End-to-end physics-informed deep neural network optimization of sub-Nyquist lenses.

In this paper, an approach for optimizing sub-Nyquist lenses using an end-to-end physics-informed deep neural network is presented. The simulation and optimization of these sub-Nyquist lenses is investigated for image quality, classification performance, or both. This approach integrates a diffractive optical model with a deep learning classifier, forming a unified optimization framework that facilitates simultaneous simulation and optimization. Lenses in this work span numerical apertures from approximately 0.1 to 1.0, and a total of 707 models are trained using the PyTorch-Lightning deep learning framework. Results demonstrate that the optimized lenses produce better image quality in terms of mean squared error (MSE) compared to analytical lenses by reducing the impact of diffraction order aliasing. When combined with the classifier, the optimized lenses show improved classification performance and reduced variability across the focal range. Additionally, the absence of correlation between the MSE measurement of image quality and classification performance suggests that images that appear good according to the MSE metric may not necessarily be beneficial for the classifier.

Measurement of the internal stress and electric field in a resonating piezoelectric transformer for high-voltage applications using the electro-optic and photoelastic effects.

The high output voltages from piezoelectric transformers are currently being used to accelerate charged particle beams for x-ray and neutron production. Traditional methods of characterizing piezoelectric transformers (PTs) using electrical probes can decrease the voltage transformation ratio of the device due to the introduction of load impedances on the order of hundreds of kiloohms to hundreds of megaohms. Consequently, an optical diagnostic was developed that used the photoelastic and electro-optic effects present in piezoelectric materials that are transparent to a given optical wavelength to determine the internal stress and electric field. The combined effects of the piezoelectric, photoelastic, and electro-optic effects result in a time-dependent change the refractive indices of the material and produce an artificially induced, time-dependent birefringence in the piezoelectric material. This induced time-dependent birefringence results in a change in the relative phase difference between the ordinary and extraordinary wave components of a helium-neon laser beam. The change in phase difference between the wave components was measured using a set of linear polarizers. The measured change in phase difference was used to calculate the stress and electric field based on the nonlinear optical properties, the piezoelectric constitutive equations, and the boundary conditions of the PT. Maximum stresses of approximately 10 MPa and electric fields of as high as 6 kV/cm were measured with the optical diagnostic. Measured results were compared to results from both a simple one-dimensional (1D) model of the piezoelectric transformer and a three-dimensional (3D) finite element model. Measured stresses and electric fields along the length of an operating length-extensional PT for two different electrical loads were within at least 50 % of 3D finite element simulated results. Additionally, the 3D finite element results were more accurate than the results from the 1D model for a wider range of electrical load impedances under test.