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arxiv: 2512.18039 · v2 · submitted 2025-12-19 · 🌌 astro-ph.IM · astro-ph.SR

Characterization of telecentric dual-etalon Fabry-P\'erot systems from observational data. Properties of the CRISP2 instrument at the Swedish 1-m Solar Telescope

J. de la Cruz Rodr\'iguez , G. B. Scharmer , P. S\"utterlin , J. Leenaarts , M. G. L\"ofdahl , D. Kiselman , T. Hillberg , O. Andriienko This is my paper

Pith reviewed 2026-05-16 20:22 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.SR
keywords Fabry-Perot interferometerCRISP2solar instrumentationspectral imagingetalon characterizationtelecentric configurationinstrumental profilequiet-Sun calibration
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The pith

The CRISP2 dual-etalon instrument has cavity separation uniform to under 2 nm RMS across its field of view.

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

The paper introduces a forward-modeling method that fits solar observations to derive spatially resolved maps of cavity separation and reflectivity for telecentric dual-etalon Fabry-Perot systems. It combines an assumed transmission profile with a single average quiet-Sun spectrum to solve for the etalon parameters without external lamps or optical changes. Applied to CRISP2 data at 617.3 nm, the fit shows both etalons are extremely flat and have small reflectivity variations. This level of characterization is required to remove instrumental signatures when inferring velocities, temperatures, and magnetic fields from spectral imaging. The code is released publicly so the same approach can be used on other current and planned FPI instruments.

Core claim

A forward model of the dual-etalon transmission profile, including secondary peaks at one free spectral range and a measured prefilter curve, is fitted to observed quiet-Sun spectra to recover spatially varying cavity separations and reflectivities. For CRISP2 the resulting cavity-separation maps have RMS variation below 2 nm over the full field for both etalons, while reflectivity RMS values are 0.4 percent and 0.3 percent at 617.3 nm.

What carries the argument

Forward model of FPI instrumental degradation fitted to observational data using a template quiet-Sun spectrum to extract spatially resolved etalon cavity separation and reflectivity.

If this is right

  • Solar atmospheric parameters inferred from CRISP2 spectra can be modeled with reduced systematic error once the measured instrumental profile is used.
  • The same fitting procedure applies directly to any other telecentric dual-etalon FPI without hardware modification.
  • Accurate reflectivity values require inclusion of the secondary transmission peaks and a detailed prefilter curve in the model.
  • Public release of the code enables routine characterization of existing and future FPI instruments at solar telescopes.

Where Pith is reading between the lines

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

  • Maps of this uniformity can be used to correct residual field-dependent wavelength shifts in velocity or magnetic-field inversions.
  • The method offers a practical route to cross-calibrate FPI performance between different observatories that lack identical external sources.
  • Repeated application to the same instrument over time could detect slow drifts in etalon properties caused by temperature or mechanical stress.
  • Future instruments could embed a similar quiet-Sun fitting step for automated, real-time monitoring of etalon health.

Load-bearing premise

A single average quiet-Sun template spectrum at disk center plus the chosen functional forms for the transmission profile are enough to determine the spatially varying parameters uniquely.

What would settle it

Direct laboratory interferometry of the etalon plates performed outside the telescope should reproduce the same cavity-separation map derived from the solar data.

Figures

Figures reproduced from arXiv: 2512.18039 by D. Kiselman, G. B. Scharmer, J. de la Cruz Rodr\'iguez, J. Leenaarts, M. G. L\"ofdahl, O. Andriienko, P. S\"utterlin, T. Hillberg.

