Related papers: Spherical Trigonometry of the Projected Baseline A…
We demonstrate that the angle between star's rotation axis and the observer's line-of-sight, usually called the inclination angle, can be reliably determined for Be stars via H$\alpha$ emission-line profile fitting. We test our method on a…
A short review of recent results in long-baseline optical interferometry pertaining to fundamental stellar parameters and the future possibilities this area over the next decade. Included are discussions of accurate stellar masses, links…
It is possible to learn about the orientation of a star's rotation axis by combining measurements of the star's rotation velocity ($v$) and its projection onto our line of sight ($v\sin i$). This idea has found many applications, including…
This paper is a sequel to arXiv:2511.01024 (Base 1), where an axiomatic framework for angles and the foundations of difference-angle geometry were introduced. In difference-angle geometry, where the difference of slopes of lines is treated…
Detecting the angles and orbits of remote targets precisely has been playing crucial roles in astrophysical research. Due to the resolution limitations imposed by the Airy disk in a single telescope, optical interferometric schemes with at…
The Fresnel Interferometric Imager is a space-based astronomical telescope project yielding milli-arc second angular resolution and high contrast images with loose manufacturing constraints. This optical concept involves diffractive…
The study of fundamental properties (such as temperatures, radii, masses, and ages) and interior processes (such as convection and angular momentum transport) of stars has implications on various topics in astrophysics, ranging from the…
We construct constraints from consistency between estimated parameters from different spheres, termed inter-sphere consistency. It facilitates more flexible calibration using only two spheres, which has been considered a challenging and not…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
Given the extreme accuracy reached by future global space astrometry, one needs a global relativistic modeling of observations. A relativistic definition of astrometric observables is then essential to find uniquely coordinates, parallax…
Several types of Wavefront Sensors (WFS) are nowadays available in the field of Adaptive Optics (AO). Generally speaking, their basic principle consists in measuring slopes or curvatures of Wavefront Errors (WFE) transmitted by a telescope,…
A new astronomical photo-polarimeter that can measure linear polarization of point sources simultaneously in three spectral bands was designed and built in Indian Institute of Astrophysics. The polarimeter has a Calcite beam-displacement…
An algorithm is developed and tested for the problem posed by photometric observations of the bulge of the Milky Way. The latter subtends a non-trivial solid angle on the sky, and we show that this permits inversion of the projected…
A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry.
A set of points $S$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is called a 2-distance set if the set of pairwise distances between the points has cardinality two. The 2-distance set is called spherical if its points lie on the unit…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
In radio interferometric observations, the main source of information is the complex visibility function, which includes amplitude and phase. In this paper, the dependence of the phase of the visibility function on the base projection is…
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…
Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these…
It has been recently demonstrated that integrated optics could enhance accuracy, stability, and ease of use of stellar interferometry techniques. The subject of this thesis is the study of an optical component based on singlemode waveguides…