## Separation of absorption and scattering profiles in spectroscopic optical coherence tomography using a least-squares algorithm

Optics Express, Vol. 12, Issue 20, pp. 4790-4803 (2004)

http://dx.doi.org/10.1364/OPEX.12.004790

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### Abstract

In spectroscopic optical coherence tomography, it is important and useful to separately estimate the absorption and the scattering properties of tissue. In this paper, we propose a least-squares fitting algorithm to separate absorption and scattering profiles when near-infrared absorbing dyes are used. The algorithm utilizes the broadband Ti:sapphire laser spectrum together with joint time-frequency analysis. Noise contribution to the final estimation was analyzed using simulation. The validity of our algorithm was demonstrated using both single-layer and multi-layer tissue phantoms.

© 2004 Optical Society of America

## 1. Introduction

1. 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]

4. U. Morgner, W. Drexler, F. C. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. **25**, 111–113 (2000). [CrossRef]

5. R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, “Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography,” Opt. Lett. **25**, 820–822 (2000). [CrossRef]

6. D. J. Faber, E. G. Mik, M. C. G. Aalders, and T. G. van Leeuwen, “Light absorption of (oxy-) hemoglobin assessed by spectroscopic optical coherence tomography,” Opt. Lett. **28**, 1436–1438 (2003). [CrossRef] [PubMed]

*a priori*, such as when highly absorbing near-infrared (NIR) dyes are used. In addition, the dyes can be chosen such that the dye absorption spectra are very different from the scattering spectra of the tissue. These two pieces of prior information can make separation of absorption from scattering possible.

*et al*. proposed a method for eliminating first-order wavelength-dependent contributions from scattering by three-point spectral triangulation using three narrow-band sources centered at 760 nm, 795 nm and 830 nm, and a differential absorption method to retrieve the depth-resolved location of differential absorption change [12]. In this work, we consider using a single broadband source for quantitative, depth-resolved SOCT. Using a single board band source permits analysis of spectral modification over a broad wavelength range in a single experiment. With the help of time-frequency analysis, the use of broadband sources is equivalent to using multiple narrow-band sources simultaneously. The tradeoff between spatial resolution and spectral resolution can be optimized after data collection, offering both better precision and flexibility [13]. In addition, this approach offers many other advantages, typically permitting better spatial localization of the absorbing object, reducing the complexity of the instruments, and eliminating the artifacts resulting from sample movement and the necessity of registering multiple images. In this paper we propose a new algorithm for differentiating the contributions from absorption and scattering in SOCT using a single broadband laser for the case where NIR dyes are used. This method utilizes time-frequency analysis and a least-square fitting algorithm. The proposed algorithm was tested using both single-layer and multi-layer tissue phantoms. Theoretical and simulated noise analysis is also included.

## 2. A Model of SOCT Signals

*I(A, z)*collected from a given depth

*z*can be expressed as the multiplication of source spectrum

*S(λ)*and the modulation effect which includes the contributions from spectral backscattering profile

*H*, the lumped spectral modification

_{r}(λ, z)*Hm(λ, z)*by media before that scatter, and the total spectral modification

*H*by optical components in the system, such as the beamsplitter, along the optical paths [6

_{s}(λ, z)6. D. J. Faber, E. G. Mik, M. C. G. Aalders, and T. G. van Leeuwen, “Light absorption of (oxy-) hemoglobin assessed by spectroscopic optical coherence tomography,” Opt. Lett. **28**, 1436–1438 (2003). [CrossRef] [PubMed]

14. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Differential absorption imaging with optical coherence tomography,” J. Opt. Soc. Am. A **15**, 2288–2296 (1998). [CrossRef]

*S(λ)*and

*H*are stationary and known

_{s}(λ,z)*a priori*. Therefore measuring

*I(λ, z)*offers the opportunity to study the material properties in the sample. For the cases of multiple scatterers within a coherence length, in general the resulting

*I(λ, z)*has spectral modulation due to interference of signals from neighboring scatterers. However, this modulation is random due to the random spacing between the scatterers. Therefore, un-modulated spectra can be recovered with high accuracy if sufficient compounding and averaging are applied.

*H*by media has both scattering and absorption contributions. In most cases, they follow Beer’s law:

_{m}(λ, z)*μ*and

_{a}(λ, z)*μ*are wavelength-dependent and spatially-varying absorption coefficients and scattering coefficients of the imaged media, respectively. Assuming the sample is composed of collections of small scatterers of similar sizes and random positions,

_{s}(λ, z)*H*can be approximated by a separable function in

_{r}(λ, z)*λ*and

*z*. Disregarding the dispersion and chromatic aberrations in the optical system,

*H*is also a separable function in

_{s}(λ, z)*λ*and

*z*:

*R*(

*z*) =

*H*(

_{r}*z*)

*H*(

_{s}*z*).

