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

[CrossRef]

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

[CrossRef]

Y. Li, “Optical valve using bar codes,” Optik (Jena) 79, 67–74 (1988).

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571–1575 (1987).

[CrossRef]

X. Yang and C. Yin, “A new method for the design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34–37 (1986).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

Y. Li, “Optical valve using bar codes,” Optik (Jena) 79, 67–74 (1988).

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571–1575 (1987).

[CrossRef]

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

[CrossRef]

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

J. Saez-Landete, S. Salcedo-Sanz, F. Cruz-Roldan, P. Amo-Lopez, and M. Blanco-Velasco, “Design of two-dimensional optical alignment signals robust to diffractive effects,” J. Lightwave Technol. 26, 1702–1707 (2008).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

J. Saez-Landete, S. Salcedo-Sanz, F. Cruz-Roldan, P. Amo-Lopez, and M. Blanco-Velasco, “Design of two-dimensional optical alignment signals robust to diffractive effects,” J. Lightwave Technol. 26, 1702–1707 (2008).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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

[CrossRef]

X. Yang and C. Yin, “A new method for the design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34–37 (1986).

[CrossRef]

X. Yang and C. Yin, “A new method for the design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34–37 (1986).

[CrossRef]

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

[CrossRef]

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571–1575 (1987).

[CrossRef]

X. Yang and C. Yin, “A new method for the design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34–37 (1986).

[CrossRef]

Y. Li, “Optical valve using bar codes,” Optik (Jena) 79, 67–74 (1988).

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

[CrossRef]

If no design was done, we may randomly generate a binary 2D ZRC c. In this case, however, we still need an extra operation to fix the number of 1s in the binary strings to n1. This can be carried out by the restricted search operator , which randomly adds or removes the necessary 1s to meet the number of the transparent pixels.

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