Constraining the Adaptive Optics Point-Spread Function in Crowded Fields: Measuring Photometric Aperture Corrections^*

The point-spread function (PSF) of an adaptive optics (AO) system is often poorly known. This ignorance can lead to significant systematic errors. Since the degree of AO correction is sensitive to the observing conditions (seeing, wind speed, brightness of the wave front reference, etc.), it would be desirable to estimate the PSF from the data themselves rather than from observations of a PSF star at another time. We have developed a method to estimate the PSF delivered by an AO system in the case where the scene consists of a crowded star field. We model the modulation transfer function (MTF) of several key components of the imaging system (atmosphere filtered by an AO system, telescope pupil, and pixel array). The power spectrum of the image, even a dense star field, can be used to constrain our model, which in turn can be used to reconstruct the PSF. In the case of circularly symmetric PSFs, we demonstrate that the power spectrum of the source distribution function can be successfully removed from the measured MTF and that our fit successfully recovers input parameters from a model data set constructed from these parameters. We also show that the method yields reasonable fit parameters and a useful approximation to the PSF when applied to data from the laser guide star (LGS) AO system at the Keck Observatory. Comparison of Keck LGS AO data and Hubble Space Telescope observations with NICMOS show that photometric accuracy of a few percent can be achieved for data with Strehl ratios as low as 4%.