Model-based optimization of gravity sagging for a horizontally mounted optical flat.

A practical and generalized model-based gravity sagging reconstruction method for a horizontally mounted optical flat is proposed. It is a practical and generalized approach based on the finite element method (FEM) model and real experiment results. Gravity sagging and misalignment parameters are retrieved by solving the multivariable unconstrained optimization problem with a least squares sense. Finally, the accurate true surface figure can be obtained by subtracting the optimized gravity sagging from the test result in the practical mounting state. A reasonable agreement with the outcomes of the FEM analysis and the real experiment is achieved through the proposed method. The effectiveness of the method was verified by comparison with the result measured by three-flat calibration. Experimental results demonstrated that this reverse optimization method can effectively reconstruct the sagging information due to gravity, is generalized, and is computationally efficient in practice.

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