Real-time hybrid fringe pattern analysis using a linear digital phase lockedloop for demodulation and unwrapping

The use of a second-order digital phase-locked loop (DPLL) to demodulate fringe patterns is presented. The second-order DPLL has better tracking ability and more noise immunity than the first-order loop. Consequently, the second-order DPLL is capable of demodulating a wider range of fringe patterns than the first-order DPLL. A basic analysis of the first- and the second-order loops is given, and a performance comparison between the first- and the second-order DPLL's in analyzing fringe patterns is presented. The implementation of the second-order loop in real time on a commercial parallel image processing system is described. Fringe patterns are grabbed and processed, and the resultant phase maps are displayed concurrently.

This paper proposes the use of the two‐dimensional continuous Paul wavelet transform to extract the phase of spatial carrier fringe patterns. The proposed algorithm has been tested using computer‐generated and real fringe patterns, and these tests have demonstrated the suitability of the proposed technique for the phase demodulation of fringe patterns. Additionally, this algorithm is compared to three two‐dimensional continuous wavelet algorithms that have figured prominently in the literature, specifically the Morlet, advanced Morlet and fan mother wavelets. This comparison has revealed that the proposed algorithm outperforms the other three mother wavelets in terms of its suitability for extracting the phase of fringe patterns that exhibit large phase variations.

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.

In a recent published work, we proposed a technique to recover the absolute phase maps of fringe patterns with two selected fringe wavelengths. To achieve higher anti-error capability, the proposed method requires employing the fringe patterns with longer wavelengths; however, longer wavelength may lead to the degradation of the signal-to-noise ratio (SNR) in the surface measurement. In this paper, we propose a new approach to unwrap the phase maps from their wrapped versions based on the use of fringes with three different wavelengths which is characterized by improved anti-error capability and SNR. Therefore, while the previous method works on the two-phase maps obtained from six-step phase-shifting profilometry (PSP) (thus 12 fringe patterns are needed), the proposed technique performs very well on three-phase maps from three steps PSP, requiring only nine fringe patterns and hence more efficient. Moreover, the advantages of the two-wavelength method in simple implementation and flexibility in the use of fringe patterns are also reserved. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.

Phase-shifting interferometry is a highly accurate technique for obtaining phase distribution from the recorded fringe patterns. Generally, phase-shifting interferometry requires recording several fringe patterns with varying phase shifts experimentally and during the acquisition, the object must be stable. Also, the atmospheric turbulence and mechanical conditions should also remain constant during this time. These requirements limit the use of these phase-shifting interferometric techniques in dynamic event studies. In the present work, we introduce Riesz transformed based digital four-step phase-shifting interferometer to obtain phase distribution from a single recorded fringe pattern. All the experimental phase-shifting setups necessary to realize the phase-shifting are removed. The idea is based on the recording of a single fringe pattern, and computes its Riesz transform at first, second and third-orders. The obtained Riesz transform components are combined to generate three π/2 phase-shifted fringe patterns, and then, the phase distribution is obtained from these phase-shifted fringe patterns. The performance of this method is demonstrated first by using numerical simulation and the quantitative appraisal is given by using image quality index. Further, we apply this technique on a real fringe pattern recorded in digital speckle pattern interferometry (DSPI). The obtained results reveal that our method provides a simple and accurate solution for phase evaluation, therefore, makes it suitable for real-time measurements.

A phase unwrapping method suitable for high frequency fringe based on edge feature

In a recently published work, we proposed a technique to recover the absolute phase maps from the wrapped ones with three different fringe wavelengths. It was noticed that when the wrapped phase maps are obtained by three-step phase shifting method, errors in fringe order still occur, leading to significant error in the recovered absolute phase maps. In this paper, the characteristic and reason of the errors are analysed, and a method to avoid these errors is also proposed. The theoretical conclusions in this paper are validated with experimental results.

Reconstruction of isolated moving objects with high 3D frame rate based on phase shifting profilometry

A transform-domain fringe pattern denoising technique is presented. The Discrete Cosine Transform (DCT) is applied in a sliding window manner to get an overcomplete image expansion, and then the transform coefficients are thresholded to reduce the noise. We investigate the proper size of the sliding window and the proper threshold level. The latter is determined individually for each window position using a local noise variance estimate. In order to deal with a rather inadequate but simplified noise model, a proportionality factor, related with the speckle size, is found by experiments with digitally simulated speckle fringes. Such a proportionality factor suggests that the technique could be made fully automatic. We demonstrate promising results in denoising of real speckle fringe patterns, obtained through an out-of-plane sensitive Digital Speckle Pattern Interferometry (DSPI) set-up in a process of non-destructive testing of reinforced composite materials deformation.

