Abstract

The particle sizing capabilities of light scattering spectroscopy (LSS) and the spatial localization of optical coherence tomography (OCT) are brought together in a new modality known as scattering-mode spectroscopic OCT. An analysis is presented of the spectral dependence of the light collected in spectroscopic OCT for samples comprised of spherical particles. Many factors are considered including the effects of scatterer size, interference between the fields scattered from closely adjacent scatterers, and the numerical aperture of the OCT system. The modulation of the spectrum of the incident light by scattering of a plane wave from a single sphere is a good indicator of particle size and composition. However, it is shown in this work that the sharp focusing of fields causes the spectral signature to shift and the presence of multiple scatterers has dramatic modulation effects on the spectra. Approaches for accurately matching physical structure with the observed signals under various conditions are discussed.

© 2005 Optical Society of America

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Appl. Opt.

Biophys. J.

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

J. Biomed. Opt.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

C. Yang, L. T. Perelman, A. Wax, R. R. Dasari, and M. S. Feld, "Feasibility of field-based light scattering spectroscopy," J. Biomed. Opt. 5, 138-143 (2000).
[CrossRef] [PubMed]

J. Chem. Phys.

A. Ben-Reuven and N. D. Gershon, "Light scattering by orientational fluctuations in liquids," J. Chem. Phys. 51, 893-902 (1969).
[CrossRef]

S. R. Aragon and E. Pecora, "Theory of dynamic light scattering from large anisotropic particles," J. Chem. Phys. 66, 2506-2516 (1977).
[CrossRef]

Laser Surgical Medicine

J. R. Mourant, "Spectroscopic diagnosis of bladder cancer with elastic light scattering," Laser Surgical Medicine 17, 350-357 (1995).
[CrossRef]

Nature

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Muller, Q. Zhang, G. Zonios, E. Kline, T. Mcgillican, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, "Detection of preinvasive cancer cells," Nature 406, 35-36 (2000).
[CrossRef] [PubMed]

Nature Medicine

R. Gurjar, V. Backman, J. M. Peralta, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, "Imaging human epithelial properties with polarized light-scattering spectroscopy," Nature Medicine 7, 1245-1248 (2001).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. and Biol.

A. Dubois, G. Moneron, K. Grieve, and A. C. Boccara, "Three-dimensional cellular-level imaging using full-field optical coherence tomography," Phys. Med. and Biol. 49, 1227-1234 (2004).
[CrossRef]

Phys. Rev. Lett.

P. S. Carney, V. A. Markel, and J. C. Schotland, "Near-field tomography without phase retrieval," Phys. Rev. Lett. 86, 5874-5877 (2001).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Schields, 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).

Rep. Prog. Phys.

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]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

Diagram of wavelength-dependent single-scattering from a Gaussian beam, where r 0 is the position of the scatterer relative to the center of the Gaussian beam at the waist. The functions fi (k, r) and fc (k, r) describe the incident and collection Gaussian modes, respectively, D is the beam diameter incident on the lens, and f is the focus length of the achromatic lens.

Fig. 2.
Fig. 2.

Beam wavelength-dependent spectral patterns for (a) centered large spheres (r=5λ) and (b) small spheres (r=λ). In each case, the incident laser beam has different beam waist sizes.

Fig. 3.
Fig. 3.

Scattering spectral patterns for in-focus off-center spheres (r=5λ) for different offcenter positions and different beam waist sizes w 0. (a): w 0=5λ 0; (b): w 0=λ 0.

Fig. 4.
Fig. 4.

Scattering spectral patterns for off-focus spheres (r=5λ) for different off-focus positions and different beam waist sizes w 0. (a): w 0=5λ 0; (b): w 0=λ 0.

Fig. 5.
Fig. 5.

Examples of spectral modulation patterns due to multiple scatterers (three scatterers here) in the imaging volume for (a) large spheres (r=5λ) and (b) small spheres (r=λ). In each case, the incident laser beam waist size was w 0=5λ 0.

Fig. 6.
Fig. 6.

Examples of spectral modulation patterns due to multiple scatterers of the same volume density (10%) for spheres of radius (a) 5 µm (N<1), and (b) 1 µm. In each case, the incident laser beam waist size was w 0=5λ 0 and the scatterer radius was λ 0.

Fig. 7.
Fig. 7.

(a) Reduction of spectral modulation by incoherent averaging. (b) Examples of spectral modulation patterns after incoherent averaging (three scatterers with N=16). The incident laser beam waist size was w 0=5λ 0 and the scatterer radius was λ 0.

Fig. 8.
Fig. 8.

Examples of spectral modulation patterns for a large scatterer (radius=5λ 0) surrounded by many small scatterers (radius=λ 0): (a) when the large scatterer is at the center of the beam; (b) when the large scatterer is off-center by w 0 ; (c) when the large scatterer is off-center by 2w 0. The number of smaller scatterers was chosen such that they occupied the same total volume as the large scatterer.

Equations (17)

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

f i ( x , y , k 0 ) = 1 w 0 ( k 0 ) exp [ x 2 + y 2 w 0 2 ( k 0 ) ] ,
w 0 ( k 0 ) = 4 f k 0 D .
F i ( q i , k 0 ) = 1 2 w 0 ( k 0 ) exp [ w 0 2 ( k 0 ) 4 q i 2 ] ,
U i ( q i , k 0 ) = C ( k 0 ) F i ( q i , k 0 ) = 1 2 C ( k 0 ) w 0 ( k 0 ) exp [ w 0 2 ( k 0 ) 4 q i 2 ] .
U s ( q s , k 0 ) = C ( k 0 ) F i ( q i , k 0 ) e i [ r 0 ( k i k s ) ] R ( q i , q s , k 0 , P ) d 2 q i ,
R ( q i , q s , k 0 , P ) = l = 0 A l P l ( k i · k s k 0 2 ) ,
A l = i β l k 0 ( β l i γ l ) ,
β l = j l ( nk 0 a ) j l ( k 0 a ) nj l ( nk 0 a ) j l ( k 0 a ) ,
γ l = nj l ( nk 0 a ) n l ( k 0 a ) j l ( nk 0 a ) n l ( k 0 a ) .
S ( k 0 , P ) = U s ( q s , k 0 ) F c ( q s , k 0 )
= C ( k 0 ) F i ( q i , k 0 ) e i [ r 0 ( k i k s ) ] R ( q i , q s , k 0 , P ) F c ( q s , k 0 ) d 2 q i d 2 q s .
S ( k 0 , P ) = C ( k 0 ) F i ( q i , k 0 ) e i [ r 0 ( k i k s ) ] R ( q i , q s , k 0 , P ) F i * ( q s , k 0 ) d 2 q i d 2 q s .
I ( k 0 , P ) = S ( k 0 , P ) U R ( k 0 ) exp [ i ϕ ( k 0 ) ] ,
I ( k 0 , P ) = C ( k 0 ) S ( k 0 , p ) .
I ( k 0 ) = C ( k 0 ) H ( k 0 ) * n = 1 N S n ( k 0 , P n ) ,
n = 1 N S n ( k 0 , P n ) = n = 1 N C ( k 0 ) F i ( q i ) F i * ( q s ) e i [ r n · ( k i k s ) ] R ( k i , k s , k 0 , P n ) d 2 k i d 2 k s ,
Error = k N 1 2 ,

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