High-Capacity Spatial Structured Light for Robust and Accurate Reconstruction.

Spatial structured light (SL) can achieve three-dimensional measurements with a single shot. As an important branch in the field of dynamic reconstruction, its accuracy, robustness, and density are of vital importance. Currently, there is a wide performance gap of spatial SL between dense reconstruction (but less accurate, e.g., speckle-based SL) and accurate reconstruction (but often sparser, e.g., shape-coded SL). The central problem lies in the coding strategy and the designed coding features. This paper aims to improve the density and quantity of reconstructed point clouds by spatial SL whilst also maintaining a high accuracy. Firstly, a new pseudo-2D pattern generation strategy was developed, which can improve the coding capacity of shape-coded SL greatly. Then, to extract the dense feature points robustly and accurately, an end-to-end corner detection method based on deep learning was developed. Finally, the pseudo-2D pattern was decoded with the aid of the epipolar constraint. Experimental results validated the effectiveness of the proposed system.

Development of point diffraction interferometer by a dimension-reduction-based phase-shifting algorithm.

To avoid exhaustive calibration of the shifter device in point diffraction interferometers, we present a dimension-reduction-based method to reconstruct the phase map from more phase-shifting fringe patterns with three or more frames. The proposed method assumes that the intensity space can be described adequately by the sine and cosine of multiple phase shifts introduced, which are the basis of the intensity space. Then, low-dimensional approximations of high-dimensional intensity spaces are determined by the newly developed reduced basis decomposition technique. Finally, the phase is reconstructed using the low-dimensional surrogates of the intensity spaces without the knowledge of accurate phase steps. Numerical and experimental studies demonstrated that the proposed method outperforms the existing popular phase reconstruction techniques in terms of accuracy and efficiency. Moreover, the performance of the proposed method is not limited by variations in the background and modulation, unlike the existing phase-shifting-algorithm-based approaches.

Phase-shift extraction of multiple-frame randomly phase-shifted interferograms by analysis of the amplitude of the analytic signal.

We present a powerful phase-shift extraction algorithm for multiple-frame random phase-shifting fringe patterns. The proposed method is based on changing the regularity of the amplitude of a demodulated analytic signal with respect to different phase shifts and a one-dimensional optimization method. Compared with the existing universal phase-reconstruction method, the proposed method is accurate, stable, and efficient. Both numerical simulations and experimental data demonstrate the high accuracy and efficiency of the proposed method.

Random phase shifting shadow moiré using a one-dimensional minimizer.

The introduction of a random phase-shifting technique into a shadow moiré system, where an equal and known (or unknown) phase step is used to demodulate the phase of interest, is beneficial for the improvement of measurement accuracy. However, in spite of recent advances in optical metrology phase-shifting techniques, simultaneously estimating unequal and unknown phase shifts from three random phase-shifting fringe patterns remains a significant challenge. This paper presents a one-dimensional minimizer-based technique to address this ill-posed problem of phase demodulation from random phase-shifting patterns. In this method, two new sets of connected fringe patterns, without background illumination, are constructed through normalizing the secondary fringe patterns. Then, a generalized phase-shifting algorithm is developed by utilizing the character of the modulation factor's standard deviation distribution. Both numerical simulations and optical experiments are performed to demonstrate the high accuracy and robustness of the proposed method.

Random phase-shifting algorithm by constructing orthogonal phase-shifting fringe patterns.

The intensity distribution of fringe patterns becomes nonsinusoidal in real testing environments. Thus, the performance of existing phase shift extraction algorithms, which usually compute the desired phase shift by arccosine function or arcsine function, may be affected. In the presented paper, we report an arctangent-function-based technique to solve this disturbance. First, two orthogonal fringe patterns are constructed through subtraction and addition of two background-removed images. Second, the unequal amplitude between two new fringe patterns is eliminated using a normalization process. Third, the phase shift is determined by computing the norms of the two new images. The proposed method is fast and can be implemented easily in many applications. We verify the algorithm performance and robustness using both simulated and experimental data, indicating the high accuracy of the presented method.

