Abstract

A new type of optical instrument, the curved hologram, is introduced that allows us the unique opportunity to independently control its spatial phase function and its shape (whereas in reflecting or refracting optical elements the shape uniquely determines the spatial phase function). We show how proper design of the hologram shape (using a simple analytic procedure) yields perfect uniform collimation and also collimation and concentration of diffuse (monochromatic) light at the thermodynamic limit of brightness conservation. The results of our experimental demonstration as well as those of our numerical ray-tracing simulations verify our design.

© 2002 Optical Society of America

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References

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  1. H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.
  2. I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 161–226.
  3. N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.
  5. W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
    [CrossRef]
  6. W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
    [CrossRef]
  7. N. Davidson, A. A. Friesem, “One-dimensional concentration of diffuse light,” Opt. Commun. 99, 162–166 (1993).
    [CrossRef]
  8. R. Winston, W. T. Welford, High Collection Nonimaging Optics (Academic, New York, 1989).
  9. H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
    [CrossRef]
  10. M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).
    [CrossRef]
  11. N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
    [CrossRef]
  12. N. Davidson, L. Khaykovich, E. Hasman, “High-resolution spectrometry for diffuse light by use of anamorphic concentration,” Opt. Lett. 24, 1835–1837 (1999).
    [CrossRef]
  13. D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
  14. N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).
  15. S. Yamaguchi, T. Kobayashi, Y. Saito, K. Chiba, “Efficient Nd:YAG laser end pumped by a high-power multistripe laser-diode bar with multiprism array coupling,” Appl. Opt. 35, 1430–1435 (1996).
    [CrossRef] [PubMed]
  16. D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
    [CrossRef]

2001 (3)

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

1999 (2)

N. Davidson, L. Khaykovich, E. Hasman, “High-resolution spectrometry for diffuse light by use of anamorphic concentration,” Opt. Lett. 24, 1835–1837 (1999).
[CrossRef]

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).
[CrossRef]

1997 (1)

D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
[CrossRef]

1996 (1)

1994 (1)

1993 (1)

N. Davidson, A. A. Friesem, “One-dimensional concentration of diffuse light,” Opt. Commun. 99, 162–166 (1993).
[CrossRef]

1975 (1)

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

1973 (1)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

Bassett, I. M.

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 161–226.

Berry, M. V.

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).
[CrossRef]

Bodenschatz, E.

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).
[CrossRef]

Bokor, N.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

Bortz, J. C.

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

Chiba, K.

Davidson, N.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

N. Davidson, L. Khaykovich, E. Hasman, “High-resolution spectrometry for diffuse light by use of anamorphic concentration,” Opt. Lett. 24, 1835–1837 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, “One-dimensional concentration of diffuse light,” Opt. Commun. 99, 162–166 (1993).
[CrossRef]

Friesem, A. A.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

N. Davidson, A. A. Friesem, “One-dimensional concentration of diffuse light,” Opt. Commun. 99, 162–166 (1993).
[CrossRef]

Gabor, D.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.

Hasman, E.

Keming, D.

D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
[CrossRef]

Khaykovich, L.

Kobayashi, T.

Loosen, P.

D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
[CrossRef]

Muschaweck, J.

H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.

Ries, H.

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

Ries, H. R.

H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.

H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
[CrossRef]

Saito, Y.

Scherrer, P.

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

Shatz, N. E.

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

Shechter, R.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

Timinger, A.

H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.

Welford, W. T.

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

R. Winston, W. T. Welford, High Collection Nonimaging Optics (Academic, New York, 1989).

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 161–226.

Winston, R.

H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
[CrossRef]

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 161–226.

R. Winston, W. T. Welford, High Collection Nonimaging Optics (Academic, New York, 1989).

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

Yamaguchi, S.

Yan, L.

D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (5)

D. Keming, L. Yan, P. Loosen, “Nd:YAG slab laser end-pumped by laser-diode stacks and its beam shaping,” Opt. Commun. 140, 53–56 (1997).
[CrossRef]

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–147 (2001).
[CrossRef]

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

N. Davidson, A. A. Friesem, “One-dimensional concentration of diffuse light,” Opt. Commun. 99, 162–166 (1993).
[CrossRef]

Opt. Lett. (1)

Opt. Photon. News (1)

H. R. Ries, J. Muschaweck, A. Timinger, “New methods of reflector design,” Opt. Photon. News, August2001, pp. 46–49.

Other (5)

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 161–226.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

R. Winston, W. T. Welford, High Collection Nonimaging Optics (Academic, New York, 1989).

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.

N. E. Shatz, J. C. Bortz, H. Ries, P. Scherrer, R. Winston, “Nonrotationally symmetric nonimaging systems that overcome the flux-transfer performance limit imposed by skewness conservation,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 76–85 (1997).

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Figures (7)

Fig. 1
Fig. 1

(a) Recording and (b) readout geometry of a curved holographic collimator of arbitrary shape Z(X). β is the angle between the direction of a reconstructing ray and the Z axis. The corresponding coordinates of the hologram surface are X(β) and Z(β).

Fig. 2
Fig. 2

Sections of two collimator shapes for an isotropic source (illustrated by a uniform angular density of emerging rays) with the same paraxial focal length F. (a) holographic (UC), described by Eq. (4); collimated rays are equally spaced, indicating uniform intensity of the collimated beam. (b) (PR); the spacing between collimated rays increases for larger X, indicating a reduction in intensity.

Fig. 3
Fig. 3

Calculated intensity distributions for an isotropic source collimated by a UC (solid line) and a PR (dotted curve), showing a uniform collimated intensity in the case of the UC and a nonuniform intensity in case of the PR [as shown schematically in the ray diagrams in Figs. 2(a) and 2(b)].

Fig. 4
Fig. 4

Diffuse-light concentration onto a small cylindrical target by (a) the UC and (b) the PR. For the PR the reflected-light cones have the same angular spread as the incoming-light cones, resulting in poor concentration for large β. For the UC, for β0 the diffracted-light cones are narrower than the incoming-light cones (2α2α), resulting in ideal concentration for all β.

Fig. 5
Fig. 5

Calculated normalized concentration ratio onto a small cylindrical target as a function of |βmax| for the UC (solid line) and the PR (dotted curve) with incoming half-divergence angle α<5°, indicating that the UC reaches the thermodynamic limit of concentration for |βmax|180°, whereas the optimum performance of the PR is 1/π worse than the theoretical limit.

Fig. 6
Fig. 6

Experimental data for characterizing the performance of the UC as a diffuse-light concentrator onto a small cylindrical target. The measured light intensity not blocked by the cylindrical target as a function of the illumination angle (diamonds) shows good agreement with the theoretical calculations for the UC (solid curve). Also included in the figure is the theoretical graph for the PR (broken curve), showing poor performance of the PR as a diffuse-light concentrator. Note that any measured intensity below the ideal cut angle of 4.3° results from nonideal concentration.

Fig. 7
Fig. 7

UC profiles for small Lambertian sources of different shapes located at (X=0, Z=0). The collimator profiles correspond to the following source shapes: one sided (vertical) flat source (solid curve), double sided (horizontal) flat source (dashed curve), and isotropic source (dotted curve). All collimators have the same paraxial focal length F and extend to -180°<β<+180° (except the one-sided flat source, which is limited to -90°<β<+90°).

Equations (4)

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S(β)dβ=I(X)dX,
dX/dβ=FS(β),
Z(β)=X(β)/tan β.
Z(X)=X/tan(X/F).

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