Reconstruction of the high resolution phase in a closed loop adaptive optics system

Rihuan Ke, Roland Wagner, Ronny Ramlau, Raymond Chan

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)

Abstract

Adaptive optics is a commonly used technique to correct the phase distortions caused by the Earth’s atmosphere to improve the image quality of the ground-based imaging systems. However, the ob-served images still suffer from the blur caused by the adaptive optics residual wavefront. In this paper, we propose a model for reconstructing the residual phase in high resolution from a sequence of deformable mirror data. Our model is based on the turbulence statistics and the Taylor frozen flow hypothesis with knowledge of the wind velocities in atmospheric turbulence layers. A tomography problem for the phase distortions from different altitudes is solved in order to get a high quality phase reconstruction. We also consider inexact tomography operators resulting from the uncertainty in the wind velocities. The wind velocities are estimated from the deformable mirror data and, additionally, by including them as unknowns in the objective function. We provide a theoretical analysis on the existence of a minimizer of the objective function. To solve the associated joint optimization problem, we use an alternating minimization method which results in a high resolution reconstruction algorithm with adaptive wind velocities. Numerical simulations are carried out to show the effectiveness of our approach.

Original languageEnglish
Pages (from-to)775-806
Number of pages32
JournalSIAM Journal on Imaging Sciences
Volume13
Issue number2
DOIs
Publication statusPublished - 2020

Bibliographical note

Funding Information:
The work of the first author was supported by the Hong Kong Research Grants Council grant CUHK14306316 and by the Austrian Science Fund (FWF) in the Doctoral Program ?Computational Mathemat-ics? grant W1214-Project 8. The work of the second and third authors was supported by the Austrian Science Fund (FWF) project F 6805-N36: ?SFB Tomography Across the Scales? and by the Austrian Ministry of Research (Hochschulraumstrukturmittel) in the project ?Beobachtungsorientierte Astrophysik in der E-ELT Ara.? The work of the fourth author was supported by the Hong Kong Research Grants Council grants CUHK14306316, CUHK14301718, CityU Grant 9380101, CRF grant C1007-15G, and AoE/M-05/12.Acknowledgment. We thank the anonymous reviewers for their thorough review helping us to improve the paper.

Funding Information:
∗Received by the editors April 26, 2019; accepted for publication (in revised form) January 27, 2020; published electronically May 5, 2020. https://doi.org/10.1137/19M1258426 Funding: The work of the first author was supported by the Hong Kong Research Grants Council grant CUHK14306316 and by the Austrian Science Fund (FWF) in the Doctoral Program “Computational Mathematics” grant W1214 - Project 8. The work of the second and third authors was supported by the Austrian Science Fund (FWF) project F 6805-N36: “SFB Tomography Across the Scales” and by the Austrian Ministry of Research (Hochschulraumstrukturmittel) in the project “Beobachtungsorientierte Astrophysik in der E-ELT Ara.” The work of the fourth author was supported by the Hong Kong Research Grants Council grants CUHK14306316, CUHK14301718, CityU Grant 9380101, CRF grant C1007-15G, and AoE/M-05/12.

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.

Keywords

  • Adaptive optics
  • Astronomical imaging
  • Image improvement

Fingerprint

Dive into the research topics of 'Reconstruction of the high resolution phase in a closed loop adaptive optics system'. Together they form a unique fingerprint.

Cite this