Accurate nonlinear phase step estimation in phase shifting interferometry

We propose a new method for the accurate estimation of nonlinear response of the PZT to the applied voltage. The method uses discrete chirp Fourier transform for the coarse estimation followed by a fine search method for the accurate estimation of the phase step and nonlinearity. The method can be extended to the cases of extraction of multiple phases in the configurations involving multiple PZTs such as holographic moiré in the presence of nonlinearity. The robustness of the proposed method is verified by comparing with Cramér-Rao lower bound. Experimental results prove the method’s feasibility.     

A novel approach for characterizing the nonlinear phase steps of the PZT in interferometry

We propose a novel approach to estimate the phase distribution in the presence of nonlinear response of the PZT. The proposed method is an outcome of two different concepts based on the discrete chirp Fourier transform (DCFT) and the maximum-likelihood estimator for the estimation of nonlinear phase step. The robustness of the proposed method is tested for various magnitudes of nonlinearity and harmonics. Comparison of our proposed method with the bench marking algorithm by Hibino et al.'s six and nine sample algorithm in the presence of noise shows that our method is highly efficient.     

Generalized linear prediction method in phase-shifting interferometry in the presence of noise

The effectiveness of phase-shifting interferometry (PSI) techniques employing piezoelectric device PZT in the estimation of phase depends largely on the accuracy with which the phase shifts are imparted to the device and the noise influencing the measurement. Several effective algorithms have been proposed to compute the phase shifts imparted to the device and subsequently obtain the phase using least-squares estimation technique. In this paper, we propose a generalized approach, which accurately estimates the phase shifts in the presence of noise. The method is based on the idea of linear prediction and explores the fact that sampling more data frames yields a reliable phase step estimate in a least-squares sense. We also compare our method with a commonly used generalized phase-shifting method based on histogram analysis and show that our proposed approach is highly effective. We also present simulation and experimental validations of our proposed method.     

Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise

A phase-shifting piezo device commonly employed in phase-shifting interferometry exhibits a nonlinear response to applied voltage. Hence, a method for estimation of phase distribution in the presence of nonlinear phase steps is presented. The proposed method compensates for the harmonics present in the intensity fringe, allows the use of arbitrary phase-step values between 0 and tau rad, and does not impose constraints on the selection of particular phase-step values for minimizing nonlinearity and compensating for the harmonics. The comparison of the proposed method with other well-known benchmarking algorithms shows that our method is highly efficient and also works well in the presence of noise.     

Maximum-likelihood estimator for dual phase extraction in holographic moire

A maximum-likelihood (ML) method based on spectral estimation theory for the extraction of dual phase distributions in holographic moire in the presence of nonsinusoidal waveforms, noise, and the miscalibration of piezoelectric (PZT) devices is proposed. The extraction of these phases requires incorporating two PZTs into the moire setup. ML estimators are asymptotically efficient for sufficient data samples. The approach presented uses a direct stochastic algorithm called probabilistic global search Lausanne for minimizing the ML function.     

Nonlinear piezoelectricity in PZT ceramics for generating ultrasonic phase conjugate waves

We have succeeded in the generation of acoustic phase conjugate waves with nonlinear PZT piezoelectric ceramics and applied them to ultrasonic imaging systems. Our aim is to make a phase conjugator with 100% efficiency. For this purpose, it is important to clarify the mechanism of acoustic phase conjugation through nonlinear piezoelectricity. The process is explained by the parametric interaction via the third-order nonlinear piezoelectricity between the incident acoustic wave at angular frequency omega and the pump electric field at 2 omega. We solved the coupling equations including the third-ordered nonlinear piezoelectricity and theoretically derived the amplitude efficiency of the acoustic phase conjugation. We compared the efficiencies between the theoretical and experimental values for PZT ceramics with eight different compositions. Pb[(Zn1/3Nb2/3)(1 - x)Tix]O3 (X = 0.09, PZNT91/9) piezoelectric single crystals have been investigated for high-performance ultrasonic transducer application, because these have large piezoelectric constants, high electrical-mechanical coupling factors and high dielectric constants. We found that they have third-order nonlinear piezoelectric constants much larger than PZT and are hopeful that the material as a phase conjugator has over 100% efficiency.     

