Related papers: A disk-covering problem with application in optica…
Radio interferometry is the current method of choice for deep space astronomy, but in the past few decades optical techniques have become increasingly common. This research seeks to characterize the performance of aperture masking…
Pre-transitional disks are protoplanetary disks with a gapped disk structure, potentially indicating the presence of young planets in these systems. In order to explore the structure of these objects and their gap-opening mechanism, we…
The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every straight line passing through S. In spite of its simplicity,…
Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in…
The imaging of disks around young stars presents extreme challenges in high dynamic range, angular resolution, and sensitivity. Recent instrumental advances have met these challenges admirably, leading to a marked increase in imaging…
The $k$-coverage problem is to find the minimum number of disks such that each point in a given plane is covered by at least $k$ disks. Under unit disk condition, when $k$=1, this problem has been solved by Kershner in 1939. However, when…
In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not…
The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
Given N points in the plane $P_1 P_2...P_N$ and a location $\Omega$, the union of discs with diameters $[\Omega P_i], i = 1, 2,...N$ covers the convex hull of the points. The location $\Omega_s$ minimizing the area covered by the union of…
Pupil mapping is a promising and unconventional new method for high contrast imaging being considered for terrestrial exoplanet searches. It employs two (or more) specially designed aspheric mirrors to create a high-contrast amplitude…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
A microscope based on the Linnik interferometer was designed, built, and tested. Two methods were used for interference pattern measurement: phase-shifting and polarized single-shot methods. The former uses a low coherence light emitting…
We consider the situation where one is given a set S of points in the plane and a collection D of unit disks embedded in the plane. We show that finding a minimum cardinality subset of D such that any path between any two points in S is…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
In this paper, I review how optical spectro-interferometry has become a particularly well suited technique to study the close environment of young stars, by spatially resolving both their IR continuum and line emission regions. I summarize…
We consider the set multi-cover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to find a minimum cardinality subset of F such that each point p in P is covered by (contained…
This letter casts the problem of optimum discrete beamforming as the computation of the Minkowski sum of convex polygons, which is itself a convex polygon. The number of vertices of the latter is at most the sum of the number of vertices of…
Large mm surveys of star forming regions enable the study of entire populations of planet-forming disks and reveal correlations between their observable properties. Population studies of disks have shown that the correlation between disk…
The $L_p$-Minkowski problem deals with the existence of closed convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed $p$-area measures. It extends the classical Minkowski problem and embraces several important geometric and physical…