1. Mirror Results Presentation AKA Let’s PartY, PartX

2. Review of Goals Figure out spring arrangement to limit mirror deflection to 10 nm = 1e-8 m –Target Axial Distortion ± 1e-8 m X direction (Axial Direction) is 100 times as important as Y direction.

3. Best Uniform Solution Optimal Spring Geometry: –20 rows of springs, evenly spaced –10 springs per row, evenly spaced –Spring constant 1 N / m Max distortion – 72.75e-6 m Axial distortion – ±43.8e-8 m RMS of the dx – 0.285676 arcseconds Uses standard coil springs on the foam base

4. Fully Optimized Solution Optimal Spring Geometry: –22 rows of springs placed at angles 21 springs per row, evenly spaced –Spring constant 0.2 N / m Max distortion– 2.4227e-6 m Axial distortion– ± 2.09e-8 m RMS of the dx – 0.812209 arcseconds Uses standard coil springs on the foam base

5. The Angles (in Degrees) Thanks, MATLAB! The Angles (in Degrees) Thanks, MATLAB! [0.03, 0.8889, 4.2365, 7.2313, 11.9344, 11.9955, 15.9555, 16.1586, 16.4575, 16.4934, 22.2276, 23.4992]

6. Axial Deformation

7. Same Angles, Springs w/ Area

8. How we optimized Used the MATLAB/COMSOL interface to generate a script Performed a parameter search to find the optimal evenly spaced spring solution Used these values to generate a simulation that optimized row location Iteratively checked for improvements in dx RMS

9. How we optimized (cont’d) dΘdΘ 1) Measure Slope 2) Move Spring Position 3) Overshot, Move Back 4) Take a smaller step 5) Arrive at correct value

11. Steps Towards a Viable Solution Optimized spring angle values = exact Real spring placement ≠ exact –Placement error ~ 5e-4 m Rounding: –4 nearly coincident rows – double K? Offset springs along axis? Rounded RMS is 2.92e-9 m off optimal

12. This one’s for you, Mike