Sparse reconstruction of wavefronts using an 1 over-complete phase dictionary
Abstract:
Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the Zernike polynomial basis. While the Cartesian basis is adept at capturing high-frequency features, it is susceptible to overfitting and inefficiencies due to the high number of degrees of freedom. The Zernike basis efficiently represents common optical aberrations but struggles with complex or non-standard wavefronts such as optical vortices, Bessel beams, or wavefronts with sharp discontinuities. This paper introduces a novel approach to wavefront reconstruction using an over-complete phase dictionary combined with sparse representation techniques. By constructing a dictionary that includes a diverse set of basis functions — ranging from Zernike polynomials to specialized functions representing optical vortices and other complex modes — we enable a more flexible and efficient representation of complex wavefronts. Furthermore, a trainable rigid transform is implemented to account for misalignment. Utilizing principles from compressed sensing and sparse coding, we enforce sparsity in the coefficient space to avoid overfitting and enhance robustness to noise.On the localization of the high-intensity region of simultaneous space-time foci
Abstract:
<jats:p>Simultaneous space-time focusing (SSTF) is sometimes claimed to reduce the longitudinal extent of the high-intensity region near the focus, in contradiction to the original work on this topic. Here we seek to address this confusion by using numerical and analytical methods to investigate the degree of localization of the spatio-temporal intensity of an SSTF pulse. The analytical method is found to be in excellent agreement with numerical calculations and yields, for bi-Gaussian input pulses, expressions for the three-dimensional spatio-temporal intensity profile of the SSTF pulse, and for the on-axis bandwidth, pulse duration, and pulse-front tilt (PFT) of the SSTF pulse. To provide further insight, we propose a method for determining the transverse input profile of a non-SSTF pulse with equivalent spatial focusing. We find that the longitudinal variations of the peak axial intensities of the SSTF and spatially equivalent (SE) pulses are the same, apart from a constant factor, and hence that SSTF does not constrain the region of high intensity more than a non-SSTF pulse with equivalent focusing. We demonstrate that a simplistic method for calculating the pulse intensity exaggerates the degree of intensity localization, unless the spatio-temporal couplings inherent to SSTF pulses are accounted for.</jats:p>Lattice stability of ultrafast-heated gold
Abstract:
First principle simulations within the framework of the finite-temperature density functional formalism predict the existence of nonthermal phase transitions in gold on ultrafast timescales with increasing electron temperature. The Gibbs free energy phase diagram as a function of electronic temperature indicates two solid-solid phase transitions of fcc→hcp at an electronic temperature of 1.2 eV and hcp→bcc at an electron temperature of 6.8 eV, while the ion lattice remains cold at zero temperature. We present a detailed analysis of the process of phonon-hardening in ultrafast-heated gold, using finite-temperature density functional perturbation theory simulations of the phonon spectra, the quantum thermodynamic phase diagram, and the thermoelastic properties.