Correcting Fabry-Perot etalon effects in solar observations

Data processing pipelines of Fabry-P\'erot interferometers (FPI) must take into account the side effects these devices introduce in the observations. Interpretation of these observations without proper correction can lead to inaccurate or false results, with consequent impact on their physical interpretation. Corrections typically require prior knowledge of the properties of the etalon and the way they affect the incoming light in order to calibrate the data successfully. We have developed an algorithm to derive etalon properties from flat-field observations and tested its applicability and accuracy using simulated observations and real measurements. We employed analytical expressions of the transmission profiles for FPIs in collimated and telecentric configurations to derive their expected impact on the observations. These analytical expressions allowed us to develop a customized optimization algorithm capable of inferring the properties of the etalon from the observations. The algorithm's performance has been tested on simulated observations with an etalon in collimated and telecentric setups employing various noise levels and spectral samplings. Additionally, we explored how tilting the etalon in a telecentric configuration influences the algorithm's effectiveness. Lastly, we also applied the algorithm to a set of real flat-field observations taken with the high-resolution telescope of the Polarimetric and Helioseismic Imager on board the Solar Orbiter mission (HRT-SO/PHI). The algorithm is able to retrieve the gain and etalon induced transmission velocity shifts (cavity map), with an average accuracy ranging between 0. 4\ and 0. 1\ for the former and between 120 and 30 ms^ for the latter. Both reducing the noise level and increasing the spectral sampling of the observations proved to greatly increase the algorithm's performance, as expected. Results also suggest that determination of the observed object from the data is possible but an additional error between 40 ms^ and 10 ms^ is to be expected in the inferred cavity map. Furthermore, we show that neglecting the asymmetries arising from either tilts of the etalon or imperfections in the telecentrism can lead to large errors when determining the gain. Tests with HRT-SO/PHI data have verified the applicability of the algorithm in real cases. Our presented method enabled us to derive the transmission profile of FPIs from observations of collimated and telecentric configurations. It has proven to be robust against the presence of noise and limited spectral line sampling. The results reported here also show the importance of accounting for the asymmetries arising in real telecentric mounts when interpreting the results of real instruments.