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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 25 — Dec. 15, 2003
  • pp: 3445–3454
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Time-resolved diffusive optical imaging using pseudo-random bit sequences

Nan Guang Chen and Quing Zhu  »View Author Affiliations


Optics Express, Vol. 11, Issue 25, pp. 3445-3454 (2003)
http://dx.doi.org/10.1364/OE.11.003445


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Abstract

We have experimentally implemented a time-resolved diffusive optical tomography system via a novel spread spectrum approach. A low power (~5 mW) laser diode modulated with pseudo-random bit sequences replaces the short pulse laser used in conventional time-resolved optical systems, while the time-resolved transmittance is retrieved by correlating the detected signal with the stimulation sequence. Temporal point spread functions of diffusive light propagating through a turbid medium have been measured with remarkably low noise levels and a temporal resolution of 2.24 nanosecond. We also present results of 2-dimensional scanning imaging experiments as evidences of the great potential of this new imaging technique.

© 2003 Optical Society of America

1. Introduction

In all conventional time-resolved optical measurement systems, a pulsed light source is necessary. For diffusive optical imaging, a picosecond or femtosecond laser is used to illuminate a sample while various detection schemes may be employed. The cost of such a system is always prohibitory due to the use of an ultra-short pulse (picosecond or femtosecond) laser and ultra-fast detection channels. It can be even more costly if multiple wavelengths are needed for functional imaging. Usually, a TPSPC system offers the best dynamic range and temporal linearity at the expense of very long data acquisition time. We have been exploring an entirely new approach, which is called spread spectrum time-resolved method. In such a spread spectrum time-resolved system, a low power (<100 mW) laser diode modulated with a pseudo-random bit sequence (PRBS) replaces the pulsed laser as the light source. When the coded excitation sequence propagates through a turbid medium, it is split into a group of components that have different path lengths going into the detector. The correlation of the detected signals with the excitation sequence can pick up each component with a specific delay. We have previously predicted the feasibility of such a time-resolve DOT system with computer simulation [25

25. N. G. Chen and Q. Zhu, “Time-resolved optical measurements with spread spectrum excitation,” Opt. Lett. , 27, 1806–1808 (2002). [CrossRef]

]. However, this is the first time that we report its experimental implementation with a nanosecond temporal resolution. In addition, the potential of our method toward high spatial resolution is demonstrated with results from two-dimensional scanning imaging experiments.

2. System architecture

Fig. 1. Time-resolved diffusive optical tomography system architecture. Thick black arrows indicate flows of broadband signals, while thin ones correspond to low frequency signals. The double-line red arrow represents modulated light propagating through a sample under investigation.

The system was calibrated with neutral density filters inserted between the laser diode and the detector. The total attenuation factor was about 10-5. The black curve in Fig. 2 is the measured TPSF (temporal point spread function), or the impulse response, of the system. If all the components used in this system had wide enough bandwidths, the TPSF should be similar to a triangle near the origin and the FWHM (full width at half magnitude) would be 1.61 ns [25

25. N. G. Chen and Q. Zhu, “Time-resolved optical measurements with spread spectrum excitation,” Opt. Lett. , 27, 1806–1808 (2002). [CrossRef]

]. Nonetheless, the measured TPSF was slightly wider than the theoretical predication for ideal situations. This was due to the limited bandwidths of some components in this prototype instrument. For example, the APD had a high cutoff frequency around 400 MHz. The transimpedance amplifier should have a flat frequency response from dc to 600 MHz in ideal situations. However, the terminal capacitance of the APD was about 10 pF, which might deteriorate the high frequency performance of the TIA. Consequently, the temporal resolution, or the FWHM of the TPSF, was measured about 2.24 ns. While it is necessary to move further into the sub-nanosecond regime for high resolution optical imaging, a nanosecond temporal resolution could also prove useful for certain applications. In addition, our approach provides an outstanding signal to noise ratio and short data acquisition time. Experimental results are provided in the following section to demonstrate the capability and potential of this new technique.

Fig. 2. TPSF of the spread spectrum time-resolved system. The measured temporal profile (black) is slightly wider than the theoretical predication (blue).

