Bayesian calibration of quasi-static field distortions in HARMONI

Abstract

ABSTRACT The high angular resolution monolithic optical and near-infrared Integral field spectrograph is the first light visible and near-infrared integral field spectrograph for the Extremely Large Telescope. To reach the diffraction limit of the telescope (≈ 10 mas) and maintain an optimal image quality over long exposures, an accurate measurement of geometrical distortions in the instrument’s guide star field is needed. Geometrical distortions affecting the guide stars map directly to pointing errors of the science field. The systematic contribution to the pointing error can be calibrated and removed by a corrective model. In this work, we propose a formulation of the corrective model that aims to calibrate the geometrical field distortions down to a given target residual, as well as reducing the time spent in calibrations. We also propose a calibration procedure that accounts for the uncertainties of the measurement process. We developed a tool named harmoni-pm to simulate the expected pointing error caused by geometrical distortions and validate the effectiveness of the proposed corrective model. We also relied on pseudo Zernike polynomials to formulate the model, and the Bayesian theoretical framework to study the propagation of uncertainties along the calibration process. Compared with the classical calibration algorithm, the Bayesian calibration algorithm was able to reduce the number of calibration points required to reach the same model residual. Additionally, we were able to optimize the hardware of the Geometrical Calibration Unit and reduce the time required to achieve the calibration goal.