Based on the eigenvalues of the ray transformation matrix, a classification of ABCD systems is proposed and some nuclei (i.e., elementary members) in each class are described. In the one-dimensional case, possible nuclei are the magnifier, the lens, and the fractional Fourier transformer. In the two-dimensional case we have-in addition to the obvious concatenations of one-dimensional nuclei-the...

Studying Gaussian beam is a method to investigate laser beam propagation and ABCD matrix is a fast and simple method to simulate Gaussian beam propagation in different mediums. Of the ABCD matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. However in previous work the incident beam and the principle axis of surface are in parallel...

The ABCD matrix method is used to simplifying the theoretical coupling efficiency calculation of Elegant Hermite-Cosh-Gaussian (EHChG) laser beams to a Single Mode Fiber (SMF) with a quadric lens formed on the tip. The integrals of coupling efficiency relation are calculated numerically by Boole method. Meanwhile, the structure parameters of surface-lensed fiber are optimized in numerical simul...

We consider least squares semidefinite programming (LSSDP) where the primal matrix variable must satisfy given linear equality and inequality constraints, and must also lie in the intersection of the cone of symmetric positive semidefinite matrices and a simple polyhedral set. We propose an inexact accelerated block coordinate descent (ABCD) method for solving LSSDP via its dual, which can be r...

The two-by-two ABCD matrix plays a central role in optical sciences. The four elements of this matrix are all real, and its determinant is one. Thus, it has three independent parameters. Yet, it has a rich mathematical content which could lead to interesting results in physics. It is generally assumed that this matrix can be diagonalized by a rotation, but this is not the case as shown in our p...

BACKGROUND/PURPOSE It is known that the standard features for lesion classification are ABCD features, that is, asymmetry, border irregularity, colour variegation and diameter of lesion. However, the observation that skin patterning tends to be disrupted by malignant but not by benign skin lesions suggests that measurements of skin pattern disruption on simply captured white light optical skin ...

BACKGROUND AND PURPOSE The ABCD system was developed to predict early stroke risk after transient ischemic attack. Incorporation of brain imaging findings has been suggested, but reports have used inconsistent methods and been underpowered. We therefore performed an international, multicenter collaborative study of the prognostic performance of the ABCD(2) score and brain infarction on imaging ...

Analytical formula for the cross-spectral density matrix of a twisted electromagnetic Gaussian Schell-model (TEGSM) beam propagating through an astigmatic ABCD optical system in gain or absorbing media is derived based on the unified theory of coherence and polarization. Generalized tensor ABCD law in media is derived. As an application example, the evolution properties of the degree of polariz...