I have a preliminary calculation to post here. This does not include noise sources from cavity fluctuations and main frequency noise. But it gives some idea about shot noise and frequency noise of AUX laser conttribution to the noise in calibration.

What's included?

• I have put in measured PZT transfer function of ECDL at ANU upto 25 kHz. Above this point, they did not measure it so I couldn't make it artificially dirty. I just assumed 1/f roll off above (which is definitely incomplete picture).
• I have included phase effects of cavity FSR in the loop by adding the resonance features as mentioned here.
• I have added attempted resonance compensation for 1kHz and 2kHz features in the PZT after fitting the data with poles and zeros and iverting them.
• 10mW of incident AUX light is assumed on the arm cavity.
• Total 10 mW of combined power at 709 nm is assumed to fall on the beatnote. So AUX light would be frequency doubled for this beatnote.

What's left?

• Need to add seismic noise and other measured excess noise that come from the cavity motion.
• Need to add laser frequency noise of main laser, however, it must be small since it is locked to mode cleaner.
• Need to add digital delay of Red Pitaya or whatever filter would be used for PZT resonance compensation.
• Need to model PZT transfer function of ECDL above kHz properly. ANU replied that they can't measure it for higher frequencies due to lack of time.
• Need to do time domain stability analysis. This I haven't been able to do as I have just been using python-controls package as black box to compute impulse and step responses of state space systems. When simply adding easured transfer function data, I couldn't create the state stpace representation for the system. I tried to fit multiple resonances above 2 kHz but couldn't really capture the magnitude of the response well. Maybe I can just assume higher harmonics of the 1kHz and 2kHz resonances?

Attachments:

• Page 1 is the measured PZT transfer function fo 1900 nm ECDL from ANU along with the modeled 1/f roll off after 25 kHz.
• Page 2 is the open loop transfer function of the AUX PDH loop for the three different finesse cases studies. Note that the blue curve is hidden beneate the other two curves. Before objections came, I know this is unreal and incomplete, but I have to start somewhere.
• Page 3 is the calibration noise budget with different colors showing the three finesse cases.
  • This is also incomplete but we can takeaway what the shot noise contribution would look like and initiate a dialogue about the integration time chosen (which is 100s here), the SNR aim chosen (1000 here) and what drive strength would be good enough.
  • From notes of Craig and Gautum, I think we can drive the mirrors at 0.1pm ampltude in the calibration band. From my first and only calibration measurement in 40m, I could drive upto a pm without loosing lock in the cavities.
  • But that was a simple single arm lock and full ifo lock must be more sensitive. So is 0.1 pm drive strength good enough or do we want to aim lower?