Abstract

This paper complements our previous study on testing a 25.4 mm diameter diamond-turned 90° off-axis commercial-quality parabolic mirror with a spherical test wave in a phase-shifting Fizeau interferometer (Opt. Express 17, 3196–3210 (2009). In this study I reverse the optical system and use the Fizeau interferometer with a planar reference surface, auxiliary components, and the surface of the transmission sphere as a reflecting spherical return surface. As in the previous paper, I present a description of the necessary steps for alignment and measurement validation. The reversal of the optical system, and associated co-ordinate systems, necessitates some changes of hardware and analysis that provide insight into the underlying symmetries, and may prove useful in a wider context.

© 2009 Optical Society of America

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References

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  1. R. N. Wilson, Reflecting Telescope Optics (Springer, Heidelberg, 2004), Chap. 1.
  2. U. Birnbaum and R. Schreiner, "Machining and measuring of an off-axis paraboloid," Proc. SPIE 5965, 59650T (2005).
    [CrossRef]
  3. U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
    [CrossRef]
  4. J. Burke, K. Wang, and A. Bramble, "Testing of an off-axis parabolic mirror. I. Configuration with spherical reference wave and flat return mirror," Opt. Express 17, 3196-3210 (2009).
    [CrossRef] [PubMed]
  5. D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 1992), Appendix 2.
  6. http://www.cerbec.com/TechInfo/TechSpec.asp.
  7. R. E. Parks, "Making and testing an f/0.15 parabola," Appl. Opt. 13, 1987-1989 (1974).
  8. G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, "Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field," Appl. Opt. 47, 5570-5584 (2008).
    [CrossRef] [PubMed]
  9. R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).
  10. WYKO 6000 is a 150 mm aperture Fizeau interferometer made by WYKO Corp. now owned by Veeco Tucson, Inc., 2650 E. Elvira Rd., Tucson, AZ 85706, USA.
  11. L. C. Maxey, "Automated interferometric alignment system for paraboloidal mirrors," US Patent 5249033, 1-14 (1993).
  12. J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
    [CrossRef]
  13. M. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001).
    [CrossRef]
  14. U. Griesmann, "Three-flat test solutions based on simple mirror symmetry," Appl. Opt. 45, 5856-5865 (2006).
    [CrossRef] [PubMed]
  15. M. Vannoni and G. Molesini, "Iterative algorithm for three flat test," Opt. Express 15, 6809-6816 (2007).
    [CrossRef] [PubMed]
  16. T. Dresel, N. Lindlein, and J. Schwider, "Empirical strategy for detection and removal of misalignment aberrations in interferometry," Optik 112, 304-308 (2001).
    [CrossRef]
  17. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
    [CrossRef]
  18. E. W. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).
  19. P. Arguijo and M. Strojnik Scholl, "Exact ray-trace beam for an off-axis paraboloid surface," Appl. Opt. 42, 3284-3289 (2003).
    [CrossRef] [PubMed]
  20. J. Burke, "Rapid and reliable reference sphere calibration for Fizeau interferometry," Opt. Lett. 33, 2536-2538 (2008).
    [CrossRef] [PubMed]
  21. G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, "Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field," Appl. Opt. 47, 5570-5584 (2008).
    [CrossRef] [PubMed]
  22. D. I. Farrant and J. N. Petzing, "Sensitivity errors in interferometric deformation metrology," Appl. Opt. 42, 5634-5641 (2003).
    [CrossRef] [PubMed]

2008

2007

2006

U. Griesmann, "Three-flat test solutions based on simple mirror symmetry," Appl. Opt. 45, 5856-5865 (2006).
[CrossRef] [PubMed]

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

2005

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

U. Birnbaum and R. Schreiner, "Machining and measuring of an off-axis paraboloid," Proc. SPIE 5965, 59650T (2005).
[CrossRef]

2003

2001

M. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001).
[CrossRef]

T. Dresel, N. Lindlein, and J. Schwider, "Empirical strategy for detection and removal of misalignment aberrations in interferometry," Optik 112, 304-308 (2001).
[CrossRef]

1986

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

1977

R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).

1974

Arguijo, P.

Berger, A.

Bernitzki, H.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

Birnbaum, U.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

U. Birnbaum and R. Schreiner, "Machining and measuring of an off-axis paraboloid," Proc. SPIE 5965, 59650T (2005).
[CrossRef]

Burke, J.

J. Burke, "Rapid and reliable reference sphere calibration for Fizeau interferometry," Opt. Lett. 33, 2536-2538 (2008).
[CrossRef] [PubMed]

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Dresel, T.

T. Dresel, N. Lindlein, and J. Schwider, "Empirical strategy for detection and removal of misalignment aberrations in interferometry," Optik 112, 304-308 (2001).
[CrossRef]

Falkenstörfer, O.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

Farrant, D. I.

Griesmann, U.

U. Griesmann, "Three-flat test solutions based on simple mirror symmetry," Appl. Opt. 45, 5856-5865 (2006).
[CrossRef] [PubMed]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Konermann, H.

Küchel, M.

M. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001).
[CrossRef]

Lauth, H.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

Leuchs, G.

Lindlein, N.

Mantel, K.

Molesini, G.

Nemati, B.

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

Oreb, B.

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

Parks, R. E.

Peschel, U.

Petzing, J. N.

Platt, B.

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

Schreiner, R.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

U. Birnbaum and R. Schreiner, "Machining and measuring of an off-axis paraboloid," Proc. SPIE 5965, 59650T (2005).
[CrossRef]

Schwider, J.

