  The quantum interference of two wavelength-entangled photons overlapping at a
beamsplitter results in an oscillating interference pattern. The frequency of
the beat note is dependent on the wavelength separation of the entangled
photons but is robust to wavelength scale perturbations that can limit the
practicality of standard interferometry. Here we use two-colour entanglement
interferometry to evaluate the variation in thickness of a semi-transparent
sample in combination with two-dimensional raster scanning. The axial precision
and the dynamic range of the microscope are actively controlled by adjusting
the wavelength separation of the entangled photon pairs. Sub-$\mu m$ precision
is reported using up to $12.3~nm$ of detuning and $\sim10^4$ detected photon
pairs.
