Abstract

Programmable apodizers written on a liquid crystal spatial light modulator (LCSLM) offer the possibility of modifying the point spread function (PSF) of an optical system in monochromatic light with a high degree of flexibility. Extension to polychromatic light has to take into account the liquid crystal response dependence on the wavelength. Proper control of the chromatic properties of the LCSLM in combination with the design of the correct apodizer is necessary for this new range of applications. In this paper we report a successful application of a programmable amplitude apodizer illuminated with polychromatic light. We use an axial apodizing filter to compensate the longitudinal secondary axial color (LSAC) effects of a refractive optical system on the polychromatic PSF. The configuration of the LCSLM has been optimized to obtain a good amplitude transmission in polychromatic light. Agreement between experimental and simulated results shows the feasibility of our proposal.

© 2005 Optical Society of America

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References

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Appl. Opt. (7)

J. Mod Opt. (1)

A. Márquez, C. Cazorla, M. J. Yzuel and J. Campos, �??Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,�?? J. Mod Opt. 52, 633-650 (2005)
[CrossRef]

J. Mod. Opt. (4)

C.S Chung and H.H. Hopkins, �??Influence of non-uniform amplitude on PSF,�?? J. Mod. Opt. 35, 1485-1511 (1988)
[CrossRef]

J. Campos and M.J. Yzuel, �??Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,�?? J. Mod. Opt. 36, 733-749 (1989)
[CrossRef]

J. C. Escalera, M. J. Yzuel and J. Campos, �??Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,�?? J. Mod. Opt. 38, 1703-1720 (1991)
[CrossRef]

J. Campos, J. C. Escalera, C. J. R. Sheppard and M. J. Yzuel, �??Axially invariant pupil filters,�?? J. Mod. Opt. 47, 57-68 (2000)

J. Opt. Soc. Am. A (2)

McGraw-Hill (1)

W. J. Smith, Modern Optical Engineering, (McGraw-Hill, 3rd Ed., 2000), 402-412.

Micron (1)

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West and K. Matsuda, �??Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,�?? Micron 34, 327-332 (2003)
[CrossRef]

Opt. Commun. (1)

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

Opt. Eng. (2)

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno and A. Robert, �??Characterization of edge effects in twisted nematic liquid crystal displays,�?? Opt. Eng. 39, 3301-3307 (2000)
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos and M. J. Yzuel, �??Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,�?? Opt. Eng. 40, 2558-2564 (2001)
[CrossRef]

Opt. Lett. (4)

Optica Acta (1)

M. J. Yzuel and F. Calvo, �??A study of the possibility of image optimization by apodization filters with residual aberrations,�?? Optica Acta 26, 1397-1406 (1979)
[CrossRef]

Proc. SPIE (1)

M. J. Yzuel, J. C. Escalera, G. Cansado and J. Campos, �??Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,�?? Proc. SPIE 1013, 120-127 (1988)

Other (2)

H.J. Coufal, D. Psaltis and B.T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000)

V. G. Chigrinov, Liquid crystal devices: physics and applications (Artech House, 1999)

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Figures (11)

Fig. 1.
Fig. 1.

(a) Scheme of the imaging system. The pupil is located behind the optical system. (b) Longitudinal chromatic aberration for the imaging system expressed with respect to the BIP for the green (514 nm) and the blue (488 nm).

Fig. 2.
Fig. 2.

Simulated results for the 3-D PSF considering the exit pupil with no filter. Plots (b), (c) and (d) are in lab coordinates: (a) Amplitude transmission along the exit pupil with no filter. The transmission is equal to one for the three wavelengths; (b) Intensity along the axis. We note the defocus between the various wavelengths; Intensity at the BIP for (c) the green (z=0 mm) and (d) the red (z=3.16 mm).

Fig. 3.
Fig. 3.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5. Plots (b), (c) and (d) are in lab coordinates: (a) Amplitude transmission along the exit pupil; (b) Intensity along the axis. We note that the depth of focus has increased for the various wavelengths; Intensity at the BIP for (c) the green (z=0 mm) and (d) the red (z=3.16 mm).

Fig. 4.
Fig. 4.

Modulation response of the LCSLM for the three wavelengths used in this work. Symbols correspond to the experimental measurements and continuous lines to the theoretical predictions. (a) Intensity transmission and (b) phase shift.

Fig. 5.
Fig. 5.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5 together with the transmission curve of the LCSLM for each of the wavelengths. Plots (c) and (d) are in lab coordinates: (a) Amplitude transmission and (b) coupled phase profile along the exit pupil for the three wavelengths; Intensity along the axis considering that (c) there is no coupled phase, and (d) considering the coupled phase.

Fig. 6.
Fig. 6.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5 together with the amplitude transmission and coupled phase given by the LCSLM for each of the wavelengths. Intensity at the BIP (a) for the green (z=0 mm) and (b) for the red (z=3.16 mm). Plots are in lab coordinates.

Fig. 7.
Fig. 7.

Scheme of the imaging set-up with the optical system under analysis. The aperture of the LCSLM (16.52 mm of diameter) determines the exit pupil of the system. P1 and P2 are the polarizers; MO is the microscope objective. The distance d from the exit pupil to the image plane is about 50 cm; the distance dMO is fixed to capture magnified images with the same magnification.

Fig. 8.
Fig. 8.

PSF obtained with the system without filter. The first and the second rows correspond to the BIP for the green (z=0 mm) and for the red (z=3.16 mm) respectively. The first three columns are the monochromatic PSF for the 633 nm, 514 nm and 458 nm wavelengths. The last column is a pseudocolored image obtained from the three monochromatic ones.

Fig. 9.
Fig. 9.

PSF obtained with the supergaussian filter Ω=0.17, α=1, t0=0.5. The first and the second rows correspond to the BIP for the green (z=0 mm) and for the red (z=3.16 mm) respectively. The first three columns are the monochromatic PSF for the 633 nm, 514 nm and 458 nm wavelengths. The last column is a pseudocolored image obtained from the three monochromatic ones.

Fig. 10.
Fig. 10.

Pseudocolored images of the PSF obtained in the BIP for the green, z=0 mm (first row), and for the red, z=3.16 mm (second row), for the system without filter (column 1), and with supergaussian filters (columns 2, 3 and 4) centered at the same position t0=0.4 and for different widths given by Ω. In all cases the degree of the supergaussian is α=1.

Fig. 11.
Fig. 11.

Pseudocolored images of the PSF obtained in the BIP for the green, z=0 mm (first row), and for the red, z=3.16 mm (second row), for the system without filter (column 1), and with supergaussian filters (columns 2, 3 and 4) of the same width Ω=0.17 and centered in different positions given by t0. In all cases the degree of the supergaussian is α=1.

Equations (7)

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

G λ ( ρ ) = ( 1 λ ) 2 F λ ( ρ ) 2 ,
F λ ( ρ ) = A f λ ( r ) J 0 ( 2 π r ρ ) r dr ,
f λ ( r ) = { τ λ ( r ) exp [ i 2 π W λ ( r ) ] within A 0 outside ,
G λ ( ρ , W 20 ) = ( 1 λ ) 2 F λ ( ρ , W 20 ) 2 ,
F λ ( ρ , W 20 ) = A f λ ( r ) exp ( i 2 π W 20 r 2 ) J 0 ( 2 π r ρ ) r dr .
s = λ NA ρ , z = 2 λ NA 2 W 20 ,
τ ( t ) = K exp [ ( t t 0 Ω ) 2 α ]

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