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.     

Three-dimensional phase step profilometry with a multicore optical fiber

This paper demonstrates the feasibility of using phase stepping and a multicore optical fiber to calculate an object's depth profile. An interference pattern is projected by an optical fiber onto the object. The distorted interference pattern containing the object information is captured by a CCD camera and processed using a phase step interferometry method. The phase step method is less computationally intensive compared to two-dimensional Fourier transform profilometry and provides more accuracy when measuring objects of high frequency spatial variations.     

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.     

Fringe visibility analysis with different scale apertures in speckle photography

Abstract

The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.     

Hybrid optical-digital method for local-displacement analysis by use of a phase-space representation

A method for evaluating the local deformation or displacement of an object in speckle metrology is described. The local displacements of the object in one direction are digitally coded in a one-dimensional specklegram. By optically performing the local spectrum of this pattern, one simultaneously achieves information about the local displacement and its spatial position. The good performance of this technique is demonstrated with computer-generated test signals.     

Optical processing with vortex-producing lenses

We discuss two types of optical processing using vortex-producing angular phase plates. In the most common spatial-filtering operation, an input object is Fourier transformed (either by Fraunhofer diffraction or with a lens system). The Fourier transform is then multiplied by an angular phase pattern, and the product is again Fourier transformed. The output is a space-invariant, edge-enhanced version of the input object. Alternatively we can directly image the object using a lens multiplied by the angular phase. The space-variant image is severely distorted along the optical axis of the system. We encode the phase plates onto a liquid-crystal display and present experimental results on both systems.     

High-resolution scanning phase retrieval with a probe beam of unknown modulus

A high-resolution phase-retrieval method for an imaging system with scanning illumination that is capable of reconstructing the modulus and phase of an object without a holographic reference wave is proposed. Reconstruction involves the synthesis of the reconstructed objects from the data of zero- and higher-frequency components of two Fourier intensity measurements: the Fourier intensity of the product of the object and a probe beam that is scanned across the object and the Fourier intensity of the product of the object and a probe beam that is modulated with an exponential filter. This method improves on the resolution of a reconstructed object by previous methods that make use of the data of only the zero-frequency components of the two Fourier intensities. In addition, phase retrieval in the scanning-illumination system with a probe of unknown modulus can be treated by use of the synthetic procedure, provided the phase of the probe function is a constant or a known distribution. Computer-simulated examples of the reconstruction of one- and two-dimensional complex objects demonstrate that reconstruction is robust.     

A New Approach to Two-dimensional Phase Retrieval

This paper proposes a method for solving the phase retrieval problem from the observed modulus at the Fourier transform plane of an object in two dimensions. This method consists of the logarithmic Hilbert transform in one dimension, based on the reduction by the sampling theorem of the two-dimensional (2-D) Fourier transform of the object to the one-dimensional (1-D) Fourier transform of an effective object function. The usefulness of the method is shown in computer simulation studies of the phase retrieval from the 2-D modulus at the Fourier transform plane, for the 2-D real and positive objects. The zero information in the complex lower half-plane must be obtained from another observation for the phase evaluation using the logarithmic Hilbert transform.     

Specklegram in a multiple-mode fiber and its dependence on longitudinal modes of the laser source

A specklegram in a multimode fiber (MMF) has successfully been used as a sensor for detecting external disturbance. Our experiments showed that the sensitivity in the sensor with a multiple longitudinal-mode laser as its source was much higher than that with a single longitudinal-mode laser. In addition, the near-field pattern observations indicated that the coupling between different transverse modes in the MMF is quite weak. Based on the experimental results, a theoretical model for the speckle formation is proposed, taking a bend-caused phase factor into consideration. It is shown in the theoretical analysis that the interferences between different longitudinal modes make a larger contribution to the specklegram signals.     

Three-dimensional displacement measurement for diffuse object using phase-shifting digital holography with polarization imaging camera

The amount of displacement of a diffused object can be measured using phase-shifting digital holography with a polarization imaging camera. Four digital holograms in quadrature are extracted from the polarization imaging camera and used to calculate the phase hologram. Two Fourier transforms of the phase holograms are calculated before and after the displacement of the object. A phase slope is subsequently obtained from the phase distribution of division between the two Fourier transforms. The slope of the phase distribution is proportional to the lateral displacement of the object. The sensitivity is less than one pixel size in the lateral direction of the movement. The longitudinal component of the displacement can be also measured separately from the intercept on the phase axis along the phase distribution of the division between two Fourier transforms of the phase holograms.     

Phase evaluation and speckle averaging in pulsed television holography

Double-pulsed (image-plane) TV holograms of transient bending waves in plates are recorded on separate frames in a CCD camera. A small angular offset between the reference and object beams, giving a spatial-frequency bias to the recorded pattern, permits quantitative evaluation of the phase of the interference. The Fourier spectrum of the image exhibits distinct parts that can be filtered out and inverse transformed to yield the phase information. Three different apertures of the imaging system are tested: a single slit, a double slit, and a three-hole aperture. Spatial speckle averaging is possible in the cases of the double-slit and three-hole apertures.     

