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Chris Chrzanowski Charles Frohlich Swales Aerospace, Inc.

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Presentation on theme: "Chris Chrzanowski Charles Frohlich Swales Aerospace, Inc."— Presentation transcript:

1 Using Nastran and Matlab to Predict Surface Figure Error of a Spherical Mirror
Chris Chrzanowski Charles Frohlich Swales Aerospace, Inc. 5050 Powder Mill Rd. Beltsville, MD, 20705, USA May 4-5, 2005

2 Introduction Two non-flight prototype mirrors for use on the JWST/NIRSpec instrument were received from Galileo Avionica (Florence, Italy), for optical testing at NASA/Goddard Space Flight Center 1: Silicon Carbide (SiC), coated with SiC CVD 2: Carbon-reinforced Silicon Carbide (C/SiC), coated with Si-SiC CVD Spherical optical surface, ROC = 600mm Polished to microroughness of 3.5 nm RMS Lightweighted aft surface Integral mount C/SiC mounting plate also provided as an interface to the integral mount C/SiC Mirror May 4-5, 2005

3 Goals Design and build a mount to hold each mirror in a cryogenic dewar Hold in horizontal orientation (gravity perpendicular to optical axis) Maintain high thermal conductivity between mirror and dewar cold plate when cooling from room temperature to 20K Minimize surface figure error (SFE) induced by CTE mismatches among the materials; SiC and C/SiC have a very low CTE at cryo temperatures Use finite element analysis (FEA) in MSC.NASTRAN 2001 to predict the deformed mirror shapes Optical post-processing SigFit: characterize surface with Zernike polynomials for optical analysis Matlab: “best fit sphere” function to calculate SFE For this project, SFE defined as the deviation from a perfect sphere May 4-5, 2005

4 Kinematic Mount Design
Kinematically constrains the mirror in six degrees of freedom (DOF), allowing the mirror to expand or contract, isolated from the CTE mismatch of the Copper cold plate Three low-friction ball bearings in a configuration rest on a conical seat, V-groove, and flat surface, respectively Spring plungers preload the bearings to support the weight of the mirror in the horizontal configuration May 4-5, 2005

5 Kinematic Mount Design
Low-stress Copper thermal straps used for thermal conductivity Belleville spring washers used on each fastener stack to maintain preload when going cold, or to prevent fastener from compressing mirror material SiC Mirror C/SiC Plate Spring Plunger Invar Bracket Spherical Bearing CRES Bracket Cu Thermal Strap Cu Mount Ring May 4-5, 2005

6 Mirror FEM Detailed finite element model (FEM) based on drawings and specifications from Galileo Avionica Constructed with FEMAP v8.1a for use in MSC.NASTRAN 2001 SiC Mirror: 45,000 elements; 34,000 nodes May 4-5, 2005

7 Mirror FEM SiC substrate modeled as solid elements
SiC CVD modeled as thin plate elements 100 mm thick where deposited 40 mm thick on polished surface Solid masked from coating on 4 flat edges and tops of mounting feet Optical surface at least two solid elements thick May 4-5, 2005

8 Assembly FEM FEM comprised of parts that directly affect the SFE of the optical surface C/SiC mounting plate – solids Invar support brackets – plates Titanium fasteners – bars Ball bearings modeled as single point constraints, in appropriate DOF Analysis Load Cases Gravity (1G in the –Y axis) at room temperature Cooling from room temperature to 20K without gravity Cooling from room temperature to 20K with gravity May 4-5, 2005

9 Optical Analysis SFE defined as the change in figure error from unmounted R/T Initial figure error is zero; optical surface nodes aligned in FEMAP to a 600mm ROC sphere SigFit post-processing Deformed shape defined by NASTRAN data deck and nodal displacements, output in .PCH format Zernike polynomials fit to the deformed surface, after subtracting out the original undeformed surface “Subtract Best Fit Plane and Power” option also removes the first 3 Zernike terms (bias, tilt, and power) from the RMS calculations as an approximation of a sphere Matlab post-processing Deformed shape defined by FEMAP list of node locations and displacements, in .LST format Matlab function fits a sphere to the deformed shape using a least-squares method, and calculates the residual RMS error May 4-5, 2005

10 Zernike Polynomials A surface can be defined as the sum of Zernike polynomials Figure adapted from SigFit Reference Manual, v R2, sec  Sigmadyne, Inc. May 4-5, 2005

11 Method Comparison - SigFit
Mirror face test model Cooldown from R/T to 20K without gravity All elements have identical CTE Only deformation is ROC decrease SigFit contour with BFP and Power removed Shows the error after the original 600mm sphere and best fit paraboloid are subtracted from the new spherical shape SFE estimate: waves RMS Higher order spherical terms cannot be used to better approximate a sphere because they may remove real errors on the actual mirror Order Aberration Magnitude Residual Residual K N M (Waves) RMS P-V Input(wrt zero) Bias Tilt Power (Defocus) Pri Astigmatism Pri Coma Pri Spherical Pri Trefoil Sec Astigmatism Sec Coma Sec Spherical Pri Tetrafoil Sec Trefoil Ter Spherical Pri Pentafoil Sec Tetrafoil Qua Spherical Qin Spherical May 4-5, 2005

12 Method Comparison - Matlab
Order Aberration Magnitude Residual Residual K N M (Waves) RMS P-V Input(wrt zero) Bias Tilt Power (Defocus) Pri Astigmatism Pri Coma Pri Spherical Pri Trefoil Sec Astigmatism Sec Coma Sec Spherical Pri Tetrafoil Sec Trefoil Ter Spherical Pri Pentafoil Sec Tetrafoil Qua Spherical Qin Spherical Matlab sphere fit SFE: waves RMS Identical to the error after SigFit subtracts higher order terms Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-008 Microns Waves May 4-5, 2005

13 SiC Kinematic Results R/T, 1G 20K 20K, 1G May 4-5, 2005 Mirror Radius
Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-008 Microns Waves Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-007 Microns Waves Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-007 Microns Waves May 4-5, 2005

14 C/SiC Kinematic Results
R/T, 1G 20K 20K, 1G Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-007 Microns Waves Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-007 Microns Waves Mirror Radius R Undeformed Deformed Difference Non-Spherical Mirror Deformations P to V RMS inches e e-007 Microns Waves May 4-5, 2005

15 Conclusions Kinematic mount shown to be an effective mechanism to support mirrors in a cryogenic dewar Mount CTE mismatches do not induce large SFE SFE for both mirrors predicted ~10.5nm RMS, near project goal of 10nm Matlab function shown to match proven optical post-processor Accurate measurement of SFE as a deviation from a perfect sphere Quick interaction between structural and optical analysis, with both visual and numeric output of SFE Simple data transfer from FEMAP Pre- & Post-Processor May 4-5, 2005

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