Abstract

We present a method for full spatial phase and amplitude control of a laser beam using a twisted nematic LCD combined with a spatial filter. By spatial filtering we combine four neighboring pixels into one superpixel. At each superpixel we are able to independently modulate the phase and the amplitude of light. We experimentally demonstrate the independent phase and amplitude modulation using this novel technique. Our technique does not impose special requirements on the spatial light modulator and allows precise control of fields even with imperfect modulators.

© 2008 Optical Society of America

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References

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2008

2007

S. Chavali, P. M. Birch, R. Young, and C. Chatwin, “Synthesis and reconstruction of computer generated holograms by a double pass technique on a twisted nematic-based liquid crystal spatial light modulator,” Optics and Lasers in Engineering 45, 413-418 (2007).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309-2311 (2007).
[CrossRef] [PubMed]

2004

2003

2001

J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator,” Opt. Eng. 40, 327-329 (2001).
[CrossRef]

P. Birch, R. Young, D. Budgett, and C. Chatwin, “Dynamic complex wave-front modulation with an analog spatial light modulator,” Opt. Lett. 26, 920-922 (2001).
[CrossRef]

J.-F. Le Gargasson, M. Glanc, and P. Léna, “Retinal imaging with adaptive optics,” C. R. Acad. Sci. Ser. IV Astrophys. 2, 1131-1138 (2001).

2000

1998

1997

A. R. L. Travis, “The display of three-dimensional video images,” Proc. IEEE 85, 1817-1832 (1997).
[CrossRef]

1996

1994

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

1993

J. M. Beckers, “Adaptive optics for astronomy--principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13-62 (1993).
[CrossRef]

Annu. Rev. Astron. Astrophys.

J. M. Beckers, “Adaptive optics for astronomy--principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13-62 (1993).
[CrossRef]

Appl. Opt.

C. R. Acad. Sci. Ser. IV Astrophys.

J.-F. Le Gargasson, M. Glanc, and P. Léna, “Retinal imaging with adaptive optics,” C. R. Acad. Sci. Ser. IV Astrophys. 2, 1131-1138 (2001).

Computer

D. Psaltis and G. Burr, “Holographic data storage,” Computer 31, 52-60 (1998).
[CrossRef]

Opt. Eng.

J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator,” Opt. Eng. 40, 327-329 (2001).
[CrossRef]

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Optics and Lasers in Engineering

S. Chavali, P. M. Birch, R. Young, and C. Chatwin, “Synthesis and reconstruction of computer generated holograms by a double pass technique on a twisted nematic-based liquid crystal spatial light modulator,” Optics and Lasers in Engineering 45, 413-418 (2007).
[CrossRef]

Proc. IEEE

A. R. L. Travis, “The display of three-dimensional video images,” Proc. IEEE 85, 1817-1832 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Experimental modulation plot for the SLM illuminated with vertical polarized light. After modulation the light with a horizontal polarization is detected. This plot shows the amplitude versus the phase modulation. The arbitrary phase reference is chosen such that the maximum amplitude coincides with the a zero phase modulation. The modulation voltage increases in the direction of the gray arrows.

Fig. 2
Fig. 2

Experimental setup to decouple phase and amplitude modulation. Four neighboring pixels (pixels 1, 2, 3, and 4) are combined to one superpixel that can modulate one complex value. The modulated light is focused by a lens, L 1 , onto a diaphragm placed in the focal plane. The focal length of L 1 is 200 mm . The diaphragm is positioned such that it only transmits light under a certain angle. This angle is chosen so that, in the horizontal dimension, two neighboring pixels are exactly π / 2 out of phase with each other as can be seen from the inset. Behind the diaphragm the light is collimated by a lens, L 2 .

