Related papers: Two-mirror Schwarzschild aplanats. Basic relations
We review the Schwarzschild orbit-superposition approach and present a new implementation of this method, which can deal with a large class of systems, including rotating barred disk galaxies. We discuss two conceptuals problems in this…
In this paper, we systematically investigate the optical appearance of a Schwarzschild black hole illuminated by three geometrically thin accretion disk models under varying observational inclination angles. Based on the geometric…
In 1822 A. Fresnel described an experiment to separate a beam of light into its right- and left- circular polarization components using chiral interfaces. Fresnel's experiment combined three crystalline quartz prisms of alternating…
Current sky surveys have been conducted very accurately in order to understand our universe. One of the phenomena survey maps provide is gravitational effect. Albert Einstein (1936) first discussed the possibilities of gravitational lensing…
In the 1930's, Tarski introduced his plank problem at a time when the field discrete geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric as well as…
The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the…
A spherical periscope in multi-dimensional space is a system of two ideal mirrors that reflect the rays emanating from a fixed point to the rays coming back to the same point, and a reversed periscope is a system of two mirrors that reflect…
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of…
Active optics is defined as the control of the shape and the alignment of the components of an optical system at low temporal frequencies. For modern large telescopes with flexible monolithic or segmented primary mirrors and also flexible…
Curved reflective mirrors play an indispensable role in widely-employed Cassegrain-type optics, which consequently are inevitably bulky, and thus neither integratable nor well extendable. Through substituting geometric phase based…
Mirror facets of the H.E.S.S. imaging atmospheric Cherenkov telescopes are aligned using stars imaged onto the closed lid of the PMT camera, viewed by a CCD camera. The alignment procedure works reliably and includes the automatic analysis…
We model the supermassive dark object $M87^*$ as a Schwarzschild lens and study the variations in tangential, radial, and total (the product of tangential and radial) magnifications of images (primary, secondary, and relativistic) against…
Technological advances will allow the placement of many Terahertz detectors at the focal plane of a single telescope. For a telescope of a given diameter and wavelength of operation, there is a limit to the number of usable detectors…
The mirror theorem is generalized to any smooth projective variety X. That is, a fundamental relation between the Gromov-Witten invariants of X and Gromov-Witten invariants of complete intersections Y in X is established.
We investigate whether a three-mirror system, having secondary and the tertiary mirrors with surfaces warped by Zernike polynomials generated by active vase mirrors, is suitable to do the corrections of a fixed parabolic mirror observing at…
In the current article we discuss an illumination problem proposed by Urrutia and Zaks. The focus is on configurations of finitely many two-sided mirrors in the plane together with a source of light placed at an arbitrary point. In this…
This article describes the Schwarzschild orbit superposition method. It is the state-of-the-art dynamical modelling tool for early-type galaxies. Tests with analytic models show that masses and orbital anisotropies of not too face-on…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
The current standard time delay formula (CSTD) in gravitational lensing and its claimed relation to the lens equation through Fermat's principle (least time principle) have been puzzling to the author for some time. We find that the…
We introduce a coordinate system that complements the Kruskal--Szekeres extension. Like the standard construction, it covers the maximally extended Schwarzschild manifold in its entirety, while offering an additional advantage of expressing…