Nondestructive measurement of two-dimensional refractive index profiles by deflectometry

Di Lin; James R. Leger

doi:10.1117/12.2184856

21 June 2015 Nondestructive measurement of two-dimensional refractive index profiles by deflectometry

Di Lin, James R. Leger

Proceedings Volume 9526, Modeling Aspects in Optical Metrology V; 95260Q (2015) https://doi.org/10.1117/12.2184856
Event: SPIE Optical Metrology, 2015, Munich, Germany

Abstract

We present a method for calculating a two-dimensional refractive index field from measured boundary values of beam position and slope. By initially ignoring the dependence of beam trajectories on the index field and using cubic polynomials to approximate these trajectories, we show that the inverse problem can be reduced to set of linear algebraic equations and solved using a numerical algorithm suited for inverting sparse, ill-conditioned linear systems. The beam trajectories are subsequently corrected using an iterative ray trace procedure so that they are consistent with the ray equation inside the calculated index field. We demonstrate the efficacy of our method through computer simulation, where a hypothetical test index field is reconstructed on a 15 × 15 discrete grid using 800 interrogating rays and refractive index errors (RMS) less than 0.5% of the total index range (n_max-n_min) are achieved. In the subsequent error analysis, we identify three primary sources of error contributing to the reconstruction of the index field and assess the importance of data redundancy. The principles developed in our approach are fully extendable to three-dimensional index fields as well as more complex geometries.

Citation Download Citation

Di Lin and James R. Leger "Nondestructive measurement of two-dimensional refractive index profiles by deflectometry", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260Q (21 June 2015); https://doi.org/10.1117/12.2184856

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Laser beam diagnostics

Deflectometry

Ray tracing

Refractive index

GRIN lenses

Quantization

Error analysis

Show All Keywords

Keywords/Phrases

Search In:

Publication Years