An interferometric microscope for making interferometric measurements of locations within an object that is in a medium, there being a mismatch between indices of refraction of said object and said medium, the microscope including a source for generating an input beam; an interferometer which is configured to receive the input beam and generate therefrom a measurement beam, to focus the measurement beam onto a selected spot in the object and produce for that selected spot a return measurement beam, and to combine the return measurement beam and a reference beam to produce an interference beam; and a detector system which is positioned to receive the interference beam, wherein the return measurement beam travels along a path from the object to the detector system and wherein the interferometer includes a compensating layer of material positioned in the path of the return measurement beam, the compensating layer producing a mismatch in the index of refraction along the path of the return measurement beam that compensates for the mismatch between the indices of refraction of the object and the medium.