Image Processing Techniques Applied to Enhancement of Holographic Fringe Patterns

In this paper, a novel methodology to process fringe pattern is presented. The core of the signal processing technique is the use of the direction information, a modulo 2pi quantity that locally informs about the direction along which fringes grow with maximum rate. By using this information, it was possible to perform adaptive, direction- and orientation-based operations on fringe images in order to remove unwanted effects, to enhance the contrast and to extract the phase information encoded. The method has been applied on shadow moire interferograms with carrier fringes in order to measure the surface of small objects. The developed algorithm allows to process fringes whose phase information is not monotonically increasing everywhere and to more accurately estimate the phase itself. Results from two experimental fringe patterns are presented. Results are compared with measurements performed by means of a conoscopic system used as a reference. Hence, it was possible to calculate the uncertainty of the performed measurements. Besides the possibility to decode fringe patterns presenting closed fringes, the proposed method provides measurements characterized by an uncertainty more than halved compared to Fourier-based methods

A novel phase-shifting profilometry to realize temporal phase unwrapping simultaneously with the least fringe patterns

In order to obtain a higher quantity absolute phase, a novel phase unwrapping model by combination of dual-frequency heterodyne and segmented quantifization phase coding method is proposed in this research. This model also provides a generalized phase order error correction method for eliminate phase order jump errors. Only ten fringe patterns are used for the projection in this study. The workflow of the devised model starts with acquisition of the low frequency wrapped phase by using the classic double-frequency heterodyne method, and then it moves to obtain the fringe order of low frequency wrapped phase based on the projected segmented quantifization phase coding patterns. In this step, two-dimensional scanning lookup method is used to eliminate the noise points caused by the rounding operation. Then, new fringe order can be obtained by combination of the obtained fringe order of low frequency wrapped phase and the new projected binary fringe pattern with complementarity, and this new fringe order combined with the previous fringe order can be used to unwrap the heterodyne phase. Finally, the wrapped phase of the dual-frequency is unwrapped through unwrapped heterodyne phase and the highest frequency phase. This study applies metal workpiece measurements as case studies to test the validity of the proposed model. The experimental results show that the error effects of fringe order can be eliminated, and the high frequency fringes retain more information on the measure workpiece surfaces.

This paper presents an absolute phase calculation method from one composite RGB fringe pattern image by using Wavelet transform algorithm and the optimum fringe number selection. Three fringe patterns having optimum fringe numbers are projected simultaneously onto an object surface via the red, green and blue channels of a DLP (Digital Light Processing) projector. From a different viewpoint, a CCD camera captures the deformed fringe patterns with respect to the object shape to get a composite RGB image. After compensating for the crosstalk and chromatic aberration between color channels, three fringe patterns are extracted from the composite color image. Wavelet Transform algorithm is studied to calculate wrapped phase from one fringe pattern. Therefore, three wrapped maps are obtained from the three extracted fringe patterns. An absolute phase map is calculated pixel by pixel after applying the optimum three-fringe numbers selection method to the three obtained wrapped phase maps. Simulated and experimental data demonstrate the algorithm's validity of calculating the absolute phase and shape information. The proposed method can measure 3D shape information of moving objects since the system needs only one RGB fringe pattern image.

It is the foundation that the absolute fringe order is discerned in 3-D image measurement methods, such as spatial pattern projection technique and Moire topography. The reason is that the depth range of the object is computed from the correspondence relation between the fringe order of a reflective pattern and the depth of an object. Multiple images are need by the conventional method for discerning the fringes order. Moreover, it has a problem of phase unwrapping in the phase analysis method of a Moire pattern or other interfering pattern. So it is difficult to calculate the absolute phase or to discern the relation between the fringes, especially in cases of which the fringes are discontinuous or the objects are isolated, and so forth. The technique of using modulation projection with 3-D information is presented. A new fringes pattern whose fringe intensity or color changes with its order is produced. Thus the fringe order can be extracted easily from the fringe intensity or color, and then the absolute phase and the absolute depth range can be obtained also. This technique needs only a single image or double images.

Grating interferometry that features long range and nanometer resolution is presented. The optical system was established based on a single long metrology grating. The large fringe multiplication was achieved by properly selecting two high-order diffraction beams to form a fringe pattern. The fringe pattern collected by a linear array was first tailored to a few multiples of fringes in order to suppress the effect of the energy leakage on phase-extracting precision when the fast Fourier transform (FFT) algorithm was used to calculate its phase. Thus, the phase-extracting precision of a tailored fringe pattern by FFT was greatly improved. Based on this, a novel subdividing method, which exploited the time-shift property of FFT, was developed to subdivide the fringe with large multiple and high accuracy. Numerical results show that the system resolution reaches 1 nm. The experimental results obtained against a capacitive sensor in the sub-mm range show that the measurement precision of the system is less than 10 nm.

The research focuses on isochromatic photoelastic fringe patterns in solid materials by using reflection mode in dark field polariscope. The optical setup consists of light source, polarizers, quarter wave plates, 577 nm optical pass filter, compensator and digital camera system. The fringe patterns were produced on the sample and fractional / integer number of fringe order was observed using Babinet compensator and digital camera system. The samples were circular and rectangular shape of PMMA coated with silver spray and compressed by hydraulic system at the top and the bottom. The results of the isochromatic fringe pattern were analyzed in horizontal and vertical positions. It was found that force and the number of isochromatic photoelastic fringe order depended on shape of sample, which reflects stress distribution behavior.

