Abstract

We present a cross-entropy (CE)-based method to design 2-D zero reference codes (ZRCs) with minimum diffractive effects. Without diffraction effects, the optimum ZRC design problem is known as autocorrelation approximation. However, in high-resolution grating systems, limitations are given by the diffraction in the design of ZRCs. If the diffraction is considered, the output signal registered in the photodiode will widen and degrade, invalidating the autocorrelation approximation for the 2-D ZRC design. To minimize the diffractive effects in the design of 2-D ZRC, this paper first formulates the 2-D ZRC design problem with diffractive effects as a particular combinatorial optimization problem. Next, it proposes the application of the CE method to solve the problem. Compared with the conventional genetic algorithm (GA)-assisted 2-D ZRC design method, the simulation results show that the proposed CE method obtains better 2-D ZRCs that are less sensitive to diffractive effects. About 11.43 times less searching is required for the proposed CE method than for the GA. This indicates that the proposed CE method can obtain good ZRCs with minimum diffractive effects while maintaining low complexity.

© 2011 IEEE

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  2. W. Huang, "Nanoalignment mask fabricated directly on Si by AFM," Surf. Interface Anal. 32, 130-132 (2001).
  3. Y. Chen, W. Huang, "Optimization of zero-reference grating considering tip distortions for scanning probe microscopy drift measurement," J. Nanosci. Nanotechnol. 10, 7055-7059 (2010).
  4. X. Yang, C. Yin, "A new method for the design of zero reference marks for grating measurement systems," J. Phys. E Sci. Instrum. 19, 34-37 (1986).
  5. Y. Li, "Optical valve using bar codes," Optik 79, 67-74 (1988).
  6. Y. Chen, W. Huang, X. Dang, "Design and analysis of two-dimensional zero-reference marks for alignment systems," Rev. Sci. Instrum. 74, 3549-3553 (2003).
  7. J. Saez-Landete, J. Alonso, E. Bernabeu, "Design of two-dimensional zero reference codes by means of a global optimization method," Opt. Exp. 13, 4230-4236 (2005).
  8. J. Saez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Eusebio, A. Bernabeu, "Design of two-dimensional zero reference codes with a genetic algorithm," Opt. Lett. 31, 1648-1650 (2006).
  9. J.-C. Chen, C.-K. Wen, "Design of two-dimensional zero reference codes with cross-entropy method," Appl. Opt. 49, 3560-3565 (2010).
  10. J. Sáez-Landete, S. Salcedo-Sanz, F. Cruz-Roldán, P. Amo-López, M. Blanco-Velasco, "Design of two-dimensional optical alignment signals robust to diffractive effects," J. Lightw. Technol. 26, 1702-1707 (2008).
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  13. J. Li, G. Biondini, W. L. Kath, H. Kogelnik, "Outage statistics in a waveplate hinge model of polarization-mode dispersion," J. Lightw. Technol. 28, 1958-1968 (2010).
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  15. S. Salcedo-Sanz, G. Camps-Valls, F. Perez-Cruz, J. Sepulveda-Sanchis, C. Bousono-Calzon, "Enhancing genetic feature selection through restricted search and Walsh analysis," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev. 34, 398-406 (2004).
  16. Y. Zhang, C. Ji, W. Malik, D. O'Brien, D. Edwards, "Receive antenna selection for MIMO systems over correlated fading channels," IEEE Trans. Wireless Commun. 8, 4393-4399 (2009).

2010 (3)

Y. Chen, W. Huang, "Optimization of zero-reference grating considering tip distortions for scanning probe microscopy drift measurement," J. Nanosci. Nanotechnol. 10, 7055-7059 (2010).

J.-C. Chen, C.-K. Wen, "Design of two-dimensional zero reference codes with cross-entropy method," Appl. Opt. 49, 3560-3565 (2010).

J. Li, G. Biondini, W. L. Kath, H. Kogelnik, "Outage statistics in a waveplate hinge model of polarization-mode dispersion," J. Lightw. Technol. 28, 1958-1968 (2010).

2009 (2)

J.-C. Chen, "Design of zero reference codes using cross-entropy method," Opt. Exp. 17, 22163-22170 (2009).

Y. Zhang, C. Ji, W. Malik, D. O'Brien, D. Edwards, "Receive antenna selection for MIMO systems over correlated fading channels," IEEE Trans. Wireless Commun. 8, 4393-4399 (2009).

2008 (1)

J. Sáez-Landete, S. Salcedo-Sanz, F. Cruz-Roldán, P. Amo-López, M. Blanco-Velasco, "Design of two-dimensional optical alignment signals robust to diffractive effects," J. Lightw. Technol. 26, 1702-1707 (2008).

