In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.
An invertible discrete Zernike transform, DZT is proposed and implemented. Three types of non-redundant samplings, random, hybrid (perturbed deterministic) and deterministic (spiral) are shown to provide completeness of the resulting sampled Zernike polynomial expansion. When completeness is guaranteed, then we can obtain an orthonormal basis, and hence the inversion only requires transposition of the matrix formed by the basis vectors (modes). The discrete Zernike modes are given for different sampling patterns and number of samples. The DZT has been implemented showing better performance, numerical stability and robustness than the standard Zernike expansion in numerical simulations. Non-redundant (critical) sampling along with an invertible transformation can be useful in a wide variety of applications.
In this work, we report a comparative study of the laser ablation threshold of borosilicate, fused silica, sapphire, and soda-lime glass as a function of the pulse width and for IR laser wavelengths. We determine the ablation threshold for three different pulse durations: τ=500 fs, 10 ps, and 20 ns. Experiments have been performed using a single laser pulse per shot in an ambient (air) environment. The results show a significant difference, of two orders of magnitude, between the group of ablation thresholds obtained for femtosecond, picosecond, and nanosecond pulses. This difference is reduced to 1 order of magnitude in the soda-lime substrate with tin impurities, pointing out the importance of the incubation effect. The morphology of the marks generated over the different glass materials by one single pulse of different pulse durations has been analyzed using a scanning electron microscope (FESEM ULTRA Plus). Our results are important for practical purposes, providing the ablation threshold data of four commonly used substrates at three different pulse durations in the infrared regime (1030-1064 nm) and complete data for increasing the understanding of the differences in the mechanism's leading ablation in the nanosecond, picosecond, and femtosecond regimes.
We propose a hybrid optical-digital imaging system that can provide high-resolution retinal images without wavefront sensing or correction of the spatial and dynamic variations of eye aberrations. A methodology based on wavefront coding is implemented in a fundus camera in order to obtain a high-quality image of retinal detail. Wavefront-coded systems rely simply on the use of a cubic-phase plate in the pupil of the optical system. The phase element is intended to blur images in such a way that invariance to optical aberrations is achieved. The blur is then removed by image postprocessing. Thus, the system can provide high-resolution retinal images, avoiding all the optics needed to sense and correct ocular aberration, i.e., wavefront sensors and deformable mirrors.
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