Single-mode fibers transform phase distortions into intensity fluctuations in a stellar interferometer. This is an worthy trade-off, as the scintillation can easily be monitored, and we have seen how these signals are used to correct interferograms from the photometric fluctuations. The correction is essentially a deconvolution, and a criterion was established to reject those scans for which this operation is not numerically stable. Corrected interferograms then lead to coherence factor measurements that are linked to the object visibility by a purely instrumental transfer function, where atmospheric turbulence is not involved. This feature greatly improves the accuracy of object visibility measurements.
One turbulence mode, however, is not filtered out by the fibers: the differential piston, which can be either removed by a fringe tracking system or reduced (at the expense of increasing detection noise) by scanning the OPD more rapidly. If there is no piston we saw that the data contain both spatial and spectral information on the source. This is the basis of double Fourier interferometry, a very promising technique for instruments which are equipped with a fringe tracker. Double Fourier interferometry with fibers can be achieved only if time and wavelength are effectively independent variables in the starlight injection function, and further work remains to be done in order to determine what this implies in terms of optical bandpass and input wavefront quality.
When piston perturbations exist, the phase and spectral information on the source is lost: then only the modulus of the coherence factor, integrated over the optical bandpass, can be accessed, through the amount of energy in the high frequency part (fringe signal) of the Fourier transform of the interferogram. An expression was derived for a noise bias free estimator of the squared modulus of the coherence factor. It depends (in a non critical way) of a spectral weighting factor, whose numerical value is given for different types of sources. The dispersion of the measured squared coherence factor is caused mainly by detector and piston noise, in relative proportions that can be evaluated.
The end result is an object visibility measurement with a statistical accuracy than can be better than 1% in a few tens of interferograms. The large gain in precision provided by single-mode fibers over conventional (dioptric) optics opens long baseline interferometry to a whole new class of astrophysical problems (Perrin et al. 1977).
Acknowledgements
Most of this work was performed as the author was a Ph.D. student at the Département de Recherches Spatiales (DESPA) of Observatoire de Paris.