The linear variable differential transformer (LVDT) position sensor for gravitational wave interferometer low-frequency controls

Low-power, Ultra-High-Vacuum compatible, non-contacting position sensors with nanometer resolution and centimeter dynamic range have been developed, built and tested. They have been designed at Virgo as sensor for low frequency modal damping of Seismic Attenuation System chains in Gravitational Wave interferometers and sub-micron absolute mirror positioning. One type of these LVDT’s has been designed to be also insensitive to transversal displacement thus allowing 3D movement of the sensor head while still precisely reading its position along the sensitivity axis. A second LVDT geometry has been designed to measure the displacement of the vertical seismic attenuation filters from their nominal position. Unlike the commercial LVDTs, mostly based on magnetic nuclei, the LVDTs described here exert no force on the measured structure. Introduction One of the most simple and effective Seismic noise Attenuation Systems for Gravitational Wave Detection interferometers is a chain of pendula suspended from a very low frequency stage called Inverted Pendulum (IP). The IP 10 , 9 has the triple function of, • Pre-filtering low frequency seismic noise to diminish the excitation of the rigid body motion resonance of the attenuation chain; • Provide a suitable platform to damp the above mentioned resonance; • Provide the mechanical compliance to allow precision positioning of the mirror suspended from the chain using small forces. The attenuation chains provide seismic attenuation in the frequency region of interest for gravitational wave detection and are capable of delivering the required seismic attenuation factors (~10) above 5 to 10 Hz, depending on the pendula lengths. The IP is composed of three flex joints, each supporting a leg. At the top, the three legs are connected to a rigid table by means of small flexures. The IP has two translational modes and one torsional mode. A triplet of accelerometers is mounted at 120, in pinwheel geometry, at the periphery of the IP top table. It is designed to detect the acceleration in the IP’s three degrees of freedom. Their signal is fed to actuators to damp the rigid body resonant modes of the chain, and hence reduce the mirror r.m.s. residual motion of the suspended mirror to a few tens of nanometers in the frequency band between 10 mHz and 5 Hz. The accelerometers are inertial sensors, totally insensitive to velocity, and cannot provide positioning of the IP table (and of the mirror suspended from it) with respect to a local frame. Additionally, at low frequency (typically below 100 Hz, depending on the mechanics precision and ground stability) inertial sensors can be more sensitive to tilts than to real accelerations. In order to take full advantage of the accelerometer performance it is necessary to complement them with a set of high precision position sensors. The specifications of these position sensors are as follows: • Linearity within 1% over +/-10 mm, to match the typical IPs dynamic range • Position resolution ~ 10 nm r.m.s. to allow the reduction of mirror residual motion • Insensitivity to movements in the directions orthogonal to the sensing axis, to allow for free movements of the IP on the horizontal plane and not to re-inject seismic signals from the orthogonal directions in the feed back loop • Force-free and contact-free, to avoid short circuiting of the seismic excitation to the IP table • Only passive components inside the vacuum system, for reliability reasons • Fully UHV compatible, to prevent contamination of the vacuum conditions. Special LVDT position transducers have been designed for the GW interferometer VIRGO, to satisfy all the above requirements. Note, also, that all the electronic circuitry is placed outside the vacuum enclosure to satisfy the passive instrument requirement. The LVDT are driven and read-out at the end of 20 or more meters of twisted shielded cable without loss of resolution. They turned out to be so versatile that a modified, smaller version (that has been defined as a “second type”) has been designed, which is being used in several other locations of the GW interferometer seismic attenuation systems, as a sensor for all the Virgo superattanuator filter vertical working point, in the TAMA MGASF top filter, and as generic precision position sensor in mechanics R&D. The LVDT working principle The LVDT is composed of three coils whose cross section is shown in Figure 1. The central emitter coil, driven with a sinusoidal signal at a frequency between 10 and 20 kHz, mounted between two larger receiver coils; the two receiver coils are identical, counter-wound and connected either in series or in parallel. The emitter is mounted on the IP table while the two receivers are attached on a reference structure; when the emitter is exactly in the mid point between the twin receiver coils, no net signal is induced. When the table movements move the emitter coil in a direction, a sinusoidal signal appears on the receiver coils. This signal has amplitude roughly proportional to the displacement from the center position. If the coil is moved in the opposite direction the sign of the induced sinusoid is changed. By a careful choice of the coil geometry it was possible to get better than one percent linearity over 25 mm of movement range with less than a percent sensitivity to transversal movements. Also the sophisticated design of the lock in amplifier circuit allowed for better than 10 nm r.m.s. position resolution over the afore mentioned range. The coils are made of Kapton-coated copper wire, wound around glass or Peek supports, and are therefore completely UHV compatible. Although the coils were accurately spooled, the lumped coil of this design makes it quite insensitive to the spooling precision. Unlike conventional magnetic core LVDTs, this arrangement has no ferromagnetic components and does not generate to unwanted forces when exposed to external magnetic fields Figure 1: Schematic view, sectioned along the symmetry axis, of a LVDT position transducer. The three coils appear as the six darkly shaded rectangles. The coil spools are made of either glass or Peek, the coil supports are made of slotted and mutually isolated aluminum parts to avoid eddy current loops. No effort is made to make thermally compensated supports because they are intended for use in a thermally stabilized vacuum