Abstract

The novel optical system based on converging spherical wave illumination for analysis of bacteria colonies diffraction patterns, is proposed. The complex physical model of light transformation on bacteria colonies in this system, is presented. Fresnel diffraction patterns of bacteria colonies Escherichia coli, Salmonella enteritidis, Staphylococcus aureus grown in various conditions, were examined. It was demonstrated that the proposed system enables the characterization of morphological changes of colony structures basing on the changes of theirs Fresnel diffraction patterns.

© 2011 OSA

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2011

E. Bae, A. Aroonnual, A. K. Bhunia, and E. D. Hirleman, “On the sensitivity of forward scattering patterns from bacterial colonies to media composition,” J. Biophotonics 4(4), 236–243 (2011).
[CrossRef] [PubMed]

2010

I. Buzalewicz, K. Wysocka-Król, and H. Podbielska, “Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms,” Opt. Express 18(12), 12992–13005 (2010).
[CrossRef] [PubMed]

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

T. Ersek and Z. Nagy, “Species hybrids in the genus Phytophthora with emphasis on the alder pathogen Phytophthora alni: a review,” Eur. J. Plant Pathol. 22(1), 31–39 (2010).

2009

A. C. Samuels, A. P. Snyder, D. K. Emge, D. Amant, J. Minter, M. Campbell, and A. Tripathi, “Classification of select category A and B bacteria by Fourier transform infrared spectroscopy,” Appl. Spectrosc. 63(1), 14–24 (2009).
[CrossRef] [PubMed]

I. Buzalewicz, K. Wysocka, and H. Podbielska, “Exploiting of optical transforms for bacteria evaluation in vitro,” Proc. SPIE 7371, 73711H, 73711H-6 (2009).
[CrossRef]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

2008

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008).
[CrossRef] [PubMed]

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
[CrossRef] [PubMed]

A. Maninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross-sections from airborne microsized particle,” Appl. Opt. 47(7), 110–115 (2008).

2007

2006

2005

R. T. Noble and S. B. Weisberg, “A review of technologies for rapid detection of bacteria in recreational waters,” J. Water Health 3(4), 381–392 (2005).
[PubMed]

S. Sarasanandarajah, J. Kunnil, B. V. Bronk, and L. Reinisch, “Two-dimensional multiwavelength fluorescence spectra of dipicolinic acid and calcium dipicolinate,” Appl. Opt. 44(7), 1182–1187 (2005).
[CrossRef] [PubMed]

2004

S. B. Levy and B. Marshall, “Antibacterial resistance worldwide: causes, challenges and responses,” Nat. Med. 10(12Suppl), S122–S129 (2004).
[CrossRef] [PubMed]

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

S. Holler, S. Zomer, G. F. Crosta, Y. L. Pan, R. K. Chang, and J. R. Bottiger, “Multivariate analysis and classification of two-dimensional angular optical scattering patterns from aggregates,” Appl. Opt. 43(33), 6198–6206 (2004).
[CrossRef] [PubMed]

J. Thomason, “Spectroscopy takes security into the field,” Photon. Spectra 38, 83–85 (2004).

P. Leonard, S. Hearty, J. Quinn, and R. O’Kennedy, “A generic approach for the detection of whole Listeria monocytogenes cells in contaminated samples using surface plasmon resonance,” Biosens. Bioelectron. 19(10), 1331–1335 (2004).
[CrossRef] [PubMed]

2003

2002

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
[CrossRef] [PubMed]

L. J. Radziemski, “From LASER to LIBS, the path of technology development,” Spectrochim. Acta, B At. Spectrosc. 57(7), 1109–1113 (2002).
[CrossRef]

2001

2000

P. H. Kaye, J. E. Barton, E. Hirst, and J. M. Clark, “Simultaneous light scattering and intrinsic fluorescence measurement for the classification of airborne particles,” Appl. Opt. 39(21), 3738–3745 (2000).
[CrossRef] [PubMed]

