Abstract

The Extremely Large Telescope (ELT) projects presuppose segmented primary mirrors. The metrology of the off-axis aspherical segments is particularly challenging in terms of global form, mid spatial frequencies and matching of the base-radius and conic constant. We propose to use a swing arm profilometer (SAP) to provide verification independent of interferometry. In this paper we present results of a simulation of the swing arm profilometer as applied to mirror segments, and experimental verification of the simulation using a prototype instrument.

©2010 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Measurement of influence function using swing arm profilometer and laser tracker

Hongwei Jing, Christopher King, and David Walker
Opt. Express 18(5) 5271-5281 (2010)

Modeling and validation of polishing tool influence functions for manufacturing segments for an extremely large telescope

Hongyu Li, David Walker, Guoyu Yu, and Wei Zhang
Appl. Opt. 52(23) 5781-5787 (2013)

References

  • View by:
  • |
  • |
  • |

  1. Astronet, “The astronet Infrastructure Roadmap: A Strategic Plan for European Astronomy,” (2008). http://www.astronet-eu.org/IMG/pdf/Astronet_Infrastructure_Roadmap.pdf .
  2. ESO the European ELT, The European Extremely Large Telescope project,” (2009). http://www.eso.org/sci/facilities/eelt/ .
  3. G. H. Sanders, The Thirty Meter Telescope Project,” (2005). http://www.tmt.org/whats-new/G-Sanders-Jan05-AAS.pdf .
  4. G. H. Sanders, Thirty Meter Telescope, Focus on-Glass,” (2006). http://www.tmt.org/newsletter/focus-0606.html .
  5. 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]
  6. N. Yaitskova and K. Dohlen, “Tip-tilt error for extremely large segmented telescopes: detailed theoretical point-spread-function analysis and numerical simulation results,” J. Opt. Soc. Am. A 19(7), 1274–1285 (2002), http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-7-1274 .
    [Crossref]
  7. D. Malacara, Optical Shop Testing, 2nd edition (Wiley, New York, 1992)
  8. J. R. P. Angel and R. E. Parks, “Generation of off-axis aspherics,” Proc. SPIE 332, 316–326 (1982).
  9. 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.
  10. D. S. Anderson and J. H. Burge, “Swing arm Profilometry of Aspherics,” Proc. SPIE 2356, 269–279 (1995).
  11. 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).
  12. 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.
  13. A. Efstathiou, Design considerations for a hybrid swing arm profilometer to measure large aspheric optics (Ph.D thesis, London, 2007)
  14. A. Lewis, Uncertainty budget for the NPL-UCL swing arm profilometer operating in comparator mode (HMSO and Queen’s printer, London, 2008).

2005 (1)

2002 (1)

1995 (1)

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

1982 (1)

J. R. P. Angel and R. E. Parks, “Generation of off-axis aspherics,” Proc. SPIE 332, 316–326 (1982).

Anderson, D. S.

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

Angel, J. R. P.

J. R. P. Angel and R. E. Parks, “Generation of off-axis aspherics,” Proc. SPIE 332, 316–326 (1982).

Burge, J. H.

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

Dohlen, K.

Kim, D. W.

Kim, S.-W.

Parks, R. E.

J. R. P. Angel and R. E. Parks, “Generation of off-axis aspherics,” Proc. SPIE 332, 316–326 (1982).

Yaitskova, N.

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Proc. SPIE (2)

J. R. P. Angel and R. E. Parks, “Generation of off-axis aspherics,” Proc. SPIE 332, 316–326 (1982).

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

Other (10)

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).

Astronet, “The astronet Infrastructure Roadmap: A Strategic Plan for European Astronomy,” (2008). http://www.astronet-eu.org/IMG/pdf/Astronet_Infrastructure_Roadmap.pdf .

ESO the European ELT, The European Extremely Large Telescope project,” (2009). http://www.eso.org/sci/facilities/eelt/ .

G. H. Sanders, The Thirty Meter Telescope Project,” (2005). http://www.tmt.org/whats-new/G-Sanders-Jan05-AAS.pdf .

G. H. Sanders, Thirty Meter Telescope, Focus on-Glass,” (2006). http://www.tmt.org/newsletter/focus-0606.html .

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.

D. Malacara, Optical Shop Testing, 2nd edition (Wiley, New York, 1992)

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1 Principle of swing arm profilometer
Fig. 2
Fig. 2 Original position of the mirror segment
Fig. 3
Fig. 3 Transformed mirror segment
Fig. 4
Fig. 4 Circular traces on segment
Fig. 5
Fig. 5 Expected traces of model example 1
Fig. 6
Fig. 6 Expected traces of model example 2
Fig. 8
Fig. 8 Trace pattern of the concentric circles. The circles on the SUT are the traces we are going to measure, which are concentric with the rotary axis of rotary table.
Fig. 7
Fig. 7 Experimental setup
Fig. 9
Fig. 9 The expected traces
Fig. 10
Fig. 10 The actual traces
Fig. 11
Fig. 11 The residual traces of the actual traces to the expected traces
Fig. 12
Fig. 12 The filtered residual traces of the actual traces to the expected traces
Fig. 13
Fig. 13 The reconstructed residual surface using the measured traces (PV = 389nm, rms = 58nm)
Fig. 14
Fig. 14 The interferometry results of the mirror (PV = 358nm, rms = 63nm)
Fig. 15
Fig. 15 The difference surface between the SAP results and the
 interferometric results (PV = 157nm, rms = 14nm)

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

θ = arcsin ( L R )
Z = X 2 + Y 2 R + R 2 ( K + 1 ) × ( X 2 + Y 2 )
α 1 = arccos ( f x ( 1 + f x 2 + f y 2 ) )
f = X 2 + Y 2 R + R 2 ( K + 1 ) × ( X 2 + Y 2 ) Z
f x = f X
f y = f Y
f z = f Z = 1
β 1 = arccos ( f y ( 1 + f x 2 + f y 2 ) )
γ 1 = arccos ( 1 ( 1 + f x 2 + f y 2 ) )
{ α = f y | f y | × ( π 2 | arctan ( 1 f y ) | ) β = ( π 2 α 1 ) γ = 0
[ X 1 Y 1 Z 1 ] = r z × r y × r x × [ X Y Z ]
r x = [ 1 0 0 0 cos ( α ) sin ( α ) 0 sin ( α ) cos ( α ) ]
r y = [ cos ( β ) 0 sin ( β ) 0 1 0 sin ( β ) 0 cos ( β ) ]
r z = [ cos ( γ ) sin ( γ ) 0 sin ( γ ) cos ( γ ) 0 0 0 1 ]
[ X c Y c Z c ] = r z × r y × r x × [ X s n Y s n Z s n ]
[ X 2 Y 2 Z 2 ] = [ X 1 X c Y 1 Y c Z 1 Z c ]
D e v = R ( X 2 0 ) 2 + ( Y 2 0 ) 2 + ( Z 2 R ) 2
X e x t 2 + Y e x t 2 = r 2

Metrics