Figure 1
Figure 1. Figure 1: CRISP2 transmission profile at 617.3 nm. Top: HRE, LRE and full transmission profiles, where the prefilter shape is also indicated. Bottom: transmission profile and transmission profile multiplied by the prefilter transmission, illustrating the attenuation of secondary lobes by the prefilter. 5000 5500 6000 6500 7000 7500 8000 8500 wavelength [˚A] 60 80 100 120 CRISP-2 FWHM [m˚A] Mg I 5173 ˚A Fe I 5250 ˚A … view at source ↗
Figure 2
Figure 2. Figure 2: Factory-measured reflectivities of the etalons (red) and the cor￾responding instrumental profile FWHM for the CRISP2 instrument (black). The solid red line depicts the reflectivity of the high-resolution etalon, whereas the dashed-red line corresponds to the reflectivity of the low-resolution etalon. The FWHM of the profile was calculated assum￾ing perfect co-tuning of the profiles from the two etalons and… view at source ↗
Figure 3
Figure 3. Figure 3: Central lobe of the CRISP2 transmission profile calculated with three different recipes: perpendicular incidence (ray, black), telecentric beam without etalon tilt (conv, blue) and the full calculation including the tilt of the LRE (full, red). Top: Transmission profiles. Bottom: peak￾normalized transmission profiles, where the blueshift induced by the angular integral has been compensated in the conv and … view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of inclination angles across the (circular) pupil for a non-tilted case (α = 0, left) and a tilt of α = 1/2F in the y-axis (right). of CRISP and CRISP2, the LRE is tilted by 0.5/F, inducing an asymmetry in the integrated LRE transmission profile and a slightly lower transmission. To include the effect of tilting the LRE etalon, the tilt angle in one axis must be added to the convergence angles… view at source ↗
Figure 5
Figure 5. Figure 5: Observed mean intensity (black) and the derived fit (red) in the 617.3 nm spectral window. The inferred prefilter curve is plotted with a dashed gray line. The light-gray spectrum represents the FTS atlas multiplied by the prefilter curve. The fitted curve is the result of the FTS spectrum multiplied with the prefilter curve and convolved with the nominal CRISP2 transmission profile. around the disk center… view at source ↗
Figure 7
Figure 7. Figure 7: Observed spectrum (dots) and best-fit (solid line) from three locations in the FOV. An offset of ±0.2 was applied to the blue and red curves to improve readability. The locations of these points are indicated in panel (a) of [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Inferred parameter maps from the prefilter and HRE model. (a) is the HRE cavity error map, (b) is the HRE reflectivity map, (c) is the prefilter central wavelength, (d) is the prefilter FWHM, and (e)-(g) are the coefficients of the polynomial prefilter components. The crosses indicated in (a) correspond to the fits shown if [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Inferred parameter maps from the LRE model fit and three fit examples. (a) the LRE cavity error map, (b) the LRE reflectivity map, and (c) illustrates three observed LRE scan spectra (dots) and the cor￾responding fits (solid line). The locations of these spectra in the FOV are marked in panel (a) with cross markers using the same color coding than in panel (c). A vertical offset of ±0.35 was applied to the… view at source ↗
Figure 12
Figure 12. Figure 12: Prefilter-corrected 2D histogram of the observed data. Each wavelength bin has been normalized by the total to better illustrate the spread of the data points. The cavity error map has been compensated in the wavelength array of each (x, y) location in the FOV. utilized by Scharmer et al. (2013) [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: Variation of the FWHM of the FPI transmission profile for CRISP at 630.2 nm (left) and a hypothetical FPI instrument with iden￾tical cavity separations but the same high reflectivity R = 93.5% in both etalons (right). The lower resolution etalon helps minimizing the variation of the profile properties across the FOV. The mean FWHM is 66.5 mÅ. maps and reflectivities at 617.3 nm, we have generated the FOV￾… view at source ↗
Figure 13
Figure 13. Figure 13: Sample science dataset acquired in the wing (left, ∆λ = −1.5 Å) and in the code (right) of the Hα line. Article number, page 10 of 13 [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
read the original abstract

Imaging Fabry-P\'erot Interferometer (FPI) observations are commonly used in solar physics to infer physical parameters in the photosphere and chromosphere through modeling of the observations. Such techniques require detailed knowledge of the spectral instrumental profile in order to produce accurate results. In this study we present a method to characterize the spatial variation of parameters of dual-etalon FPI instruments mounted in telecentric configuration: spatially-resolved cavity separation and reflectivities of both etalons, as well as the prefilter variation across the field-of-view. Here, we aim at characterizing the field-of-view dependence of the parameters of the new CRISP2 FPI. We have implemented a forward model of the FPI instrumental degradation combined with a template average quiet-Sun spectrum at disk center in order to model two sets of observational data. Our method does not require any change in the optical setup or the utilization of external sources of illumination. We assess the validity of several functional forms in the calculation of the FPI transmission profiles. Our results show that (generally) the inclusion of the secondary transmission peaks at 1 FSR and a detailed estimate of the prefilter curve is necessary to obtain accurate values of both etalon reflectivities. Our results show that the cavity separation of CRISP2 is very flat, with an RMS variation below 2 nm over the entire field-of-view for both etalons. Reflectivity RMS variations are 0.4% and 0.3% for the primary and secondary etalons at 617.3 nm. The methods described in this paper are relevant for the characterization of present and future FPI instruments and we have made them publicly available to the solar community.

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 paper describes a forward-modeling method to characterize the spatially varying parameters of the CRISP2 dual-etalon Fabry-Pérot interferometer in telecentric configuration at the Swedish 1-m Solar Telescope. Using observational line scans and a single fixed average quiet-Sun template spectrum at disk center, the approach fits maps of cavity separation d(x,y), reflectivities R1(x,y) and R2(x,y), and prefilter transmission without requiring external calibration sources or changes to the optical setup. The authors evaluate different functional forms for the FPI transmission profile and conclude that secondary peaks at one free spectral range plus a detailed prefilter are needed for accurate reflectivity recovery. They report that the cavity separation is very flat (RMS variation below 2 nm across the field of view for both etalons) and that reflectivity RMS variations are 0.4 % and 0.3 % at 617.3 nm. The methods are made publicly available.