S. G. B. Amyes, “The rise in bacterial resistance,” Br. Med. J. 320(7229), 199–200 (2000).
[CrossRef] [PubMed]

M. A. Bees, P. Andresén, E. Mosekilde, and M. Givskov, “The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens,” J. Math. Biol. 40(1), 27–63 (2000).
[CrossRef] [PubMed]

1999

D. Ivnitski, I. Abdel-Hamid, P. Atanasov, and E. Wilkins, “Biosensors for detection of pathogenic bacteria,” Biosens. Bioelectron. 14(7), 599–624 (1999).
[CrossRef]

Y. L. Pan, S. Holler, R. K. Chang, S. C. Hill, R. G. Pinnick, S. Niles, and J. R. Bottiger, “Single-shot fluorescence spectra of individual micrometer-sized bioaerosols illuminated by a 351- or a 266-nm ultraviolet laser,” Opt. Lett. 24(2), 116–118 (1999).
[CrossRef] [PubMed]

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

D. L. Rosen, “Bacterial endospores detection using photoluminescence from terbium dipicolinate,” Rev. Anal. Chem. 18(1-2), 1–22 (1999).
[CrossRef]

1998

A. S. Colsky, R. S. Kirsner, and F. A. Kerdel, “Analysis of antibiotic susceptibilities of skin wound flora in hospitalized dermatology patients. The crisis of antibiotic resistance has come to the surface,” Arch. Dermatol. 134(8), 1006–1009 (1998).
[CrossRef] [PubMed]

1997

1982

1968

Abdel-Hamid, I.

D. Ivnitski, I. Abdel-Hamid, P. Atanasov, and E. Wilkins, “Biosensors for detection of pathogenic bacteria,” Biosens. Bioelectron. 14(7), 599–624 (1999).
[CrossRef]

Adam, P.

Adil, A.

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

Alfano, R. R.

Alimova, A.

Amant, D.

Amouroux, J.

Amyes, S. G. B.

S. G. B. Amyes, “The rise in bacterial resistance,” Br. Med. J. 320(7229), 199–200 (2000).
[CrossRef] [PubMed]

Andresén, P.

M. A. Bees, P. Andresén, E. Mosekilde, and M. Givskov, “The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens,” J. Math. Biol. 40(1), 27–63 (2000).
[CrossRef] [PubMed]

Aptowicz, K.

Aptowicz, K. B.

Aroonnual, A.

E. Bae, A. Aroonnual, A. K. Bhunia, and E. D. Hirleman, “On the sensitivity of forward scattering patterns from bacterial colonies to media composition,” J. Biophotonics 4(4), 236–243 (2011).
[CrossRef] [PubMed]

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

Atanasov, P.

D. Ivnitski, I. Abdel-Hamid, P. Atanasov, and E. Wilkins, “Biosensors for detection of pathogenic bacteria,” Biosens. Bioelectron. 14(7), 599–624 (1999).
[CrossRef]

Auger, J. C.

Badrane, H.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Bae, E.

E. Bae, A. Aroonnual, A. K. Bhunia, and E. D. Hirleman, “On the sensitivity of forward scattering patterns from bacterial colonies to media composition,” J. Biophotonics 4(4), 236–243 (2011).
[CrossRef] [PubMed]

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

Bai, N.

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

Baker, H. V.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Banada, P. P.

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

Bartlett, K.

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
[CrossRef] [PubMed]

Barton, J. E.

Baum, D.

Bayraktar, B.

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

Bees, M. A.

M. A. Bees, P. Andresén, E. Mosekilde, and M. Givskov, “The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens,” J. Math. Biol. 40(1), 27–63 (2000).
[CrossRef] [PubMed]

Bhunia, A. K.

E. Bae, A. Aroonnual, A. K. Bhunia, and E. D. Hirleman, “On the sensitivity of forward scattering patterns from bacterial colonies to media composition,” J. Biophotonics 4(4), 236–243 (2011).
[CrossRef] [PubMed]

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

Bottiger, J.

S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. L. Pan, J. Bottiger, B. V. Bronk, S. Holler, and R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40(18), 3005–3013 (2001).
[CrossRef] [PubMed]

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Bottiger, J. R.

