As an adaptive optics that can modulate phase of lights, spatial light modulators (SLMs) are widely used in laser shaping, telescopes, and surface figure interferometric tests. The phase control accuracy of SLMs affects the performance of these optical systems. However, the traditional birefringence effects-based phase control method has relatively low accuracy due to the non-linear phase response of SLMs. To this end, a diffractive interferogram-based phase control method is proposed. The general model for describe the diffraction-based phase control method is established. The phase control error model of the diffractive interferogram-based phase control method is analyzed theoretically. Theoretical analysis was conducted to analyze the phase quantization and discretization that influence the phase accuracy. By applying the discretized interference pattern with appropriate quantization level of a given phase and a standard reference phase into the SLM, phase control accuracy can be enhanced up to about λ/30 (λ=632.8 nm) root-mean-square. Comparisons of phase control accuracy of the proposed method with the traditional phase control method are conducted to verify the accuracy enhancement. Using the proposed method, the SLMs can be applied in systems with collimated or divergent beams configuration that requires high phase control accuracy such as interferometric surface figure tests.
X-ray mirrors are widely utilized in light source devices like synchrotron radiation (SR) and free electron laser (FEL) light source. The Root-Mean-Square (RMS) value of surface figure accuracy required for these mirrors is typically sub-micro radian or sub-nanometer, and their aperture can be hundreds of millimeters or even meters. To achieve this accuracy, deterministic figuring is required and surface figure error is the premise. Interferometric stitching test is commonly utilized. Interferometric test obtains the surface figure of the tested X-ray mirrors mounted on a mounting support. Due to the low stiffness of the X-ray caused by the large ratio of length/width and length/height. The mechanical stress induced by the mounting supports may have a non-negligible influence on the surface figure of the mirror surface. Moreover, this can result in the poor reproductivity when testing the mirror under different mounting situations and with different mounting craft. What kind of aberration will be introduced by the X-ray under different mounting supports and whether it can be neglected is still an issue. To this end, the reproductivity of a typical silicon X-ray mirror with size of 500 mm × 50 mm × 50 mm were tested on different typical supports with a 24” zygo interferometer. Comparison of the introduced aberration type and aberration amplitude were conducted to reveal the deformation of the X-ray mirror on different typical supports. The results of this paper may attract the community that fabricates, tests, or uses X-ray mirror to pay a special attention to the mounting supports when testing the surface figure the X-ray mirrors.
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