Abstract

A model for forward scattering from bacterial colonies is presented. The colonies of interest consist of approximately 10121013 individual bacteria densely packed in a configuration several millimeters in diameter and approximately 0.10.2mm in thickness. The model is based on scalar diffraction theory and accounts for amplitude and phase modulation created by three macroscopic properties of the colonies: phase modulation due to the surface topography, phase modulation due to the radial structure observed from some strains and species, and diffraction from the outline of the colony. Phase contrast and confocal microscopy were performed to provide quantitative information on the shape and internal structure of the colonies. The computed results showed excellent agreement with the experimental scattering data for three different Listeria species: Listeria innocua, Listeria ivanovii, and Listeria monocytogenes. The results provide a physical explanation for the unique and distinctive scattering signatures produced by colonies of closely related Listeria species and support the efficacy of forward scattering for rapid detection and classification of pathogens without tagging.

© 2007 Optical Society of America

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  1. J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  10. P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
    [CrossRef]
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    [CrossRef]
  14. C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific Publishers, 1997).
  15. E. A. Hovenac and E. D. Hirleman, "Use of pinholes and reticles for calibration of cloud droplet instrumentation," J. Atmos. Ocean. Technol. 8, 166-171 (1991).
    [CrossRef]
  16. H. Mühlenweg and E. D. Hirleman, "Reticles as standards in laser diffraction spectroscopy," Part. Part. Syst. Charact. 16, 47-53 (1999).
    [CrossRef]
  17. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
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2001 (3)

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

B. V. Bronk, Z. Z. Li, and J. Czégé, "Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria," J. Appl. Toxicol. 21, 107-113 (2001).
[CrossRef] [PubMed]

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

2000 (2)

Z. Lan, F. Fiedler, and S. Kathariou, "A sheep in wolf's clothing: Listeria innocua strains with teichoic acid-associated surface antigens and genes characteristics of Listeria monocytogenes serogroup 4," J. Bacteriol. 182, 6161-6168 (2000).
[CrossRef] [PubMed]

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

1999 (2)

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

H. Mühlenweg and E. D. Hirleman, "Reticles as standards in laser diffraction spectroscopy," Part. Part. Syst. Charact. 16, 47-53 (1999).
[CrossRef]

1998 (1)

1992 (1)

B. V. Bronk, W. P. Van De Merwe, and M. Stanley, "In vivo measure of average bacterial cell size from a polarized light scattering function," Cytometry 13, 155-162 (1992).
[CrossRef] [PubMed]

1991 (1)

E. A. Hovenac and E. D. Hirleman, "Use of pinholes and reticles for calibration of cloud droplet instrumentation," J. Atmos. Ocean. Technol. 8, 166-171 (1991).
[CrossRef]

1989 (1)

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

1985 (1)

L. Beerden, E. L. M. Flerackers, and H. J. Janssen, "Phase-contrast microscopy," Eur. J. Phys. 6, 139-142 (1985).
[CrossRef]

1984 (1)

Bae, E.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Banada, P. P.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Barton, J.

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

Bayraktar, B.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Beerden, L.

L. Beerden, E. L. M. Flerackers, and H. J. Janssen, "Phase-contrast microscopy," Eur. J. Phys. 6, 139-142 (1985).
[CrossRef]

Berche, P.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Bhunia, A. K.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Bottiger, J. R.

Bronk, B. V.

B. V. Bronk, Z. Z. Li, and J. Czégé, "Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria," J. Appl. Toxicol. 21, 107-113 (2001).
[CrossRef] [PubMed]

B. V. Bronk, W. P. Van De Merwe, and M. Stanley, "In vivo measure of average bacterial cell size from a polarized light scattering function," Cytometry 13, 155-162 (1992).
[CrossRef] [PubMed]

Chakraborty, T.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Chang, R. K.

Clark, D.

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

Curtis, G. D.

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

Czégé, J.

B. V. Bronk, Z. Z. Li, and J. Czégé, "Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria," J. Appl. Toxicol. 21, 107-113 (2001).
[CrossRef] [PubMed]

Dominguez-Bernal, G.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Fiedler, F.