Bronk, B. V.

Buzalewicz, I.

I. Buzalewicz, K. Wysocka-Król, and H. Podbielska, “Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms,” Opt. Express 18(12), 12992–13005 (2010).
[CrossRef] [PubMed]

I. Buzalewicz, K. Wysocka, and H. Podbielska, “Exploiting of optical transforms for bacteria evaluation in vitro,” Proc. SPIE 7371, 73711H, 73711H-6 (2009).
[CrossRef]

Campbell, M.

Chang, R. K.

J. C. Auger, K. B. Aptowicz, R. G. Pinnick, Y.-L. Pan, and R. K. Chang, “Angularly resolved light scattering from aerosolized spores: observations and calculations,” Opt. Lett. 32(22), 3358–3360 (2007).
[CrossRef] [PubMed]

G. E. Fernandes, Y. L. Pan, R. K. Chang, K. Aptowicz, and R. G. Pinnick, “Simultaneous forward- and backward-hemisphere elastic-light-scattering patterns of respirable-size aerosols,” Opt. Lett. 31(20), 3034–3036 (2006).
[CrossRef] [PubMed]

S. Holler, S. Zomer, G. F. Crosta, Y. L. Pan, R. K. Chang, and J. R. Bottiger, “Multivariate analysis and classification of two-dimensional angular optical scattering patterns from aggregates,” Appl. Opt. 43(33), 6198–6206 (2004).
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Y. L. Pan, K. B. Aptowicz, R. K. Chang, M. Hart, and J. D. Eversole, “Characterizing and monitoring respiratory aerosols by light scattering,” Opt. Lett. 28(8), 589–591 (2003).
[CrossRef] [PubMed]

S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. L. Pan, J. Bottiger, B. V. Bronk, S. Holler, and R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40(18), 3005–3013 (2001).
[CrossRef] [PubMed]

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Y. L. Pan, S. Holler, R. K. Chang, S. C. Hill, R. G. Pinnick, S. Niles, and J. R. Bottiger, “Single-shot fluorescence spectra of individual micrometer-sized bioaerosols illuminated by a 351- or a 266-nm ultraviolet laser,” Opt. Lett. 24(2), 116–118 (1999).
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Chen, B. T.

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Chen, S.

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
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K. Christen, “Bioterrorism and waterborne pathogens: how big is the threat?” Environ. Sci. Technol. 35(19), 396A–397A (2001).
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Colsky, A. S.

A. S. Colsky, R. S. Kirsner, and F. A. Kerdel, “Analysis of antibiotic susceptibilities of skin wound flora in hospitalized dermatology patients. The crisis of antibiotic resistance has come to the surface,” Arch. Dermatol. 134(8), 1006–1009 (1998).
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Copeland, R. A.

Crosta, G. F.

Dennis, C.

C. Dennis, “The bugs of war,” Nature 411(6835), 232–235 (2001).
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Dostálek, J.

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
[CrossRef] [PubMed]

Elmieh, N.

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
[CrossRef] [PubMed]

Emge, D. K.

Ersek, T.

T. Ersek and Z. Nagy, “Species hybrids in the genus Phytophthora with emphasis on the alder pathogen Phytophthora alni: a review,” Eur. J. Plant Pathol. 22(1), 31–39 (2010).

Eversole, J. D.

Faris, G. W.

Feather, G.

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Fell, N. F.

Fernandes, G. E.

Garvey, D. M.

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Givskov, M.

M. A. Bees, P. Andresén, E. Mosekilde, and M. Givskov, “The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens,” J. Math. Biol. 40(1), 27–63 (2000).
[CrossRef] [PubMed]

Gottlieb, P.

Gulig, P. A.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Guo, S.

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

Hart, M.

Hearty, S.

P. Leonard, S. Hearty, J. Quinn, and R. O’Kennedy, “A generic approach for the detection of whole Listeria monocytogenes cells in contaminated samples using surface plasmon resonance,” Biosens. Bioelectron. 19(10), 1331–1335 (2004).
[CrossRef] [PubMed]

Hernberg, R.