*z*= 0, we have:

*S(λ)*,

*H*and

_{r}(λ)*H*can be eliminated by:

_{s}(λ)*μ*and

_{a}(λ, z)*μ*are separable functions in

_{s}(λ, z)*λ*and

*z*, i.e.,

*f*represents the absorber concentration and

_{a}(z)*f*represents the scatterer concentration at a particular depth

_{s}(z)*z*. The functions

*ε*and

_{a}(λ)*ε*represent the absorption and scattering per unit concentration and per unit pathlength. They can be measured by a laboratory spectrometer or by integrating spheres. Then, the exponent term in Eq. (6) can be rewritten as:

_{s}(λ)*F*,

_{a}(z)*F*, and

_{s}(z)*C(z)*are wavelength independent functions that we want to find.

*Y(λ, z)*can be obtained by time-frequency analysis of the OCT signals.

## 3. Solving absorption and scattering profiles using least-squares method

*λ*,

_{1}*λ*] represents the laser spectral range. We can choose the weighting function

_{2}*W(λ)*such that more accurate data (such as the spectral information around the central region of the laser spectrum) are emphasized. One possible choice of

*W(λ)*is a smoothed function of laser spectral density while another possible choice is a rectangular window corresponding to the FWHM of the laser spectrum.

*E(z)*in Eq. (11) with respect to

*F*,

_{a}(z)*F*, and

_{s}(z)*C(z)*and setting them equal to zero, the resulting three Eq. can be written in matrix format:

**A**is independent of depth

*z*. After

*F*,

_{a}(z)*F*, and

_{s}(z)*C(z)*are solved by Eq. (12), the absorber concentration profile

*f*and the scattering profile

_{a}(z)*f*can be solved from Eq. (10).

_{s}(z)*ε*can be approximated by a linear function, i.e.,

_{s}(λ)*ε*(λ) =

_{s}*a*λ +

*b*, then Eq. (12) can be further simplified as:

*D*(

*z*) =

*C*(

*z*) -

*bF*(

_{s}*z*).

*ε*is difficult to measure or when

_{s}(λ)*ε*virtually has no wavelength dependence such that it can not be differentiated from the

_{s}(λ)*C(z)*term. Eq. (13) is also useful when we are only interested in retrieving the absorber concentration profile, for example, when NIR dyes are used for contrast-enhancement experiments.

*C(z)*in Eq. (12) and

*D(z)*in Eq. (13) are not of interest because

*R(z)*can be estimated from a structural OCT image. In practice, all the above procedures are discretized on

*z*and

*λ*.

*Y(λ, z)*corresponding to outliers is usually very different from the expected data in SOCT experiments. After Eq. (12) or (13) is solved, the error function (11) is calculated for all

*z*positions. The outliers can be removed by setting appropriate thresholds on the histograms of the error function. The

*Y(λ, z)*corresponding to outliers can be replaced by interpolation methods or be excluded from the data sets, depending on the location of outliers. Equation (12) or (13) are then re-solved using updated data.

*F*and

_{a}(z)*F*should be smooth functions of z. The second-order derivatives of

_{s}(z)*F*and

_{a}(z)*F*should be very close to zero. Therefore, a Laplacian operator can be chosen for

_{s}(z)**L**. Notice that the smoothing constraint should not be applied to

*C(z)*or

*D(z)*because they are functions of

*R(z)*, which typically is not smooth. Although the sizes of vectorized

**A**and

**L**matrices are large corresponding to the numbers of the depth points), Eq. (16) can be rapidly solved numerically because all matrices are very sparse.

*F*and scattering

_{a}(z)*F*are calculated. The absorber profile

_{s}(z)*f*and scatterer profile

_{a}(z)*f*can be retrieved with piece-wise curve-fitting and solving Eq. (10).

_{s}(z)## 4. Noise analysis and simulation

*ε*and

_{a}(λ)*Y(λ, z)*are experimentally determined and the windowing function

*W(λ)*is chosen. The values for the variable

*ε*are typically measured by a precision spectrometer (error ~ 0.1%), therefore they can be assumed to be highly accurate.

