Origin of the unexplained ~48 nm RMS seeing-unrelated wavefront error limiting granulation contrast at the Swedish 1-m Solar Telescope

Even with adaptive optics and image restoration, the RMS contrast of solar granulation observed with the Swedish 1-m Solar Telescope (SST) falls short of the values predicted by 3D magnetohydrodynamic (MHD) simulations: reconciling the measured multi-wavelength contrast with simulations and the inferred Strehl ratios requires postulating an additional, seeing-unrelated wavefront error of about 48 nm RMS (1/13 wave at 630 nm, scaling inversely with wavelength), of which the known small-scale aberrations of the telescope optics account for at most half. Identifying the physical origin of this residual error — static small-scale aberrations in the primary optics or the Schupmann corrector, non-common-path aberrations in the optics feeding the adaptive-optics wavefront sensor, degradation by the adaptive-optics system itself that mimics a static error, or calibration and analysis systematics — and thereby closing the telescope's wavefront-error budget remains an open problem, with direct consequences for whether optical surface quality or atmospheric seeing sets the ultimate image-quality limit of ground-based solar telescopes.

Background

Solar granulation — the pattern of bright convective upflows and dark downflows covering the solar photosphere — provides a standard image-quality yardstick for solar telescopes: the root-mean-square (RMS) intensity contrast of quiet-Sun granulation images, which theoretical 3D magnetohydrodynamic (MHD) convection simulations predict to be far higher (e.g. about 22% at 485 nm and 20% at 525 nm) than any ground-based telescope has ever measured, because Earth's turbulent atmosphere spreads light and washes out the fine structure.

Three concepts frame the problem. First, the Fried parameter $r_0$ (the atmospheric coherence length) characterizes the strength of seeing; it is estimated at solar telescopes from differential image motion, i.e. the apparent jitter of images recorded through different subapertures or at separated field points. Second, adaptive optics (AO) systems measure the instantaneous atmospheric wavefront distortion with a Shack–Hartmann wavefront sensor (WFS) — a lenslet array that samples the wavefront in many subapertures — and correct it in real time with a deformable mirror (DM); the correction quality is conventionally summarized by the Strehl ratio, the peak intensity of the delivered point-spread function (PSF) relative to a perfect diffraction-limited one. Third, for solar telescopes the RMS granulation contrast itself serves as a Strehl proxy, because it is directly proportional to the Strehl ratio calculated from the residual small-scale wavefront error.

The Swedish 1-m Solar Telescope on La Palma is a vacuum telescope with a 1-meter singlet objective whose chromatic aberration is removed by a Schupmann corrector (a compensating lens-and-mirror assembly used in double pass). After its 2013–2016 revamp — an 85-electrode monomorph DM (a deformable mirror whose single glass face sheet is bent directly by 85 electrode actuators) and a new tip-tilt mirror polished to exceptionally high optical quality, feeding the CRISP (the CRisp Imaging Spectropolarimeter, on the red beam) and CHROMIS (its blue-beam counterpart), both narrowband Fabry–Pérot interferometric-filter re-imaging systems — Scharmer, Löfdahl, Sliepen and de la Cruz Rodríguez (A&A 626, A55, 2019) measured simultaneously seeing and granulation contrast at wavelengths from 395 nm to 853.6 nm. They found that the measured contrast varies linearly with the Strehl ratio inferred from $r_0$ and the assumed AO correction, and that reasonable agreement with the data is obtained if the AO system has an efficiency of about 40–50%, as defined by Roddier's effective-number-of-corrected-modes description. However, the extrapolated 'seeing-free' granulation contrast remains well below the 3D MHD simulated values unless one adds an ad-hoc, seeing-unrelated wavefront error of about 48 nm RMS.