3. Experimental setup

Phantom experiments were performed to demonstrate our prototype spread spectrum time-resolved system. Shown in Figure 3 is the geometry of our experimental setup. A rectangular transparent container was filled with 0.5% Intralipid solution, which had similar optical properties to human soft tissues. The dimension of Intralipid solution was 21cm by 5.5 cm in the X and Z directions, and 10 cm in height. The origin of the coordinate system was located at the up-left corner of a 6 cm by 4 cm imaging area (enclosed by the purple rectangle). The output beam of the light source pointed perpendicularly to one side of the phantom, while the detector was placed on the opposite side. The source and the detector were so aligned that the ballistic path was parallel to the Z-axis. A 3-dimensional translation stage was used to scan the source detector pair at a 2 mm step in both X and Y directions.

Fig. 3. Geometry of the experimental setup for 2-D scanning imaging. The purple rectangle (dashed-dotted) indicates the imaging area.

Three targets of different type were embedded in the Intralipid solution for image acquisition (Fig. 4). The first was a black cylinder 5.5 mm in diameter and 15 mm long. It was nearly a pure absorber. The second was a sphere 18 mm in diameter, with µa≈0.07cm -1 and µ′s≈9cm -1. Its absorption and reduced scattering coefficients were slightly higher than the background values. The third was a small clear glass bottle sealed with glue, which made a void region in the turbid background. The outer diameter of the bottle was 14 mm, while the total length was 31 mm. In each image acquisition, one target was placed around the center of the imaging area, equal distant to the interfaces to both the light source and the detector.

Fig. 4. Targets used in imaging experiments.

4. Results

No target was embedded inside the Intralipid solution when the background TPSF of the transmitted diffusive light wave was acquired. The time delay was scanned at a 0.6 ns interval from -2.4 ns to 9.6 ns. The data acquisition time for each point was about 0.1 second. The corresponding measurement errors are represented by the error bars superimposed on the curve (Fig. 5). The measured TPSF should be perceived as a convolution of the real TPSF with the system response (Fig. 2). As a consequence of the 2.24 ns temporal resolution, the measured TPSF stretches out into the negative time delay region and the rising edge became less steep due to mixed contributions from diffusive photons. The oscillation between 6 to 9.6 ns was mainly caused by the low cutoff frequency of the mixer (around 0.5 MHz).

Fig. 5. TPSF of the light transmittance through the phantom in Fig. 3.

Three specific time delay points were selected for 2-dimensional scanning imaging, i. e., - 0.6 ns, 0 ns, and 1.2 ns. The first two involve near diffusive photons, while the last one corresponds to the peak value the background TPSF. For each target, images were acquired with these three time delays. Images associated with various target and time delays are compared in Fig. 6 through Fig. 8. In Fig. 6 and 7, the absorbing targets caused decrease in transmittance in the target regions. The images are scaled between zero and the maximum background values. For Fig. 8, the void target resulted in increased transmittance and the images are scaled between zero and the maximum transmittance in the target regions.

Fig. 6. 2-dimensional scanning images with a black cylinder as the target. The time delays are (a) -0.6 ns, (b) 0 ns, and (c) 1.2 ns, respectively.
Fig. 7. 2-dimensional scanning images with a spherical target (see the text for its optical properties). The time delays are (a) -0.6 ns, (b) 0 ns, and (c) 1.2 ns, respectively.
Fig. 8. 2-dimensional scanning images with clear glass bottle as the target. The time delays are (a) -0.6 ns, (b) 0 ns, and (c) 1.2 ns, respectively.
Fig. 9. Line profiles across the center of the void target in the X direction. The solid line, circles, and asterisks correspond to -0.6 ns, 0 ns, and 1.2 ns, respectively.

In the void target case, image qualities for time delays -0.6 ns (Fig. 8(a)) and 0 ns (Fig. 8(b)) are close. However, Fig. 8(a) is slightly better that one can even identify the outline of the bottleneck. Fig. 8(c) appears much more blurred with a lower contrast. Plotted in Fig. 9 are line profiles extracted from images in Fig. 8 at Y=24 mm. The maximal perturbation decreases from 52.1% for -0. 6 ns and 50.6% for 0 ns to 26.5% for 1.2 ns. However, for absorbing targets, the differences in the maximal perturbation among different time delays are not significant.

To quantify the effect of time delay on spatial resolution, two parameters are employed. One is the FWHM of the representative profile along a horizontal scanning line across the target centers. Another is the maximal absolute edge slope normalized with respect to the maximal perturbation, denoted as Knorm. The bigger Knorm, the smaller edge spread and the higher spatial resolution. Summarized in Table 1 are these parameters for three targets at different time delays. According to this table, improvement in the spatial resolution due to reduced time delay is more evident for absorbing targets than for the void target.

