Utilization of the Wavefront Sensor and Short-Exposure Images for Simultaneous Estimation of Quasi-static Aberration and Exoplanet Intensity

Abstract

This paper provides a framework for the incorporation of the wavefront sensor measurements in the context of observing modes in which the science camera takes millisecond exposures. In this formulation, the wavefront sensor measurements provide a means to jointly estimate the static speckle and the planetary signal. The ability to estimate planetary intensities in as little as few seconds has the potential to greatly improve the efficiency of exoplanet search surveys. Unlike currently used methods, in which increasing the observation time beyond a certain threshold is useless, this method produces estimates whose error covariances decrease more quickly than inversely proportional to the observation time. This is due to the fact that the estimates of the quasi-static aberrations are informed by a new random (but approximately known) wavefront every millisecond. The method can be extended to include angular (due to diurnal field rotation) and spectral diversity. Numerical experiments are performed with wavefront data from the AEOS Adaptive Optics System sensing at 850 nm. These experiments assume a science camera wavelength $\lambda$\ of $1.1 \, \mu$, that the measured wavefronts are exact, and a Gaussian approximation of shot-noise. The effects of detector read-out noise and other issues are left to future investigations. A number of static aberrations are introduced, including one with a spatial frequency exactly corresponding the planet location, which was at a distance of $\approx 3\lambda/D$\ from the star. Using only 4 seconds of simulated observation time, a planetary intensity, of $\approx 1$ photon/ms, a stellar intensity of $\approx 10^5$\ photons/ms (contrast ratio $10^5$), the short-exposure estimation method recovers the amplitudes static aberrations with a 1% accuracy, and the planet brightness with a with 20% accuracy.