One-dimensional gradient-index metrology based on ray slope measurements using a bootstrap algorithm

The refractive index profile of one-dimensional gradient-index (GRIN) samples can be measured using the incident and exit beam angles of multiple beams passing through the sample at different positions along the index gradient. Beginning from a region of known refractive index, the collective angular deflection measurement of multiple beams is boot-strapped to compute the index profile of the entire sample. An alternative method using an approximate beam displacement model and a corrective algorithm is also presented. The two techniques are used to measure the index profile of a thick GRIN sample, and experimental results show good agreement with a maximum discrepancy of 1.5 x 10(-3) in the calculated index. An index accuracy of 5 x 10(-4) is predicted for the bootstrap method employing typical micron-level spatial measurements. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)