Mirror Results Mirror Results PresentationPresentation

AKA Let’s PartY, PartXAKA Let’s PartY, PartX

Review of GoalsReview 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 SolutionBest 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

Fully Optimized SolutionFully 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

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

Axial DeformationAxial Deformation

Same Angles, Springs w/ AreaSame Angles, Springs w/ Area

How we optimizedHow 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)How we optimized (cont’d)

dΘ

1) MeasureSlope

2) Move Spring Position

3) Overshot, Move Back

4) Take a smaller step

5) Arrive at correct value

Steps Towards a Viable Steps Towards a Viable SolutionSolution

• 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