Phase discontinuity predictions using a machine-learning trained kernel

Ultrafast spatial phase unwrapping algorithm with accurately correcting transient phase error

In fringe projection profilometry, the wrapped phase is easily polluted by many factors such as noise, shadow, and so on. In this Letter, we propose an ultrafast bi-staggered spatial phase unwrapping (BSPU) method. By constructing another staggered phase, the fringe order jump (FOJ) and local transient phase error (LTPE) can be accurately and quickly located at the same time owing to a simple difference operation. For the first time, to the best of our knowledge, a pioneering threshold separation model is established to precisely distinguish FOJ and LTPE. Based on the continuity assumption, LTPE is effectively corrected by introducing the concept of "non-integer fringe order." The range of measurable discontinuity height is improved owing to the distinction between real phase jump and random error in the spatial phase unwrapping. In addition, it is thousands of times faster than the traditional path-dependent algorithm and even has higher measurement accuracy. Experimental results show the effectiveness and robustness of the proposed method in various complex measurement environments.

Multi-anchor spatial phase unwrapping for fringe projection profilometry

Phase unwrapping is a necessary step in fringe-projection profilometry that produces accurate depth maps. However, the original wrapped phase is often corrupted by errors, and thus conventional spatial unwrapping suffers from error propagation, such as scanline-based unwrapping, and high complexity, such as quality-guided methods. In this paper, we propose a fast and robust spatial unwrapping method called multi-anchor scanline unwrapping (MASU). Different from previous work, when unwrapping each pixel, MASU refers to multiple anchors in the scanline, where each anchor has a threshold adapting to its location. In such a manner, a set of fringe order candidates are predicted by the anchors according to phase smoothness assumption, and the one with the highest number of votes is chosen. After that, with the obtained fringe order, the absolute phase and depth are computed. Simulation and experiments have shown that even corrupted by severe phase errors, the proposed MASU can still produce robust unwrapped results. In addition, MASU is thousands of times faster than quality-guided unwrapping with comparative or even superior depth accuracy.

Absolute Depth Measurement Using Multiphase Normalized Cross-Correlation for Precise Optical Profilometry

In a multifrequency phase-shifting (MFPS) algorithm, the temporal phase unwrapping algorithm can extend the unambiguous phase range by transforming the measurement range from a short fringe pitch into an extended synthetic pitch of two different frequencies. However, this undesirably amplifies the uncertainty of measurement, with each single-frequency phase map retaining its measurement uncertainty, which is carried over to the final unwrapped phase maps in fringe-order calculations. This article analyzes possible causes and proposes a new absolute depth measurement algorithm to minimize the propagation of measurement uncertainty. Developed from normalized cross-correlation (NCC), the proposed algorithm can minimize wrong fringe-order calculations in the MFPS algorithm. The experimental results demonstrated that the proposed measurement method could effectively calibrate the wrong fringe order. Moreover, some extremely low signal-to-noise ratio (SNR) regions of a captured image could be correctly reconstructed (for surface profiles). The present findings confirmed measurement precision at one standard deviation below 5.4 µm, with an absolute distance measurement of 16 mm. The measurement accuracy of the absolute depth could be significantly improved from an unacceptable level of measured errors down to 0.5% of the overall measuring range. Additionally, the proposed algorithm was capable of extracting the absolute phase map in other optical measurement applications, such as distance measurements using interferometry.

Phase unwrapping in optical metrology via denoised and convolutional segmentation networks

The interferometry technique is commonly used to obtain the phase information of an object in optical metrology. The obtained wrapped phase is subject to a 2π ambiguity. To remove the ambiguity and obtain the correct phase, phase unwrapping is essential. Conventional phase unwrapping approaches are time-consuming and noise sensitive. To address those issues, we propose a new approach, where we transfer the task of phase unwrapping into a multi-class classification problem and introduce an efficient segmentation network to identify classes. Moreover, a noise-to-noise denoised network is integrated to preprocess noisy wrapped phase. We have demonstrated the proposed method with simulated data and in a real interferometric system.

Fuzzy c-means clustering based segmentation and the filtering method for discontinuous ESPI fringe patterns

The filtering of ESPI fringe patterns with both noise and discontinuity is a challenging problem raised in recent years. Discontinuity-detectable and discontinuity-aware processing techniques are demanded. In this paper, a fuzzy c-means (FCM) clustering based fringe segmentation method is proposed. By applying the FCM clustering method to the estimated fringe orientation, we segment the discontinuous ESPI fringe patterns into continuous segments, thus the discontinuous region is identified and a discontinuous region mask is generated. Then, the discontinuous region mask is introduced into the controlling speed function, and an adaptive shape-preserving oriented partial differential equation (OPDE) model is proposed for discontinuous ESPI fringe patterns denoising. According to our method, the discontinuous regions are effectively found and with the proposed adaptive shape-preserving OPDE, the noise is well eliminated, the shape of fringes and the discontinuity are well kept. The performance of our method is illustrated with three computer-simulated and one experimentally obtained discontinuous ESPI fringe patterns and comparison with related segmentation methods and OPDEs.