A new holographic technique combining digital holographic microscopy with the use of low coherence light has been developed and the potential of the resulting method for vision in turbid media and biomedical imaging has been evaluated. In digital holography the hologram is recorded on a CCD camera and reconstructed numerically on a PC, giving direct access to the phase and the amplitude of the reconstructed wave front. This technique is combined with low coherence light, creating the possibility to perform optical sectioning. Series of holograms corresponding to slices at different depths in the specimen are recorded and each of these holograms contain phase and amplitude information of the light originating from the corresponding tomographic slice in the object. Sub micrometer lateral resolution is obtained experimentally and the phase distribution of the reconstructed object corresponds to a depth resolution of approximately 10 nm for a depth range of a couple of micrometers. A second level depth resolution is achieved using low coherence illumination. The thickness of a tomographic layer in water is 11 µm. Vision through 18 mean free paths (mfp) of turbid media (micro sphere suspension) is demonstrated with depth resolved reconstruction of the phase. Both amplitude and phase is reconstructed through 17 mfp's of turbid media. Tomographic imaging of a USAF test target hidden behind a 100 µm thick onion cell membrane is performed with phase and amplitude reconstructions of the test target as well as the surface of the onion cell membrane. Tomography of a biological specimen is demonstrated by the images of an onion shell, with structures visible down to a depth of 1 mm and by the images of a St-Paulia leaf presenting two cellular layers separated by 200 µm. Two structures of the anterior eye, the iris and the cornea, are studied on enucleated porcine eyes. A tomography of the iris border close to the pupil was performed and the penetration into the iris tissue is good. The cornea is first imaged without contact medium giving images strongly dominated by the air-cornea reflection. These images contain valuable information on the superficial epithelial cells in spite the presence of the tear film on the cornea. A water immersion configuration is also applied to enable a tomography of the cornea. A z-scan profile of the cornea is obtained and phase and amplitude images are reconstructed for different locations in the cornea (epithelium, stroma and endothelium).