Simultaneous phase-shifting interferometry based on a 2×2 retarder array with random fast-axes (RARF-SPSI) is proposed for real-time wavefront measurements. The retarder array is used as the phase-shift component, where the phase retardances are π/2, π, 3π/2, and 2π and the four fast-axes of the four retarders can be somewhat random. In this paper, the mathematical model of RARF-SPSI is built by using a Stokes vector and a Mueller matrix, the phase demodulation method through solving equations is derived, and the coefficient matrix of the equations that is associated with the azimuth of the fast-axes is calculated by Fourier analysis. Then the corresponding simulation analysis is executed. In the experiment, four simultaneous phase-shifting interferograms are captured and the phase distribution under test is demodulated through the proposed method. Compared with the four-bucket phase-shifting algorithm adopted in traditional simultaneous phase-shifting interferometry, the ripple error is suppressed well. The advantage of the proposed RARF-SPSI is that there is no need to calibrate the fast-axes of the phase-shift component before measuring; in other words, the phase demodulation error caused by the azimuth error of fast-axes is eliminated.

A single-shot reflective shearing point diffraction interferometer (S-SRSPDI) is designed for large-aperture dynamic wavefront measurements. The PDI is integrated on the small substrate with properly designed thin film. The wavefront under test is reflected by the front and rear surfaces of the substrate respectively to generate an interferogram with high linear-carrier frequency, which is used to reconstruct the wavefront by means of the Fourier transform algorithm. In this paper, the analytic formula of intensity distribution of the interferogram is derived. The parameters related with the carrier frequency of fringes are discussed. The method to optimize the contrast of the interferogram is proposed by analyzing the reflective polarization effects. In addition, the spurious fringes of the interferogram are removed by the proper designed blocking film. S-SRSPDI was applied to detect the dynamic wavefront with a diameter of 400 mm. The measured aberrations are in good agreement with those obtained by the shearing method, which verifies that the proposed S-SRSPDI is a powerful tool for large-aperture dynamic wavefront measurements.

ABSTRACTA novel point diffraction interferometer with reflective shearing optical structure is developed. The substrate of interferometer has an angle with optical axis, and the incident converging spherical wavefront will be reflected by the front and rear surfaces of the substrate, respectively. Then, an interferogram with carrier frequency is obtained. Using Fourier transform algorithm, the wavefront can be retrieved from one single interferogram. In this article, the intensity distribution formulas of interferogram are derived, and the system error and the major parameters of interferometer are also discussed. The new design with compact structure and high resolution is contrast adjustable and suitable for dynamic wavefront measurement. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:2845–2848, 2015

为检测瞬态波前的三维分布,提出了一种共光路结构的剪切干涉测试系统.该系统使用棋盘光栅与光阑,将待测波前分解为四支互相错位的波前,这些波前两两相干,最终叠加形成一幅高载频的干涉图.根据光强传输方程以及傅里叶光学理论,建立了剪切干涉测试系统的理论模型,采用傅里叶变换算法提取待测波前.提出了一种剪切量标定算法,通过讨论线性载频的影响因素与光栅的衍射效率,给出了棋盘光栅的具体设计参数.实验搭建了瞬态波前检测装置,实现了自动化高精度测量,波面检测结果的峰谷(PV)值、均方根(RMS)值以及Zernike拟合系数均与SID4波前探测器所测波面结果一致.因此采用该技术能够实现瞬态波前检测.

A quadratic polar coordinate transform technique is proposed to improve the demodulation accuracy of the circular carrier interferogram. Through the quadratic coordinate transform, the circular carrier interferogram is converted to the linear carrier interferogram with uniform spatial frequency, whose signal spectrum is significantly separated from the unwanted ones. Thus, the phase under test can be accurately retrieved by the conventional Fourier transform technique. Both the simulant and experimental results demonstrate that the proposed technique can be used for precise demodulation of the phase distribution of a circular carrier interferogram.