Tuning the TTF to the required bandpass

J. Bland-Hawthorn

[Dire warning][TTF control system][Physical scan range][Fixing the resolution][Table of values]

Dire warning

Let me start by saying that you must not try to tune the CS100 to a new bandpass without consulting JBH, CMC or EJP. For both the BTTF and RTTF, there is a very real chance that you might squash the plates together. Repolishing and recoating the plates costs about $10K. If there was ever a single point failure of the TTF system, this is it. This will not be a problem with the new automatic control system since the software will stop you from causing damage, but this has yet to be fully commissioned. Your support astronomer will have dialled up the values requested in your proposal, and this should be enough.

However, several observers have demanded to know more so here we go. Please completely absorb this material before even contemplating a change in bandpass. . . .

TTF control system

The CS100 control system (shown above) is a three-channel bridge system which uses capacitance micrometers and PZT actuators, incorporated into the etalon, to monitor and correct errors in mirror parallelism and spacing. Two channels (XY) control parallelism and the third (Z) maintains spacing by referencing the cavity length-sensing capacitor to a high stability standard reference capacitor, also located in the etalon. Because this is a closed-loop system, non-linearity and hysteresis in the PZT drive are eliminated entirely, as of course are drifts in cavity parallelism and spacing.

The CS100 controller is central to the operation of the TTF. Our Mark I version of the CS100 can be operated manually from front panel controls, or under computer control using an RS232 interface. This expensive machine keeps the TTF plates parallel and allows the plate spacing to be tuned - from an optical point of view - over a very large physical range. The CS100 is attached to the exterior of TAURUS-2 in the Cass cage (bottom right). If you lie on the floor and look up, you should see it.

The front panel of the CS100 has a number of analogue dials and switches shown in the figure below. The X, Y and Z settings for the TTF are controlled through these analogue switches, although of course we have limited software control through the SMS window in the control room.

In the figure, the manual switches to the left are:

\begin{displaymath}\begin{array}{ccc}X_{fine} & X_{coarse} & X_{res} \\Y_{fin......arse} & Y_{res} \\Z_{fine} & Z_{coarse} & Z_{res}\end{array}\end{displaymath}

For our antiquated CS100, there are rather more switches below the meters than shown here but do not worry. Below, we use the subscript "f" for "fine" and "c" for "coarse".

You may have seen your support astronomer tweaking X and Y to check whether the TTF plates are roughly parallel. This is best done either (a) through the quadrant check under SMS, or (b) by eye at the access port using the Ne lamp when Zc = +5. For the purposes of tuning the bandpass, we can forget about X and Y, since Z is the variable that relates linearly to the spacing of the TTF plates.

The software variables under SMS which control X, Y and Z are called Xs, Ys and Zs. The next section explains the all important relations between the analogue coarse and fine dials, and the software variables.

Physical scan range of the TTF plates

A crucial point to understand is the physical range allowed by the CS100 and the TTF. The piezo-stack lengths are about 15$\mu$m. For completeness, we include details on the XY movement although it is the Z movement which is directly relevant to the bandpass tuning.
 

XY physical movement. The maximum allowed XY amplitude is 3.21$\mu$m. The analogue Coarse range at the controller is (-5,+5) which corresponds to (-1,+1)$\mu$m. The Fine control gives an additional (0$\rightarrow$10) or 0.21$\mu$m. The SMS control interface allows for (-2048,+2048) which corresponds to (-0.5,0.5)$\mu$m. Since the Fine control gives only a positive voltage, the total physical scan range is (-1.5,+1.71)$\mu$m.
 

Z physical movement.The maximum allowed Z amplitude is 13.05$\mu$m. The analogue Coarse range at the controller is (-5,+5) which corresponds to (-5,+5)$\mu$m. The Fine control gives an additional (0$\rightarrow$10) or 1.05$\mu$m. The SMS control interface allows for (-2048,+2048) which corresponds to (-1,1)$\mu$m. Since the Fine control gives only a positive voltage, the total physical scan range is (-6,+7.05)$\mu$m.
 
 

An illustration of the different instrumental response profiles for a range of gap spacings (shown on the left hand side). The integer series indicates the order of interference. For comparison, the RTTF filter set is shown above to the same wavelength scale.