Hill, S. C.

Hilliard, L. R.

S. J. Mechery, X. J. Zhao, L. Wang, L. R. Hilliard, A. Munteanu, and W. Tan, “Using bioconjugated nanoparticles to monitor E. coli in a flow channel,” Chem. Asian J. 1(3), 384–390 (2006).
[CrossRef] [PubMed]

Hirleman, E. D.

E. Bae, A. Aroonnual, A. K. Bhunia, and E. D. Hirleman, “On the sensitivity of forward scattering patterns from bacterial colonies to media composition,” J. Biophotonics 4(4), 236–243 (2011).
[CrossRef] [PubMed]

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

Hirst, E.

Holler, S.

Homola, J.

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
[CrossRef] [PubMed]

Huff, K.

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

Hurrell, Ch.

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
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Irudayaraj, J.

A. Subramanian, J. Irudayaraj, and T. Ryan, “A mixed self-assembled monolayer-based surface plasmon immunosensor for detection of E. coli O157:H7,” Biosens. Bioelectron. 21(7), 998–1006 (2006).
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D. Ivnitski, I. Abdel-Hamid, P. Atanasov, and E. Wilkins, “Biosensors for detection of pathogenic bacteria,” Biosens. Bioelectron. 14(7), 599–624 (1999).
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Jiang, S.

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
[CrossRef] [PubMed]

Jin, S.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Joyeux, D.

Katz, A.

Kaye, P. H.

Kerdel, F. A.

A. S. Colsky, R. S. Kirsner, and F. A. Kerdel, “Analysis of antibiotic susceptibilities of skin wound flora in hospitalized dermatology patients. The crisis of antibiotic resistance has come to the surface,” Arch. Dermatol. 134(8), 1006–1009 (1998).
[CrossRef] [PubMed]

Keskinen, J.

Kirsner, R. S.

A. S. Colsky, R. S. Kirsner, and F. A. Kerdel, “Analysis of antibiotic susceptibilities of skin wound flora in hospitalized dermatology patients. The crisis of antibiotic resistance has come to the surface,” Arch. Dermatol. 134(8), 1006–1009 (1998).
[CrossRef] [PubMed]

Kunnil, J.

Lary, T.

Laurila, T.

Leonard, P.

P. Leonard, S. Hearty, J. Quinn, and R. O’Kennedy, “A generic approach for the detection of whole Listeria monocytogenes cells in contaminated samples using surface plasmon resonance,” Biosens. Bioelectron. 19(10), 1331–1335 (2004).
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Levy, S. B.

S. B. Levy and B. Marshall, “Antibacterial resistance worldwide: causes, challenges and responses,” Nat. Med. 10(12Suppl), S122–S129 (2004).
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W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Lim, D. V.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Litherland, S. A.

W. Lian, S. A. Litherland, H. Badrane, W. Tan, D. Wu, H. V. Baker, P. A. Gulig, D. V. Lim, and S. Jin, “Ultrasensitive detection of biomolecules with fluorescent dye-doped nanoparticles,” Anal. Biochem. 334(1), 135–144 (2004).
[CrossRef] [PubMed]

Lowenthal, S.

Maninen, A.

Marjamäki, M.

Marshall, B.

S. B. Levy and B. Marshall, “Antibacterial resistance worldwide: causes, challenges and responses,” Nat. Med. 10(12Suppl), S122–S129 (2004).
[CrossRef] [PubMed]

McDowall, W.

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
[CrossRef] [PubMed]

Mechery, S. J.

S. J. Mechery, X. J. Zhao, L. Wang, L. R. Hilliard, A. Munteanu, and W. Tan, “Using bioconjugated nanoparticles to monitor E. coli in a flow channel,” Chem. Asian J. 1(3), 384–390 (2006).
[CrossRef] [PubMed]

Minter, J.

Morel, S.

Mortelmans, K.

Mosekilde, E.

M. A. Bees, P. Andresén, E. Mosekilde, and M. Givskov, “The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens,” J. Math. Biol. 40(1), 27–63 (2000).
[CrossRef] [PubMed]

Munteanu, A.