Palmprint and hand shape, as two kinds of important biometric characteristics, have been widely studied and applied to human identity recognition. The existing research is based mainly on 2D images, which lose the third-dimensional information. The biological features extracted from 2D images are distorted by pressure and rolling, so the subsequent feature matching and recognition are inaccurate. This paper presents a method to acquire accurate 3D shapes of palmprint and hand by projecting full-field composite color sinusoidal fringe patterns and the corresponding color texture information. A 3D imaging system is designed to capture and process the full-field composite color fringe patterns on hand surface. Composite color fringe patterns having the optimum three fringe numbers are generated by software and projected onto the surface of human hand by a digital light processing projector. From another viewpoint, a color CCD camera captures the deformed fringe patterns and saves them for postprocessing. After compensating for the cross talk and chromatic aberration between color channels, three fringe patterns are extracted from three color channels of a captured composite color image. Wrapped phase information can be calculated from the sinusoidal fringe patterns with high precision. At the same time, the absolute phase of each pixel is determined by the optimum three-fringe selection method. After building up the relationship between absolute phase map and 3D shape data, the 3D palmprint and hand are obtained. Color texture information can be directly captured or demodulated from the captured composite fringe pattern images. Experimental results show that the proposed method and system can yield accurate 3D shape and color texture information of the palmprint and hand shape.

Fringe pattern profilometry using triangular patterns and intensity ratios is a robust and computationally efficient method in three-dimensional shape measurement technique. However, similar to other multiple-shot techniques, the object must be kept static during the process of measurement, which is a challenging requirement for the case of fast-moving objects. Errors will be introduced if the traditional multiple-shot techniques are used directly in the measurement of a moving object. A new method is proposed to address this issue. First, the movement of the object is measured in real time and described by the rotation matrix and translation vector. Then, the expressions are derived for the fringe patterns under the influence of the two-dimensional movement of the object, based on which the normalized fringe patterns from the object without movement are estimated. Finally, the object is reconstructed using the existing intensity ratio algorithm incorporating the fringe patterns estimated, leading to improved measurement accuracy. The performance of the proposed method is verified by experiments.

Fringe projection profilometry (FPP) is a three-dimensional (3D) shape measurement method that involves projecting fringe patterns onto the object. A phase map retrieved from these fringe images is used for reconstructing the 3D surface of the object. Fourier transform and phase-shifting are two of the widely used fringe analysis techniques for performing 3D shape measurement using FPP. Fourier transform profilometry (FTP) has the advantage of performing high-speed measurement due to its single-shot nature. However, the reconstructed 3D surface has artifacts and high noise, specifically on the edges. On the other hand, phase-shifting profilometry (PSP) has the advantage of higher accuracy (relatively less noise level) but compromises on measurement speed. In this research, we propose a deep learning method to enhance the quality of the FTP phase maps using an efficient deep learning model called phase map enhancement net (PMENet). PMENet takes an FTP phase map as input and predicts a high-quality phase map in a supervised manner by using the phase maps obtained from 18-step PSP as ground truth. The training dataset was generated using a virtual FPP system. Validations were conducted on both the simulated data (generated by virtual FPP system) and the real-world data. The experimental results demonstrate that the trained neural network model can successfully improve the quality of the 3D geometric reconstruction with FTP and reduced the mean and root-mean-square error by 66% and 43%, respectively.

Laser interferometry is widely used in scientific research and industry due to its non-contact nature and high accuracy. Phase recovery is fundamental to interferometry, as it determines the accuracy and reliability of the measurement results. The wrapped phase map must be extracted from the interferograms prior to phase unwrapping. However, noisy wrapped phase maps with steep gradients often exhibit fringe shearing and adhesion, leading to discontinuities. This occurs particularly when the fringes are undersampled or when the measured surface is relatively rough. These discontinuities can readily lead to phase unwrapping errors. To address this challenge, this paper proposes a novel phase recovery method based on simulated phase modulation and phase map inpainting. This approach employs these two preprocessing techniques to generate high-quality wrapped phases, thereby reducing the complexity of phase unwrapping and enhancing the accuracy and reliability of the results. Comparative experiments demonstrate that the proposed method effectively mitigates issues such as excessively dense fringes and phase discontinuities (jumps) in wrapped phase maps, outperforming traditional phase recovery methods. The results validate the feasibility of combining simulated phase modulation with phase map inpainting as a preprocessing strategy. Furthermore, the integration of simulated phase modulation and phase map inpainting provides valuable insights for phase recovery methodologies in related research fields.

Removing harmonic distortion of measurements of a defocusing three-step phase-shifting digital fringe projection system

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.