After change the new servo, we tried a lot to make it work well. Now we can get a stable operation by using this new loop. So it's time to characterize our new locking.

The green calibration factor was got in this way:

1.Measure the ratio between the point before servo(Y) and the point after servo(X). Actually the second point is PZT monitor, so we need to multiply PZT monitor by 100 to get X.

2.According the loop flow chart, we can present Y/X by using transfer function of plant and filter. And we know the laser will actuate with 10^6 V/Hz. The SHG gives a factor of 2. We also measured the open-loop transfer function and we call it G. You can refer to attached picture 1, the blue line is Y/PZTmonitor. We can see from the phase, only high frequency has good shape. So we trust only high frequency and we use it for the calculation afterwards.

3.Now we can get the the correction of PZT(in other word, the slope of error signal). The unit of it is V/Hz. The equation to get it is K=(Y/(X*100))*(1+abs(rho(G)*e^(-iphi(G))))*sqrt(1+f^2/f_0^2)/10^6/2

The result is calibration factor(green)=1/K=552 Hz/V.(Here f is frequency, f_0 is the pole of filter cavity)

The infrared calibration factor was got in this way:

1.We give a tri-angular modulation for AOM, it is pk-pk 4000Hz, T 5s. This means 1600Hz/s.

2.We save the error signal of infrared, we calculate the pk-pk of this error signal. Then we divide it by their corresponding time. Let's say the result is slope(V/s). The calibration factor is 2*slope(V/s)/1600(Hz/s)

The result is calibration factor(infrared)=13.33 Hz/V

Finally, we get the error signal.