S. J. Mechery, X. J. Zhao, L. Wang, L. R. Hilliard, A. Munteanu, and W. Tan, “Using bioconjugated nanoparticles to monitor E. coli in a flow channel,” Chem. Asian J. 1(3), 384–390 (2006).
[CrossRef] [PubMed]

Nagy, Z.

T. Ersek and Z. Nagy, “Species hybrids in the genus Phytophthora with emphasis on the alder pathogen Phytophthora alni: a review,” Eur. J. Plant Pathol. 22(1), 31–39 (2010).

Nicol, A. M.

A. M. Nicol, Ch. Hurrell, W. McDowall, K. Bartlett, and N. Elmieh, “Communicating the risks of a new, emerging pathogen: the case of Cryptococcus gattii,” Risk Anal. 28(2), 373–386 (2008).
[CrossRef] [PubMed]

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R. T. Noble and S. B. Weisberg, “A review of technologies for rapid detection of bacteria in recreational waters,” J. Water Health 3(4), 381–392 (2005).
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O’Kennedy, R.

P. Leonard, S. Hearty, J. Quinn, and R. O’Kennedy, “A generic approach for the detection of whole Listeria monocytogenes cells in contaminated samples using surface plasmon resonance,” Biosens. Bioelectron. 19(10), 1331–1335 (2004).
[CrossRef] [PubMed]

Orr, C.-S.

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Pan, Y. L.

Pan, Y.-L.

J. C. Auger, K. B. Aptowicz, R. G. Pinnick, Y.-L. Pan, and R. K. Chang, “Angularly resolved light scattering from aerosolized spores: observations and calculations,” Opt. Lett. 32(22), 3358–3360 (2007).
[CrossRef] [PubMed]

R. G. Pinnick, S. C. Hill, S. Niles, D. M. Garvey, Y.-L. Pan, S. Holler, R. K. Chang, J. Bottiger, B. V. Bronk, B. T. Chen, C.-S. Orr, and G. Feather, “Real–time measurement of fluorescence spectra from single airborne biological particles,” Field Anal. Chem. Technol. 3(4-5), 221–239 (1999).
[CrossRef]

Pinnick, R. G.

Podbielska, H.

I. Buzalewicz, K. Wysocka-Król, and H. Podbielska, “Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms,” Opt. Express 18(12), 12992–13005 (2010).
[CrossRef] [PubMed]

I. Buzalewicz, K. Wysocka, and H. Podbielska, “Exploiting of optical transforms for bacteria evaluation in vitro,” Proc. SPIE 7371, 73711H, 73711H-6 (2009).
[CrossRef]

Putkiranta, M.

Quinn, J.

P. Leonard, S. Hearty, J. Quinn, and R. O’Kennedy, “A generic approach for the detection of whole Listeria monocytogenes cells in contaminated samples using surface plasmon resonance,” Biosens. Bioelectron. 19(10), 1331–1335 (2004).
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L. J. Radziemski, “From LASER to LIBS, the path of technology development,” Spectrochim. Acta, B At. Spectrosc. 57(7), 1109–1113 (2002).
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Ragheb, K.

Rajwa, B.

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
[CrossRef] [PubMed]

Rasooly, A.

J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002).
[CrossRef] [PubMed]

Reinisch, L.

Robinson, J. P.

E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, and E. D. Hirleman, “Modeling light propagation through bacterial colonies and its correlation with forward scattering patterns,” J. Biomed. Opt. 15(4), 045001 (2010).
[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time-resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. 13(1), 014010 (2008).
[CrossRef] [PubMed]

M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008).
[CrossRef] [PubMed]

E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007).
[CrossRef] [PubMed]

P. P. Banada, S. Guo, B. Bayraktar, E. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007).
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D. L. Rosen, “Airborne bacterial endospores detected by use of an impinger containing aqueous terbium chloride,” Appl. Opt. 45(13), 3152–3157 (2006).
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D. L. Rosen, “Bacterial endospores detection using photoluminescence from terbium dipicolinate,” Rev. Anal. Chem. 18(1-2), 1–22 (1999).
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[CrossRef] [PubMed]

P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Label-free detection of multiple bacterial pathogens using light-scattering sensor,” Biosens. Bioelectron. 24(6), 1685–1692 (2009).
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Figures (14)

Fig. 1
Fig. 1

Proposed optical system configuration for characterization of bacteria colonies diffraction patterns: L0 transforming lens in (x0,y0) plane, bacteria colonies on Petri dish in (x1,y1) plane, observation plane (x2,y2).

