An iterative approach to measuring two-dimensional gradient-index profiles based on external measurements of laser beam deflection

We present a numerical method for retrieving the refractive index distribution in two-dimensional gradient-index media from external measurements of laser beam deflection. Using an iterative approach to ascertain the boundary positions and angles of probe beams that transit the optical medium and constructing approximate beam trajectories that satisfy these boundary values, we show that the inverse problem can be reduced to the inversion of a sparse linear algebraic system. The beam trajectories are subsequently corrected using an iterative ray trace procedure that continually refines the computed solution and the associated boundary values. We demonstrate our method in simulation by calculating the refractive index distribution of a hypothetical 2-D gradient-index element from computer-generated external beam deflection data, where RMS index errors below 1% of the index range (n_max'n_min) are achieved.