Pith. sign in

REVIEW 4 major objections 4 minor 38 references

The classical four-sided pyramid wavefront sensor can reconstruct spatial frequencies beyond the pixel-imposed Shannon-Nyquist cutoff and can also estimate amplitude aberrations from the same intensity measurements.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Offset sampling grids in a pyramid wavefront sensor double the number of reconstructable wavefront modes and, with full-rank intensity processing, allow simultaneous phase and amplitude sensing.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection A plausible, clearly argued extension of super-resolution to a single pyramid WFS, with the expected caveats: the 2D case is under-derived and the gain rests on offset calibration that is never quantified. the 4 major comments →

arxiv 2512.17469 v2 pith:IIOB4RQH submitted 2025-12-19 astro-ph.IM

Super-resolution wavefront reconstruction in adaptive-optics with pyramid sensors

Carlos M. Correia , Charlotte Z. Bond , Jo\~ao Aveiro , Fran\c{c}ois Leroux , C\'edric Ta\"issir Heritier , Christophe V\'erinaud This is my paper
classification astro-ph.IM
keywords adaptive opticspyramid wavefront sensorsuper-resolutionwavefront reconstructionamplitude aberrationsscintillationFourier opticsperiodic non-uniform sampling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper argues that the classical four-sided pyramid wavefront sensor (PyWFS), which splits a star's focal-plane field into four pupil images, has been under-used: the four quadrant intensities contain more information than the traditional 'slope' signals extract. By differentially offsetting the four re-imaged pupil grids by half a pixel (achieved, for instance, by adjusting the pyramid apex angles), the quadrants sample different sub-pixel locations; combining these interleaved samples reconstructs spatial frequencies beyond the pixel's Shannon-Nyquist cutoff. In a closed-loop physical-optics simulation, a 20x20 super-resolved PyWFS controls roughly 600 Karhunen-Loève modes, about twice the ~314 modes of the nominal configuration. The same full-rank intensity processing can instead be used, in the nominal configuration, to separate Hermitian from non-Hermitian parts of the field, recovering both phase and amplitude aberrations—though both capabilities cannot be used at once without making the system under-determined. A sympathetic reader would care because this suggests higher-density deformable-mirror control, better resilience to mis-registration, and scintillation sensing without new optics, at no more than a factor-two increase in real-time computation.

Core claim

The central claim is that the 4-sided PyWFS, long regarded as a reduced-rank phase sensor, is actually a full-information sensor. When the four re-imaged pupil grids are mutually offset by a fraction of a pixel, their intensity maps constitute interleaved low-resolution samples; with full-rank 'intensity-maps' processing rather than the customary slope-map subtraction, this periodic non-uniform sampling extends the reconstructed spatial-frequency cutoff beyond the pixel-imposed Nyquist limit. The paper derives a closed-form linearized model (Fourier-mask propagation with Heaviside quadrant masks), proves by a full-rank linear system that the four Fourier coefficients recovered per input freq

What carries the argument

The working horse is the Fourier-mask model of the PyWFS: i_q(x) = |F^{-1}{ H_q(κ) F{ A e^{iψ} } }|^2, where each quadrant q applies a Heaviside spatial-frequency mask H_q, possibly including a phase tilt α_q that offsets the re-imaged pupil. From this, the intensity difference between opposite quadrants is shown to contain both even (real) and odd (imaginary) terms; the traditional slope signal keeps only the odd parts, whereas full-rank intensity processing keeps all of them. The reported capabilities rest on two mechanisms: the Hermitian property of the focal-plane field for a real pupil function (making opposite quadrants redundant), its breakdown when log-amplitude terms are present, an

Load-bearing premise

The whole construction assumes the small-signal linearized diffraction model is accurate and that the sub-pixel offsets between the four quadrant grids are precisely known and stable; if calibration of the sample coordinates is off or the offsets drift (pupil distortion, chromatic shifts, flexure), the interleaved samples add aliasing instead of resolution, and the extra modes collapse.

