Control of TTF Plates

For peak performance of a Fabry-Perot device the error in plate parallelism must be much less than deviations from flatness in the plate surface. The coated plates in TTF are individually flat to $\lambda/140$ and normally parallelism must be established and maintained to at least $\lambda/500$ during use. To achieve this, the plates of TTF are controlled through an active feedback loop that constantly corrects the plates when small changes from plate position occur ([Hicks & Atherton 1997]; q.v. [Ramsay 1962]). Such closed loop control is essential for a device such as TTF, where plate stability could otherwise be influenced by variations in temperature, humidity and gravity on the plates as the telescope moves.

Hicks, Reay & Atherton (1984) pioneered the technique of Fabry-Perot stabilization using a capacitance bridge. Their Fig. 1 shows the components employed in the active feedback system used by TTF. Four capacitors around the edge of the inner plate surfaces (labelled in their Fig. 1 as CX₁, CX₂, CY₁ and CY₂) detect changes in plate spacing. Such changes permit measurement of the plate tilt along the direction of the x-y axes defined by the two capacitor pairs. This capacitance micrometry is capable of detecting displacements of 10^-12 m ([Jones & Richards 1973]). Tilt information from the capacitors is fed to piezo-electric transducers (PZTs) which compensate for the amount of deviation. There are three PZTs, each located around the plate edge between the capacitors and separated by $120^{\circ}$. An additional reference capacitor measures the gap spacing with respect to a fixed capacitor built onto one of the plates.

When the plates are parallel, capacitance will not be equal between either the CX₁, CX₂ or CY₁, CY₂ pairs. This is why the feedback system can only maintain parallelism and not establish it in the first place. Electronic offsets are applied to compensate for variations in capacitance whenever they occur. These can arise from temperature gradients across the Fabry-Perot or continual changes in the piezo dimensions due to creep in the PZT lattice structure. All such capactitance changes are continually balanced and nulled automatically by the system electronics.

We are able to introduce fixed vertical offsets Z_X, Z_Y, along the x and ydirections through three levels of control: coarse, fine and software. Both coarse and fine are analogue inputs directly through the hardware of the TTF controller. Software control allows precision adjustment of the plates via digital input. The maximum Z_X and Z_Y amplitudes are 3.21 $\mu$m. Clearly, it is crucial to ensure the plates are parallel before attempting to achieve gaps smaller than about 7$\mu$m. The vertical deviation along the x-axis from the zero-point is given by

 

Z_X = 0.2 X_c + 0.021 X_f + X_s /4096 (1)

where Z_X is in microns and X_c, X_f and X_s are the respective coarse, fine and software settings in X. Each control has its own range: $X_c \in [-5,+5]$, $X_f \in [0,10]$ and $X_s \in [-2048,+2048]$. An identical calibration relates Z_Ywith Y_c, Y_f and Y_s, across identical settings.

No gap scanning is done through the Z_X or Z_Y movements. They are purely offsets that remain fixed unless adjusted for parallelism. Scanning is controlled through a third parameter Z which has the much larger amplitude of 13.05 $\mu$m. It too can be adjusted through three levels of coarse, fine and software control,

 

Z = Z_c + 0.105 Z_f + Z_s /2048 + 5.488, (2)

although with a much larger range in the coarse setting than Z_X or Z_Y. Equation (2) is the absolute calibration used to tune the plates to arbitrary gap (and therefore wavelength) during normal observing. It depends on the values of ( X_c, X_f, X_s) and ( Y_c, Y_f, Y_s) at the time of calibration; in the case of Eqn. (2), for the TTF, (X_c, X_f, X_s) = (0.0, 3.90, 0.0) and (Y_c, Y_f, Y_s) = (0.1, 8.00, 0.0). Although the setting limits of Z_c, Z_f and Z_s are identical to those of x and y, the corresponding physical ranges are much larger. Since Z_c and Z_f are analogue controls, all gap scanning is done through automated stepping of Z_s in software. The units of Z in Eqn. (2) are microns.

The amount of offset is derived directly from the parallelism test and refined through successive iterations. We describe the test in the following section.