An improved phase retrieval algorithm for optical aspheric surface measurement

In order to overcome the measurement and calculation difficulty for aspheric surface with phase retrieval technology, an improved phase retrieval algorithm was proposed. Due to significant departure from sphere surface, reflected light from different part of the aspheric surface under test will overlap in some areas in the collected images by CCD with general phase retrieval measurement setup, which will lead to the failure to recover the surface phase. The proposed algorithm will only use those areas without light overlapping in each image in the iteration process and employ several defocused images to recover the whole surface. This algorithm can improve the measurement range for aspheric surface with phase retrieval technology. The experimental system was established and a 180 mm diameter, f/1.6 parabolic mirror and a 180 mm effective diameter, f/1.33 hyperboloid mirror were tested by the proposed method. The experimental results show that the retrieved surface errors are in good consistent with that obtained by interferometer, which confirms the validity of the proposed algorithm.     

Full field deformation measurement of centimeter sized objects using optical phase retrieval

Most papers in the field of optical phase retrieval either consider only the intensity (or amplitude) profile of the object under inspection (or scatterer location in the X-ray version), or a uniform tilt/rotation of the object beam. However, phase retrieval is able to recover the phase profile of the object (beam) as well, which theoretically makes the observable interference of phase retrieved object waves possible. In this paper we demonstrate this principle experimentally on centimeter sized deformable reflective objects (as large as 40 mm by 40 mm) and corresponding simulations are also presented. When the CCD camera is moved along the optical axis in the Fresnel region, the interference fringes of the displacement field have low contrast. On the other hand, when an imaging setup is built, and the camera moves near the image plane, high fringe contrast can be obtained. These fringes however suffer from some phase error. In our work the iterative modulus projection algorithm was used as a simply implementable phase retrieval method.     

A spatial domain constraint iterative phase retrieval method for the propagation based X ray phase contrast imaging

Based on the propagation X ray phase contrast imaging theory, a spatial domain constraint iterative phase retrieval method is described in detail. This algorithm limits the object spatial domain according to the actual sample size firstly, and modify the image plane data with the actual test data, then the iteration can be terminated until iteration precision or the number of iterations meet the preset requirements. Finally the numerical simulation is made to evaluate the rapid phase retrieval algorithm performance, and a real column fiber material experiment is carried out using a micro focus X ray phase contrast imaging experiment platform, the phase distribution image of the column fiber is calculated out by this algorithm. The results show that this phase retrieval algorithm is effective, and the method has a potential stability and accuracy for X ray phase contrast imaging technology.     

Information verification and encryption based on phase retrieval with sparsity constraints and optical inference

A novel optical information verification and encryption method is proposed based on inference principle and phase retrieval with sparsity constraints. In this method, a target image is encrypted into two phase-only masks (POMs), which comprise sparse phase data used for verification. Both of the two POMs need to be authenticated before being applied for decrypting. The target image can be optically reconstructed when the two authenticated POMs are Fourier transformed and convolved by the correct decryption key, which is also generated in encryption process. No holographic scheme is involved in the proposed optical verification and encryption system and there is also no problem of information disclosure in the two authenticable POMs. Numerical simulation results demonstrate the validity and good performance of this new proposed method.     

相位差波前检测方法应用于平移误差检测的实验研究

相位差波前检测方法由于其结构简单,对环境要求低,测量精度较高等优点,被应用于诸多领域.本文针对拼接型天文望远镜中主镜的共相位检测问题,对相位差波前检测方法在拼接主镜各子镜间平移误差测量进行理论分析,并搭建了实验光路.实验结果表明:相位差波前检测方法对拼接镜平移误差的测量精度高于λ/20(λ为波长),满足系统对拼接平移误差的要求.     