What would settle it

On a testbed with a real pyramid sensor, introduce a high-order sinusoidal phase at, say, 17 cycles per pupil on a 20-pixel-per-pupil system (above the nominal Nyquist of 10), with a known half-pixel quadrant offset; reconstruct with intensity-map processing. If the recovered frequency is not 17 but its 3-cycles/pupil alias, the SR claim fails. Likewise, illuminate with a known scintillation pattern in nominal configuration and check whether the estimated amplitude matches the linear-model prediction; and measure reconstruction error as a function of intentional offset mismatch (e.g., 0.05, 0.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A 20x20 super-resolved PyWFS controls about 600 Karhunen-Loève modes in closed-loop simulation, roughly twice the ~314 modes of the nominal (non-offset) configuration.
  • The classical 4-sided PyWFS can estimate both phase and amplitude aberrations from its four intensity maps, because the Hermitian/non-Hermitian decomposition yields a full-rank linear system per spatial frequency.
  • Estimating both super-resolved phase and amplitude simultaneously is impossible without making the system under-determined; a design must trade one against the other.
  • Super-resolution only works with full-rank intensity-map processing; the standard slope-map combination cancels the extra interleaved information in the offset case.
  • Because the 2D frequency cutoff rises by √2, a 40x40 PyWFS could in principle drive a DM with about 56x56 actuators, making SR a route to higher actuator densities from smaller detectors.

Where Pith is reading between the lines

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

  • Editorial extension: the sensitivity to high-frequency modes is still attenuated by the pixel-averaging (sinc) response, so the factor-2 mode gain observed in simulation (600 vs 314, not 1256) suggests the practical SR benefit is bounded by detector noise and modulation; the paper leaves this discrepancy incompletely explained.
  • Editorial extension: the proposed differential-binning test implies that existing over-sampled pyramid systems could emulate SR without new optics—simply by binning pixels with opposite sub-pixel shifts—making the technique testable on current instruments.
  • Editorial extension: the amplitude-sensing result could enable real-time scintillation monitoring or even a single PyWFS driving two deformable mirrors in different planes, since the sensor would deliver separate phase and amplitude estimates; the paper mentions these applications but does not simulate them.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper argues that a single four-sided pyramid wavefront sensor (PyWFS) can achieve super-resolution wavefront reconstruction by introducing known sub-pixel offsets between the sampling grids of the four re-imaged pupil intensity patterns. In the small-disturbance regime, the authors linearize the PyWFS diffraction model (Eq. 21) and treat the four quadrant intensities as multiple low-resolution samples of the same field. They claim that this allows reconstruction of spatial frequencies beyond the pixel-imposed Shannon-Nyquist cutoff (Conclusions 1 and 2), and that the same full-rank intensity processing can simultaneously estimate phase and amplitude aberrations by exploiting Hermitian and non-Hermitian components of the focal-plane field (Conclusion 3). The supporting evidence consists of a 1D analytic example and rank analysis (Eqs. 33-46), noise-propagation calculations, and closed-loop physical-optics simulations (Figs. 7-10) showing that a 20x20 PyWFS can control about 600 KL modes versus about 314 in the nominal configuration. The paper also includes application examples for Keck and ELT systems and a proposed experimental test.

Significance. If the central claim holds, the result is practically significant: it would allow a lower-resolution PyWFS detector to drive a higher-density deformable mirror, or to improve robustness to misregistration. The 1D demonstration is clean, the rank analysis of Eq. (46) is explicit, and the closed-loop physical-optics simulations provide a nontrivial, falsifiable indication of a real effect. The paper also honestly flags its own limitations, including the statement in §6.1 that the 600-mode behavior is 'not fully understood.' However, the manuscript's strongest claims rest on two under-supported pillars: the 2D super-resolution cutoff in Eq. (36) is asserted rather than derived, and the calibration tolerance for the sub-pixel offsets is never quantified. These issues need to be addressed before the central conclusions can be regarded as fully established.