_{a}(λ)*Y (λ, z)*, on the other hand, has non-negligible system and experimental errors due to laser spectral drift, laser intensity and spectral noise, presence of chromatic aberrations, dispersion mismatch, angle- and wavelength-dependent back reflection, electronics noise, and errors introduced by data acquisition and time-frequency analysis. Even after extensive averaging, the errors in SOCT measurements still range from 2% to 10%, which have been estimated by analyzing known experimental settings such as measuring the back reflected spectra from upper and lower cuvette interfaces [8

8. B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher, and W. Drexler, “Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography,” Opt. Express **12**, 1677–1688 (2004). [CrossRef] [PubMed]

**A**is exact, we have:

*b*are the elements of

_{ij}**A**

^{-1}.

*I(λ, z)*is constructed based on Eq. (4) using the measured laser spectrum, the dye absorption coefficients, and the scattering coefficients from a real sample containing microbeads (refer to the later experimental section for details). The sample has a μ

_{a,800nm}= 0.5 mm

^{-1}and a μ

_{s,800nm}= 0.5 mm

^{-1}. R(z) was chosen to be a uniformly-distributed random vector with values between [0.5, 1.5]. The wavelength range was set between 700 nm and 900 nm and the maximum sample depth was set as 1 mm. White Gaussian noise of specified SNR was added to

*I(λ, z)*. The windowing function was chosen to be the laser source spectrum. Figure 1 shows the effect of noisy time-frequency analysis on the accuracy of the final dye concentration retrieval. The standard deviations for 100 runs at different SNRs are measured as a means of quantifying the accuracy and repeatability of the absorption retrieval.

*δf*/

_{a}*f*, or standard deviation over the mean) as a function of SNR in the time-frequency analysis of the SOCT signal

_{a}*I(λ, z)*. From Fig. 1, it can be seen that the error increases with worsening SNR. In order to have error percentage smaller than 5%, the time-frequency analysis from the SOCT signals should have a SNR larger than 14dB for this case.

## 5. Experiments

_{2}O

_{3}laser source was used (KM Labs, Δ

_{c}= 810nm, Δλ = 130 nm, P

_{out}= 300 mW). Dispersion and polarization were matched in the interferometer arms. A thin lens with a 40 mm focal length was chosen to focus the sample-arm beam and to minimize the effect of chromatic aberrations and dispersion. A precision linear optical scanner was used to scan the reference arm. Non-linearities in the reference scanning rate were accounted for by acquiring a reference fringe pattern using a laser diode (λ

_{c}= 776 nm, Δλ = 1 nm), followed by the application of a data-correction algorithm. The OCT system provided 4

*μm*axial and 26

*μm*lateral resolution with a 3.2 mm depth of focus in air. The system SNR was 110 dB with 11 mW of sample power. The typical power incident on the sample for these studies was 10 mW. The interfering signal and reference light was detected using an auto-balancing detector (Model 2007, New Focus, Inc.). The signal was amplified and anti-aliasing low-pass filtered by a custom-made analog circuit. A high-speed (5 Msamples/s, 12-bit) A/D converter (NI-PCI-6110, National Instruments) was used to acquire interferometric fringe data.

15. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. **42**, 204–217 (2003). [CrossRef] [PubMed]

*F*of the analytical signal and the corresponding light wavelength

*λ*could be calculated by:

*λ*is the laser diode center wavelength.

_{LD}*F*and

_{high}*F*correspond to the digital frequency ranges used in the down-sampling step.

_{low}*F*is the digital frequency obtained from SOCT using a laser diode and a perfect mirror. After data processing, the spectra were averaged over 512 scan lines to reduce noise.

_{LD}*W(λ)*. Because the emission spectrum of the Ti:sapphire laser had a somewhat flattened top with a fast fall-off at each end, a rectangular

*W(λ)*corresponding to the FWHM of the laser spectrum was chosen.

*δλ*) using the STFT can be roughly estimated by

*l*is the short window length and λ

_{STFT}_{c}is the center wavelength of the laser spectrum. The exact spectral resolution can be measured by performing an analysis of SOCT signals obtained from a narrow-band laser diode source and a mirror as the sample. A general guideline for choosing the window size is that the window size should be large enough such that absorption features of the dye are distinguishable with sufficient accuracy but not overly degrade the spatial resolution.