Fixing the resolution

At last, we arrive at how to dial up a given bandpass for a chosen wavelength. If you are working on-axis, the all important equation is $m\lambda = 2\mu \ell$ where $\mu =1$. Thus, the physical gap is $\ell = m(\lambda/2)$ where m is the order of interference which basically determines the resolving power.

Note from the equation for$\ell$ that each order of interference corresponds to a $\lambda/2$ physical displacement of the plates. This is how far the plates move when they are scanned over a free spectral range. By now, you will know that the instrumental response repeats over a free spectral range, as you will have seen when scanning the plates using the variable Zs under the SMS control window.

Remember that, in software, regardless of what resolution you are working at, the free spectral range in Zs is always the same. At H$\alpha$, this is about 340. The free spectral range in Z scales linearly with wavelength, i.e. FSR(Zs) corresponds to about 205 at 400nm.

The resolving power at any wavelength is $R\approx 33 m$, in other words, $R \approx 66\ell/\lambda$. This leads to a nice mnemonic at H$\alpha$: the gap in microns is 1% of the resolving power. The available range of resolving powers at every wavelength is shown here.

Therefore, for a chosen bandpass $\delta\lambda$, the gap you want is $\ell = 66\delta\lambda/\lambda^2$. Below, we have determined a complete set of physical gaps for the primary settings of Zc, Zf and Zs. For convenience, choose a setting with Zf set to 0.

Note something fundamental to a fixed interferometric spacing. The bandpass goes like $\lambda^2$ which can be a real problem. At any specific analogue setting, the software control allows you to tune over a 2$\mu$m range. So at small gap spacings, tuning over the full Zs range can partly offset the effect. In other words, if you have set up the BTTF to work at H$\alpha$ and [OII]3727, observe the former at high Zs and the latter at low Zs. At large gap spacings, the $\lambda^2$ effect will be a problem until the new automatic control system is commissioned, at which time you will be able to tune over the full physical range in software.

The next step is IMPORTANT ! After you have dialed up the required settings from the table below, it is crucial that you force the software environment to accept these values. This is trivial to do.  Simply turn off the external control and open the CS100 loop in software, then turn external control back on, and close the loop again. To wit,  if you are familiar with the SMS key pad -- which I presume you are otherwise you wouldn't have come this far -- hit "." and then type

obeyw taurus EXTERNAL false
obeyw taurus CLOSE_LOOP false
and after a few seconds or so, type
obeyw taurus EXTERNAL true
obeyw taurus CLOSE_LOOP true
If you prefer to mess with the SMS window system, go to setup / change_cs100 and do the equivalent operations there.
 

Table of Values

PLEASE NOTE: You must never turn Zc below -2 (`below' means `more negative') in case you squash the plates together. For the expert, please do not attempt to access a setting in (Zc, Zf, Zs) smaller than 3 microns.


ANALOGUE DIAL SETTINGS

  
          Zc     Zf       Zs     gap (um)
 
