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USING FARO ARM FOR COORDINATE MEASUREMENTS IN OPTICAL APPLICATIONS

Mike Borden - University of Arizona

Christian Drouet d'Aubigny - University of Arizona

Richard Nelson –New River Kinematics

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SORAL, Steward Observatory, and the University of Arizona (U of A)

U of A is located in Tucson, AZ World class astronomy and optical science university

Steward Observatory Offers an astronomy program for graduate and

undergraduate students Develops hardware and instrumentation, including some of

the worlds largest telescope mirrors SORAL – Steward Observatory Radio Astronomy

Laboratory Builds receivers for observing in sub-millimeter

wavelengths



Mike Borden

Mike Borden is an Optical Science graduate student working with SORAL Supporting radio telescope receiver SuperCam and

Antarctic balloon telescope Stratospheric Terahertz Observatory (STO)

Following research was part of an Masters Thesis in Optical Science



Accurate measuring is important

Optical performance can suffer if alignment of components is poor.

Incorrect surface figure also degrades optical performance Accurate measuring can verify surface figure

In sub-millimeter astronomy, accurate coordinate measuring with a Portable CMM is adequate for alignment and surface figure measurements. Not the case with shorter wavelengths, require too high of a

tolerance



Research Overview

Using a portable CMM to determine surface figure accuracy of machined optical surfaces Effect on optical system performance

Mirror alignment using portable CMM Aligning 7 mirror array for radio telescope relay optics



SuperCam

SuperCam is a 64 pixel heterodyne receiver used for radio astronomy Observes at 350 GHz = 857um wavelength 64 pixel array at this frequency is largest ever built This fall will be installed on the Submillimeter Telescope

(SMT) on Mount Graham near Safford, AZ



SuperCam Relay Mirror Array

7 mirror optical array was designed to relay sky beam from SMT to SuperCam

All 7 mirrors were fabricated at low cost 5 flat mirror and 2

with curvature



SuperCam Relay Mirror Array

Questions arose about surface figure of mirrors



Hardware and Software

Hardware Utilized 8’ Quantum FARO Arm

Software Utilized Spatial Analyzer MATLAB SolidWorks ZEMAX



VERIFYING SURFACE FIGURE OF OPTICS WITH FARO ARM



Surface Figure Accuracy: The Challenge

The fabrication of optical components Machine shops can be challenged by complex optical

surfaces Polishing surfaces can have an undesirable effect on

surface figure

Verifying surface figure of optical components How accurately was optical surface made? How does this surface affect optical performance of

system?



Surface Figure Accuracy:The Solution

FARO Arm and Spatial Analyzer were used to verify the surface figure on an optical surface

Measured surface was then entered into ZEMAX (optical design software) to determine resulting optical performance



Measuring an Optical Surface

Mount mirror in stable position

Measure surface of mirror with the arm.

Export dataset



Generating a Theoretical Surface

Theoretical CAD surface created in SolidWorks

Conic equation of optical surface used to model surface:

c – radius of curvaturek – conic constantr – radial coordinate



Generating a Theoretical Surface

Theoretical surface is then rotated so center of mirror is at the origin and its surface normal is vertical

Mirror is then cut to correct size



Preparing Measured Dataset

Measured data translated to mimic theoretical CAD surface Center of mirror at origin (0,0,0)

Using MATLAB, dataset interpolated and probe radius offset is accounted for



Preparing Measured Dataset

MATLAB’s surface normal function is used

New dataset is created and output from MATLAB



Optimizing Surface Figure to CAD

CAD model and MATLAB’s probe offset data is imported into Spatial Analyzer

Best-Fit Transformation used to optimize point group to CAD surface



Resulting Surface Figure Error

Plots of error between measured and theoretical surface generated



Resulting Surface Figure Error

Average error from best-ft transformation: M4 - 21.1um / point M7 – 26.5um / point (shown in previous slide)

These errors represent fabrication error in mirrors

Conclusion: Neither mirror was fabricated perfectly Need to import measured surfaces into ZEMAX to determine

optical performance



Zernike Polynomials

Zernike polynomials are set of equations used to represent a curved surface

Can be used to enter a surface into ZEMAX



Generating and Using Zernike Polynomials

Coefficients of Zernike polynomials generated using open source MATLAB script



Resulting Optical System Performance

Zernike coefficients entered on top of optical surfaces in ZEMAX

Neither curved surface (M4, M7) were found to be ideal

Resulting wavefront error was λ/20

Optical performance slightly degraded but overall performance acceptable Ray trace of system



ALIGNING MIRRORS WITH FARO ARM AND SA



Mirror Array Alignment:The Challenge

Using CMM to align mirror array

Optical surface difficult to use as mechanical alignment reference Tough to constrain location of probe Erroneous surface makes poor reference surface



Mirror Array Alignment:The Solution

FARO Arm was used to align SuperCam mirror array Range of motion is ideal for 3D coordinate measuring

problem

Mechanical fiducials used to couple optical surface to mechanical reference Cone shape constrains probe



Creating Mechanical References

Conical reference fiducials machined into mirrors FARO Arm measures coordinates of reference

fiducials and optical surface



Optimizing Surface Figure to CAD

Identical best-fit transformation as done in “Verifying optical surface” procedure Measured fiducial references are transformed along with

optimized surface data

Result is measured reference coordinates coupled to theoretical surface



Modeling Reference Fiducials into CAD

Cones are created from reference fiducial points Bottom of cone represents the center of the FARO probe

CAD mirror now matches reality



Updating CAD Assembly and Importing into SA

Modeled mirrors are mated into CAD assembly of mirror array

Mirror array exported from SolidWorks and imported into SA

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Mirror Alignment using SA

Reference fiducials of M7 are measured and mated to corresponding fiducials in CAD model




FARO Arm is correctly located in relation to M7




Fiducials on each remaining mirror are measured Coordinates are compared to theory / CAD in SA Mirrors are adjusted based on error between theory / CAD

and measured point

Results to date Early stages of alignment have been tested and appear

promising SuperCam mirrors not ready for alignment as of 7/15/11

rcn15



rcn15 Richard Nelson, 7/20/2011



Verifying Alignment of Array

FARO Laser tracker will be used to verify alignment

Hot / cold loads will be used to determine where pixels in SuperCam instrument are aligned



Conclusions

Verifying surface figure of optics: FARO Arm can be used to adequately measure and qualify the

surface figure of sub-millimeter optical components.

Aligning mirror array: FARO Arm will likely be an adequate alignment tool for sub-

millimeter optics.

Both procedures*: Shorter wavelength optics require too high of a precision for

FARO Arm’s accuracy and these procedures.



QUESTIONS



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