In order to decide what frequencies to dither the 4 degrees of freedom (M1-pitch&yaw, M2-pitch&yaw) at, I took the power spectrum of the X and Y-arm green transmission (C1:ALS-TRX_OUT, C1:ALS-TRY_OUT). Plots showing the power spectra are attached. Looking at the power spectra, I would think that for the X-arm, it would be okay to dither at 40, 50, 60 and 70 Hz. In order to check if the piezos could respond to these frequencies, I used my QPD setup and shook the PZTs with a 100Hz, 1Vpp sinusoid, and saw that the spot moved smoothly on the QPD.

 As for choosing the modulation amplitude, I did a simplistic approximation assuming that the misalignment only rotates the beam axis relative to the cavity axis, and determined what angle coupled 10% of the power into the next eigenmode. Assuming that this is small enough such that if we are already locked to TEM00, the dither won't kick it up to some higher-order mode, the LO amplitude should be in the range of 30-60 digital counts (determined using the PZT calibration constants determined here. This corresponds to a sine-wave of ~50mV amplitude reaching the PZTs (after HV amplification). I am not sure if this is too small, but according to the PZT datasheet, these platforms are supposed to have a resolution of 0.02 urad, which would correspond to the input signal changing by ~0.1 mV, so this signal should be capable of dithering the tip-tilt. 

 I have already added band-pass filters centered at these frequencies to the model (with a passband of 5Hz, 2Hz on either side), and low-pass filters to pull out the DC component of the output of the lock-in amplifiers. It remains to tune the gains of the filter stages. These parameters (frequency, amplitude of the LOs) may also have to be changed after tests). Hopefully the PZTs can be plugged in tomorrow, and I can try and make a measurement of the output matrix. 

Koji also suggested that it may be good to have a path in the model that feeds back to the PZTs by dithering the cavity mirrors as opposed to the PZT mounted mirrors. I will work on incorporating this into the SIMULINK model (c1asx.mdl) and also into the master medm screen.

Notes:

1. The spot size of the X-arm green transmission on the PD was larger than the active surface. I moved the GTRX PD a little back and put in a lens (KPX085, 62.9mm FL, AR.14) in front of the PD, such that the spot is now occupying about 1/4th of the active surface area. The lens was mounted in a Thorlabs LMR1mount, and has been labelled.
2. I made a slight change to the SIMULINK model, so as to calibrate the PZT sliders to (approximately) volts (I added a multiplier block that multiplies the slider value by constant value 3267.8). The idea is that we can approximately relate the slider value to tilt, knowing the calibration constant in mrad/V for the PZTs.

Power Spectra of Arm Green Transmission: