Summary 

I have been working on setting up a QPD which can eventually be used to calibrate the PZT, and also orient the PZT in the mount such that the pitch and yaw axes roughly coincide with the vertical and horizontal.

The calibration constants have been determined to be:

X-axis: -3.69 V/mm

Y-axis: -3.70V/mm

Methodology:

I initially tried using the QPD setup left behind by Chloe near MC2, but this turned out to be dysfunctional. On opening out the QPD, I found that the internal circuitry had some issues (shorts in the wrong places etc.) Fortunately, Steve was able to hand me another working unit. For future reference, there are a bunch of old QPDs which I assume are functional in the cabinet marked 'Old PDs' along the Y-arm. 

I then made a circuit with which to read out the X and Y coordinates from the QPD. This consists of 4 buffer amplifiers (one for each quadrant), and 3 summing amplifiers (outputs are A+B+C+D = sum, B+C-A-D = Y-coordinate, and A+B-C-D = X-coordinate) that take the appropriate linear combinations of the 4 quadrants to output a voltage that may be calibrated against displacement of the QPD. 

The output from the QPD is via a sub-D connector on the side of the pomona box enclosing the PD and the circuitry, with 7 pins- 3 for power lines, and 4 for the 4 quadrants of the QPD. It was a little tricky to figure the pin-out for this connector, as there was no way to use continuity checking to map the pins to quadrants. Therefore, I used a laser pointer, and some trial and error (i.e. shine the light on a given quadrant, and check the sign of the X and Y voltages on an oscilloscope) to map the pin outs. Steve tells me that these QPDs were made long before colour code standardisation, but I note here the pin outs in any case for future reference (the quadrant orientations are w.r.t the QPD held with all the circuitry above it, with the active surface facing me):

Red= +Vcc

Black= -Vcc

Green = GND

Blue = Upper Left Quadrant

White = Upper Right Quadrant

Purple = Lower Left Quadrant

Grey = Lower Right Quadrant

Chloe had noted that there was some issue with the voltage regulators on her circuit (overheating) but I suspect this may have been due to the faulty internal circuitry. Also, she had used 12 V regulators. I checked the datasheet of the QPD, Op-Amp LF347 (inside the pomona box) and the OP27s on my circuit, and found that they all had absolute maximum ratings above 18V, so I used 15V voltage regulators. The overheating problem was not a problem anymore.

I then proceeded to arrange a set up for the calibration (initially on the optical bench next to MC2, but now relocated to the SP table, and a cart adjacent to it). It consists of the following:

• He-Ne laser source
• Y2 2-inch mirror (AR and HR coated for 532nm) glued onto the PZT and mounted on a machined Newport U100P  - see this elog for details.
• QPD mounted on a translational stage whose micrometers are calibrated in tenths of an inch (in the plots I have scaled this to mm)
• A neutral density filter (ND = 2.0) which I added so that the QPD amplifier output did not saturate. I considered using a lens as well to reduce the spot size on the QPD but found that after adding the ND filter, it was reasonably small.
• High-voltage power supply (on cart)
• Two SR power supplies (for the PZT driver board and my QPD amplifier
• SR function generator
• Laser power source
• Two oscilloscopes
• Breadboard holding my QPD amplifier circuit

Having set everything up and having done the coarse alignment using the mirror mount, I proceeded to calibrate the X and Y axes of the QPD using the translational stage. The steps I followed were:

• Centre spot on QPD using coarse adjustment on the mirror mount: I gauged this by monitoring the X and Y voltage outputs on an oscilloscope, and adjusted things till both these went to zero.
• Used the tilt knob on the translational stage to roughly decouple the X and Y motion of the QPD.
• Kept Y-coordinate fixed, took the X-coordinate to close to its maximum value (I gauged this by checking where the voltage stopped changing appreciably for changes in the QPD position.
• Using this as a starting point, I moved the QPD through its X range, noting voltage output of the X-coordinate (and also the Y) on an oscilloscope.
• Repeated the procedure for the Y-coordinate.
• Analysis follows largely what was done in these elogs. I am attaching the script I used to fit an error function to the datapoints, this is something MATLAB should seriously include in cftool (note that it is VERY sensitive to the initial guess. I had to do quite a bit of guessing).

The plots are attached, from which the calibration values cited above are deduced. The linear fits for the orthogonal axis were done using cftool. There is some residual coupling between the X and Y motions of the QPD, but I think this os okay my purposes. 

My next step would be to first tweak the orientation of the PZT in the mount while applying a small excitation to it in order to decouple the pitch and yaw motion as best as possible. Once this is done, I can go ahead and calibrate the angular motion of the PZT in mrad/V.

                                                            X-Axis                                                                                                                                Y-axis