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arxiv: 2603.02817 · v2 · submitted 2026-03-03 · 🌌 astro-ph.IM

Recognition: no theorem link

Single-star optical turbulence profiling techniques for the SHIMM and other Shack-Hartmann instruments

Ryan Griffiths , Timothy Butterley , Richard Wilson , James Osborn
Authors on Pith no claims yet

Pith reviewed 2026-05-15 16:55 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords optical turbulenceShack-HartmannSHIMMCn2 profilingcoherence timesite characterizationMonte Carlo simulationexposure correction
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The pith

SHIMM derives Z-tilt weighting functions and exposure corrections to recover accurate four-layer optical turbulence profiles from single-star Shack-Hartmann data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops techniques for continuous optical turbulence profiling with the SHIMM instrument, a fast infrared Shack-Hartmann sensor that operates on a single star. It derives and validates Z-tilt weighting functions, implements corrections for finite exposure times, and combines the resulting profile with the Fast Defocus method to estimate coherence time. End-to-end Monte Carlo simulations of the instrument and atmosphere show that integrated turbulence parameters match the input values with correlation coefficients near one, small RMS errors, and low bias. A four-layer model recovers each layer with high fidelity even under daytime conditions, and the work indicates a practical Cn2 sensitivity floor near 2x10^{-15} m^{2/3} together with evidence of cross-talk between the ground layer and the first elevated layer.

Core claim

Advances in Shack-Hartmann profiling on the SHIMM include derivation and validation of Z-tilt weighting functions, methods for correcting non-zero exposure times, and estimation of coherence time by coupling the profile to the Fast Defocus method. When tested in end-to-end Monte Carlo simulations, all integrated OT parameters agreed closely with the known inputs, while the four-layer model showed high correlation for every layer even in daytime turbulence; the study reports a Cn2 sensitivity limit near 2x10^{-15} m^{2/3} and notes cross-talk between the strong ground layer and the first atmospheric layer.

What carries the argument

Z-tilt weighting functions that convert Shack-Hartmann image-motion measurements into layer-resolved Cn2 values, augmented by explicit exposure-time corrections and coupling to the Fast Defocus method for coherence time.

If this is right

  • Integrated optical turbulence parameters can be measured continuously day and night with near-unit correlation to true values.
  • A simple four-layer model recovers individual layer strengths with high accuracy even during daytime conditions.
  • Coherence time can be obtained directly from the derived turbulence profile without separate instrumentation.
  • The instrument reaches a practical Cn2 sensitivity limit around 2x10^{-15} m^{2/3}.
  • Cross-talk between the ground layer and the first elevated layer must be accounted for in profile interpretation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same Z-tilt and exposure-correction methods could be ported to other single-star Shack-Hartmann sensors already operating at observatories.
  • The observed layer cross-talk implies that increasing the number of layers or adding angular diversity may be needed to separate closely spaced turbulence.
  • Continuous profiling at this sensitivity would allow real-time input to adaptive-optics systems and optical-communication link budgets.
  • The simulation-validated sensitivity floor suggests a clear threshold for designing future site-characterization campaigns.

Load-bearing premise

The end-to-end Monte Carlo simulations of the SHIMM instrument and atmospheric conditions accurately capture all relevant real-world effects without unmodeled systematics or biases.

What would settle it

On-sky SHIMM observations that yield integrated turbulence parameters differing by more than a few percent from simultaneous measurements by an independent profiler such as DIMM under the same conditions.

Figures

Figures reproduced from arXiv: 2603.02817 by James Osborn, Richard Wilson, Ryan Griffiths, Timothy Butterley.

