Deflectometry for measuring inhomogeneous refractive index fields in two-dimensional gradient-index elements

Area of Science:

• Optical Engineering
• Computational Physics
• Materials Science

Background:

• Gradient-index (GRIN) materials offer unique optical properties.
• Accurate characterization of inhomogeneous refractive index fields is crucial for optical element design.
• Existing methods may face limitations in reconstructing complex GRIN profiles.

Purpose of the Study:

• To develop and validate a numerical method for calculating inhomogeneous refractive index fields in rectangular GRIN elements.
• To reconstruct GRIN elements from measured ray boundary data.
• To identify and analyze error sources in the reconstruction process.

Main Methods:

• Approximation of ray trajectories from measured boundary positions and slopes.
• Reduction of the inverse problem to a system of linear algebraic equations.
• Solution using a pseudo-inverse algorithm for sparse linear equations and iterative ray trace correction.

Main Results:

• Successful reconstruction of a hypothetical rectangular GRIN element on a 15x15 grid using 800 rays.
• Achieved Root Mean Square (RMS) refractive index errors below 0.5% of the index range.
• Identification of three primary error sources and assessment of data redundancy and system conditioning.

Conclusions:

• The presented numerical method is effective for calculating inhomogeneous refractive index fields in rectangular GRIN elements.
• The method demonstrates high accuracy and provides insights into error mitigation strategies.
• This work contributes to the precise characterization and fabrication of advanced optical materials.