Beginning last week, I have been helping Koji with some of the IO work that must be done for the 40m upgrade. The first thing he asked me to do is to help with the alignment of the MC.
As I understand, it became apparent that the IFO beam was not centered on all (or any) of the MC mirrors, which is disadvantageous for obvious reasons. We are trying to correct this, using the following strategy:
 Adjust the MC mirrors into rough alignment, isolate a strong TEM_{00}, and lock the cavity
 Finetune the alignment by minimizing the REFL power when locked (in these first two steps, we adjusted only MC2 & MC3, assuming that the REFL beam was centered on the PD, and wanting to keep it that way). At this point, the cavity is resonating some asymmetric mode, looking something like (not to scalefor illustration only):
 Shake all three mirrors (in succession) in pitch and yaw, each time demodulating the error signal at the frequency used for the excitation and recording the magnitude and phase of the response.
 Move one mirror's DC orientation, repeat step 3, and then restore the mirror to its original position
 Repeat step 4 for both angular degrees of freedom of each mirror
Using the results of these measurements, it is possible to evaluate the components of a blockdiagonal matrix M which relates the tilttodisplacement coupling of each DOF to each mirror's misalignment in that degree, i.e.,
a = M x
with a a 6dimensional vector containing the coupling of each degree of freedom to the length of the cavity and x a 6dimensional vector containing the angular misalignments of each. Due to orthogonality of pitch and yaw, M will take the form of a 6x6 matrix with two nonzero 3x3 blocks along the diagonal and zero matrices on the offdiagonal blocks.
The idea is to isolate components of M by moving one mirror at a time, solve for them, then find the inverse M^{1} that should give us the required angular adjustments to obtain the beamcentered ideal cavity mode.
In theory, this need only be done once; in practice, our measurement error will compound and M will not be accurate enough to get the beams exactly centered, so we will have to iterate.
NOTE: The fact that we are adjusting the three cavity mirrors to obtain the ideal mode means that we will necessarily tarnish our coupling into the cavity. Once we have adjusted the mirrors once, we will need to resteer the input beam and center it on the REFL diode.
Status: This process has been completed once through step 5. I am in the process of trying to construct the matrix for the first adjustment.
