Abstract

We introduce an approach to generate holographic data for diffractive optical elements fabricated by means of a diamond-turning process. The aim is to project a predefined intensity distribution in the far-field domain of the corresponding diffractive surface. The method takes into consideration typical constraints that result from the fabrication process, such as the spiral path of the turning tool and the fact that only the phase distribution of the incident light can be manipulated.

© 2009 Optical Society of America

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References

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  1. W. Jiang, D. L. Shealy, and K. M. Baker, “Development and testing of a holographic projection system,” Appl. Opt. 35, 5994-5998 (1996).
    [CrossRef] [PubMed]
  2. J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
    [CrossRef]
  3. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
    [CrossRef]
  4. G. S. Spagnolo and D. Ambrosini, “Diffractive optical element-based profilometer for surface inspection,” Opt. Eng. 40, 44-52 (2001).
    [CrossRef]
  5. S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470-2472 (1996).
    [CrossRef]
  6. E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).
  7. C. G. Blough, M. Rossi, S. K. Mack, and R. L. Michaels, “Single-point diamond turning and replication of visible and near-infrared diffractive optical elements,” Appl. Opt. 36, 4648-4654 (1997).
    [CrossRef] [PubMed]
  8. L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
    [CrossRef]
  9. J. Goodman, Introduction To Fourier Optics, 2nd ed (McGraw-Hill, 1996).
  10. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).
  11. E. Whittaker, “On the functions which are represented by the expansion of the interpolation theory,” Proc. R. Soc. Edinburgh Sect. A 35, 181-194 (1915).
  12. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
    [CrossRef]

2008 (1)

J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
[CrossRef]

2006 (1)

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

2001 (2)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

G. S. Spagnolo and D. Ambrosini, “Diffractive optical element-based profilometer for surface inspection,” Opt. Eng. 40, 44-52 (2001).
[CrossRef]

1997 (1)

1996 (2)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

1915 (1)

E. Whittaker, “On the functions which are represented by the expansion of the interpolation theory,” Proc. R. Soc. Edinburgh Sect. A 35, 181-194 (1915).

Ambrosini, D.

G. S. Spagnolo and D. Ambrosini, “Diffractive optical element-based profilometer for surface inspection,” Opt. Eng. 40, 44-52 (2001).
[CrossRef]

Baker, K. M.

Benatar, A.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Blough, C. G.

Brinksmeier, E.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Cao, Q.

J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
[CrossRef]

Chen, Y.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Dankwart, C.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Falldorf, C.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Gläbe, R.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Goodman, J.

J. Goodman, Introduction To Fourier Optics, 2nd ed (McGraw-Hill, 1996).

Grewell, D. A.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Grier, D. G.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Huang, C.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Jahns, J.

J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
[CrossRef]

Jiang, W.

Lai, S.

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470-2472 (1996).
[CrossRef]

Li, L.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Lünemann, B.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Mack, S. K.

Michaels, R. L.

Rossi, M.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

Shealy, D. L.

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Sinzinger, S.

J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
[CrossRef]

Spagnolo, G. S.

G. S. Spagnolo and D. Ambrosini, “Diffractive optical element-based profilometer for surface inspection,” Opt. Eng. 40, 44-52 (2001).
[CrossRef]

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

von Kopylow, C.

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

Whittaker, E.

E. Whittaker, “On the functions which are represented by the expansion of the interpolation theory,” Proc. R. Soc. Edinburgh Sect. A 35, 181-194 (1915).

Yi, A. Y.

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Appl. Opt. (2)

Laser Photon. Rev. (1)

J. Jahns, Q. Cao, and S. Sinzinger, “Micro- and nanooptics--an overview,” Laser Photon. Rev. 2, 249-263 (2008).
[CrossRef]

Opt. Eng. (3)

G. S. Spagnolo and D. Ambrosini, “Diffractive optical element-based profilometer for surface inspection,” Opt. Eng. 40, 44-52 (2001).
[CrossRef]

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470-2472 (1996).
[CrossRef]

L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, “Fabrication of diffractive optics by use of slow tool servo diamond turning process,” Opt. Eng. 45, 113401(2006).
[CrossRef]

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

Proc. R. Soc. Edinburgh Sect. A (1)

E. Whittaker, “On the functions which are represented by the expansion of the interpolation theory,” Proc. R. Soc. Edinburgh Sect. A 35, 181-194 (1915).

Rev. Sci. Instrum. (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Other (2)

E. Brinksmeier, B. Lünemann, R. Gläbe, C. von Kopylow, C. Falldorf, and C. Dankwart, “Open loop fast tool servo with nanometer accuracy for diamond machining of diffractive structures,” in Proceedings of the 23rd American Society for Precision Engineering Annual Meeting (ASPE) and the 12th International Conference on Precision Engineering (ICPE) (American Society for Precision Engineering, 2008).

J. Goodman, Introduction To Fourier Optics, 2nd ed (McGraw-Hill, 1996).

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Figures (2)

Fig. 1
Fig. 1

(a) Coherent light incident on a DOE fabricated by the diamond-turning process. The aim is to achieve a predefined intensity distribution in the back focal plane of the lens. (b) Example of a diamond-turned DOE (diameter d = 20 mm ).

Fig. 2
Fig. 2

Example of application: (a) logo to be projected across the far field, (b) close detail ( 50 × 40 points) of the calculated phase distribution arg { t [ m , n ] } of the discrete complex transmittance, (c) detail ( 250 μm × 200 μm ) of the height profile of the fabricated surface, and (d) observed intensity in the back focal plane of the lens.

Equations (8)

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U ( u ) = 1 i λ f · F { U ( x ) } ( u λ f ) .
t k + 1 ( x ) = P { F 1 { P { F { u 0 · t k ( x ) } } · | U ( u ) | } } .
t [ m , n ] = t ( x ) · m = 0 M n = 0 N δ ( m · Δ x x i , n · Δ x x j ) .
1 B = Δ x λ f .
t R ( x ) = m = n = t [ m , n ] · sinc [ π ( x i / Δ x m ) ] sinc [ π ( x j / Δ x n ) ] .
t R [ l ] = t R ( x ) · l = 0 L δ ( x x l ) .
x l = l Δ r R ( cos [ 2 π R l ] sin [ 2 π R l ] ) ,
t R [ l ] = exp { i 4 π λ h [ l ] } .

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