Fig. 3
Fig. 3

The electric field of a superpixel is superposed out of four distinct neighboring pixels whose phases are all shifted over π / 2 with respect to each other. In this figure we show a limited modulation range of pixels 1, 2, 3, and 4. The numbers outside the plot relate the curves to the pixel numbers. By choosing the right pixel values for the different pixels, every complex value can be synthesized by the superpixel. In the figure, pixels 1 and 3 are used to modulate a value on the real axis. The electric fields E 1 and E 3 are chosen such that their imaginary parts cancel and E 1 E 3 lies on the real axis. Pixels 2 and 4 are used in a similar way to modulate any value on the imaginary axis (not shown).

Fig. 4
Fig. 4

Calculation of the reconstructed field in the x direction for the case where the 128th superpixel is set to 1 + i while the other superpixels are set to 0. The vertical lines represent the borders of the superpixels. The reconstructed real and imaginary parts are spatially separated by a / 4 .

Fig. 5
Fig. 5

Results of the measurements to demonstrate the independent phase and amplitude modulation. Using the superpixels we synthesized a plane wave of which we varied the amplitude and the phase. In this plot see the relative amplitude A / I 0 from intensity measurements as a function of the programed phase. The intensity I 0 = 19.7 · 10 3 counts/seconds. The relative amplitudes are set to 0.25, 0.5, and 0.75, corresponding to the red, green, and blue lines, respectively.

Fig. 6
Fig. 6

Results of the measurements demonstrate that the set phase difference corresponds with the actual phase difference. In this plot we show the relative measured intensity of a grating interference experiment. The intensities are plotted as a function of the set phase difference Δ θ , and are reference to I 0 = 4.56 · 10 3 counts/seconds. The experiment was done for multiple amplitude differences between the rules and the notches of the grating. The solid lines represent the expected intensities.

Fig. 7
Fig. 7

Demonstration of complex modulation using the novel modulation technique. In this experiment we encoded the Fourier transform of an image containing the two words “Phase” and “Amplitude” onto the SLM and reconstructed the image in the far-field. This plot shows the measured intensity in the far-field on a logarithmic scale. The intensities are in counts/seconds.

Equations (11)

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E 1 = E 1 r + i Δ ,
E 3 = E 3 r + i Δ ,
E 1 r E 3 r = g ,
E 2 = E 2 r + i ϵ ,
E 4 = E 4 r + i ϵ ,
E 2 r E 3 r = h .
f s ( x , y ) = m , n = δ ( y m a / 4 ) [ δ ( x n a ) E 1 ( x , y ) + δ ( x 1 / 4 a n a ) E 2 ( x 1 / 4 a , y ) + δ ( x 1 / 2 a n a ) E 3 ( x 1 / 2 a , y ) + δ ( x 3 / 4 a n a ) E 4 ( x 1 / 4 a , y ) ] ,
F s ( Ω x , ω y ) = 1 2 π k , l = { E ˜ 1 r ( Ω x k , ω y l ) E ˜ 3 r ( Ω x k , ω y l ) e i a Ω x 2 + i [ E ˜ 2 r ( Ω x k , ω y l ) E ˜ 4 r ( Ω x k , ω y l ) e i a Ω x 2 ] e i a Ω x 4 + i [ Δ ˜ ( Ω x k , ω y l ) + ϵ ˜ ( Ω x k , ω y l ) e i a Ω x 4 ] [ 1 e i a Ω x 2 ] } ,
f r ( x , y ) = m , n = δ ( y m a / 4 ) [ δ ( x n a ) E 1 ( x , y ) δ ( x 1 / 2 a n a ) E 3 ( x 1 / 2 a , y ) + i δ ( x 1 / 4 a n a ) E 2 ( x 1 / 4 a , y ) i δ ( x 3 / 4 a n a ) E 4 ( x 1 / 4 a , y ) ] 2 w a 2 sinc ( x w a , 4 y a ) .
I = A 2 + B 2 + 2 A B cos ( Δ θ ) .
g ( V 1 ) = E r ( V 1 ) E r ( V L ( E i ( V 1 ) ) ) .

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