We report on a method called Digital Holographic Microscopy (DHM) for the numerical reconstruction of digital holograms taken with a microscope. It allows for simultaneous amplitude and quantitative phase contrast imaging. The reconstruction method computes the propagation of the complex optical wavefront diffracted by the object and is used to determine the refractive index and/or shape of the object with an accuracy in the nanometer range along the optical axis. A single hologram is needed for reconstruction. The method requires the adjustment of several reconstruction parameters. The adjustment is performed automatically by using a suitable algorithm. The method has been applied to the measurement of several integrated optics devices, MOEMS, and integrated micro-optical components: microlenses.