Attachment 1 shows the case when excitation is sent at control point i.e. the PZT output. As before, free running laser noise in units of Hz/rtHz is added after the actuator and I've also shown shot noise being added just before the detector.
Again, we have a access to three output points for measurement. right at the output of mixer (the PDH error signal), the feedback signal to be applied by uPDH box (PZT Mon) and the output of the summing box SR560.
Doing loop algebra as before, we get:
So measurement of can be done by
- For frequencies, where is large enough, to have an SNR of 100, we need that ratio of to integrated noise is 100.
**Assuming you are averaging for 'm' number of cycles in your swept sine measurement**, time of integration for the noise signal would be where f is the frequency point of the seeping sine wave.
- This means, the amplitude of integrated laser frequency noise at either or would be
- Therefore, signal to laser free running noise ratio at f would be .
- This means to keep a constant SNR of S, we need to shape the excitation amplitude as
- Putting in numbers for X end Green PDH loop, laser free-running frequency noise ASD is 1e4/f Hz/rtHz, laser PZT actuation is 1MHz/V, then for 10 integration cycles and SNR of 100, we get:
**Assuming you are averaging for a constant time in swept sine measurement, then** the amplitude of integrated laser free noise would be
- In this case, signal to laser free-running noise ratio at f would be
- This means to keep a constant SNR of S, we need to shape the excitation amplitude as
- Again putting in numbers as above and integration time of 1s, we need an excitation amplitude shape
This means at 100 Hz, with 10 integration cycles, we should have needed only 3 mV of excitation signal to get an SNR of 100. However, we have been unable to get good measurements with even 25 mV of excitation. We tried increasing the cycles, that did not work either.
This post is to summarize this analysis. We need more tests to get any conclusions. |