Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors

Quasi-monochromatic light will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of the illuminated object. In a prior paper [J. Opt. Soc. Am. A 19, 444 (2002)], it was shown that two intensities of two speckle patterns and their interference are sufficient to produce an unambiguous (except for object translation) band-limited image of the object, based on a root-matching technique described therein, in the absence of measurement error and in the case of distinct roots of the field polynomials and their complex conjugates. On the other hand, algorithms based on the root-matching technique are found to be slow and sensitive to noise. So motivated, several other techniques are applied to the problem, including phase retrieval, expectation maximization, and statistical maximization. The phase-retrieval and expectation-maximization techniques proved to be most effective for reconstructions of complex objects larger than 10 pixels across, and high-quality images were formed by using three independent sets of two-field data (three frames of two-wavelength data), each comprising two speckle intensity patterns and their interference. Two additional results of note are reported. First, the expectation-maximization algorithm produced relatively good images when three or more frames each of only one speckle intensity pattern (data at just one wavelength) were used and second, the phase-retrieval algorithm when only the object autocorrelation was used also produced relatively good images for the chosen test object.     

Vibration Phase‐Based Ordering of Vibration Patterns Acquired With a Shearing Speckle Interferometer and Pulsed Illumination

Abstract: A method for both temporal and spatial characterisation of harmonic vibrations is presented. The method is based on simultaneous acquisition of phase‐stepped speckle interference patterns using a shearing speckle interferometer and the vibration phase for a series of vibration states within the vibration period. An unsynchronised free‐running pulse laser is used for illuminating a vibrating object yielding speckle interference patterns in random vibration phase order. Two π/2 phase‐stepped speckle interference patterns are acquired simultaneously for each recorded vibration state. The data set is sorted using vibration phase as the sorting key. The sorted speckle interference patterns are processed using a two‐bucket algorithm for the calculation of phase difference and by applying temporal phase unwrapping to finally obtain unwrapped phase distributions for any vibration state of the vibration cycle.     

Speckle-based three-dimensional velocity measurement using spatial filtering velocimetry

We present an optical method for measuring the real-time three-dimensional (3D) translational velocity of a diffusely scattering rigid object observed through an imaging system. The method is based on a combination of the motion of random speckle patterns and regular fringe patterns. The speckle pattern is formed in the observation plane of the imaging system due to reflection from an area of the object illuminated by a coherent light source. The speckle pattern translates in response to in-plane translation of the object, and the presence of an angular offset reference wave coinciding with the speckle pattern in the observation plane gives rise to interference, resulting in a fringe pattern that translates in response to the out-of-plane translation of the object. Numerical calculations are performed to evaluate the dynamic properties of the intensity distribution and the response of realistic spatial filters designed to measure the three components of the object's translational velocity. Furthermore, experimental data are presented that demonstrate full 3D velocity measurement.     

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.     

Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors

Quasi-monochromatic light will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of the illuminated object. Further information can be obtained if two colors of coherent light are used, provided that the colors are sufficiently close in wavelength that the interference is also measurable. It is shown that no more than two intensities of two speckle patterns and their interference are required to produce an unambiguous band-limited image of an object, to within an overall spatial translation of the image, in the absence of measurement errors and in the case where all roots of both fields and their complex conjugates are distinct. This result is proven with a root-matching technique, which treats the electric fields as polynomials in the pupil plane, the coefficients of which form the desired complex object. Several root-matching algorithms are developed and tested. These algorithms are generally slow and sensitive to noise. So motivated, several other techniques are applied to the problem, including phase retrieval, expectation maximization, and probability maximization in a sequel paper [J. Opt. Soc. Am. A 19, 458 (2002)]. The phase-retrieval and expectation-maximization techniques proved to be most effective for reconstructions of complex objects larger than 10 pixels across.     

