Synthetic phase-shifting for optical testing: Point-diffraction interferometry without null optics or phase shifters

Abstract

An innovative iterative search method called the synthetic phaseshifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

Reflective shearing point diffraction interferometer

“…One-parameter reconfigurable antennas have been realized using PIN diodes, liquid switches, or microelectromechanical system (MEMS) switches and so on [4][5][6][7]. However, few reconfigurable antennas can simultaneously achieve both frequency and radiation pattern selectivity on account of the correlation between the different parameters.…”

“…An almost ideal spherical wavefront can be generated through a pinhole which can be regarded as reference wavefront instead of using reference sphere, and it can achieve an extremely high precision test of the wavefront theoretically. This is why point diffraction interferometer (PDI) [2] has been widely applied [3][4][5][6][7][8][9][10][11]. The main drawback of the PDI lies in the fact that it is difficult to extract the phase information from the PDI interferograms using the traditional methods.…”

Point Diffraction Interferometry Based on Phase Demodulation Technique for Circular Carrier Interferogram

“…共光路型的红外点衍射干涉仪， 认为该种干涉仪可以得到与 Twyman Green 干涉仪相似的高对比度条纹。由 于点衍射干涉仪的共光路结构给分离测试光与参考光带来困难， 很难在其中引入附加相位形成移相。国内 外一些学者针对此点展开研究， 提出了一系列移相式点衍射方案： Neal 等 [3] 提出基于电光晶体以及镀双折射 膜点衍射板的偏振式点衍射干涉仪， 通过改变电光晶体的电压实现移相；Paturzo 等 [4] 在铌酸锂晶体上沉积铝 膜制作点衍射板， 并利用其电光效应实现了点衍射干涉仪的移相； Gao 等 [5] 构建了一种基于双光栅的准共光 路点衍射干涉结构， 通过横向移动其中一个光栅实现移相； Wang 等 [6][7] 采用反射式点衍射板实现了参考光与 测试光的分离， 并利用压电陶瓷(PZT)实现移相， 之后又分析了针孔尺寸带来的影响； Ramírez 等 [8] 制作了一种 特 殊 的 液 态 晶 体 波 片 点 衍 射 板 ， 通 过 对 点 衍 射 板 加 电 压 改 变 其 延 迟 量 实 现 移 相 ； Bai 等 [9] 则 采 用 多 个 棱 镜 分 光实现了一种同步移相移相式点衍射干涉术。移相式点衍射干涉术系统复杂度较高， 对点衍射板加工工艺 要求较高， 装调难度也相对较大， 因此也有一些学者开始关注非移相式的点衍射干涉术： Du 等 [10] 构建了一种 Circular common-path 结构， 得到线性载频的点衍射干涉图， 并利用傅里叶变换法实现了相位测量； Park 等 [11] 仅采集单幅点衍射干涉图， 采用迭代搜索策略实现了点衍射干涉图所包含相位的 Zernike 系数求解。 [3] U ( )…”

Estimating transmitted wavefronts in a broad bandwidth based on Zernike coefficients

“…As such, wavefront measurements are widely used in a variety of applications in the industrial and scientific fields, as the quality of an optical transmission system can be evaluated using the magnitude of wavefront distortion observed in a transmitted beam [2][3][4]. Several wavefront measurement techniques have been studied [5][6][7][8][9], including laser phase-shifting interferometers such as the Fizeau interferometer, which is commonly used for very high accuracy testing of a transmitted wavefront [10]. Wavefronts are often expressed in the form of Zernike polynomials, with each term representing a specific type of aberration.…”