Improvements to dispersed reference interferometry: beyond the linear approximation

Interferometric instruments with dispersion introduced in the reference arm have previously been created, as the controlled dispersion can be used to generate a signal that contains a clearly identifiable point, the location of which relates to the position of the scattering surface in the measurement arm. In the following, we illustrate that the linear approximations that have been used previously can lead to significant errors, and that second-order terms need to be included in order to correct this. These corrections are vital if these instruments are to be used for metrological applications.