Modeling the wavefront degeneration and optimizing the CGH interferometric null test

Abstract

The high-accuracy phase description of the coherent light propagation is important to assess and optimize far-field and astigmatic optical systems, such as interferometric surface test, etc. Usually, the wavefront propagation is simulated by the physical optics theory throughout each optical element, which might be time-consuming and incur computational complexity. In this article, we analyze the wavefront degeneration in the CGH interferometric null test by the complex ray tracing. We sample the wavefront by a series of elliptical Gaussian beamlets, which is consistent with the Eula formula in the differential geometry. The propagation of elliptical Gaussian beamlets through the optical system can be calculated by the tiny ray bundle theory and geometric optics. In the output space, the wavefront can be described by an elliptical Gaussian beam originated from the propagated Gaussian waist through the system. Therefore, the phase distribution at the output space can be characterized by the sum of series of elliptical Gaussian beams, which gives a high-accuracy analytical simulation of phase distribution better than 30mrad with time about 0.2s. As an example, we apply our method to the analysis of the wavefront degeneration in the interferometric null test of a ⌀3m aspheric mirror. After the optimization, the instrumental transfer function increased from 0 to 0.65 at 0.4 Nyquist frequency.