Aim: To find the combinations of mounting prism+PZT+curved mirror to build two PZT sub-assemblies that best minimises the total vertical beam deviation.
(In short, attachment 1 shows the two chosen sets of components and the configuration according which they must be bonded to minimize the total vertical angular deviation.)
The specfic components and configuration were chosen as follows, closely following Section 2.3.3 of T1500060:
Available components:
Mounting prisms: 1,2,12,14,15 (Even though there is mention of M17 in the attachments, it can not be used because it was chipped earlier.)
PZTs: 12,13
Curved mirrors: 10,13
Method:
For a given choice of prism, PZT and mirror, the PZT can be placed either at 0deg or 180deg, and the mirror can rotated. This allows us to choose an optimal mirror rotation and PZT orientation which minimises the vertical deviation.
Total vertical angle 
 was measured by Koji as described in elog 369.
![\theta_{v, wedge} [\text{arcsec}] = \theta_{PZT} \sin{\frac{\pi \phi_{PZT}}{180}}](https://latex.codecogs.com/gif.latex?%5Ctheta_%7Bv%2C%20wedge%7D%20%5B%5Ctext%7Barcsec%7D%5D%20%3D%20%5Ctheta_%7BPZT%7D%20%5Csin%7B%5Cfrac%7B%5Cpi%20%5Cphi_%7BPZT%7D%7D%7B180%7D%7D) ,  are the wedge angle and orientation respectively and were measured earlier and shown in elog 373 .
![\theta_{v, mirror} [\text{arcsec}] = \frac{180 \times 3600 \times d}{\pi R_{RoC}} \times \sin{\frac{\pi (\phi-\phi_{ROT})}{180}}](https://latex.codecogs.com/gif.latex?%5Ctheta_%7Bv%2C%20mirror%7D%20%5B%5Ctext%7Barcsec%7D%5D%20%3D%20%5Cfrac%7B180%20%5Ctimes%203600%20%5Ctimes%20d%7D%7B%5Cpi%20R_%7BRoC%7D%7D%20%5Ctimes%20%5Csin%7B%5Cfrac%7B%5Cpi%20%28%5Cphi-%5Cphi_%7BROT%7D%29%7D%7B180%7D%7D) , The measurement of the location of the curvature bottom (d,  ) of the mirrors is shown in elog 372 . The optimal  is to be found.
These steps were followed:
- For every combination of prism, PZT, and mirror, the total vertical deviation was minimized with respect to the angle of rotation of the curved mirror computationally (SciPy.optimize.minimize). The results of this computation can be found in Attachment 2: where Tables 1.1 and 2.1 show the minimum achievable deviations for mirrors C10 and C13 respectively, and Tables 1.2 and 2.2 show the corresponding angle of rotation of the mirrors .
- From the combinations that show low total deviations (highlighted in red in Attachment 2), the tolerances for 5 arcsec and 10 arcsec deviations with mirror rotation were calculated, and is shown in Tables 1.3, 1.4, 2.3, 2.4 of Attachment 2.
- While calculating the tolerances, the dependence of the vertical deviations with rotation were also plotted (refer Attachment 3).
- Two sets from available components with low total deviation and high tolerance were chosen.
Result:
These are the ones that were chosen:
- M14 + PZT13 at 0deg + C13 rotated by 169deg anticlockwise (tot vertical dev ~ -3 arcsec)
- M12 + PZT12 at 0deg + C10 rotated by 88deg clockwise (tot vertical dev ~0 arcsec)
The method of attaching them is depicted in Attachment 1.
|