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Phase error scaling law in two-wavelength adaptive optics
  • Milo Hyde,
  • Matthew Kalensky,
  • Mark F Spencer
Milo Hyde

Corresponding Author:[email protected]

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Matthew Kalensky
Mark F Spencer


We derive a simple, physical, closed-form expression for the optical-path difference (OPD) of a two-wavelength adaptive-optics (AO) system. Starting from Hogge and Butts’ classic OPD variance integral expression [J. Opt. Soc. Am. 72, 606 (1982)], we apply Mellin transform techniques to obtain series and asymptotic solutions to the integral. For realistic two-wavelength AO systems, the former converges slowly and has limited utility. The latter, on the other hand, is a simple formula in terms of the separation between the AO sensing (i.e., the beacon) and compensation (or observation) wavelengths. We validate this formula by comparing it to the OPD variances obtained from the aforementioned series and direct numerical evaluation of Hogge and Butts’ integral. Our simple asymptotic expression is shown to be in excellent agreement with these exact solutions. The work presented in this paper will be useful in the design and characterization of two-wavelength AO systems.
03 May 2024Submitted to TechRxiv
09 May 2024Published in TechRxiv