Freeform metrology using subaperture stitching...

| © Copyright QED Technologies 2016

Presented By:

Freeform metrology using subaperture stitching interferometry APOMA November 10-11, 2016

Christopher Hall QED Optics Sr. Engineer, QED Technologies


Interferometry Without Nulls - SSI

Key benefits of sub-aperture metrology: − Magnify − Locally null

Higher resolution resolves more fringes QED Algorithms − Enable automation − Compensate for systematic errors

Motion Reference wave Re-trace

SSI-A

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Subaperture Stitching Interferometry for Freeform

Two new developments − QIS: QED Interferometer

optimized for Stitching − Algorithms extended to

freeform geometries QIS − Enables capture of higher

fringe densities New Algorithms − From rotationally symmetric

only → freeform shapes − New motion equations & other

algorithm extensions − Maintains all the benefits of

stitching parts with rotational symmetry (reference wave calibration, distortion calibration, etc.)

− Still under development 3


Subaperture Stitching Interferometry

Interferometry can typically provide higher lateral resolution and precision than CMM metrology or profilometry ASI platform excels at measuring mid-spatial frequency errors Extended some aspects of our stitching algorithms to support non-rotationally symmetric geometries − Freeform geometry input

− Freeform motion equations

− Still more work to be done

Using a 4” f/7.2, a 5 mm subaperture patch could be measured − ~16 µm freeform departure over 5 mm Φ

− 166 sub-aps collect to cover 28 mm Φ area; ~600 µm freeform departure

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Subaperture Stitching Interferometry Results Low order error agrees very well Greatly increased resolution over CMM − 1200 pix (SSI) vs 60 pix (CMM) − 23 µm/pix vs 460 µm/pix

Mid-spatial frequencies are characterized much more clearly by SSI − Vertical trough is clearly seen in SSI

measurement, but barely visible in CMM measurement

− Horizontal ripples have higher definition

For high precision figure correction, both CMM and SSI measurements are valuable

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SSI CMM

Vertical trough seen by SSI but not by CMM

Color Scale +/- 40 µm

Color Scale +/- 0.75 µm

POW & alignment errors removed

4 mm high-pass filter

28 mm

26 m

m


Freeform telescope mirror

Dominant terms in Q-polynomial freeform representation:

106 μm PV departure from best-fit sphere

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https://www.pec.ncsu.edu/research/design-of-reflective-three-mirror-anastigmat-telescope/

𝑄02 = −66 µm (astigmatism-like) 𝑄11 = 50 µm (coma-like)

𝑄00 = 21 µm (spherical-like) 𝑄03 = 20 µm (trefoil-like)


Metrology of telescope mirror – CGH vs SSI

For CGH: − 4” interferometer on horizontal table − 4” f/1.5 TS − ~600 x 600 pixels

For Stitching: − ASI(Q) Interferometer − 6” f/3.5 TS − 47 Subapertures − ~2K x 2K pixels

All data reported over 100 mm clear aperture

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Lattice Design


ASI Repeatability

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RMS: 76 nm RMS: 77 nm RMS: 78 nm

Three repeat measurements

Pixel-by-pixel mean and standard deviation

RMS: 2 nm RMS: 77 nm

ASI(Q) gives very repeatable

measurements


Comparison with CGH Metrology

Difficulty of measurement execution Lateral resolution Mid-spatial frequency characterization Distortion

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Comparison with CGH metrology

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CGH Null ASI(Q) – Freeform stitching

>10x more pixels

(250,000 vs 3,000,000)

Results agree very closely

PV = 518 nm RMS = 77 nm

PV = 527 nm RMS = 77 nm

ASI(Q) gives very good low-order accuracy


ASI measurement is easier to execute Software-assisted alignment (initial setup takes minutes instead of hours) Automatic subaperture positioning Easy-to-use data analysis tools

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Actual fringes Expected fringes


ASI measurement is easier to analyze

Automatic removal of alignment error − On a freeform, can’t remove Zernikes like you can for a sphere or

asphere (no 1-1 relationship between alignment errors & Zernikes) X shift: Z1, Z5, and Z6 (X tilt, Y primary astigmatism, and X primary coma), Y shift: Z2, Z4, and Z7 (Y tilt, X primary astigmatism, and Y primary coma), and Rotation: Z5, Z6, and Z9 (Y primary astigmatism, X primary coma, and X trefoil).

− Instead, figure error due to rigid-body alignment errors are removed

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RMS: 72 nm RMS: 35 nm RMS: 77 nm

Rigid-body alignment error removal Zernike removal Difference

If Zernike removal is performed instead of a

rigid-body fit, some figure error will be mistakenly attributed to alignment

error.


ASI gives higher resolution metrology

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CGH data appears to have higher level of MSF, but ASI(Q) data shows result is actually quite smooth at this level

PSD Data of central subaperture

Red curve = CGH data Green curve = ASI(Q) data


ASI gives better MSF fidelity

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Hotspots from higher-

order diffraction visible in

CGH data

Again, CGH data has MSF information that is not actually true surface shape information


ASI gives better MSF fidelity

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Ripple from ghost fringes

ASI(Q) Freeform Stitching has accurate low-order information, and has more high-frequency information and accuracy at the same time


ASI gives distortion-free measurement

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In ASI measurements, rings are at the same radial position at +Y and -Y

In CGH measurements,

distortion causes rings to appear at different distances

from the center, making a

deterministic correction of these features impossible

+Y

-Y

ASI – distortion free

CGH – Up to 1.2mm lateral error


Correction with MRF

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Initial After MRF

7x rms improvement demonstrates high convergence as a result of reproducible metrology


Summary

ASI(Q) Freeform Stitching is bringing high accuracy and high resolution to full 3-D freeform metrology −Critical for deterministic figure and MSF correction using

processes like MRF Freeform measurements are very repeatable and show very good agreement with CGH cross-tests Several benefits of ASI measurement over CGH − Easier measurement execution − Improved lateral resolution − Better fidelity of mid-spatial frequency (MSF) features − Distortion-free measurement

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Freeform metrology using subaperture stitching...

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