Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)

Co-linear common-path shearography with a zero-approaching shear amount and separate control of the spatial carrier for single-shot phase measurement

A co-linear common-path shearography is proposed with spatial phase shift for single-shot phase measurement. The co-linear common-path configuration brings an enhanced robustness and stability of the measuring system, because the two laterally sheared interfering object waves propagate essentially along the same path, which cancels out the disturbance and noise in surroundings. Two functional features, which break through the limitations in conventional co-linear common-path shearography, are proposed and implemented, namely the zero-approaching shear amount and the separate control of the spatial carrier. Seldom shearography configured by co-linear common-path structure possesses with these two features, because the linearly aligned optics restricts the control parameters in regards to the shear amount and the spatial carrier. In the proposed scheme, an intermediate real image plane is created in the linearly aligned light path to address the issue of zero-approaching shear amount. A 4-f imaging system is embedded with an aperture in between to implement a separate control of the spatial carrier. The zero-approaching shear amount provides the sufficiently small shear to make sure the strain or slope field of complex deformation is resolvable. Meanwhile, the separate control of the spatial carrier further guarantees a well-distributed spatial frequency spectrum when the required zero-approaching shear amount is configured.

Binarization for low-quality ESPI fringe patterns based on preprocessing and clustering

Massive inherent speckle noise and extremely low contrast make it difficult to binarize electronic speckle pattern interferometry (ESPI) fringe patterns. In this paper, we present a binarization based on preprocessing and fuzzy C-means (FCM) clustering for low-quality ESPI fringe patterns. First, we use the multiscale retinex (MSR) algorithm to enhance the original fringe pattern to improve the contrast between the bright and dark fringes. Then, the local entropy of the enhanced fringe pattern is calculated and the second-order oriented partial differential equation algorithm is introduced to filter the local entropy map. Finally, the FCM is applied to cluster the local entropy filtering map, and the pixels of the fringe pattern are classified into two categories: bright fringes and dark fringes. To verify the reliability and universality of the proposed method, we provide a qualitative evaluation of six experimental ESPI subtraction fringe patterns and two computer-simulated ESPI addition fringe patterns. Experimental results exhibit that the proposed method can provide good binarization performances.

Measurement of In-Plane Displacement in Two Orthogonal Directions by Digital Speckle Pattern Interferometry

The measurement of in-plane displacement in two orthogonal directions is of considerable significance for modern industries. This paper reports on a spatial carrier phase-shift digital speckle pattern interferometry (DSPI) for the simultaneous measurement of in-plane displacement in two orthogonal directions. The object is illuminated from a single direction and observed from four symmetrical directions simultaneously. One pair of the four observation directions is sensitive to in-plane displacement in one direction, and the other pair is sensitive to in-plane displacement in the perpendicular direction, resulting in the displacement in two directions being measured independently. The polarization property of light is used to avoid cross-interference between the two pairs of beams. Spatial carrier frequencies are generated by aperture misalignment, and the displacement in two directions is modulated onto the same interferogram. With a spatial carrier phase-shift technique, the displacement can be separated in the frequency domain and the phase can be evaluated from a single interferogram in real time. The capability of DSPI is described by theoretical discussions and experiments.

Dual-directional shearography based on a modified common-path configuration using spatial phase shift

This paper describes a dual-directional shearography system to address the issue of two-dimensional characterization of the surface strain. A common-path configuration coupled with an additional light path is used to provide the shearing in two directions. One of the three interfering beams is shared by both directional shearograms to improve the light efficiency and enhance the robustness of the system. The two directional shearograms are carried by different spatial carriers to distinguish one from the other. The spatial carrier is introduced by the single-aperture-lens Wollaston prism configuration. Rather than the conventional method in which the aperture is fixed at the front focal point of the imaging lens, a general case is considered by introducing a variable distance between the aperture and the imaging lens. The influence of the aperture-lens distance on the spatial carrier is then analyzed, which enables the separate control of the shearing amount and the spatial carrier. Two types of dual-directional shearography are presented to demonstrate the feasibility and the flexibility of the system. Type I is the simultaneous dual lateral shearography in orthogonal directions, and Type II is the simultaneous lateral and radial shearography. The spatial carrier introduced by the single-aperture-lens Wollaston prism configuration is discussed, and a configuration in which the Wollaston prism and the aperture are located at different sides of the lens is recommended for further shearography applications.