Fig. 2
Fig. 2

Model of the convex shaped bacteria colony.

Fig. 3
Fig. 3

The absorption spectra of: (a) Columbia agar, (b) Nutrient agar,(c) MacConkey medium.

Fig. 4
Fig. 4

The schematic configuration of proposed optical system (explanation in text).

Fig. 5
Fig. 5

Different diffraction patterns of the exit pupil of the optical system: (a) z2=2 cm, (b) z2=9 cm,(c) z2=15 cm Fresnel patterns for increasing distance from the transforming lens, (d) z2=28.8 cm Fraunhofer pattern in the back focal plane of the transforming lens (aperture diameter: 2 mm).

Fig. 6
Fig. 6

The change of the dimension of Fresnel diffraction patterns in the case of Salmonella enteritidis colony with decreasing the distance z1:(a) 28 cm, (b) 26.5 cm, (c) 25.3 cm, (d) 24.5cm (bacteria colony diameter: approx. 0.8 mm, beam diameter: approx. 1 mm).

Fig. 7
Fig. 7

The change of the of Fresnel diffraction patterns of Staphylococcus aureus colony with decreasing the distance z1.: (a) 28 cm, (b) 27cm (bacteria colony diameter: 2.1 mm, beam diameter: approx. 2.1 mm).

Fig. 8
Fig. 8

(a) Fresnel patterns of Escherichia coli colony incubated at 37°C, (b), (c) Fresnel patterns of bacteria colonies exposed on low- temperature stress at 15°C (bacteria colony diameter:. 2 mm, beam diameter: approx. 2.3 mm).

Fig. 9
Fig. 9

(a) Shadowgraph image of bacteria colony internal structure (the red circle indicates the area of bacteria colony shown on the microscopic image), (b) microscopic image of analyzed area of the colony, (c) Fresnel diffraction pattern of Escherichia coli colony (approx. beam diameter 2 mm), (d) the same Fresnel pattern in case of smaller diameter of the laser beam (approx. beam diameter 1.5 mm).

Fig. 10
Fig. 10

(a), (b) Fresnel patterns of Escherichia coli incubated at 24°C (c) shadowgraph image of the internal structure of the colony exposed to 0°C (d) Fresnel pattern of bacteria colony exposed to 0°C.

Fig. 11
Fig. 11

Microscopic images of Escherichia coli colonies grown on: (a) Columbia agar, (b) MacConkey medium, (c) nutrient agar.

Fig. 12
Fig. 12

Time depended changes of Fresnel diffraction patterns of Escherichia coli colonies grown on three different nutrient media at temperature 37°C.

Fig. 13
Fig. 13

The computational simulations of diffraction patterns of the circular aperture with the same observation distances as on Fig. 5.

Fig. 14
Fig. 14

The microscopic image of the Escherichia coli colony grown on MacConkey medium after 22 hours of incubation with additional spectral filter increasing the contrast.

