In this paper, the cyclic shift method is provided to solve the phase wrapping problem of relative phase due to the initial wavelength error by a pure theoretical algorithm in optical frequency domain reflectometry (OFDR) system. The method reduces the experimental equipment requirements and can be extended to all the system uses relative phase demodulation system. The Hilbert-Euclidean distance substitution method is presented to solve the phase wrapping problem in the strain area with complete preservation of all phase information. What's more, the wavelet denoising two-dimensional weighted relative phase map is proposed, which is able to measure the strain with the spatial resolution of 9.07 mm, the accuracy of 0.5 μϵ and the maximum error of 0.225 μϵ in the range of 36 m, based on eight measurements. This method has lower error than the cross-correlation method and the relative phase averaging method, and it can make full use of multiple sets of relative phase information in every point, which solves the problem of high spatial resolution and high accuracy static strain measurement in the medium measurement distance.

Consider the convex optimization problem min_x f (g(x)) where both f and g are unknown but can be estimated through sampling. We consider the stochastic compositional gradient descent method (SCGD) that updates based on random function and subgradient evaluations, which are generated by a conditional sampling oracle. We focus on the case where samples are corrupted with Markov noise. Under certain diminishing stepsize assumptions, we prove that the iterate of SCGD converges almost surely to an optimal solution if such a solution exists. Under specific constant stepsize assumptions, we obtain finite-sample error bounds for the averaged iterates of the algorithm. We illustrate an application to online value evaluation in dynamic programming.

To study the law that governs the complex movements of the mechanism in the process of automatic weapon operation, the velocity tracking test technology of photon Doppler velocimetry is introduced to accurately measure velocity, displacement and acceleration, on the condition that there are long displacement and rapid velocity change. In the traditional way, out of interference signal time-frequency (TF) transformation draws TF distribution, and then by modulus maxima frequency extraction, comes to the law of velocity change. Due to the influence resulting from the change of fundamental signal as well as that of light intensity signal in the test, based on the TF distribution obtained by TF transformation, the traditional modulus maxima frequency extraction can extract frequency signals, but they show abnormal sudden changes at some moments, making the velocity discontinuous, unsmooth and unreal, which brings obvious errors to the subsequent calculation of acceleration and accurate displacement. Addressing the above-mentioned problems, this paper proposes a ridge extracting correction algorithm based on modulus maxima frequency extraction; this method, based on a large number of experiments where rodless cylinders are used to simulate the motion of a gun automatic mechanism, conducts a detailed calculation and analysis of the experimental results. A comparison of the two algorithms’ processing results, in terms of the speed, displacement and acceleration, suggests that the ridge extracting correction algorithm successfully corrects the frequency selection error, which draws a more continuous and, therefore, effective curve of the velocity change, and by so doing, the error of the displacement test (within 1.36 m displacement) is reduced from more than 3.6% to less than 0.58%, and the uncertainty dropped 97.07%. All these show that the accurate measurement of velocity, displacement and acceleration, with sudden and rapid velocity changes considered, is realized successfully.

Using orbital angular momentum (OAM) encoding for signal transmission enables optical communication in the spatial domain. However, during the transmission process of vortex optical communication, environmental factors such as atmospheric turbulence and haze cause scattering effects, resulting in the degradation of signal quality and increasing the complexity of decoding. Our goal is to design a framework that can recover the encoded signal from the speckle field, reducing the effects of scattering. We have designed a neural network model that combines a generative adversarial network (GAN) and U-Net, which utilizes the image segmentation capability of U-Net to guide the GAN in generating accurate information. We have demonstrated its effectiveness in experiments, with Pearson correlation coefficient (PCC) and peak signal-to-noise ratio (PSNR) values of 0.99 and 46.7, respectively. Compared to other works, our work focuses on the conjugate superimposed of perfect vortex beam (PVB), offering valuable insights into the beneficial aspects of vortex optical communication in long-distance transmission, interference resistance, and enhanced data transfer performance.

The relative phase method in strain demodulation based on OFDR has received much attention for its high accuracy and spatial resolution, but has the unique phase wrapping problem with different proposed solutions. Some relative phase information is lost in these solutions, and the complex algorithms make it difficult to implement in devices. This paper proposes a fractional cyclic shift method that matches any slope, which provides a non-destructive solution to phase wrapping and is easy to implement. Additionally, the paper presents the theory of cyclic shifts with zero padding, conversion formulae for fractional shift points, and the mathematical relationship between relative phase slope and optical frequency domain shift under the same strain. Using fractional cyclic shift and peak finding method based on variance statistic, the paper accurately determines the start and end positions of the strain, providing basic strain phase information. Finally, the method achieves the strain measurement with spatial resolution of 0.907 mm, distance of 36.7 m, strain accuracy of 0.5 με, maximum error of 0.2 με and standard deviation of 0.077 με through bidirectional Chebyshev low-pass filtering, providing low-error strain demodulation with sub-millimeter resolution in the medium distance. The paper also compares different filtering methods finding that bidirectional Chebyshev filtering avoids phase distortion and has one-third the error of FIR filtering with different windows.