Moiré gauging of in-plane displacement using double aperture imaging

Experimental assessment of a low-cost aberration-free compact double aperture four-hololens imaging system: application to the enhancement of sensitivity and accuracy of in-plane displacement measurement

In this work, an experimental analysis of hololens imaging configuration consisting of four holographic lenses has been carried out to realize Duffy's double aperture speckle interferometer. It is demonstrated that using holographic lenses recorded for typical f-number in the four-hololens imaging system, the sensitivity of measurement is not limited due to the f-number of the lens. However, the sensitivity can be significantly enhanced by increasing the angle between the plane and spherical waves while recording the holographic lenses. In-plane displacements were measured using holographic lenses recorded at nearly equal f-number and with different beam angles between the plane and spherical waves. Experimental results show that holographic lenses recorded with a large beam angle between the plane and the spherical waves give a higher measurement sensitivity in comparison to those holographic lenses that were recorded with a lower beam angle at an equal f-number. This work shows that a four-hololens imaging system can be used advantageously as a low-cost alternative to Duffy's double aperture interferometer to overcome the need for expensive diffraction-limited low f-number lenses for higher measurement accuracy and sensitivity.

Polarizing white light interferometry for phase measurements using two simultaneous interferograms

Our research introduces a design for a polarization phase-shifting white light interferometric system (PPS-WLIS) that operates in a transmissive mode for measuring the slope phase of transparent objects. It comprises a cyclic path interferometer (lateral shear interferometer) coupled with a multiplexing Michelson interferometer. The system uses polarization to produce two parallel interferograms with polarization modulated with relative shifts simultaneously. To determine the optical phase, we used a two-step algorithm for phase demodulation that does not necessitate precise phase shifts, making the system more straightforward to operate. As a result, we could observe variations in the object associated with optical phase changes. Furthermore, our method simplifies the phase-shift interferometry process by requiring only one capture, making it an effective way to examine objects at dynamic events. As an illustration, we demonstrated the temperature measurement generated by a section of a candle flame.

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.

Phase stepping through polarizing modulation in electronic speckle pattern interferometry

We have demonstrated a speckle out-of-plane interferometer that employs phase-stepping procedures by means of polarization modulation. The system generates circular polarization states with opposite signs at each arm of the system, which overlap at the output of the interferometer, to generate phase shifts operating a conventional linear polarizer; the emerging polarization states have been analyzed to obtain the shifts needed to process the optical phase. The phase-stepping technique is demonstrated with a two-step algorithm to measure out-of-plane displacement on a flat metal plate.

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.

Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing

This paper suggests the use of adjustable aperture multiplexing (AAM), a method which is able to introduce multiple tunable carrier frequencies into a three-beam electronic speckle pattern interferometer to measure the out-of-plane displacement and its first-order derivative simultaneously. In the optical arrangement, two single apertures are located in the object and reference light paths, respectively. In cooperation with two adjustable mirrors, virtual images of the single apertures construct three pairs of virtual double apertures with variable aperture opening sizes and aperture distances. By setting the aperture parameter properly, three tunable spatial carrier frequencies are produced within the speckle pattern and completely separate the information of three interferograms in the frequency domain. By applying the inverse Fourier transform to a selected spectrum, its corresponding phase difference distribution can thus be evaluated. Therefore, we can obtain the phase map due to the deformation as well as its slope of the test surface from two speckle patterns which are recorded at different loading events. By this means, simultaneous and dynamic measurements are realized. AAM has greatly simplified the measurement system, which contributes to improving the system stability and increasing the system flexibility and adaptability to various measurement requirements. This paper presents the AAM working principle, the phase retrieval using spatial carrier frequency, and preliminary experimental results.

Three-degree-of-freedom displacement measurement using grating-based heterodyne interferometry

A heterodyne grating-based interferometer for three-degree-of-freedom (3-DOF) displacement measurement is proposed. This technique has the merits of both heterodyne interferometry and grating interferometry. A heterodyne light beam is obtained using an electro-optic modulating technique for amplitude modulation. While the heterodyne light beam is normally incident into a transmission-type 2D grating, two detection parts for in-plane and out-of-plane displacement measurements will be obtained. The heterodyne light beam is utilized to carry the optical phase variation that results from grating displacement in three directions. The experimental results demonstrate that the proposed interferometer is capable of sensing the displacement of a motion stage in 3-DOF. The resolution and range of the measurement can achieve up to nanometric and millimetric levels.