Fiber Ring Laser In-cavity Phase Modulation

In this paper, experimental results of the in-cavity phase modulation induced by dithering PZT is reported. The dithering PZT can produce strong phase modulation, reshaping the laser output spectrum, but does not affect the laser linewidth, which is measured by homodyne method.     

Fiber Ring Laser In-cavity Phase Modulation

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Polarization shifting interferometric profilometer

A phase sensitive Michelson interferometer based on interference microscope configuration with a polarization adjustment approach is proposed to determine the two-dimensional (2-D) surface profile of optical grating with real time capability. In the proposed method, nonlinear behavior of a PZT phase shifter is avoided by use of polarization stepping and a phase map is developed with the four-bucket algorithm. The phase map is unwrapped to give the true surface profile of the sample. A close agreement of measurements is found between the measured result determined by the proposed method and that determined by an atomic force microscope (AFM). We also analyzed the estimated uncertainty of measurement in the nanometer range for the random fluctuations of the experimental parameters.     

An automated self-marking phase-shifting system for measuring the full field phase distribution of interference fringe patterns

A technique based on the repetition of the interference fringe pattern for the automated marking of the PZT phase shifting interference system is described. A closed-loop control is used to circumvent the inherent hysteresis and nonlinear characteristics of PZT. The whole interference system integrated under LabVIEW graphic programming environment provides users a friendly and ease-of-maintenance interface. An application of the algorithm is used to demonstrate the promotion of the Zygo GPI-LC model interferometer to upgrade its phase resolution ability.     

外加电场对铁电薄膜相变的影响

采用热力学非线性理论,研究了外加电场对立方基底Pb(Zr_0.3Ti_0.7)O₃(PZT)铁电薄膜相变的影响.通过数值计算,得到了"失配应变-外加电场"相图,及外加电场与极化强度的关系.当外加电场达到186 kV/cm时,能使生长在SrTiO₃ 基底上PZT铁电薄膜从单斜r相转变为c相.在实验上,采用扫描探针显微镜通过对PZT薄膜施加不同的极化电场来研究了它的电畴翻转.从得到的压电响应相图可以看出,绝大多数的电畴是清晰可 关键词： 铁电薄膜 相变 扫描探针显微镜 失配应变     

Incident-angle dependence of the phase conjugate reflectivity by nonlinear piezoelectric interaction in PZT ceramics.

The reflectivity of an acoustic phase conjugator by nonlinear piezoelectric interaction in PZT ceramics was measured as a function of the incident angle. The phase conjugator was designed as a solid block with a flat surface for the acoustic incidence from water. The phase conjugate reflectivity showed incident angle dependence, which is mainly determined by the transmissivity of the acoustic waves, together with some effects of anisotropy. The field-reconstructing ability of this phase conjugator was simulated for focused incident beams.     

Preisach modelling of nonlinear response in electrically biased lead zirconate titanate-based piezoceramics

The alteration of the high-field electrical permittivity (nonlinear response) of PZT-based ceramics when an electrical bias field is applied is reported in this work. Large differences are observed between soft and hard PZT behaviours. While in soft PZT a bias field does not modify the nonlinear behaviour, a notable dependence is verified in hard PZT. The Preisach model is satisfactorily used to describe experimental results. A distribution function containing the first terms of the Maclaurin development series of a function composed by two Gaussian-like functions of different amplitudes is proposed. The model gives a satisfactory explanation for the fact that the permittivity depends not only on the amplitude of the applied electric field, but also on the bias field, both for soft and hard ceramics and for poled or unpoled samples.     

Fringe projection profilometry with nonparallel illumination: a least-squares approach

Under a nonparallel illumination condition, fringe patterns projected on an object have unequal fringe spacing that would introduce a nonlinear carrier phase component. This Letter describes a nonlinear carrier removal technique based on a least-squares approach. In contrast with conventional methods, the proposed algorithm would not magnify phase measurement uncertainty, nor does it require direct estimation of system geometrical parameters. The theoretical expression of the carrier phase function on the reference is derived and expanded in a power series. The unknown coefficients in the series are determined by a least-squares method. By subtracting the calculated carrier phase function from the unwrapped phase map, the phase distribution of the object profile is obtained.     

