Valenciabrink2562

To illustrate the new VMEM, we analyze the transmission of light through an elliptic aperture in a metallic film, and the scattering of light by elliptic gold cylinders on a substrate.A new approach for calculating the field in the focal region along lines through the focal point of a lens is presented. In particular, the method is applied to a circular aperture. It is also applied to other shaped apertures, including circular sectors or segments, such as a semicircular aperture or Hilbert mask, and to polygonal shapes. The diffracted field is calculated by a one-dimensional Fourier transform, and can be used for accurate calculation at observation points distant from the focus. The approach gives new insight to appreciating the asymptotic behavior of the diffracted field, and the existence of intensity zeros, for different aperture shapes.Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.Mueller matrix spectroscopic ellipsometry becomes increasingly important for determining structural parameters of periodic line gratings. CK-666 concentration Because of the anisotropic character of gratings, the measured Mueller matrix elements are highly azimuthal angle dependent. Measurement results are interpreted by basic principles of diffraction on gratings. The spectral and azimuthal angle dependent intensity changes are correlated to so-called Rayleigh singularities, i.e., wavelengths where the number of diffraction orders changes. The positions of the Rayleigh singularities are calculated analytically and overlapped with measured spectra of two different types of photomasks with transparent and reflecting substrates. For both types of gratings, the Rayleigh singularities reproduce the contours of the spectra. Increasing grating periods result in a shift of these contours to longer wavelengths. Characteristic differences between the two photomasks are explained by the influence of the transmission orders, which are determined by the substrate transparency.Mirage is a fascinating phenomenon that has attracted many scientists to report their observations and descriptions about it. There are two different approaches to mirage formation. The more popular one is attributed to total internal reflection that occurs in the near ground air layers on hot sunny days. According to the other approach, mirage is an image in a rough surface that is observed at grazing angles of incidence. Most of the existing descriptions are qualitative and some include calculations based on guessing temperature change with no concrete experiments. In this report, first we show that Fermat's principle also concerns the wave nature of light and covers the constructive and destructive interference that is essential for image formation. Then, we provide a brief review of the image formation theory in a rough plane and demonstrate by experiments in the lab and deserts that the temperature gradient in the near ground air layers does not lead to mirage formation.In an oceanic optical communications link, the received intensity fluctuations, quantified by the scintillation index, are formulated and evaluated when a multimode laser is used. The variations of the scintillation index versus the oceanic turbulence parameters are examined for different multimode laser structures. Oceanic turbulence parameters used are the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, the Kolmogorov inner scale, and the parameter w that defines the ratio of temperature to salinity contributions to the refractive index spectrum. The results in this paper can be used to improve performance in the design of oceanic optical communications links.The classical reciprocity relation of radiative transfer fails for two points placed in regions having different indices of refraction. A modified reciprocity relation that involves the relative refractive index between the two points considered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (DE) [J. Opt. Soc. Am. A14, 486 (1997)]. In this paper, we extend these findings to the time-dependent DE and we discuss some implications to diffuse optical tomography.The presence of a bright light in the visual field has two main effects on the retinal image reduced contrast and increased retinal illuminance because of scattered light; the latter can, under some conditions, lead to an improvement in retinal sensitivity. The combined effect remains poorly understood, particularly at low light levels. A psychophysical flicker-cancellation test was used to measure the amount and angular distribution of scattered light in the eye for 40 observers. Contrast thresholds were measured using a functional contrast sensitivity test. Pupil-plane glare-source illuminances (i.e., 0, 1.35, and 19.21  lm/m2), eccentricities (5°, 10°, and 15°), and background luminances (1, 2.6, and 26  cd/m2) were investigated. Visual performance was better than predicted, based on a loss of retinal image contrast caused by scattered light, particularly in the mesopic range. Prediction accuracy improved significantly when the expected increase in retinal sensitivity in the presence of scattered light was also incorporated in the model.In the last decades, Gaussian Mixture Models (GMMs) have attracted considerable interest in data mining and pattern recognition. A GMM-based clustering algorithm models a dataset with a mixture of multiple Gaussian components and estimates the model parameters using the Expectation-Maximization (EM) algorithm. Recently, a new Locally Consistent GMM (LCGMM) has been proposed to improve the clustering performance by exploiting the local