major comments (4)
  1. [§4.2, Eq. (36)] The 2D super-resolution cutoff fSR_max = sqrt(2) fmax is stated without derivation. The 1D case (Eq. 35) follows from a half-pixel offset between two sampling combs, but in 2D the four quadrant images are not four independent samples: for phase-only Hermitian fields, diagonal quadrants are redundant, leaving only two effective measurements. A diagonal half-pixel offset produces a quincunx lattice whose usable bandwidth is not obviously sqrt(2) fmax. Because this formula is used in Eq. (49) to motivate the Keck 58x58 DM application, it is load-bearing and needs either a derivation or a clearly stated empirical justification.
  2. [Introduction and §4.2, Fig. 10] The SR construction assumes exact, stable sub-pixel offsets between the quadrant sampling grids. Eq. (34) encodes a perfect d/2 shift, and the text states 'accurate calibration of the sample coordinates is obtained before operation' without quantifying the tolerance. Fig. 10 varies a common, perfectly known offset, but not per-quadrant calibration errors such as pupil distortion, chromatic shifts, or flexure. If the assumed offset differs from the true offset by a small fraction of a pixel, the interleaved grid is no longer a valid denser lattice, and high-frequency content aliases back into low-order KL modes. The absence of a sensitivity analysis on calibration error makes the reported 2x mode gain conditional on an unquantified premise. Please provide a tolerance budget or simulations with random, unknown per-quadrant offset errors.
  3. [§3.2 and Conclusion 3] The amplitude/phase estimation claim is demonstrated only for the 1D system in Eq. (20). The extension to 2D is given in one sentence: 'This naturally extends to the 2-dimensional case.' In 2D there are four pupil images and independent x/y derivative functions, but the linearized coupling between phase and amplitude modes must be shown explicitly; a full-rank 1D 4x4 matrix does not automatically imply a full-rank 2D operator. Please provide the 2D linearization or explicit small-signal simulations with scintillation to support this conclusion.
  4. [§6.1] The paper reports that the SR-enabled PyWFS controls about 600 modes, while a full SR mimic of a 40x40 system would control about 1256 modes, and the authors state that the reasons for this behavior are 'not fully understood.' The claimed factor-of-two improvement over the nominal 314-mode configuration is supported by the simulations, but the gap from the naive 4x expectation suggests that the mechanism is not fully captured by the presented theory. This self-flagged uncertainty should be reconciled with the theoretical claims in §4.2 before the central conclusions are stated as strongly as they are.
minor comments (4)
  1. [Throughout] Several typographical errors: 'electic' (after Eq. 3), 'formailism' (reference Give’On), 'Deutchland' (affiliations), 'T able 1' (Table 1).
  2. [Eq. (49)] The notation f_max(nsa = 40x40) is overloaded; clarify that fmax depends on the pixel sampling step and that the sqrt(2) factor comes from Eq. (36), which itself needs justification.
  3. [Eq. (20)] The scaling factors f_i are introduced after the matrix T; please define them explicitly before use to avoid ambiguity.
  4. [§7] The proposed experimental test is useful, but it assumes that the differential binning offsets are exactly known. Since calibration error is the main practical risk, the test description should include how the offsets are measured or verified.

Circularity Check

0 steps flagged

No significant circularity: the super-resolution and phase/amplitude claims follow from the paper's own Fourier-optics sampling model, and no prediction reduces to a fitted input.

full rationale

The central derivation is self-contained rather than circular. Section 4.1 derives the diffracted-intensity model from the Fourier transform of a step function (Eq. 23) and the resulting knife-edge field (Eqs. 25–32), so the sensor model is not merely imported as an ansatz. Section 4.2 introduces the half-pixel offset as an explicit sampling assumption (Eq. 34) and then computes the rank of the resulting interaction matrix (Eq. 46) and the achievable cut-off frequencies (Eqs. 35–36); these are mathematical consequences of interleaved sampling, not parameters fitted to the target claim. Section 3.2 derives the full-rank phase/amplitude system (Eq. 20) from a first-order expansion of E = P e^{\chi+i\psi}, and the rank is computed, not assumed. The closed-loop simulations in §6 use the same Fourier-masking forward model both to generate the data and to build the reconstructor, so they are self-consistency checks rather than external benchmarks; that affects evidential weight but is not circularity. Likewise, the paper's explicit assumption that accurate calibration of sample coordinates is obtained before operation is a stated robustness premise, not a hidden fit. The self-citations to Oberti et al. (2022), Correia et al. (2022), and Verinaud and Correia (2023) are motivational or explanatory and are not load-bearing: the derivation does not reduce to a self-citation chain, and no uniqueness theorem or external ansatz is invoked to force the result. The paper itself flags in §6.1 that the 600-mode behaviour is 'not fully understood' and calls for further investigation; these are limitations on confidence, not indicators that the derivation is equivalent to its inputs. No equation in the paper reduces to its own input by construction, and no fitted quantity is renamed as a prediction.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 0 invented entities

