Abstract

We report a wavelength-compensated three-channel (RGB) joint transform correlator (JTC) for color pattern recognition using a ferroelectric liquid-crystal spatial light modulator (SLM) operating in binary pure phase modulation. We apply a previously reported time-multiplexing technique useful in creating wavelength-compensated diffraction patterns, based on the synchronization of properly scaled diffraction masks with the input wavelength selection obtained by applying a rotating RGB color-filter wheel to an Ar–Kr laser. The application of this technique to a JTC architecture permits real-time color object detection. In order to achieve a high light efficiency for the correlation process, we combine the design of zero-order joint power spectra in all color channels with the selection of a certain polarization configuration of the SLM, producing a broadband phase-only modulation. Excellent experimental results demonstrating color-object detection are provided.

© 2010 Optical Society of America

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References

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  1. R. C. González and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).
  2. E. Valencia and M. S. Millán, “Colour in digital images captured by camera: framework for colorimetric image analysis and applications,” Opt. Pura Apl. 40, 253–265 (2007).
  3. M. S. Millán, M. J. Yzuel, J. Campos, and C. Ferreira, “Different strategies in optical pattern recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
    [CrossRef] [PubMed]
  4. D. Mendlovic, P. García-Martínez, J. Garcia, and C. Ferreira, “Color encoding for polychromatic single channel optical pattern recognition,” Appl. Opt. 34, 7538–7544 (1995).
    [CrossRef] [PubMed]
  5. P. García-Martínez, J. Otón, J. J. Vallés, and H. H. Arsenault, “Nonlinear pattern recognition correlators based on color-encoding single channel systems,” Appl. Opt. 43, 425–432(2004).
    [CrossRef] [PubMed]
  6. I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, and M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
    [CrossRef] [PubMed]
  7. A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
    [CrossRef]
  8. C. S. Weaver and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  9. F. T. S. Yu and Y. S. Cheng, “White-light joint-transform correlator,” Opt. Lett. 15, 192–194 (1990).
    [CrossRef] [PubMed]
  10. Y. S. Cheng, “Analysis of a white-light joint-transform correlator with application to color-object detection,” Opt. Commun. 99, 252–263 (1993).
    [CrossRef]
  11. P. Andrés and V. Climent, “Chromatic compensation of light diffraction: Achromatic diffraction based application,” Proc. SPIE CR74, 11–40 (1999).
  12. M. Deutsch, J. García, and D. Mendlovic, “Multichannel single-output color pattern recognition by use of a joint-transform correlator,” Appl. Opt. 35, 6976–6982 (1996).
    [CrossRef] [PubMed]
  13. M. S. Alam and C. N. Wai, “Color pattern recognition using fringe-adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
    [CrossRef]
  14. M.-L. Hsieh, K. Y. Hsu, and H. Zhai, “Color image recognition by use of a joint transform correlator of three liquid-crystal televisions,” Appl. Opt. 41, 1500–1504 (2002).
    [CrossRef] [PubMed]
  15. F. T. S. Yu, Z. Yang, and K. Pan, “Polychromatic target identification with a color liquid-crystal-TV based joint-transform correlator,” Appl. Opt. 33, 2170–2172 (1994).
    [CrossRef] [PubMed]
  16. G. Lu, Z. Zhang, S. Wu, and F. T. S. Yu, “Implementations of DC spectra-free joint transform correlator using phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
    [CrossRef] [PubMed]
  17. C. Li, S. Yin, and F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
    [CrossRef]
  18. A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
    [CrossRef]
  19. A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31, 392–394 (2006).
    [CrossRef] [PubMed]
  20. M. S. Millán, J. Otón, and E. Pérez-Cabré, “Dynamic compensation of chromatic aberration in a programmable diffractive lens,” Opt. Express 14, 9103–9111 (2006).
    [CrossRef] [PubMed]
  21. J. L. Martínez, A. Martínez-García, and I. Moreno, “Wavelength-compensated color Fourier diffractive optical elements using a ferroelectric liquid crystal on silicon display and a color-filter wheel,” Appl. Opt. 48, 911–918 (2009).
    [CrossRef] [PubMed]
  22. B. V. K. Vijaya Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006(1990).
    [CrossRef]
  23. A. B. Carlson, P. B. Crilly, and J. C. Rutledge, Communication Systems (McGraw–Hill, 2002).
  24. I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
    [CrossRef]
  25. J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
    [CrossRef]
  26. A. Martínez-García, I. Moreno, M. M. Sánchez-López, and P. García-Martínez, “Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude and phase diffraction gratings,” Appl. Opt. 48, 2903–2914(2009).
    [CrossRef] [PubMed]
  27. I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
    [CrossRef]
  28. T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
    [CrossRef]