Critical needs of fringe-order accuracies in two-color holographic interferometry

A fringe analysis method, which combines the Fourier transform with the fractional fringe order method for measuring the absolute thickness of a block gauge, is presented. An approximate integer part of the fringe order is estimated by mechanical measurements, and the fractional part is determined by Fourier analysis of the interferometric fringe patterns. The fringe patterns are obtained with a Michelson interferometer by illumination of several selected wavelengths, respectively. The use of the fractional fringe order method can determine accurately more than 2ϖ phase jumps. The measured thickness of a block gauge is 5999115.0 ± 0.7 nm, which is comparable with the standard thickness of 6 mm. The influence of wavelength and approximate integer part of fringe order on the measurement accuracy is discussed.

In the present paper, the method of simultaneous moiré-like fringe pattern projection for Fourier transform profilometry is described. The photorefractive holographic interferometric process produces controlled moiré-like patterns with two or more different variation directions. Each low spatial frequency fringe pattern is experimentally obtained as a result of the superposition of two high spatial frequency sinusoidal gratings, with slightly different pitches, for each fringe variation direction. These dynamic moiré-like patterns are induced due to an optical holographic beating of the sinusoidal induced gratings in the volume of the photorefractive Bi₁₂TiO₂₀ (BTO) crystal sample used as dynamic holographic medium. Two or more moiré-like fringe patterns, with at least two different variation directions, simultaneously (or not), are projected onto the object surface. Thus, this is the 2D fringe projection stage of our proposed Fourier transform procedure to determine the profile of a simple object.

In the present work we present a simple comparative analysis of the results in the optical Fourier transform profilometry which fringe projection is produced by two different methods, dynamic moiré-like patterns and Michelson interferometer. First, the Fourier transform profilometry technique is applied in the projected moiré fringe pattern onto an object surface. Then, this result is compared to the Michelson fringe pattern projection in the same method of profilometry that is applied using the same test object. We have conclude that dynamic moiré-like fringe patterns could be used with some advantages, comparatively to the results obtained by the classical Michelson fringe patterns.

Two practical computer-aided optical techniques for full-field surface shape measurement are presented, one for diffuse surfaces and the other for specularly reflective surfaces. The former technique is based on projecting a computer-generated fringe pattern onto a diffuse surface, and the latter is based on reflecting the fringe pattern from a specularly reflective surface. The fringe pattern is perturbed in accordance with the object surface with the fringe phase bearing information on the depth/slope of the object surface. The computer-generated fringe pattern conveniently enables the fringe phase to be manipulated, and hence the determination of the phase distribution using a phase extraction algorithm. Instead of deriving the mathematical relationship between the fringe phase distribution and the surface depth/slope, this relationship is obtained by calibration. The techniques described can be easily implemented for rapid measurement of 3-D surface shapes in an industrial setting.

Using a modulated-fringe technique with double exposure holographic interferometry results in a monotonically ordered fringe pattern. This monotonic feature removes the ambiguity in determining the fringe values. For relatively small flat objects, the carrier fringes are straight and parallel. Using a reference area around the object and in the same plane as the object allows for easy determination of the undeformed and deformed carrier fringes with a single hologram. For 3-D objects, the carrier fringes are curved and non-uniformly spaced. In this case, a single hologram can produce only one of the two necessary fringe patterns. This paper presents a method in which the undeformed and deformed carrier fringe patterns can be obtained and processed by computer. This technique utilizes real-time holography and computer imaging to produce the two fringe patterns without having to reproduce the exact motion of the point source which creates the carrier fringes. The removal of the ambiguity in determining the fringe orders in the two digitally stored fringe patterns allows for the automation of measuring surface deflections of 3-D objects.

A novel scanning fringe projection method is developed to simultaneously measure the variations in both position and shape of a swimming fish. This method combines the commonly used fringe pattern projection method and a laser scanning technique into one optical system. In this new system, one or more reference fringes are generated by an acousto-optic deflector, and laser triangulation is used to determine the order of the reference fringe. These reference fringes are then combined with the conventional fringe pattern, and the fringe order is determined from the reference fringes. The method enables us to simultaneously measure the position and shape of a moving object. We successfully apply the method to a swimming fish.

To reveal the fundamental aspects hidden behind a variety of transient events in mechanics, physics, and biology, the highly desired ability to acquire three-dimensional (3D) images with ultrafast temporal resolution has been long sought. As one of the most commonly employed 3D sensing techniques, fringe projection profilometry (FPP) reconstructs the depth of a scene from stereo images taken with sequentially structured illuminations. However, the imaging speed of current FPP methods is generally capped at several kHz, which is limited by the projector-camera hardware and the number of fringe patterns required for phase retrieval and unwrapping. Here we report a novel learning-based ultrafast 3D imaging technique, termed single-shot super-resolved FPP (SSSR-FPP), which enables ultrafast 3D imaging at 100,000 Hz. SSSR-FPP uses only one pair of low signal-to-noise ratio (SNR), low-resolution, and pixelated fringe patterns as input, while the high-resolution unwrapped phase and fringe orders can be deciphered with a specific trained deep neural network. Our approach exploits the significant speed gain achieved by reducing the imaging window of conventional high-speed cameras, while “regenerating” the lost spatial resolution through deep learning. To demonstrate the high spatio-temporal resolution of SSSR-FPP, we present 3D videography of several transient scenes, including rotating turbofan blades, exploding building blocks, and the reciprocating motion of a steam engine, etc., which were previously challenging or even impossible to capture with conventional methods. Experimental results establish SSSR-FPP as a significant step forward in the field of 3D optical sensing, offering new insights into a broad spectrum of dynamic processes across various scientific disciplines.