We present a numerical method for calculating inhomogeneous refractive index fields in rectangular gradientindex (GRIN) elements from measured boundary positions and slopes of a collection of rays that transit the medium. The inverse problem is reduced to a set of linear algebraic equations after approximating ray trajectories from the measured boundary values and is solved using a pseudo-inverse algorithm for sparse linear equations. The ray trajectories are subsequently corrected using an iterative ray trace procedure to ensure consistency in the solution. We demonstrate our method in simulation by reconstructing a hypothetical rectangular GRIN element on a 15 ? 15 discrete grid using 800 interrogating rays, in which RMS refractive index errors less than 0.5% of the index range (nmax - nmin ) are achieved. Furthermore, we identify three primary sources of error and assess the importance of data redundancy and system conditioning in the reconstruction process.
|Original language||English (US)|
|Number of pages||12|
|Journal||Journal of the Optical Society of America A: Optics and Image Science, and Vision|
|State||Published - 2015|
Bibliographical noteFunding Information:
This work was funded by DARPA (contract HQ0034-14-D-0001). The views, opinions, and/or findings contained in this article are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. This document is approved for public release, distribution unlimited.