After checking around, I just found out that the changing noise level of ACAV's RFPD caused by the loosen connector for power supply
I remeasured the noise from both RFPDs for RCAV and ACAV again. By blocking the beam and measuring the signal from V_RF out.
Power supply connector for ACAV's RFPD was a bit loose which causes the RFPD to not fully work . It gave out DC signal, but not for V_RF.
(That's why I didn't notice it. when I centered the beam on the RFPD, I checked that V_DC was maximum, so I thought there's nothing wrong with the power supply)
As Rana suggested, I checked V_RF in time domain signal before re-measuring the noise and saw that it's offset by 1.5 V, which is too high
(RCAV's RFPD offset is ~ 7 mV,)
so I suspected that something's going on with the power supply. It was loosen a bit, so I fixed it.
Now the noise from both PD look reasonable. They reflect the shape of their TF,see this entry. The offset is back to ~5 mV which is comparable to that of RCAV's RFPD.
The RFPD noise is quite low, so I used an amplifier to boost the signal, it amplifies by a factor of 30, see previous entry.
4395A's noise floor should be ~ 7nV/ rtHz flat, I chose the wrong span when I saved the data, so it's cover only small BW
The noise from the amp is lower than the amplified RFPD noise.
Divide the measured RFPD noise with 30 to get the real signal, which is about 10 nV /rt Hz for both RFPDs
The noise will be compared with LISO models to see if RFPD working correctly.
We also need to check if the RFPD is shot noise limited or not for the setup.
The noise from V_RF can be converted to PD current noise i_n ( = V_RF/ impedance) generated at the PD.
i_n will be compared with the current originated from shot noise of the incoming light,
i_shot = sqrt( 2e i_dc ), where i_dc is the current generated by the averaged power input.
To get i_dc, I thought I can measure the laser power on the PD, and V_DC. i_DC = V_DC/R / gain in the RFPD,
where R is the corresponding impedance for V_DC. Thus, I can related power input, Pin, to i_dc.
So I measure V_DC and Pin for both RFPD to get the calibration factors which are,
cal factor for RCAV's RFPD = 160 V/ W
for ACAV's RFPD = 179 V/W
Koji suggested a way to measure the shot noise limit level of the PD, I'll try that.
So the reason I could not lock RCAV loop with ACAV's RFPD yesterday might be from the loosen connector. Before I try that, I'll find the correct projection factor for
error signal to frequency noise first.