Absolute total photodetachment cross sections of O(-) and OH(-) anions stored in a multipole radio frequency trap have been measured using a novel laser depletion tomography method. For OH(-) the total cross sections of 8.5(1)(stat)(3)(syst) and 8.1(1)(stat)(7)(syst)x10(-18) cm(2), measured at 662 and 632 nm, respectively, were found constant in the temperature range of 8-300 K. The O(-) cross sections 5.9(1)(stat)(2)(syst) and 6.3(1)(stat)(2)(syst)x10(-18) cm(2) measured at 170 K at 662 and 532 nm, respectively, agree within error estimations with preceding experiments and increase the accuracy of the widely used calibration standard for relative photodetachment measurements of diverse atomic and molecular species.