Mirror Results Presentation AKA Let’s PartY, PartX

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.

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 – arcseconds Uses standard coil springs on the foam base

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– e-6 m Axial distortion– ± 2.09e-8 m RMS of the dx – arcseconds Uses standard coil springs on the foam base

The Angles (in Degrees) Thanks, MATLAB! The Angles (in Degrees) Thanks, MATLAB! [0.03, , , , , , , , , , , ]

Axial Deformation

Same Angles, Springs w/ Area

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

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

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

This one’s for you, Mike