Solar physicists use instruments called polarimeters to measure the polarization of sunlight, which reveals the strength and structure of the Sun's magnetic field. Before a polarimeter can deliver reliable measurements, it must be calibrated by feeding known polarization states into the instrument. Calibration takes time, and telescope time is precious — particularly for solar telescopes, where intense sunlight limits how long calibration optics can safely remain in the beam. This raises a key question: what sequence of calibration measurements yields the most accurate result in a given amount of time?
In this paper (Alfred de Wijn, David Harrington, Roberto Casini), we introduce a mathematical framework to answer that question. We define a calibration efficiency — a measure of how effectively a calibration sequence converts measurement signal into knowledge about the instrument — directly analogous to the previously developed concept of modulation efficiency used to optimize how polarimeters encode polarization signals. Together, these two metrics provide a unified description of how noise propagates through a polarimetric measurement from start to finish. We apply the framework to design an optimized calibration scheme for a hypothetical broadband solar instrument covering 587–1083 nm, demonstrating that a compound two-retarder design achieves near-optimal calibration efficiency across the full wavelength range simultaneously.
Calibration states generated by the optimized two-retarder scheme at four wavelengths spanning 587–1083 nm, shown as projections onto the Poincaré sphere — the standard geometric representation of polarization states. Each point represents a distinct input polarization state used during calibration; arrows indicate the sequence in which they are produced. The reported calibration efficiencies η show that the scheme achieves near-optimal performance simultaneously at all wavelengths, analogous to the broadband modulation efficiency already used in the design of modern solar polarimeters.