For the purposes of ASC I diagonalized the ASC pitch and yaw actuation channels using the diagonalized oplev. The procedure yielded coupling ratios below 2% between pitch and yaw with a subtantial reduction of coherenece at low frequencies. The coupling ratios from pitch and yaw to length are  4e-3 µm/µrad and 0.01 µm/µrad respectively. From length to pitch and yaw there was no coherence after the correction.

Notes

• Eventually the wavefront sensor will be used as sensor, however, for this preliminary procedure the oplev was used.
• The ASC actuation may be appplied directly onto the IM or hierarchically  on the IM through the optic; for this diagonalization the direct application is selected, therefore, the switch after the ISC INPUT FILTERS block (in the payload screen in the optic section) was set to 0, which means off.
• The diagonalization matrix was written in the DRIVEALIGN block in the IM section of the medm screen.
• The DRIVEALIGN matrix has blocks for filters for frequency dependent diagonalization, but now I only use the gain field.
• As suggested by entry 11063, making this measurement at DC yields the same result as for frequencies below 100 mHz, therefore, for the sake of speed I'll do it in DC and check the final result measuring in AC and comparing with report 11037.
• As pointed out below, the result using the measurements in DC was good to reduce large amounts of coupling, however, in order to achieve further improvement it's likely necessary to inject a line.
• I applied the actuation using the IM LOCK block in the IM section of the payload medm screen.
• I set the suspension in Guardian ALIGNED state, disabled the oplev DC control loop onto the IM and recovered the alignment by applying actuation offsets using the OPTIC ALIGN block.
• Note that this diagonalization is independent from the IM DoF diagonalization; the DRIVEALIGN matrix is in an independent path from the the SENSALIGN matrix.

Method

1. I applied Lact = 300 counts of actuation in pitch, noted by how much the optic moved in length, pitch and yaw; and calculated the relative displacement with respect to the aligned position without actuation:  ΔL_P = 0 µm, ΔP_P = 79 µrad , ΔY_P= -9 µrad.
2. I removed the actuation in pitch and did a similar calculation by appliyng Yact = 200 counts in yaw, which yielded the parameters: ΔL_Y = -2 µm , ΔP_Y = 1 µrad , ΔY_Y = 84 µrad.
3. An analogous procedure yielded parameters ΔL_L = 4 µm , ΔP_L = - 2 µrad ,  ΔY_L = 57 µrad  when actuating in length with Lact = 15,000 counts. (I had to use a large amount of counts because we're using a LPCD for IM-H DoF.)
4. I calculated the transfer functions in DC for each DoF in units of µm/cnt for length per unit of actuation and µrad/cnt for pitch and yaw per unit of actuation, respectively:
   • ResL_L =  ΔL_L / Lact, ResP_L = ΔP_L / Lact, ResY_L = ΔY_L / Lact
   • ResL_P = ΔL_P / Pact, ResP_P = ΔP_P / Pact, ResY_L = ΔY_P / Pact
   • ResY_Y = ΔL_Y / Yact, ResP_Y = ΔP_Y / Yact, ResY_L = ΔY_Y / Yact
5. The elements of the DRIVEALIGN block are, therefore,
   • L2P = - ResP_L / ResP_P , L2Y = - ResY_L / ResY_Y,
   • P2L = - ResL_P / ResL_L , P2Y = - ResY_P / ResY_Y,
   • Y2L = - ResL_Y / ResL_L , Y2P = - ResP_Y / ResP_P.

Although careful examination of the ratios displayed in item 5 should reveal their physical meaning, for the sake of clarity let's explain one of them. For example, for the P2Y parameter, for a given amount of actuation pitch (in counts), the numerator calculates how much the optic moves in yaw (in µrad) and the denominator calculates how much actuation is needed in the yaw channel (in counts) order to compensate for it.

Results

Before correction

After correction

• The coherence at low frequencies reduced subtantially after the correction was implemented, thefore the values below are just a rough approximation.
• In order to achieve further improvement it might be necessary to inject a line at a frequency of interest, at 100 mHz for example.

Files and directories

Directory:

/kagra/Dropbox/Subsystems/VIS/TypeBData/BS/TF/Measurements/20191018/

Matlab file:

diagonalization_IM_DRIVEALIGN_at_DC.m

Directory:

/kagra/Dropbox/Subsystems/VIS/TypeBData/BS/TF/Measurements/20191023/

Files:

ASC_L_EXC_PAYLOAD_20191023.xml

ASC_P_EXC_PAYLOAD_20191023_lower_actuation.xml

ASC_Y_EXC_PAYLOAD_20191023.xml

Reference: entry 11037.