高精度干涉检验移相算法对振动误差的免疫能力

对移相干涉测量中影响移相稳定性,从而产生测量误差的小幅度机械振动进行了研究,建立了振动误差模型,仿真分析了Wyant84b三步算法、Hariharan87五步算法、七步算法和十三步算法4种不同移相算法对振动的免疫能力。模拟结果显示,十三步算法对振动的免疫能力最好,与已发表文献成果吻合,说明本文的模拟具有较高的可信度,在一定程度上能够对影响干涉仪精度的振动误差进行合理预测,并能够起到评价和筛选移相算法的作用。     

Multi-step phase-shifting algorithms insensitive to linear phase shift errors

We describe and analyse a group of multi-step phase calculation algorithms for evaluation of interferometric measurements using the phase-shifting technique. Phase-shifting algorithms are proposed, with a constant but arbitrary phase shift between captured frames of the irradiance of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process is not dependent on linear phase shift errors. An advantage of the described algorithms is their ability to determine the phase shift value at every point of the detector plane. Moreover, a complex error analysis of proposed algorithms is performed and the algorithms are compared to several common error compensating phase stepping algorithms.     

Identification of nonlinear recording error in phase shifting interferometry

The phase shifting method for quantitative fringe pattern analysis provides high accuracy if stringent requirements on the component interferogram recording are met. In the paper the issue of detection and identification of error sources in the two-beam interferogram phase shifting experiment is discussed. The phase shift angle histogram and lattice-site representation are applied for that purpose. Special attention is paid to possible nonlinear recording of component interferograms in the presence of linear and nonlinear phase step errors. Four and five step phase shifting algorithms are considered. The superiority of the lattice-site representation is shown. In the case of phase steps equal to π/2, however, the lattice-site representation of shift angles for five frame algorithm does not allow to detect recording nonlinearity. The four frame counterpart shows to be very helpful in this respect. Its properties related to the fringe pattern profile under study, including a defocused Ronchi grating, are discussed.     

Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time.     

Volume-grating phase-shifting digital speckle pattern interferometry used for measurement of out-of-plane displacement field

A new digital speckle pattern interferometry, called volume-grating phase-shifting digital speckle pattern interferometry, is discussed in this paper. The out-of-plane displacement field of a bent plate can be quantitatively measured using volume-grating phase-shifting digital speckle pattern interferometry proposed in this paper. Theoretical and experimental results, as well as absolute errors, are given.     

A comparative study of phase-shifting algorithms in digital speckle pattern interferometry

Digital speckle pattern interferometry (DSPI) is a tool for making qualitative as well as quantitative measurements of deformation of objects. Phase-shifting algorithms in DSPI are useful for extracting quantitative deformation data from the system. Comparative studies of the different phase-shifting algorithms in DSPI for object deformation measurement are presented. Static and quasi-dynamic deformation of the object can be measured using these algorithms. Error compensating five-step phase-shifting method is used for the algorithms.     

Fast image-processing technique in phase-shifting holographic interferometry

A fast image-processing method in phase shifting holographic interferometry is proposed, in which the complicated phase calculation is completed with a logic circuit and look-up table. An electronic circuit was designed for the purpose. With these techniques, the processing time can be greatly reduced.     

移相干涉测量中的抗振技术

移相干涉测量技术是一种众所周知的非接触式的高精密测量方法,具有广泛的应用范围。环境振动是移相干涉仪测量误差的主要来源之一,国际上一些从事干涉测量的工作人员提出了许多抗振的方法,大体上分为主动技术和被动技术。主动抗振技术主要是系统自身探测振动并通过反馈回路对振动进行补偿,被动抗振技术则是通过各种技术措施尽量减小干涉仪对环境振动和气流影响的敏感度。从这两方面对干涉仪的抗振技术研究的进展做简单介绍,并介绍了作者所在课题组在这两个方面所进行的研究工作。     

A novel phase-recovering algorithm for the intensity quantization error in the digital grating phase-shifting profilometry

In this paper, a novel phase-recovering algorithm is proposed to overcome the phase error cause by the image quantization procedure. As the quantization error level is different in one period of the sinusoidal fringe pattern, the intensity errors in the wave crest and wave valley area are much lager than that of other areas. By increasing the phase-shifting steps, the phase value in each point can be extracted without the intensity data from the wave crest and wave valley area. The phase-recovering algorithm is deduced in the whole period. Finally, the validity of the proposed algorithm is proved by data simulation method.     

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.     

Measurement of edge residual stresses in glass by the phase-shifting method

Control and measurement of residual stress in glass is of great importance in the industrial field. Since glass is a birefringent material, the residual stress analysis is based mainly on the photoelastic method. This paper considers two methods of automated analysis of membrane residual stress in glass sheets, based on the phase-shifting concept in monochromatic light. In particular these methods are the automated versions of goniometric compensation methods of Tardy and Sénarmont. The proposed methods can effectively replace manual methods of compensation (goniometric compensation of Tardy and Sénarmont, Babinet and Babinet-Soleil compensators) provided by current standards on the analysis of residual stresses in glasses.     

