Image Ellipticity from Atmospheric Aberrations

We investigate the ellipticity of the point-spread function (PSF) produced byimaging an unresolved source with a telescope, subject to the effects ofatmospheric turbulence. It is important to quantify these effects in order tounderstand the errors in shape measurements of astronomical objects, such asthose used to study weak gravitational lensing of field galaxies. The PSFmodeling involves either a Fourier transform of the phase information in thepupil plane or a ray-tracing approach, which has the advantage of requiringfewer computations than the Fourier transform. Using a standard method,involving the Gaussian weighted second moments of intensity, we then calculatethe ellipticity of the PSF patterns. We find significant ellipticity for theinstantaneous patterns (up to more than 10%). Longer exposures, which weapproximate by combining multiple (N) images from uncorrelated atmosphericrealizations, yield progressively lower ellipticity (as 1 / sqrt(N)). We alsoverify that the measured ellipticity does not depend on the sampling intervalin the pupil plane using the Fourier method. However, we find that the resultsusing the ray-tracing technique do depend on the pupil sampling interval,representing a gradual breakdown of the geometric approximation at high spatialfrequencies. Therefore, ray tracing is generally not an accurate method ofmodeling PSF ellipticity induced by atmospheric turbulence unless someadditional procedure is implemented to correctly account for the effects ofhigh spatial frequency aberrations. The Fourier method, however, can be useddirectly to accurately model PSF ellipticity, which can give insights intoerrors in the statistics of field galaxy shapes used in studies of weakgravitational lensing.Comment: 9 pages, 5 color figures (some reduced in size). Accepted for publication in the Astrophysical Journa