Leveraging the orthogonality of Zernike modes for robust free-space optical communication

Konwar, Santanu; Boruah, Bosanta R.

doi:10.1038/s42005-020-00468-1

Cited by 17 publications

(6 citation statements)

References 38 publications

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“…We then measure this shift to find the slope and estimate the phase using the equations (8,9). For a Z 5 Zernike aberration mode, the reconstructed phase using SHWS is shown in fig.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…4,5 Therefore, these modes find applications in testing optical systems, adaptive optics, wavefront sensing and free space optical (FSO) communication systems. [6][7][8][9] Zernike modes have been used in ophthalmology for corneal study, 10 wavefront corrections for surface and thickness profile mesurement of thin film 8,11,12 and wavefront estimation, 13,14 aberration correction in microscopy [15][16][17] and micromanipulation of optical trapping. 18,19 In all these applications, the orthogonal property is the primary reason for their use.…”

Section: Introductionmentioning

confidence: 99%

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

Chauhan

Sherpa

Kumar³

et al. 2023

Quantitative Phase Imaging IX

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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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“…We then measure this shift to find the slope and estimate the phase using the equations (8,9). For a Z 5 Zernike aberration mode, the reconstructed phase using SHWS is shown in fig.…”

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chauhan

Sherpa

Kumar³

et al. 2023

Quantitative Phase Imaging IX

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“…The phase mismatch becomes increasingly severe owing to turbulence effects in the channel [28]. The wavefront distortion from the phase mismatch is described by the Zernike polynomial as follows [29]:…”

Section: Phase Wavefront Distortionmentioning

confidence: 99%

Effect of Wavefront Distortion on the Performance of Coherent Detection Systems: Theoretical Analysis and Experimental Research

Yang

Xing

et al. 2023

Photonics

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Atmospheric turbulence causes signal beam wavefront distortion at the receiving end of a coherent detection system, which decreases the system mixing efficiency. Based on the coherent detection theory, this study establishes a mathematical model of wavefront distortion with mixing efficiency and mixing gain. It also analyzes the improvement limits of wavefront correction on mixing efficiency and mixing gain under different atmospheric turbulence intensities and experimentally measures them. Simulation results show that the mixing efficiency can be improved to 51%, 55%, and 60% after correcting for tilt, defocus, and astigmatism terms, respectively, when turbulence intensity D/r0 is 2. The mixing gain with homodyne detection is 3 dB higher than heterodyne detection. Meanwhile, the wavefront correction orders required for optimal mixing efficiency are higher than the heterodyne correction order. In the experiment, Haso4 NIR + DM 40 was used, and the turbulence intensity D/r0 was 2. After the closed-loop control algorithm corrects the tilt, defocus, and astigmatism terms, the indoor experimental results showed that the mixing efficiency is improved to 36%, 47%, and 62%, respectively. The outdoor experimental results showed that the mixing efficiency improved to 36%, 51%, and 68%, respectively.

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“…[7][8][9] It has also been used in free-space optical communication to transmit and receive the data accurately. [10][11][12][13][14] Shack-Hartmann wavefront sensor (SHWS) is a well-known and widely used wavefront sensor that employs an array of microlenses to measure the shape of the wavefront. [15][16][17] In SHWS, the detector is placed at the common focal plane of the lenslet array.…”

Section: Introductionmentioning

confidence: 99%

Improvement in wavefront measurement accuracy in grating array-based zonal wavefront sensors by modulating the intensity profile of the incident beam

Kumar¹,

Choudhury²,

Sherpa³

et al. 2023

Practical Holography XXXVII: Displays, Materials, and Applications

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The wavefront measurement accuracy of a grating array based zonal wavefront sensor (GAWS) can be affected by the non-uniform focal spot array and unwanted orders in the detector plane. The non-uniform focal spot array is the outcome of the non-uniform nature of the incident illumination beam’s intensity profile. This paper describes a method that dynamically modulates the laser beam’s intensity using computer generated holography, making the focal spot array uniform and eliminating unwanted spots in a detector plane, thereby enhancing the accuracy of the wavefront measurement. Here, we present proof-of-principle simulation results that demonstrate the working of the proposed improvements in GAWS.

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Leveraging the orthogonality of Zernike modes for robust free-space optical communication

Cited by 17 publications

References 38 publications

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

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

Effect of Wavefront Distortion on the Performance of Coherent Detection Systems: Theoretical Analysis and Experimental Research

Improvement in wavefront measurement accuracy in grating array-based zonal wavefront sensors by modulating the intensity profile of the incident beam

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