Spatial phase-shift dual-beam speckle interferometry

The spatial phase-shift technique has been successfully applied to an out-of-plane speckle interferometry system. Its application to a pure in-plane sensitive system has not been reported yet. This paper presents a novel optical configuration that enables the application of the spatial phase-shift technique to pure in-plane sensitive dual-beam speckle interferometry. The new spatial phase-shift dual-beam speckle interferometry (SPS-DBSP) uses a dual-beam in-plane electronic speckle pattern interferometry configuration with individual aperture shears, avoiding the interference in the object plane by the use of a low-coherence source, and different optical paths. The measured object is illuminated by two incoherent beams that are generated by a delay line, which is larger than the coherence length of the laser. The two beams reflected from the object surface interfere with each other at the CCD plane because of different optical paths. A spatial phase shift is introduced by the angle between the two apertures when they are mapped to the same optical axis. The phase of the in-plane deformation can directly be extracted from the speckle patterns by the Fourier transform method. The capability of SPS-DBSI is demonstrated by theoretical discussion as well as experiments.

Measurement of transient deformations using digital image correlation method and high-speed photography: application to dynamic fracture

The digital image correlation method is extended to the study of transient deformations such as the one associated with a rapid growth of cracks in materials. A newly introduced rotating mirror type, multichannel digital high-speed camera is used in the investigation. Details of calibrating the imaging system are first described, and the methodology to estimate and correct inherent misalignments in the optical channels are outlined. A series of benchmark experiments are used to determined the accuracy of the measured displacements. A 2%-6% pixel accuracy in displacement measurements is achieved. Subsequently, the method is used to study crack growth in edge cracked beams subjected to impact loading. Decorated speckle patterns in the crack tip vicinity at rates of 225,000 frames per second are registered. Two sets of images are recorded, one before the impact and another after the impact. Using the image correlation algorithms developed for this work, the entire crack tip deformation history, from the time of impact to complete fracture, is mapped. The crack opening displacements are then analyzed to obtain the history of failure characterization parameter, namely, the dynamic stress intensity factor. The measurements are independently verified successfully by a complementary numerical analysis of the problem.

Speckle interferometry: three-dimensional deformation field measurement with a single interferogram

An electronic speckle interferometer, arranged for out-of-plane sensitivity and with an off-axis reference beam to produce spatial phase bias, is used for three-dimensional deformation field measurements. The complex amplitude of the object wave is calculated by application of a Fourier-transform method to a single interferogram. The change in phase after object deformation yields the out-of-plane component of the displacement field. The two in-plane components are obtained by cross correlation of subimages of the reconstructed object wave's intensity, a method that is also referred to as digital speckle photography. The Fourier-transform algorithm is extended and modified, leading to random measurement errors that are below widely accepted theoretical limits and also to an extended measuring range. These properties and the mutually combined information improve the accuracy of both methods compared with their usual single implementation. The performance is evaluated in experiments with pure out-of-plane, pure in-plane, and combined deformations and compared with theoretical values. An example of a practical application is given.

Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis

A novel interferometric method named statistical interferometry is proposed and studied. In the method, in contrast to the conventional deterministic interferometry, the complete randomness of the two interfering light fields, i.e., the random interference of the fully developed speckle fields, plays an essential role and is used as a standard of phase in a statistical sense. Preliminary experiments were conducted to verify the validity of the method, followed by a computer simulation. As an experimental result, the accuracy of the measurements of an out-of-plane displacement was confirmed up to lambda/800 by comparison with the heterodyne interferometer. The method has the advantage of simplicity of the optical system required, while at the same time providing high accuracy.

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.

Dual in-plane electronic speckle pattern interferometry system with electro-optical switching and phase shifting

A dual in-plane electronic speckle pattern interferometry (ESPI) system has been developed for in situ measurements. The optical setup is described here. The system uses an electro-optical switch to change between the illumination directions for x and y sensitivity. The ability of the electro-optic device to change the polarization of the laser light forms the basis of this switch. The electro-optic device is a liquid-crystal layer cemented between two optically flat glass plates. An electric field can be set up across the layer by application of a voltage to electrodes. The speckle interferometry system incorporates two additional liquid-crystal devices to facilitate phase shifting, and the overall system is controlled by advanced software, which allows switching between the two perpendicular planes in quasi real time. The fact that there are no moving parts is an advantage in any ESPI system for which mechanical stability is vital.