manifold structure of the data using a p nearest neighbor graph. In addition to the underlying manifold structure, many other forms of prior knowledge may guide the clustering process and improve the performance. In this paper, we introduce a Semi-Supervised LCGMM (Semi-LCGMM), where the prior knowledge is provided in the form of class labels of partial data. In particular, the new Semi-LCGMM incorporates the prior knowledge into the maximum likelihood function of the original LCGMM, and the model parameters are estimated using the EM algorithm. It is worth noting that, in our algorithm, each class may be modeled by multiple Gaussian components while in the unsupervised setting each class is modeled by a single Gaussian component. Our algorithm has shown promising results in many different applications, including clustering breast cancer data, heart disease data, handwritten digit images, human face images, and image segmentation.We present a new method for computing optimized channels for channelized quadratic observers (CQO) that is feasible for high-dimensional image data. The method for calculating channels is applicable in general and optimal for Gaussian distributed image data. Gradient-based algorithms for determining the channels are presented for five different information-based figures of merit (FOMs). Analytic solutions for the optimum channels for each of the five FOMs are derived for the case of equal mean data for both classes. The optimum channels for three of the FOMs under the equal mean condition are shown to be the same. This result is critical since some of the FOMs are much easier to compute. Implementing the CQO requires a set of channels and the first- and second-order statistics of channelized image data from both classes. The dimensionality reduction from M measurements to L channels is a critical advantage of CQO since estimating image statistics from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. In a simulation study we compare the performance of ideal and Hotelling observers to CQO. The optimal CQO channels are calculated using both eigenanalysis and a new gradient-based algorithm for maximizing Jeffrey's divergence (J). Optimal channel selection without eigenanalysis makes the J-CQO on large-dimensional image data feasible.We present a theoretical study of various definitions of laser beam width in a given cross section. Quality of the beam is characterized by dimensionless beam propagation products (BPPs) Δx·Δθ(x)/λ, which are different for the 21 definitions presented, but are close to 1. Six particular beams are studied in detail. In the process, we had to review the properties for the Fourier transform of various modifications and the relationships between them physical Fourier transform (PFT), mathematical Fourier transform (MFT), and discrete Fourier transform (DFT). We found an axially symmetric self-MFT function, which may be useful for descriptions of diffraction-quality beams. In the appendices, we illustrate the thesis "the Fourier transform lives on the singularities of the original."We use light scattering to study spatial correlations in the pore space of Vycor glass upon draining a wetting fluid. We analyze the transmission spectrum of forward-scattered light on the basis of the theory of dielectric constant fluctuation, whereas conventional light scattering analyzes the scattered light at small angles of monochromatic incident light. Assuming that the drained pores, which are surrounded by filled pores, exhibit long-range correlations of a fractal dimension of 2.5, we analytically derive the corresponding turbidity. The slight deviation from the λ(-4) Rayleigh wavelength dependence directly provides the correlation length of the interconnected network of drained pores. The estimated length, ranging from 0.5 to 18 nm at most, is almost the same order as that indirectly estimated from our previous simple effective Rayleigh scatterer model.In time harmonic analysis, media composed of sub-wavelength metallic or dielectric inclusions are described by complex and dispersive effective constitutive parameters. A study of such parameters based on the conservation law of energy and causality is presented. We derive a set of general constraints on the real and imaginary parts of the constitutive parameters for lossy and lossless media in terms of electric and magnetic loss tangents. It is shown that a passive medium can indeed have a negative imaginary part of either the permeability or permittivity over a range of frequencies. These findings are consistent with the principles of causality and energy conservation.The circulating phase gradient component of a singular beam gets modified when focused by a low-numerical-aperature system suffering from coma aberration. The gradient due to this coma aberration splits the higher charge vortex into elementary vortices and distributes them spatially. This splitting depends on the charge and polarity of the incident singular beam as well as the sign and magnitude of the aberration coefficient. The transverse component of the Poynting vector field distribution at the focal plane is decomposed into the curl or solenoidal component and divergence or irrotational component using the Helmholtz-Hodge decomposition technique. The solenoidal component that relates to the orbital angular momentum carries the circulating energy, while the irrotational component shows the sources and sinks of the energy. Intriguing results of the study of energy flow around the edge dislocations apart from the point phase defects in the irrotational components are also presented.