## 6. Results

8. B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher, and W. Drexler, “Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography,” Opt. Express **12**, 1677–1688 (2004). [CrossRef] [PubMed]

^{-1}according to procedures outlined by Hermann

*et al*. [8

8. B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher, and W. Drexler, “Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography,” Opt. Express **12**, 1677–1688 (2004). [CrossRef] [PubMed]

^{-1}attenuation at 800 nm. These solutions were placed into 1-mm-thick glass cuvettes and imaged with SOCT. The cuvette direction was adjusted such that light reflecting from glass/liquid interfaces went straight back to the fiber collimator. The maximized specular reflections collected by the detector from the glass/liquid and liquid/glass interfaces were much greater (at least 40 times larger) than the light scattered from the microbeads. Neutral density filters were used to avoid saturation of the detector. The interference data from light scattered back from the top glass/dye interface and the bottom dye/glass interface were recorded and analyzed using a Fourier transform window size of 10 coherence lengths to extract the SOCT spectra. Figure 4 shows the attenuation spectra extracted with SOCT from the solutions, and their respective separation results using prior spectral measurement of

*ε*and

_{a}(λ)*ε*obtained with a spectrometer. The algorithm successfully separated the absorption and scattering profiles with a mean error percentage of 4% and a maximum error percentage of 11% from 750 nm to 850 nm.

_{s}(λ)^{-1}. The microbead concentration was chosen to give a scattering coefficient of 0.25 mm

^{-1}at 800 nm for all 5 samples. To evaluate the ability of SOCT to resolve different scatterer concentrations in the presence of dyes, another series of 5 samples were constructed with the same concentration of dye (peak absorption at 0.25 mm

^{-1}) but different microbeads concentrations such that the scattering coefficients at 800 nm were 0.1, 0.2, 0.3, 0.4 and 0.5 mm

^{-1}. The solutions were placed inside a 1 mm-pathlength cuvette and imaged with SOCT. The cuvette was tilted such that specular reflections off the interfaces were off axis and the light collected at the detector from the interfaces was small.

*F*and

_{a}(z)*F*) along with their respective linear-regression curve-fitting from the 10 samples obtained by solving Eq. (12) and Eq. (10). Along the axial scan depth, the cumulative absorption/scattering curves can be roughly divided into three regions: the glass region, top media region, and bulk media region. In the glass region, the signals were mostly noise because there was virtually no scatterer in the upper and bottom glass walls of the cuvette. The top media region ranges from the top glass/liquid interface to 0.1 mm into the sample. The SOCT data from this region was used to obtain the reference spectrum

_{s}(z)*I(λ, z*=

*0)*used in Eq. (5). Hence

*F*and

_{a}(z)*F*are mostly flat in this region. The bulk media region ranges from about 0.1 mm into the media to the bottom liquid/glass interface. This region was used to retrieve the absorber/scatterer concentrations. From Fig. 5, the algorithm successfully resolved different absorber (scatterer) concentrations despite the presence of scatterers (absorbers). The errors associated with the resolved scatterer concentration were larger than the error associated with the resolved absorber concentration. This error discrepancy might be due to the presence of multiple scatterings that the algorithm is not able to resolve. The errors of different samples have similar dependency on the depth, indicating the presence of system errors due to non-idealty in OCT system and signal processing algorithms.

_{s}(z)^{-1}, and an average scattering loss of 0.2 mm

^{-1}, while the bottom layer had a peak absorption of 0.4 mm

^{-1}, and an average scattering loss of 0.2 mm

^{-1}. Figure 6 shows the cumulative absorber and scatterer concentrations extracted from the two-layer samples, along with their respective linear-regression curve-fitting obtained by solving Eq. (13) and Eq. (10). Similarly, the cumulative absorption/scattering curves can also roughly be divided into three regions: glass region, top media region and bulk media region. The top media region ranges from the top glass/liquid interface to 0.1 mm into the sample in the top layer. As seen from Fig. 6, the algorithm successfully resolved the relative absorber and scatterer concentrations with reasonable accuracy along different depths in the same sample.

*a priori*, and the scattering spectra of scatterers within the sample are relatively uniform. However, for many important applications, these prerequisites can be met. Absorbing contrast agents, such as NIR dyes, have known absorption profiles and can be site-specifically added as labels in biological tissue. Our algorithm can be used to quantitatively map out the spatial distribution of such contrast agents. In natural biological tissue, strong absorbers such as blood or melanin have well-characterized absorption profiles that if not known, can typically be measured using integrating spheres. However, because there are likely to be multiple absorbers co-existing in the tissue, precise characterization of the absorption profiles will require even more sophisticated multi-component spectral analysis methods.

