Modified phase contrast for recording of holographic optical elements

A modified phase contrast method is described for the fabrication of holographic optical elements with in-line diffraction patterns. In this method, a liquid crystal phase modulator is addressed by computer-generated holograms to achieve variable phase gratings. The phase gratings are imaged onto photosensitive material by a phase contrast method without a Fourier filter. We show the analytical treatment of the modified phase contrast method and demonstrate the application in holographic recording.     

Method for designing arbitrary two-dimensional continuous phase elements

We propose a method for designing arbitrary two-dimensional continuous phase elements. The phase anomalies that are due to amplitude zeros that occur in conventional design methods can be avoided completely with this method. Therefore the method is also useful for designing holographic elements that are free from amplitude zeros. The method is based on an iterative Fourier-transform algorithm. In the iteration process the method operates on the unwrapped phase. Consequently, a subsequent continuation step is not needed.     

Improved phase hologram design for generating symmetric light spots and its application for laser writing of waveguides

The improved method for calculation of a phase hologram and its application to laser writing of waveguides with a spatial light modulator are presented. It was found that the amplitude and phase distributions of light spots generated by a phase hologram can be distorted compared to those of a focused single beam. The distortion of light spots could be reduced by adding a simple constraint, in which light intensities around a light spot should be as small as possible, to the conventional calculation method of a phase hologram. It was also demonstrated that the improved calculation method can be considered essential for laser writing of waveguides.     

Multi-STFT for adaptive SCPS phase determination

This paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.     

Phase unwrapping method along radial coordinates for speckle image reconstruction

We describe a phase estimating technique for a stellar speckle image reconstruction, which is based on the phase unwrapping method in polar coordinates. The phase unwrapping along radial lines is favorable to reduce accumulating errors in the phase estimation. This method is combined with Bruck-Sodin method which gives the estimate of the modulus of an object transform without a point reference source. Computer simulations of the image reconstruction are presented.     

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

SEM扫描云纹法的相移技术研究

提出一种扫描电镜(SEM)扫描云纹法的相移新技术,通过SEM系统控制电镜电子束扫描线移动,对获取的云纹图像实现0-2π范围内的四步相移,从而获得了更高的位移测量灵敏度。同时对SEM扫描云纹法的测量原理以及相移实验技术的原理进行了详细的阐述。并将该技术应用到电子封装试件栅的相移分析中。实验结果证明了该方法的可行性,该方法为微米云纹法的条纹处理提供了一种新途径。     

准平行光干涉的滤波型多抖动相控方法研究

正提出了一种准平行光干涉的滤波型多抖动相控方案,对该方案的相干光强进行了理论分析,在此基础上提出了滤波型多抖动法的相控原理,进行了滤波型多抖动法的相控数值分析和模拟实验.结果表明:该方法可识别出各路光波的相位差,反馈与相位差信号成比例的直流电压去控制相位调制器,可实现相位差的校正,相位控制电压输出范围为0.03—4.45 V,控制带宽为2.5 kHz.     

大气湍流随机相屏模拟方法研究

对几种模拟随机湍流相位屏的方法进行了总结,利用结构函数对每种方法进行了分析,并从Zernike多项式分解的思路和激光大气传输的角度,通过焦斑扩展和焦斑质心漂移对几种方法进行了完整比较,最后对湍流低频倾斜信息的补偿方式进行了探讨。通过分析发现:傅里叶变换(FFT)法模拟的相屏体现的湍流高频信息较充分,但低频信息不足;Zernike法模拟的相屏体现的湍流低频信息较充分,但高频信息不足。随着采用的Zernike多项式阶数的增加,其体现的高频信息会得到改善,但这些高频信息主要集中在圆域的边缘区域。分形法模拟的相屏体现的湍流高低频信息均较好。针对焦斑扩展和焦斑质心漂移,除分形法外,其他算法均存在不同缺陷。采用FFT法与Zernike多项式展开法相结合的方式或FFT法与湍流自相似理论相结合的方式模拟大气湍流随机相屏,也不失为一种较有效的方式,但从激光大气传输的角度来说,采用分形法模拟湍流随机相屏最好。     

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

Phase modulated gray-scale data pages for digital holographic data storage

We propose a method for gray level holographic digital data storage by using three-gray levels in the phase mode. Gray level data pages are displayed on a SLM operating in the phase mode to obtain a homogenized Fourier spectrum by suppressing the extremely high intensity DC component in the Fourier spectrum of conventional amplitude based binary/gray level data pages. Holographic interferometry has been used to recover the gray level amplitude data page from phase data page. Numerical simulation results are presented for three-gray level data pages. Fourier plane homogeneity, bit-error-rate, storage density, phase modulation error of the SLM, and misalignment tolerances are investigated through computer modeling. A comparison of the present method with the amplitude-modulated gray level case with and without using a phase mask in conjunction with the data page is carried out. An experimental demonstration of the proposed three-gray level phase data page method is also presented.     

利用相移片实现激光自准直的新方法

介绍两种实现激光自准直的方法和实验，阶梯相移片法的特点在于巧妙地利用相移片对入射光进行调制，实现高精度激光自准直和角度的测量；微点相移片法是比较入射光与反射光通过相移点的衍射图形，达到激光自准直的目的。用夫琅和费标量衍射量论分析和计算了激光经过两各片调制后的光能分布，并对制作公差进行了讨论。     

两步相移实现投影栅相位测量轮廓术

提出一种新的投影栅相位测量方法--两步相移法。该方法只需两幅相移条纹图，因此计算量小，速度快。给出了实验及计算结果，并同四步相移法进行了比较，证明了该方法具有较高的精度。     

一种校正相位测量轮廓术量化误差的算法

为了减小相位测量轮廓术中因数字化设备内部结构的量化处理过程引起的相位量化误差,提高相位测量精度。针对相位测量精度要求较高且表面凹凸变化不大的被扫描物体提出了一种能够有效校正相位测量轮廓术量化误差的算法,测量相位中的每一个像素点利用其相邻像素点进行校正。实验结果显示,校正之后,相位量化误差标准差减小了41.38%,相位测量的精度得到了提高。     

Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

A new multi-frequency inverse-phase method was proposed to compensate for nonlinear phase errors in fringe projection profilometry and to measure the three-dimensional shape of discontinuous objects. After introducing a phase offset of π/4 into the multi-frequency four-step phase-shifting method the corresponding nonlinear phase error reversed its sign, which allowed the addition of unwrapped phases before and after the phase-offset operation to compensate for the error. For the four-step phase-shifting method, simulation analysis showed that the nonlinear phase error had quadrupled the fringe frequency. Moreover, experimental results verified the feasibility and applicability of the proposed method.     

A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope

While considering measurements of grating-type samples with the retardation-modulated differential interference contrast (RM-DIC) microscope, we found a problem of phase objects. The problem is that smaller measured values than the actual phase distribution are obtained when phase objects are beyond the weak phase approximation range. We analyze the image characteristics of phase objects and show that the problem is caused by the effect of an image component which is proportional to the square of the phase distribution.To overcome this disadvantage, we propose a new analysis method named self phase-correction (SPC). The SPC method corrects the phase distribution of the first order approximation under the weak phase condition and obtains the actual phase distribution of an object’s phase beyond the weak phase approximation range. We propose a two-image SPC method and a three-image SPC method for the RM-DIC microscope, and examine the suitability of these methods.We confirm that the three-image SPC method effectively overcomes the problem, and that the measurement range of the RM-DIC microscope can thus be extended to a half-wavelength phase difference.     

孔径扩展中相位修正因子估计的改进算法

传统的扩展拖曳阵列尺寸算法(Extended Towed Array Measurement,ETAM)在信噪比不够高、相位修正因子的相位角处于以间断点为中心的"跳变区间"时,扩展孔径均有可能失效。针对传统的ETAM算法中互相关相位角的间断点导致的算法不稳定问题,提出了一种相位修正因子估计的改进算法。该算法使用归一化互相关复向量的统计平均值作为相位修正因子的最小二乘估计,消除了互相关相位角的间断点带来的不利影响。数值仿真和实验数据分析结果表明:对于相位稳定甚至相位随机的单目标信号,改进算法均能有效扩展孔径,获得相对于常规波束形成(Conventional Beamforming,CBF)更高的方位分辨率和检测信噪比;相比于传统的ETAM算法,改进算法提高了相位修正因子的估计准确性,从而有效提高了算法的稳定性。      

基于双音外差的电光相位调制器半波电压自校准测量方法

电光相位调制器是光纤通信系统、微波光子系统和相干光通信系统中的关键器件之一. 作为器件本征参数, 电光相位调制器的半波电压通常利用光谱方法和电谱方法进行测量. 光谱方法受到光源线宽和光谱仪分辨率限制, 测量的分辨率较低; 电谱方法则需要光电检测之前将相位调制转换成强度调制, 电谱方法的主要困难在于需要对探测器的不平坦响应进行额外校准. 提出了利用双音外差实现电光相位调制器半波电压自校准测量新方法, 该方法利用双音电光相位调制的边带与移频光载波的外差拍频, 对外差拍频信号进行频谱分析, 获得电光相位调制器的半波电压; 通过设定双音调制信号的频率关系, 克服了探测器光电转换中的不平坦频率响应, 实现了自校准测量. 该方法可扩展探测器和频谱仪的测试频率两倍以上, 节省至少一半的带宽需求. 与光谱测量方法相比, 该方法测试分辨率大幅提高且避免了光源线宽的影响; 与传统电域测量方法相比, 该方法无须额外校准, 无驱动功率和工作波长限制, 且对测试仪器带宽需求降低一半以上. 实验证实了所提方法获得的电光相位调制器半波电压的测量结果与光谱分析法获得的结果一致, 且大幅度地提高了测量范围和分辨率. 该方法提供了非常简单的电光相位调制器微波特性化分析方法, 对其他光电子器件分析也提供了参考.     

Detection of coupling between oscillators with analytic tests for significance

To detect coupling between two oscillators from a time series, we suggest a method based on the estimation of the phase increments correlation with an analytic test for significance. With exemplary oscillators, we show that the suggested method complements a widely used approach based on the estimation of the mean phase coherence. In particular, the suggested method allows efficient detection of a non-synchronizing coupling and, due to a less restrictive null hypothesis, it is applicable to a wider range of situations, including arbitrarily strong phase nonlinearities.