Figure 1
Figure 1. Figure 1: Theoretical response functions for the SHIMM using a four layer model. The graph contrasts the response functions calculated using the original profiling method laid out in [22] (top) with the method detailed in this work (bottom) which combines the slopes and intensities in the inversion. to be an on-axis point source. It is collected in an aperture with a normalised pupil function 𝑃(x). This setup leads … view at source ↗
Figure 2
Figure 2. Figure 2: Left: A comparison of a cut-through of the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Weighting functions used by the SHIMM profiling technique. The top row shows a 2D plot of the weighting functions for a layer at 10 km for the (from left to right) x-slopes, y-slopes and intensity fluctuations, given as a function of the sub-aperture separations 𝛿𝑖, 𝛿 𝑗. The bottom row shows a cross-section through of the centre of the weighting functions in the 𝛿 𝑗 direction. These cross-sections have bee… view at source ↗
Figure 4
Figure 4. Figure 4: Condition number of the weighting function matrix [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Effect of changing exposure time on three terms in the [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The structure function of defocus calculated from simulation of two layers with [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Parameter measurement methods were tested via end-to-end Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results of measurements of the coherence time (left) and effective wind velocity [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scatter plots of the true 𝐶 2 𝑛 (ℎ) dℎ values for 248 SCIDAR profiles binned to four layers using the response functions against 𝐶 2 𝑛 (ℎ) dℎ measured by the SHIMM simulation for the four layer model. The top left panel plots the ground layer response, top right the 4 km layer, bottom left the 12 km layer and bottom right the 20 km layer. The solid line in each panel represents a perfect response, 𝑦 = 𝑥. L… view at source ↗
Figure 10
Figure 10. Figure 10: Residual 𝐶 2 𝑛 (ℎ) dℎ between the SHIMM simulation measurements and binned SCIDAR profiles for the 0 km layer plotted against that of the 4 km layer. The red dashed line is the best-fit line calculated from linear regression. profile. This problem was solved, after subtraction of noise bias, with a non-negative least squares algorithm. This new formulation was shown to be superior to the previous approach… view at source ↗
Figure 11
Figure 11. Figure 11: Histograms of the input profile 𝐶 2 𝑛 (ℎ) dℎ values that make up figure 9. Blue bars represent values with a non-zero estimate from the simulation, red bars a "missing" estimate. The layer heights are labelled on the right hand side and the missing percentage given in the top-left of each plot. SHIMM layers relied on the response to each layer being sufficiently independent. To identify measurements falli… view at source ↗
read the original abstract

Atmospheric optical turbulence (OT) monitoring is crucial for site characterisation at astronomical observatories and optical communications ground stations. The Shack-Hartmann Image Motion Monitor (SHIMM) instrument implements a fast, infrared Shack-Hartmann sensor to measure a low-resolution OT profile continuously throughout the day and night. This work presents advances made in Shack-Hartman optical turbulence profiling techniques implemented on the SHIMM, including the derivation and validation of Z-tilt weighting functions, implementation of methods for correcting for non-zero exposure times, and for estimating the coherence time of optical turbulence using the profile coupled with the Fast Defocus method. These techniques were tested via end-to-end Monte Carlo simulations of the SHIMM instrument. All measurements of integrated OT parameters were found to be in strong agreement with the simulation inputs evidenced by correlation coefficients close to one, small RMS error and bias. The accuracy of a four-layer model was also investigated, which showed high correlation with simulation inputs for all layers even in daytime OT conditions. This study suggests a Cn^2 sensitivity limit in the region of 2x10^-15 m^(1/3) and displays evidence of a cross-talk effect between the strong ground layer and first atmospheric layer.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents advances in single-star optical turbulence profiling for the Shack-Hartmann Image Motion Monitor (SHIMM), deriving Z-tilt weighting functions, exposure-time corrections, and coherence-time estimation via the profile combined with the Fast Defocus method. These are tested exclusively through end-to-end Monte Carlo simulations of the instrument and atmosphere, which report correlation coefficients near unity, small RMS errors and bias for integrated OT parameters, high fidelity for a four-layer model (including daytime conditions), a suggested Cn² sensitivity limit of ~2×10^{-15} m^{1/3}, and evidence of cross-talk between the ground layer and first atmospheric layer.

Significance. If the simulation results translate to real data, the techniques would provide a practical route to continuous low-resolution OT profiling day and night, directly benefiting site characterization for astronomy and free-space optical communications. The reported performance metrics on integrated parameters and the four-layer recovery constitute a concrete step forward for Shack-Hartmann-based profilers.

major comments (2)
  1. [Abstract] Abstract and validation description: the reported cross-talk between the strong ground layer and first atmospheric layer is noted but not traced to its source (weighting functions, inversion matrix, or simulated atmosphere); if it is an artifact of the method rather than the input turbulence, the claimed accuracy of the four-layer model and the 2×10^{-15} m^{1/3} sensitivity limit would not hold under real conditions.
  2. [Validation] Validation section: all quantitative claims rest on end-to-end Monte Carlo simulations matching known inputs; without an independent real-data comparison or a description of how the inversion is performed without using the same inputs that generated the data, the support for the central claims remains simulation-specific.
minor comments (2)
  1. Specify the exact simulation parameters (telescope diameter, wavelength range, exposure times, number of realizations) and any data-exclusion criteria so that the Monte Carlo results can be reproduced.
  2. Clarify the notation for the Z-tilt weighting functions and the exposure-time correction formula; ensure they are written explicitly rather than referenced only by name.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful comments on our manuscript. We address each of the major comments below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and validation description: the reported cross-talk between the strong ground layer and first atmospheric layer is noted but not traced to its source (weighting functions, inversion matrix, or simulated atmosphere); if it is an artifact of the method rather than the input turbulence, the claimed accuracy of the four-layer model and the 2×10^{-15} m^{1/3} sensitivity limit would not hold under real conditions.

