Abstract

A proposal to dynamically compensate chromatic aberration of a programmable phase Fresnel lens displayed on a liquid crystal device and working under broadband illumination is presented. It is based on time multiplexing a set of lenses, designed with a common focal length for different wavelengths, and a tunable spectral filter that makes each sublens work almost monochromatically. Both the tunable filter and the sublens displayed by the spatial light modulator are synchronized. The whole set of sublenses are displayed within the integration time of the sensor. As a result the central order focalization has a unique location at the focal plane and it is common for all selected wavelengths. Transversal chromatic aberration of the polychromatic point spread function is reduced by properly adjusting the pupil size of each sublens. Longitudinal chromatic aberration is compensated by making depth of focus curves coincident for the selected wavelengths. Experimental results are in very good agreement with theory.

© 2006 Optical Society of America

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References

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  1. D. Faklis, G. M. Morris, "Broadband imaging with holographic lenses," Opt. Eng. 28, 592-598 (1989).
  2. P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, and A. W. Lohmann, "All-incoherent dispersion- compensated optical correlator," Opt. Lett. 24, 1331-1333 (1999).
    [CrossRef]
  3. V. Laude, "Twisted-nematic liquid-crystal pixilated active lens," Opt. Commun. 153, 134-152 (1998).
    [CrossRef]
  4. A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, "Achromatic diffractive lens written onto a liquid cristal display," Opt. Lett. 31, 392-394 (2006).
    [CrossRef] [PubMed]
  5. M. S. Millán, J. Otón, E. Pérez-Cabré, "Chromatic compensation of programmable Fresnel lenses," Opt. Express 14, 6226-6242 (2006)
    [CrossRef] [PubMed]
  6. J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
    [CrossRef]
  7. D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, "Multiple imaging phase-encoded optical elements, written as programmable spatial light modulators," Appl. Opt. 29, 2505-2509 (1990).
    [CrossRef] [PubMed]
  8. http://www.cri-inc.com">http://www.cri-inc.com.
  9. R. D. Juday, "Optical realizable filters and the minimum Euclidean distance principle," Appl. Opt. 32, 5100-5111 (1993).
    [CrossRef] [PubMed]
  10. I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
    [CrossRef]

2006 (2)

1999 (1)

1998 (1)

V. Laude, "Twisted-nematic liquid-crystal pixilated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

1995 (1)

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

1993 (1)

1990 (1)

1989 (1)

D. Faklis, G. M. Morris, "Broadband imaging with holographic lenses," Opt. Eng. 28, 592-598 (1989).

1986 (1)

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Altamirano, J. H.

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Andrés, P.

Bescós, J.

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Campos, J.

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, "Achromatic diffractive lens written onto a liquid cristal display," Opt. Lett. 31, 392-394 (2006).
[CrossRef] [PubMed]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

Climent, V.

Cottrell, D. M.

Davis, J. A.

Faklis, D.

D. Faklis, G. M. Morris, "Broadband imaging with holographic lenses," Opt. Eng. 28, 592-598 (1989).

Gorecki, C.

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

Hedman, T. R.

Iemmi, C.

Juday, R. D.

Lancis, J.

Laude, V.

V. Laude, "Twisted-nematic liquid-crystal pixilated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

Lilly, R. A.

Lohmann, A. W.

Márquez, A.

Millán, M. S.

Mínguez-Vega, G.

Moreno, I.

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

Morris, G. M.

D. Faklis, G. M. Morris, "Broadband imaging with holographic lenses," Opt. Eng. 28, 592-598 (1989).

Otón, J.

Pérez-Cabré, E.

Plaza, A.

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Santamaria, J.

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Tajahuerce, E.

Yzuel, M. J.

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, "Achromatic diffractive lens written onto a liquid cristal display," Opt. Lett. 31, 392-394 (2006).
[CrossRef] [PubMed]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

Appl. Opt. (2)

J. Optics (Paris) (1)

J. Bescós, J. H. Altamirano, J. Santamaria, and A. Plaza, "Apodizing filters in colour imaging," J. Optics (Paris) 17, 91-96 (1986).
[CrossRef]

Jpn. J. Appl. Phys. (1)

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jpn. J. Appl. Phys. 34, 6423-6432 (1995).
[CrossRef]

Opt. Commun. (1)

V. Laude, "Twisted-nematic liquid-crystal pixilated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

Opt. Eng. (1)

D. Faklis, G. M. Morris, "Broadband imaging with holographic lenses," Opt. Eng. 28, 592-598 (1989).

Opt. Express (1)

Opt. Lett. (2)

Other (1)

http://www.cri-inc.com">http://www.cri-inc.com.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of three phase Fresnel sublenses for the selected wavelengths λ1=650nm, λ2=550nm, λ3=450nm. The phase variation is represented in intensity levels. The radius Ri of each sublens fulfils the PSFI-condition. Pixels whose distance from the center is longer than Ri , are assigned a constant phase value (medium intensity of outer ring in lenses l 2 and l 3). Integration of λ i -sublenses is achieved by time multiplexing.

Fig. 2.
Fig. 2.

Schematic of the rotating multisector spectral filter placed before the time multiplexed programmable lens for compensation of chromatic aberration.

Fig. 3.
Fig. 3.

Configuration of maximum phase modulation with minimum coupled amplitude modulation of the twist-nematic liquid-crystal display SLM (XGA2-CRL) obtained experimentally for λ=543nm. (a) Plot of the joint phase and amplitude modulation with the addressed gray level; (b) phase variation vs. gray level for λ=543nm (solid blue line). Linearly extended curves for wavelengths λ=500nm (dashed green line) and λ=650nm (dashed red line).

Fig. 4.
Fig. 4.

Intensity distributions obtained with a programmable lens of focal length f 0=1250mm successively illuminated by the wavelengths λ=500, 550, 600, 650 nm. Experimental results for the various wavelengths are compared with the theoretical curve calculated for 550 nm (in solid black line, labelled as Th 550 in the legend).

Tables (1)

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Table 1. Technical specifications of liquid crystal display used in the experiment

Equations (9)

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l ( x , y ) = exp { j π λ f 0 ( x 2 + y 2 ) } ,
l i ( x , y , t ) = rect ( t t i T i ) τ i ( Δ λ ) [ circ ( 1 R i ( x 2 + y 2 ) 1 2 ) exp { j π λ i f 0 ( x 2 + y 2 ) }
× n , m δ ( x n Δ , y m Δ ) ] rect ( x Δ x , y Δ y ) ,
f 0 f r ( λ i ) = M Δ 2 λ i .
L ( x , y , t ) = i = 1 N [ l i ( x , y , t ) + rect ( t t ε i ε i ) ] p = 0 δ ( t pT S ) ,
t ε i = t i + 1 2 ( T i + ε i ) ,
t i + 1 = t i + T i 2 + ε i + T i + 1 2 ,
t 1 = T 1 2 .
U 00 i ( u , v ) = τ i ( Δ λ ) π d i R i Δ 2 [ 2 J 1 ( 2 π d i ( u 2 + v 2 ) 1 2 ) 2 π d i ( u 2 + v 2 ) 1 2 ] rect ( u Δ x , v Δ y ) ,

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