## 7. Conclusion

## Acknowledgments

## References and links

1. | 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 |

2. | J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Biomedical imaging and optical biopsy using optical coherence tomography,” Nature Medicine |

3. | A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys, |

4. | U. Morgner, W. Drexler, F. C. Kartner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. |

5. | R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, “Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography,” Opt. Lett. |

6. | D. J. Faber, E. G. Mik, M. C. G. Aalders, and T. G. van Leeuwen, “Light absorption of (oxy-) hemoglobin assessed by spectroscopic optical coherence tomography,” Opt. Lett. |

7. | C. Xu, J. Ye, D. L. Marks, and S. A. Boppart, “Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography,” Opt. Lett. |

8. | B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher, and W. Drexler, “Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography,” Opt. Express |

9. | K. D. Rao, M. A. Choma, S. Yazdanfar, A. M. Rollins, and J. A. Izatt, “Molecular contrast in optical coherence tomography by use of a pump-probe technique,” Opt. Lett. |

10. | C. Yang, M. A. Choma, L. E. Lamb, J. D. Simon, and J. A. Izatt, “Protein-based molecular contrast optical coherence tomography with phytochrome as the contrast agent,” Opt. Lett. |

11. | M. Born and E. Wolf, |

12. | C. Yang, M. A. Choma, J. D. Simon, and J. A. Izatt. “Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper SB3. |

13. | C. Xu and S. A. Boppart. “Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography,” Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14–17, 2004, Paper FH9. |

14. | J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Differential absorption imaging with optical coherence tomography,” J. Opt. Soc. Am. A |

15. | D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. |

**OCIS Codes**

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(290.0290) Scattering : Scattering

(290.7050) Scattering : Turbid media

(300.1030) Spectroscopy : Absorption

(300.6360) Spectroscopy : Spectroscopy, laser

**ToC Category:**

Research Papers

**History**

Original Manuscript: August 2, 2004

Revised Manuscript: September 16, 2004

Published: October 4, 2004

**Citation**

Chenyang Xu, Daniel Marks, Minh Do, and Stephen Boppart, "Separation of absorption and scattering profiles in spectroscopic optical coherence tomography using a least-squares algorithm," Opt. Express **12**, 4790-4803 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4790

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### References

- 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]
- J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. E. Bouma, M. R. Hee, J. F. Southern and E. A. Swanson, "Biomedical imaging and optical biopsy using optical coherence tomography," Nature Medicine 1, 970-972 (1995). [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]
- U. Morgner, W. Drexler, F. C. Kartner, X. D. Li, C. Pitris, E. P. Ippen and J. G. Fujimoto, "Spectroscopic optical coherence tomography," Opt. Lett. 25, 111-113 (2000). [CrossRef]
- R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker and A. F. Fercher, "Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography," Opt. Lett. 25, 820-822 (2000). [CrossRef]
- D. J. Faber, E. G. Mik, M. C. G. Aalders and T. G. van Leeuwen, "Light absorption of (oxy-) hemoglobin assessed by spectroscopic optical coherence tomography," Opt. Lett. 28, 1436-1438 (2003). [CrossRef] [PubMed]
- C. Xu, J. Ye, D. L. Marks and S. A. Boppart, "Near-infrared dyes as contrast-enhancing agents for spectroscopic optical coherence tomography," Opt. Lett. 29, 1647 (2004). [CrossRef] [PubMed]
- B. Hermann, K. Bizheva, A. Unterhuber, B. Povazay, H. Sattmann, L. Schmetterer, A. F. Fercher and W. Drexler, "Precision of extracting absorption profiles from weakly scattering media with spectroscopic time-domain optical coherence tomography," Opt. Express 12, 1677-1688 (2004). [CrossRef] [PubMed]
- K. D. Rao, M. A. Choma, S. Yazdanfar, A. M. Rollins and J. A. Izatt, "Molecular contrast in optical coherence tomography by use of a pump-probe technique," Opt. Lett. 28, 340-342 (2003). [CrossRef] [PubMed]
- C. Yang, M. A. Choma, L. E. Lamb, J. D. Simon and J. A. Izatt, "Protein-based molecular contrast optical coherence tomography with phytochrome as the contrast agent," Opt. Lett. 29, 1396-1398 (2004). [CrossRef] [PubMed]
- M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, 1999).
- C. Yang, M. A. Choma, J. D. Simon and J. A. Izatt. "Spectral triangulations molecular contrast OCT with indocyanine green as contrast agent." Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14-17, 2004, Paper SB3.
- C. Xu and S. A. Boppart. "Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography." Optical Society of American Biomedical Optics Topical Meetings, Miami, FL, April 14-17, 2004, Paper FH9.
- J. M. Schmitt, S. H. Xiang and K. M. Yung, "Differential absorption imaging with optical coherence tomography," J. Opt. Soc. Am. A 15, 2288-2296 (1998). [CrossRef]
- D. L. Marks, A. L. Oldenburg, J. J. Reynolds and S. A. Boppart, "Digital algorithms for dispersion correction in optical coherence tomography for homogeneous and stratified media," Appl. Opt. 42, 204-217 (2003). [CrossRef] [PubMed]

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