Zernike polynomials as a basis for modal fitting in lateral shearing interferometry: a discrete domain matrix...

Area of Science:

• Optical Engineering
• Interferometry
• Wavefront Sensing

Background:

• Lateral shearing interferometry is a key technique for wavefront measurement.
• Traditional methods for calculating shear matrices can be complex and limit higher-order analysis.
• Zernike polynomials are widely used for representing wavefront aberrations.

Purpose of the Study:

• To propose a novel Zernike-polynomials-based method for wavefront reconstruction in lateral shearing interferometry.
• To simplify the calculation of shear matrices using matrix transformation.
• To improve the accuracy and extend the applicability of wavefront reconstruction to higher-order terms.

Main Methods:

• Developed a method to calculate shear matrices via matrix transformation.
• Utilized Zernike polynomials for wavefront representation.
• Performed simulations to validate the proposed method.

Main Results:

• The proposed matrix transformation method yields identical shear matrices compared to traditional mathematical derivation.
• The method facilitates easy computation of high-order shear matrices.
• Simulations confirmed the feasibility and accuracy of the approach.

Conclusions:

• The Zernike-polynomials-based method offers an efficient and accurate approach to wavefront reconstruction.
• This technique enables the extension of wavefront analysis to higher-order Zernike terms.
• The proposed method improves reconstruction accuracy in lateral shearing interferometry.