The 2019 paper could not explain this residual. Manufacturer metrology of the main optics (two 1.4 m flats at 8–9 nm RMS each and the 1-meter lens at about 10 nm RMS) combines to only about 16 nm RMS, and the Schupmann corrector contributes about 8 nm RMS (possibly doubled in double pass), so the primary optical system supplies at most half the required variance. Candidate explanations include small-scale aberrations in the non-common path between the science beams and the WFS — notably the beam-splitter cube and right-angle prism that feed the sensor — as well as AO-related effects that masquerade as a static error: without AO telemetry (control-loop data, in the sense of Véran, Rigaut, Maître and Rouan, Journal of the Optical Society of America A 14, 3057, 1997), the true modal efficiency of the AO system and the fraction of high-order modes that are only partially corrected cannot be separated from genuine static aberrations. Two analysis systematics compound the uncertainty: the accuracy of the compensation for light back-scattered from the CCD at 853 nm (where the data deviate most from theory) and the possibility that the 20–30 s averaging interval used as reference for the differential-image-motion measurements overestimates $r_0$ by missing the slowest seeing fluctuations. Because the SST has an unusually simple optical design with few, very high-quality surfaces, the existence of such a residual there suggests the conjecture — 'the sky is not the limit' — that for more complex solar telescopes the attainable image quality may be set by the number and quality of optical surfaces rather than by atmospheric seeing, a question of direct importance for the design of future large solar telescopes such as the European Solar Telescope (EST). The same 48 nm residual is still required 'to explain the data' in the SST 85-electrode AO system paper of 2024, which attributes the problem to the additional seeing-unrelated error whose origin remains unknown.

Problem Statement

Identify the physical origin of the approximately 48 nm RMS seeing-unrelated wavefront error that is required, in addition to the residual atmospheric error, to reconcile the measured RMS granulation contrast of the Swedish 1-m Solar Telescope at wavelengths from 395 nm to 853.6 nm with 3D MHD simulation contrasts and with the Strehl ratios inferred from simultaneous $r_0$ measurements.

A complete answer must quantitatively attribute the residual among the candidate sources enumerated in the source work — or show that other sources dominate: (i) static small-scale aberrations of the primary optical system, including the two 1.4 m flats, the 1-meter objective lens, and the Schupmann corrector used in double pass (together known to contribute at most about half of the required variance); (ii) non-common-path aberrations between the science beams and the AO wavefront sensor, particularly the beam-splitter cube and right-angle prism that feed the sensor; (iii) AO-related degradation — the true modal efficiency of the 85-electrode system and high-order modes that are only partially corrected — which without AO telemetry is observationally degenerate with a static error; and (iv) analysis and calibration systematics, notably the accuracy of the CCD back-scatter compensation at 853 nm and a possible overestimate of $r_0$ from the 20–30 s averaging interval used as reference for differential image motion. The attribution must close the error budget consistently across all measured wavelengths and both re-imaging beams.

References

1. Scharmer, G. B., Löfdahl, M. G., Sliepen, G., de la Cruz Rodríguez, J. 2019, 'Is the sky the limit? Performance of the revamped Swedish 1-m Solar Telescope and its blue- and red-beam re-imaging systems', Astronomy & Astrophysics 626, A55, DOI 10.1051/0004-6361/201935735, https://doi.org/10.1051/0004-6361/201935735 (also arXiv:1905.05588, https://arxiv.org/abs/1905.05588)
2. Scharmer, G. B., Sliepen, G., Sinquin, J.-C., Löfdahl, M. G., Lindberg, B., Sütterlin, P. 2024, 'The 85-electrode adaptive optics system of the Swedish 1-m Solar Telescope', Astronomy & Astrophysics 685, A32, DOI 10.1051/0004-6361/201936005, https://doi.org/10.1051/0004-6361/201936005 (also arXiv:2311.13690, https://arxiv.org/abs/2311.13690)
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6. de la Cruz Rodríguez, J., Scharmer, G. B., Sütterlin, P., Leenaarts, J., Löfdahl, M. G., Kiselman, D., Hillberg, T., Andriienko, O. 2026, 'Characterization of telecentric dual-etalon Fabry-Pérot systems from observational data. Properties of the CRISP2 instrument at the Swedish 1-m Solar Telescope', Astronomy & Astrophysics 711, A99, DOI 10.1051/0004-6361/202558701, https://doi.org/10.1051/0004-6361/202558701 (preprint arXiv:2512.18039, December 2025, https://arxiv.org/abs/2512.18039)
7. Véran, Jean-Pierre; Rigaut, François; Maître, Henri; Rouan, Daniel 1997, 'Estimation of the adaptive optics long exposure point spread function using control loop data', Journal of the Optical Society of America A 14, 3057, DOI 10.1364/josaa.14.003057, https://doi.org/10.1364/josaa.14.003057
8. Löfdahl, M. G., Scharmer, G. B. 2012, 'Sources of straylight in the post-focus imaging instrumentation of the Swedish 1-m Solar Telescope', Astronomy & Astrophysics 537, A80, DOI 10.1051/0004-6361/201117980, https://doi.org/10.1051/0004-6361/201117980 (also arXiv:1110.2663, https://arxiv.org/abs/1110.2663)