Improvement of accuracy in digital holography by use of multiple holograms

Speckle pattern decorrelation reduces the accuracy of interferometric shape and deformation measurements. We introduce a technique for the reduction of speckle noise in digital holography. The method is not based on classical filtering techniques such as median filters. Instead it utilizes the shift theorem of the Fourier transform. For this method several holograms of the same object under test are recorded. The reconstruction leads to a set of object wave fields with different speckle patterns. A proper averaging procedure, taking into account the properties of the wrapped phases, leads to an improvement of the accuracy in the resulting phase difference. The theory of the applied method is described and our first results for technical components with an improvement of accuracy up to 1/57 of the wavelength are presented.     

Three-dimensional mapping and range measurement by means of projected speckle patterns

We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.     

Additive-Subtractive Two-Wavelength ESPI Contouring by Using a Synthetic Wavelength Phase Shift

The addition correlation of two speckle fields by simultaneousillumination at different wavelengths is used for object contouring ina Twyman-Green-type interferometer. Fringe visibility is enhancedwhen the stochastic speckle background intensity obtained from areference plane modulation is subtracted. We calculate the contourphase map by using a phase-shift algorithm in the syntheticwavelength. A comparison with a sequential illumination, phasedifference method based on a laser wavelength phase shift isgiven. The test setup does not need to be stable on aninterferometric scale, and therefore a method is provided that lendsitself to applications in noisy environments.     

Computer-aided speckle pattern interferometry

An on-line computer system for measuring the deformation of a diffuse object with a speckle interferometer is presented. Methods for evaluating a speckle interferogram using digital image processing techniques are also discussed. The system consists of an interferometric optical setup and a computer-TV image processing facility. A speckle interferogram is generated arithmetically between two digitized speckle patterns before and after deformation of the object. The information about the deformation is extracted by two procedures in analyzing the interferogram: (a) automatic analysis using digital image processing techniques such as gray scale modification, linear spatial filtering, thresholding, and skeletoning; (b) man-machine interactive method for simple high-speed processing of the interferogram using a light pen. The determined fringe order numbers are interpolated and differentiated spatially to give strain, slope, and bending moment of the deformed object. Some examples of processed patterns are presented.     

Disk-growing algorithm for phase-map unwrapping: application to speckle interferograms

Interferometric techniques combined with phase shifting allow computation of the phase that is linked to the displacement of the object under study. The phases before and after displacement are computed from three or more interferograms (called specklegrams when speckle is used as the information carrier). Subtraction of these two phase patterns leads to a raw phase map. Phase unwrapping restores the 2π discontinuities and gives a continuous phase map. The disk-growing algorithm presented allows the inner and the outer propagation of the unwrapping from a growing disk and so avoids the main problem of anisotropic error propagation for noisy phase maps. It works successfully in speckle interferometry.     

The Extension of the Electronic Speckle Photography to the Measurement of In-Plane Displacement

In this paper, a modified speckle photography technique is demonstrated for the measurement of a variable range of the in-plane displacement. The modification focuses on coupling the diode pump solid state laser DPSS with the conventional speckle photography technique. The DPSS laser emerges different wavelengths to provide speckle patterns of suitable size to measure the desired range of the in-plane displacement. The second harmonic generation in a nonlinear crystal of wavelength 532 nm and the principle diode laser wavelength 808 nm are employed in identifying the object positions within a lateral displacement made by a standard linear stage in the range from few microns up to 1.2 mm. The sensitivity and the correlation of the speckles formed by both wavelengths suit both small and large movements. A continues measurement by the modified technique can be achieved by identifying a scale factor in the uniform area in which both wavelengths are effective, and high correlation between the results obtained by 532 and 808 nm is maintained. The uncertainty in measuring 1.2 mm lateral movement by the modified speckle photography is found to be 26.8 μm.     

Phase-error correction in digital holography

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.     

Electronic speckle pattern interferometry based on spatial information using only two sheets of speckle patterns

Abstract

Speckle interferometry is an important deformation measurement method for an object with a rough surface. In this paper, a novel fringe analysis method is proposed that uses a new optical system, which uses a plane wave as the reference beam of the speckle interferometer. When the optical system is employed in fringe analysis, the deformation information and the bias components of the speckle patterns are clearly separated in the frequency domain. Therefore, the deformation information can be readily extracted using a Fourier transform, which gives a pair of real and imaginary components concerning the information. The specklegram is calculated using such a pair of components, and the phase map is obtained from the specklegram. Experimental results confirmed that the resolution power of this measurement method is higher than 1/261 of the wavelength of the light source of the optical system.     

