I modified our existing c1ass model to include alignment of input steering TT1 and TT2 for YARM and BS for XARM. Corresponding medm screens are also created.
ETM_PIT: frequency = 6 Hz, amplitude = 100 cnts
ETM_YAW: 8 Hz, 400 cnts
ITM_PIT: 11 Hz, 800 cnts
ITM_YAW: 14 Hz, 1200 cnts
These values were chosen by looking at cavity transmission and length signals - excitation peaks should be high enough but do not shake the optics too much.
LO for each degree of freedom is mixed with cavity length and transmission signals that are first bandpassed at LO frequency. After mixing low-pass filter is applied. Phase rotation is chosen to minimize Q component
8 * 8 matrix was measured by providing excitation at 0.03 Hz to optics and measuring the response in the demodulated signals. Excitation amplitude was different for each optics to create cavity transmission fluctuations of 25%
Though coherence was > 0.95 during the measurement for each element (except for TT -> Length signals), after inverting and putting it to control servo, loops started to fight each other. So I decided to try a simple diagonal matrix:
TT1_PIT -> ETM_PIT_TRANS, TT1_YAW -> ETM_YAW_TRANS, TT2_PIT -> ITM_PIT_TRANS, TT2_YAW -> ITM_YAW_TRANS,
ITM_PIT -> ETM_PIT_LENGTH, ITM_YAW -> ETM_YAW_LENGTH, ETM_PIT -> ITM_PIT_LENGTH, ETM_YAW -> ITM_YAW_LENGTH
And this matrix worked much better.
8 loops are running at the same time. UGF for input steering loops is 20 mHz, for cavity axis loops - 80 mHz. Slower loop is stronger at low frequencies so that cavity axis servo follows input steering alignment.
When I started experiment the cavity was misaligned, transmission was ~0.4. Servo was able to align the cavity in ~30 seconds. This time depends on mirrors misalignment as well as input optics and cavity axis misalignment relative to each other.
When servo converged I disturbed ETMY, ITMY, TT1 and TT2. Servo was able to compensate for this.
Excitation lines seen by transmission and length of the cavity are suppressed as shown on the attached as pdf figures.
Though the servo is able to align the cavity during my tests, this does not mean it will work perfectly any time. So please, if you lock, try to use the servo for alignment. If something goes wrong we'll fix it. This is better then to align IFO by hands every time.