Processing optical measurements using a regressive Fourier series: A review

In this article a generalized regressive Fourier series approach is shown which does not suffer from the so-called leakage effects prone to frequency domain approaches. This parametric approach will be used to tackle a number of optical techniques. Due to the fact that the technique offers an approximation and not an estimate of the data, it is possible to reduce the spatial data of operational mobility shapes measured by e.g. a laser Doppler vibrometer (LDV). It also allows a reduction of measurement time of this former technique. The LDV will also be used to visualize and localize acoustic sources.     

Fourier fringe processing using a regressive Fourier-transform technique

Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has led to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However, the basic processing technique, in case of the 2D-Fourier transform, is subject to a major drawback. Because this technique supposes periodicity in a fringe image, the so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive Fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier-transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

Introduction of the Impulse Response Function in Common-Path Interferometers with Fourier Plane Filters

In the present paper it will be shown how the introduction of a Fourier plane filter can create various types of common-path interferometers for measuring changes in surface tilt or curvature of an object surface. This is obtained by placing a holographic optical element in the Fourier plane of a 4-f optical system. The interferometers are analysed by using the paraxial approximation of the Huygens-Fresnel integral formalism, and the interferometer functions are given by a novel formalism using impulse response functions. Based on this technique, an interferometer for measuring dedicated changes in surface deflection is presented. This interferometer is insensitive to rigid surface rotations and displacements. The interferometer can be embedded in systems based on single point measurement of a time dependent deflection, i.e. vibrometers, as well as in full-field measurements such as electronic speckle interferometers.This paper was originally presented at the 2001 International Conference (2nd Joint OSJ-SPIE Conference) on Optical Engineering for Sensing and Nanotechnology, ICOSN 2001 which was held June 6-8, 2001 at the Pacifico-Yokohama Conference Center, Yokohama, Japan.     

Ultrashort pulse generation and measurement techniques

The first section will discuss the generation of picosecond and femtosecond laser pulses, their propagation and compression in optical fibers, and their amplification for nonlinear spectroscopic applications. Laser systems for different wavelength regimes and pulse measurement techniques will be described. The second section will extend the discussion of picosecond and femtosecond measurement to studies of ultrafast processes in materials. Pump-probe and transient four-wave-mixing methods will be analyzed. Examples of application to both molecular and solid state systems will be presented.     

Measurement of optical nonlinearity by antiresonant ring interferometric nonlinear spectroscopic (ARINS) technique

We have reported the measurement of third-order optical nonlinearity by antiresonant ring interferometric nonlinear spectroscopic (ARINS) technique and discussed its usefulness over other popular measuring techniques such as Z-scan, degenerate four wave mixing (DFWM) and third harmonic generation (THG). The measurement has been simulated theoretically by taking different numerical values as well as sign of δ, which is a key parameter of ARINS. The technique has been benchmarked using toluene and the theoretical simulation has been substantiated experimentally by measuring the nonlinear optical coefficients (n₂ and β) of two different samples. The disadvantages of the technique have also been discussed. However, a number of advantages of ARINS override its disadvantages and therefore, ARINS may be preferred over other measuring techniques for the measurement of nonlinear optical parameters.     

Reducing measurement time for a laser Doppler vibrometer using regressive techniques

In the last decade the laser Doppler vibrometer (LDV) has become a widely spread instrument for measuring vibrations. It often offers accurate measurements with a high spatial resolution. However, the measurement time of the LDV and especially for the scanning LDV is long. Therefore, reducing the measurement time is an attractive objective. A way to achieve this is to use a single sine excitation (on a resonance frequency). However, this technique has two major drawbacks: the inability to provide information on the damping and a operational deflection shape that can differ from the true mode shape. In this article two methods will be introduced to reduce measurement time without these defaults. In the first method introduced in this article a narrow band multisine is used as excitation signal and the measured vibration signal in the time domain is represented by a model using sines and cosines with these fixed narrow band frequencies. The coefficients of those sines and cosines are then estimated on a global scale by means of a least-squares estimator. An important advantage of this particular technique is that one does not have to measure a full period of the signal, reducing time. The second method accelerates the measurement time for scanning LDV measurements. Using the time domain sequence from each previous scan point and a limited number of time samples from the current scan point, the full time domain sequence of the current scan point can be estimated. Both these methods are a key benefit for in-line quality control, which can have upwards of 1000 spatial measurement locations. The proposed techniques will be validated on both simulations and experiments of varying complexity.     

Z-扫描技术与非线性光学材料性质的测量

介绍了Z-扫描技术的基本原理，以及Z-扫描技术在测量非线性光学介质的非线性折射率、非线性吸收系数和光学限制器等方面的应用，以细菌视紫红质(bR膜)、碘的酒精溶液和偶氮材料CN2为例，分别介绍了它们的测量结果，给出了提高Z-扫描灵敏度的改进方法，介绍了其发展装状况。     

电子散斑干涉载频调制形貌测量方法的分析

根据电子散斑干涉载频调制测量物体形貌的基本原理,物体表面的微小偏转可引入包含物体高度信息的载波干涉条纹。将物体的偏转视为变形,对物体变形与载波干涉条纹之间的关系进行了讨论,得出了离面位移引入载波和面内位移引入含有物体高度信息相位的结论。发现利用典型电子散斑干涉系统测量物体形貌效果最好,并通过实验得到了验证。     

移相干涉测量术及其应用

为了对移相式数字干涉仪在光学元件测量中的应用有全面了解，介绍了移相干涉术的基本原理。结合激光数字波面干涉仪，阐述移相干涉术的四步重叠平均算法、压电晶体移相器(PZT)的结构、3 PZT的组合方法、移相器的标定误差和非线性误差的校正方法、波面相位解包的自适应种子算法、波面相位的评价指标等内容。结合移相数字波面干涉仪，叙述了移相干涉测量技术在普通光学元件、红外光学元件、大口径光学元件、非球面光学元件等测量中的应用并指出了应用过程中的注意事项。最后明确指出光干涉技术正沿着高相位分辨率、高空间分辨率、宽波段和瞬态高速测量的方向发展，并将会在瞬态波前测量、微机械的微结构动态分析等方面有着越来越广泛的应用。     

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear Schr?dinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.     

深空光通信中图像信标的捕获和跟踪

用激光进行深空探测科学数据回传,上行信标光衰减严重,不能提供足够高的跟踪速率,因此常采用自然天体图像作为信标。对该信标的捕获和跟踪是深空光通信链路成功建立和保持的关键。在航天器上存储一幅目标天体图像做参考,利用该图像和探测图像的相关性对该信标进行捕获,理论分析和仿真结果都表明,可以精确地确定光通信天线的初始对准方向,使跟瞄系统进入跟踪模式。基于离散傅里叶变换和极大似然方法对信标的平移进行计算,需要解一个非线性方程组,线性近似计算结果表明平移量总误差在0.5个像素以内,X方向的平移误差为3.3%,Y方向的平移误差为2.7%,可以满足深空通信的要求,因而是一种可行的方案。     

计算机控制光学表面成形驻留时间算法研究

光学非球面的使用可以提高光学系统的性能、简化系统结构、减小系统体积,减轻系统重量,计算机控制光学表面成形（ＣＣＯＳ）方法是加工光学非球面的重要方法。介绍了ＣＣＯＳ原理,给出了ＣＣＯＳ中关键技术驻留时间计算的三种算法———基于加工仿真的算法、基于傅立叶变换的算法和基于滑动平均与傅立叶变换的算法。基于加工仿真的驻留时间算法需要做大量的卷积计算,计算时间较长,残余误差较大;基于傅立叶变换的驻留时间算法与基于滑动平均和傅立叶变换的驻留时间算法计算时间短,计算后的残余误差小。磨头单位去除函数形状与磨头大小对误差的去除也有明显的影响,小的磨头和陡峭的单位去除函数对于去除局部误差更为有利,但是加工时间较长     

傅里叶变换轮廓术中相位失真的预矫正方法

介绍了一种基于傅里叶变换轮廓术的三维面形测量系统中相位失真的预矫正方法。由于投影系统和成像系统的空间三角位置关系、投影仪的发散照明和两套系统蕴含的光学畸变,投影一幅相位与空间坐标成理想线性关系的标准正弦光场,拍摄到的条纹相位和空间坐标不再呈线性分布,引起相位失真,甚至会影响系统测量精度。该方法借鉴反向条纹投影的思想,计算拍摄光场的非线性相位分布与理想的线性相位分布之间的关系,预先矫正,反算出一个新的待投影光场。实验结果表明这种方法能有效地减小该类相位失真所导致的测量误差,获得了更好的测量结果．     

三阶非线性光学材料及其表征技术研究进展

介绍三阶非线性光学材料及其表征技术的研究进展。分析几种典型的三阶非线性光学材料及今后的发展趋势，指出介质物理材料的非线性光学特性将成为今后的研究热点。随着表征技术研究的进一步拓展，准波导技术将可能作为一种新的表征技术应用于非线性光学材料研究中。     

Development of an optical sensor for dynamic monitoring of off-round and eccentric errors of cylindrical parts

An optical angular deflection sensor has been implemented to assess the shape and axis position of rotating cylindrical parts. The deviation of the shape from the nominal circular cross-section (the off-round error) and the departure of the rotation axis from the geometric axis of the parts (the eccentric error) are determined. The technique is simple and inexpensive, with acceptable accuracy for mechanical engineering, is capable of monitoring rotating parts and has the potential to gauge parts on the production line.     

基于瞬态光克尔效应的超快光学快门技术

系统介绍了几种基于瞬态光克尔效应的超快光学快门技术,包括传统的光克尔双折射快门技术,瞬态光栅快门技术,以及利用瞬态克尔透镜效应的光学快门技术。这些技术都是在泵浦-探测的实验配置基础上,利用门控光对克尔介质折射率的瞬态调制导致的信号光的相位（偏振态）、传播方向或光束发散角等光学特性的改变实现对信号光的超快时间分辨测量。对比讨论了这些超快快门技术的工作原理和实验配置,结果表明瞬态光束偏折快门技术相比其他快门技术具有无偏振配置要求、无相位匹配条件、超宽带光谱响应范围的特点,在光与物质相互作用的超快动力学研究中具有更为广阔的应用前景。     

Optical 3-D dynamic measurement system and its application to polymer membrane inflation tests

An optical surface measurement system, which is capable of measuring transient surface shape, has been developed by using a high-speed digital camera. The system is based on the grating projection and Fourier transform technique. A calibration procedure is developed to allow the system to generate Cartesian coordinates directly, which are with respect to a fixed coordinate system in 3-D space. The measurement accuracy (±50 μm) is defined and verified as the maximum error between measured values and the known values of standard objects both flat and curved. The camera and a grating projector are mounted into a portable sensor head to allow in situ measurements. In addition, external force or pressure signals can be correlated with each measurement through a device called the multi-channel data link. The system is capable of digitizing a 3-D curved surface into an array of points with known xyz coordinates at a sampling rate from 30 to 1000 Hz. As an application, the system is used to measure the transient surface shape during a polymer membrane inflation test. The measurement results along with the pressure information provide an approach to determine the material parameters used in different material models.     

Polar light and symmetry of electro-optical effects

General regularities of the interaction of a polar light wave synthesized from the Fourier harmonics of a fundamental frequency with a transparent centrosymmetric optically nonlinear medium are considered. The notion of light polarity is introduced and transverse electro-optical effects specific for the problem of interaction between polar light and isotropic nonlinear media (optical rectification and the linear electro-optical effect) are analyzed. Estimates of values of the effects in combination with published experimental data on optically encoded second harmonic generation in glasses indicate promising opportunities for practical application of the effects of the interaction of polar light and matter in optical systems of information recording and processing.     

基于低采样率模数转换器的延时复用频分多址无源光网络

基于正交频分复用技术的无源光网络中,光网络单元为了获得其所属小部分下行数据,需高采样率模数转换器将所有频宽的信号恢复才能分出其所需要数据.同时正交频分信号峰均比很高,传输中容易引起非线性效应.为此,本文提出一种基于低采样模数转换器的延时复用频分多址无源光网络.在光线路终端将数据序列交错排序并在时域映射为正交幅度调制信号;再通过离散傅里叶变换扩频技术,将信号转换为频域信号并映射到子载波上.通过预先发送和回传训练信号,估测包括延时采样和低采样接收在内的信道频响;再将频域信号利用估测信息在光线路终端做预处理,从而使信号传输中的失真得到有效预补偿.本文实验演示了含有多个光网络单元的系统,对于含有M个光网络单元的无源光网络,模数转换器的采样率可以降低到1/M Nyquist采样率,实验中模数转换器的采样率可以降低到1/32 Nyquist采样率;由于下行信号通过光线路终端预处理实现失真预补偿,光网络单元接收到的信号不需要均衡,不需要傅里叶变换和傅里叶逆变换,避免了与之对应的相关计算量,降低了光网络单元的计算复杂度;由于使用了扩频技术,信号波形具有更低的峰均比,从而降低了非线性对信号的影响,增加了功率预算.此外,随着光网络单元的增加,信号的误码率几乎没有增加,光网络单元个数增加到32时,向前纠错极限为10~(-3)的功率代价小于0.5 dB;系统对光网络单元采样时刻偏离具有一定容限;25 km光纤传输的功率代价大约0.5 dB.理论和实验均证明本方案能够简化光网络单元,降低无源光网络的成本;与传统的无源光网络相比具有明显优势.