We use high quality echelle spectra of 24 QSOs to provide a calibrated measurement of the total amount of Ly \alpha forest absorption ( DA ) over the redshift range 2.2 < z < 3.2 .
Our measurement of DA excludes absorption from metal lines or the Ly \alpha lines of Lyman limit systems and damped Ly \alpha systems .
We use artificial spectra with realistic flux calibration errors to show that we are able to place continuum levels that are accurate to better than 1 % .
When we combine our results with our previous results between 1.6 < z < 2.2 , we find that the redshift evolution of DA is well described over 1.6 < z < 3.2 as A ( 1 + z ) ^ { \gamma } , where A = 0.0062 and \gamma = 2.75 .
We detect no significant deviations from a smooth power law evolution over the redshift range studied .
We find less H I absorption than expected at z = 3 , implying that the UV background is about 40 % higher than expected .
Our data appears to be consistent with an H I ionization rate of \Gamma \sim 1.4 \times 10 ^ { -12 } s ^ { -1 } .