An optimization algorithm to be used in point-source corneal topographers is developed for the reconstruction of the topography of aspheric corneal surfaces. It is based on the damped least-squares technique. The reconstructions obtained with a topographer comprising 48 or 90 point sources for corneas having different forms (spherical, conicoidal, complex) and apical radii (5-16 mm) were simulated numerically. Zernike polynomials up to the seventh radial order were used for the description of the shape of the anterior corneal surface. With no noise, i.e. uncertainty in the position of the image of each object point, it is shown that this approach allows reconstruction of the surface with a root-mean-square (RMS) error of<5 x 10(-7) microm for the elevation map and 3 x 10(-7) diopter for the refraction map. With noise, to get an averaged surface elevation RMS error of <1 microm, or an averaged refraction RMS error of <0.25 diopter, each spot must be located (in the image plane) with an error <1 microm.
Achieving high repeatability and efficiency in laser-induced strong shock wave excitation remains a significant technical challenge, as evidenced by the extensive efforts undertaken at large-scale national laboratories to optimize the compression of light element pellets. In this study, we propose and model a novel optical design for generating strong shocks at a tabletop scale. Our approach leverages the spatial and temporal shaping of multiple laser pulses to form concentric laser rings on condensed matter samples. Each laser ring initiates a two-dimensional focusing shock wave that overlaps and converges with preceding shock waves at a central point within the ring. We present preliminary experimental results for a single ring configuration. To enable high-power laser focusing at the micron scale, we demonstrate experimentally the feasibility of employing dielectric metasurfaces with exceptional damage threshold, experimentally determined to be 1.1 J/cm2, as replacements for conventional optics. These metasurfaces enable the creation of pristine, high-fluence laser rings essential for launching stable shock waves in materials. Herein, we showcase results obtained using a water sample, achieving shock pressures in the gigapascal (GPa) range. Our findings provide a promising pathway towards the application of laser-induced strong shock compression in condensed matter at the microscale.
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