Three-dimensional Displacement Analysis by Windowed Phase-shifting Digital Holographic Interferometry

Abstract:  Phase-shifting digital holography is a new method for measuring the displacement distribution on the surface of an object. The authors previously proposed a windowed phase-shifting digital holographic interferometry (windowed PSDHI). This method provides accurate displacement distributions by decreasing the effect of speckle patterns. In this study, the method is extended to analyse three-dimensional displacement components in a microscope. Three object laser beams in the optical system are used. Four phase-shifted holograms are recorded for each object laser beam. The complex amplitude of each reconstructed light at the object is calculated by the Fresnel diffraction integral of the complex amplitude of the hologram. The reconstructed distance is obtained at the point with the maximum of the standard deviation of the intensities of the object reconstructed with changing the reconstruction distance. The three phase-difference values between before and after deformation provide the three-dimensional displacement components. Theoretical treatment and experimental results of three-dimensional displacement measurement using this method are shown.     

Denoising in digital speckle pattern interferometry using fast discrete curvelet transform

In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.     

Measurement of Surface Shape and Position by Phase‐Shifting Digital Holography

Abstract: Phase‐shifting digital holography is applied to measure the shapes and positions of rough surfaces from the averaged conjugate product of the reconstructed complex amplitudes, named complex coherence factor, corresponding to dual wavelengths. The phase of the averaged product at the object plane provides the shape of the surface, whereas the peak position of the modulus with respect to reconstruction distance provides the position of the surface. The phase is almost free from speckle noise and easy to be unwrapped. The resultant resolution of surface shape amounts to a few tens of micrometres. The sensitivity of the position measurement that requires no marking on the object is several per cent of object distance from a charge‐coupled device (CCD). The method corresponds to the detection of the position of maximum contrast of the fringes to be observed in conventional holographic interferometry. It makes use of fringe phase for shape measurement and fringe contrast for position measurement. Both the theory explaining the principle and experimental results are presented.     

Measurement of nanometric displacements by correlating two speckle interferograms

This paper presents a method to measure nanometric displacement fields using digital speckle pattern interferometry, which can be applied when the generated correlation fringes show less than one complete fringe. The method is based on the evaluation of the correlation between the two speckle interferograms generated by both deformation states of the object. The performance of the proposed method is analyzed using computer-simulated speckle interferograms. A comparison with the performance given by a phase-shifting technique is also presented, and the advantages and limitations of the proposed method are discussed. Finally, the performance of the proposed method to process real data is illustrated.     

Vibration measurement by temporal Fourier analyses of a digital hologram sequence

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.     

Digital holographic interferometry for simultaneous orthogonal radial vibration measurements along rotating shafts

A digital holographic interferometry setup used to measure radial vibrations along a rotating shaft is presented. A continuous Nd:YAG laser and a high-speed digital camera are used for recording the holograms. The shaft was polished optically smooth to avoid speckle noise from the rotating surface. The light reflected from the shaft was directed onto a diffuser which in turn was imaged by the holographic system. Simultaneous measurements with a laser vibrometer were performed at one point and comparisons between the signals showed good agreement. It is shown that different vibration components of a rotating shaft can be simultaneously measured with this technique.     

Miniaturized digital holography sensor for distal three-dimensional endoscopy

A miniaturized sensor head for endoscopic measurements based on digital holography is described. The system was developed to measure the shape and the three-dimensional deformation of objects located at places to which there is no access by common measurement systems. A miniaturized optical sensor, including a complete digital holographic interferometer with a CCD camera, is placed at the end of a flexible endoscope. The diameter of the head is smaller than 10 mm. The system enables interferometric measurements to be made at speeds of as many as five reconstructions per second, and it can be used outside the laboratory under normal environmental conditions. Shape measurements are performed with two wavelengths for contouring, and the deformation is measured by digital holographic interferometry. To obtain full three-dimensional data in displacement measurements we illuminate the object sequentially from three different illumination directions. To increase the lateral resolution we use temporal phase shifting.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

Speckle Reduction by Unidirectional Averaging

It is shown that for the holographic reconstruction of diffuse objects the use of a vibrating coherent source decreases the contrast of the speckle pattern, and that for certain classes of objects resolution is not affected. This is true in particular for grating-like objects when the source is vibrated in a direction parallel to the lines of the grating, and an important application is to the pattern of straight, parallel fringes commonly obtained in holographic interferometry. When a more complex object is used, the speckle reduction would be accompanied by a loss of resolution.     

Measurement error caused by speckle noise in heterodyne and quasi-heterodyne holographic interferometry

In heterodyne and quasi-heterodyne holographic interferometry, the measuring accuracy is limited by speckle noise. It is important to know the relation between measurement accuracy and speckle noise in both theory and application. This problem has been discussed in the past under the assumption that the speckle noise produces only a small measuring error. However, this assumption is not reasonable in practice. The effect of speckle noise on the measurement accuracy is analyzed by the use of a general statistical method. The results obtained reveal the general relation between the measuring accuracy and system parameters, and thus constitute important guidelines to the application of these techniques.     