   1     -5.    0.00   -2048.     -0.51         (negative gaps do exist!)
   2     -5.    0.00       0.      0.49         DO NOT USE
   3     -5.    0.00    2048.      1.49         DO NOT USE
   4     -5.    5.00   -2048.      0.01         DO NOT USE
   5     -5.    5.00       0.      1.01         DO NOT USE
   6     -5.    5.00    2048.      2.01         DO NOT USE
   7     -5.   10.00   -2048.      0.54         DO NOT USE
   8     -5.   10.00       0.      1.54         DO NOT USE
   9     -5.   10.00    2048.      2.54         DO NOT USE
  10     -4.    0.00   -2048.      0.49         DO NOT USE
  11     -4.    0.00       0.      1.49         DO NOT USE
  12     -4.    0.00    2048.      2.49         DO NOT USE
  13     -4.    5.00   -2048.      1.01         DO NOT USE
  14     -4.    5.00       0.      2.01         DO NOT USE
  15     -4.    5.00    2048.      3.01         DO NOT USE
  16     -4.   10.00   -2048.      1.54         DO NOT USE
  17     -4.   10.00       0.      2.54         DO NOT USE
  18     -4.   10.00    2048.      3.54
  19     -3.    0.00   -2048.      1.49         DO NOT USE
  20     -3.    0.00       0.      2.49         DO NOT USE
  21     -3.    0.00    2048.      3.49
  22     -3.    5.00   -2048.      2.01         DO NOT USE
  23     -3.    5.00       0.      3.01         DO NOT USE
  24     -3.    5.00    2048.      4.01
  25     -3.   10.00   -2048.      2.54         DO NOT USE
  26     -3.   10.00       0.      3.54
  27     -3.   10.00    2048.      4.54
  28     -2.    0.00   -2048.      2.49         DO NOT USE
  29     -2.    0.00       0.      3.49
  30     -2.    0.00    2048.      4.49
  31     -2.    5.00   -2048.      3.01         DO NOT USE
  32     -2.    5.00       0.      4.01
  33     -2.    5.00    2048.      5.01
  34     -2.   10.00   -2048.      3.54
  35     -2.   10.00       0.      4.54
  36     -2.   10.00    2048.      5.54
  37     -1.    0.00   -2048.      3.49
  38     -1.    0.00       0.      4.49
  39     -1.    0.00    2048.      5.49
  40     -1.    5.00   -2048.      4.01
  41     -1.    5.00       0.      5.01
  42     -1.    5.00    2048.      6.01
  43     -1.   10.00   -2048.      4.54
  44     -1.   10.00       0.      5.54
  45     -1.   10.00    2048.      6.54
  46      0.    0.00   -2048.      4.49
  47      0.    0.00       0.      5.49
  48      0.    0.00    2048.      6.49
  49      0.    5.00   -2048.      5.01
  50      0.    5.00       0.      6.01
  51      0.    5.00    2048.      7.01
  52      0.   10.00   -2048.      5.54
  53      0.   10.00       0.      6.54
  54      0.   10.00    2048.      7.54
  55      1.    0.00   -2048.      5.49
  56      1.    0.00       0.      6.49
  57      1.    0.00    2048.      7.49
  58      1.    5.00   -2048.      6.01
  59      1.    5.00       0.      7.01
  60      1.    5.00    2048.      8.01
  61      1.   10.00   -2048.      6.54
  62      1.   10.00       0.      7.54
  63      1.   10.00    2048.      8.54
  64      2.    0.00   -2048.      6.49
  65      2.    0.00       0.      7.49
  66      2.    0.00    2048.      8.49
  67      2.    5.00   -2048.      7.01
  68      2.    5.00       0.      8.01
  69      2.    5.00    2048.      9.01
  70      2.   10.00   -2048.      7.54
  71      2.   10.00       0.      8.54
  72      2.   10.00    2048.      9.54
  73      3.    0.00   -2048.      7.49
  74      3.    0.00       0.      8.49
  75      3.    0.00    2048.      9.49
  76      3.    5.00   -2048.      8.01
  77      3.    5.00       0.      9.01
  78      3.    5.00    2048.     10.01
  79      3.   10.00   -2048.      8.54
  80      3.   10.00       0.      9.54
  81      3.   10.00    2048.     10.54
  82      4.    0.00   -2048.      8.49
  83      4.    0.00       0.      9.49
  84      4.    0.00    2048.     10.49
  85      4.    5.00   -2048.      9.01
  86      4.    5.00       0.     10.01
  87      4.    5.00    2048.     11.01
  88      4.   10.00   -2048.      9.54
  89      4.   10.00       0.     10.54
  90      4.   10.00    2048.     11.54
  91      5.    0.00   -2048.      9.49
  92      5.    0.00       0.     10.49
  93      5.    0.00    2048.     11.49
  94      5.    5.00   -2048.     10.01
  95      5.    5.00       0.     11.01
  96      5.    5.00    2048.     12.01
  97      5.   10.00   -2048.     10.54
  98      5.   10.00       0.     11.54
  99      5.   10.00    2048.     12.54
 
          Zc     Zf       Zs     gap (um)


The next generation control system. One could increase this scan range with an analogue switch summation point in the circuitry. The new look TTF interface will circumvent the CS100 control panel and allow the full physical range to be scanned with an 18-bit bus, or a unique step of $5\times 10^{-5}\mu$m, equivalent to 0.5Å. The commissioning should be complete by the end of the millenium.