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.     

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.     

Object-image-based method to construct an unweighted quality map for phase extraction and phase unwrapping

A method to construct an unweighted quality map for phase extraction and phase unwrapping is proposed, based on an object image pattern. The object image pattern must be recorded under the same conditions as that of the corresponding interference patterns, except that the lights coming from the reference arm of the interferometer are hidden. An unweighted quality map that can represent the valid and invalid regions in the interference patterns is completed successfully, based on two factors: the fact that the object region in the object image pattern is homologous with the valid region (i.e., the interference region) in the interference patterns, and on distinguishing between the object and background regions in the object image pattern using neighbor window threshold filtering and fitting the boundary of the object image. The application of the proposed method to the real measurement shows its feasibility and correctness. This paper might provide an alternative method for constructing an unweighted quality map for phase extraction and phase unwrapping.     

Multi-directional shearography based on multiplexed Mach–Zehnder interference system

ABSTRACT

Shearography is only sensitive to deformation in the shearing direction, and the deformation of object defects after loading may occur in multiple directions. This work reports a multi-direction shearography system that uses spatial phase-shift methods to detect the object from multi-shearing directions, effectively avoiding the missed detection of directional defects. A single laser is utilized to illuminate an object, and a single CCD camera records images in the multiplexed Mach–Zehnder interference system. First, the aperture stops in suitable size and location are set to produce different spatial carrier frequencies. Second, the shearing amount is independently adjusted by using different devices. Finally, the Fourier transform method is used to extract the phase information from the frequency domain. This system can be used for nondestructive testing of multi-directional defects and the feasibility of the method is verified by theoretical analysis and experiment.     

Speckle Method for the Measurement of Helical Motion of a Rigid Body

The helical motion of an object having the rotation axis parallel to the axis of the optical system is measured by the double exposure speckle technique. The object is illuminated with a multimode dye laser light, and the amounts of the rotation angle as well as the translation are obtained from the interference fringes modulating the optical Fourier transforms of specific points on the exposed photographic plate.     

Simultaneous multidimensional deformation measurements using digital holographic moiré

This paper proposes an elegant technique for the simultaneous measurement of in-plane and out-of-plane displacements of a deformed object in digital holographic interferometry. The measurement relies on simultaneously illuminating the object from multiple directions and using a single reference beam to interfere with the scattered object beams on the CCD plane. Numerical reconstruction provides the complex object wave-fields or complex amplitudes corresponding to prior and postdeformation states of the object. These complex amplitudes are used to generate the complex reconstructed interference field whose real part constitutes a moiré interference fringe pattern. Moiré fringes encode information about multiple phases which are extracted by introducing a spatial carrier in one of the object beams and subsequently using a Fourier transform operation. The information about the in-plane and out-of-plane displacements is then ascertained from the estimated multiple phases using sensitivity vectors of the optical configuration.     

Diffraction tomography reconstruction algorithms for quantitative imaging of phase objects.

A new reconstruction algorithm for phase-object imaging is proposed that is based on the principle of diffraction tomography and utilizes the Fourier transformation property of a finite-size phase object. From the measured scattered intensity, the imaginary part of the Fourier transform of the object can be extracted, and the three-dimensional structure of the object can be reconstructed. Numerical simulations show that the algorithm also can be used for a weak absorption object if the phase shift is much larger than the absorption.     

Measurement of small rotation angles by using a parallel interference pattern

We propose a method for measuring rotation angles by using a parallel interference pattern. At two points on a parallel interference pattern reflected by an object, we detect phase changes in the reflected parallel interference pattern caused by rotations of the object. A high sensitivity, or a high ratio of the phase change to the rotation angle, 17 mrad/arcsec, can be achieved by determining the positions of two detection points. A high spatial resolution of ~0.5 mm is also obtained. We analyze the measurement error caused by the alignment of the parallel interference pattern and a random measurement error caused by the phase detection. The theoretical analyses and the experimental results make the characteristics of the method clear and show that the method has an accuracy of 0.2 arcsec for small rotation angles.     

基于傅里叶变换的点衍射干涉术

在相移算法的点衍射干涉术的基础上,提出了基于傅里叶变换的点衍射干涉测量术.基于傅里叶变换的点衍射干涉测量术是一种建立在点光源衍射干涉理论基础上的测量方法,它采用傅里叶条纹分析方法来求解干涉条纹的相位分布,运用基于BFGS的拟牛顿算法进行三坐标的迭代计算,确定点光源的三维空间坐标.通过计算机模拟实验,验证了该方法在有噪声干扰的情况下,可以有效降低干扰噪声对测量的影响.