2006 (2)

Z. Chenggang, W. Yingnan, C. Yuhang, H. Wenhao, "Alignment measurement of two-dimensional zero-reference marks," Precis. Eng. 31, 1648-1650 (2006).

J. Saez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Eusebio, A. Bernabeu, "Design of two-dimensional zero reference codes with a genetic algorithm," Opt. Lett. 31, 1648-1650 (2006).

2005 (1)

J. Saez-Landete, J. Alonso, E. Bernabeu, "Design of two-dimensional zero reference codes by means of a global optimization method," Opt. Exp. 13, 4230-4236 (2005).

2004 (1)

S. Salcedo-Sanz, G. Camps-Valls, F. Perez-Cruz, J. Sepulveda-Sanchis, C. Bousono-Calzon, "Enhancing genetic feature selection through restricted search and Walsh analysis," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev. 34, 398-406 (2004).

2003 (1)

Y. Chen, W. Huang, X. Dang, "Design and analysis of two-dimensional zero-reference marks for alignment systems," Rev. Sci. Instrum. 74, 3549-3553 (2003).

2001 (1)

W. Huang, "Nanoalignment mask fabricated directly on Si by AFM," Surf. Interface Anal. 32, 130-132 (2001).

1988 (1)

Y. Li, "Optical valve using bar codes," Optik 79, 67-74 (1988).

1986 (1)

X. Yang, C. Yin, "A new method for the design of zero reference marks for grating measurement systems," J. Phys. E Sci. Instrum. 19, 34-37 (1986).

Appl. Opt. (1)

IEEE Trans. Syst., Man, Cybern. C, Appl. Rev. (1)

S. Salcedo-Sanz, G. Camps-Valls, F. Perez-Cruz, J. Sepulveda-Sanchis, C. Bousono-Calzon, "Enhancing genetic feature selection through restricted search and Walsh analysis," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev. 34, 398-406 (2004).

IEEE Trans. Wireless Commun. (1)

Y. Zhang, C. Ji, W. Malik, D. O'Brien, D. Edwards, "Receive antenna selection for MIMO systems over correlated fading channels," IEEE Trans. Wireless Commun. 8, 4393-4399 (2009).

J. Lightw. Technol. (2)

J. Sáez-Landete, S. Salcedo-Sanz, F. Cruz-Roldán, P. Amo-López, M. Blanco-Velasco, "Design of two-dimensional optical alignment signals robust to diffractive effects," J. Lightw. Technol. 26, 1702-1707 (2008).

J. Li, G. Biondini, W. L. Kath, H. Kogelnik, "Outage statistics in a waveplate hinge model of polarization-mode dispersion," J. Lightw. Technol. 28, 1958-1968 (2010).

J. Nanosci. Nanotechnol. (1)

Y. Chen, W. Huang, "Optimization of zero-reference grating considering tip distortions for scanning probe microscopy drift measurement," J. Nanosci. Nanotechnol. 10, 7055-7059 (2010).

J. Phys. E Sci. Instrum. (1)

X. Yang, C. Yin, "A new method for the design of zero reference marks for grating measurement systems," J. Phys. E Sci. Instrum. 19, 34-37 (1986).

Opt. Exp. (2)

J. Saez-Landete, J. Alonso, E. Bernabeu, "Design of two-dimensional zero reference codes by means of a global optimization method," Opt. Exp. 13, 4230-4236 (2005).

J.-C. Chen, "Design of zero reference codes using cross-entropy method," Opt. Exp. 17, 22163-22170 (2009).

Opt. Lett. (1)

Optik (1)

Y. Li, "Optical valve using bar codes," Optik 79, 67-74 (1988).

Precis. Eng. (1)

Z. Chenggang, W. Yingnan, C. Yuhang, H. Wenhao, "Alignment measurement of two-dimensional zero-reference marks," Precis. Eng. 31, 1648-1650 (2006).

Rev. Sci. Instrum. (1)

Y. Chen, W. Huang, X. Dang, "Design and analysis of two-dimensional zero-reference marks for alignment systems," Rev. Sci. Instrum. 74, 3549-3553 (2003).

Surf. Interface Anal. (1)

W. Huang, "Nanoalignment mask fabricated directly on Si by AFM," Surf. Interface Anal. 32, 130-132 (2001).

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

R. Y. Rubinstein, D. P. Kroese, The Cross-Entropy Method (Springer-Verlag, 2004).

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