First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment Sean Leavey and the AEI 10m Prototype Team Albert Einstein Institute Hanover Germany 26th March 2014
The AEI 10m Prototype Test bed for sub-SQL experiments Michelson interferometer with Fabry-Perot arm cavities Suspended mirrors on isolated tables Nearly-unstable Fabry-Perot cavities Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 2 / 28
The Single Arm Test Single Arm Test 1.00 Arm Cavity g-factor South arm of the interferometer 0.95 commissioned as a test 0.90 Opportunity to learn about control of cavities close to 0.85 instability ( g 1 g 2 = 1) Iterative process of moving 0.80 cavity length closer and closer 0.016 to 11 . 395 m 0.014 Spot Size [m] 0.012 Advanced LIGO will have 0.010 g-factor of 0 . 832 and Advanced 0.008 Virgo will have 0 . 871 0.006 The single arm test will reach 0.004 g-factors of 0 . 998 0.002 0.000 10.8 10.9 11.0 11.1 11.2 11.3 11.4 Arm Cavity Length [m] Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 3 / 28
Alignment Sensing and Control Split Photodiode 1.0 Amplitude [arb units] The Single Arm Test mirrors 0.8 need to be aligned 0.6 Misalignments to cavity mirrors 0.4 can be sensed with quadrant 0.2 photodiodes 0.0 A misaligned cavity mirror will 0.2 1.0 0.5 0.0 0.5 1.0 Surface Position [arb units] couple light from the 0th order into the 1st order cavity mode, proportionally to the Split Photodiode 1.0 misalignment (for small Power [arb units] 0.8 angles) 0.6 A suitable QPD can detect the 0.4 amount of 1st order light indirectly through summing and 0.2 subtraction of quadrants 0.0 1.0 0.5 0.0 0.5 1.0 Surface Position [arb units] Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 4 / 28
Alignment Sensing and Control ITM For stable cavities, mirrors are separated in gouy space ETM RF photodiodes can be ‘tuned’ to listen to a certain gouy phase associated with certain mirrors We want a matrix that is as diagonal as possible, simplifying correctional actuation Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 5 / 28
Alignment Sensing and Control PD 1 PD 2 ITM One approach is to align each photodiode 90 ◦ from each mirror in ETM gouy space This would provide alignment signals that are completely orthogonal However, PDs would need to be realigned for each cavity length Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 6 / 28
Alignment Sensing and Control PD 2 PD 1 ITM Another approach is to use orthogonal (in gouy space) ETM photodiodes PD 1’s signal is ‘tuned’ to the ITM’s gouy phase, seeing all of ITM, plus a small amount of ETM PD 2’s signal contains none of ITM but most of ETM Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 7 / 28
Alignment Sensing and Control The sensing matrix for this configuration might then look like: � a ITM , 1 � � 1 . 0 � a ITM , 2 0 . 0 = a ETM , 1 a ETM , 2 0 . 1 0 . 9 where a i , j is the component of rotation in the ITM or ETM on PD 1 and PD 2. We only see the total in each column on our photodiodes, the vectors a 1 and a 2 . We want a ITM and a ETM , and it’s still possible to obtain them with elementary row operations. Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 8 / 28
Sensing and Control Close to Instability ETM ITM What happens close to instability? As the cavity length becomes longer (i.e. as g 1 g 2 → 1), the mirrors’ gouy phases become more degenerate Cavity alignment becomes harder to control Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 9 / 28
Sensing and Control Close to Instability Why does it become harder to control? PD 1 contains a lot more of the ETM signal, and PD 2 contains a lot less of the ETM signal PD 2 ETM PD 1 ITM Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 10 / 28
Sensing and Control Close to Instability Why does it become harder to control? Even though the amount of 1st order mode and 0th order mode on the photodiodes changes, the total light power stays reasonably constant and so the signal to noise level on PD 2 decreases . The diagonalisation process of the control matrix then contains more noise for longer cavity lengths. For a cavity close enough to instability, the signal to noise level will be low enough that the readout noise becomes an issue . At this point the cavity will potentially be ‘uncontrollable’. It’s important, therefore, to know the signal degeneracy towards cavity instability so a proper noise budget can be calculated. Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 11 / 28
Simulations of the Single Arm Test Layout A FINESSE model was developed using the parameters of the mirrors already purchased for the Single Arm Test. Two split photodiodes were positioned behind the ITM to look at light reflected from the cavity In FINESSE it is possible to set arbitrary gouy phases for spaces in the model A B C D E Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 12 / 28
Simulations of the Single Arm Test Tuning of Gouy Phases Setting gouy phases D = 0 ◦ and E = 90 ◦ forces the photodiodes to be orthogonal Rotating the ETM and ITM in separate steps lets us look at the effect on the two photodiodes from each mirror Varying C ’s gouy phase lets us align one photodiode to maximise the signal it sees of one mirror’s rotation A B C D E Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 13 / 28
Simulations of the Single Arm Test Varying the Cavity Length Changing the cavity length over multiple steps lets us look at how the signals degrade towards instability A B C D E Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 14 / 28
Simulations of the Single Arm Test ETM Rotation PD1 ETM Rotation PD2 0.010 0.005 0.000 0.005 0.010 xbeta [rad] (M_ETM_HR) xbeta [rad] (M_ETM_HR) ITM Rotation PD1 ITM Rotation PD2 0.010 0.005 0.000 0.005 0.010 -1e-06 -5e-07 0e+00 5e-07 1e-06 -1e-06 -5e-07 0e+00 5e-07 1e-06 xbeta [rad] (M_ITM_HR) xbeta [rad] (M_ITM_HR) Control Matrix For each cavity length and common gouy phase, we want to see four split photodiode signals crossing zero Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 15 / 28
Simulations of the Single Arm Test The Brute Force Approach For the kind of granularity we desire, this involves two simulations per gouy phase per cavity length at C . If we want gouy phase ‘resolution’ of 1 ◦ , that means 180 × 2 = 360 simulations per cavity length (ignoring smarter processes like Jacobian optimisations). For, say, ten cavity lengths, and with each simulation taking of order 4 s to complete, that’s a lot of simulations to perform and store, and a long time. A B C D E Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 16 / 28
Simulations of the Single Arm Test Iteration To perform these simulations, we have two options: SimTools - a MATLAB library for FINESSE PyKat - the new kid on the block SimTools SimTools runs in MATLAB, so any PyKat results produced can be stored in a PyKat recreates the FINESSE MATLAB matrix or similar. environment as Python objects, However, there is no direct access to which can be manipulated directly in FINESSE object attributes in Python. This is what I used! SimTools, and instead it performs string substitution. Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 17 / 28
Simulations of the Single Arm Test Storing the Results Would be better to store the results in a file PyTables is a hierarchical dataset manager similar to ROOT used by particle physicists It stores data in rows in a single file, and this file can be queried for specific sets, e.g. all rows with gouy phase 48 ◦ Prevents simulations being performed twice if the results already exist Future Analyses All data produced by FINESSE/PyKat is stored in PyTables This separates the simulations from the analyses It is possible to run a different analysis on the data by making a new Python script This will hopefully be useful later on when more parameters are known or constrained Sean Leavey (Albert Einstein Institute) First Steps Towards the AEI 10m Prototype Single Arm Test Auto Alignment 26th March 2014 18 / 28
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