The relative mechanical displacements of the test cylinders in the X and Y directions of the plane perpendicular to the spin axis are read by two capacitance bridges, rotating with the system, whose four sensing plates (Fig. 5) are located in between the test cylinders with a clear gap of 5 mm on either side. The electronic circuit of each bridge is sketched in Fig. 9. The smallest fractional capacitance unbalance that the circuit was sensitive to in bench tests corresponds to mechanical displacements of 5 picometer in 1 s of integration time ("GALILEO GALILEI" (GG), Phase A Report, 1998, Section 2.1.3). A voltage signal of high frequency is applied to the bridge in order to shift the signal of interest to a high frequency band with reduced 1/f noise. Since the capacitance bridges rotate with the accelerometer, power and data transfer must be ensured between the rotating and the non-rotating frame. For power transfer we use rotating contacts. The high frequency bridge measurements are first demodulated and then converted from analog to digital to be optically transferred outside the vacuum chamber. The (rotating) electronics which is needed to perform these tasks, as well as the electronics of the bridges, is located on an annular dish mounted around the suspension tube (Figs. 2 and 3).

In order to be able to transform the relative displacements as measured by the bridges in the rotating frame of the rotor to the non-spinning reference frame of the laboratory, we need to know, in correspondence of each data point, also the phase angle of the rotor. For this purpose a simple optical device has been mounted at the top of the rotor which provides a reference signal with the rotor phase information. A microprocessor outside the chamber takes care of combining the reference signal with the X and Y measurements and of providing the resulting combined data in RS232 data format for computer acquisition (through a serial port) as a binary file which is then transformed into a text file for data analysis. The reference signal is also acquired, independently of the capacitance bridges data, by another computer (through a National Instruments card) for independent checks of the spin rate of the system and for various other tests to ensure that the data combination procedure has been performed correctly.

The capacitance bridges are calibrated by displacing the outer test cylinder with respect to the inner one by a known amount (by means of a micrometric screw mounted on the frame for this purpose only; not shown in Fig. 3) and recording the voltage signal read by the capacitance sensors. Displacements are applied in both X and Y directions and linearity checks of the calibration curve are performed in both cases.

The electric zero of the capacitance bridges is first set at its nominal value, by setting the value of the variable capacitance of the circuit (Fig. 9). More accurate checks are performed with the system in rotation, first below and then above the natural frequency of differential oscillations of the test cylinders, as discussed in Section 4.

Mechanical balancing should be achieved to ensure that the capacitance plates of the bridges be located halfway in between the outer surface of the inner test cylinder and the inner surface of the outer one, a configuration which provides the best sensitivity to differential displacements. The capacitance plates shown in Fig. 5 (two for each one of the two bridges in the X and Y directions), are rigidly connected (via an insulating frame) to the suspension tube (see Fig. 2). The linear dimensions of the frame are dictated by the linear dimensions of the test cylinders (outer radius of inner cylinder and inner radius of the outer one), which are chosen on the basis of the desired gap between the two. Since all parts are precisely manufactured according to the design (their dimensions are checked a posteriori to less than 1 µm with a 3D measuring machine equipped with a contact point sensor) it is possible to design and manufacture the insulating frames of the plates (see Fig. 5) so that they provide a configuration as close as possible to the nominal one corresponding to perfect mechanical balancing. This procedure has provided considerable improvement with respect to a previous set up in which all parts of the frame were manufactured, mounted and adjusted independently.