Jeff K. Thomas V.

We have found a non-linear relationship between the way the translation stage moves and the way we were reading out the measurements.  We need to double check the calculations as well as the methodology on retrieving data.  This latter is difficult because even though there is a micrometer on the translation stage it is covered by the laser enclosures, which if we take off, it will introduce ambient light onto the QPD.  We are currently investigating solutions.

T. Vo, J. Kissel

Pulling out a spare translation stage and measuring the displacement response (in [mm]) to controller demands (in [ct]), we found the following attached relation. Immediately turned off by the non-linearity seen, from our experience with the controlers jolting the translation stage upon power on/off, and from Kissel's recollection of the controllers in i/eLIGO (of which these controls are the same), we've launched into a more sophisticated characterization of the controllers. Given that the non-linearity is roughly 1 [um] over the 1 [mm] range measured, we might be barking up the wrong tree and just be over-reacting, but it should be a quick round of measurements to assess it in more detail.

It should also be noted that the controller can demand from 0 to ~8600 [ct], and we've thus far only exercised it from 0 to 150, since we only need ~1 [mm] range given the size of the Oplev QPD.

T. Vo, J. Kissel

Here're the results from the more detailed characterization. It looks like, within a small range of operation the controller is indeed linear to the desired level. However, over the full range of the controller, there's certainly some non-linearities present.


Notes:
Linear UP -- commanding the stage to move from 0 (4000) up to 150 (4150), in linear 10 [ct] increments.
Linear DOWN -- commanding the stage to move from 0 (4000) up to 150 (4150), in linear 10 [ct] increments.
Random -- going to each data point in a random order

Each of these should yield the same answer if it's a truly linear system.

Jeff Kissel Thomas Vo

After reviewing the linearity of the translation stage as shown in ALOG 3737, we found that the non-linear regime of the translation stage resides near the end of the rails of the stage but the approximate middle yielded linear results.  We're confident that the increments that we used to translate the stage during calibration for both test masses were small enough and far enough away from the edges so that the non-linearity would have a small affect on our results, this will require further testing to truly be valid (in progress).  That being said, after correcting some errors in the calculations and double checking our numbers, we used the original data to apply to the calibration.  

A noteworthy point: Jeff Kissel used the edrawing from the solidworks model in,

LHO Corner Station: D0901469-v5 
LHO EY Station: D0901467-v6 

to find a more accurate number for the lever arms than previously used, ITMY = 56.4m and ETMY = 6.6m, as opposed to 70m and 6m respectively.  This was taken into account for our last calculation.

Onto the good stuff, the values of the slopes below are in micro-radians*meters:

ITMY
        Slope         Y-Intercept
Pitch [ 25.93274501  -0.51461109]
Yaw   [ 30.81584154  -0.5957635 ]



ETMY
        Slope         Y-Intercept
Pitch [ 54.53112025  -1.01505634]
Yaw   [ 56.56393367   0.79879263]


Attached are the graphs of the linear response curves, the python fitting scripts and the EXCEL spreadsheets to help visualize the underlying calibration calculations. In particular, the excel spreadsheets shows the conversion from controller units into millimeters and then into meters and micro-radians.  Hope this is the last time we'll need to repeat this post, sorry for the troubles!