研究目的
To propose a new method for absolute test of flatness that uses only two flats, avoids precise alignment, and incorporates multiple translations and a 90° rotation with tilt measurement to achieve accurate surface reconstruction.
研究成果
The proposed SRAT method effectively subtracts systematic errors in the reference surface, achieving high accuracy in absolute flatness testing with only two flats and simplified procedures. Simulations and experiments confirm its robustness against noise and errors, making it a practical alternative to traditional three-flat tests.
研究不足
The method requires accurate tilt measurement, and errors in tilt estimation or rotation can affect reconstruction accuracy. Environmental noise and the quality of the reference surface also impose constraints. The experimental setup involves precise equipment and may be sensitive to vibrations and alignment errors.
1：Experimental Design and Method Selection:
The method involves using a Fizeau interferometer for topography capture and a compact wavefront interferometer for tilt measurement. The test surface is shifted with different intervals and rotated 90°, with relative tilts measured during shifts. Mathematical models based on rotation and shift differences are used to reconstruct the absolute surface figure without interpolation or assumptions.
2：Sample Selection and Data Sources:
Two optical flats are used: one as the reference surface (RS) and one as the test surface. The RS has a square aperture with N x N pixels, and sub-apertures are selected during shifts.
3：List of Experimental Equipment and Materials:
Includes a Zygo interferometer, a μPhase interferometer, a linear scanning stage (PI-M511D), tip-tilt stage, and high precision reflecting flat.
4：Experimental Procedures and Operational Workflow:
Steps include measuring the test surface in original position, rotating the RS by 90°, shifting the test surface with intervals s1 and s2, measuring relative tilts during shifts, capturing interference fringes, and reconstructing the surface using least-squares solution from derived equations.
5：Data Analysis Methods:
Data from interferometers are processed to compute differences in measurements. Tilt parameters are incorporated, and the test surface is reconstructed by solving linear equations using least-squares methods. Noise and error effects are analyzed through simulations and experiments.
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