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 Fri Nov 14 19:20:42 2008, Yoichi, Update, PSL, Reference cavity ring down 
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 Fri Nov 14 20:35:47 2008, rana, Update, PSL, Reference cavity ring down
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Fri Nov 14 22:40:51 2008, Yoichi, Update, PSL, Reference cavity ring down
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Mon Nov 17 15:07:06 2008, Yoichi, Update, PSL, Reference cavity ring down
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Message ID: 1140
Entry time: Mon Nov 17 15:07:06 2008
In reply to: 1138
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| Author: |
Yoichi |
| Type: |
Update |
| Category: |
PSL |
| Subject: |
Reference cavity ring down |
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I used MATLAB's system identification tool box to estimate the response of the reference cavity, i.e. cavity pole.
What I did was basically to estimate a model of the RC using the time series of the measured input and output power.
First, I prepared the input and output time series for model estimation.
The input is the input power to the RC, which I produced by inverting the PBS reflected light power and adding an offset
so that the signal is zero at t=0. Offset removal was necessary to make sure that the input time series does not give an
unintentional step at t=0.
The output time series is the transmission power of the RC. I also added an offset to make it zero at t=0.
Then I commanded MATLAB to compute the response of a first order low-pass filter to the input and try to fit
the computed response to the measured output by iteratively changing the gain and the cut-off frequency.
("pem" is the name of the command to use if you are interested in).
The result is shown in the attachment.
Blue curve is the input signal (I added a vertical offset to show it separately from the output).
The green curve is the measured output (RC transmission). The red curve is the response of the estimated model.
The estimated cut-off frequency was about 45kHz.
You can see that the red curve deviates a lot from the green curve after t=15usec.
By looking at this, I realized that the bandwidth of the RC cavity servo was too high.
The time scale we are looking at is about 50kHz whereas the FSS bandwidth is about 400kHz.
So when the input light was cut off, the error signal of the FSS becomes meaning less and the
input laser frequency was quickly moved away from the resonance. This is why the green curve does not
respond to the large peaks in the blue curve (input). The cavity was already off-resonance when the input power
showed bumps.
Since the red curve matches nicely with the green curve at the very beginning of the ring down, the estimated 45kHz
cavity pole is probably not that a bad estimate.
To make a better measurement, I will try to reduce the bandwidth of the RC servo by using only the PZT actuator.
If there were no ringing in the input light power, we wouldn't have to worry about the bandwidth of the servo because our
feedback is all made to the laser, not the cavity length.
In order to reduce the ringing in the input power, I asked Bob to make new HV cables using HV grade coax cables. |
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