Wavefront reconstruction of a Shack-Hartmann sensor with insufficient lenslets based on an extreme learning machine

Modeling of ringdown cavity maladjustment based on the extreme learning machine

In the cavity ringdown technique, cavity maladjustment may affect the accuracy of measurement. The effect of maladjustment is complex and nonlinear. Therefore, a neural network method of an extreme learning machine is presented to model the nonlinear relation between the intracavity loss and the cavity maladjustments. This method was tested by two-dimensional angular scanning simulations and experiments. After dataset training, this method finely predicted the intracavity loss at certain maladjustments. The root mean square values of the prediction deviation were about 0.27 ppm in simulation and about 0.44 ppm in experiment. This method was further applied to a cavity ringdown system for high reflectivity measurement. The measurement uncertainty was improved from ±0.0025% to ±0.0019%.

A Method Used to Improve the Dynamic Range of Shack-Hartmann Wavefront Sensor in Presence of Large Aberration

With the successful application of the Shack-Hartmann wavefront sensor in measuring aberrations of the human eye, researchers found that, when the aberration is large, the local wavefront distortion is large, and it causes the spot corresponding to the sub-aperture of the microlens to shift out of the corresponding range of the sub-aperture. However, the traditional wavefront reconstruction algorithm searches for the spot within the corresponding range of the sub-aperture of the microlens and reconstructs the wavefront according to the calculated centroid, which leads to wavefront reconstruction errors. To solve the problem of the small dynamic range of the Shack-Hartmann wavefront sensor, this paper proposes a wavefront reconstruction algorithm based on the autocorrelation method and a neural network. The autocorrelation centroid extraction method was used to calculate the centroid in the entire spot map in order to obtain a centroid map and to reconstruct the wavefront by matching the centroid with the microlens array through the neural network. This method breaks the limitation of the sub-aperture of the microlens. The experimental results show that the algorithm improves the dynamic range of the first 15 terms of the Zernike aberration reconstruction to varying degrees, ranging from 62.86% to 183.87%.

Wavefront Restoration Technology of Dynamic Non-Uniform Intensity Distribution Based on Extreme Learning Machine

Non-uniform intensity distribution of laser near-field beam results in the irregular shape of the spot in the wavefront sensor. The intensity of some sub-aperture spots may be too weak to be detected, and the accuracy of wavefront restoration is seriously affected. Therefore, an extreme learning machine method is proposed to realize high precision wavefront restoration under dynamic non-uniform intensity distribution. The simulation results show that this method has better accuracy of wavefront restoration than the classical modal algorithm under dynamic non-uniform intensity distribution. The root mean square error of the residual wavefront for the proposed method is only 2.9% of the initial value.

Deep learning wavefront sensing method for Shack-Hartmann sensors with sparse sub-apertures

In this letter, we proposed a deep learning wavefront sensing approach for the Shack-Hartmann sensors (SHWFS) to predict the wavefront from sub-aperture images without centroid calculation directly. This method can accurately reconstruct high spatial frequency wavefronts with fewer sub-apertures, breaking the limitation of d/r₀ ≈ 1 (d is the diameter of sub-apertures and r₀ is the atmospheric coherent length) when using SHWFS to detect atmospheric turbulence. Also, we used transfer learning to accelerate the training process, reducing training time by 98.4% compared to deep learning-based methods. Numerical simulations were employed to validate our approach, and the mean residual wavefront root-mean-square (RMS) is 0.08λ. The proposed method provides a new direction to detect atmospheric turbulence using SHWFS.