Abstract

Computer generated holograms (CGHs) are used for testing aspherical surfaces. They are also used for certifying null lens systems that are in turn used to test large aspheric mirrors. We demonstrate that, in order to minimize size, a null-corrector-certifying CGH can be located at a ray caustic. This placement minimizes the required size of the CGH and so makes it possible to certify some null correctors that otherwise, due to current size limitations of high-precision CGHs, could not be certified. Fabrication limits of precision CGHs are in the size range of 200–250 mm and one part in 105 in feature placement. Our proof of principle involves a CGH that is about 20mm in diameter with a fabrication tolerance of one part in 104.

© 2005 Optical Society of America

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References

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  1. J. H. Burge, Advanced techniques for measuring primary mirrors for astronomical telescopes, PhD Dissertation, Univ. of Arizona, Optical Sciences Center, Tucson, AZ (1993).
  2. Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
    [CrossRef]
  3. Iwona A. Palusinski and Jose M. Sasian, “Sag and phase descriptions for null corrector certifiers,” Opt. Eng. 43(3), 697–701 (2004).
    [CrossRef]
  4. Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
    [CrossRef]
  5. E.N. Leith and J. Upatneiks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964).
    [CrossRef]
  6. J.D. Armitage and A.W. Lohmann, “Theta modulation in optics,” Appl. Opt 4, 399–403 (1965).
    [CrossRef]
  7. J.R. Fienup, “Color images from computer-generated holograms,” Proc. SPIE 48, 101–105 (1974).
  8. H. Bartelt, “Space multiplexing with computer holograms,” Opt. Commun. 23, 203–206 (1977).
    [CrossRef]
  9. W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, E.D. B.R. Frieden, (Springer-Verlag, Heidelberg, 1980).
  10. Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
    [CrossRef] [PubMed]
  11. Jack D. Gaskill, “Harmonic Analysis”, in Linear Systems, Fourier Transforms, and Optics, (John Wiley and Sons, New York, 1978).
  12. John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
    [CrossRef]

2004 (1)

Iwona A. Palusinski and Jose M. Sasian, “Sag and phase descriptions for null corrector certifiers,” Opt. Eng. 43(3), 697–701 (2004).
[CrossRef]

2003 (2)

Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
[CrossRef] [PubMed]

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

2002 (2)

Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
[CrossRef]

1977 (1)

H. Bartelt, “Space multiplexing with computer holograms,” Opt. Commun. 23, 203–206 (1977).
[CrossRef]

1974 (1)

J.R. Fienup, “Color images from computer-generated holograms,” Proc. SPIE 48, 101–105 (1974).

1965 (1)

J.D. Armitage and A.W. Lohmann, “Theta modulation in optics,” Appl. Opt 4, 399–403 (1965).
[CrossRef]

1964 (1)

Armitage, J.D.

J.D. Armitage and A.W. Lohmann, “Theta modulation in optics,” Appl. Opt 4, 399–403 (1965).
[CrossRef]

Bagwell, Brett

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Bartelt, H.

H. Bartelt, “Space multiplexing with computer holograms,” Opt. Commun. 23, 203–206 (1977).
[CrossRef]

Burge, J. H.

J. H. Burge, Advanced techniques for measuring primary mirrors for astronomical telescopes, PhD Dissertation, Univ. of Arizona, Optical Sciences Center, Tucson, AZ (1993).

Burge, James H.

Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
[CrossRef]

Dallas, W. J.

W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, E.D. B.R. Frieden, (Springer-Verlag, Heidelberg, 1980).

Descour, Michael R.

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Fienup, J.R.

J.R. Fienup, “Color images from computer-generated holograms,” Proc. SPIE 48, 101–105 (1974).

Gaskill, Jack D.

Jack D. Gaskill, “Harmonic Analysis”, in Linear Systems, Fourier Transforms, and Optics, (John Wiley and Sons, New York, 1978).

Jabbour, Ghassan

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Kim, Taehee

Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
[CrossRef]

Kimbrough, Bradley T.

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Lee, Yunwoo

Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
[CrossRef]

Leith, E.N.

Lohmann, A.W.