No genuinely new physical entities are introduced. The 'super-resolved PyWFS' is a configuration of existing optics plus signal processing; the 'confusion map' is cited from the authors' prior work. The main free design parameter is the sub-pixel offset, and the linearization/discretisation assumptions are the explicit axioms the claims rest on.

free parameters (1)
  • Relative quadrant sampling offset = 0.5 detector pixel (1/4-pixel in x and y for the 2D case; optimal ~0.5 sub-aperture in Fig. 10)
    The offset is the key enabler of SR; chosen by design (apex angles/rotation) rather than fitted to data, but the value is hand-selected and the paper scans it in Fig. 10.
axioms (6)
  • domain assumption Monochromatic, scalar electric field with Fraunhofer (Fourier) propagation to the focal plane
    Used throughout (Eq. 3–4) and stated as the starting point; neglects chromaticity and polarization.
  • ad hoc to paper Small-disturbance expansion e^{iψ} ≈ 1 + iψ − ψ²/2 + ... truncated to first order
    Eq. (13) linearizes the field to build the 4x4 phase/amplitude estimation system and the interaction matrix; validity is limited to small residuals.
  • domain assumption Infinite pupil, instantaneous integration time, no modulation, point-like object in the 1D analytic derivation
    Explicitly stated at the start of §4.1; the finite-pupil and modulation cases are only covered by simulation, not by the analytic derivation.
  • domain assumption Detector sampling model: convolution with pixel averaging function Π(x/d) and Dirac comb III(x/d) with prescribed offsets
    Eqs. (33–34) are the discretisation model that produces the offset samples; the entire SR argument depends on this model being the correct physical description.
  • domain assumption PyWFS diffraction model with Fourier masking Hq (Correia et al. 2020; Fauvarque et al. 2016)
    Eq. (21) is the authors' earlier model, adopted here without re-derivation; all intensity-maps and interaction matrices are computed from it.
  • standard math The Hermitian property of the focal-plane electric field for real-valued pupil functions
    Invoked in §3 and §4.1 to argue diagonally opposite quadrants are redundant; the SR argument relies on breaking/exploiting this property.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Super-resolution wavefront reconstruction in adaptive-optics with pyramid sensors." pith.science (2026). https://pith.science/paper/IIOB4RQH

@misc{pith2026251217469,
  author       = {Pith},
  title        = {Pith review of: Super-resolution wavefront reconstruction in adaptive-optics with pyramid sensors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IIOB4RQH}},
  note         = {Machine review of arXiv:2512.17469}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Super-resolution (SR) refers to a combination of optical design and signal processing techniques jointly employed to obtain reconstructed wave-fronts at a higher-resolution from multiple low-resolution samples, overcoming the intrinsic limitations of the latter. After compelling examples have been provided on multi-Shack-Hartman (SH) wave-front sensor (WFS) adaptive optics systems performing atmospheric tomography with laser guide star probes, we broaden the SR concept to pyramid sensors (PyWFS) with a single sensor and a natural guide star. We revisit the analytic PyWFS diffraction model to claim two aspects: i) that we can reconstruct spatial frequencies beyond the natural Shannon-Nyquist frequency imposed by the detector pixel size and/or ii) that the PyWFS can be used to measure amplitude aberrations (at the origin of scintillation). SR offers the possibility to control a higher actuator density deformable mirror from seemingly fewer samples, the quantification of which is one of the goals of this paper. A super-resolved PyWFS is more resilient to mis-registration, lifts alignment requirements and improves performance (against aliasing and other spurious modes AO systems are poorly sensitive to) with only a factor up to 2 increased real-time computational burden.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

38 extracted references · 4 canonical work pages

  1. [1]

    Journal of Astronomical Telescopes, Instruments, and Systems 6, 039003 (2020) 27

    Bond, C.Z., Cetre, S., Lilley, S., Wizinowich, P., Mawet, D., Chun, M., Wetherell, E., Jacobson, S., Lockhart, C., Warmbier, E., Ragland, S., Alvarez, C., Guyon, O., Goebel, S., Delorme, J.-R., Jovanovic, N., Hall, D.N., Wallace, J.K., Taheri, M., Plantet, C., Chambouleyron, V.: Adaptive optics with an infrared pyramid wavefront sensor at Keck. Journal of...

