Abstract

An eigenvector analysis based algorithm is presented for estimating refractive index changes from 2-D reflectance/dispersion images obtained with spectro-angular surface plasmon resonance systems. High resolution over a large dynamic range can be achieved simultaneously. The method performs well in simulations with noisy data maintaining an error of less than 10-8 refractive index units with up to six bits of noise on 16bit quantized image data. Experimental measurements show that the method results in a much higher signal to noise ratio than the standard 1-D weighted centroid dip finding algorithm.

© 2008 Optical Society of America

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  2. X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
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  5. H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
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    [CrossRef] [PubMed]
  20. Q5. K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Act. B 117,401-407 (2006).
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    [CrossRef]

2007 (6)

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
[CrossRef]

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
[CrossRef]

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

B. K. Singh and A. C. Hillier, "Multicolor surface plasmon resonance imaging of ink jet-printed protein microarrays," Anal. Chem. 79,5124-5132 (2007).
[CrossRef] [PubMed]

C. J. Alleyne, A. G. Kirk, R. C. McPhedran, N. A. Nicorovici, and D. Maystre, "Enhanced SPR sensitivity using periodic metallic structures," Opt. Express 15,8163-8169 (2007).
[CrossRef] [PubMed]

2006 (2)

Q5. K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Act. B 117,401-407 (2006).
[CrossRef]

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
[CrossRef] [PubMed]

2005 (1)

Q4. P. Tobiska and J. Homola, "Advanced data processing for SPR biosensors," Sens. and Act. B 107,162-169 (2005).
[CrossRef]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424,824- 830 (2003).
[CrossRef] [PubMed]

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

2000 (2)

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumental resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

1998 (1)

A. V. Kabashin and P. I. Nikitin, "Surface plasmon resonance interferometer for bio- and chemical-sensors," Opt. Commun. 150,5-8 (1998).
[CrossRef]

1996 (2)

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54,6227-6244 (1996).
[CrossRef]

1980 (1)

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Aide, A.

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Aizawa, H.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Alleyne, C. J.

Bardin, F.

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
[CrossRef]

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424,824- 830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54,6227-6244 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
[CrossRef]

Bellemain, A.

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
[CrossRef]

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Bradberry, G. W.

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
[CrossRef]

Brillante, A.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Butter, J. Y. P.

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
[CrossRef] [PubMed]

Byun, K. M.

Q5. K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Act. B 117,401-407 (2006).
[CrossRef]

Canva, M.

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
[CrossRef]

Crenshaw, B. R.

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424,824- 830 (2003).
[CrossRef] [PubMed]

Duval, A.

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424,824- 830 (2003).
[CrossRef] [PubMed]

Gordon, J. G.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Hecht, B.

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
[CrossRef] [PubMed]

Higuchi, M.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Hillier, A. C.

B. K. Singh and A. C. Hillier, "Multicolor surface plasmon resonance imaging of ink jet-printed protein microarrays," Anal. Chem. 79,5124-5132 (2007).
[CrossRef] [PubMed]

Hoa, X. D.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
[CrossRef]

Homola, J.

Q4. P. Tobiska and J. Homola, "Advanced data processing for SPR biosensors," Sens. and Act. B 107,162-169 (2005).
[CrossRef]

Johansen, K.

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumental resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

Kabashin, A. V.

A. V. Kabashin and P. I. Nikitin, "Surface plasmon resonance interferometer for bio- and chemical-sensors," Opt. Commun. 150,5-8 (1998).
[CrossRef]

Kim, D.

Q5. K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Act. B 117,401-407 (2006).
[CrossRef]

Kim, P. S.

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

Kim, S. J.

Q5. K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Act. B 117,401-407 (2006).
[CrossRef]

Kirk, A. G.

C. J. Alleyne, A. G. Kirk, R. C. McPhedran, N. A. Nicorovici, and D. Maystre, "Enhanced SPR sensitivity using periodic metallic structures," Opt. Express 15,8163-8169 (2007).
[CrossRef] [PubMed]

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
[CrossRef]

Kitson, S. C.

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54,6227-6244 (1996).
[CrossRef]

Kobayashi, K.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Kurosawa, S.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Lee, G.

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

Liedberg, B.

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumental resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

Lundstrom, I.

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumental resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

Maystre, D.

McPhedran, R. C.

Moreau, J.

Q3. A. Duval, F. Bardin, J. Moreau, A. Aide, A. Bellemain, and M. Canva, "Polarimetric surface Plasmon resonance imaging biosensor," Proc. SPIE 6631,66310P-663112 (2007).
[CrossRef]

Nicorovici, N. A.

Nikitin, P. I.

A. V. Kabashin and P. I. Nikitin, "Surface plasmon resonance interferometer for bio- and chemical-sensors," Opt. Commun. 150,5-8 (1998).
[CrossRef]

Oh, C. H.

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

Philpott, M. R.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Pockrand, I.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54,6227-6244 (1996).
[CrossRef]

Reddy, S. M.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Roger, G.

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
[CrossRef]

Sambles, J. R.

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54,6227-6244 (1996).
[CrossRef]

Santo, R.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Singh, B. K.

B. K. Singh and A. C. Hillier, "Multicolor surface plasmon resonance imaging of ink jet-printed protein microarrays," Anal. Chem. 79,5124-5132 (2007).
[CrossRef] [PubMed]

Song, S. H.

