Abstract

In contemporary optics, the spatial light modulator (SLM) is effectively used as a flexible optoelectronic device playing the key role in a number of experiments of science and technology. Its operation is optimal when using almost monochromatic light but an extremely strong diffractive dispersion occurs when white light is applied. In this paper, the design concepts are proposed resulting in optimization and implementation of a refractive corrector cooperating with the SLM. The corrector maintains the operation of the SLM unchanged for the central wavelength of light and ensures an achromatic dispersion compensation throughout the visible region in applications based on a lens-pattern formation. A significant improvement of the imaging performance of the achromatic SLM was proved by the computer simulation and measurement of the chromatic focal shift and the image contrast of the resolution target.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2013 (3)

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

P. Bouchal, Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
[CrossRef]

X. Lai, S. Zeng, X. Lv, J. Yuan, L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38, 1896–1898 (2013).
[CrossRef] [PubMed]

2012 (2)

2011 (5)

2009 (2)

2007 (2)

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

J. Rosen, G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

2004 (1)

1999 (1)

1998 (1)

1997 (1)

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

1993 (1)

1992 (2)

1988 (1)

Andrés, P.

Ares, J

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Arines, J

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Badieirostami, M.

Bar, S

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Bergmann, R.

T. Meeser, C. Falldorf, Ch. von Kopylow, R. Bergmann, “Reference wave adaptation in digital lensless Fourier holography by means of a spatial light modulator,” Optical Measurement Systems for Industrial Inspection, Proc. of SPIE 8082, 808206 (2011).
[CrossRef]

Bernet, S.

Beversluis, M. R.

Bouchal, P.

Bouchal, Z.

Brooker, G.

Buralli, D. A.

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

Chang, B. J.

Chang, Y. C.

Chiang, S. Y.

Chmelík, Radim

Chou, L. J.

Climent, V

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Climent, V.

Davidson, N.

Duer, R.

Durán, V

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Esumi, Y.

Falldorf, C.

T. Meeser, C. Falldorf, Ch. von Kopylow, R. Bergmann, “Reference wave adaptation in digital lensless Fourier holography by means of a spatial light modulator,” Optical Measurement Systems for Industrial Inspection, Proc. of SPIE 8082, 808206 (2011).
[CrossRef]

Fernanández-Alonso, M.

Flores, A.

Forbes, A.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

Friesem, A.

Friesem, A. A.

Fu, L.

Furhaupt, S.

Gauza, S.

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

George, N.

Haist, T.

Hasman, E.

Jaroszewicz, Z

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

S. Bernet, A. Jesacher, S. Furhaupt, Ch. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14, 3792–3805 (2006).
[CrossRef] [PubMed]

Johnson, R. B.

R. Kingslake, R. B. Johnson, Lens Design Fundamentals (Elsevier, 2010).

Kabir, M. D.

Kannari, F.

Kapitán, J.

Kingslake, R.

R. Kingslake, R. B. Johnson, Lens Design Fundamentals (Elsevier, 2010).

Lai, X.

Lancis, J

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Lancis, J.

Lee, S. F.

Lew, M. D.

Li, J.

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

Lu, R.

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

Lv, X.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Maurer, Ch.

Meeser, T.

T. Meeser, C. Falldorf, Ch. von Kopylow, R. Bergmann, “Reference wave adaptation in digital lensless Fourier holography by means of a spatial light modulator,” Optical Measurement Systems for Industrial Inspection, Proc. of SPIE 8082, 808206 (2011).
[CrossRef]

Millán, M. S.

Moerner, W. E.

Moreno, V.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Morris, G. M.

Ngcobo, S.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

Novotny, L.

Otón, J.

Pérez-Cabré, E.

Prado, P

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Reicherter, M.

Ritsch-Marte, M.

Román, J. F.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Rosen, J.

Salgueiro, J. R.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Siegel, N.

Steiger, R.

Stone, T.

Stranick, S. J.

Tajahuerce, E

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

Tajahuerce, E.

Tiziani, H. J.

von Kopylow, Ch.

T. Meeser, C. Falldorf, Ch. von Kopylow, R. Bergmann, “Reference wave adaptation in digital lensless Fourier holography by means of a spatial light modulator,” Optical Measurement Systems for Industrial Inspection, Proc. of SPIE 8082, 808206 (2011).
[CrossRef]

Wagemann, E. U.

Wang, M. R.

Wen, Ch. H.

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

Wu, S. T.

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

Yang, J. J.

Yuan, J.

Zeng, S.

Am. J. Phys. (1)

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Appl. Opt. (5)

J. Display Technol. (1)

J. Li, Ch. H. Wen, S. Gauza, R. Lu, S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Display Technol. 1, 1551–1561 (2005).
[CrossRef]

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

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Nature Commun. (1)

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nature Commun. 4, 2289 (2013).
[CrossRef]

New J. Phys. (1)

P. Bouchal, Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
[CrossRef]

Opt. Express (9)

J Arines, V Durán, Z Jaroszewicz, J Ares, E Tajahuerce, P Prado, J Lancis, S Bar, V Climent, “Measurement and compensation of optical aberrations using a single spatial light modulator,” Opt. Express 23, 15287–15292 (2007).
[CrossRef]

M. R. Beversluis, L. Novotny, S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14, 2650–2656 (2006).
[CrossRef] [PubMed]

S. Bernet, A. Jesacher, S. Furhaupt, Ch. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14, 3792–3805 (2006).
[CrossRef] [PubMed]

M. S. Millán, J. Otón, E. Pérez-Cabré, “Dynamic compensation of chromatic aberration in a programmable diffractive lens,” Opt. Express 14, 9103–9112 (2006).
[CrossRef] [PubMed]