Z. Lan, F. Fiedler, and S. Kathariou, "A sheep in wolf's clothing: Listeria innocua strains with teichoic acid-associated surface antigens and genes characteristics of Listeria monocytogenes serogroup 4," J. Bacteriol. 182, 6161-6168 (2000).
[CrossRef] [PubMed]

Flerackers, E. L. M.

L. Beerden, E. L. M. Flerackers, and H. J. Janssen, "Phase-contrast microscopy," Eur. J. Phys. 6, 139-142 (1985).
[CrossRef]

Goebel, W.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Gonzalez-Zorn, B.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Griffin, E. J.

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

Guo, S.

S. Guo, "Optical scattering for bacterial colony detection and characterization," M.S. thesis (Purdue University, 2004).

Guo, S. L.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Hill, S. C.

Hillis, D. B.

Hirleman, E. D.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

H. Mühlenweg and E. D. Hirleman, "Reticles as standards in laser diffraction spectroscopy," Part. Part. Syst. Charact. 16, 47-53 (1999).
[CrossRef]

E. A. Hovenac and E. D. Hirleman, "Use of pinholes and reticles for calibration of cloud droplet instrumentation," J. Atmos. Ocean. Technol. 8, 166-171 (1991).
[CrossRef]

Hirst, E.

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

Holler, S.

Hovenac, E. A.

E. A. Hovenac and E. D. Hirleman, "Use of pinholes and reticles for calibration of cloud droplet instrumentation," J. Atmos. Ocean. Technol. 8, 166-171 (1991).
[CrossRef]

Janssen, H. J.

L. Beerden, E. L. M. Flerackers, and H. J. Janssen, "Phase-contrast microscopy," Eur. J. Phys. 6, 139-142 (1985).
[CrossRef]

Kathariou, S.

Z. Lan, F. Fiedler, and S. Kathariou, "A sheep in wolf's clothing: Listeria innocua strains with teichoic acid-associated surface antigens and genes characteristics of Listeria monocytogenes serogroup 4," J. Bacteriol. 182, 6161-6168 (2000).
[CrossRef] [PubMed]

Kaye, P.

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

King, A. F.

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

Kochneva, G. V.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Kreft, J.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Kuhn, M.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Lan, Z.

Z. Lan, F. Fiedler, and S. Kathariou, "A sheep in wolf's clothing: Listeria innocua strains with teichoic acid-associated surface antigens and genes characteristics of Listeria monocytogenes serogroup 4," J. Bacteriol. 182, 6161-6168 (2000).
[CrossRef] [PubMed]

Li, Z. Z.

B. V. Bronk, Z. Z. Li, and J. Czégé, "Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria," J. Appl. Toxicol. 21, 107-113 (2001).
[CrossRef] [PubMed]

Maltsev, V. P.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Mitchell, R. G.

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

Mühlenweg, H.

H. Mühlenweg and E. D. Hirleman, "Reticles as standards in laser diffraction spectroscopy," Part. Part. Syst. Charact. 16, 47-53 (1999).
[CrossRef]

Pan, Y.

Petrov, A. K.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Rajwa, B.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Richter, J. L.

Robinson, J. P.

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Saunders, S.

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific Publishers, 1997).

Shotton, D. M.

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific Publishers, 1997).

Shvalov, A. N.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Sivolobova, G. F.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Soini, J. T.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Stanley, M.

B. V. Bronk, W. P. Van De Merwe, and M. Stanley, "In vivo measure of average bacterial cell size from a polarized light scattering function," Cytometry 13, 155-162 (1992).
[CrossRef] [PubMed]

Suiter, H. R.

H. R. Suiter, Star Testing Astronomical Telescopes (Willmann-Bell, 2003).

Surovtsev, I. V.

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Van De Merwe, W. P.

B. V. Bronk, W. P. Van De Merwe, and M. Stanley, "In vivo measure of average bacterial cell size from a polarized light scattering function," Cytometry 13, 155-162 (1992).
[CrossRef] [PubMed]

Vazquez-Boland, J. A.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics (Prentice-Hall, 1995).

Wehland, J.

