  The measurement of very low reflection coefficients of anti-reflective coated
interfaces has become a key issue for the realization of precision instruments
such as the giant interferometers used for the detection of gravitational
waves. We propose in this paper a method, based on low coherence interferometry
and balanced detection, which not only allows to obtain the spectral dependence
of this reflection coefficient in amplitude and phase, with a sensitivity of
the order of 0.1 ppm and a spectral resolution of 0.2 nm, but also to eliminate
any spurious influence related to the possible presence of uncoated interfaces.
This method also implements a data processing similar to that used in Fourier
transform spectrometry. After establishing the formulas that control the
accuracy and the signal-to-noise ratio of this method, we present the results
that provide a complete demonstration of its successful operation in various
experimental conditions.
