A method for measuring shape or thickness information of a substrate, comprising: a) placing a substrate in an optical cavity formed between first and second reference flats (32, 52) in first and second interferometer channels to map first and second test surfaces of the substrate such that first and second surfaces of the substrate are substantially parallel with corresponding first and second reference surfaces of the first and second reference flats (32, 52); b) positioning at least one damping plate (80, 90) proximate the portion of the first or second surface of the substrate that does not overlap the first or second reference surface, the at least one damping plate (80, 90) having a damping surface oriented parallel to the first or second reference surface c) providing light to and from the cavity via the first and second interferometer channels; wherein the light has a coherence length greater than twice the length of the gap between the reference flat (32, 52) and the surface (33, 53) of the substrate; d) measuring cavity characteristics of the reference surfaces forming the cavity using the first or second interferometer channels; e) providing a first phase shift in the interferometer channels to map at least a portion of the first and second test surfaces of the substrate; f) providing a second phase shift for measuring the characteristics of the first and second test surfaces; and g) determining the shape or thickness information of the substrate from interferometer maps of the first and second test surfaces and the characteristics of the first and second test surfaces;wherein the first and second reference flats (32, 52) are of a size smaller than the substrate, whereby a portion of the first or second surface of the substrate does not overlap the first or second reference surface. a) placing a substrate in an optical cavity formed between first and second reference flats (32, 52) in first and second interferometer channels to map first and second test surfaces of the substrate such that first and second surfaces of the substrate are substantially parallel with corresponding first and second reference surfaces of the first and second reference flats (32, 52); b) positioning at least one damping plate (80, 90) proximate the portion of the first or second surface of the substrate that does not overlap the first or second reference surface, the at least one damping plate (80, 90) having a damping surface oriented parallel to the first or second reference surface c) providing light to and from the cavity via the first and second interferometer channels; wherein the light has a coherence length greater than twice the length of the gap between the reference flat (32, 52) and the surface (33, 53) of the substrate; d) measuring cavity characteristics of the reference surfaces forming the cavity using the first or second interferometer channels; e) providing a first phase shift in the interferometer channels to map at least a portion of the first and second test surfaces of the substrate; f) providing a second phase shift for measuring the characteristics of the first and second test surfaces; and g) determining the shape or thickness information of the substrate from interferometer maps of the first and second test surfaces and the characteristics of the first and second test surfaces;wherein the first and second reference flats (32, 52) are of a size smaller than the substrate, whereby a portion of the first or second surface of the substrate does not overlap the first or second reference surface.