Abstract

An improved implementation of the reverse phase contrast (RPC) method for rapid optical transformation of amplitude patterns into spatially similar phase patterns using a high-speed digital micromirror-array device (DMD) is presented. Aside from its fast response, the DMD also provides an electronically adjustable and inherently aligned input iris that simplifies the optimization of the RPC system. In the RPC optimization, we illustrate good agreement between experimentally obtained and theoretically predicted optimal iris size. Finally, we demonstrate the conversion of a binary amplitude grating encoded on the DMD into a binary (0-π) phase grating.

© 2006 Optical Society of America

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References

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  1. P. C. Mogensen and J. Glückstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
    [CrossRef]
  2. P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
    [CrossRef]
  3. P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
    [CrossRef]
  4. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
    [CrossRef]
  5. R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
    [CrossRef]
  6. T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
    [CrossRef]
  7. J. Glückstad and P. C. Mogensen, "Reverse phase contrast for the generation of phase-only spatial light modulation," Opt. Commun. 197, 261-266 (2001).
    [CrossRef]
  8. P. C. Mogensen and J. Glückstad, "Reverse phase contrast: an experimental demonstration," Appl. Opt. 41, 2103-2110 (2002).
    [CrossRef] [PubMed]
  9. L. Yoder, W. Duncan, E. M. Koontz, J. So, T. Bartlett, B. Lee, B. Sawyers, D. A. Powell, and P. Rancuret, "DLPTM Technology: Applications in Optical Networking," in Spatial Light Modulators: Technology and Applications; U. Efron, ed., Proc. SPIE 4457, 54-61 (2001).
    [CrossRef]

2005 (1)

R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
[CrossRef]

2002 (1)

2001 (3)

J. Glückstad and P. C. Mogensen, "Reverse phase contrast for the generation of phase-only spatial light modulation," Opt. Commun. 197, 261-266 (2001).
[CrossRef]

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
[CrossRef]

2000 (1)

1999 (1)

T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
[CrossRef]

1991 (1)

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Crossland, W. A.

T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
[CrossRef]

Denz, C.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Eriksen, R. L.

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
[CrossRef]

Glückstad, J.

P. C. Mogensen and J. Glückstad, "Reverse phase contrast: an experimental demonstration," Appl. Opt. 41, 2103-2110 (2002).
[CrossRef] [PubMed]

J. Glückstad and P. C. Mogensen, "Reverse phase contrast for the generation of phase-only spatial light modulation," Opt. Commun. 197, 261-266 (2001).
[CrossRef]

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
[CrossRef]

John, R.

R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
[CrossRef]

Joseph, J.

R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
[CrossRef]

Kapsalis, V.

T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
[CrossRef]

Mogensen, P. C.

P. C. Mogensen and J. Glückstad, "Reverse phase contrast: an experimental demonstration," Appl. Opt. 41, 2103-2110 (2002).
[CrossRef] [PubMed]

J. Glückstad and P. C. Mogensen, "Reverse phase contrast for the generation of phase-only spatial light modulation," Opt. Commun. 197, 261-266 (2001).
[CrossRef]

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
[CrossRef]

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Singh, K.

R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
[CrossRef]

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Wilkinson, T. D.

T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
[CrossRef]

Appl. Opt. (2)

J. Opt. A: Pure Appl. Opt. (1)

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, "High capacity optical encryption system using ferro-electric spatial light modulators," J. Opt. A: Pure Appl. Opt. 3, 10-15 (2001).
[CrossRef]

Opt. Commun. (2)

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

J. Glückstad and P. C. Mogensen, "Reverse phase contrast for the generation of phase-only spatial light modulation," Opt. Commun. 197, 261-266 (2001).
[CrossRef]

Opt. Eng. (1)

T. D. Wilkinson, W. A. Crossland, and V. Kapsalis, "Binary phase-only 1/f joint transform correlator using a ferroelectric liquid-crystal spatial light modulator," Opt. Eng. 38, 357-360 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

R. John, J. Joseph, and K. Singh, "Holographic digital data storage using phase modulated pixels," Opt. Lasers Eng. 43, 183-194 (2005).
[CrossRef]

Opt. Lett. (1)

Other (1)

L. Yoder, W. Duncan, E. M. Koontz, J. So, T. Bartlett, B. Lee, B. Sawyers, D. A. Powell, and P. Rancuret, "DLPTM Technology: Applications in Optical Networking," in Spatial Light Modulators: Technology and Applications; U. Efron, ed., Proc. SPIE 4457, 54-61 (2001).
[CrossRef]

Supplementary Material (2)

» Media 1: GIF (146 KB)     
» Media 2: GIF (146 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Photograph of the reverse phase contrast (RPC) 4f setup for converting an amplitude-only pattern displayed on a digital micromirror-array device (DMD) into a spatially similar phase pattern at the output plane. (b) Schematic diagram of the whole setup. The expanded and collimated laser beam is made incident to the DMD chip at an angle of ~24°, twice the micromirror tilt angle |γ|, such that the beam coming out normal to the chip (at ON-state) is the strongest Fraunhofer diffraction order and the only order that passes through the optical train. CCD camera 1 detects the intensity at the output plane. CCD camera 2 captures the optical Fourier transform of the iris-truncated output pattern. Identical lenses with 100-mm focal length are used. A phase-only filter (made from an optical flat with a tiny circular pit) is used to create a phase shift of π over an on-axis circular region (diameter, 2R~39 µm) in the common Fourier plane of the two 4f setup lenses. BS, beam splitter.

Fig. 2.
Fig. 2.

(GIF, ~140 kB) Comparison of the theoretical and experimental intensity profiles at the output plane of the 4f setup that images a circular iris of diameter, 2Δr=(a) 3.65 mm, (b) 3.15 mm, (c) 2.65 mm, (d) 2.15 mm, (e) 1.65 mm, and (f) 1.15 mm with the phase-only filter centered at the Fourier plane common to the two lenses. Each experimentally obtained intensity profile is a diagonal line-scan through the center of the CCD-captured image (inset). [Media 1, Media 2]

Fig. 3.
Fig. 3.

Intensity profiles measured along a diagonal (perpendicular to grating bars) for the DMD-encoded binary amplitude grating (red) and for the corresponding phase pattern (blue) produced via RPC when the filter is centered at the Fourier plane. The CCD-captured 2D images for the binary amplitude grating and the RPC output are shown in the upper and bottom insets, respectively.

Fig. 4.
Fig. 4.

Measured far-field diffraction profiles of the circular iris’ image at the output of the 4f setup without the phase-only filter (circles) and the binary phase pattern produced via RPC (with binary amplitude-only input from the DMD) when the filter is centered at the Fourier plane (triangles). The latter shows the suppressed 0th and even diffraction orders and the dominant +1 and -1 orders each with strength (four times the actual) approximately equal to the theoretical value of ~0.41 for a 50% duty-cycle, 0-π binary phase pattern.

Equations (5)

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e ( x , y ) = circ ( r Δ r ) α ( x , y ) ,
I ( x , y ) = [ circ ( r Δ r ) α ( x , y ) 2 α ̅ g ( r ) ] 2 ,
g ( r ) = 2 π Δ r 0 Δ f r J 1 ( 2 π Δ r f r ) J 0 ( 2 π r f r ) d f r
α ̅ = ( π ( Δ r ) 2 ) 1 x 2 + y 2 Δ r α ( x , y ) d x d y ,
I ( x , y ) = { [ 0 g ( r ) ] 2 for ( x , y ) OFF [ 1 g ( r ) ] 2 for ( x , y ) ON ,

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