We present an overview of the ST ScI calibration program and the reduction, smoothing, and analysis capabilities we have developed to deal with Transfer Functions. The Transfer Function (TF) is the name for the fringe visibility curve produced by the Koesters prism interferometer in the Fine Guidance Sensors (FGSs). The TF for a single, point, monochromatic source becomes modified — in different ways — when we observe a real source with a typical stellar energy spectrum, a finite disc, or a double system. Thus, we have constructed an in depth calibration program and designed and developed a comprehensive set of TF analysis algorithms. The ST ScI calibration program includes the acquisition of reference TFs at 19 different places in the astrometer FGS (there are field–dependent aberrations beyond the well–publicized spherical aberration of the primary mirror). In addition, for Cycle 2, both stars with finite angular diameters and minor planets will be observed. The software to implement our correlation–based analysis techniques has been extensively tested on artificial binary stars created by combining real TFs and re-introducing photon noise. A wide variety of synthetic binaries — with separations from 10 to 135 milli-arcseconds and magnitude differences from 0 to 4.2 mag — were used so that we can objectively and quantitatively characterize the capability of both the software and the instrument to resolve close pairs and to detect faint companions. Separations to a few milli-arcseconds, position angles to , and magnitude differences to are attainable for primaries brighter than V = 13 mag and Δm < 3 mag. The software is being incorporated into IRAF/STSDAS at the ST ScI.