Multi-subzone algorithm for absolute phase retrieval in digital fringe projection profilometry.

Codewords are important in encoded absolute phase retrieval techniques such as two-frequency, gray-code, and phase-coding. Each sinusoidal fringe is marked by a unique codeword so that an absolute fringe order can be determined by decoding the codeword. However, due to the limited number of unique codewords, sinusoidal fringe patterns do not contain high-frequency fringes without the use of additional patterns. A multi-subzone coding and decoding algorithm is thus proposed to overcome this limitation. Three multi-subzone coding methods based on two-frequency, gray-code, and phase-coding techniques are presented. The coding creates multiple subzones of unique codewords and the decoding enables it to use non-unique codewords to identify absolute fringe order. Specifically, the range of fringe order is estimated by the use of a wrapped phase map and the absolute fringe order is identified by a codeword. Experimental studies demonstrate the advantages of the proposed algorithm over existing coding methods. The proposed algorithm is suitable to measure objects with large step-height surface discontinuities.

Quantitative vibration analysis using a single fringe pattern in time-average speckle interferometry.

In this paper, a novel technique for quantitative vibration analysis using time-average electronic speckle pattern interferometry is proposed. An amplitude-varied time-average refreshing reference frame method is used to capture a fringe pattern with a better fringe contrast than the conventional reference frame technique. The recorded fringe patterns with improved contrast provide better mode shape visibility and are easier to process. A derivative-based regularized phase tracker model is used to retrieve vibration amplitudes from a single fringe pattern. The method does not require a phase shifter to obtain the mode shape or amplitude. The method provides unwrapped amplitude and amplitude derivatives maps directly, so a separate phase unwrapping process is not required. Experimental work is carried out using a circular aluminum plate test specimen and the results are compared with a finite element method modal analysis. Both experimental and numerical results show that the proposed method is robust and accurate.

Multiple-image encryption by space multiplexing based on compressive sensing and the double-random phase-encoding technique.

In this paper, a new multiple-image encryption and decryption technique that utilizes the compressive sensing (CS) concept along with a double-random phase encryption (DRPE) has been proposed. The space multiplexing method is employed for integrating multiple-image data. The method, which results in a nonlinear encryption system, is able to overcome the vulnerability of classical DRPE. The CS technique and space multiplexing are able to provide additional key space in the proposed method. A numerical experiment of the proposed method is implemented and the results show that the proposed method has good accuracy and is more robust than classical DRPE. The proposed system is also employed against chosen-plaintext attacks and it is found that the inclusion of compressive sensing enhances robustness against the attacks.

Multichannel Fourier-transform interferometry for fast signals.

Multichannel Fourier transform interferometry to measure the spectrum of arbitrarily short pulses and of fast time-varying signals was achieved using a micro/nanomanufactured multimirror array. We describe the performance of a demonstrator FTIR that works in the mid-infrared (MIR) range of 700-1400 cm(-1) and reaches a spectral resolution of 10 cm(-1) taking into account apodization. Spectral measurements down to pulse lengths of 319 µs were carried out using a mechanical camera shutter. Arbitrarily short pulses are expected feasible provided the source can deliver enough photons to overcome the noise equivalent number of photons.

Motion detection using extended fractional Fourier transform and digital speckle photography.

Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

Optical edge-projection method for three-dimensional profilometry.

A novel optical edge-projection method is proposed for surface contouring of an object with low reflectivity. A structured light edge is projected onto a dark surface, and the image is captured by a CCD camera. The object contour is evaluated with an active triangular projection algorithm, and one obtains a whole-field three-dimensional contour of the object by scanning the optical edge over the entire object surface. The proposed method is applied to a black nonreflective object made from woven carbon fiber and is also applied to measure the profile of a small object (a coin). The results show that an accurate profile of the specimen can be obtained.

Beam-splitting cube for fringe-projection, holographic, and shearographic interferometry.