Resolution-enhanced Fourier transform method for the estimation of multiple phases in interferometry

A phase shifting method based on high-resolution frequency estimation and Fourier transform technique is introduced. This method, also referred to as the eigenvector method, draws on the complementary strengths of both these methods. The salient feature of the method lies in its ability to handle nonsinusoidal wave-forms, multiple piezoelectric transducers, and arbitrary phase steps in an optical configuration. The method does not need the addition of carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.     

压电晶体位移特性曲线干涉自动测量方法

本文提出了压电晶体(PZT)位移物曲线自动干涉测量方法,该方法利用干涉仪把PZT的微位移量转化成干涉条纹相位变化量,通过快速傅里叶变换(FFT)方法自动复原干涉条纹中包含的相位的变化量,从而高精度地检测出PZT的位移特性曲线.根据该方法,利用CCD摄象机、图象板和干涉仪组合成一套光、机、电一体化的微位移自动测试系统,实际测量了我们研制的PZT随电压变化的位移特性曲线.实验表明,该方法原理实现简单,且能实现高精度、自动、实时和动态测量.     

Phase determination in holographic Moiré in presence of nonsinusoidal waveforms and random noise

This paper proposes a subspace parameter estimation method which besides allowing for accommodating multiple PZTs in an optical interferometer permits for extracting in real time values of phase shifts between data frames at each pixel point. The technique enables to freely choose values of phase shifts between 0 and π. A generalized phase measurement algorithm allows for computing multiple phase information present in the interferometer. The method facilitates the use of spherical beams, addresses errors arising from the miscalibration of the phase shifting devices, and is capable of handling nonsinusoidal waveforms in an effective manner. Numerical simulations demonstrate that phase distributions can be measured with high accuracy even in the presence of noise.     

用于PZT调制干涉仪的外触发式差动数字鉴相技术

基于相位测量的外差干涉系统以其信号处理方面的优势在光学计量领域得到了广泛的应用。介绍了采用机械调制方法的差动单频干涉系统的干涉信号小数级次的相位测量实现方法。针对机械调制干涉系统的信号有相位跃变点且周期不均匀的特点 ,提出了利用外触发信号对干涉信号进行整周期截取而后再鉴相的方法。研制了基于 FPGA的外触发式差动数字鉴相系统。实验测试表明 ,该鉴相系统在信号频率为 30 0 Hz～ 10 k Hz范围内达到的指标为 :示值稳定性优于± 0 .0 15°,极限偏差小于± 0 .0 7°     

Model-based processing of a holographic moiré

A state space model for the determination of dual phase distributions in a holographic moiré in the presence of nonsinusoidal waveforms, random noise, and miscalibration of the piezoelectric (PZT) devices is proposed. The extraction of these phase terms requires incorporating two PZTs into the moiré setup. A Toeplitz approximation method (TAM) is applied for phase determination, and modification to the Toeplitz covariance matrix formed from the phase-shifted moiré fringes by application of a denoising step in the state-feedback matrix is proposed. This step ensures that the phase terms can even be estimated at a signal-to-noise ratio much lower than that of the original TAM or by our previously suggested polynomial based method.     

Terfenol-D/PZT磁电复合材料的磁电相位移动研究

采用粘合法制备了叠层结构的块体Terfenol-D/PZT磁电复合材料,测量了不同频率下的磁电回线,采用新的极坐标下的方式做图.从极坐标下的磁电回线中可以看出,随直流磁场的变化,非谐振频率下的磁电相位发生了轻微移动,移动幅度随频率的增加而增加;而在谐振频率下,伴随着巨磁电效应,磁电相位发生了显著移动,移动幅度达到了近90°.与粉末Terfenol-D/环氧树脂/PZT磁电复合材料对比之后表明,非谐振频率下块体Terfenol-D/PZT的磁电相位移动主要由涡流引起;而谐振频率下大幅度相位移动则主要来源于Terfenol-D的磁致弹性变化.