Application of Double‐Focus Speckle Interferometry for Non‐Destructive Testing

Abstract: This paper deals with the application of a speckle interferometer, which works on the new operating principle of double‐focusing presented by the authors in recent studies, to the field of non‐destructive testing (NDT). Using this interferometer, the components of displacement given by holographic interferometry can be measured, but with no need for an external reference beam. The implementation of this interferometry can be indifferently carried out by adopting a Michelson or a Mach–Zender configuration. In the paper a double‐focus interferometer based on the Michelson design and sensitive to out‐of‐plane displacements was implemented and applied to a metallic specimen which simulates the deformations of a typical debonding.     

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.     

数字散斑干涉在振动测量中的应用

在动态测试领域中,数字散斑干涉技术常用到的相位处理方法有时问平均法和空间载波相移法.空间载波相移法因其简单性和实用性,被应用于双脉冲散斑干涉测量中.     

Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors

The advantages of spatial phase shifting (SPS) compared with temporal phase shifting in the field of electronic speckle pattern interferometry are described. Some periodic phase reconstruction errors occurring in SPS are discussed. It is shown that these errors become minimal for a spatial phase-shift angle of 2pi/3. Furthermore, a modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced.     

Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying quantities like the object-illuminating intensity, the beam ratio, the speckle size and shape, and the fringe density allows characteristic behaviors of both phase-shifting methods to be explored.     

ESPI Measurements of Strain on a CFRP‐Reinforced Bending Beam1

Abstract: This paper presents 3D electronic speckle pattern interferometry (ESPI) measurement results of strain components at the end of a carbon‐fibre reinforced polymer (CFRP) plate adhesively bonded to a reinforced concrete beam. To minimise speckle decorrelation because of the inevitable rigid‐body motion of the measured specimen, the load was increased in small increments. Two evaluation schemes are compared: the step‐by‐step addition of the measured displacement components and regain of the correlation by image shifting. Strain is evaluated by interpolating the in‐plane displacement measurements along selected lines, and is compared with results from finite element analysis (FEA). An uncertainty estimate is given.     

Digital holographic interferometry for measurement of temperature in axisymmetric flames

In this paper, experimental investigations and analysis is presented to measure the temperature and temperature profile of gaseous flames using lensless Fourier transform digital holographic interferometry. The evaluations of the experimental results give the accuracy, sensitivity, spatial resolution, and range of measurements to be well within the experimental limits. Details of the experimental results and analysis are presented.     

High resolution speckle interferometry using virtual speckle pattern produced by information of deformation process

A high resolution new fringe analysis method for ESPI with only one camera is proposed by using features of speckle interferometry in a deformation process of a measured object. The profile of intensity of each speckle of the speckle patterns in the deformation process is analyzed by the Hilbert transform. A virtual speckle pattern for creating a carrier fringe image is produced artificially by using the information of profiles of intensities of speckles. The deformation map of the measured object can be detected by the virtual speckle pattern in an operation based on the spatial fringe analysis method. Experimental results show that the difference between the results by the new and the ordinary methods is 0.1 rad as standard deviation. From the results, it is confirmed that the high resolution measurement can be performed by this method the same as compared to the ordinary measurement method which needs to employ three speckle patterns.     

数字同轴和数字离轴全息系统分析

利用最高空间频率分析法,通过逐点分析记录在 CCD 上的空间频率信息,研究了物体可允许记录的最大横向尺寸、最小记录距离、全息图的信息量、空间分辨力、再现像的横向分辨力、轴向分辨力及散斑大小,并得到了数学表达式。理论分析和实验结果表明,数字同轴全息系统放宽了对 CCD 分辨力的要求,有较高的分辨力,较低的散斑噪声、灵活、简单的系统结构及较高的 CCD 空间带宽利用率,在增强系统性能方面要优于数字离轴全息系统。这一研究为数字全息系统的设计和操作提供了一定的理论和实验指导。     

Spatiotemporal digital microholography

We develop the theoretical background of a holographic method in which the hologram is sampled simultaneously in space and in time by a charge-coupled device (CCD) sensor. With the use of temporal heterodyning (rather than spatial heterodyning, which is employed in conventional holography), in-line, single-sideband holograms of fields having an arbitrary degree of spatial coherence are recorded in an exposure time that can theoretically be as short as four frames of the CCD. The method is applied to microholography and is shown to avoid the main drawbacks of conventional holographic microscopy, namely, the need for high-spatial-bandwidth detectors and for a high degree of spatial coherence, which unavoidably leads to speckle noise. The possibility of a posteriori aberration compensation is demonstrated, and experimental results are presented.