2009 (2)

2008 (2)

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

2007 (1)

E. Valencia and M. S. Millán, “Colour in digital images captured by camera: framework for colorimetric image analysis and applications,” Opt. Pura Apl. 40, 253–265 (2007).

2006 (2)

2004 (1)

2002 (4)

M.-L. Hsieh, K. Y. Hsu, and H. Zhai, “Color image recognition by use of a joint transform correlator of three liquid-crystal televisions,” Appl. Opt. 41, 1500–1504 (2002).
[CrossRef] [PubMed]

A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
[CrossRef]

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

2001 (1)

M. S. Alam and C. N. Wai, “Color pattern recognition using fringe-adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

1999 (1)

P. Andrés and V. Climent, “Chromatic compensation of light diffraction: Achromatic diffraction based application,” Proc. SPIE CR74, 11–40 (1999).

1998 (2)

C. Li, S. Yin, and F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

1997 (1)

1996 (2)

1995 (1)

1994 (1)

1993 (1)

Y. S. Cheng, “Analysis of a white-light joint-transform correlator with application to color-object detection,” Opt. Commun. 99, 252–263 (1993).
[CrossRef]

1992 (1)

1990 (2)

1966 (1)

Alam, M. S.

M. S. Alam and C. N. Wai, “Color pattern recognition using fringe-adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

Andrés, P.

P. Andrés and V. Climent, “Chromatic compensation of light diffraction: Achromatic diffraction based application,” Proc. SPIE CR74, 11–40 (1999).

Arsenault, H. H.

Bouzid, A.

A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
[CrossRef]

Campos, J.

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

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

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, and M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

M. S. Millán, M. J. Yzuel, J. Campos, and C. Ferreira, “Different strategies in optical pattern recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

Carlson, A. B.

A. B. Carlson, P. B. Crilly, and J. C. Rutledge, Communication Systems (McGraw–Hill, 2002).

Cheng, Y. S.

Y. S. Cheng, “Analysis of a white-light joint-transform correlator with application to color-object detection,” Opt. Commun. 99, 252–263 (1993).
[CrossRef]

F. T. S. Yu and Y. S. Cheng, “White-light joint-transform correlator,” Opt. Lett. 15, 192–194 (1990).
[CrossRef] [PubMed]

Climent, V.

P. Andrés and V. Climent, “Chromatic compensation of light diffraction: Achromatic diffraction based application,” Proc. SPIE CR74, 11–40 (1999).

Crilly, P. B.

A. B. Carlson, P. B. Crilly, and J. C. Rutledge, Communication Systems (McGraw–Hill, 2002).

Crossland, W. A.

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

Deutsch, M.

Fares, A.

A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
[CrossRef]

Ferreira, C.

Garcia, J.

García, J.

García-Martínez, P.

González, R. C.

R. C. González and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Goodman, J. W.

Hamdi, M.

A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
[CrossRef]

Hassebrook, L.

Hsieh, M.-L.

Hsu, K. Y.

Ichihashi, Y.

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

Iemmi, C.

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

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

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

Ito, T.

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

Kober, V.

I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, and M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

Lashin, V.

Li, C.

C. Li, S. Yin, and F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Lizana, A.

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

Lu, G.

Manolis, I. G.

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

Márquez, A.

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

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

Martínez, J. L.

Martínez-García, A.

Masuda, N.

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

Mendlovic, D.

Millán, M. S.

Moreno, I.

Nicolás, J.

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

Otón, J.

Pan, K.

