Hybrid compensation method for testing large-aperture low-sag freeform mirrors

A computer-generated hologram (CGH) is a high-precision method for testing complex surfaces. However, its applicability is limited by the aperture constraints of the fabrication equipment, rendering it challenging to effectively measure large-aperture, high-precision freeform mirrors. In this study, we propose a hybrid compensation approach combining CGH and a spherical mirror for testing large-aperture low-sag freeform mirrors. By introducing a virtual equivalent surface, we developed a hybrid computational method to calculate the CGH phase function. An interferometric data-processing model was established by incorporating mapping distortion correction, surface error reconstruction, and spherical mirror error removal. Experimental validation was performed on a rounded rectangular off-axis freeform mirror with a clear aperture of 698 mm × 210 mm, and comparative measurements were conducted using Dutch United Instruments. Root mean square density analysis shows that the hybrid compensation method achieves a low-frequency measurement accuracy of 3.6 nm root mean square (RMS) and a clear aperture surface measurement accuracy of 8.3 nm RMS. This method enables high-precision testing of large-aperture, low-sag freeform surfaces, and the spherical mirror compensator demonstrates a degree of general applicability.