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 free space optical communications, long-distance transmission leads to the attenuation of beacon light, where we adopt a quadrant detector (QD) to receive the weak signal. However, the background light interferes so strongly that the output signal-to-noise ratio (SNR) of QD is at a low level, which causes a decrease in accuracy of the direct detection method. This requires finding a new light spot detection method, so an improved detection method is proposed. Because the dark current noise and the background light noise are both white noise, we adopt a Kalman filter to estimate the real output of four electric signals of QD. Unfortunately, running these through an amplifier introduces some direct current (DC) offsets into the signals. In order to balance the effect of the DC offsets, we consider using the modulation method, where we employ a sine signal to modulate the intensity of the beacon light at the transmitting end, after which we can give an inverse gain to move the center of signals to near zero to eliminate the DC offsets when we calculate the data. In Kalman filtering, we use the peak values of the signals in every period after the analog to digital converter (ADC) as the elements of the measurement matrix. Experimental results show that even when QD output SNR is about −10 dB, the detection root-mean-square errors decrease by 51.5% using the improved detection method compared with the direct detection method. Moreover, Kalman filtering does not require a large amount of data, which means it works efficiently, can reduce the cost of hardware resources, and is available for the real-time calculation of spot position.

Stochastic parallel gradient descent (SPGD) is the most frequently used optimization algorithm for correcting wavefront distortion in the wavefront sensorless adaptive optics(WFS-Less AO)system. However, the convergence speed of the SPGD algorithm becomes slow rapidly as increasing of distortion, and the probability of falling into local optimum is rising owing to the fixed gain coefficient. It cannot meet the requirement of real-time wavefront distortion correction. Therefore, a novel algorithm is proposed in this paper, called as adaptive gain stochastic parallel gradient descent (AGSPGD) based on the AMSGrad optimizer in the deep learning, to improve the convergence speed of the algorithm and to reduce the probability of falling into local optimum. The AGSPGD algorithm adopts the first-order moment and the second-order moment of the performance index, which are combined to dynamically adjust the gain. The numerical simulations are completed in this article. The results of ${\bm{D}}/\ {{\bm{r}}}_0 = \ 2.5$ conditions demonstrate that the AGSPGD can reduce the number of iterations by 25%, and the probability of the algorithm falling into local optimum is reduced from 16% to 4%. In addition, the AGSPGD still outperforms the SPGD as ${\bm{D}}/{{\bm{r}}}_0$ increasing.