    2020

  2. [2]

    IEEE Transactions on Pattern Analysis and Machine Intelligence 24(9), 1167–1183 (2002)

    Baker, S., Kanade, T.: Limits on super-resolution and how to break them. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(9), 1167–1183 (2002)

    2002

  3. [3]

    In: Schreiber, L., Schmidt, D., Vernet, E

    Bond, C.Z., Sauvage, J.-F., Schwartz, N., Levraud, N., Chambouleyron, V., Correia, C., Fusco, T., Neichel, B.: HARMONI at ELT: wavefront control in SCAO mode. In: Schreiber, L., Schmidt, D., Vernet, E. (eds.) Adaptive Optics Systems VIII. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 12185, p. 121851 (2022) Clénet, Y., ...

    2022

  4. [4]

    (eds.) Adaptive Optics Systems VIII

    Schreiber, L., Schmidt, D., Vernet, E. (eds.) Adaptive Optics Systems VIII. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 12185, p. 121854 (2022)

    2022

  5. [5]

    Champagnat, F., Besnerais, G.L., Kulcsár, C.: Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework. J. Opt. Soc. Am. A 26(7), 1730–1746 (2009)

    2009

  6. [6]

    Correia, C.M., Fauvarque, O., Bond, C.Z., Chambouleyron, V., Sauvage, J.- F., Fusco, T.: Performance limits of adaptive-optics/high-contrast imagers with pyramid wavefront sensors. Monthly Notices of the Royal Astronom- ical Society 495(4), 4380–4391 (2020) https://doi.org/10.1093/mnras/staa843 https://academic.oup.com/mnras/article-pdf/495/4/4380/3337179...

    work page doi:10.1093/mnras/staa843 2020

  7. [7]

    In: Schreiber, L., Schmidt, D., Vernet, E

    Kulas, M., Coppejans, H., Orban de Xivry, G., Scheithauer, S., Bertram, T.: ELT METIS wavefront control strategy. In: Schreiber, L., Schmidt, D., Vernet, E. (eds.) Adaptive Optics Systems VIII. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 12185, p. 1218512 (2022)

    2022

  8. [8]

    Technical report, LAOG/ONERA (2003)

    Conan, R.: Fourier optics and distribution theory applied to pyramid wavefront sensors. Technical report, LAOG/ONERA (2003)

    2003

  9. [9]

    (eds.) Adaptive Optics Systems VIII, vol

    Schmidt, D., Vernet, E. (eds.) Adaptive Optics Systems VIII, vol. 12185, p. 121850. SPIE, ??? (2022). International Society for Optics and Photonics 28

    2022

  10. [10]

    IEEE Signal Processing Magazine 20(3), 75–86 (2003)

    Capel, D., Zisserman, A.: Computer vision applied to super resolution. IEEE Signal Processing Magazine 20(3), 75–86 (2003)

    2003

  11. [11]

    In: Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol

    Deo, V., Gendron, É., Rousset, G., Vidal, F., Buey, T.: A modal approach to optical gain compensation for the pyramid wavefront sensor. In: Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10703, p. 1070320 (2018)

    2018

  12. [12]

    In: Tyson, R.K., Hart, M

    Gherardi, A., Brusa, G., Miller, D., Guerra, J.C., Stefanini, P., Salinari, P.: Large Binocular Telescope Adaptive Optics System: new achievements and perspectives in adaptive optics. In: Tyson, R.K., Hart, M. (eds.) Astronomical Adaptive Optics Systems and Applications IV. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. ...

    2011

  13. [13]

    PhD thesis (2001)

    Feeney, O.A.: Theory and laboratory characterisation of novel wavefront sensor for adaptive optics systems. PhD thesis (2001)

    2001

  14. [14]

    Optica 3(12), 1440–1452 (2016)

    Fauvarque, O., Neichel, B., Fusco, T., Sauvage, J.-F., Girault, O.: General formalism for fourier-based wave front sensing. Optica 3(12), 1440–1452 (2016)

    2016

  15. [15]

    Optics Letters 40(15), 3528 (2015) https://doi.org/10.1364/OL.40.003528 arXiv:1507.07387 [astro-ph.IM]

    Fauvarque, O., Neichel, B., Fusco, T., Sauvage, J.-F.: Variation around a pyramid theme: optical recombination and optimal use of photons. Optics Letters 40(15), 3528 (2015) https://doi.org/10.1364/OL.40.003528 arXiv:1507.07387 [astro-ph.IM]

