An automatic method that fully compensates the quantitative phase measurements in off-axis digital holographic microscopy (DHM) is presented. The two main perturbations of the quantitative phase measurements in off-axis DHM are automatically removed. While the curvature phase flaw introduced by the microscope objective is avoided by the use of an optimized telecentric imaging system for the recording of the holograms, the remaining phase perturbation due to the tilt of the reference wave is removed by the automatic computation of a digital compensating reference wave. The method has been tested on both nonbiological and biological samples with and improving on the quality of the recovered phase maps.