Abstract
The pyramid wavefront sensor (PWFS) is the currently preferred design for high-sensitivity adaptive optics (AO) systems for extremely large telescopes (ELTs). Yet, nonlinearities of the signal retrieved from the PWFS pose a significant problem for achieving the full correction potential using this sensor, a problem that will only worsen with the increasing dimension of telescopes. This paper investigates the so-called optical gain (OG) phenomenon, a sensitivity reduction and an overall modification of the sensor response induced by the residual wavefront itself, with considerable effects in standard observation conditions for ELT-sized AO systems. Through extensive numerical analysis, this work proposes a formalism to measure and minimize the first-order nonlinearity error caused by optical gain variation, which uses a modal compensation technique of the calibrated reconstructor; this enables a notable increase in performance in faint guide stars or important seeing scenarios, for example from 16 to 30% H-band Strehl ratio for a sixteenth magnitude star in r0 = 13 cm turbulence. Beyond the performance demonstrated by this compensation, a complete algorithm for realistic operation conditions is designed, which from dithering a few deformable mirror modes retrieves the optimal gains and updates the command matrix accordingly. The performance of this self-updating technique – which successfully allows automatic OG compensation regardless of the turbulent conditions, and its minimal interference with the scientific instrument are demonstrated through extensive end-to-end numerical simulations, all at the scale of an ELT instrument single-conjugate AO system.
Highlights
A continuous effort is being provided by the adaptive optics (AO) community to drive forward the usability of the pyramid wavefront sensor (PWFS)
We compare the overall performance of the PWFS without modal optical gain (OG) compensation – that is, flat, unit optical gain coefficients (OGCs) – and with automatic, weighted OGCs
In this work, the authors propose a thorough analysis of the optical gain phenomenon with the PWFS, OG being defined as a modification of the first-order response of the sensors between the calibration regime – with a flat wavefront, and operational regimes when the PWFS is shown a closed-loop residual wavefront
Summary
A continuous effort is being provided by the adaptive optics (AO) community to drive forward the usability of the pyramid wavefront sensor (PWFS). The PWFS exhibits a strongly nonlinear behavior, as in-loop residual wavefronts dramatically alter the response of the sensor. This response modification between the calibration and on-sky operations is mainly expressed through a spatial-frequency-dependent sensitivity reduction, a phenomenon named optical gain (OG). Numerical values in median seeing conditions – for example r0 of 14 cm at sensor visible wavelength – for an ELT typically range within 50–80 % of perceived attenuation of closed-loop residuals when compared to small-signal calibrations. The fluctuation of sensitivity with on-sky external parameters prevents a well adjusted subtraction of the calibrated noncommon path aberrations (NCPAs) through the application of the reference slopes, with OG affecting the system as an unforeseen transformation between the acquired setpoint and the runtime measurements
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