Abstract
Exoplanet direct imaging with large ground based telescopes requires eXtreme Adaptive Optics that couples high-order adaptive optics and coronagraphy. A key element of such systems is the high-order wavefront sensor. We study here several high-order wavefront sensing approaches, and more precisely compare their sensitivity to noise. Three techniques are considered: the classical Shack-Hartmann sensor, the pyramid sensor and the recently proposed LIFTed Shack-Hartmann sensor. They are compared in a unified framework based on precise diffractive models and on the Fisher information matrix, which conveys the information present in the data whatever the estimation method. The diagonal elements of the inverse of the Fisher information matrix, which we use as a figure of merit, are similar to noise propagation coefficients. With these diagonal elements, so called "Fisher coefficients", we show that the LIFTed Shack-Hartmann and pyramid sensors outperform the classical Shack-Hartmann sensor. In photon noise regime, the LIFTed Shack-Hartmann and modulated pyramid sensors obtain a similar overall noise propagation. The LIFTed Shack-Hartmann sensor however provides attractive noise properties on high orders.
Highlights
Exoplanet direct imaging is made difficult by the huge intensity contrast between the star and its companion
The comparison method based on the Fisher information matrix. Using this method we evaluate on one hand the noise propagation for the classical and LIFTed Shack-Hartmann sensors, and we study on the other hand the pyramid sensor with and without modulation
One may think that the number of pixels taken into account (16 × 16) in each subaperture will affect the sensitivity to read-out noise, but LIFT, to a Weighted Center of Gravity (WCoG), uses weighting functions on the image to make its estimation
Summary
Exoplanet direct imaging is made difficult by the huge intensity contrast between the star and its companion. We compare wavefront sensors based on the inverse of the Fisher information matrix This metric corresponds to the fundamental limit of wavefront sensors sensitivity to noise when using unbiased estimators, and determines their relative performance when using biased estimators. We present here a detailed comparison, in the context of high-order wavefront sensing, of these three wavefront sensors in a unified framework: modeling each sensor with a precise diffractive model, and comparing them with the Fisher information matrix, accounting for both photon and read-out noise. Using this method we evaluate on one hand the noise propagation for the classical and LIFTed Shack-Hartmann sensors, and we study on the other hand the pyramid sensor with and without modulation (see section 4).
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