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The total magnification due to a point lens has been of particular interest as the theorem that gravitational lensing results in light amplification for all observers appears to contradict the conservation of photon number. This has been…

The computation of the magnification of a finite source by an arbitrary gravitational lens can be reduced from a two-dimensional to a one-dimensional integral using a generalization of Stoke's theorem. For a large source lensed by a…

If an extended source, such as a galaxy, is gravitationally lensed by a massive object in the foreground, the lensing distorts the observed image. It is straightforward to simulate what the observed image would be for a particular lens and…

We prove a gravitational lensing theorem: the magnification of a source of uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A, where A is the area of the source and R_E and R_L are the Einstein radius and size of…

We study approximate solutions of the gravitational lens equation and corresponding lens magnification factor near the critical point. This consideration is based on the Taylor expansion of the lens potential in powers of coordinates and an…

We investigate the finite source size effect in the context of the wave optics in the gravitational lensing. The magnification of an extended source is presented in an analytic manner for the singular isothermal sphere lens model as well as…

Calculations are presented detailing the gravitational lens diffraction due to the steep brightness gradient of the limb of a stellar source. The lensing case studied is the fold caustic crossing. The limb diffraction signal greatly exceeds…

We present a rigorous, detailed study of the generic, quantitative properties of gravitational microlensing near cusp catastrophes. We derive explicit formulas for the total magnification and centroid of the images created for sources…

In gravitational lensing, the magnification effect changes the luminosity and size of a background galaxy. If the image sizes are not small compared to the scale over which the magnification and shear vary, higher-order distortions occur…

We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from…

We investigate imaging point sources with a monopole gravitational lens, such as the Solar Gravitational Lens in the geometric optics limit. We compute the light amplification of the lens used in conjunction with a telescope featuring a…

We discuss the classic theorem according to which a gravitational lens always produces a total magnification greater than unity. This theorem seems to contradict the conservation of total flux from a lensed source. The standard solution to…

The extended source effect on microlensing magnification is non-negligible and must be taken into account for in an analysis of microlensing. However, the evaluation of the extended source magnification is numerically expensive because it…

Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…

In this brief communication a new method is outlined for modelling magnification patterns on an observer's plane using a first order approximation to the null geodesic path equations for a point mass lens. For each ray emitted from a…

An exact analytical expression for the bending angle of light due to a non-rotating massive object, considering the actual distances from source and observer to the gravitational mass, is derived. Our novel formula generalizes Darwin…

We demonstrate that for several of the gravitational lens models used to describe galaxies, there exists a quantity we dub the magnification invariant, equaling the sum of the signed magnifications of the images, that is a constant when the…

Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…

Strong gravitational lens systems with extended sources are of special interest because they provide additional constraints on the models of the lens systems. To use a gravitational lens system for measuring the Hubble constant, one would…

Extended source effects can be seen in gravitational lensing events when sources cross critical lines. Those events probe the stellar intensity profile and could be used to measure limb darkening coefficients to test stellar model…