We resume the LO phase locking work. MICH was locked with an offset of 80 cts. LO and AS beams were aligned to maximize the BHD readout visibility on ndscope.

We lock the LO phase on a fringe (DC locking) actuating on LO1.

Attachment 1 shows BHD readout (DCPD_A_ERR = DCPD_A - DCPD_B) spectrum with and without fringe locking while LO2 line at 318 Hz is on. It can be seen that without the fringe locking the dithering line is buried in the A-B noise floor. This is probably due to multiple fringing upconversion. We figured that trying to directly dither-lock the LO phase might be too tricky since we cannot resolve the dither line when the LO phase is unlocked.

We try to handoff the lock from the fringe lock to the AC lock in the following way: Since the AC error signal reads the derivative of the BHD readout it is the least sensitive to the LO phase when the LO phase is locked on a dark fringe, therefore we offset the LO to realize an AC error signal. LO phase offset is set to ~ 40 cts (peak-to-peak counts when LO phase is uncontrolled is ~ 400 cts).

We look at the "demodulated" signal of LO1 from which the fringe locking error signal is derived (0 Hz frequency modulation 0  amplitude) and the demodulated signal of LO2 where a ~ 700 Hz line is applied. We dither the LO phase at ~ 50Hz to create a clear signal in order to compare the two error signals. Although the 50 Hz signal was clearly seen on the fringe lock error signal it was completely unresolved in the LO2 demodulated signal no matter how hard we drove the 700Hz line and no matter what demodulation phase we chose. Interestingly, changing the demodulation phase shifted the noisy LO2 demodulated signal by some constant. Will post a picture later.

Could there be some problem with the modulation-demodulation model? We should check again but I'm almost certain we saw the 700Hz line with an SNR of ~ 100 in diaggui, even with the small LO offset changes in the 700Hz signal phase should have been clearly seen in the demodulated signal. Maybe we should also check that we see the 50Hz side-bands around the 700Hz line on diaggui to be sure.