对一种线性相位反演波前测量方法的数值仿真

利用数值仿真方法对一种基于线性相位反演波前测量方法的性能进行了详细分析。讨论了这种线性相位反演波前测量方法的定标过程,描述了基于线性相位反演算法的波前传感器的基本组成结构。利用数值仿真计算,分析了系统自身像差和模式标定系数对这种波前传感器性能的影响,通过复原矩阵条件数,分析了靶面像素和这种波前测量方法的空间分辨力的关系。仿真结果验证了该种新型线性相位反演波前测量方法的可行性。     

对一种线性相位反演波前测量方法的数值仿真

 利用数值仿真方法对一种基于线性相位反演波前测量方法的性能进行了详细分析。讨论了这种线性相位反演波前测量方法的定标过程,描述了基于线性相位反演算法的波前传感器的基本组成结构。利用数值仿真计算,分析了系统自身像差和模式标定系数对这种波前传感器性能的影响,通过复原矩阵条件数,分析了靶面像素和这种波前测量方法的空间分辨力的关系。仿真结果验证了该种新型线性相位反演波前测量方法的可行性。     

A comparison of iterative algorithms and a mixed approach for in-line X-ray phase retrieval

Previous studies have shown that iterative in-line X-ray phase retrieval algorithms may have higher precision than direct retrieval algorithms. This communication compares three iterative phase retrieval algorithms in terms of accuracy and efficiency using computer simulations. We found the Fourier transformation based algorithm (FT) is of the fastest convergence, while the Poisson-solver based algorithm (PS) has higher precision. The traditional Gerchberg-Saxton algorithm (GS) is very slow and sometimes does not converge in our tests. Then a mixed FT-PS algorithm is presented to achieve both high efficiency and high accuracy. The mixed algorithm is tested using simulated images with different noise level and experimentally obtained images of a piece of chicken breast muscle.     

A review of iterative phase retrieval for measurement and encryption

Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed.     

一种线性相位反演波前测量方法的实验研究

 描述了基于线性相位反演算法的波前传感器的基本组成结构。在实验室内搭建了相应的演示验证实验装置,对该种新型波前测量方法的特性进行了实验研究。实验计算结果表明：这种根据入射全孔径远场光斑强度分布直接反演出入射波前相位的线性相位反演新方法原理是可行的。只需实时测量一幅焦平面图像,根据焦平面上光强分布的微小变化量与入射孔径面上的相位分布的微小变化量之间存在的近似线性关系,就可以用模式复原的原理复原出入射波前相位。传感器对于离焦,像散等像差模式都可以进行较为准确的测量,误差率都小于1。对称系统像差中存在少量的非对称像差对复原结果的准确性影响不大。     

一种线性相位反演波前测量方法的实验研究

描述了基于线性相位反演算法的波前传感器的基本组成结构。在实验室内搭建了相应的演示验证实验装置,对该种新型波前测量方法的特性进行了实验研究。实验计算结果表明：这种根据入射全孔径远场光斑强度分布直接反演出入射波前相位的线性相位反演新方法原理是可行的。只需实时测量一幅焦平面图像,根据焦平面上光强分布的微小变化量与入射孔径面上的相位分布的微小变化量之间存在的近似线性关系,就可以用模式复原的原理复原出入射波前相位。传感器对于离焦,像散等像差模式都可以进行较为准确的测量,误差率都小于1。对称系统像差中存在少量的非对称像差对复原结果的准确性影响不大。     

波差与表面斜率误差评价方法的讨论

对用波差与表面斜率误差评价光学元件面形误差的方法进行了比较和讨论。以具有不同面形精度的光学元件 ,在不同的数据处理方法下得到的结果为例 ,说明此两种面形评价方法在数据处理方法不同时在数值上的联系。     

An effective method in calibrating nonlinear errors for phase-shifting interferometry

In phase measurement or digital holography for phase-shifting interferometry, the key role is the variation of reference light wave and recover algorithm based on interferograms and reference phase, so the calculation result is directly affected by phase-shift accuracy. However, because of the errors of nonlinear and other random factors, it is difficult to control the actual phase-shifting amount accurately. In this paper, we aim to propose an efficient method for phase-shifting interferometry which does not require accurate initial estimation of phase-shift amounts, only a few pixels with several randomly shifted interferograms are sufficient for accurate extraction of phase information. This method has reduced the dependence of reference phase, and can obtain phase-shifting amount directly without using complex revised algorithm for correcting phase-shifting nonlinear errors.     

Optical surface profile measurement using phase retrieval by tuning the illumination wavelength

In this paper, we present a method for measuring the surface profile of an object by using diffraction intensity patterns recorded at different illumination wavelengths. The main advantages of this technique are: simple optical set-up, high immunity to noise and environmental disturbance, since no reference beam (like in holography) or additional moving parts are needed. Two iterative calculations are synchronously performed using two sequences of diffraction intensity patterns, producing fast convergence to the expected result. The effects of different parameters on the accuracy and efficiency of the method are investigated. Simulation and experimental results are presented.     

