I've done some preliminary modeling to see if there is a good candidate for an IR DARM control signal that is available before the AS55 sign flip. From a DC sweep point of view, ASDC/(TRX+TRY) may be a candidate for further exploration. 

As a reminder, both Finesse and MIST predict a sign flip in the AS55 Q control signal for DARM in the PRFPMI configuration, at a CARM offset of around 118pm.

The CARM offset where this sign flip occurs isn't too far off of where we're currently losing lock, so we have not had the opportunity to switch DARM control off of ALS and over to the quieter IR RF signal of AS55. 

Here are simulated DC DARM sweep plots of our current PRFPMI configuration, with a whole bunch of potential signals that struck me. 

Although the units of most traces are arbitrary in each plot (to fit on the same scale), each plot uses the same arbitrary units (if that makes any sense) so slopes and ratios of values can be read off. 

In the 300 and 120pm plot, you can see that the zero crossing of AS55 is at some considerable DARM offset, and normalizing by TRX doesn't change much about that. "Hold on a second," I hear you say. "Your first plots said that the sign flip happens at around 120pm, so why does the AS55 profile still look bad at 50pm?!" My guess is that, probably due to a combination of Schnupp and arm length asymmetry, CARM offsets move where the peak power is in the DARM coordinate. This picture makes what I mean more clear, perhaps:

Thus, once we're on the other side of the sign flip, I'm confident that we can use AS55 Q without much problem. 

Now, back to thoughts about an interim signal:

ASDC by itself does not really have the kind of behavior we want; but the power out of AS as a fraction of the ARM power (i.e. ASDC/TRX in the plot) seems to have a rational shape, that is not too unlike what the REFLDC CARM profile looks like.

Why not use POPDC or REFLDC? Well, at the CARM offsets we're currently at, POPDC is dominated by the PRC resonating sidebands, and REFLDC has barely begun to decline, and at lower CARM offsets, they each flatten out before the peak of the little ASDC hill, and so don't do much to improve the shape. Meanwhile, ASDC/TRX has a smooth response to points within some fraction of the DARM line width in all of the plots. 

Thus, as was discussed at today's meeting, I feel it may be possible to lock DARM on ASDC/(TRX+TRY) with some offset, until AS55 becomes feasible.

(In practice, I figure we would divide by the sum of the powers, to reduce the influence of the DARM component of just TRX; we don't want to have DARM/DARM in the error signal for DARM)

Two caveats are:

• The slope of this signal actually looks more quadratic than linear. Is this ok/manageable?
• I have not yet made any investigation into the frequency dependent behavior of this thing. Transmission in the denominator will have the CARM pole in it, might get complicated. 

[Code and plots live in /svn/trunk/modeling/PRFPMI_radpressure]