A crucial aspect of any lock acquisition procedure is the bootstrapping process, whereby one can start from a state with no knowledge of the interferometer, and via a predetermined sequence of steps, can measure or deduce the settings necessary to acquire lock. These settings include such things as DC optical alignment, control loop gains, and control loop triggering thresholds.
In order to lock a suspended interferometer with multiple length DOFs, hundreds of parameters must be determined. It is highly advantageous to be able to determine these settings in a man- ner which is automated and which does not have any cyclical dependencies, where more than one parameter must be deduced simultaneously.
In this section, we begin the discussion after some of the simpler bootstrapping has been done–this includes roughly aligning the mirrors, setting the demodulation phases (for the single demodulation signals), and determining the feedback filters and gains necessary for locking the subinterferometers (single arm cavity, Michelson, PRMI, DRMI).
8.5.1 Interferometer subsets
Bootstrapping depends upon using subsets of the interferometer which are simpler to understand and control. Subsets are created by temporarily grossly misaligning the optics not involved in the
subset. These subsets, along with simple length and alignment error signals, are in table8.1. These are the signals used during the bootstrapping.
8.5.2 Alignment
The first stage is optimizing the interferometer alignment, which is done following the order shown in figure8.2. Each stage has the minimum number of elements which much be varied to reach an optimum, the order is chosen such that there are no cyclical dependencies, and each stage is simple enough to be simply debugged. No stage has more than three DOFs which must be locked, nor more than one high finesse DOF; this is meaningful, as experience has shown that acquisition time increases dramatically as one goes from three DOFs to four DOFs or when combining independent, high finesse DOFs.
The alignment signals are all (by choice) quadratic in the alignment degree of freedom—they are at a minimum (or maximum) for optimal alignment. The best alignment is thus obtained through dithering an optic in angle at a low frequency (several Hz) and coherently demodulating the alignment signal; this then yields an error signal that is linear in the alignment, and goes through zero at the alignment optimum.
First the transmitted (XARM) arm is aligned; this establishes the input steering alignment and the alignment of ITMX and ETMX. Next is the YARM. This establishes the BS, the ITMY, and the ETMY. Following that is MICH, which can be used for a finer BS alignment, but also is used by locking MICH to bright fringe (instead of the usual dark fringe) to align the steering into the output mode cleaner. This then establishes the output alignment. Next is the PRMI, which uses a SPOB signal to establish alignment of the PRM, followed by the DRMI, which REFL 166Q to establish the alignment of the SRM. Recall that the Q-phase signal in reflection is proportional to the sideband imbalance; since only the +f2sideband resonates in the SRC, this is a reasonable alignment signal.
IFO DOFs Length Alignment
Single Arm XARM POX 33I TRX
YARM POY 33I TRY
MICH MICH AS 166Q AS DC
PRMI MICH REFL 33I
PRC REFL 33I SPOB
DRMI
MICH REFL 33Q
PRC REFL 331
SRC REFL 166I REFL 166Q
Table 8.1: Length and alignment error signals for bootstrapping. The length error signals are linear in the degree of freedom, while the alignment signals are quadratic. The best alignment is thus obtained through dithering at a low frequency (several Hz) and minimizing the spectral content of the alignment signal at that frequency.
OMC OMC
OMC OMC
IFO PZTs ETMX
ITMX
BS ETMY
ITMY
OMC PZTs PRM SRM
TRX TRX TRX QPD
TRY TRY TRY QPD
OMCT SPOB REFL2 Q
Alignment Actuator
Alignment Signal Length DOF (error signal) XARM
(POX I)
YARM
(POY I) MICH
(AS1 Q)
PRC (REFL1 I)
SRC (REFL2 I)
LASER LASER
OMC
LASER LASER LASER
Figure 8.2: Signals and DOFs for bootstrapping the interferometer alignment prior to lock acquisition.
8.5.3 Double Demodulation signals
Once the DRMI optics have been aligned, it can be locked again using the initial acquisition signals (table8.1). This permits the tuning of the double demodulation signals, which can only be done in a DRMI state. While the DRMI is locked using the initial signals, the DDM signal demodulation phases are adjusted to provide zero offset (in the error signal). Note that this isnot actually the precise demodulation phase where the actual length offset will be zero (cf. section 6.3.3), because the single demodulation signals in table8.2alsohave offsets resulting from the detuned signal cavity (and RF sideband imbalance) at this point. There is no known way to get around this problem.
After the demodulation phases are set, the length degrees of freedom MICH, PRCL, and SRCL are successively excited at a frequency where the loop gains are low (∼3×UGF) and the DDM signals are coherently demodulated. This yields a subset of the sensing matrixMat the excitation frequency. This matrix subset can then be inverted and used as the input matrix for these degrees of freedom (cf. section6.3.5).
DOF Initial Signal Final Signal
MICH REFL 33Q
DDM signal
PRC REFL 33I → matrix
SRC REFL 166I
Table 8.2: Hand off of short DOFs. The DDM signal matrix mixes the signals from REFL IM, REFL IP, PO IM, PO IP, AS QM, and AS QP.