Abstract

It is shown that the lens count in a Fourier holographic projector can be reduced by encoding the equivalent lens power in sets of Fresnel holograms. By using appropriately calculated Fresnel holograms in a reflective configuration to effectively share a lens between the beam-expansion and demagnification stages of a holographic projector, a reduction in lens count from four to one is demonstrated.

© 2010 Optical Society of America

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References

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2010

E. Buckley, J. Display Technol. 6, 1 (2010).
[CrossRef]

2008

2006

2002

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

1996

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 73–75.

1995

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 114, 230 (1995).
[CrossRef]

1994

Bernet, S.

Bryngdahl, O.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 114, 230 (1995).
[CrossRef]

Buckley, E.

E. Buckley, J. Display Technol. 6, 1 (2010).
[CrossRef]

E. Buckley, in Proceedings SID Symposium 2008 (2008), paper 70.2, pp. 1074–1078.
[CrossRef]

E. Buckley, A. Cable, T. Wilkinson, and N. Lawrence, Appl. Opt. 45, 7334 (2006).
[CrossRef] [PubMed]

Cable, A.

Christmas, J.

Collings, N.

Crossland, W. A.

Davey, A.

Dorsch, R.

Fetthauer, F.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 114, 230 (1995).
[CrossRef]

Georgiou, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 73–75.

Jesacher, A.

Jeziorska-Chapman, A.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

Kolodziejczyk, A.

Lawrence, N.

Lohmann, A. W.

Makowski, M.

Maurer, C.

Moore, J.

Ritsch-Marte, M.

Schnars, U.

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

Schwaighofer, A.

Sinzinger, S.

Sypek, M.

Weissbach, S.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 114, 230 (1995).
[CrossRef]

Wilkinson, T.

Appl. Opt.

J. Display Technol.

E. Buckley, J. Display Technol. 6, 1 (2010).
[CrossRef]

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

Opt. Commun.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 114, 230 (1995).
[CrossRef]

Opt. Express

Other

E. Buckley, in Proceedings SID Symposium 2008 (2008), paper 70.2, pp. 1074–1078.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 73–75.

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Figures (5)

Fig. 1
Fig. 1

Fraunhofer diffraction geometry. When the hologram h u v is illuminated by coherent light, the image F x y is formed in the back focal plane of a lens by Fraunhofer diffraction.

Fig. 2
Fig. 2

Optical design for a simple holographic projector. Beam expansion of the laser diode is performed by lenses L 1 and L 2 , and demagnification by lenses L 3 and L 4 .

Fig. 3
Fig. 3

Fresnel diffraction geometry. When the hologram h u v is illuminated by coherent light, the RPF F x y is formed at a distance z by Fresnel (or near-field) diffraction.

Fig. 4
Fig. 4

Experimental results of the variable demagnification principle described. The scale of the RPFs (a) to (c) is determined by the effective focal length z of N = 24 sets of Fresnel holograms displayed on a dynamically addressable SLM.

Fig. 5
Fig. 5

Optical setup (a) and resultant RPF (b) of a lens-sharing projector design, utilizing a Fresnel hologram with z = 100 mm displayed on the SLM. Polarizers are omitted for clarity. The demagnification caused by the combination of L 4 and the hologram causes optical enlargement of the RPF by a factor of approximately 3.

Equations (4)

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

F x y = F [ h u v ] .
F x y = FR [ h u v ] = F x y ( 1 ) · F [ f u v ( 2 ) h u v ] ,
F x y ( 1 ) = Δ x Δ y j λ z exp j 2 π z λ exp j π λ z [ ( x N Δ x ) 2 + ( y M Δ y ) 2 ] ,
f u v ( 2 ) = exp j π λ z ( u 2 Δ x + v 2 Δ y ) .

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