Abstract

A modified phase contrast method is described for the fabrication of holographic optical elements with in-line diffraction patterns. In this method, a liquid crystal phase modulator is addressed by computer-generated holograms to achieve variable phase gratings. The phase gratings are imaged onto photosensitive material by a phase contrast method without a Fourier filter. We show the analytical treatment of the modified phase contrast method and demonstrate the application in holographic recording.

© 2007 Optical Society of America

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References

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  1. R. C. Fairchild and J. R. Fienup, Opt. Eng. (Bellingham) 21, 133 (1982).
  2. H. Bartelt and S. K. Case, Appl. Opt. 21, 2886 (1982).
    [CrossRef] [PubMed]
  3. S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
    [CrossRef]
  4. C. Hofmann, Die Optische Abbildung (Akademische Verlagsgesellschaft Geest & Portig, 1980), p. 380.
  5. J. Glückstad and P. C. Mogensen, Appl. Opt. 40, 268 (2001).
    [CrossRef]
  6. H. H. Hopkins, Proc. Phys. Soc. London, Sect. B 66, 331 (1953).
    [CrossRef]
  7. D. Malacara, Optical Shop Testing (Wiley, 1992).
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

2006 (1)

S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
[CrossRef]

2001 (1)

1982 (2)

R. C. Fairchild and J. R. Fienup, Opt. Eng. (Bellingham) 21, 133 (1982).

H. Bartelt and S. K. Case, Appl. Opt. 21, 2886 (1982).
[CrossRef] [PubMed]

1953 (1)

H. H. Hopkins, Proc. Phys. Soc. London, Sect. B 66, 331 (1953).
[CrossRef]

Bartelt, H.

Case, S. K.

Fairchild, R. C.

R. C. Fairchild and J. R. Fienup, Opt. Eng. (Bellingham) 21, 133 (1982).

Fienup, J. R.

R. C. Fairchild and J. R. Fienup, Opt. Eng. (Bellingham) 21, 133 (1982).

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hofmann, C.

C. Hofmann, Die Optische Abbildung (Akademische Verlagsgesellschaft Geest & Portig, 1980), p. 380.

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. London, Sect. B 66, 331 (1953).
[CrossRef]

Krüger, S.

S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 1992).

Mogensen, P. C.

Osten, S.

S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
[CrossRef]

Steinhoff, A.

S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
[CrossRef]

Appl. Opt. (2)

Opt. Eng. (Bellingham) (1)

R. C. Fairchild and J. R. Fienup, Opt. Eng. (Bellingham) 21, 133 (1982).

Proc. Phys. Soc. London, Sect. B (1)

H. H. Hopkins, Proc. Phys. Soc. London, Sect. B 66, 331 (1953).
[CrossRef]

Tech. Mess. (1)

S. Osten, S. Krüger, and A. Steinhoff, Tech. Mess. 73, 149 (2006).
[CrossRef]

Other (3)

C. Hofmann, Die Optische Abbildung (Akademische Verlagsgesellschaft Geest & Portig, 1980), p. 380.

D. Malacara, Optical Shop Testing (Wiley, 1992).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (6)

Fig. 1
Fig. 1

Holographic setup for recording HOEs with CGHs.

Fig. 2
Fig. 2

Phase contrast setup for imaging a LCoS display: (a) phase pattern visualized by a gray-level picture, (b) intensity pattern of the OWF in the observation plane without the RWF from the mirror, and (c) intensity pattern of the OWF superposed with the RWF.

Fig. 3
Fig. 3

Intensity curve of the object wave, reference wave, and the synthetic RWF: (a) the PZT mirror was moved from 0 to 543.5 nm . (b) To test the repeatability of the setup, the PZT mirror was removed, replaced, and realigned. The intensity curves were recorded again while moving the mirror.

Fig. 4
Fig. 4

Phase disturbance to intensity mapping as a function of the axial phase difference δ.

Fig. 5
Fig. 5

Phase contrast imaging of a 0 and π striped phase grating for several axial phase differences δ.

Fig. 6
Fig. 6

Results of recorded HOEs: (a) and (c) diffraction patterns reconstructed by the LCoS display, (b) and (d) diffraction patterns reconstructed by the recorded HOEs.

Equations (4)

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I ( x , y ) = U ( x , y ) U * ( x , y ) = circ ( r Δ r ) 2 exp [ i ϕ ( x , y ) ] exp [ i ϕ ( x , y ) ] = circ ( r Δ r ) 2 ,
U ( x , y ) = circ ( r Δ r ) ( exp [ i ϕ ( x , y ) ] + exp [ i δ ] ) .
I ( x , y ) = circ ( r Δ r ) 2 ( 2 + exp [ i ϕ ( x , y ) ] exp [ i δ ] + exp [ i ϕ ( x , y ) ] exp [ i δ ] ) = circ ( r Δ r ) 2 ( 2 + 2 cos ϕ ( x , y ) cos δ + 2 sin ϕ ( x , y ) sin δ ) .
I ( x , y ) = circ ( r Δ r ) 2 [ 2 2 cos ϕ ( x , y ) ] .

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