Tara and I measured the transfer function coupling RIN to Frequency noise over a wider range of power levels. 

Setup and Measurements:

RCAV power was set to.3mW. We varied ACAV power, and added the rf amplifier mentioned in Elog 1022  after the rfpd to compensate for low power levels. We measured the visibility of the cavity to be 72%, and including this number should slightly  improve the accuracy of the input power level used in calculations. The TF was measured at the following power levels: 2.7mW, .84mW, .32mW, and the results plotted with the TFs measured last week at: 1.6mW, 1.4mW, 1.3mW, 1.2mW, 1.0mW. It should be noted that the visibility was not measured during data collection for the TFs measured last week, so in scaling the power I assumed a visibility of 72%. This may not be perfectly accurate, however as of now it only affects the labeling of the power, since the creation of the following plots does not depend on input power. The upper power limit for measurement was set by the saturation of the photodiode, which we found out saturates at about 10.2V. While inserting a filter after the photodiode would allow us to measure at higher powers, it would also mean we would need to recalibrate, so we just measured up to the saturation of the photodiode for these measurements. 

Data and Results:

The following plot shows the raw data collected for all eight TFs, in dB and degrees:

The transfer functions appear quite consistent and thus don't seem to depend on the power level. We expected to see more of a common mode effect for the measurements where ACAV power was comparable to RCAV's .3mW power. This effect is apparently absent, and we plan to do further measurements to investigate it further. We also measured the coherence between the AOM feedback signal and intensity noise, as well as frequency responses for the three recently measured transfer functions, as shown below:

A white noise excitation was used for the frequency response and coherence measurements. The coherence was measured to be essentially zero without excitation. It is possible there was an error in measurement for the .32mW measurements, as the frequency response does not seem to follow the appropriate trend, which should be consistent with the magnitude of the transfer function. 

I converted the 2.7mW transfer function magnitude to units of Hz/Watt and plotted it against the calculations using Cerdonio's and Farsi's results:

The voltage to power calibration factor is still a main source of error in this conversion.