The HI opacity of the intergalactic medium at redshifts 1.6<z<3.2

We use high-quality echelle spectra of 24 quasi-stellar objects 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 per cent. 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 f1.6 < 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 ultraviolet background is similar to 40 per cent higher than expected. Our data appears to be consistent with an H i ionization rate of Gamma similar to 1.4 x 10(-12) s(-1).