Sphere Tiling

A telescope covers a circular area of the sky in each observation. Let the total number of observations be limited to N. The objective of a survey telescope is to scan the sky such that the coverage is well distributed. This problem is high-dimensional in nature, for the LSST, N = 3 × 106. The variables of the problem are (1) locations of the tile centers, (xi,yi,zi), i = 1,...,N (2) weights of the tiles, Wl ≤ wi ≤ Wu, i = 1,...,N (the amount of time that the telescope stays in that location).

Adopting the notion of ”hyperuniformity” and using my computational tool, originally developed for the Density of Packing, I am searching for ”uniform” configurations.

I believe that what makes this problem different from similar applications in different fields are (1) much higher sensitivity of astronomical inferences to systematic errors that are caused by the inhomogeneity of the coverage. (2) much higher number of tiles which brings curse of dimensionality to the computational methods.

[github]