Abstract

We demonstrate a novel technique to determine the size of Mie scatterers with high sensitivity. Our technique is based on spectral domain optical coherence tomography measurements of the phase dispersion that is induced by the scattering process. We use both Mie scattering predictions and dispersion measurements of phantoms to show that the scattering dispersion is very sensitive to small changes in the size and/or refractive index of the scatterer. We also show the light scattered from a single sphere is, in some cases, non-minimum phase. Therefore, the phase is independent of the intensity of the scattered light, and both intensity and phase must be measured directly in order to characterize more completely the scattering problem. Phase dispersion measurements may have application to distinguishing the size and refractive index of scattering particles in biological tissue samples.

© 2006 Optical Society of America

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2005 (2)

C. Xu, P. S. Carney, and S. A. Boppart, "Wavelength-dependent scattering in spectroscopic optical coherence tomography," Opt. Express 13, 5450-5462 (2005).
[CrossRef] [PubMed]

K. Nikolova, I. Panchev, and S. Sainov, "Optical characteristics of biopolymer films from pectin and gelatin," J. Optoelectronics Adv. Mater. 7, 1439-1444 (2005).

2004 (2)

D. C. Adler, T. H. Ko, P. R. Herz, and J. G. Fujimoto, "Optical coherence tomography contrast enhancement using spectroscopic analysis with spectral autocorrelation," Opt. Express 12, 5487-5501 (2004).
[CrossRef] [PubMed]

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

2003 (4)

J. W. Pyhtila, R. N. Graf, and A. Wax, "Determining nuclear morphology using an improved angle-resolved low coherence interferometry system," Opt. Express 11, 3473-3484 (2003).
[CrossRef] [PubMed]

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

A. Wax, C. Yang, and J. A. Izatt, "Fourier-domain low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 28, 1230-1232 (2003).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

2002 (2)

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

V. Laude, "Noise analysis of the measurement of group delay in Fourier white-light interferometric cross correlation," J. Opt. Soc. Am. B 19, 1001-1008 (2002).
[CrossRef]

2001 (2)

2000 (1)

1998 (2)

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

1996 (1)

1991 (1)

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

1990 (1)

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

1983 (1)

1908 (1)

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Adler, D. C.

Backman, V.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Badizadegan, K.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

Beck, M.

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

Bertie, J. E.

Boone, C. W.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

Boppart, S. A.

Brezinski, M. E.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

Brock, R. S.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Carney, P. S.

Clement, T. S.

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

Cooper, P. R.

Crawford, J. M.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Dasari, R. R.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

A. Wax, C. H. Yang, R. R. Dasari, and M. S. Feld, "Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 26, 322-324 (2001).
[CrossRef]

Dienstfrey, A.

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J.G. Fujimoto, "Spectroscopic optical coherence tomography," Opt. Lett. 25, 111-113 (2000).
[CrossRef]

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

Feld, M. S.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

A. Wax, C. H. Yang, R. R. Dasari, and M. S. Feld, "Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 26, 322-324 (2001).
[CrossRef]

C. Yang, A. Wax, and M. S. Feld, "Measurement of the anomalous phase velocity of ballistic light in a random medium by use of a novel interferometer," Opt. Lett. 26, 235-237 (2001).
[CrossRef]

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Fujimoto, J. G.

Fujimoto, J.G.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

Graf, R. N.

Hale, P. D.

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

Hamano, T.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Herz, P. R.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Hu, X.-H.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ippen, E. P.

Itzkan, I.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Izatt, J. A.

Jacobs, K. M.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Kafka, J. D.

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

Kärtner, F. X.

Keenan, D. A.

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

Ko, T. H.

Lan, Z.

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Laude, V.

Lenz, G.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

Li, X. D.

Lima, C.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Liu, B.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

Lu, J. A.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Macdonald, E. A.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

Madsen, C. K.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

Manoharan, R.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Mie, G.

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Morgner, U.