P. Bouchal, J. Kapitán, Radim Chmelík, Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express 19, 15603–15620 (2011).
[CrossRef] [PubMed]

J. Rosen, N. Siegel, G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
[CrossRef]

R. Steiger, S. Bernet, M. Ritsch-Marte, “SLM-based off-axis Fourier filtering in microscopy with white light illumination,” Opt. Express 20, 15377–15384 (2012).
[CrossRef] [PubMed]

B. J. Chang, L. J. Chou, Y. C. Chang, S. Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express 17, 14710–14721 (2009).
[CrossRef] [PubMed]

Y. Esumi, M. D. Kabir, F. Kannari, “Spatiotemporal vector pulse shaping of femtosecond laser pulses with a multi-pass two-dimensional spatial light modulator,” Opt. Express 17, 19153–19159 (2009).
[CrossRef]

Opt. Lett. (5)

Optical Measurement Systems for Industrial Inspection, Proc. of SPIE (1)

T. Meeser, C. Falldorf, Ch. von Kopylow, R. Bergmann, “Reference wave adaptation in digital lensless Fourier holography by means of a spatial light modulator,” Optical Measurement Systems for Industrial Inspection, Proc. of SPIE 8082, 808206 (2011).
[CrossRef]

Other (1)

R. Kingslake, R. B. Johnson, Lens Design Fundamentals (Elsevier, 2010).

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Figures (7)

Fig. 1
Fig. 1

Concept of the dispersion compensation of the SLM: (a) material dispersion of the afocal refractive corrector, (b) diffractive dispersion of the SLM, (c) achromatic correction of the SLM.

Fig. 2
Fig. 2

Combinations of the Abbe numbers of the corrector lenses providing an achromatic correction of the SLM for different values of the design parameter κ.

Fig. 3
Fig. 3

Experimental setup for measurement of the chromatic focal shift of the SLM and the secondary spectrum of the corrected SLM by means of the S-H sensor: L ... laser, MO ... microscope objective, AL ... achromatic lens, AC ... three-lens afocal corrector, BS ... beam splitter, P ... polarizer.

Fig. 4
Fig. 4

The measured and calculated chromatic focal shift for the uncorrected SLM with extremely strong diffractive dispersion (blue) and the achromatic correction of the SLM carried out by a three-lens afocal system (red).

Fig. 5
Fig. 5

Testing of the imaging performance of the uncorrected and achromatic SLM by means of the USAF resolution target: HL ... halogen lamp, HM ... hot mirror, GF ... green filter, ... LG light guide, L ... laser, MO ... microscope objective, BS ... beam splitter, AL ... achromatic lens, AC ... afocal corrector, P ... polarizer, ID ... iris diaphragm, C ... CMOS camera.

Fig. 6
Fig. 6

Measured contrast (10, 20 and 40 cycles/mm) and the calculated modulation transfer function for the imaging implemented by the uncorrected and achromatic SLM: (a) NA=0.02, (b) NA=0.06.

Fig. 7
Fig. 7

Snapshots of the USAF resolution target taken in the broadband light (532 nm, FWHM 80 nm): uncorrected SLM (left), achromatic SLM (right).

Equations (23)

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

d K d λ | λ 0 = K ( λ 0 ) [ n ( λ 0 ) 1 ] d n d λ | λ 0 .
δ K ( λ 1 , λ 2 ) = K ( λ 0 ) V M ,
V M = n ( λ 0 ) 1 n ( λ 1 ) n ( λ 2 ) .
t = exp [ i Φ ( r ) ] , where Φ ( r ) = π λ 0 | r | 2 f 0 .
ψ ( r , λ ) exp ( i π | r | 2 λ z ) FT { exp [ i π | r | 2 ( 1 λ 0 f 0 1 λ z ) ] } ,
z f ( λ ) = λ 0 λ f 0 ,
δ K ( λ 1 , λ 2 ) = K ( λ 0 ) V D ,
V D = λ 0 λ 1 λ 2 .
t ( λ ) = exp [ i Φ ( r , λ ) ] , where Φ ( r , λ ) = π λ 0 n ( λ ) n ( λ 0 ) | r | 2 f 0 ,
f ( λ ) = n ( λ 0 ) n ( λ ) λ 0 λ f 0 .
δ K ( λ 1 , λ 2 ) = K ( λ 0 ) V M D ,
V M D = Λ 0 Λ 1 Λ 2 ,
1 V 1 1 V 2 + 1 κ V D = 0 ,
κ = f D ( λ 0 ) f L ( λ 0 ) ,
δ K ( λ 0 , λ 1 ) = 1 f ( λ 0 ) 1 f ( λ 1 ) δ f ( λ 0 , λ 1 ) f 2 ( λ 0 ) .
δ f ( λ 0 , λ 1 ) = f 2 ( λ 0 ) f L ( λ 0 ) [ P 1 V 1 P 2 V 2 + P D κ V D ] ,
P j = n j ( λ 1 ) n j ( λ 0 ) n j ( λ 1 ) n j ( λ 2 ) , j = 1 , 2 ,
P D = λ 1 λ 0 λ 1 λ 2 ,
δ f ( λ 0 , λ 1 ) = f 2 ( λ 0 ) f L ( λ 0 ) [ P 1 P D V 1 P 2 P D V 2 ] .
ν m = 1 2 π Φ ( r ) | r | | | r | = R ,
f 2 Δ r R λ ,
η m ( λ ) = sinc 2 [ π ( λ 0 λ m ) ] ,
η ¯ m = 1 λ 2 λ 1 λ 1 λ 2 η m ( λ ) d λ .

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