation progress is analyzed while the reflection is amended by considering the saggital height of the reflection point. The separated distance of the given (m,n) orders ray is proved reaching micron degree. The filtering condition is expressed as an inequalities system. The gradient descent method with Karush Kuhn Tucker condition is used for optimal solution of the constrained optimization problem. Finally, design example is presented and the parameter optimization for testing off-axis aspheric mirrors is proved to have a high precision, which providing extensive applicability possibility in designing freeform testing system.