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

Stalberg, R.

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumental resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
[CrossRef]

Swalen, J. D.

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Tabrizian, M.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
[CrossRef]

Tobiska, P.

Q4. P. Tobiska and J. Homola, "Advanced data processing for SPR biosensors," Sens. and Act. B 107,162-169 (2005).
[CrossRef]

Tozuka, M.

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
[CrossRef] [PubMed]

Weder, C.

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
[CrossRef] [PubMed]

Yoon, J.

J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
[CrossRef]

Am. J. Phys. (1)

J. D. Swalen, J. G. Gordon, II, M. R. Philpott, A. Brillante, I. Pockrand, and R. Santo, "Plasmon surface polariton dispersion by direct optical observation," Am. J. Phys. 48,669-672 (1980).
[CrossRef]

Anal. Chem. (1)

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Anal. Chim. Acta (1)

H. Aizawa, M. Tozuka, S. Kurosawa, K. Kobayashi, S. M. Reddy, and M. Higuchi, "Surface plasmon resonance-based trace detection of small molecules by competitive and signal enhancement immunoreaction," Anal. Chim. Acta 591,191-194 (2007).
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Biosensors Bioelectron. (1)

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosensors Bioelectron. 23,151-160 (2007).
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J. Appl. Phys. (2)

S. C. Kitson, W. L. Barnes, G. W. Bradberry, and J. R. Sambles, "Surface profile dependence of surface plasmon band gaps on metallic gratings," J. Appl. Phys. 79,7383-7385 (1996).
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J. Yoon, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, "Surface-plasmon photonic band gaps in dielectric gratings on a flat metal surface," J. Appl. Phys. 94,123-129 (2003).
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J. Chem. Phys. (1)

J. Y. P. Butter, B. Hecht, B. R. Crenshaw, and C. Weder, "Absorption and fluorescence of single molecules," J. Chem. Phys. 125,154710-154711 (2006).
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Meas. Sci. Technol. (2)

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K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, "Surface plasmon resonance: instrumenta resolution using photodiode arrays," Meas. Sci. Technol. 11,1630-1638 (2000).
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Nature (1)

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Opt. Express (1)

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Proc. SPIE (2)

Q2. F. Bardin, A. Bellemain, G. Roger, and M. Canva, "Surface plasmon resonance spectro-imaging sensor and associated data processing for biomolecular surface interaction characterization," Proc. SPIE 6450, 64500N- 645010 (2007).
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A. D. Boardman, Electromagnetic Surface Modes (Wiley-Interscience, Toronto, 1982).Q1

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Figures (9)

Fig. 1.
Fig. 1.

A 2-D SPR reflectance/dispersion image (a), and a 1-D SPR dip (b). The 1-D curve represents a slice from the 2-D image taken at either a fixed angle or wavelength.

Fig. 2.
Fig. 2.

Spectro-angular SPR configuration. (Pol=polarizer, CL=cylindrical lens).

Fig. 3.
Fig. 3.

RCWA simulated 2-D reflectance/dispersion image from a spectro-angular SPR system having either a smooth 50nm thick gold surface (a) or a corrugated (period 300nm) gold surface (b). The structure for (b) is shown in (c).

Fig. 4.
Fig. 4.

Summary of refractive index estimation method.

Fig. 5.
Fig. 5.

Comparison of estimation errors, εrms , for a test set of reflectance/dispersion images w.r.t. bases of various sizes (N=80,40,20,10) and corresponding index of refraction intervals (ΔnB=0.001, 0.002, 0.004, 0.008 RIU). The εrms values are calculated between n=1.305 and 1.375 in order to ignore edge effects.

Fig. 6.
Fig. 6.

Estimation errors for basis sets of various sizes (N=80,60,40, and 20 from largest to smallest). All use ΔnB=0.001 RIU in the training set.

Fig. 7.
Fig. 7.

Performance of the algorithm as a function of the number of bits, Nb , of additive Gaussian noise (Eq. 7) in the reflectance/dispersion images, calculated for a series of candidate test images over index values ranging from 1.305 to 1.375 and using ΔnB=0.002 RIU to build the basis (N=40). Results are shown for both 8-bit and 16-bit cameras, at three different resolutions (256×256, 512×512, and 1024×1024). Note the graph labeled “Sum of squared diffs” which indicates the best-case performance (1024×1024 16-bit camera) of a variation of the algorithm that uses a simple sum of squared differences as the error measure between training set and candidate test images for building the solution vector s, rather than the full method involving the projection against the basis.

Fig. 8.
Fig. 8.

Comparison of (a) simulated reflectance/dispersion image and (b) experimentally captured image.

Fig. 9.
Fig. 9.

Index value jumps from salt solutions on a flat gold surface over time as measured by (a) the proposed method and (b) the standard weighted centroid dip finding algorithm.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Λ B = λ sp 2 = λ o 2 ε mr + ε D ε mr ε D
b i b j = 0 , if i j 0 , if i =j
A ij = a i b j
a i = N A ij b j ( i , j = 1 . . N )
w j = v b j
s = A w
σ N b = 2 N b 1 2 n 1
SNR = 10 log ( x ̅ σ )

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