Nikolova, K.

K. Nikolova, I. Panchev, and S. Sainov, "Optical characteristics of biopolymer films from pectin and gelatin," J. Optoelectronics Adv. Mater. 7, 1439-1444 (2005).

Nusrat, A.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Panchev, I.

K. Nikolova, I. Panchev, and S. Sainov, "Optical characteristics of biopolymer films from pectin and gelatin," J. Optoelectronics Adv. Mater. 7, 1439-1444 (2005).

Perelman, L.T.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Pitris, C.

Pyhtila, J. W.

Sainov, S.

K. Nikolova, I. Panchev, and S. Sainov, "Optical characteristics of biopolymer films from pectin and gelatin," J. Optoelectronics Adv. Mater. 7, 1439-1444 (2005).

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

Seiler, M.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Sengers, J. M. H. L.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

Shields, S.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Slusher, R. E.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

Stamper, D. L.

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

Straub, J.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

Van Dam, J.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Wallace, M.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Walmsley, I. A.

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

Wax, A.

Williams, D. F.

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

Xu, C.

Yang, C.

Yang, C. H.

Yang, P.

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Zonios, G.

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Appl. Opt. (1)

Appl. Spectrosc. (1)

Biophys. J. (1)

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular organization and substructure measured using angle-resolved low-coherence interferometry," Biophys. J. 82, 2256-2264 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, "Dispersive properties of optical filters for WDM systems," IEEE J. Quantum Electron. 34, 1390-1402 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. Dienstfrey, P. D. Hale, D. A. Keenan, T. S. Clement, and D. F. Williams, "Minimum-phase calibration of sampling oscilloscopes," IEEE Trans. Microwave Theory Tech. (to be published).

J. Opt. Soc. Am. B (1)

J. Optoelectronics Adv. Mater. (1)

K. Nikolova, I. Panchev, and S. Sainov, "Optical characteristics of biopolymer films from pectin and gelatin," J. Optoelectronics Adv. Mater. 7, 1439-1444 (2005).

J. Phys. Chem. Reference Data (1)

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, "Refractive-index of water and steam as function of wavelength, temperature, and density," J. Phys. Chem. Reference Data 19, 677-717 (1990).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Med. Biol. (2)

B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, "Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography," Phys. Med. Biol. 49, 923-930 (2004).
[CrossRef] [PubMed]

X. Ma, J. A. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

L.T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Phys. Rev. Lett. 80, 627-630 (1998).
[CrossRef]

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A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
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C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1983), Chap. 4.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9.

T. A. Germer, SCATMECH: Polarized Light Scattering C++ Class Library, available at http://physics.nist.gov/scatmech.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1975), Chap. 2.3.3.

H. Dym and H. P. McKean, Fourier Series and Integrals (Academic Press, New York, 1972), Chap. 3.5.

M. E. Froggatt, T. Erdogan, J. Moore, and S. Shenk, "Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings," in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (Optical Society of America, Washington, DC, 1999), pp. 227-229.

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, "Frequency-domain optical coherence tomography based on minimum-phase functions," in Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine X, V. V. Tuchin, J. A. Izatt, and J. G. Fujimoto, eds., Proc. SPIE 6079, 607912 (2006).
[CrossRef]

http://www.dow.com/glycerine/resources/dwnlit.htm, http://www.2spi.com/catalog/standards/microspheres.shtml.

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Figures (8)

Fig. 1.
Fig. 1.

Relative group delay predicted from Mie theory for different sphere diameters. The group delay of 3 mm of water is also shown for comparison.

Fig. 2.
Fig. 2.

Predicted magnitudes of the backscattered light from a single 10 μm sphere, calculated for two different refractive indices of the sphere.

Fig. 3.
Fig. 3.

Group delay of computed “true” phase (solid) and minimum phase (dashed). Note that for Re(ns ) = 1.41, the true group delay resonances at λ = 1313 nm and 1373 nm have opposite sign compared to the resonances predicted assuming minimum phase.

