Abstract

We present a novel method to accurately measure 3D polishing influence functions by using a swing arm profilometer (SAP) and a laser tracker. The laser tracker is used to align the SAP and measure the parameters of the SAP setup before measuring the influence function. The instruments and the measurement method are described, together with measurement uncertainty analysis. An influence function deliberately produced with asymmetric form in order to create a challenging test is measured, and compared with that of a commercial 3D profilometer. The SAP result is 48.2μm in PV, 7.271mm3 in volume. The 3D profilometer result is 48.4μm in PV, 7.289mm3 in volume. The forms of the two results show excellent correlation. This gives confidence of the viability of the SAP method for larger influence functions out of range of the commercial instrument.

© 2010 OSA

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References

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  1. D. W. Kim, W. H. Park, S.-W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5656 .
    [CrossRef] [PubMed]
  2. L. Huang, C. Rao, and W. Jiang, “Modified Gaussian influence function of deformable mirror actuators,” Opt. Express 16(1), 108–114 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-108 .
    [CrossRef] [PubMed]
  3. D. W. Kim and S.-W. Kim, “Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes,” Opt. Express 13(3), 910–917 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-910 .
    [CrossRef] [PubMed]
  4. C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005).
    [CrossRef]
  5. J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).
  6. D. S. Anderson, R. E. Parks, and T. Shao, “A versatile profilometer for aspheric optics,” in Proceedings of OF&T Workshop Technical Digest (Academic, Monterrey, CA 1990), Vol. 11, pp. 119–122.
  7. D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).
  8. P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc.SPIE 7426, 74260J–74260J −8 (2009).
  9. A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry - traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, Mexico, 2006), pp. 101–105.
  10. A. Efstathiou, Design considerations for a hybrid swing arm profilometer to measure large aspheric optics (Ph.D thesis, London, 2007)
  11. A. Lewis, Uncertainty budget for the NPL-UCL swing arm profilometer operating in comparator mode (HMSO and Queen’s printer, London, 2008).
  12. H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18(3), 2036–2048 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2036 .
    [CrossRef] [PubMed]

2010

2009

2008

2007

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

2005

1995

D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).

Anderson, D. S.

D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).

Burge, J. H.

D. W. Kim, W. H. Park, S.-W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5656 .
[CrossRef] [PubMed]

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005).
[CrossRef]

Huang, L.

James, H.

D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).

Jiang, W.

Jing, H.

Kim, D. W.

Kim, S.-W.

King, C.

Park, W. H.

Rao, C.

Su, P.

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

Walker, D.

Zehnder, R.

C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005).
[CrossRef]

Zhao, C.

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005).
[CrossRef]

Zobrist, T.

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

Opt. Eng.

C. Zhao, R. Zehnder, and J. H. Burge, “Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker,” Opt. Eng. 44(9), 090506 (2005).
[CrossRef]

Opt. Express

Proc. SPIE

J. H. Burge, P. Su, C. Zhao, and T. Zobrist, “Use of a commercial laser tracker for optical alignment,” Proc. SPIE 6676, 6676E (2007).

D. S. Anderson and H. James, “Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).

Other

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc.SPIE 7426, 74260J–74260J −8 (2009).

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry - traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, Mexico, 2006), pp. 101–105.

A. Efstathiou, Design considerations for a hybrid swing arm profilometer to measure large aspheric optics (Ph.D thesis, London, 2007)

A. Lewis, Uncertainty budget for the NPL-UCL swing arm profilometer operating in comparator mode (HMSO and Queen’s printer, London, 2008).

D. S. Anderson, R. E. Parks, and T. Shao, “A versatile profilometer for aspheric optics,” in Proceedings of OF&T Workshop Technical Digest (Academic, Monterrey, CA 1990), Vol. 11, pp. 119–122.

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Figures (11)

Fig. 1
Fig. 1

Measurement instruments (SAP + Laser Tracker)

Fig. 2
Fig. 2

XY coordinates measurement principle

Fig. 3
Fig. 3

Measurement pattern. The arc is the swinging path of the arm. The concentric circles are probe traces of the scans.

Fig. 4
Fig. 4

Data clouds of SAP (left) and 3D Talysurf profilometer (right)

Fig. 5
Fig. 5

Reconstructed surface of SAP data (PV: 48.2μm, volume = 7.271mm3)

Fig. 6
Fig. 6

Reconstructed surface of Talysurf profilometer data (PV: 48.4μm, volume = 7.289mm3)

Fig. 7
Fig. 7

Difference surface of SAP and Talysurf measurement (PV: 2.3μm, rms = 0.3μm)

Fig. 8
Fig. 8

Profiles in Y = 0mm

Fig. 9
Fig. 9

Difference profile in Y = 0mm(PV: 2.0μm, rms = 0.4μm)

Fig. 10
Fig. 10

Profiles in X = 5mm

Fig. 11
Fig. 11

Difference profile in X = 5mm(PV: 1.0μm, rms = 0.3μm)

Equations (14)

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X = L × cos ( β ) × 2 × ( 1 cos ( α ) )
Y = L × sin ( β ) × 2 × ( 1 cos ( α ) )
u a r m l e n g t h x y = 0.05 × 2 × ( 1 cos ( 3.670 ) ) = 3.2 μ m
u R T x y = 0.1 μ m
u a r m b e a r i n g x y = 0.025 μ m
u t e m p x y = 2.51 μ m
u c x y = u a r m l e n g t h x y 2 + u R T x y 2 + u a r m b e a r i n g x y 2 + u t e m p x y 2 = 3.2 2 + 0.1 2 + 0.025 2 + 2.51 2 = 4.1 μ m
U x y = k × u c x y = 2 × 4.1 μ m = 8.2 μ m
u p r b z = 0.5 μ m
u R T z = 0.025 μ m
u a r m b e a r i n g z = 0.1 μ m
u t e m p z = 0.87 μ m
u c z = u p r b z 2 + u R T z 2 + u a r m b e a r i n g z 2 + u t e m p z 2 = 0.5 2 + 0.025 2 + 0.1 2 + 0.87 2 = 1 μ m
U z = k × u c z = 2 × 1 μ m = 2 μ m

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