Three-frame self-calibration phase shift algorithm using the Gram-Schmidt orthonormalization approach.

Affected by the height dependent effects, the phase-shifting shadow moiré can only be implemented in an approximate way. In the technique, a fixed phase step around π/2 rad between two adjacent frames is usually introduced by a grating translation in its own plane. So the method is not flexible in some situations. Additionally, because the shadow moiré fringes have a complex intensity distribution, computing the introduced phase shift from the existing arccosine function or arcsine function-based phase shift extraction algorithm always exhibits instability. To solve it, we developed a Gram-Schmidt orthonormalization approach based on a three-frame self-calibration phase-shifting algorithm with equal but unknown phase steps. The proposed method using the arctangent function is fast and can be implemented robustly in many applications. We also do optical experiments to demonstrate the correction of the proposed method by referring to the result of the conventional five-step phase-shifting shadow moiré. The results show the correctness of the proposed method.

Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique.

We propose an elliptical sub-aperture stitching (ESAS) method to measure the aspheric surfaces. In our method, the non-null configuration is used to overcome the disadvantages of the null testing. By adding the dynamic tilt, the different local nearly null fringe patterns are obtained and the corresponding phase data in the elliptical masks is extracted with negligible retrace errors. In order to obtain the full aperture result, a stitching algorithm is developed to stitch all the phase data together. We firstly show the principle of our method. Then the performance of the proposed method is analyzed by simulation experiments. In the end, practical examples are given to demonstrate the correctness of the proposed method. The stitching result shows a good agreement with the full-aperture null testing result.

Shadow moiré technology based fast method for the measurement of surface topography.

We present a fast phase-shifting shadow moiré device for surface topography measurement. In our setup, multiple light sources located at different positions are controlled to illuminate the grating sequentially. Therefore, the phase shift across the field of view shadow moiré is introduced by changing the distance between the light source and the camera. Thanks to the necessity for mechanical movement being omitted here, the proposed setup can capture the phase-shifting fringe patterns at a high speed. However, affected by the bias modulation and amplitude modulation of the captured fringe patterns, the phase of interest cannot be demodulated by the standard phase-shifting algorithm directly. Thus the principal component analysis (PCA) demodulation approach is used to extract the wrapped phase map. In addition, we develop an iterative procedure to reduce the detuning error introduced by the PCA algorithm. The proposed method implements a fast way to determine the topography of a surface through a simple experimental setup. It is applied to obtain an external surface of a specimen. Both the simulation results and the experimental results show the validity of the proposed technique.

Color fringe-projected technique for measuring dynamic objects based on bidimensional empirical mode decomposition.

A triple-frequency color fringe-projected technique is presented to measure dynamic objects. Three fringe patterns with a carrier frequency ratio of 1:3:9 are encoded in red, green, and blue channels of a color fringe pattern and projected onto an object's surface. Bidimensional empirical mode decomposition is used for decoupling the cross talk among color channels and for extracting the fundamental frequency components of the three fringe patterns. The unwrapped phase distribution of the high-frequency fringe is retrieved by a three-step phase unwrapping strategy to recover the object's height distribution. Owing to its use of only a single snapshot, the technique is suitable for measuring dynamically changing objects with large discontinuity or spatially isolated surfaces.

Phase-shifting shadow moiré based on iterative self-tuning algorithm.

We proposed a general algorithm for phase-shifting shadow moiré by an iterative self-tuning algorithm. In our proposed system, the grating is translated in equal distance to introduce phase shifts across the field of view. The proposed algorithm produces accurate phase information with five interferograms and can calibrate the precise phase step during the process of the height demodulation. Compared with the traditional method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase-shift shadow moiré when reconstructing surfaces from fringe patterns. Numerical simulations and optical experiments show that the proposed method can eliminate the nonuniform phase-shift error and possesses a superior performance to existing typical phase-shifting algorithms.