Complementary Gray code N step phase shift algorithm has been widely used because of its high detection accuracy. In order to solve its low detection efficiency and real-time detection, this paper proposes a grating projection profilometry based on the combination of complementary Gray code and Fourfold-N step phase shift algorithm. When the number of phase shift steps is an integral multiple of four, divide images into N/4 groups according to the same phase difference, then get the wrapped phase of each group images and fuse them. Finally, unwrap phase with complementary Gray code. The algorithm in this paper can quickly eliminate periodic phase error and obtain high-precision unwrapped phase. In order to prove the effectiveness of this algorithm, the algorithm in this paper is compared with the N step phase shift algorithm of complementary Gray code and the Double N step phase shift algorithm of complementary Gray code with different N-values. Experimental result shows that the proposed algorithm can achieve high-precision phase unwrapping and improve the efficiency by 5%-20%.

Diameter detection plays an important role in the production of circular workpieces. It is very difficult to obtain the accurate measurement of diameter when the circular workpiece is red-hot because of the existence of lots of noise. Although Hough transform (HT) has many advantages for diameter detection of circular workpieces, it has still suffered from some serious problems, which include the requirements of a large amount of computation and memory occupancy. To address these problems, we propose an intelligent Hough transform method with Jaya (IHTJ). The key points are as follows. We analyze the problem of diameter detection for red-hot circular workpieces, which is essentially the problem of ellipse fitting. Then the problem of ellipse fitting with HT is converted into searching optimal solution in parameter space, and we construct the fitness function based on the principle of ellipse fitting with HT. In order to fit the ellipse accurately and rapidly, we introduce Jaya to search the optimal ellipse parameters in parameter space at last, and the computation burden and memory occupancy of HT are greatly reduced. Compared with direct least-square (DLS), randomized Hough transform (RHT) and random sample consistency (RANSAC), IHTJ can fit the ellipse rapidly while the advantages of strong robustness and high accuracy of HT are retained. Some simulations and practical experiments are carried out to verify the effectiveness of IHTJ.

During the growth of silicon single crystals, it is critical to detect the liquid level of the silicon melt to ensure their high quality production. Because noise statistics are difficult to determine in measured values of the liquid level, a particle filter with unknown statistics has been presented to estimate the liquid level. However, this approach leads to inaccurate results due to sample impoverishment. To alleviate this problem, we propose an intelligent particle filter method with an adaptive Metropolis-Hastings (M-H) resampling strategy. To accomplish this, we first design an M-H resampling strategy with two proposed distributions to resample low-weight particles. These distributions randomly select high-weight particles for Gaussian mutations or high-weight and low-weight particles for crossover operations, so as to promote the movement of low-weight particles to high probability regions. We also construct a self-adaptive function to further improve the overall particle quality, which is used to calculate the selection probability of these two proposed distributions according to the proportion of low-weight particles in all of the particles. Finally, the liquid level is estimated according to the particles after the modified resampling strategy is applied. A comparative evaluation of the proposed method with the adaptive genetic particle filter (AGPF) and the firefly algorithm intelligence optimized particle filter (FAIOPF) is conducted. Some results of the simulation and the practical experiment are presented; they indicate the proposed method offers accuracy improvements in the liquid level estimation during the silicon crystal growth. More specifically, compared with the AGPF and the FAIOPF the mean absolute error (MAE) of the proposed method has been reduced by approximately 53.3% and 99.5%, respectively

Phase-to-height mapping is one of the important processes in three dimensional phase measurement profilometry. But, in traditional phase-to-height mapping method, the measurement accuracy is affected by device attitude, so it needs saving a large amount of mapping equations to achieve high-quality phase-to-height mapping. In order to improve that, this paper proposes an improved phase-to-height mapping method combine with device attitude. Firstly, we get the unwrapped phase of the target. Then, using generalized regression neural network is used to reduce the offset of phase information at the same height due to the randomness of device attitude. Last, the phase-to-height mapping is completed by substituting the unwrapped phase (the difference between having detected object and no detected object) of eliminate the offset into improved phase-to-height mapping method. Experimental results show that the proposed method could achieve high-quality phase-to-height mapping with less mapping equation and less memory space. Compared with the nonlinear phase-to-height mapping method (probabilistic neural network to eliminate phase offset), its accuracy is improved by 44.30%. Compared with the nonlinear phase-to-height mapping method (radial basis function neural network to eliminate phase offset), the accuracy is improved by 39.58%.

For a fractional order system (FOS) affected by input noise, the result of general fractional Kalman filter (GFKF) is biased. To overcome this, this brief proposes a new fractional Kalman filter (FKF) algorithm considering input noise. Firstly, it is proved that the result of the GFKF method is biased when the input vector includes the noise. Secondly, we redefine the criterion function of the error of state estimation during the derivation process of the FKF, in which a term about the input noise is added into the covariance matrix during the prior-estimation. Then an improved covariance matrix and Kalman gain are gotten, respectively. Due to the consideration of the input noise, this method can remove the error caused by the input noise. Experiment results illustrate that the algorithm of this brief has superior performance for systems with input noise compared with the GFKF method.