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.     

Chirp estimation in phase-shifting interferometry

We propose a new approach for estimating the phase in the presence of a nonlinear response of a phase-shifting device: a piezoelectric transducer (PZT). The method is complemented well by the high resolution and the maximum likelihood estimation techniques in the estimation of the phase step and the nonlinear coefficient. The advantage of the proposed method is that it can be extended to the extraction of multiple phases in configurations involving multiple PZTs in the presence of nonlinearity. Symmetricity in the phase steps is not required in this method. Hence hysteresis of the PZT does not have any influence on the accuracy of the phase estimation. The effectiveness of the method is shown by experimental results.     

Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search

A new phase-shifting interferometric technique that uses an unknown phase step is described in which the phase step is determined by use of an algorithm called Probabilistic Global Search Lausanne (PGSL). One of the main sources of error in phase stepping is piezoelectric device (PZT) nonlinearity. The PGSL algorithm identifies the characteristics of the response of the PZT to the applied voltage through matching predicted and measured responses. The unknown phase step is also calculated with 0.097% error. This approach overcomes the limitations of existing techniques to determine unknown phase steps. Linear regression is subsequently applied for interference phase determination.     

一种在二步相移数字全息中实现准确相移的方法

相移数字全息中的相移准确性决定了重建结果的质量,本文提出了在二步相移数字全息中.实现准确相移的方法.该方法使用数字电压源开环控制普通的压电陶瓷微位移器,通过连续以微小的间隔来改变施加在压电陶瓷微位移器上的电压,可以获得一系列对应于不同相移角的全息图像,进而可以利用这些全息图像重建出来物光波在全息面上的强度分布.实验中采...     

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.     

一种在二步相移数字全息中实现准确相移的方法

相移数字全息中的相移准确性决定了重建结果的质量,本文提出了在二步相移数字全息中实现准确相移的方法.该方法使用数字电压源开环控制普通的压电陶瓷微位移器,通过连续以微小的间隔来改变施加在压电陶瓷微位移器上的电压,可以获得一系列对应于不同相移角的全息图像,进而可以利用这些全息图像重建出来物光波在全息面上的强度分布.实验中采用已被CCD直接记录的物光波在全息面上的强度分布作为标准来评价前面重建结果的质量,计算了这些重建结果和评价标准之间的相关系数,结果表明相关系数达到最大时对应的全息图具有准确的相移角π/2.实验中比较了使用所确定准确相移角和理论相移角分别重建出来物光波的质量,计算机模拟和实验的结果证实了该方法的有效性.     

Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations

We describe an adaptive aberration correction technique based on an ant colony algorithm for solid-state lasers and a general class of other adaptive optics systems. We show that it is possible to compensate phase aberrations without wavefront sensing in this approach, which iteratively adjusts the control voltages of a deformable mirror to maximize certain system performance metrics of the far-field intensity distribution of the laser beam. The effectiveness of this approach is analyzed numerically by use of a 37-element piezoelectric deformable mirror and a variation of the Strehl ratio as the metric. Results demonstrate that this approach can effectively compensate the phase distortions of laser beams and significantly improve beam quality. A comparison indicates that this approach is much faster than a genetic algorithm while achieving almost the same beam quality.     

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.     

A theoretical model of acoustoelectric transducer with a nonuniform distribution of piezoelectric coefficient: application to transducer optimization

A general equation is derived that describes the behavior of a piezoelectric transducer with a nonuniform distribution of piezoelectric coefficient within its bulk, when submitted to an arbitrary distribution of acoustic pressure. Based on this equation, an expression for the receiving transfer function of the transducer is calculated. The results demonstrate the dependence of the transfer function on the distribution of piezoelectric coefficient, and that it is possible to benefit from a nonuniform distribution to optimize the transfer function. The general equation also describes the influence of the external electric circuit loading the transducer, which leads to another independent means of optimizing the transfer function. The proposed model combines effects of piezoelectric material characteristics, acoustic backing, and electric loading, without resorting to Mason or other equivalent circuits for the transducer.     

一种基于移相误差估计的5步移相算法

移相误差是用移相法进行相位测量的主要误差。本文提出一种 5步移相算法 ,分两步进行相位计算 ,首先估计实际步进移相的线性移相误差 ,然后再利用此移相误差估计值计算相位分布。移相误差估计公式和相位计算公式简洁 ,算法简单易行 ,对线性移相误差和二次谐波的敏感度低 ,可基本消除线性移相误差对解调相位的影响。对本文提出的算法进行了仿真研究 ,同时给出了 Hariharan 5步算法、Surrel 6步最小算法的仿真结果。结果表明 :本算法明显优于以上两种算法 ,可基本消除线性移相误差引起的相位偏移。本算法适用于作等步移相的相位测量或移相的标定。     

Phase shifting interferometry using a robust parameter estimation method

The paper proposes a maximum-likelihood (ML) method based on spectral estimation theory for the estimation of phase distribution in interferometry in the presence of nonsinusoidal waveforms, noise, and the miscalibration of the piezoelectric device. The proposed method also allows the use of arbitrary phase steps. ML estimators are asymptotically efficient for large number of data samples. The method is complemented well by the incorporation of global search algorithm known as Probabilistic Global Search Lausanne for minimizing the ML function. The performance of the proposed method is studied in the presence of noise.     

Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals

In this study the attenuation coefficient and dispersion (frequency dependence of phase velocity) are measured using a phase sensitive (piezoelectric) receiver in a phantom in which two temporally overlapping signals are detected, analogous to the fast and slow waves typically found in measurements of cancellous bone. The phantom consisted of a flat and parallel Plexiglas plate into which a step discontinuity was milled. The phase velocity and attenuation coefficient of the plate were measured using both broadband and narrowband data and were calculated using standard magnitude and phase spectroscopy techniques. The observed frequency dependence of the phase velocity and attenuation coefficient exhibit significant changes in their frequency dependences as the interrogating ultrasonic field is translated across the step discontinuity of the plate. Negative dispersion is observed at specific spatial locations of the plate at which the attenuation coefficient rises linearly with frequency, a behavior analogous to that of bone measurements reported in the literature. For all sites investigated, broadband and narrowband data (3-7 MHz) demonstrate excellent consistency. Evidence suggests that the interference between the two signals simultaneously reaching the phase sensitive piezoelectric receiver is responsible for this negative dispersion.     

Love wave propagation in functionally graded piezoelectric material layer

An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.     

Piezoelectric relaxations in polymers: Spherical dispersion model

For the interpretation of piezoelectric relaxation in oriented polymers, a spherical dispersion model is proposed in which piezoelectric spheres are dispersed in a nonpiezoelectric medium. The influence of the dielectric and elastic relaxations in the medium and the sphere on the piezoelectric stress constant and strain-constant is analyzed in detail. The origins of piezoelectric relaxations in oriented poly-γ-methyl-L-glutamate are assigned to the elastic relaxation (at about ?70°) and the dielectric relaxation (at about 0°C) in the piezoelectric phase, and the elastic relaxation (at about 100°C) in the non-piezoelectric phase, respectively.     

High-resolution frequency estimation technique for recovering phase distribution in interferometers

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.     

Power dissipation and temperature distribution in piezoelectric ceramic slabs

A method is presented to determine power dissipation in one-dimensional piezoelectric slabs with internal losses and the resulting temperature distribution. The length of the slab is much greater than the lateral dimensions. Losses are represented using complex piezoelectric coefficients. It is shown that the spatially non-uniform power dissipation density in the slab can be determined by considering either hysteresis loops or the Poynting vector. The total power dissipated in the slab is obtained by integrating the power dissipation density over the slab and is shown to be equal to the power input to the slab for special cases of mechanically and electrically excited slabs. The one-dimensional heat equation that includes the effect of conduction and convection, and the boundary conditions, are then used to determine the temperature distribution. When the analytical expression for the power dissipation density is simple, direct integration is used. It is shown that a modified Fourier series approach yields the same results. For other cases, the temperature distribution is determined using only the latter approach. Numerical results are presented to illustrate the effects of internal losses, heat conduction and convection coefficients, and boundary conditions on the temperature distribution.     

X-Ray “knife” as a submicrometer tool for studying focusing lens quality

A mobile x-ray “knife” developed by the authors is described. The device is intended for determining the profile of the spatial intensity distribution in the ionizing radiation beam. Its automated motion system combines two actuator types. Significant displacements are performed using a goniometric module with a piezoelectric actuator. The angular step of this module is 1 arc second, which corresponds to a linear displacement of 0.97 μm. As a “fine” drive, a rotating module with a piezoelectric column is used. Its linear step can be varied from 0.01 to 1 μm at a total number of steps of 1000. The x-ray knife was experimentally tested at the Kurchatov Center of Synchrotron Radiation for diagnostics of the parameters of a short-focus x-ray lens at a photon energy of 18 keV. In the vertical direction, the width of the profile for the intensity distribution in the beam formed by the lens was 2.4 μm.     

Object plane detection and phase-amplitude imaging based on transport of intensity equation

By using transport of intensity equation (TIE), phase distribution of an object is retrieved from through-focus intensity images. This technique allows simple and robust phase imaging compared with an interferometric approach. However, it is hard to measure phase distribution when a dynamic object moves in the direction of an optical axis. To clear this problem, autofocusing TIE which is based on local statistics is proposed. The proposed technique achieves the detection of the object plane and the retrieval of a focused object phase distribution simultaneously. In this approach, an object plane is determined by the focusing techniques based on local statistics such as variance, gradient, and Laplacian of amplitude distribution, after phase distribution in an image sensor plane is retrieved by the TIE. The performance of these three statistics is evaluated in numerical and optical experiments, and a suitable focus value is determined for precise phase imaging.     

Optimized iterative quantization algorithm for phase-only beam shaping masks

In this work, we present a novel and improved method for designing a quantized phase-only beam shaping mask. The algorithm is based on iteratively quantizing the phase while forcing the phase error to produce energy outside the area of interest.The new approach performs well for binary phase-only masks even when a gray level output distribution is required. While comparing to other well-known methods, the proposed approach was found to have fast, simple and stable numerical convergence with low root mean square error as well as high efficiency and signal to noise ratio.     

Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.