Significance. If the derived parameter maps are robust, the work supplies a practical, in-situ calibration technique for existing and future imaging FPI instruments that avoids dedicated calibration hardware. The public release of the code is a clear strength. However, the absence of reported fit residuals, parameter uncertainties, or cross-validation against independent monochromatic sources limits the immediate impact; the claimed flatness and low reflectivity variations would be more consequential once their precision is quantified.

major comments (2)
  1. [Abstract and Results] Abstract and Results: the central claims of RMS cavity-separation variation <2 nm and reflectivity RMS values of 0.4 % / 0.3 % are presented without accompanying fit residuals, reduced-χ² maps, or posterior widths. Without these diagnostics it is impossible to judge whether the quoted RMS figures represent true instrument properties or are partly set by the fixed-template assumption.
  2. [Methods] Methods: the forward model treats the quiet-Sun template spectrum as fixed while allowing d(x,y), R1(x,y), R2(x,y) and the prefilter to vary. No Jacobian, degeneracy analysis, or Monte-Carlo test is described that would demonstrate that mismatches between the template and local spectra (velocity fields, blends, center-to-limb effects) are not absorbed into the fitted parameters. The skeptic note correctly flags this as a load-bearing assumption for the uniqueness of the solution.
minor comments (2)
  1. [Results] The manuscript would benefit from a short table or figure showing example observed vs. modeled line profiles at a few field positions so readers can visually assess the quality of the fits.
  2. [Results] Clarify in the text whether the reported RMS values are computed after any spatial smoothing or masking; if so, state the exact procedure.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive review. We address the two major comments point by point below, agreeing that additional diagnostics are required to support the reported RMS values and to test the fixed-template assumption. The revised manuscript will incorporate the suggested analyses.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results: the central claims of RMS cavity-separation variation <2 nm and reflectivity RMS values of 0.4 % / 0.3 % are presented without accompanying fit residuals, reduced-χ² maps, or posterior widths. Without these diagnostics it is impossible to judge whether the quoted RMS figures represent true instrument properties or are partly set by the fixed-template assumption.

    Authors: We agree that the central claims require supporting diagnostics. In the revised manuscript we will add full-field maps of the fit residuals and reduced-χ² values. Because the fitting procedure is deterministic least-squares minimization rather than Bayesian sampling, posterior widths are not available; instead we will include a sensitivity study that perturbs the template spectrum and quantifies the resulting scatter in the derived RMS cavity and reflectivity variations. revision: yes

  2. Referee: [Methods] Methods: the forward model treats the quiet-Sun template spectrum as fixed while allowing d(x,y), R1(x,y), R2(x,y) and the prefilter to vary. No Jacobian, degeneracy analysis, or Monte-Carlo test is described that would demonstrate that mismatches between the template and local spectra (velocity fields, blends, center-to-limb effects) are not absorbed into the fitted parameters. The skeptic note correctly flags this as a load-bearing assumption for the uniqueness of the solution.

    Authors: The fixed-template assumption is indeed central. The revised version will contain an explicit degeneracy analysis in which controlled velocity shifts and weak blends are added to the template before refitting; we will show that the resulting changes in the cavity-separation and reflectivity maps remain smaller than the quoted RMS values. We will also describe Monte-Carlo experiments that add realistic noise to the observed line scans and report the scatter in the recovered parameters. revision: yes

standing simulated objections not resolved
  • Cross-validation against independent monochromatic sources cannot be performed, because the method is deliberately designed for in-situ characterization from quiet-Sun observations without any hardware changes or external calibration sources.

Circularity Check

0 steps flagged

No circularity: parameters fitted from independent observational data against external template

full rationale

The derivation fits spatially varying cavity separation d(x,y), reflectivities R1(x,y), R2(x,y) and prefilter by minimizing residuals between observed line scans and a forward model that incorporates a fixed external average quiet-Sun template spectrum at disk center. This is a standard data-driven inverse problem; the fitted quantities are not defined in terms of themselves, no fitted input is relabeled as a prediction, and no self-citation chain or uniqueness theorem is invoked to force the result. The reported RMS values (<2 nm for d, 0.3–0.4 % for R) are direct outputs of the fit to real data rather than tautological re-expressions of the inputs. The method is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the chosen functional forms for the FPI transmission profile (including secondary peaks) and the adopted quiet-Sun template spectrum are adequate representations of reality; no free parameters are explicitly listed in the abstract, but the choice of functional form itself functions as an implicit modeling choice.

axioms (2)
  • domain assumption A single average quiet-Sun spectrum at disk center is representative of the true incident spectrum across the field of view.
    Invoked when the forward model is fitted to observational data.
  • domain assumption The mathematical forms tested for the etalon transmission profile (including secondary peaks at 1 FSR) are sufficient to capture the true instrumental response.
    Stated as necessary for accurate reflectivity recovery.

pith-pipeline@v0.9.0 · 5678 in / 1491 out tokens · 20519 ms · 2026-05-16T20:22:47.550890+00:00 · methodology

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Reference graph

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