  We analyze the photometric redshift catalog of the Sloan Digital Sky Survey
Data Release 5 (SDSS DR5) to estimate the Fisher information in the galaxy
angular power spectrum with the help of the Rimes-Hamilton technique. It is
found that the amount of Fisher information contained in the galaxy angular
power spectrum is saturated at lensing multipole scale 300<= l <= 2000 in the
redshift range 0.1<= photo-z <0.5. At l=2000, the observed information is two
orders of magnitude lower than the case of Gaussian fluctuations. This supports
observationally that the translinear regime of the density power spectrum
contains little independent information about the initial cosmological
conditions, which is consistent with the numerical trend shown by
Rimes-Hamilton. Our results also suggest that the Gaussian-noise description
may not be valid in weak lensing measurements.