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biosens. Bioelectron. (1)

P. P. Banada, S. L. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Optical forward scattering for colony identification and differentiation of Listeria species," Biosens. Bioelectron. 22, 1664-1671 (2001).
[CrossRef]

Clin. Microbiol. Rev. (1)

J. A. Vazquez-Boland, M. Kuhn, P. Berche, T. Chakraborty, G. Dominguez-Bernal, W. Goebel, B. Gonzalez-Zorn, J. Wehland, and J. Kreft, "Listeria pathogenesis and molecular virulence determinants," Clin. Microbiol. Rev. 14, 584-640 (2001).
[CrossRef] [PubMed]

Cytometry (2)

B. V. Bronk, W. P. Van De Merwe, and M. Stanley, "In vivo measure of average bacterial cell size from a polarized light scattering function," Cytometry 13, 155-162 (1992).
[CrossRef] [PubMed]

A. N. Shvalov, J. T. Soini, I. V. Surovtsev, G. V. Kochneva, G. F. Sivolobova, A. K. Petrov, and V. P. Maltsev, "Individual Escherichia coli cells studied from light scattering with the scanning flow cytometer," Cytometry 41, 41-45 (2000).
[CrossRef] [PubMed]

Eur. J. Phys. (1)

L. Beerden, E. L. M. Flerackers, and H. J. Janssen, "Phase-contrast microscopy," Eur. J. Phys. 6, 139-142 (1985).
[CrossRef]

J. Appl. Toxicol. (1)

B. V. Bronk, Z. Z. Li, and J. Czégé, "Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria," J. Appl. Toxicol. 21, 107-113 (2001).
[CrossRef] [PubMed]

J. Atmos. Ocean. Technol. (1)

E. A. Hovenac and E. D. Hirleman, "Use of pinholes and reticles for calibration of cloud droplet instrumentation," J. Atmos. Ocean. Technol. 8, 166-171 (1991).
[CrossRef]

J. Bacteriol. (1)

Z. Lan, F. Fiedler, and S. Kathariou, "A sheep in wolf's clothing: Listeria innocua strains with teichoic acid-associated surface antigens and genes characteristics of Listeria monocytogenes serogroup 4," J. Bacteriol. 182, 6161-6168 (2000).
[CrossRef] [PubMed]

Lett. Appl. Microbiol. (1)

G. D. Curtis, R. G. Mitchell, A. F. King, and E. J. Griffin, "A selective medium for the isolation of Listeria monocytogenes," Lett. Appl. Microbiol. 8, 85-98 (1989).
[CrossRef]

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

H. Mühlenweg and E. D. Hirleman, "Reticles as standards in laser diffraction spectroscopy," Part. Part. Syst. Charact. 16, 47-53 (1999).
[CrossRef]

Proc. SPIE (1)

J. Barton, E. Hirst, P. Kaye, S. Saunders, and D. Clark, "Airborne particle characterization by spatial scattering and fluorescence," Proc. SPIE 3855, 92-100 (1999).
[CrossRef]

Other (6)

S. Guo, "Optical scattering for bacterial colony detection and characterization," M.S. thesis (Purdue University, 2004).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

J. T. Verdeyen, Laser Electronics (Prentice-Hall, 1995).

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

H. R. Suiter, Star Testing Astronomical Telescopes (Willmann-Bell, 2003).

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (BIOS Scientific Publishers, 1997).

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Figures (6)

Fig. 1
Fig. 1

Schematic of bacterial rapid detection using optical scattering technology (BARDOT) platform.

Fig. 2
Fig. 2

(a) Coordinates for source, colony, and image plane. (b) Side and top view and geometric parameter of the bacteria colony.

Fig. 3
Fig. 3

(Color online) Phase contrast microscopic images of colonies of (a) Listeria innocua, (b) Listeria ivanovii, (c) Listeria monocytogenes.

Fig. 4
Fig. 4

Confocal microscope image for the colony of a green-fluorescence-protein- (GFP-) expressing Listeria monocytogenes strain. (a) Maximum intensity projection, (b) cross section along the Y axis of a 3D stack of confocal microscope images.

Fig. 5
Fig. 5

Comparison of intensity distribution across radial direction of proposed model and reference sample at z = 57 mm. (a) Circular aperture with 800 μm diameter, and (b) circular block with 800 μm diameter.

Fig. 6
Fig. 6

Comparison of BARDOT image (left column) and proposed model (right column). (a) and (b) Listeria innocua, (c) and (d) Listeria ivanovii, (e) and (f) Listeria monocytogenes.