Table 1. Spatial parameters vs. time delay

table-icon
View This Table

5. Discussions

Images shown in Fig. 6 through 8 are simply 2-dimensional projections without any image processing, and thus should not be directly compared with those tomographic images reconstructed with dedicated inversion algorithms. If we define the spatial resolution as the reciprocal of Knorm, then its value for the black cylinder increases from about 5.5 mm to 8.1 mm with increasing time delay. Interestingly, the improvement in spatial resolution depends on the type of targets embedded, as suggested by our study. However, rigorous assessment of the achievable spatial resolution via the time-resolved approach needs more extensive investigations. Incorporation of reconstruction algorithms to the time-resolved measurement system is definitely necessary, while optimization of the scan geometry might be equally important. These issues are beyond the scope of this paper, but will be investigated in our future studies.

The signal to noise ratio also plays a critical role for higher image quality. For our spread spectrum time-resolved system, the noise level is consistent through the time domain. Consequently, the signal to noise ratio becomes lower for early arriving photons as the signal strength decreases. Compromises should be made to balance the spatial resolution, the noise level, and the data acquisition time for a specific application. As a prototype system, our time-resolved instrument has manifested a superior signal to noise ratio. The relative measurement error is about 0.81% for the peak value of the TPSF, or 0.49% for the integrated signal (the total transmittance). This is already better than the shot noise alone (about 1%) for a TCSPC system that works in an ideal condition with a 105 count/s photon-counting rate and the same data acquisition time of 0.1 second. The signal to noise ratio has not been explicitly specified in most literatures on time-resolved DOT systems based on TCSPC. It is argued that the noise levels of such systems are dominated by the shot noise after subtraction of background counts caused by environmental lights. However, the noise and stability of ultrafast lasers are usually worse than 1% and will definitely degrade the system performance. Another problem with TCSPC is that the ultimate signal to noise ratio is limited by the detector, or more specifically, the counting rate. The light source has to be maintained at a rather low output level in order to fulfill the requirement of single photon counting and not to damage the detector. On the other hand, the noise level of our system can be further reduced by about 20 dB by simply increasing the source power by a factor of 10. Actually the noise level of our system is dominated by the electronic circuitry noises (including the preamplifier noise) and has much room to improve before reaching the shot noise floor.

To compare the performance of our prototype system with frequency domain systems, a virtual 200 MHz system is picked [26

26. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal to noise analysis,” Appl. Opt. 36, 75–92 (1997). [CrossRef] [PubMed]

] because of the similar imaging geometry. The amplitude noise is about 0.32% for a 10 Hz bandwidth if only the shot noise is considered, and it should become around 0.5% if taking into account the excess noise factor of PMT. In a practical situation, the noises from the detector itself, the preamplifier, and the light source will also contribute to the total noise of the system. For example, the 50 MHz frequency domain system developed at the University of Pennsylvania has an estimated amplitude noise of 1% and phase noise of 0.3 degree [27

27. Y. Chen, X. Intes, S. Zhou, C. Mu, M. Holboke, A. G. Yodh, and B. Chance, “Detection sensitivity and optimization of phased array system,” Proc. SPIE 4250, 211–218 (2001). [CrossRef]

]. In addition, the PMT used in those systems generally have an internal gain (typically 105–107) several orders higher than that of the APD in our system, which is around 100. Using high-speed PMT is another option to increase the sensitivity and the signal to noise ratio for our system.

Higher temporal resolution is definitely desirable for retrieval of the time-resolved transmittance or reflectance more accurately. Fortunately, components for 2.5 Gb/s and even 10 Gb/s data rates are readily available from the telecommunication industry. By using a higher bit rate pattern generator together with wider bandwidth laser diodes and detectors (APD or photomultiplier tube), it would be highly feasible to reach a 100-ps temporal resolution. It should be noted that the method presented in the report could be well adopted in a wide range of other applications, such as time-resolved fluorescence spectroscopy and imaging.

6. Summary

We have developed a prototype spread spectrum time-resolved diffusive optical imaging system, which has a temporal resolution of 2.24 ns. Phantom experiments with such a system have demonstrated the great potential of this new technique to improve diffusive optical tomography in terms of the spatial resolution and the signal to noise ratio.

