Abstract

We demonstrate tomographic imaging of the refractive index of turbid media using bifocal optical coherence refractometry (BOCR). The technique, which is a variant of optical coherence tomography, is based on the measurement of the optical pathlength difference between two foci simultaneously present in a medium of interest. We describe a new method to axially shift the bifocal optical pathlength that avoids the need to physically relocate the objective lens or the sample during an axial scan, and present an experimental realization based on an adaptive liquid-crystal lens. We present experimental results, including video clips, which demonstrate refractive index tomography of a range of turbid liquid phantoms, as well as of human skin in vivo.

© 2003 Optical Society of America

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References

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Adv. Mater. (1)

P. G. McCormick, T. Tsuzuki, J. S. Robinson, J. Ding, �??Nanoparticle synthesis by mechanochemical processing,�?? Adv. Mater. 13, 1008-1010 (2001).
[CrossRef]

Appl. Opt. (4)

Dermatol. (1)

J. M. Schmitt, M. Yadlowsky, R. F. Bonner, �??Subsurface imaging of living skin with optical coherence tomography,�?? Dermatol. 191, 93-98 (1995).
[CrossRef]

IEEE J. Selected Top. Quantum Electron. (1)

J. A. Izatt, M. D. Kulkarni, H.-W. Wang, K. Kobayashi, M. V. Sivak, �??Optical coherence tomography and microscopy in gastrointestinal tissues,�?? IEEE J. Selected Top. Quantum Electron. 2, 1017-1028 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. V. Sorin and D. F. Gray, �??Simultaneous thickness and group index measurement using optical low-coherence refractometry,�?? IEEE Photon. Technol. Lett. 4, 105-107 (1992).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, �??In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,�?? IEEE Trans. Biomed. Eng. 47, 1266-1270 (2000).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

X. W. Suna and H. S. Kwok, �??Optical properties of epitaxially grown zinc oxide films on sapphire by pulsed laser deposition,�?? J. Appl. Phys. 86, 408-411 (1999).
[CrossRef]

J. Biomed. Opt. (2)

A. Knüttel and M. Boehlau-Godau, �??Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,�?? J. Biomed. Opt. 5, 83-92 (2000).
[CrossRef] [PubMed]

X. Wang, C. Zhang, L. Zhang, L. Xue, J. Tian, �??Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,�?? J. Biomed. Opt. 7, 628-632 (2002).
[CrossRef] [PubMed]

J. Invest. Dermatol. (1)

P. J. Caspers, G. W. Lucassen, E. A. Carter, H. A. Bruining, G. J. Puppels, �??In vivo confocal Raman microspectroscopy of the skin: noninvasive determination of molecular concentration profiles,�?? J. Invest. Dermatol. 116, 434-442 (2001).
[CrossRef] [PubMed]

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

Laser-induced interstitial thermotherapy (1)

V. V. Tuchin, �??Optical and thermal properties of biological tissue�?? in Laser-induced interstitial thermotherapy, G. Müller, A. Roggan, eds. (SPIE Press, Bellingham, USA, 1995).

Nat. Med. (2)

S. A. Boppart, B. E. Bouma, C. Pitris, J. F. Southern, M. E. Brezinski, J. G. Fujimoto, �??In vivo cellular optical coherence tomography imaging,�?? Nat. Med. 4, 861 (1998).
[CrossRef] [PubMed]

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, M. S. Feld, �??Imaging human epithelial properties with polarized light-scattering spectroscopy,�?? Nat. Med. 7, 1245 (2002).

Opt. Express (1)

Opt. Lett. (7)

Optom. Vision Sci. (1)

J. F. Koretz and C. A. Cook, �??Aging of the optics of the human eye: Lens refraction models and principal plane locations,�?? Optom. Vision Sci. 78, 396-404 (2001).
[CrossRef]

Phys. Med. Biol. (1)

M. Kohl, M. Essenpreis, M. Cope, �??The influence of glucose concentration upon the transport of light in tissue-simulating phantoms,�?? Phys. Med. Biol. 40, 1267-1287 (1995).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. Knüttel, S. Bonev, C. Kugler, �??In vivo evaluation of locally mapped refractive indices with OCT,�?? in Progress in Biomedical Optics and Imaging, V. V. Tuchin et al., eds., Proc. SPIE 4251, 136-143 (2001).
[CrossRef]

Rep. Prog. Phys. (1)

B. B. Das, F. Liu, R. R. Alfano, �??Time-resolved fluorescence and photon migration studies in biomedical and random media,�?? Rep. Prog. Phys. 60, 227-292 (1997).
[CrossRef]

Other (3)

V. V. Tuchin, ed., Tissue Optics (SPIE Press, Washington, USA, 2000), Chap. 1.

R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1973) Chap. 5.