投影光刻物镜波像差的公差分析方法

为保证投影光刻物镜的成像性能并降低制造成本,提出了一种更全面可靠的公差分析方法。该方法在以波像差均方根(RMS)值作为评价标准的传统分析方法基础上,添加波像差峰谷(P-V)值作为评价指标,并据此选择合理的补偿器组合。在系统波像差的RMS值和P-V值均满足要求的情况下,采用了较少的补偿器,从而有效地降低了系统的制造难度和成本。结合实验室设计的一套90nm投影光刻物镜进行了公差分析和补偿器优选。结果表明,利用该方法选择的7个补偿器,使得系统在97.7%置信区间内,全视场波像差的RMS值≤0.0412λ,P-V值≤0.2469λ,满足了90nm投影光刻物镜的像质要求。     

多参数背景场误差模型在散射计资料台风风场反演中的应用

利用散射计资料反演海面风场时, 台风区域普遍存在降雨使得风场反演误差很大, 引入降雨地球物理模型函数 (GMF+Rain) 及多解方案 (MSS), 结合二维变分(2DVAR) 模糊去除思想风速反演误差很大程度减小, 但风向反演误差仍有待进一步改善, 如何进一步减小风向反演误差有待进一步研究. 文章介绍了2DVAR模糊去 除方法的基本思想, 针对背景场误差较大时, 2DVAR模糊去除风向误差较大, 引入包含若干参数的背景场误差模型. 基于台风个例数值试验结果, 着重从理论分析角度讨论各参数关于2DVAR模糊去除效果的敏感性, 进而提出最优参数设置方案以改善风向模糊去除效果. 2006年“摩羯”台风QuikSCAT数据风场反演数值试验结果结合理论分析表明: 引入多参数误差模型, 通过设置粗糙误差概率等于0, 2DVAR风向模糊去除效果明显改善; 同时, 背景场的影响可通过增大背景场误差方差, 减小背景场误差相关尺度和减小粗糙误差概率而减小, 进而减小在背景场误差较大情况下的风向反演误差. 关键词： 台风风场反演 二维变分 多参数误差模型 散射计资料     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

相位差法波前传感系统自身误差的分析及消除方法

针对附加像差为离焦的情况,对焦面位置误差、离焦量误差、图像对准误差以及图像噪声等因素带来的波前传感误差进行了数值模拟,并给出了确定焦面位置、对准焦面图像和离焦面图像、精确计算分光比、确定离焦量以及处理图像噪声的方法。使得传感结果的均方根误差分别由0.088 8λ,0.059 0λ,0.128 4λ,4.170 6λ,0.152 6λ降为0.002 1λ,0.002 1λ,0.002 1λ,0.002 1λ,0.029 2λ。结果表明:这些方法可以有效地减小传感误差,大大提高了传感精度,为相位差法的实际应用提供了重要的技术支持。     

相位差法波前传感系统自身误差的分析及消除方法

 针对附加像差为离焦的情况,对焦面位置误差、离焦量误差、图像对准误差以及图像噪声等因素带来的波前传感误差进行了数值模拟,并给出了确定焦面位置、对准焦面图像和离焦面图像、精确计算分光比、确定离焦量以及处理图像噪声的方法。使得传感结果的均方根误差分别由0.088 8λ,0.059 0λ,0.128 4λ,4.170 6λ,0.152 6λ降为0.002 1λ,0.002 1λ,0.002 1λ,0.002 1λ,0.029 2λ。结果表明:这些方法可以有效地减小传感误差,大大提高了传感精度,为相位差法的实际应用提供了重要的技术支持。     

Phase retrieval in optical fiber modal interference for structural health monitoring

A method based on data dependent system (DDS) for extraction of phase in fiber modal interference is presented. The interference patterns of LP₀₁ & LP₁₁, LP₀₁ & LP₀₂ and LP₀₆ &LP₀₇ within the fiber have been recorded under different launching conditions. The patterns were characterized by means of autoregressive model and the self coherence functions of the corresponding interferogram were determined. It would provide the phase distribution of the pattern and the modulation of group delay due to the measurand. An application has been made for measuring strain in a simply supported beam under different loading conditions. Results are presented for the applied strain in the range of 270-1500 μ strain.