    Authors: We agree that identifying the source of the observed cross-talk is crucial for validating the method's robustness. In the revised version, we will expand the validation section to include an analysis tracing the cross-talk to the specific form of the Z-tilt weighting functions for adjacent layers and the conditioning of the inversion matrix. This will demonstrate that the effect is inherent to the single-star profiling geometry rather than the particular simulated turbulence, thereby supporting the reported accuracy and sensitivity limits within the context of the simulation framework. revision: yes

  2. Referee: [Validation] Validation section: all quantitative claims rest on end-to-end Monte Carlo simulations matching known inputs; without an independent real-data comparison or a description of how the inversion is performed without using the same inputs that generated the data, the support for the central claims remains simulation-specific.

    Authors: The quantitative claims are indeed derived from end-to-end Monte Carlo simulations. We will revise the validation section to explicitly describe the inversion procedure, clarifying that the algorithm recovers the turbulence profile from the simulated Shack-Hartmann images without direct access to the input Cn² values used to generate the atmospheric phase screens. This ensures the validation is not circular. While we acknowledge that real-data validation would further strengthen the claims, the current study focuses on the development and simulation-based testing of the new techniques; we will add a discussion of this limitation and outline plans for future on-sky validation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; validation uses independent simulation inputs

full rationale

The paper derives Z-tilt weighting functions, exposure-time corrections, and four-layer profiling methods, then tests them via end-to-end Monte Carlo simulations whose input Cn2 profiles and integrated parameters are known a priori. Reported agreement (high correlation, low RMS/bias) is a direct comparison of recovered outputs to those independent inputs rather than any reduction of results to fitted parameters by construction. No equations, self-citations, or ansatzes are shown to force the central claims; the derivation chain remains self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

All validation claims rest on the assumption that the Monte Carlo model faithfully reproduces instrument and atmospheric physics; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption End-to-end Monte Carlo simulations accurately represent the SHIMM instrument response and atmospheric turbulence statistics
    All reported agreement metrics depend on this model fidelity

pith-pipeline@v0.9.0 · 5519 in / 1429 out tokens · 72739 ms · 2026-05-15T16:55:11.344040+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    The ESO differential image motion monitor,

    M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys.227, 294–300 (1990)

    work page 1990

  2. [2]

    MASS: a monitor of the vertical turbulence distribution,

    V. Kornilov, A. A. Tokovinin, O. Vozyakova,et al., “MASS: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II,P. L. Wizinowich and D. Bonaccini, eds. (2003), p. 837

    work page 2003

  3. [3]

    LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude resolution,

    R. Avila, J. L. Avils, R. W. Wilson,et al., “LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude resolution,” Mon. Notices Royal Astron. Soc.387, 1511–1516 (2008)

    work page 2008

  4. [4]

    SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,

    R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Notices Royal Astron. Soc.337, 103–108 (2002)

    work page 2002

  5. [5]

    FASS: a turbulence profiler based on a fast, low-noise camera,

    A. Guesalaga, B. Ayancán, M. Sarazin,et al., “FASS: a turbulence profiler based on a fast, low-noise camera,” Mon. Notices Royal Astron. Soc.501, 3030–3045 (2021)

    work page 2021

  6. [6]

    Measurement of turbulence profile from defocused ring images,

    A. Tokovinin, “Measurement of turbulence profile from defocused ring images,” Mon. Notices Royal Astron. Soc. 502, 794–808 (2021)

    work page 2021

  7. [7]

    Phase estimation at the point-ahead angle for AO pre-compensated ground to GEO satellite telecoms,

    P. Lognoné, J.-M. Conan, G. Rekaya, and N. Védrenne, “Phase estimation at the point-ahead angle for AO pre-compensated ground to GEO satellite telecoms,” Opt. Express31(2023)

    work page 2023

  8. [8]

    Pre-distortion adaptive optics for optical feeder links: simulations and performance analyses,