Fig. 4.
Fig. 4.

Diagram of the OCT system used for dispersion metrology.

Fig. 5.
Fig. 5.

Comparison of measured and predicted group delay of phantoms constructed from polystyrene spheres embedded in a glycerin/water solution. We added arbitrary constants to each of the curves to separate them.

Fig. 6.
Fig. 6.

Measured RGD of an 18 μm sphere embedded in porcine gelatin. The curve has the shape of approximate delta functions, and there is a clear sign reversal between peaks, qualitatively similar to that predicted by the non-minimum phase analysis.

Fig. 7.
Fig. 7.

Comparison of the RGD measured from a single 15 μm sphere measured with a focused beam and the RGD from a monolayer of 15 μm spheres measured with a 1.3 mm diameter collimated beam. The sphere monolayer data was multiplied by a factor of 5 so that both curves could be shown on the same graph. Although amplitudes are different and the curves are phase shifted with respect to each other, both curves appear to have the same period.

Fig. 8.
Fig. 8.

Plot of the difference between true and minimum phase group delays after subtracting the all-pass and linear terms determined from a nonlinear fit. This is consistent with Eq. (A3), and indicates that the Re(ns ) = 1.41 case is truly an example of a non-minimum phase scattering function. The dashed vertical lines show the positions of the resonances for reference. The small features at λ = 1237 nm and 1294 nm are numerical artifacts.

Equations (16)

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( E s E s ) = e i k ( r z ) i k r ( S 2 ( θ , f ) 0 0 S 1 ( θ , f ) ) ( E i E i ) ,
t g 1 2 π d ϕ d f = 1 2 π d arg S ( f ) d f .
y ( t ) = h ( s ) x ( t s ) d s ,
H ( f ) = 0 h ( t ) exp ( i 2 π f t ) d t .
ln ( H ( f ) ) = ln ρ ( f ) + i ϕ ( f ) .
ϕ ( f ) = 2 f π 0 ln ( ρ ( f ) ) 1 f 2 s 2 d s .
P det = C 1 [ E 0 2 4 + E 0 2 8 ρ 2 ( f ) + E 0 2 2 2 ρ ( f ) cos ( ϕ ( f ) + 2 π f X 1 c 2 π f X 2 c ) ] S ( f ) ,
FT 1 ( P det ) = C 1 [ 2 π E 0 2 4 δ ( t ) + E 0 2 8 FT 1 ( ρ 2 ( f ) ) + 2 π E 0 2 2 2 h ͂ ( t + X 1 c X 2 c ) + 2 π E 0 2 2 2 h ͂ * ( t X 1 c + X 2 c ) ] * FT 1 ( S ( f ) ) ,
t g ( f ) 1 2 π d ϕ ( f ) d f = Re { FT ( t I ( t ) ) FT ( I ( t ) ) } ,
n m 2 1 n m 2 + 2 M ρ = n A 2 1 n A 2 + 2 f A M A ρ A + n B 2 1 n B 2 + 2 f B M B ρ B ,
B ( f ) = f z n f z n * ,
ln ( B ( f ) ) = ln ( B ( f ) ) + i A r g ( B ( f ) ) = i 2 cos 1 ( f f n ( f f n ) 2 + γ n 2 ) .
H ( f ) = H mp ( f ) exp ( i 2 π f τ ) n f z n f z n * .
Δ ( f ) = ϕ E ( f ) ϕ m p ( f ) = 2 π f τ + n 2 cos 1 ( f f n ( f f n ) 2 + γ n 2 ) .
t g = 1 2 π d ϕ B d f = γ n π ( ( f f n ) 2 + γ n 2 ) .
Δ t g ( f ) = 1 2 π ( d ϕ E d f d ϕ mp d f ) = τ + 1 π n γ n ( ( f f n ) 2 + γ n 2 ) .

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