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Dynamic optimization measurement of spherical wavefront radius and theoretical deviation elimination in interferometry
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DOI：10.1016/j.optlastec.2026.116065.png)
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Abstract
En 中文
In non-null interferometry, accurate elimination of theoretical deviation is essential for extracting machining errors but relies on precise calibration of the spherical wavefront radius. Conventional hardware‑based calibration is limited by alignment errors and motion inaccuracies, while existing model‑based or iterative adjustment methods are either too complex or lack engineering simplicity. To address this issue, we propose a dynamic optimization measurement method for the spherical wavefront radius. The method uses the measured surface information to convert normal deviation into axial deviation through a geometric relationship. An iterative optimizer then adjusts the spherical wavefront curvature radius until the difference between the compensated test surface and the ideal spherical wavefront is minimized. Because the theoretical surface of the test mirror is known, the objective function becomes unimodal, allowing even a simple bisection algorithm to converge reliably. Simulations on spherical, conic aspheric, and high-order aspherical surfaces, including error analysis with prior curvature uncertainty and machining errors of different spatial frequencies, demonstrate strong versatility and robustness. Experiments on a Zygo Fizeau interferometer using a two-position comparison design on spherical, aspherical, and high-order aspheric surfaces confirm that the extracted machining errors are independent of measurement position. The proposed approach requires no hardware modification, no complex system modeling, and only a single measurement. It is simple, robust, and can be directly embedded as an algorithmic module into commercial interferometers, offering a practical pathway for high‑precision, low‑cost optical metrology.
Keywords:
Spherical wavefront radius
Dynamic optimization
Theoretical deviation elimination
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