Michael and Yuhang
We measured AFG3251 phase noise in elog2745, which shows that it has higher phase noise than DDS (about a factor of 3). Especially, taking the phase noise into account using f = phi*(fsr/2*pi)/2 (wrong) and infrared cavity pole p (transfer function = sqrt(p^2/(p^2+f^2))), we find it gives locking error even larger than what we observe (Fig. 1). The green cavity pole is neglected since it acts at relatively high frequency which almost doesn't contribute to locking error. For the moment, we don't know why it happens.
If the phase noise of AOM driving signal gives any limitation, a less noisy driving signal would provide less locking error. As we know from M. Vardaro thesis, DDS provides signal with less phase noise. Therefore, we measured filter cavity locking error (IR) using DDS and AFG3251 to driving AOM separately. We forgot to calibrate this signal (will be done later), but the comparison of the locking error in these two conditions are as shown in Fig. 2. This indicates AOM driving signal phase noise maybe not a limiting noise source.
The equation used to find relation between frequency and phase should be restricted inside cavity because it comes from the term phi = 2*pi*(f*L)/c. Since we assume the cavity is kept on resonance, we have relation between f and L. So we don't compare the phase of laser inside and outside cavity.
We measured the phase noise introduced by AOM. According to Fourier transform, the frequency noise is phi/f.
Taking phi/f and cavity pole, we get the frequency noise introduced by AOM as Fig.1. We can see AOM introduce negligible frequency noise of only 25 uHz.