Pérez-Cabré, E.

Redmond, M. M.

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

Rutledge, J. C.

A. B. Carlson, P. B. Crilly, and J. C. Rutledge, Communication Systems (McGraw–Hill, 2002).

Sánchez-López, M. M.

Shimonaba, T.

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

Shiraki, A.

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

Valencia, E.

E. Valencia and M. S. Millán, “Colour in digital images captured by camera: framework for colorimetric image analysis and applications,” Opt. Pura Apl. 40, 253–265 (2007).

Vallés, J. J.

Vijaya Kumar, B. V. K.

Wai, C. N.

M. S. Alam and C. N. Wai, “Color pattern recognition using fringe-adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

Weaver, C. S.

Wilkinson, T. D.

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

Woods, R. E.

R. C. González and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Wu, S.

Yang, Z.

Yaroslavsky, L. P.

Yin, S.

C. Li, S. Yin, and F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Yu, F. T. S.

Yzuel, M. J.

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

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

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, and M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

M. S. Millán, M. J. Yzuel, J. Campos, and C. Ferreira, “Different strategies in optical pattern recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

Zhai, H.

Zhang, Z.

Appl. Opt. (11)

B. V. K. Vijaya Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006(1990).
[CrossRef]

F. T. S. Yu, Z. Yang, and K. Pan, “Polychromatic target identification with a color liquid-crystal-TV based joint-transform correlator,” Appl. Opt. 33, 2170–2172 (1994).
[CrossRef] [PubMed]

G. Lu, Z. Zhang, S. Wu, and F. T. S. Yu, “Implementations of DC spectra-free joint transform correlator using phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

D. Mendlovic, P. García-Martínez, J. Garcia, and C. Ferreira, “Color encoding for polychromatic single channel optical pattern recognition,” Appl. Opt. 34, 7538–7544 (1995).
[CrossRef] [PubMed]

M. Deutsch, J. García, and D. Mendlovic, “Multichannel single-output color pattern recognition by use of a joint-transform correlator,” Appl. Opt. 35, 6976–6982 (1996).
[CrossRef] [PubMed]

M. S. Millán, M. J. Yzuel, J. Campos, and C. Ferreira, “Different strategies in optical pattern recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

M.-L. Hsieh, K. Y. Hsu, and H. Zhai, “Color image recognition by use of a joint transform correlator of three liquid-crystal televisions,” Appl. Opt. 41, 1500–1504 (2002).
[CrossRef] [PubMed]

P. García-Martínez, J. Otón, J. J. Vallés, and H. H. Arsenault, “Nonlinear pattern recognition correlators based on color-encoding single channel systems,” Appl. Opt. 43, 425–432(2004).
[CrossRef] [PubMed]

C. S. Weaver and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

J. L. Martínez, A. Martínez-García, and I. Moreno, “Wavelength-compensated color Fourier diffractive optical elements using a ferroelectric liquid crystal on silicon display and a color-filter wheel,” Appl. Opt. 48, 911–918 (2009).
[CrossRef] [PubMed]

A. Martínez-García, I. Moreno, M. M. Sánchez-López, and P. García-Martínez, “Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude and phase diffraction gratings,” Appl. Opt. 48, 2903–2914(2009).
[CrossRef] [PubMed]

Electron. Express (1)

T. Shimonaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” Electron. Express 5, 271–278 (2008).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

I. G. Manolis, T. D. Wilkinson, M. M. Redmond, and W. A. Crossland, “Reconfigurable multilevel phase holograms for optical switches,” IEEE Photonics Technol. Lett. 14, 801–803(2002).
[CrossRef]

J. Eur. Opt. Soc.—Rapid Pub. (1)

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc.—Rapid Pub. 3, 08012 (2008).
[CrossRef]

Opt. Commun. (3)

A. Fares, P. García-Martínez, C. Ferreira, M. Hamdi, and A. Bouzid, “Multichannel chromatic transformations for nonlinear color pattern recognition,” Opt. Commun. 203, 255–261(2002).
[CrossRef]

Y. S. Cheng, “Analysis of a white-light joint-transform correlator with application to color-object detection,” Opt. Commun. 99, 252–263 (1993).
[CrossRef]