    I. R. Hristovski, J. Osborn, O. J. D. Farley,et al., “Pre-distortion adaptive optics for optical feeder links: simulations and performance analyses,” Opt. Express32, 20976 (2024)

    work page 2024

  9. [9]

    Impact of the Cn2 description on WFAO performance,

    A. Costille and T. Fusco, “Impact of the Cn2 description on WFAO performance,” inAO for ELT 2011 - 2nd International Conference on Adaptive Optics for Extremely Large Telescopes,(2011)

    work page 2011

  10. [10]

    Requirements for AO-ELT operation and ELT site monitor,

    A. Tokovinin, “Requirements for AO-ELT operation and ELT site monitor,” in1st AO4ELT conference - Adaptive Optics for Extremely Large Telescopes,(EDP Sciences, Les Ulis, France, 2010), p. 02005

    work page 2010

  11. [11]

    Limitations imposed by optical turbulence profile structure and evolution on tomographic reconstruction for the ELT,

    O. J. D. Farley, J. Osborn, T. Morris,et al., “Limitations imposed by optical turbulence profile structure and evolution on tomographic reconstruction for the ELT,” Mon. Not. R. Astron. Soc.494, 2773–2784 (2020)

    work page 2020

  12. [12]

    Filteringtechniquestoenhanceopticalturbulenceforecastperformances at short time-scales,

    E.Masciadri, G.Martelloni, andA.Turchi, “Filteringtechniquestoenhanceopticalturbulenceforecastperformances at short time-scales,” Mon. Notices Royal Astron. Soc.492, 140–152 (2020)

    work page 2020

  13. [13]

    Continuous daytime and nighttime forecast of atmospheric optical turbulence from numerical weather prediction models,

    F. Quatresooz, R. Griffiths, L. Bardou,et al., “Continuous daytime and nighttime forecast of atmospheric optical turbulence from numerical weather prediction models,” Opt. Express31, 33850 (2023)

    work page 2023

  14. [14]

    Optical turbulence forecasts at short time-scales using an autoregressive method at the Very Large Telescope,

    E. Masciadri, A. Turchi, and L. Fini, “Optical turbulence forecasts at short time-scales using an autoregressive method at the Very Large Telescope,” Mon. Notices Royal Astron. Soc.523, 3487–3502 (2023)

    work page 2023

  15. [15]

    Global atmospheric turbulence forecasting for free-space optical communications,

    J. Osborn, J.-E. Communal, and F. Jabet, “Global atmospheric turbulence forecasting for free-space optical communications,” inFree-Space Laser Communications XXXV,H. Hemmati and B. S. Robinson, eds. (SPIE, 2023), p. 51

    work page 2023

  16. [16]

    Determination of the profile of atmospheric optical turbulence strength from SLODAR data,

    T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Notices Royal Astron. Soc.369, 835–845 (2006)

    work page 2006

  17. [17]

    C_nˆ2 profile measurement from Shack-Hartmann data,

    N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, “C_nˆ2 profile measurement from Shack-Hartmann data,” Opt. Lett.32, 2659 (2007)

    work page 2007

  18. [18]

    Atmospheric turbulence profiling with multi-aperture scintillation of a Shack–Hartmann sensor,

    H. Ogane, M. Akiyama, S. Oya, and Y. Ono, “Atmospheric turbulence profiling with multi-aperture scintillation of a Shack–Hartmann sensor,” Mon. Notices Royal Astron. Soc.503, 5778–5788 (2021)

    work page 2021

  19. [19]

    Comparison of centroid computation algorithms in a Shack-Hartmann sensor,

    S. Thomas, T. Fusco, A. Tokovinin,et al., “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Notices Royal Astron. Soc.371, 323–336 (2006)

    work page 2006

  20. [20]

    Cn2 profile measurement from Shack-Hartmann data: experimental validation and exploitation,

    N. Védrenne, A. Bonnefois Montmerle, C. Robert,et al., “Cn2 profile measurement from Shack-Hartmann data: experimental validation and exploitation,” inOptics in Atmospheric Propagation and Adaptive Systems XIII,vol. 7828 K. Stein and J. D. Gonglewski, eds. (SPIE, 2010), p. 78280B

    work page 2010

  21. [21]

    SHIMM: a versatile seeing monitor for astronomy,

    S. Perera, R. W. Wilson, T. Butterley,et al., “SHIMM: a versatile seeing monitor for astronomy,” Mon. Notices Royal Astron. Soc.520(2023)

    work page 2023

  22. [22]

