We use SDSS imaging data in ugriz passbands to study the shape of the point spread function ( PSF ) profile and the variation of its width with wavelength and time .
We find that the PSF profile is well described by theoretical predictions based on von Kármán ’ s turbulence theory .
The observed PSF radial profile can be parametrized by only two parameters , the profile ’ s full width at half maximum ( FWHM ) and a normalization of the contribution of an empirically determined “ instrumental ” PSF .
The profile shape is very similar to the “ double gaussian plus power-law wing ” decomposition used by SDSS image processing pipeline , but here it is successfully modeled with two free model parameters , rather than six as in SDSS pipeline .
The FWHM variation with wavelength follows the \lambda ^ { \alpha } power law , where \alpha \approx - 0.3 and is correlated with the FWHM itself .
The observed behavior is much better described by von Kármán ’ s turbulence theory with the outer scale parameter in the range 5–100 m , than by the Kolmogorov ’ s turbulence theory .
We also measure the temporal and angular structure functions for FWHM and compare them to simulations and results from literature .
The angular structure function saturates at scales beyond 0.5 - 1.0 degree .
The power spectrum of the temporal behavior is found to be broadly consistent with a damped random walk model with characteristic timescale in the range \sim 5 - 30 minutes , though data show a shallower high-frequency behavior .
The latter is well fit by a single power law with index in the range -1.5 to -1.0 .
A hybrid model is likely needed to fully capture both the low-frequency and high-frequency behavior of the temporal variations of atmospheric seeing .