Tara and I performed additional measurements of the transfer function for the coupling between power fluctuations and frequency.

Setup:

This time we altered the setup and instead of attenuating the signal input to the ACAV servo, we added an optical attenuator before the pd. We attenuated before the pd this time because of the possibility of pd saturation in the previous setup. The setup we used today was:

Measurement and Data Analysis:

Consistent with the last measurements, the response function for the transfer function was the AOM Feedback and the reference function was the ACAV power fluctuations. We used the sine swept measurement group in the SR785 to get the data. We checked the TF by changing the power from 2.2mW to .22mW, and the data remained the same. 

We calibrated the raw data from dB to the units of Hz/RIN using the following relationship:

TF [Hz/RIN] = 10^(TF[dB]/20) *710[Hz/V] * 3.6[V] *2

where the factor of 2 accounts for the double passed AOM, the factor of 710 is the calibration for the Marconi, and the 3.6 is the DC level.

The results for the TF are plotted below:

For the magnitude, the data taken at different frequency intervals overlapped perfectly. For the phase, the data did not overlap perfectly, so the data was concatenated with a slight jump at 100Hz.

Application to Noise Budget: 

 Using the previously measured RIN, I estimated the frequency noise with the transfer function just measured. First I fit the transfer function as shown below:

Next I applied the following relationship to obtain the estimated frequency noise, and plotted it with the noise budget:

Frequency Noise: RIN * 3.6 [V] * 2 * 710 [Hz/V] * 10^(TF[dB]/20)

Compared to the RIN induced frequency noise with the previously measured TF (refer to elog entry attached to this one), the noise is lower at higher frequencies, drops off with a slightly steeper slope in the center, and slightly higher at lower frequencies (this could be due to error in fit though). Note that this RIN induced noise is only an estimate, and the calculation may be slightly incorrect due to the fact that the DC level was slightly different (by ~ a factor of 2) for the measurement of the intensity noise (previous elog) and the current transfer function measurement.

Comparing the calculated TF from elog 989 (using RIN from previous setup), the following plot is obtained:

Thus, the transfer function still does not match the calculated curve perfectly, but its a better match shapewise than the previous TF. Additionally, there still might be an error in the calculated curve.

Conclusion:

 The TF looks considerably better than before, perhaps because we optimized the phase for the EAOM two days ago, so we are driving the amplitude with more modulation.

== Note on the measurement ==

•       RCAV is locked with 100 uW input power, Common/Fast gains on the TTFSS are 950/750. The reason to use low power is that we want to make sure that the effect due to power modulation will not be common in both paths. However, we need enough power so that RCAV loop gain is still high enough so that the frequency noise in the laser is suppressed and does not cover the RIN induced noise in ACAV loop.
•       ACAV input power is 2.2 mW. To avoid having too much gain and unstable loop, we use an ND filter to reduce the power on RFPD down to the level it usually is at 1mW power (~200mV).
•       To check if the TF is real or not, we tried to lower the power down to 0.2 mW and see no change in the measured TF. This is good, since the TF should be independent of the power input.
•       The DC level from PDA100A @gain 20 is 3.6 V (the reference signal of our TF measurement). The modulation is 380mV pk-pk in sine wave form, so the TRANSPD_DC is ~ 3.6 +/- 0.19 V. We make sure that the PD is not saturated.
•  ***** The measurement is made possible because the drift is very small. For the past 5 Hrs, it has been less than 1kHz in 5 minutes. **