Sucrose conversion table, U.S. Dept. Agriculture, File code 135-A-50 (1981).

Supplementary Material (5)

» Media 1: AVI (773 KB)     
» Media 2: AVI (1157 KB)     
» Media 3: AVI (517 KB)     
» Media 4: AVI (313 KB)     
» Media 5: AVI (358 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of the BOCR system showing the sample arm in detail. LC: liquid-crystal lens; GM: galvanometer-mounted tiltable mirror; Lobj: objective lens.

Fig. 2.
Fig. 2.

Schematic diagram of the bifocal optical arrangement in the sample arm showing rays for the cases n=1 (dashed) and n>1 (solid).

Fig. 3.
Fig. 3.

(a), (b) (773 KB) Video clip (not real time, 234 OCT frames per video frame) of shifting the bifocal gate through an aqueous solution of Intralipid. Separate frames are shown in (a) and (b). GCS, glass cover slip surface; BFG, Bifocal gate signal. Scale bars represent optical pathlength. (c) Average axial profile from the images in (a) and (b), and its theoretical fit.

Fig. 4.
Fig. 4.

Refractive-index tomogram (combined mesh and color plots) of a homogeneous Intralipid aqueous solution (corresponding to Fig. 3(a), (b)).

Fig. 5.
Fig. 5.

(1157 KB) Video clip (not real time, 234 OCT frames per video frame) of the scan of one focus of the bifocal gate. An indicator in the top left corner gives the focal length of the liquid-crystal lens. Scale bar represents optical pathlength.

Fig. 6.
Fig. 6.

(a) (517 kB) Video clip (not real time, 60 OCT frames per video frame) of the bifocal-gate scan and schematic diagram of the two-layer sample. (Two montaged frames are shown in the figure and the scale bar represents optical pathlength). (b) Combined mesh and color plots of the refractive index determined from the data set displayed in (a).

Fig. 7.
Fig. 7.

Average refractive index versus axial depth of the heterogeneous sample.

Fig. 8.
Fig. 8.

(a) (313 kB) Video clip (not real time, 60 OCT frames per video frame) of the bifocal gate scan versus sugar concentration in the Intralipid aqueous solution. Scale bar represents optical pathlength. (b) Plot of sucrose concentration versus the measured average refractive index of the sample.

Fig. 9.
Fig. 9.

(a) (358 kB) Video clip (not real time, 234 frames per video frame) of the bifocal gate scan in human thick stratum corneum in vivo. (Two frames are shown in the figure and the scale bars represent optical pathlength.). (b) Refractive-index tomogram calculated from (a).

Equations (8)

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Δ l = f obj 2 f obj + f s ,
Δ l opt = n g { ( f obj a ) [ ( n 2 1 ) D 2 + 4 n 2 f obj 2 ] 1 2 2 f obj ( f a ) [ ( n 2 1 ) ( D ) 2 + 4 n 2 ( f ) 2 ] 1 2 2 f } ,
Δ l opt = n g { ( f obj a ) [ NA 2 ( n 2 1 ) + n 2 ] 1 2 ( f obj a Δ l ) [ NA 2 f obj 4 ( n 2 1 ) + ( nf Δ l ) 2 ] 1 2 f Δ l } .
Δ l opt n g n [ 1 + NA 2 ( 1 1 n 2 ) ] 1 2 Δ l .
Δ l opt n g n [ 1 + 1 2 NA 2 ( 1 1 n 2 ) ] Δ l .
x = 0 z 0 sin α [ n ( z ) ] 2 sin 2 α dz ,
dx df | z = z 0 = NA n ( z 0 ) [ n ( z 0 ) ] 2 NA 2 d z opt df | z = z 0 .
I ( l r ) 0 R ( l s ) h ( l s ) S ( Δ l i ) d l s ,

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