J.D. Armitage and A.W. Lohmann, “Theta modulation in optics,” Appl. Opt 4, 399–403 (1965).
[CrossRef]

Palusinski, Iwona A.

Iwona A. Palusinski and Jose M. Sasian, “Sag and phase descriptions for null corrector certifiers,” Opt. Eng. 43(3), 697–701 (2004).
[CrossRef]

Pruss, Christof

Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
[CrossRef] [PubMed]

Pruß, Christof

Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Reichelt, Stephan

Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
[CrossRef] [PubMed]

Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Sasian, Jose M.

Iwona A. Palusinski and Jose M. Sasian, “Sag and phase descriptions for null corrector certifiers,” Opt. Eng. 43(3), 697–701 (2004).
[CrossRef]

Tamkin, John M.

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Tiziani, Hans J.

Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
[CrossRef] [PubMed]

Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Upatneiks, J.

Appl. Opt (2)

J.D. Armitage and A.W. Lohmann, “Theta modulation in optics,” Appl. Opt 4, 399–403 (1965).
[CrossRef]

Stephan Reichelt, Christof Pruss, and Hans J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt 42, No. 22, 4468–4479(2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

H. Bartelt, “Space multiplexing with computer holograms,” Opt. Commun. 23, 203–206 (1977).
[CrossRef]

Opt. Eng. (1)

Iwona A. Palusinski and Jose M. Sasian, “Sag and phase descriptions for null corrector certifiers,” Opt. Eng. 43(3), 697–701 (2004).
[CrossRef]

Proc. SPIE (4)

Stephan Reichelt, Christof Pruβ, and Hans J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Taehee Kim, James H. Burge, and Yunwoo Lee, “Measurement of Highly Parabolic Mirror using Computer Generated Hologram,” Proc. SPIE 4778, 119–126 (2002).
[CrossRef]

J.R. Fienup, “Color images from computer-generated holograms,” Proc. SPIE 48, 101–105 (1974).

John M. Tamkin, Brett Bagwell, Bradley T. Kimbrough, Ghassan Jabbour, and Michael R. Descour, “High speed gray scale laser direct write technology for micro-optic fabrication,” Proc. SPIE 4984, 210–218 (2003).
[CrossRef]

Other (3)

Jack D. Gaskill, “Harmonic Analysis”, in Linear Systems, Fourier Transforms, and Optics, (John Wiley and Sons, New York, 1978).

W. J. Dallas, “Computer-Generated Holograms,” in The Computer in Optical Research, E.D. B.R. Frieden, (Springer-Verlag, Heidelberg, 1980).

J. H. Burge, Advanced techniques for measuring primary mirrors for astronomical telescopes, PhD Dissertation, Univ. of Arizona, Optical Sciences Center, Tucson, AZ (1993).

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Figures (5)

Fig. 1.
Fig. 1.

The caustic region of a tilted spheical mirror.

Fig. 2.
Fig. 2.

Experimental setup to demonstrate a multiplexed CGH.

Fig. 3.
Fig. 3.

Multiplexed CGH pattern

Fig. 4.
Fig. 4.

The blocked diffraction orders

Fig. 5.
Fig. 5.

Interferograms of the CGH-Spherical mirror system.

Tables (1)

Tables Icon

Table 1. Error analysis of the experimental system

Equations (4)

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Sq ( p ) = 1 2 m = = + sinc ( m 2 ) · exp ( 2 π imp )
CGH j ( r ) = Sq ( p j ) = 1 2 m = + sinc ( m 2 ) · exp ( 2 π im ρ j r ) exp ( im ϕ j )
CGH mul ( r ) = CGH 1 ( r ) CGH 2 ( r ) = Sq ( p 1 ) Sq ( p 2 ) = Sq [ ρ 1 r + ϕ 1 ( r ) 2 π ] Sq [ ρ 2 r + ϕ 2 ( r ) 2 π ]
= 1 4 m = + n = + sinc ( m 2 ) sinc ( n 2 ) · exp [ 2 π i ( m ρ 1 + n ρ 2 ) r ] exp [ i ( m ϕ 1 + n ϕ 2 ) ]

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