The installation of the Wide Field Camera 3 ( WFC3 ) on the Hubble Space Telescope ( HST ) will revolutionize the study of high-redshift galaxy populations .
Initial observations of the HST Ultra Deep Field ( UDF ) have yielded multiple z \gtrsim 7 dropout candidates .
Supplemented by the Great Observatories Origins Deep Survey ( GOODS ) Early Release Science ( ERS ) and further UDF pointings , these data will provide crucial information about the most distant known galaxies .
However , achieving tight constraints on the z \sim 7 galaxy luminosity function ( LF ) will require even more ambitious photometric surveys .
Using a Fisher matrix approach to fully account for Poisson and cosmic sample variance , as well as covariances in the data , we estimate the uncertainties on LF parameters achieved by surveys of a given area and depth .
Applying this method to WFC3 z \sim 7 dropout galaxy samples , we forecast the LF parameter uncertainties for a variety of model surveys .
We demonstrate that performing a wide area ( \sim 1 { ~ { } \mathrm { deg } } ^ { 2 } ) survey to H _ { \mathrm { AB } } \sim 27 depth or increasing the UDF depth to H _ { \mathrm { AB } } \sim 30 provides excellent constraints on the high- z LF when combined with the existing UDF GO and GOODS ERS data .
We also show that the shape of the matter power spectrum may limit the possible gain of splitting wide area ( \gtrsim 0.5 { ~ { } \mathrm { deg } } ^ { 2 } ) high-redshift surveys into multiple fields to probe statistically independent regions ; the increased root-mean-squared density fluctuations in smaller volumes mostly offset the improved variance gained from independent samples .