    Pith/arXiv arXiv 2015

  16. [16]

    Journal of Modern Optics 21, 709–72012 (1974) Give’On, A.: A unified formailism for high contrast imaging correction algorithms

    Gerchberg, R.W.: Super-resolution through error energy reduction. Journal of Modern Optics 21, 709–72012 (1974) Give’On, A.: A unified formailism for high contrast imaging correction algorithms. In:

    1974

  17. [17]

    (ed.) Techniques and Instrumentation for Detection of Exoplanets IV

    Shaklan, S.B. (ed.) Techniques and Instrumentation for Detection of Exoplanets IV. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7440, p. 74400 (2009) Give’on, A., Kern, B., Shaklan, S., Moody, D.C., Pueyo, L.: Broadband wavefront correction algorithm for high-contrast imaging systems. In: Tyson, R.K., Lloyd-

    2009

  18. [18]

    (eds.) Astronomical Adaptive Optics Systems and Applications III

    Hart, M. (eds.) Astronomical Adaptive Optics Systems and Applications III. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 6691, p. 66910 (2007)

    2007

  19. [19]

    The Astrophysical Journal 629(1), 592 (2005)

    Guyon, O.: Limits of adaptive optics for high-contrast imaging. The Astrophysical Journal 629(1), 592 (2005)

    2005

  20. [20]

    Optical Engineering 37, 247–260 (1998) 29

    Hardie, R.C., Barnard, K.J., Bognar, J.G., Armstrong, E.E., Watson, E.A.: High- resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system. Optical Engineering 37, 247–260 (1998) 29

    1998

  21. [21]

    In: Jackson, K.J., Schmidt, D., Vernet, E

    Lozi, J., Ahn, K., Blue, H., Chun, A., Clergeon, C., Deo, V., Guyon, O., Hattori, T., Minowa, Y., Nishiyama, S., Ono, Y., Oya, S., Takagi, Y., Vievard, S., Vincent, M.: AO3k at Subaru: first on-sky results of the facility extreme-AO. In: Jackson, K.J., Schmidt, D., Vernet, E. (eds.) Adaptive Optics Systems IX. Society of Photo- Optical Instrumentation Eng...

    2024

  22. [22]

    Astronomy and Astrophysics 682, 84 (2024) https://doi.org/10.1051/ 0004-6361/202346929

    Laure, Pinna, Enrico, Esposito, Simone, Fusco, Thierry: A strategy for sensing the petal mode in the presence of ao residual turbulence with the pyramid wave- front sensor. Astronomy and Astrophysics 682, 84 (2024) https://doi.org/10.1051/ 0004-6361/202346929

    2024

  23. [23]

    MNRAS 108, 428 (1948) https://doi.org/10.1093/mnras/108.6.428

    Linfoot, E.H.: On the theory of the Zonal Foucault Test. MNRAS 108, 428 (1948) https://doi.org/10.1093/mnras/108.6.428

    work page doi:10.1093/mnras/108.6.428 1948

  24. [24]

    PASP 126(940), 565 (2014)

    Currie, T., Thalmann, C., McElwain, M., Tamura, M.: On-Sky Speckle Nulling Demonstration at Small Angular Separation with SCExAO. PASP 126(940), 565 (2014)

    2014

  25. [25]

    In: Marchetti, E., Close, L.M., Véran, J.-P

    Louarn, M., Hammersley, P., Gach, J.-L., Pascal, S., Vola, P., Petit, C., Conan, J.-M., Carlotti, A., Vérinaud, C., Schnetler, H., Bryson, I., Morris, T., Myers, R., Hugot, E., Gallie, A.M., Henry, D.M.: The adaptive optics modes for HAR- MONI: from Classical to Laser Assisted Tomographic AO. In: Marchetti, E., Close, L.M., Véran, J.-P. (eds.) Adaptive Op...

