Orthogonality of Zernike modes in phase profiles estimated using Zonal wavefront sensor and transport of intensity phase retrieval method

Akanshu Chauhan; Nedup Sherpa; Nagendra Kumar; Pranjal Choudhury; S. S. Goutam Buddha; Bosanta R. Boruah

doi:10.1117/12.2648666

16 March 2023 Orthogonality of Zernike modes in phase profiles estimated using Zonal wavefront sensor and transport of intensity phase retrieval method

Akanshu Chauhan, Nedup Sherpa, Nagendra Kumar, Pranjal Choudhury, S. S. Goutam Buddha, Bosanta R. Boruah

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Proceedings Volume 12389, Quantitative Phase Imaging IX; 123890I (2023) https://doi.org/10.1117/12.2648666
Event: SPIE BiOS, 2023, San Francisco, California, United States

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Abstract

Zernike polynomials are orthogonal polynomials that form a complete basis set and can be easily used to describe aberrations present in an optical system. Zernike modes find applications in various fields like adaptive optics (AO), optical imaging, ophthalmology, free space optical (FSO) communication, etc. Since the modes are orthogonal, they can express any arbitrary wavefront as their linear combinations. The orthogonality of the modes enables the calculation of the expansion coefficients and suggests the independent behaviour of the Zernike mode. In this work, we numerically estimate the wavefront, defined as Zernike modes, using various state of the art phase retrieval methods. We use the Zonal wavefront sensor (ZWFS) and Transport of Intensity Equation (TIE) for phase reconstruction and then calculate the orthogonality between reconstructed Zernike modes. It is found that the reconstructed Zernike modes are not perfectly orthogonal, which is mainly due to the discrete representation of the Zernike modes. We further investigate how the change in the number of zones in a ZWFS affects orthogonality. We also simulate TIE to retrieve the phase and compare the orthogonality results with ZWFS. This study will be helpful in applications where a wavefront described using Zernike mode needs to be reconstructed, and improvement in the orthogonality is required, which is achieved by increasing the number of zones in the ZWFS and representing Zernike modes in a more continuous form.

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Akanshu Chauhan, Nedup Sherpa, Nagendra Kumar, Pranjal Choudhury, S. S. Goutam Buddha, and Bosanta R. Boruah "Orthogonality of Zernike modes in phase profiles estimated using Zonal wavefront sensor and transport of intensity phase retrieval method", Proc. SPIE 12389, Quantitative Phase Imaging IX, 123890I (16 March 2023); https://doi.org/10.1117/12.2648666

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