High harmonic generation (HHG) is a nonlinear process that enables table-top generation of tunable, high-energy, coherent, ultrashort radiation pulses in the extreme ultraviolet (EUV) to soft X-ray range. These pulses find applications in photoemission spectroscopy in condensed matter physics, pump-probe spectroscopy for high-energy-density plasmas, and attosecond science. However, optical aberrations in the high-power laser systems required for HHG degrade beam quality and reduce efficiency. W e present a machine learning approach to optimize aberration correction using a spatial light modulator . W e implemented and compared Bayesian optimization and convolutional neural network (CNN) methods to predict optimal Zernike polynomial coefficients for wavefront correction. Our CNN achieved promising results with 80.39% accuracy on test data, demonstrating the potential for automated aberration correction in HHG systems.

A comparison between neural network clustering (NNC), hierarchical clustering (HC) and K-means clustering (KMC) is performed to evaluate the computational superiority of these three machine learning (ML) techniques for organizing large datasets into clusters. For NNC, a self-organizing map (SOM) training was applied to a collection of wavefront sensor reconstructions, decomposed in terms of 15 Zernike coefficients, characterizing the optical aberrations of the phase front transmitted by fluidic lenses. In order to understand the distribution and structure of the 15 Zernike variables within an input space, SOM-neighboring weight distances, SOM-sample hits, SOM-weight positions and SOM-weight planes were analyzed to form a visual interpretation of the system's structural properties. In the case of HC, the data was partitioned using a combined dissimilarity-linkage matrix computation. The effectiveness of this method was confirmed by a high cophenetic correlation coefficient value (c=0.9651). Additionally, a maximum number of clusters was established by setting an inconsistency cutoff of 0.8, yielding a total of 7 clusters for system segmentation. In addition, a KMC approach was employed to establish a quantitative measure of clustering segmentation efficiency, obtaining a sillhoute average value of 0.905 for data segmentation into K=5 non-overlapping clusters. On the other hand, the NNC analysis revealed that the 15 variables could be characterized through the collective influence of 8 clusters. It was established that the formation of clusters through the combined linkage and dissimilarity algorithms of HC alongside KMC is a more dependable clustering solution than separate assessment via NNC or HC, where altering the SOM size or inconsistency cutoff can lead to completely new clustering configurations.

Optical imaging quality can be severely degraded by system and sample induced aberrations. Existing adaptive optics systems typically rely on iterative search algorithm to correct for aberrations and improve images. This study demonstrates the application of convolutional neural networks to characterise the optical aberration by directly predicting the Zernike coefficients from two to three phase-diverse optical images. We evaluated our network on 600,000 simulated Point Spread Function (PSF) datasets randomly generated within the range of -1 to 1 radians using the first 25 Zernike coefficients. The results show that using only three phase-diverse images captured above, below and at the focal plane with an amplitude of 1 achieves a low RMSE of 0.10 radians on the simulated Point Spread Function (PSF) dataset. Furthermore, this approach directly predicts Zernike modes simulated extended 2D samples, while maintaining a comparable RMSE of 0.15 radians. We demonstrate that this approach is effective using only a single prediction step, or can be iterated a small number of times. This simple and straightforward technique provides rapid and accurate method for predicting the aberration correction using three or less phase-diverse images, paving the way for evaluation on real-world dataset.

We use Machine Learning (ML) and system identification validation approaches to estimate neural network models of large-scale Deformable Mirrors (DMs) used in Adaptive Optics (AO) systems. To obtain the training, validation, and test data sets, we simulate a realistic large-scale Finite Element (FE) model of a faceplate DM. The estimated models reproduce the input-output behavior of Vector AutoRegressive with eXogenous (VARX) input models and can be used for the design of high-performance AO systems. We address the model order selection and overfitting problems. We also provide an FE based approach for computing steady-state control signals that produce the desired wavefront shape. This approach can be used to predict the steady-state DM correction performance for different actuator spacings and configurations. The presented methods are tested on models with thousands of state variables and hundreds of actuators. The numerical simulations are performed on low-cost high-performance graphic processing units and implemented using the TensorFlow machine learning framework. The used codes are available online. The approaches presented in this paper are useful for the design and optimization of high-performance DMs and AO systems.

Convolutional neural networks (ConvNets) have demonstrated an exceptional capacity to discern visual patterns from digital images and signals. Unfortunately, such powerful ConvNets do not generalize well to arbitrary-shaped manifolds, where data representation does not fit into a tensor-like grid. Hence, many fields of science and engineering, where data points possess some manifold structure, cannot enjoy the full benefits of the recent advances in ConvNets. The aneurysm wall stress estimation problem introduced in this paper is one of many such problems. The problem is well-known to be of a paramount clinical importance, but yet, traditional ConvNets cannot be applied due to the manifold structure of the data, neither does the state-of-the-art geometric ConvNets perform well. Motivated by this, we propose a new geometric ConvNet method named ZerNet, which builds upon our novel mathematical generalization of convolution and pooling operations on manifolds. Our study shows that the ZerNet outperforms the other state-of-the-art geometric ConvNets in terms of accuracy.