A scanning monochromatic spatial low-coherent interferometer (S-LCI) can be used to simultaneously measure geometric thickness and refractive index. The probe beam of the scanning S-LCI can be an off-axis converging single wavelength laser beam, and the decomposed incident angles of the beam on the sample can be accurately defined in the Fourier domain. The angle dependent phase shift of a plane parallel plate or other sample can be obtained in a single system measurement. From the angle dependent phase shift, the geometric thickness and refractive index of the sample can be simultaneously obtained. Additionally or alternatively, the S-LCI system can interrogate the sample to profile the location and refractive index of one or more layers within the sample using the disclosed techniques.