Modal wavefront reconstruction in radial shearing interferometry with general aperture shapes.

Area of Science:

• Optics and Photonics
• Computational Physics

Background:

• Wavefront reconstruction in radial shearing interferometry is often ill-conditioned, particularly with non-standard aperture shapes.
• Existing methods like least-squares can struggle with numerical stability and accuracy in these scenarios.

Purpose of the Study:

• To develop a robust and numerically stable method for off-axis wavefront reconstruction in radial shearing interferometry.
• To address the challenges posed by general aperture shapes and potential noise in the interferometric data.

Main Methods:

• A Gram-Schmidt orthogonalization method is proposed to construct orthogonal basis functions.
• Expansion coefficients are computed and transformed to reconstruct the original wavefront.
• The algorithm is validated through computer simulations and experimental measurements.

Main Results:

• The proposed method effectively alleviates the ill-conditioning of the wavefront reconstruction problem.
• It demonstrates superior numerical stability compared to the classic least-squares method.
• The algorithm performs well for non-circular apertures and in the presence of noise.

Conclusions:

• The Gram-Schmidt orthogonalization method offers a stable and accurate solution for wavefront reconstruction in radial shearing interferometry with general apertures.
• This approach enhances the reliability of interferometric measurements in complex optical systems.