    2016

  26. [26]

    Machine Vision and Applications 25, 1423–1468 (2014)

    Nasrollahi, K., Moeslund, T.B.: Super-resolution: a comprehensive survey. Machine Vision and Applications 25, 1423–1468 (2014)

    2014

  27. [27]

    Astronomy and Astrophysics 667, 48 (2022)

    Oberti, S., Correia, C., Fusco, T., Neichel, B., Guiraud, P.: Super-resolution wavefront reconstruction. Astronomy and Astrophysics 667, 48 (2022)

    2022

  28. [28]

    Prentice- Hall,Inc., ??? (1999)

    Oppenheim, A.V., Schafer, R.W.: Discrete-time Signal Processing, 2nd edn. Prentice- Hall,Inc., ??? (1999)

    1999

  29. [29]

    (eds.) Adaptive Optics Systems V

    Marchetti, E., Close, L.M., Véran, J.-P. (eds.) Adaptive Optics Systems V. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9909, p. 99093 (2016) 30

    2016

  30. [30]

    IEEE Signal Processing Magazine 20(3), 21–36 (2003) https://doi

    Park, S.C., Park, M.K., Kang, M.G.: Super-resolution image reconstruction: a tech- nical overview. IEEE Signal Processing Magazine 20(3), 21–36 (2003) https://doi. org/10.1109/MSP.2003.1203207

    Pith/arXiv arXiv 2003

  31. [31]

    The Astrophysical Journal 596(1), 702 (2003)

    Perrin, M.D., Sivaramakrishnan, A., Makidon, R.B., Oppenheimer, B.R., Graham, J.R.: The structure of high strehl ratio point-spread functions. The Astrophysical Journal 596(1), 702 (2003)

    2003

  32. [32]

    Journal of Modern Optics 43, 289–293 (1996) https://doi.org/10.1080/095003496156165

    Ragazzoni, R.: Pupil plane wavefront sensing with an oscillating prism. Journal of Modern Optics 43, 289–293 (1996) https://doi.org/10.1080/095003496156165

    work page doi:10.1080/095003496156165 1996

  33. [33]

    Journal of Astronomical Telescopes, Instruments, and Systems 7, 049001 (2021)

    Long, J.D., Mateen, M.: Three-sided pyramid wavefront sensor, part 1: simulations and analysis for astronomical adaptive optics. Journal of Astronomical Telescopes, Instruments, and Systems 7, 049001 (2021)

    2021

  34. [34]

    MNRAS 489(1), 1291–1303 (2019) https://doi.org/10.1093/mnras/stz2163 arXiv:1908.05977 [astro-ph.IM]

    Serabyn, E., Mennesson, B., Martin, S., Liewer, K., Kühn, J.: Nulling at short wavelengths: theoretical performance constraints and a demonstration of faint companion detection inside the diffraction limit with a rotating-baseline interfer- ometer. MNRAS 489(1), 1291–1303 (2019) https://doi.org/10.1093/mnras/stz2163 arXiv:1908.05977 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  35. [35]

    arXiv e-prints, 2003–07228 (2020) Vérinaud, C.: On the nature of the measurements provided by a pyramid wave-front sensor

    Schwartz, N., Sauvage, J.-F., Renault, E., Correia, C., Neichel, B., Fusco, T., Dohlen, K., El Hadi, K., Petit, C., Choquet, E., Chambouleyron, V., Paufique, J., Clarke, F., Thatte, N., Bryson, I.: Design of the HARMONI Pyramid WFS module. arXiv e-prints, 2003–07228 (2020) Vérinaud, C.: On the nature of the measurements provided by a pyramid wave-front se...

    work page doi:10.1016/j.optcom.2004.01 2003

  36. [36]

    Astronomy and Astrophysics (2023)

    Verinaud, C., Correia, C.M.: Eigenbases for a force-constrained position control of adaptive shell mirrors. Astronomy and Astrophysics (2023)

    2023

  37. [37]

    In: Adaptive Optics for Extremely Large Telescopes IV (AO4ELT4), p

    Veran, J.-P., Esposito, S., Spano, P., Herriot, G., Andersen, D.: Pyramid versus Shack- Hartmann: Trade Study Results for the NFIRAOS NGS WFS. In: Adaptive Optics for Extremely Large Telescopes IV (AO4ELT4), p. 31 (2015)

    2015

  38. [38]

    Signal Processing 128, 389–408 (2016) 31

    Yue, L., Shen, H., Li, J., Yuan, Q., Zhang, H., Zhang, L.: Image super-resolution: The techniques, applications, and future. Signal Processing 128, 389–408 (2016) 31

    2016

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.