Abstract

We demonstrate the precise figure measurement of a one-inch (25.4 mm) diamond-turned 90° off-axis commercial-quality parabolic mirror. The test is carried out with a phase-shifting Fizeau interferometer fitted with a spherical reference surface, auxiliary components and a flat return mirror. We present a detailed and systematic appraisal of the necessary steps for alignment and calibration of the instrument and the alignment of the parabolic mirror. Alignment errors and interferometric sensitivity variations are characterised and corrected, and the results give some insight into the diamond-turning process.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. N. Wilson, Reflecting Telescope Optics (Springer, Heidelberg, 2004), Chap. 1.
  2. D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 1992), Appendix 2.
  3. R. N. Shagam, R. E. Sladky, and J. C. Wyant, "Optical figure inspection of diamond-turned metal mirrors," Opt. Eng. 16, 375-380 (1977).
  4. J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
    [CrossRef]
  5. K. J. Dana and J. Wang, "Device for convenient measurement of spatially varying bidirectional reflectance," J. Opt. Soc. Am. A 21, 1-12 (2004).
    [CrossRef]
  6. H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
    [CrossRef]
  7. R. E. Parks, C. J. Evans, and L. Shao, "Test of a slow off-axis parabola at its center of curvature," Appl. Opt. 34, 7174-7178 (1995).
    [CrossRef] [PubMed]
  8. Y. Pi and P. J. Reardon, "Determining parent radius and conic of an off-axis segment interferometrically with a spherical reference wave," Opt. Lett. 32, 1063-1065 (2007).
    [CrossRef] [PubMed]
  9. R. E. Parks, C. J. Evans, and L. Shao, "Calibration of interferometer transmission spheres," in Optical Fabrication and Testing Workshop, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 80-83.
  10. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, "A simple ball averager for reference sphere calibrations," Proc. SPIE 5869, 58690S (2005).
    [CrossRef]
  11. R. E. Parks, "Alignment of off-axis conic mirrors," in Optical Fabrication and Testing, OSA Technical Digest Series (Optical Society of America, 1980), paper TuB4.
  12. C. Bond and C. A. Pipan, "How to align an off-axis parabolic mirror," Proc. SPIE 1113, 236-248 (1989).
  13. L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).
  14. L. C. Maxey, "Automated interferometric alignment system for paraboloidal mirrors," US Patent 5249033, 1-14 (1993).
  15. 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.
  16. 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]
  17. K. Creath and J. C. Wyant, "Absolute measurement of surface roughness," Appl. Opt. 29, 3823-3827 (1990).
    [CrossRef] [PubMed]
  18. B. F. Oreb, D. I. Farrant, C. J. Walsh, G. Forbes, and P. S. Fairman, "Calibration of a 300-mm-aperture phase-shifting Fizeau interferometer," Appl. Opt. 39, 5161-5171 (2000).
    [CrossRef]
  19. M. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001).
    [CrossRef]
  20. E. W. Weisstein, "Curvature," in MathWorld A. Wolfram Web Resource, http://mathworld.wolfram.com/Curvature.html.
  21. J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
    [CrossRef]
  22. J. Schwider and R. Burow, "Wave aberrations caused by misalignments of aspherics and their elimination," Opt. Appl. 9, 33-38 (1979).
  23. B. Dörband and H. J. Tiziani, "Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors," Appl. Opt. 24, 2604-2611 (1985).
    [CrossRef] [PubMed]
  24. T. Dresel, N. Lindlein, and J. Schwider, "Empirical strategy for detection and removal of misalignment aberrations in interferometry," Optik 112, 304-308 (2001).
    [CrossRef]

2008

J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
[CrossRef]

2007

2005

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

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]

2004

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]

2000

1999

J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
[CrossRef]

1997

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

1995

1992

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

1990

1989

C. Bond and C. A. Pipan, "How to align an off-axis parabolic mirror," Proc. SPIE 1113, 236-248 (1989).

1985

1979

J. Schwider and R. Burow, "Wave aberrations caused by misalignments of aspherics and their elimination," Opt. Appl. 9, 33-38 (1979).

