  In a linac driven Free Electron Laser (FEL), the shot-to-shot and
non-invasive monitoring of the electron bunch length is normally ensured by
Bunch Compressor Monitors (BCMs). The bunch-length dependent signal of a BCM
results from the detection and integration - over a given frequency band - of
the temporal coherent enhancement of the radiation spectral energy emitted by
the electron beam while experiencing a longitudinal compression. In this
letter, we present a method that permits to express the relative variation of
the bunch length as a function of the relative statistical fluctuations of the
BCM signal and charge. Furthermore, in the case of a BCM equipped with two
detectors simultaneously operating in two distinct wavelength bands, the method
permits an absolute determination of the bunch length. The presented method is
beneficial to a FEL since it permits to tune the machine compression feedback
with respect to the measured bunch length instead of the bunch-length dependent
signal. In a CW-linac driven FEL, it can offer the precious opportunity to
implement a fully non-invasive and absolute diagnostics of the bunch length.
