Measuring distances and displacements using dispersive white-light spectral interferometry

A new white-light interferometric technique characterized by the range of measurable distances dependent on the amount of dispersion in an interferometer is proposed. We show that processing of the spectral interferograms recorded by a low-resolution spectrometer and including so-called equalization wavelengths can be extended to precise the determination of positions or displacements of the interferometer mirror to reach sub-micron or even nanometer resolution. In contrary to standard spatial-domain white-light interferometry employing interferometers balanced for dispersion we use a dispersive Michelson interferometer with fused-silica optical element (optical sample or beamsplitter) of know thickness. Knowing both dispersion and the thickness of the interferometer optical element and using a least-squares fit of the theoretical spectral interferograms to the recorded ones we obtain the positions of the interferometer mirror. Within two different configurations of a dispersive Michelson interferometer, one with an optical sample and the other with one a beamsplitter, we show that the range of measurable displacements depends on the thickness of the optical element.