Placido disk methods for corneal topography use a target with concentric rings in order to obtain measurements of the corneal surface, codifying the topography from the deformations of the rings' image. Knowing exactly how the corneal surface departs from a rotational symmetric shape is difficult by using Placido rings. This is due to the fact that any ray deviations in the angular direction (sagittal transverse aberrations) are not easily detected and measured. This is the so-called skew ray error. For that reason, this technique has been considered as limited, especially when one tries to measure corneal aberrations with large rotational symmetry errors. However, we considered that the Placido disk topography has the potential to obtain a full description of the corneal surface as long as the skew ray error is fixed. Here, we present a solution based in the assumption that a corneal topography calculated with the presence of the skew ray error has hidden information that can be extracted by applying some basis of the classical Hartmann test. To achieve that solution, we improve some aspects of the Hartmann test to be later applied in the processing of Placido disk images. Our solution gives us the ability to solve the skew ray error in a simple and direct method, with an effectiveness that is probed by the computing of some simulated representative surfaces without rotational symmetry and the performance of our algorithm.The majority of spectrometers use reflective dispersion gratings with a metal-coated blazed grating profile for spectral decomposition. They achieve high diffraction efficiency at the design wavelength, which decays considerably in the adjacent longer and shorter wavelength ranges. We introduce a structured metal double-blazed grating with a high diffraction efficiency for a broadband spectral range, consisting of a sawtooth-like structured metal surface filled with a first dielectric transparent material. The planarized upper surface is covered with a second blazed profile of a different transparent material. We present a systematical theoretical analysis of the diffraction efficiency in reflection geometry, based on a scalar approach involving fundamental dispersion parameters such as Abbe numbers and relative partial dispersions of the materials. We find material combinations reducing the profile heights down to 1-2 µm.Currently, valuable tickets are scanned and verified by embedding quick response (QR) codes, but few studies have embedded encrypted information into QR codes to prevent counterfeiting. In the existing literature on color image-based QR codes, there is room for improvement in image quality and anti-counterfeiting functions. Rapamycin ic50 We propose an optically decrypted microstructure overlapping image technology, hiding the information points of two-dimensional barcodes on the image reservation area in the ticket, and using the optical principle to use the lenticular lens as a decryption component, to make the image produce continuous dynamic effects and increase the difficulty of forgery. In addition, the distribution of embedded parameters and differences will also affect the distortion of hidden information, which may cause the QR code to fail to read, so the median edge detection predictor is proposed for distortion control comparison. The experimental results prove that our method provides low distortion of information-hiding technology.Linear canonical transformation (LCT) provides a generalized and elegant mathematical framework for analyzing the coherence properties of an electromagnetic (EM) beam propagating in quadratic phase systems (QPSs). It is shown that LCT may be used to analyze coherence properties such as generalized Stokes parameters and EM degree of coherence of a partially coherent EM beam propagating through a QPS. We present simulation results of a Gaussian Schell model beam propagating through a Fourier system, fractional Fourier system, and 4f imaging system with an aperture and beam relay system.In this study, a tunable bifunctional polarization-independent metamaterial device based on Dirac semimetal films (DSFs) and vanadium dioxide (VO2) is investigated. At the VO2 insulator state, a polarization-independent electromagnetically induced reflectance effect can be achieved via destructive interference between bright and dark modes. When VO2 transitions to a metallic state, the proposed device behaves as a dual-band polarization-independent absorber with 99.9% and 94.5% absorptance at 9.06 and 10.9 THz, respectively, and is insensitive over a wide range of incidence angles. In both cases, refractive index sensing is achieved, and the response can be dynamically tuned by changing the Fermi energy of the DSF.Mueller polarimetry is a powerful imaging modality that has been successfully applied to various application fields. Decomposition of Mueller matrices in elementary components is classically considered in order to unfold complex physical phenomena taking place in probed samples or scenes. In this context, the generalized polar decomposition, also known as Lu and Chipman decomposition, plays a prominent role. In this paper, we show that the set of candidate generalized polar decompositions is richer than the set used so far. Negative-determinant Mueller matrices are naturally addressed in the proposed framework. We show that taking into account those supplementary polar decompositions addresses issues raised in the literature. Application is carried out on synthetic and on measured Mueller matrices.This work presents the implementation, numerical examples, and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape derivatives, the profile of a grating is optimized such that it maximizes the diffraction efficiency for given diffraction modes for transverse electric polarization. We provide a thorough comparison of three different optimization methods a first-order method (gradient descent); a second-order approach based on a Newton iteration, where the usual Newton step is replaced by taking the absolute value of the eigenvalues given by the spectral decomposition of the Hessian matrix to deal with non-convexity; and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, a quasi-Newton method. Numerical examples are provided to validate our claims. Moreover, two grating profiles are designed for high efficiency in the Littrow configuration and then compared to a high efficiency commercial grating.