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).

Bond, C.

C. Bond and C. A. Pipan, "How to align an off-axis parabolic mirror," Proc. SPIE 1113, 236-248 (1989).

Bot, A.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Bramble, A.

J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
[CrossRef]

Burke, J.

J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
[CrossRef]

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]

Burow, R.

J. Schwider and R. Burow, "Wave aberrations caused by misalignments of aspherics and their elimination," Opt. Appl. 9, 33-38 (1979).

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]

Creath, K.

Cuttino, J. F.

J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
[CrossRef]

Dana, K. J.

de Haas, E.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Dörband, B.

Dorlandt, P. W. F.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[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]

Dress, W. B.

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

Evans, C. J.

Fairman, P. S.

Farrant, D. I.

Forbes, G.

Griesmann, U.

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

Jenniskens, H. G.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Kleyn, A. W.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Küchel, M.

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

Lindlein, N.

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

Maxey, L. C.

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

Miller, A. C.

J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
[CrossRef]

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]

Oreb, B. F.

Parks, R. E.

Pi, Y.

Pipan, C. A.

C. Bond and C. A. Pipan, "How to align an off-axis parabolic mirror," Proc. SPIE 1113, 236-248 (1989).

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]

Reardon, P. J.

Rogers, J.

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

Schinstock, D. E.

J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
[CrossRef]

Schwider, J.

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

J. Schwider and R. Burow, "Wave aberrations caused by misalignments of aspherics and their elimination," Opt. Appl. 9, 33-38 (1979).

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).

Shao, L.

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).

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]

Tiziani, H. J.

Tobin, K. W.

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

van Essenberg, W.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Walsh, C. J.

Wang, J.

Wang, K.

J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
[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.

K. Creath and J. C. Wyant, "Absolute measurement of surface roughness," Appl. Opt. 29, 3823-3827 (1990).
[CrossRef] [PubMed]

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

Appl. Opt.

IEEE Trans. Mechatronics

J. F. Cuttino, A. C. Miller Jr., and D. E. Schinstock, "Performance optimization of a fast tool servo for single-point diamond turning machines," IEEE Trans. Mechatronics 4, 169-179 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

H. G. Jenniskens, A. Bot, P. W. F. Dorlandt, W. van Essenberg, E. de Haas, and A. W. Kleyn, "An ultrahigh vacuum (UHV) apparatus to study the interaction between adsorbates and photons," Meas. Sci. Technol. 8, 1313-1322 (1997).
[CrossRef]

Opt. Appl.

J. Schwider and R. Burow, "Wave aberrations caused by misalignments of aspherics and their elimination," Opt. Appl. 9, 33-38 (1979).

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. 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

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]

J. Burke, K. Wang, and A. Bramble, "Testing of a diamond-turned off-axis parabolic mirror," Proc. SPIE 7063, 706312 (2008).
[CrossRef]

C. Bond and C. A. Pipan, "How to align an off-axis parabolic mirror," Proc. SPIE 1113, 236-248 (1989).

L. C. Maxey, W. B. Dress, J. Rogers, and K. W. Tobin, "Automated alignment system for aspheric mirrors," Proc. SPIE 1776, 130-139 (1992).

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

Other

R. E. Parks, "Alignment of off-axis conic mirrors," in Optical Fabrication and Testing, OSA Technical Digest Series (Optical Society of America, 1980), paper TuB4.

R. E. Parks, C. J. Evans, and L. Shao, "Calibration of interferometer transmission spheres," in Optical Fabrication and Testing Workshop, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 80-83.

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

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

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

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.

E. W. Weisstein, "Curvature," in MathWorld A. Wolfram Web Resource, http://mathworld.wolfram.com/Curvature.html.

Supplementary Material (1)

» Media 1: MOV (3680 KB)     

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 (16)

Fig. 1.
Fig. 1.

