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A semi-analytical approach for rapid calculation of the Green's function inside a cavity of irregular shape over a broad range of frequency is presented. The method is based on the extraction of the Green's function at an imaginary wave number from itself to obtain a rapidly convergent hybrid spatial-spectral expansion of the Green's function. The method is applied to a V-grooved cavity, and the results are compared with the integral equation method.A direct scattering optical coherence tomography forward model was developed to simulate A-scans for both idealized and real light sources on an arbitrary given sample structure. Previous models neglected absorption, scattering, and multiple reflections at interfacial layers, and so two extended models were developed to investigate the impact of these processes. The first model uses the Beer-Lambert law to incorporate both absorption and scattering optical processes, and the second model uses a recursive form to model multiple reflections. These models were tested on a structure representative of a multilayered skin sample. find more The results show that the absorption and scattering processes have significant impact on the height of the peaks in the simulated A-scans. Conversely, the incorporation of multiple reflections has very little impact on the height of these peaks. Neither of the above processes has any impact on the locations of the A-scan peaks, which are associated with the sample interfaces between layers.Obtaining high-quality images from physical systems, objects, and processes is fundamental for a myriad of areas of science and technology. However, in many situations, the measured images contain defects and/or are accompanied by noise, degrading the quality of the measurement. Recently, a variant of the well-known Talbot self-imaging effect has been shown to redistribute the energy of a spatially periodic collection of images, obtaining output images with increased energy with respect to the input ones. In this work we experimentally demonstrate that such an energy redistribution method has the unique capabilities of increasing the coherent energy level of a periodic set of images over that of the incoherent noise, even allowing images completely buried under noise to be recovered. We further demonstrate that the process can mitigate potential faults of the periodic image structure, including blocked images, spatial jitter, and coherent noise, offering important enhancements (e.g., in regards to the quality of the recovered individual images) in the self-healing capabilities of Talbot self-imaging.Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick so that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-ray focusing at 10 keV.Research in laser-plasma interaction, high harmonic generation, and filamentation involves Gaussian beams propagating through inhomogeneous media, where the refractive index varies spatially in both the transverse and longitudinal directions. However, most analytical Gaussian beam solutions to the paraxial wave equation for inhomogeneous media are limited to media with the refractive index only varying quadratically in the transverse direction. In this paper, we present a new class of Gaussian beam solutions for a longitudinally varying medium with a transverse quadratic-index profile. We also highlight a few examples from this class of solutions, which include features such as a one-parameter generalization of the free-space Gaussian beam, beam "collimation," beam self-focusing, and the existence of multiple beam waists.Pupil size is modulated not only by the luminance at the eye position but also by that at the attended location. This study aims to examine whether pupil changes also correspond to the luminance at the spatial location to which the attention is shifted in optokinetic nystagmus. The test stimulus consisted of randomly positioned dots that moved to the left or to the right on a display screen that was bright on one side of the centerline and dark on the other. The results show that pupil size changes in accordance with the luminance at the location to which participants' attention shifts as a result of optokinetic nystagmus (i.e., eye movements in the direction opposite to that of the motion stimulus). This study suggests that pupil size is modulated by the luminance at the location to which attention shifts through unidirectional field motion.Conventional fluorescence polarization microscopy has been largely used to monitor the orientation and the structural information of biomolecules labeled with fluorescence dipoles but suffers from the optical diffraction limit. Here, we put forward a novel algorithm to simultaneously acquire the super-resolution image and the effective orientation distribution information of dipole clusters at corresponding super-resolution. In this paper, the orientation distribution of dipole clusters is statistically modeled by its mean orientation and orientation deviation, which are, respectively, represented by the middle direction and the opening angle of a sector shape. According to this model and microscopy imaging theory, the joint reconstruction algorithm is deduced mathematically in detail based on the conjugate gradient least-squares method. By applying this algorithm to different samples, the reconstructed results prove more than twice the resolution of wide-field images and the orientation distribution information at corresponding spatial resolution. Furthermore, the high accuracy of this algorithm in reconstructing super-resolution orientation distribution information is verified by Monte Carlo simulations.
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