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

Imaging Fabry-Pérot 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. 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, and the prefilter variation across the field-of-view. 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 spectra 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 times the Free Spectral Range and a detailed estimate of the prefilter curve is necessary to obtain accurate values of both etalon reflectivities. For narrow prefilters (relative to the FSR), the former requirement can be relaxed. Our results show that the cavity separation of CRISP2 is very flat, showing an RMS variation below 1.9 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. We have assessed data and modeling requirements in order to derive accurate FPI parameters and minimize errors in the determination of etalon reflectivities.

💡 Research Summary

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The paper presents a comprehensive method for characterizing the spatially varying parameters of a telecentric dual‑etalon Fabry‑Pérot interferometer (FPI) using only solar observational data, without any external calibration sources or modifications to the instrument. The authors develop a forward model that combines the theoretical transmission of each etalon, the angular distribution of the telecentric beam, and an analytical description of the pre‑filter transmission. The etalon transmission is expressed by the standard Airy function T(R, C, θ, λ) and the full‑width‑half‑maximum (FWHM) approximation λ²/(2 n F C). Because the beam in a telecentric system converges (F/140 for CRISP2), a range of incidence angles must be integrated. The authors implement two levels of integration: a “conv” model that averages over a modest number (N ≈ 5) of rays assuming no tilt, and a “full” model that also includes the intentional tilt of the low‑resolution etalon (LRE) used to suppress internal reflections. They demonstrate that for CRISP2 the tilt effect is negligible, allowing the faster conv model to be used without loss of accuracy.

A key innovation is the explicit inclusion of secondary transmission peaks at ± one free‑spectral‑range (FSR) in the forward model. By fitting observational line scans of the quiet‑Sun Fe I 6173 Å line together with the pre‑filter transmission, the authors show that neglecting these secondary peaks leads to systematic errors in the retrieved etalon reflectivities of order 0.1 %–0.2 %. Conversely, when the pre‑filter is narrow compared to the FSR, the secondary peaks have little impact and can be omitted. The pre‑filter itself is modeled by a product of a Lorentzian‑like core, a cavity term, and a low‑order polynomial (up to cubic) multiplied by an apodisation window to avoid negative wings. This flexible formulation captures real‑world deviations from the ideal interference‑filter shape.

Applying the method to the new CRISP2 instrument at the Swedish 1‑m Solar Telescope, the authors retrieve the following results: (i) the cavity separations of the high‑resolution etalon (HRE) and low‑resolution etalon (LRE) are remarkably flat across the full 120‑arcsecond field of view, with root‑mean‑square (RMS) variations below 1.9 nm. (ii) The reflectivities are 94.8 % (HRE) and 87.3 % (LRE) at 6173 Å, with RMS spatial variations of only 0.4 % and 0.3 % respectively. (iii) The pre‑filter central wavelength and FWHM are determined to better than 0.01 Å, and the fitted pre‑filter shape reproduces the observed attenuation of secondary lobes. (iv) The tilt of the LRE (α = 0.5/F) introduces less than a 2 % change in peak transmission and can be safely ignored for most data‑reduction pipelines.

The authors also compare three common approximations for the transmission profile: (a) assuming perpendicular incidence (the “ray” model), which severely underestimates the FWHM (by 12 % for CRISP and 26 % for CRISP2); (b) the conv model with angular integration, which matches the full model to within a few percent; and (c) the full model including tilt, which yields only marginal improvements for CRISP2. They strongly advise against using the simple perpendicular‑incidence formula for telecentric FPIs, as it would lead to systematic under‑estimation of instrumental broadening and consequently biased inversion results.

In summary, the paper delivers a robust, data‑driven calibration technique that simultaneously retrieves etalon cavity errors, reflectivities, and pre‑filter characteristics. It demonstrates that high‑precision instrumental profiles can be obtained from routine solar observations, eliminating the need for dedicated calibration lamps or hardware changes. This approach is directly applicable to current and future solar imaging spectropolarimeters (e.g., DKIST ViSP, EST VTF) and will improve the fidelity of spectroscopic inversions, magnetic field diagnostics, and dynamic studies of the solar atmosphere.