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 40m Log Not logged in Message ID: 6211     Entry time: Wed Jan 18 14:28:36 2012     In reply to: 6202     Reply to this: 6212
 Author: kiwamu Type: Update Category: LSC Subject: estimation of optical length between PRM and scattering object

Assuming that PRM is interfering with some other optics, I have estimated the optical distance between PRM and an object that interferes with PRM.

The optical distance is estimated to be 9.5 +/- 0.5 m.

If we believe this number the object is most likely outside of the vacuum chambers.

(The measurement)

In order to estimate the optical length between PRM and a scattering body, I swept the frequency of the main laser by actuating on the MC length.
With the sweep, the laser frequency go across some fringes and basically it allows us to estimate the FSR of a very low finesse cavity formed by PRM and the scattering body.
Therefore we get the the optical distance based on the resultant FSR.

The measurement goes as follows:
1.  Preparation : calibration of the MC2 actuator as a frequency actuator (for more details, see the next section)
2.  Set the interferometer to the single-bounce configuration such that the beam directly is reflected back from PRM
3.  Take spectra of REFL11_I without driving any optics. This spectra tells us how quiet the noise normally is.
4.  Drive MC2_POS at 10 Hz with an amplitude of 10000 counts so that we can see the high frequency up conversion noise
• The frequency was chosen such that the excitation is out of the local damping bands
• The amplitude was chosen to be as big as possible until the MC unlocked
• With this drive, the laser frequency should change by 20 MHz peak-peak at 10 Hz.
5.  Record the noisy spectrum when the MC2_POS was driven.
6.  Drive PRM instead of MC2 at 10 Hz.
• Adjust the amplitude of the excitation such that the cut-off frequency of the up conversion noise matches with that of the MC2 driven case.
• The amplitude was found to be 1700 - 2000 counts, this uncertainty is currently limiting the precision of the optical distance estimation.
• With this amount of the drive, PRM moves by 0.8 um peak-peak at 10Hz.
7. Estimate the optical length based on the amount of the drives for PRM and MC2.
• Estimate the FSR using the following relation df/FSR = dx/ (lambda/2). => FSR = 17 MHz
• Since FSR = c/ (2L),  L = c/(2 FSR) = 9.5 m or so

(Calibration of the MC2 actuator)

To do the measurement described above, the MC2 actuator must be calibrated in terms of a frequency actuator.
I did the same old technique (#4721): lock a cavity, adjust the UGF as low as possible, and shake an actuator of interest.
This time I used the half-PRM (PRM + ITMY) for this measurement.
The actuator responses are calibrated from that of displacement to frequency by using df/f = dx/L and assumed that L = 6.760 (#4585).
Also the PRM actuator was measured such that we can use this as a reference since we already know the response in displacement (#5637).
The attached plot below is the actual responses that I measured yesterday. The y-axis is calibrated to Hz/counts. Quote from #6202 Is PRM making some fringes with some other optics ??

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