We describe a simple method in which the techniques of fringe-projection, holographic, and shearographic interferometry may be readily realized with a commercial beam-splitting cube, a laser source, and a beam expander. With the use of a computer algorithm, moiré fringes may be derived digitally from the fringes that are projected onto a reference surface and onto an object surface. Successful use of the beam-splitting cube for these optical methods is attributed to the refraction of the two split beams that exit from the two adjacent faces of the cube. By careful orientation of the cube, the two refracted light beams will converge and interfere, resulting in the formation of Young's interference fringes for the fringe-projection method. When the hypotenuse of the beam-splitting cube is placed nearly normal to an illuminated object, both the image and the mirror image of the object will be formed behind the cube where a camera is placed. This optical setup thus forms the basis for double-exposure holography when these two images are fully overlapped and for shearography when the images are slightly laterally displaced.

Generation of carrier fringes in holography and shearography.

Double-exposure holography and double-exposure shearography are often used together with the carrier fringe technique, which requires additional shifting of the light source in a prescribed manner between exposures. In the holographic carrier fringe technique, difficulty in prescribing a suitable movement of the light source may be alleviated through visualization of the moiré fringes that are reconstructed by slight displacement of two overlaid families of ellipsoids in a holodiagram. Because shearography is the first differential of holography, it is often impractical to perform two successive optical differentiations on the ellipsoids to visualize the shearographic carrier fringes. A simple method of discerning holographic and shearographic carrier fringes is described. The method is based on the hyperboloids in a holodiagram that represent Young's (interference) fringes produced by the interference of two point sources. The hyperboloids are analogous to holographic carrier fringes, whereas the moiré patterns reconstructed from two overlaid hyperboloids are analogous to shearographic carrier fringes. Use of this method for explaining the formation of deformation fringes in plate bending, as well as the effect of light-source movement on the deformation fringes, is also illustrated.

Scanning moiré and phase shifting with time delay and integration imaging.

Scanning moiré is generated by undersampling of a phase-modulated grating pattern. In projection profilometry the scanning moiré pattern represents equal height and depth contours on a test object. By use of time delay and integration (TDI) imaging, it is possible to generate an on-line scanning moiré pattern from the complete periphery of a rotating cylindrical object. For automated phase and profile unwrapping from scanning moiré fringes, phase-shifting interferometry techniques are most desirable. However, lack of spatial information in the undersampled scanning moiré fringes introduces serious errors in phase unwrapping. We report a method that uses oversupply of data to balance the effect of undersampling. This oversupply is achieved with a TDI feature that permits programmable image magnification in the scanning direction.

Multiple-image shearography: a direct method to determine curvatures.

We present a modified method of shearography, known herein as multiple-image shearography, whereby the curvatures of an object can be measured directly from the resulting fringes. It employs an image-shearing camera that produces three sheared images simultaneously to interfere with each other in the image plane. When film is doubly exposed before and after an object is deformed, three sets of fringes are observed of which one set would depict the second-order derivatives of surface displacement.The theory of the multiple-image shearography technique and its application to curvature measurements in plate bending are presented.

Whole-field determination of surface roughness by speckle correlation.

A whole-field method of double-exposure speckle photography is employed to determine metal surface roughness by correlation between two speckle patterns. A movable rectangular aperture that is mounted before an image lens is shifted between the exposures, which results in a decrease in the contrast of the reconstructed Young's fringes with increasing roughness. The technique permits evaluation of the roughness of particular points on a surface as well as the average roughness of an entire surface. Four sets of random surfaces that were prepared by different machine-finishing processes and with roughnesses ranging from 0.6 to 13 µm have been tested. Different methods have been carried out to process the test data, and a practical method for the evaluation of surface roughness is proposed.

Analysis of shearogram reconstruction.

The high-pass Fourier filtering technique with an opaque stopper is commonly used for the reconstruction of shearograms. We believe that no analysis of this technique as applied to the shearogram reconstruction has been described. We present here a theoretical analysis of this reconstruction system taking into account the stopper that blocks the low-frequency region in the Fourier transform plane. The results show that the light-intensity distribution after reconstruction is different from that of the original shearogram. High fringe visibility is obtained with high-pass filtering.