Phase object data obtained from defocused laser speckle displacement

An optical technique that is based on defocused digital speckle photography is proposed for the evaluation of phase objects. Phase objects are different kinds of transparent or semi-transparent media that allow light to be transmitted. A phase object inserted in a laser speckle field introduces speckle displacement, from which information about the object may be extracted. It is shown that one may use speckle displacements to determine both the phase gradients and the positions of phase objects. As an illustration the positions and focal lengths of two weak lenses have been derived from defocused laser speckle displacement.     

Application of bispectral speckle imaging to near-diffraction-limited imaging in the presence of unknown aberrations

A laboratory experiment that demonstrates near-diffraction-limited imaging of a detailed object in the presence of unknown fixed aberrations in the imaging system is described. A random-phase plate is introduced in a pupil plane of the imaging system to eliminate the effect of fixed aberrations in the system. We employ a bispectral speckle imaging technique to recover the object from speckled images affected by both the random-phase fluctuations induced by the random-phase plate and the fixed aberrations present in the imaging system. For the case where the random phase is assumed to obey Gaussian statistics an approximate form of the bispectral speckle transfer function is obtained with an asymptotic expansion. This approximate form of the transfer function shows the diffraction-limited nature of bispectral speckle imaging when the standard deviation of the random-phase fluctuations is of the order of a wavelength of light. Experimental results are presented for fixed aberrations associated with lens tilt and defocus in the imaging system.     

Speckle-reduced three-dimensional volume holographic display by use of integral imaging

We propose a method to implement a speckle-reduced coherent three-dimensional (3D) display system by a combination of integral imaging and photorefractive volume holographic storage. The 3D real object is imaged through the microlens array and stored in the photorefractive crystal. During the reconstruction process a phase conjugate reading beam is used to minimize aberration, and a rotating diffuser located on the imaging plane of the lens array is employed to reduce the speckle noise. The speckle-reduced 3D image with a wide viewing angle can be reconstructed by use of the proposed system. Experimental results are presented and optical parameters of the proposed system are discussed in detail.     

Use of dynamic electronic speckle pattern interferometry with the Hilbert transform method to investigate thermal expansion of a joint material

A dynamic electronic speckle pattern interferometry method is applied to investigate thermal expansion of a joint material (ceramic-stainless steel) as a practical industrial object. The speckle interference signal is considered in the temporal domain and the phase is analyzed by the Hilbert transform method. Errors caused by the bias and modulation variations over the phase values are first examined by numerical simulation. Two experiments are performed with in-plane and out-of-plane sensitive systems to study the 3D deformation field thoroughly. The deformation field showed clearly the difference between the thermal expansions of the stainless steel and ceramic. It was also revealed that the boundary of materials and its vicinity suffer very large thermal strain due to the significantly large difference in the linear coefficient of thermal expansions.     

基于快速散斑结构光三维重建的在线测量系统

在流水生产线中实现工件表面三维信息的快速获取及尺寸的快速测量是当前辊压成形等制造业智能化升级过程中的迫切需求。基于散斑投影的三维重建方法仅需利用单幅物体散斑图像即可重建出物体表面的三维数据,在流水线工件快速测量中具有一定优势。本文对散斑三维重建中较为耗时的对应点搜索算法进行了优化,并在此基础上研制出适用于辊压成形制造生产线的工件快速三维测量系统。实验结果显示,该系统具有较快的三维数据重建速度,测量误差在0.035 mm范围内,能够满足辊压成形工件三维结构尺寸的快速在线测量需求。     

Wavelet analysis of speckle patterns with a temporal carrier

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer. The intensity variation of each pixel on recorded images is then analyzed along the time axis by a robust mathematical tool, i.e., a complex Morlet wavelet transform. After the temporal carrier is removed, the absolute displacement of a vibrating object is obtained without the need for temporal or spatial phase unwrapping. The results obtained by a wavelet transform are compared with those from a temporal Fourier transform.     

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.