Shagam, R. N.

R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).

Sladky, R. E.

R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).

Sondermann, M.

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Strojnik Scholl, M.

Vannoni, M.

Waak, T.

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Wyant, J. C.

R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).

Young, E. W.

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

Appl. Opt.

Opt. Eng.

R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).

Opt. Express

Opt. Lett.

Optik

M. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001).
[CrossRef]

T. Dresel, N. Lindlein, and J. Schwider, "Empirical strategy for detection and removal of misalignment aberrations in interferometry," Optik 112, 304-308 (2001).
[CrossRef]

Proc. SPIE

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
[CrossRef]

E. W. Young, "Optimal removal of all mislocation effects in interferometric tests," Proc. SPIE 661, 116-124 (1986).

J. Burke, B. Oreb, B. Platt, and B. Nemati, "Precision metrology of dihedral angle error in prisms and corner cubes for the Space Interferometry Mission," Proc. SPIE 5869, 58690W (2005).
[CrossRef]

U. Birnbaum and R. Schreiner, "Machining and measuring of an off-axis paraboloid," Proc. SPIE 5965, 59650T (2005).
[CrossRef]

U. Birnbaum, H. Bernitzki, O. Falkenstörfer, H. Lauth, R. Schreiner, and T. Waak, "Manufacturing of high-precision aspheres," Proc. SPIE 6149, 61490H (2006).
[CrossRef]

Other

J. Burke, K. Wang, and A. Bramble, "Testing of an off-axis parabolic mirror. I. Configuration with spherical reference wave and flat return mirror," Opt. Express 17, 3196-3210 (2009).
[CrossRef] [PubMed]

D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 1992), Appendix 2.

http://www.cerbec.com/TechInfo/TechSpec.asp.

R. N. Wilson, Reflecting Telescope Optics (Springer, Heidelberg, 2004), Chap. 1.

WYKO 6000 is a 150 mm aperture Fizeau interferometer made by WYKO Corp. now owned by Veeco Tucson, Inc., 2650 E. Elvira Rd., Tucson, AZ 85706, USA.

L. C. Maxey, "Automated interferometric alignment system for paraboloidal mirrors," US Patent 5249033, 1-14 (1993).

Supplementary Material (1)

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Figures (14)

Fig. 1.
Fig. 1.

(a) illustration of FR parabolic mirror test; (b) practical set-up.

Fig. 2.
Fig. 2.

(a) retroreflection from cube corner in collimated beam defines the optical axis in the resulting interferogram. Pellicle attenuator is inserted to suppress multiple reflections. (b) symmetric interference pattern after removal of all tilts.

Fig. 3.
Fig. 3.

(a) error map of a six-inch reference flat (rms 1.9 nm, PV 9.5 nm). (b) error map of one-inch subaperture on the same surface (rms 0.5 nm, PV 1.8 nm).

Fig. 4.
Fig. 4.

Reflection sphere calibration/elimination method for FR set-up.

Fig. 5.
Fig. 5.

Modelled calibration map of reflection sphere for FR set-up.

Fig. 6.
Fig. 6.

(a) definition of OAP alignment coordinate system. Dashed line across OAP: central line of symmetry. Right angles between the axes are indicated by solid black or white lines. Reflection sphere is drawn with smaller aperture than in reality for the sake of clarity; red arrows behind reflection sphere denote degrees of freedom for removal of straight fringes; black arrow denotes direction to remove focus error. (b) actual laboratory set-up (reflection sphere not shown) with controls for all degrees of freedom; however, the translations can be adjusted by moving the reflection sphere instead.

Fig. 7.
Fig. 7.

Set-up with plane mirror for retroreflection of nominally spherical converging beam.

Fig. 8.
Fig. 8.

Three iterations of the OAP alignment. “A” images: all errors present (for the respective iteration); “B” images: Δτ removed; “C” images: Δτ removed. Image 2A results from 1C by removing Δr, and starts the next iteration. Note that all iterations shown here are carried out in fringe mode.

Fig. 9.
Fig. 9.

Single-frame excerpt from a 30-s video showing rapid OAP alignment (Media 1).

Fig. 10.
Fig. 10.

(a) Brightness distribution in the object wave; recorded with reference flat tilted away from optical axis and hence, no fringes. (b) Phase map of well-aligned OAP (residual astigmatism) with retroreflection mirror. Note the bogus top-bottom symmetry.

Fig. 11.
Fig. 11.

Proportional misalignment error maps. (a) Z r (x,y) for Δ r (Z3 = 1 wave; Z3 removed from result); (b) Z z (x,y) for Δ z (Z4 = 1 wave; Z4 removed from result); (c) Δ t (x,y) for Δ t (Z5 = 1wave; Z5 removed from result).

Fig. 12.
Fig. 12.

(a) interferogram of final measurement; (b) wavefront map optimised for displacement errors. Note the difference to Fig. 10(b).

Fig. 13.
Fig. 13.

(a) spatial map of re-scaling coefficients; contour interval is 0.026. Note how the spacing is not linear because of the cosine scaling, (b) correction line grid overlaid on wavefront map: optical axis is in the centre of the mirror, and the 45° line goes through the centre of the mirror.

Fig. 14.
Fig. 14.

Final surface error map from OAP measurement in the FR configuration. Since the alignment errors have been dealt with already, the only error subtracted is tilt.

Equations (1)

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h ( x , y ) = w ( x , y ) 4 cos [ arctan ( z R ' ) R ] λ ,

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