(a) schematic illustration of SR paraboloid test; (b) hardware in the practical set-up.

Fig. 2.
Fig. 2.

(a) return flat located at focus of converging wavefront emerging from the transmission sphere; (b) comatic interference pattern after removal of all tilts.

Fig. 3.
Fig. 3.

(a) error map between an individual ball measurement and the average of all measurements (rms 4.1 nm, PV 27.1 nm). (b) final calibration file after averaging over 100 random ball positions (rms 2.7 nm, PV 29.9 nm). Red dot: centre of transmission sphere; white dot: centre of aperture (see text). Tilt and power terms are removed from the phase maps.

Fig. 4.
Fig. 4.

Figure map of λ/100 (PV 5.9 nm) mirror.

Fig. 5.
Fig. 5.

Definition of paraboloid alignment coordinate system. Dashed line: OAP’s central line of symmetry. Right angles between the axes are indicated by solid black or white lines.

Fig. 6.
Fig. 6.

Set-up with cube corner for retroreflection of nominally collimated beam.

Fig. 7.
Fig. 7.

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

Fig. 8.
Fig. 8.

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

Fig. 9.
Fig. 9.

(a) View onto the OAP from the “collimated” side through the cube corner; red lines mark 6-ray pattern imparted to wavefront; (b) view into the OAP from the “spherical” side, out of the interferometer.

Fig. 10.
Fig. 10.

(a) simulated interferogram showing image distortion. Misalignment fringes have been added solely to make the 6-ray pattern more visible. (b) plot of OAP parameters. The curvature (red line) drops fastest at 30° off-axis angle; the derivative of the curvature (blue line) has a minimum where the surface slope (black line) equals 0.5. Since C(r) is in mm-1 and ∂C/∂r is in mm-2, the curves have been normalised for a dimensionless y axis. Region of the OAP for this study is overlaid in grey.

Fig. 11.
Fig. 11.

(a) Brightness distribution in the object wave; recorded with reference sphere tilted away from optical axis and hence, no fringes. (b) Phase map of well-aligned OAP with cube corner. Note the right-left symmetry (with distortion) and the top-bottom symmetry (without distortion) in the phase map.

Fig. 12.
Fig. 12.

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

Fig. 13.
Fig. 13.

(a) interferogram of final measurement; (b) wavefront map optimised for displacement errors. Note the difference to Fig. 11(b). Surface features are interpreted below Fig. 16.

Fig. 14.
Fig. 14.

(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) angle co-ordinate grid overlaid on wavefront map: optical axis is not in the centre of the mirror, and each radial division is roughly equivalent to 1°.

Fig. 15.
Fig. 15.

Proportional error maps caused by sensitivity variations. (a) for Z3 = 1 wave (Z3 subtracted after simulation); (b) for Z4 = 1 wave (Z4 subtracted after simulation); (c) for Z5 = 1 wave (Z5 subtracted after simulation).

Fig. 16.
Fig. 16.

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

Equations (10)

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

σ meas = σ TS 2 + σ ball 2 ,
σ RDF = σ TS 2 + σ ball 2 N ,
σ ball N σ single = σ meas 1 meas 2 2 ,
σ single = σ all meas i ,
C ( r ) = 2 p ( 1 + ( 2 p r ) 2 ) 1.5 ,
C r = 24 p 3 r ( 1 + ( 2 p r ) 2 ) 2.5 ,
Δ Z k , n = ( Δ Z 3 ( Δ r ) Δ Z N ( Δ r ) Δ Z 3 ( Δ z ) Δ Z N ( Δ z ) Δ Z 3 ( Δ t ) Δ Z N ( Δ t ) ) ,
n = 3 N ( Z m , n Δ r · Δ Z r , n Δ z · Δ Z z , n Δ t · Δ Z t , n ) 2 = min ,
h ( x , y ) = w ( x , y ) 4 cos [ arctan ( z x ' ) x ] λ ,
h ( x , y ) = w ( x , y ) c ( x ) ,

Metrics