    Demonstrating 24-hour continuous vertical monitoring of atmospheric optical turbulence,

    R. Griffiths, J. Osborn, O. Farley,et al., “Demonstrating 24-hour continuous vertical monitoring of atmospheric optical turbulence,” Opt. Express31, 6730 (2023)

    work page 2023

  23. [23]

    Continuous 24-hour Shack-Hartmann optical turbulence profiling on a small telescope

    R. Griffiths, “Continuous 24-hour Shack-Hartmann optical turbulence profiling on a small telescope.” Ph.D. thesis, Durham University (2024)

    work page 2024

  24. [24]

    Application of autoregressive models for optical turbulence prediction atopticalcommunicationsites,

    F. Quatresooz, R. Griffiths, J. Osborn,et al., “Application of autoregressive models for optical turbulence prediction atopticalcommunicationsites,”inInternationalConferenceonSpaceOptics—ICSO2024,F.Bernard,N.Karafolas, P. Kubik, and K. Minoglou, eds. (SPIE, 2025), p. 229

    work page 2025

  25. [25]

    A comparison of next-generation turbulence profiling instruments at Paranal,

    R. Griffiths, L. Bardou, T. Butterley,et al., “A comparison of next-generation turbulence profiling instruments at Paranal,” Mon. Notices Royal Astron. Soc.529, 320–330 (2024)

    work page 2024

  26. [26]

    Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,

    C. Robert, J.-M. Conan, V. Michau,et al., “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A23, 613 (2006)

    work page 2006

  27. [27]

    Accurate seeing measurements with MASS and DIMM,

    A. Tokovinin and V. Kornilov, “Accurate seeing measurements with MASS and DIMM,” Mon. Notices Royal Astron. Soc.381, 1179–1189 (2007)

    work page 2007

  28. [28]

    Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,

    R. J. Sasiela and J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A10, 646 (1993)

    work page 1993

  29. [29]

    From Differential Image Motion to Seeing,

    A. Tokovinin, “From Differential Image Motion to Seeing,” Publ. Astron. Soc. Pac.114(2002)

    work page 2002

  30. [30]

    Adaptive optics for astronomy: theoretical performance and limitations,

    R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy: theoretical performance and limitations,” Mon. Notices Royal Astron. Soc.278, 39–61 (1996)

    work page 1996

  31. [31]

    The 24hSHIMM: a continuous day and night turbulence monitor for optical communications,

    R. Griffiths, J. Osborn, O. Farley,et al., “The 24hSHIMM: a continuous day and night turbulence monitor for optical communications,” inFree-Space Laser Communications XXXV,H. Hemmati and B. S. Robinson, eds. (SPIE, 2023), p. 54

    work page 2023

  32. [32]

    Restorationofturbulenceprofilefromscintillationindices,

    A.Tokovinin,V.Kornilov,N.Shatsky,andO.Voziakova,“Restorationofturbulenceprofilefromscintillationindices,” Mon. Notices Royal Astron. Soc.343, 891–899 (2003)

    work page 2003

  33. [33]

    Atmospheric scintillation in astronomical photometry,

    J. Osborn, D. Föhring, V. S. Dhillon, and R. W. Wilson, “Atmospheric scintillation in astronomical photometry,” Mon. Notices Royal Astron. Soc.452, 1707–1716 (2015)

    work page 2015

  34. [34]

    Astronomical adaptive optics. II. Experimental results of an optimized modal control

    E. Gendron and P. Lena, “Astronomical adaptive optics. II. Experimental results of an optimized modal control.” Astron. Astrophys. Suppl. Ser.111, 153–167 (1995)

    work page 1995

  35. [35]

    Bounded-Variable Least-Squares: an Algorithm and Applications,

    P. Stark and R. Parker, “Bounded-Variable Least-Squares: an Algorithm and Applications,” Comput. Stat.10(1995)

    work page 1995

  36. [36]

    R. C. Aster, B. Borchers, and C. H. Thurber,Parameter Estimation and Inverse Problems(Elsevier, 2013)

    work page 2013

  37. [37]

    Bootstrap Methods: Another Look at the Jackknife,

    B. Efron, “Bootstrap Methods: Another Look at the Jackknife,” The Ann. Stat.7(1979)

    work page 1979

  38. [38]

    Differential image motion in the short-exposure regime,

    V. Kornilov and B. Safonov, “Differential image motion in the short-exposure regime,” Mon. Notices Royal Astron. Soc.418(2011)

    work page 2011

  39. [39]