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.

In-plane strain measurement by speckle photography: A practical assessment of the use of Young's fringes

A photograph of a laser speckle pattern will diffract light, and a doubly exposed negative, which has been shifted between exposures, will produce a Young's fringe pattern with the fringe spacing inversely proportional to the displacement. This effect is used to detect the in-plane displacements of tensile specimens and cracked specimens, and changes in length of aluminium crystals due to annealing.

Multiple rotation assessment through isothetic fringes in speckle photography

The use of different pupils for storing each speckled image in speckle photography is employed to determine multiple in-plane rotations. The method consists of recording a four-exposure specklegram where the rotations are done between exposures. This specklegram is then optically processed in a whole field approach rendering isothetic fringes, which give detailed information about the multiple rotations. It is experimentally demonstrated that the proposed arrangement permits the depiction of six isothetics in order to measure either six different angles or three nonparallel components for two local general in-plane displacements.

Phase-object detection by use of double-exposure fringe-modulated speckle patterns

We study the properties of a double-exposure image specklegram of a diffuse object obtained by use of a double-aperture pupil. A phase object is placed in front of one aperture during the first or the second exposure. Also, it is assumed that a uniform displacement of the diffuser between exposures is produced. The recorded specklegram is coherently illuminated and analyzed by Fourier transform operations. The average intensity distribution and the interference fringe visibility in the Fourier plane are investigated. On this basis, an alternative interference technique to detect phase objects is proposed.

Phase-object analysis with a speckle interferometer

We describe the characteristics of a double-exposure specklegram obtained through a double-aperture system, by introduction of a wedge in front of one aperture in one exposure. It is assumed that a uniform displacement of the diffuser is produced between exposures. The average intensity distribution and visibility of the interferometric fringes in the Fourier plane are analyzed. An alternative interferometric technique for phase-object detection is proposed.

Fringe Formation in an In-Plane Displacement Measurement Configuration with Twofold Increase in Sensitivity: Theory and experiment

A fringe-formation theory for a dual-beam illumination configuration that leads to a twofold increase in sensitivity for the measurement of in-plane displacement is described. Here we have taken into account all four beams simultaneously that are generated at the image plane owing to two-beam illumination and their cross-interference terms for fringe formation. We show that the sensitivity obtainable is the usual interferometric sensitivity when we take into account all four beams simultaneously and doubles only when the retroreflected beams are observed. A detailed theory and an experimental demonstration of the method are presented.

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

Hitherto no method, to our knowledge, was known to incorporate spatial phase shifting for the measurement of pure in-plane displacements. We demonstrate that the modified Duffy two-aperture configuration [Opt. Lett. 22, 1958 (1996)], which is sensitive to only the in-plane displacement component and offers increased sensitivity, lends itself to measurement with spatial phase shifting. The configuration can also be used for obtaining displacement derivatives by the introduction of shear with the tilt of a mirror.

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.

Optical configuration for measurement in speckle interferometry

An optical configuration for measurement of in-plane displacement and for contouring is reported. In this method an object point is viewed symmetrically with respect to surface normal and combined coherently at the image plane of the imaging system. Because the beams are combined by small apertures at the image plane, decorrelation sets in rather slowly. Owing to low decorrelation, fringes have been obtained for large in-plane deformations and large angular tilts. The method is simple to implement, and its sensitivity can be varied over a wide range. The configuration, therefore, extends the range of measurement.

In-plane displacement measurement configuration with twofold sensitivity

An optical configuration is suggested that will achieve a twofold increase in sensitivity when one measures an in-plane displacement component of a deformation vector compared with the Leendertz two-beam illumination method. A theory and experimental demonstration of the method are presented.