Equations (24)

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U out. ( x 0 , y 0 )=AP( x 0 , y 0 )exp{ iπ λf ( x 0 2 + y 0 2 ) }=AP( x 0 , y 0 )ψ( x 0 , y 0 ;F ),
ψ( x,y,p )=exp{ iπp λ ( x 2 + y 2 ) }.
U( x m+1 , y m+1 )= exp( ik z m+1 ) iλ z m+1 × + + U( x m , y m )exp{ iπ λ z m+1 [ ( x m+1 x m ) 2 + ( y m+1 y m ) 2 ] }d x m d y m =, =C( λ, Z m+1 ) + + U( x m , y m ) ψ( x m+1 x m , y m+1 y m , Z m+1 )d x m d y m
U in. ( x 1 , y 1 )=C( λ, Z 1 ) + + U out. ( x 0 , y 0 )ψ( x 1 x 0 , y 1 y 0 , Z 1 )d x 0 d y 0 ,
ψ( x 1 x 0 , y 1 y 0 , Z 1 )=ψ( x 0 , y 0 , Z 1 )ψ( x 1 , y 1 , Z 1 )exp{ i2π λ Z 1 ( x 0 x 1 + y 0 y 1 ) },
ψ( x 0 , y 0 , Z 1 )ψ( x 0 , y 0 ,F)=ψ( x 0 , y 0 , Z 1 F),
U in. ( x 1 , y 1 )=C( λ, Z 1 )Aψ( x 1 , y 1 , Z 1 ) + + ψ( x 0 , y 0 , Z 1 F )exp{ i2π λ Z 1 ( x 0 x 1 + y 0 y 1 ) }d x 0 d y 0 .
{ exp{ πc( x 2 + y 2 ) } }= 1 c exp{ π c ( f x 2 + f y 2 ) },
U in. ( x 1 , y 1 )=iλ A Z 1 F C( λ, Z 1 )ψ( x 1 , y 1 , Z 1 F Z 1 F ),
U in. ( x 1 , y 1 )=( f f z 1 A )exp{ ik z 1 }ψ( x 1 , y 1 , Z 1 F Z 1 F ),
t b ( x 1 , y 1 )= t b 0 ( x 1 , y 1 )exp{ iϕ( x 1 , y 1 ) },
U( x 1 , y 1 )= U in. ( x 1 , y 1 ) t b ( x 1 , y 1 )
U in. ( x 2 , y 2 )= C 2 ( λ, Z 2 ) + + U ( x 1 , y 1 )ψ( x 2 x 1 , y 2 y 1 , Z 2 )d x 1 d y 2 .
U in. ( x 2 , y 2 )=C( λ, Z 1 , Z 2 )( fA f z 1 )ψ( x 2 , y 2 , Z 2 ) { t b ( x 1 , y 1 )ψ( x 1 , y 1 , Z ˜ ) } f x = x 2 Z 2 λ ; f y = y 2 Z 2 λ
Z ˜ = Z 2 Z 1 F Z 1 F
U in. ( x 2 , y 2 )=C( λ, Z 1 , Z 2 )( fA f z 1 )ψ( x 2 , y 2 , Z 2 ) { t b ( x 1 , y 1 ) } f x = x 2 Z ^ λ ; f y = y 2 Z ^ λ ,
Z ^ = 1 z ^ = 1 f z 1 = Z 1 F Z 1 F
ϕ( x 1 , y 1 )=k[ T o Δ( x 1 , y 1 ) n b Δ( x 1 , y 1 ) ],
Δ( x 1 , y 1 )= T 0 z b = T 0 ( r b r b 2 x 1 2 y 1 2 )= T 0 r b ( 1 1 x 1 2 + y 1 2 r b 2 ).
Δ( x 1 , y 1 )= T 0 x 1 2 + y 1 2 2 ( 1 r 1 r b )
ϕ( x 1 , y 1 )=k n b T 0 k( n b 1) x 1 2 + y 1 2 2 ( 1 r 1 r b )=kn T 0 k( n b 1 ) x 1 2 + y 1 2 2 R,
U in. ( x 2 , y 2 )= C ˜ × { t b 0 ( x 1 , y 1 )ψ( x 1 , y 1 , Z ˜ ) } f x = x 2 Z 2 λ ; f y = y 2 Z 2 λ ,
Z ˜ = Z 2 Z 1 F Z 1 F R,
C ˜ = ( fA f z 1 )exp( ik Z 1 1 )exp( ik Z 2 1 )ψ( x 2 , y 2 , Z 2 )exp( ik n p T p )exp( ik n a T a )exp( ik n b T 0 ) iλ Z 2 1 .

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