    Atmospheric coherence times in interferometry: definition and measurement,

    A. Kellerer and A. Tokovinin, “Atmospheric coherence times in interferometry: definition and measurement,” Astron. & Astrophys.461, 775–781 (2007)

    work page 2007

  40. [40]

    Review of high-contrast imaging systems for current and future ground- and space-based telescopes I: coronagraph design methods and optical performance metrics,

    E. Douglas, N. Zimmerman, G. Ruane,et al., “Review of high-contrast imaging systems for current and future ground- and space-based telescopes I: coronagraph design methods and optical performance metrics,” inSpace Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave,H. A. MacEwen, M. Lystrup, G. G. Fazio,et al., eds. (SPIE, 2018), p. 98

    work page 2018

  41. [41]

    FADE, an instrument to measure the atmospheric coherence time,

    A. Tokovinin, A. Kellerer, and V. Coudé Du Foresto, “FADE, an instrument to measure the atmospheric coherence time,” Astron. & Astrophys.477, 671–680 (2008)

    work page 2008

  42. [42]

    Roddier,Adaptive Optics in Astronomy(Cambridge University Press, 1999)

    F. Roddier,Adaptive Optics in Astronomy(Cambridge University Press, 1999)

    work page 1999

  43. [43]

    Zernike Polynomials and Atmospheric Turbulence

    R. J. Noll, “Zernike Polynomials and Atmospheric Turbulence.” J Opt Soc Am66, 207–211 (1976)

    work page 1976

  44. [44]

    AOtools: a Python package for adaptive optics modelling and analysis,

    M. J. Townson, O. J. D. Farley, G. Orban de Xivry,et al., “AOtools: a Python package for adaptive optics modelling and analysis,” Opt. Express27, 31316 (2019)

    work page 2019

  45. [45]

    A demonstration of 24-hour continuous optical turbulence monitoring in a city,

    L. Beesley, R. Griffiths, K. Hartley,et al., “A demonstration of 24-hour continuous optical turbulence monitoring in a city,” Opt. Express (2024)

    work page 2024

  46. [46]

    Optical turbulence profiling with Stereo-SCIDAR for VLT and ELT,

    J. Osborn, R. W. Wilson, M. Sarazin,et al., “Optical turbulence profiling with Stereo-SCIDAR for VLT and ELT,” Mon. Notices Royal Astron. Soc.478, 825–834 (2018)

    work page 2018

  47. [47]

    Efficient phase estimation for large-field-of-view adaptive optics,

    T. Fusco, J.-M. Conan, V. Michau,et al., “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett.24, 1472 (1999)

    work page 1999

  48. [48]

    Extruding Kolmogorov-type phase screen ribbons,

    D. L. Fried and T. Clark, “Extruding Kolmogorov-type phase screen ribbons,” J. Opt. Soc. Am. A25, 463 (2008)

    work page 2008

  49. [49]

    The effects of atmospheric turbulence in optical astronomy,

    F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt.19, 281–376 (1981)

    work page 1981

  50. [50]

    Wave-front correction by one or more synthetic beacons,

    R. J. Sasiela, “Wave-front correction by one or more synthetic beacons,” J. Opt. Soc. Am. A11, 379 (1994). A. Z-tilt power spectrum The equation describing the wavefront phase distortion,𝜑, at a position in the telescope pupil,x, resulting from a single, thin turbulent layer with a phase aberration𝜙(x) at an altitude𝑧 is given by [49], 𝜑(x)=𝜙(x) ∗ 1 𝜆𝑧 si...

    work page 1994

  51. [51]

    𝑖 √ 3 (𝜋𝑑𝑓 𝑥 cos(𝜋𝑑𝑓 𝑥) −sin(𝜋𝑑𝑓 𝑥)) (𝜋𝑑𝑓 𝑥)2 # .(41) Similarly 𝐹𝑦 (f) is given by swapping𝑓𝑥 and 𝑓𝑦 in Eq. 41. The “filter function

    From hereon, only the𝑥 slopes will be considered as the𝑦 slopes followthesamederivation. EvaluatingthepowerspectraldensityofEq.(36)requirescalculating the Fourier transform of the Zernike functions,ˆ𝑍, which is given in [43], ˆ𝑍𝑥 (f ′)= ∫ ∞ −∞ 𝑃 (x′) 𝑍2 (x′) exp[−2𝜋𝑖f ′ ·x ′]𝑑x ′.(40) The spatial frequency units aref′ =𝑑f . This integral can be evaluated ...

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