Recently, some researchers have begun to adopt the Transformer to combine or replace the widely used ResNet as their new backbone network. As the Transformer captures the long-range relations between pixels well using the self-attention scheme, which complements the issues caused by the limited receptive field of CNN. Although their trackers work well in regular scenarios, they simply flatten the 2D features into a sequence to better match the Transformer. We believe these operations ignore the spatial prior of the target object, which may lead to sub-optimal results only. In addition, many works demonstrate that self-attention is actually a low-pass filter, which is independent of input features or keys/queries. That is to say, it may suppress the high-frequency component of the input features and preserve or even amplify the low-frequency information. To handle these issues, in this paper, we propose a unified Spatial-Frequency Transformer that models the Gaussian spatial Prior and High-frequency emphasis Attention (GPHA) simultaneously. To be specific, Gaussian spatial prior is generated using dual Multi-Layer Perceptrons (MLPs) and injected into the similarity matrix produced by multiplying Query and Key features in self-attention. The output will be fed into a softmax layer and then decomposed into two components, i.e., the direct and high-frequency signal. The low- and high-pass branches are rescaled and combined to achieve all-pass, therefore, the high-frequency features will be protected well in stacked self-attention layers. We further integrate the Spatial-Frequency Transformer into the Siamese tracking framework and propose a novel tracking algorithm termed SFTransT. The cross-scale fusion based SwinTransformer is adopted as the backbone, and also a multi-head cross-attention module is used to boost the interaction between search and template features. The output will be fed into the tracking head for target localization. Extensive experiments on short-term and long-term tracking benchmarks all demonstrate the effectiveness of our proposed framework. Source code will be released at https://github.com/Tchuanm/SFTransT.git.

In the adaptive optics (AO) system, to improve the effectiveness and accuracy of wavefront sensing-less technology, a phase-based sensing approach using machine learning is proposed. In contrast to the traditional gradient-based optimization methods, the model we designed is based on an improved convolutional neural network. Specifically, the deconvolution layer, which reconstructs unknown input by measuring output, is introduced to represent the phase maps of the point spread functions at the in focus and defocus planes. The improved convolutional neural network is utilized to establish the nonlinear mapping between the input point spread functions and the corresponding phase maps of the optical system. Once well trained, the model can directly output the aberration map of the optical system with good precision. Adequate simulations and experiments are introduced to demonstrate the accuracy and real-time performance of the proposed method. The simulations show that even when atmospheric conditions D/r₀ = 20, the detection root-mean-square of wavefront error of the proposed method is 0.1307 λ, which has a better accuracy than existing neural networks. When D/r₀ = 15 and 10, the root-mean-square error is respectively 0.0909 λ and 0.0718 λ. It has certain applicative value in the case of medium and weak turbulence. The root-mean-square error of experiment results with D/r₀ = 20 is 0.1304 λ, proving the correctness of simulations. Moreover, this method only needs 12 ms to accomplish the calculation and it has broad prospects for real-time wavefront sensing.

In free space optical communication, a beacon light loses too much energy after a long-distance transmission and faces strong interference from background light. The beacon light illuminated on a quadrant detector (QD) is so weak that the output signal-to-noise ratio (SNR) of a QD is very low, which leads to a significant decrease in the accuracy of the direct position detection method. To solve this problem, an improved light spot position detecting method is proposed. Since the background light and the dark current noise are white noise, we could consider concentrating the energy of QD output signal at a certain frequency point to enhance the output SNR. Therefore, a cosine signal is used to modulate the intensity of a beacon light at the transmitting end. Then the QD output photocurrents are also cosine signals with the same frequency as the modulating signal. Putting the photocurrent signals into a cross-correlation operation with a reference signal, which is the same as the modulating signal, can enhance the QD output SNR at a certain frequency point. Unfortunately, the result of the classical cross-correlation is attenuated with increasing delay. It is hard to detect the amplitude of the classical cross-correlation result. So, we used cyclic cross-correlation to obtain a stable correlation result to detect its amplitude accurately. The experiment results show that even when the QD output SNR is less than −17 dB, the detection root-mean-square error of the proposed method is 0.0092 mm, which is a quarter of the direct position detection method. Moreover, this method only needs a small amount of data to accomplish the calculation and is especially suitable for real-time spot position detection.

In this paper, an improved method of measuring wavefront aberration based on image with machine learning is proposed. This method had better real-time performance and higher estimation accuracy in free space optical communication in cases of strong atmospheric turbulence. We demonstrated that the network we optimized could use the point spread functions (PSFs) at a defocused plane to calculate the corresponding Zernike coefficients accurately. The computation time of the network was about 6–7 ms and the root-mean-square (RMS) wavefront error (WFE) between reconstruction and input was, on average, within 0.1263 waves in the situation of D/r0 = 20 in simulation, where D was the telescope diameter and r0 was the atmospheric coherent length. Adequate simulations and experiments were carried out to indicate the effectiveness and accuracy of the proposed method.

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L₁ norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L₀ norm algorithm. However, because the L₀ norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L₀ norm from the approximate L₂ norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L₂ norm and the L₁ norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.

Acquisition, tracking, and pointing (ATP) is a key technology in free space laser communication that has a characteristically high precision. In this paper, we report the acquisition and tracking of low-Earth-orbit satellites using shipborne ATP and verify the feasibility of establishing optical links between laser communication satellites and ships in the future. In particular, we developed a shipborne ATP system for satellite-to-sea applications in laser communications. We also designed an acquisition strategy for satellite-to-sea laser communication. In addition, a method was proposed for improving shipborne ATP pointing error. We tracked some stars at sea, achieving a pointing accuracy of less than 180μrad.We then acquired and tracked some low-Earth-orbit satellites at sea, achieving a tracking accuracy of about 20μrad. The results achieved in this work experimentally demonstrate the feasibility of ATP in satellite-to-sea laser communications.