An alternative method to generate J₀ Bessel beams with controlled spatial partial coherence properties is introduced. Far field diffraction from a discrete number of source points on an annular region is calculated. The average for different diffracted fields produced at several rotation angles is numerically calculated and experimentally detected. Theoretical and experimental results show that for this particular case, the J₀ Bessel beam is a limit when the number of points tends towards infinity and the associated complex degree of coherence is also a function of the number of points.

© 2010 OSA

1. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). [CrossRef]
2. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998). [CrossRef]
3. S. H. Tao and X. Yuan, “Self-reconstruction property of fractional Bessel beams,” J. Opt. Soc. Am. A 21(7), 1192–1197 (2004). [CrossRef]
4. Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
5. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75(10), 104102 (2007). [CrossRef]
6. F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. 45(5), 864–871 (2006). [CrossRef] [PubMed]
7. Z. Bouchal and J. Perina, “Non-diffracting beams with controlled spatial coherence,” J. Mod. Opt. 49(10), 1673–1689 (2002). [CrossRef]
8. H. T. Eyyuboglu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40(1), 156–166 (2008). [CrossRef]
9. K. Saastamoinen, J. Turunen, P. Vahimaa, and A. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A 80(5), 053804 (2009). [CrossRef]
10. G. M. Niconoff, J. Ramírez San Juan, J. M. López, and P. M. Vara, “Incoherent convergence of diffraction free fields,” Opt. Commun. 275(1), 10–13 (2007). [CrossRef]
11. R. Bracewell, The Fourier Transform & Its Applications, (McGraw-Hill Science/Engineering/Math, 1999).
12. J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company Publishers, 2004).
13. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).
14. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).
15. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, (Cambridge University Press, 1992).

Appl. Opt.

• F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. 45(5), 864–871 (2006). [CrossRef] [PubMed]

J. Mod. Opt.

• Z. Bouchal and J. Perina, “Non-diffracting beams with controlled spatial coherence,” J. Mod. Opt. 49(10), 1673–1689 (2002). [CrossRef]

J. Opt. Soc. Am. A

• J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). [CrossRef]
• S. H. Tao and X. Yuan, “Self-reconstruction property of fractional Bessel beams,” J. Opt. Soc. Am. A 21(7), 1192–1197 (2004). [CrossRef]

Opt. Commun.

• Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281, 1968–1975 (2008).
• Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998). [CrossRef]
• G. M. Niconoff, J. Ramírez San Juan, J. M. López, and P. M. Vara, “Incoherent convergence of diffraction free fields,” Opt. Commun. 275(1), 10–13 (2007). [CrossRef]

Opt. Laser Technol.

• H. T. Eyyuboglu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40(1), 156–166 (2008). [CrossRef]

Phys. Rev. A

• K. Saastamoinen, J. Turunen, P. Vahimaa, and A. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A 80(5), 053804 (2009). [CrossRef]

Phys. Rev. B

• G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75(10), 104102 (2007). [CrossRef]

Other

• R. Bracewell, The Fourier Transform & Its Applications, (McGraw-Hill Science/Engineering/Math, 1999).
• J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company Publishers, 2004).
• M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).
• L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).
• W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, (Cambridge University Press, 1992).

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