Correction of wave-front retrieval errors caused by the imperfect collimation of reference beam in phase-shifting interferometry

In phase-shifting interferometry (PSI) the standard wave retrieval formulae are usually derived based on the condition of a plane reference beam normal to the recording plane. In practice, however, the reference wave may be a spherical wave of large radius or even have a slight inclination at the same time due to the imperfect collimation and coaxality of the optical system, and this fact will introduce phase distortion for the reconstructed object wave-front. A simple digital processing algorithm without any additional measurements is proposed to determine the unknown parameters of the spherical reference wave and then correct the object wave errors reconstructed with standard wave retrieval formulae. The effectiveness of this method is verified by a series of computer simulations, and its limitation is also discussed.     

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.     

Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry

The phase error and its periodic behavior caused by the partial intensity saturation of fringe patterns in the digital projection grating phase-shifting profilometry are studied. A saturation coefficient K is defined to describe the saturation degree of the fringe patterns projected on a measured object. The distribution of the phase error is analyzed through a simulation method. Moreover, a novel phase-recovering algorithm is studied to resolve the phase error issue introduced by the partial saturated fringe patterns. The real phase can be recovered by the unsaturated intensity values. A series of results corresponding to different degrees of saturation defined by K are given to prove the validity of the proposed algorithm.     

Removal of carrier frequency in phase-shifting techniques

The existence of carrier frequency is unavoidable in many phase-shifting techniques. It makes the phase-unwrapping procedure more difficult, especially when speckle-like noise exists in the wrapped phase map. In this paper, it is shown that the carrier frequency is approximately equal to the average of the first difference of the phase. To remove the carrier frequency, we compute the first difference of the phase before attaining the phase map, subtract the average of the first difference, and integrate to get the phase map without carrier frequency. Computer simulation and experimental results show this method as being profitable for phase unwrapping.     

Digital speckle interferometry for assessment of surface roughness

In this work, the principle of interferometry is used to assess the surface roughness of the machined surfaces. Interferometry produces an interference fringe pattern when two or more light waves interact with each other. It is one of the important tool for precision optical metrology and testing. Well-known advantages of the phase shifting interferometry include high measurement accuracy, rapid measurement, good result even with low contrast fringes and that the polarity of the wave front can be determined. In fringe projection techniques, a known optical fringe pattern is projected onto the surface of interest. The fringe pattern on the surface is perturbed in accordance with the profile of the test surface, thereby enabling direct derivation of surface profile.In this work, an attempt has been made to assess the surface roughness using a speckle fringe analysis method of five frame phase shift algorithm for machined surface (ground surface). As these fringes are too noisy, advanced filtering technique has been used so as to reduce noise and to get improved wrapped phase map from the phase shifted fringes. A phase unwrapping software has been developed using discrete cosine transform (DCT) to generate the three-dimensional (3-D) profiles. Finally, it is compared with R_a values measured using a mechanical stylus instrument, showing good agreement.     

Error compensation in two-step triangular-pattern phase-shifting profilometry

This paper presents an analysis of error compensation using a newly modified two-step triangular-pattern phase-shifting measurement method, developed to reduce periodic measurement errors due to gamma nonlinearity and defocus of the projector and camera. Experimental analysis revealed that a trade-off is necessary in choosing a higher minimum projector input intensity to use the more linear region of input-to-output intensity mapping, and a lower minimum input intensity for greater dynamic range of input intensity. The modified two-step triangular-pattern phase-shifting method performs two-step triangular-pattern phase-shifting twice, the second time with an initial phase offset of one-eighth of the pitch, and generates the three-dimensional object height distribution by averaging the two obtained object-height distributions. The modified two-step triangular-pattern phase-shifting method consistently had higher measurement accuracy than the unmodified method. Errors were reduced by 23.4% at the midrange of depth using an input intensity value of 40, which yielded the highest measurement accuracy and up to 64% and 54% at small and large depths, respectively.     

A method for calibrating the position error of phase retrieval with transverse translation diversity in optical wavefront measurement

We present a method for calibrating the position error of phase retrieval with transverse translation diversity in optical wavefront in situation where the position error sharply influences algorithm precision. This method involves testifying that the essence of the position error in phase retrieval is the translation in frequency domain and the minimum of iterative error against position error reaches when there is no position error. Then the least square method is used for fitting the relationship between the iterative error and the assumed position error in polynomial function. The computer simulations used to prove the validity of this method are described. The results indicated that this method can calibrate the position error to approximately 1/500 mm which nearly has no influence on the phase retrieval.     

New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor

White-light phase shifting interferometry (WLPSI) is frequently used for the precision measurement of 3D patterns in various fields. Phase error is one of the most dominant errors in WLPSI, and it is mainly generated by the scanner positioning error and mechanical vibrations. In this paper, phase error detection method by image analysis is proposed, and the numerical correction method for minimizing the phase error is also proposed. The image reconstruction method (IRM), iterative IRM (IIRM) as pre-processors, partial IRM (PIRM), least squares method (LSM) as a main processor, and surface compensation method (SCM) as a post-processor were developed for correcting phase errors. The five methods are implemented and simulated, and the pros and cons of each method are explained.Mirau type interferometry and the phase error generator using a PZT stage were used, and the measurements by WLPSI were done under various vibration conditions. The captured images were analyzed by the five correction methods, and the results were compared. Phase error was effectively minimized by the correction methods, and repeatability of 0.2 nm was obtained in the case of the specimen of 500 nm in height. Repeatability of 10 nm was obtained by conventional WLPSI algorithms for the same specimen.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.