Fringe visibility in lateral displacement measurement from double-exposure laser photographs

The measurement of lateral displacement employing a doubly exposed speckle photograph according to the methods proposed by Archbold et al. and by Butters and Leendertz has been studied. The fringe visibility has been found as a function of the displacement and the resolution of the observing system. The spatial extent of the source has also been considered when a spectral lamp is used in the observing step. The use of an incoherent source replacing the laser in the observing step proved to be of interest because it reduces the speckle in the observed fringes.

Speckle interferometric methods of measuring small out-of-plane displacements

We present two new methods for measuring small out-of-plane displacement. These methods are descendents of Leendertz's method in speckle interferometry but provide fringes of good contrast.

Multiple-aperture three-dimensional image construction utilizing fringe-modulated speckle patterns

A technique is described for recording and reconstructing two- and three-dimensional color images utilizing a fringe-modulated speckle pattern. A multiple-aperture imaging system generates the modulated speckles and produces an image plane hologram in which the various complex waveforms, passing through the individual apertures, operate simultaneously as object and reference beams. This holographic recording system is considerably less sensitive to external vibration than conventional off-axis holography and requires much less stringent temporal- and spatial-coherence specifications for its light source.

Strain analysis by one-beam laser speckle interferometry. 2: Multiaperture method

A detailed analysis of using multiple apertures to record laser speckles for strain analysis is presented. It is shown that the basic fringe-forming mechanism is no different from that of single-aperture recording, except that at the Fourier filtering stage the diffracted light energy is concentrated at the spatial frequencies admitted by the apertures. As a result, better isothetic fringes at higher frequencies are obtainable. The concept of moiré is not utilized in the analysis. Indeed, it is shown that some of the observed phenomena cannot be explained using the moire concept. Multiaperture arrangements studied include two, three, and four apertures.

Practical speckle interferometry for measuring in-plane deformation

Speckle interferometry involves making a high resolution double-exposure photograph of an object that is illuminated with coherent light. When observed in a Fourier optical data processor, fringes are observed that are indicative of the changes, such as displacements, occurring in the body between exposures. Sensitivity of the measurement is variable and may be chosen after the data are recorded. A simple calibration procedure is described and its use in measuring in-plane displacements in deformable solids is demonstrated. Also given are some limitations on the range of sensitivity that can be effectively utilized with holographic films, simple procedures, and a small laser.

Speckle-shearing interferometric technique: a full-field strain gauge

An improved speckle-shearing interferometric method is presented that allows simultaneous determination of derivatives of surface displacements of a structure with respect to four different directions. The technique relaxes several limitations associated with conventional interferometry and thus is adaptable to nonlaboratory environments. The relevant theory is presented, and the method demonstrated by determining spatial derivatives of in-plane and out-of-plane displacements of statically loaded and vibrated structures.

Optical method for testing the precision of linear motions

An interferometric method for testing the accuracy of linear motions, such as that of drilling machines and lathe tools, is described. This method uses a diffraction grating fixed to the carriage to be tested. Only the first-order diffraction terms obtained by illuminating this grating with a laser beam are superimposed on each other by an imaging lens. An interference line pattern results that extends through the space of interfering beams and that can be analyzed with a microscope. Any deviations from the direction of motion, with the exception of deviations parallel to the grating lines, will be indicated by a movement of the fringe pattern and can be determined by counting the number of fringes passing the optical axis of the microscope. An application of this method for testing the chuck guidances in contact printing machines with a measurement accuracy of 0.2 micro is presented.

The Holo-Diagram. VI: Practical Device in Coherent Optics

Ordinary interferometry, hologram interferometry, contouring, speckle, moiré, ordinary radar, Doppler radar, optical Doppler velocimeter, Doppler holography, and gated viewing are all discussed, and it is vdemonstrated how closely these methods are related to each other. One single diagram, the holo-diagram, can be used for the evaluation of each method and even for combinations of the methods. The diagram is constructed for the study of interference patterns when an object is placed in the vicinity of two focal points representing either one point of illumination and one point of observation or two points of illumination or two points of observation. It reveals interference surfaces in space and how ordinary interference fringes are formed where an object intersects these surfaces. With a common moiré analogy the three-dimensional sensitivity distribution and the fringe patterns of each of the methods can be simulated. Finally it is pointed out that the diagram demonstrates the interference limits and diffraction limits of any method of optical information retrieval.