J. Nicolás, C. Iemmi, J. Campos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. 209, 35–43 (2002).
[CrossRef]

Opt. Eng. (3)

I. Moreno, J. Campos, M. J. Yzuel, and V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator: Application to colour pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

M. S. Alam and C. N. Wai, “Color pattern recognition using fringe-adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

C. Li, S. Yin, and F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Pura Apl. (1)

E. Valencia and M. S. Millán, “Colour in digital images captured by camera: framework for colorimetric image analysis and applications,” Opt. Pura Apl. 40, 253–265 (2007).

Proc. SPIE (1)

P. Andrés and V. Climent, “Chromatic compensation of light diffraction: Achromatic diffraction based application,” Proc. SPIE CR74, 11–40 (1999).

Other (2)

R. C. González and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

A. B. Carlson, P. B. Crilly, and J. C. Rutledge, Communication Systems (McGraw–Hill, 2002).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the calculation of the binary-phase nonzero joint power spectrum. The calculation is done for each color component separately.

Fig. 2
Fig. 2

(a, d) Examples of input color images for the proposed JTC; (b, e) their corresponding color correlation outputs obtained by computer simulations; and (c, f) their 3D plots of the region of interest.

Fig. 3
Fig. 3

Performance of the PCE for the color N0JTC (solid squares), the color phase JTC (solid triangles) and color conventional JTC (solid circles) when the SNR in the input scene is varied. The noise is additive, zero-mean, and Gaussian.

Fig. 4
Fig. 4

(a) Scheme of the wavelength-compensated JTC. AL denotes achromatic lenses, and P1 and P1 denote linear polarizers. (b) Picture of the color-filter wheel.

Fig. 5
Fig. 5

(a) RGB color image composed of the noncompensated binary-phase N0JPS of the scene in Fig. 2a. The inset corresponds to the central part of the image. (b) Corres ponding scaled version of the binary-phase N0JPS to provide a wavelength-compensated correlation plane, with details of the central part in the inset.

Fig. 6
Fig. 6

Experimental correlation outputs and corresponding 3D plots for: (a,b) Nonwavelength-compensated JTC for the scene in Fig. 2a without P2; (c,d) Nonwavelength-compensated JTC for the scene in Fig. 2a with P2.

Fig. 7
Fig. 7

Experimental correlation outputs and corresponding 3D plots for: (a,b) Wavelength-compensated JTC for the scene in Fig. 2a; (c,d) Wavelength-compensated JTC for the scene in Fig. 2d.

Equations (8)

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JPS ( u , v ) = | FT { t ( x , y ) } | 2 = | R ( u , v ) exp [ j ϕ ( u , v ) ] + S ( u , v ) exp [ j ϕ ( u , v ) ] | 2 = | R ( u , v ) | 2 + | S ( u , v ) | 2 + R * ( u , v ) S ( u , v ) exp [ j 2 ϕ ( u , v ) ] + R ( u , v ) S * ( u , v ) exp [ j 2 ϕ ( u , v ) ] ,
t color ( x , y ) = i = R , G , B t i ( x , y ) = i = R , G , B r i ( x x 0 , y ) + s i ( x + x 0 , y ) .
J P S color ( u , v ) = i = R , G , B | FT { r i ( x + x 0 , y ) + s i ( x x 0 , y ) } | 2 = i = R , G , B | R i | 2 + | S i | 2 + R i * S i exp [ j 2 ϕ i ] + R i S i * exp [ + j 2 ϕ i ] ,
i = R , G , B | R i | 2 + | S i | 2
N 0 JPS color ( u , v ) = i = R , G , B R i * S i exp [ j 2 ϕ i ] + R i S i * exp [ + j 2 ϕ i ] = 2 i = R , G , B | R i | | S i | cos [ 2 ϕ i + φ i ] ,
PCE = | C ( 0 , 0 ) | 2 x , y | C ( x , y ) | 2 .
SNR = 10 log ( r ¯ 2 / n ¯ 2 ) ,
u = x / λ f and v = y / λ f ,

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