Equations (15)

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E ( x s , y s , z ) = E 0 { w 0 w ( z ) exp [ ( x s 2 + y s 2 ) w 2 ( z ) ] } × exp { [ i k z tan 1 ( z z 0 ) ] } × { exp [ i k x s 2 + y s 2 2 R ( z ) ] } ,
w 2 ( z ) = w 0 2 [ 1 + ( z z 0 ) 2 ] ,     R ( z ) = z [ 1 + ( z 0 z ) 2 ] ,
E 1 ( x a , y a , z 1 ) = E 0 exp ( ( x a 2 + y a 2 ) w 2 ( z 1 ) ) exp [ i k z 1 ] × exp [ i k ( x a 2 + y a 2 ) 2 R ( z 1 ) ] ,
E 2 ( x i , y i ) = 1 i λ Σ t ( x a , y a ) E 1 ( x a , y a ) exp [ i k ( ϕ ( x a , y a ) ) ] × exp [ i k r a i r a i ] cos θ d x a d y a ,
E 2 ( x i , y i ) C 1 Σ t ( x a , y a ) exp [ ( x a 2 + y a 2 ) w 2 ( z 1 ) ] × exp [ i k ( x a 2 + y a 2 ) 2 R ( z 1 ) ] exp [ i k ( x a 2 + y a 2 ) 2 z 2 ] × exp [ i k ϕ ( x a , y a ) ] × exp [ i 2 π ( f x x a + f y y a ) ] d x a d y a ,
C 1 = E 0 exp [ i k n 2 Δ 2 ] exp [ i k n 3 Δ 3 ] exp [ i k ( z 1 + z 2 ) ] exp [ i k 2 z 2 ( x i 2 + y i 2 ) ] i λ z 2 , f x = x i λ z 2 , f y = y i λ z 2 .
E 2 ( x i , y i ) C 1 Σ t ( x a , y a ) exp [ ( x a 2 + y a 2 ) w 2 ( z 1 ) ] × exp [ i k ϕ ( x a , y a ) ] × exp [ i 2 π ( f x x a + f y y a ) ] d x a d y a ,
E 2 ( x i , y i ) C 1 Σ 1 t 1 exp [ ( x a 2 + y a 2 ) w 2 ( z 1 ) ] exp [ i k ϕ 1 ( x a , y a ) ] × exp [ i 2 π ( f x x a + f y y a ) ] d x a d y a + C 1 Σ 2 t 2 exp [ ( x a 2 + y a 2 ) w 2 ( z 1 ) ] exp [ i k ϕ 2 ( x a , y a ) ] × exp [ i 2 π ( f x x a + f y y a ) ] d x a d y a + C 1 Σ 3 t 3 exp [ ( x a 2 + y a 2 ) w 2 ( z 1 ) ] exp [ i k ϕ 3 ( x a , y a ) ] × exp [ i 2 π ( f x x a + f y y a ) ] d x a d y a ,
ϕ 1 ( x a , y a ) = ( ( x a 2 + y a 2 ) 2 ) ( 1 R ( z 1 ) + 1 z 2 1 f 1 ) + ϕ 1 s ( x a , y a ) ,
ϕ 2 ( x a , y a ) = ( ( x a 2 + y a 2 ) 2 ) ( 1 R ( z 1 ) + 1 z 2 1 f 2 ) + ϕ 2 s ( x a , y a ) ,
ϕ 3 ( x a , y a ) = ( ( x a 2 + y a 2 ) 2 ) ( 1 R ( z 1 ) + 1 z 2 )
1 f 1 = ( n 11 1 ) ( 1 R 1 1 R ) ,
1 f 2 = ( n 12 1 ) ( 1 R 2 1 R ) ,
E 2 ( x i , y i ) = 1 i λ 0 r 0 J 0 ( k r i r a / z 2 ) exp [ i k ( r a 2 ) ( 1 z 1 + 1 z 2 ) ] r a d r a ,
E 2 ( x i , y i ) = 1 i λ r 0 J 0 ( k r i r a / z 2 ) exp [ i k ( r a 2 ) ( 1 z 1 + 1 z 2 ) ] r a d r a .

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