Acknowledgments

We would like to thank the following for their funding support: DOD ARMY Breast Cancer Program (DAMD17-00-1-0217, DAMD17-01-1-0216), and NIH (8R01EB002136-02). Dr. Bing Wang of the ECE department at University of Connecticut is gratefully acknowledged for proofreading the manuscript.

References and links

1.

B. Chance, “Near-infrared (NIR) optical spectroscopy characterizes breast tissue hormonal and age status,” Academic Radiology 8, 209–210 (2001). [CrossRef] [PubMed]

2.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-Invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000). [CrossRef] [PubMed]

3.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. M. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kashke, “Frequency-domain optical mammography: Edge effect corrections,” Med. Phys. 23, 146–157 (1996). [CrossRef]

4.

T. L. Troy, D. L. Page, and E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 1, 342–355 (1996). [CrossRef] [PubMed]

5.

Q. Zhu, T. Durduran, M. Holboke, V. Ztziachristos, and A. Yodh, “A imager that combines near infrared diffusive light and ultrasound,” Optics letters 24, 1050–1052 (1999). [CrossRef]

6.

B. Chance, Z. Zhuang, C. UnAh, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770–3074 (1993). [CrossRef] [PubMed]

7.

D. A. Boas, T. Gaudette, G. Strangman, X. F. Cheng, J. J. A. Marota, and J. B. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics” Neuroimage 13, 76–90 (2001). [CrossRef] [PubMed]

8.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002). [CrossRef] [PubMed]

9.

C. J. Aldrich, D. Dantona, J. A. D. Spencer, J. S. Wyatt, D. M. Peebles, D. T. Delpy, and E. O. R. Reynolds, “The Effect of Maternal pushing in fetal cerebral oxygenation and blood-volume during the 2nd stage of labor,” Brit. J. Obstet. Gynaec. 102, 448–453 (1995). [CrossRef] [PubMed]

10.

J. Beuthan, U. Netz, O. Minet, A. D. Klose, A. H. Hielscher, A. Scheel, J. Henniger, and G. Muller, “Light scattering study of rheumatoid arthritis,” Quantum Electronics 32, 945–952 (2002). [CrossRef]

11.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. 8, 102–110 (2003). [CrossRef] [PubMed]

12.

Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, and S. H. Kurtzman, “Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions: initial clinical results of 19 cases,” Neoplasia 5, 379–389 (2003). [PubMed]

13.

K. A. Kang, D. F. Bruley, J. M. Londono, and B. Chance, “Localization of a fluorescent object in highly scattering media via frequency response analysis of near infrared-time resolved spectroscopy spectra,” Ann. Biomed. Engr. 26,138–145 (1998). [CrossRef]

14.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001). [CrossRef]

15.

D. Grosenick, H. Wabnitz, and H. Rinneberg, “Time-resolved imaging of solid phantoms for optical mammography,” Appl. Opt. 36, 221–231 (1997). [CrossRef] [PubMed]

16.

W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38, 4237–4246 (1999). [CrossRef]

17.

F. Gao, H. J. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 778–791 (2002). [CrossRef] [PubMed]

18.

S. Behin-Ain, T. van Doorn, and J. R. Patterson, “Spatial resolution in fast time-resolved transillumination imaging: an indeterministic Monte Carlo approach,” Phys. Med. Biol. 472935–2945 (2002). [CrossRef] [PubMed]

19.

N. G. Chen and Q. Zhu, “Optical Tomography with Early Arriving Photons: Sensitivity and Resolution Analysis,” Proc. SPIE 4250, 37–44 (2001). [CrossRef]

20.

G. W. Faris and M. Banks, “Upconverting time gate for imaging through highly scattering media,” Opt. Lett. 19, 1813–1815 (1994). [CrossRef] [PubMed]

21.

R. Mahon, M. D. Duncan, L. L. Tankersley, and J. Reintjes, “Time-gated imaging through dense scatterers with a Raman amplifier,” Appl. Opt. 32, 7425–7433 (1993). [CrossRef] [PubMed]

22.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and A. A. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769–771 (1991). [CrossRef] [PubMed]

23.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000). [CrossRef]

24.

H. Eda, Oda I, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999). [CrossRef]

25.

N. G. Chen and Q. Zhu, “Time-resolved optical measurements with spread spectrum excitation,” Opt. Lett. , 27, 1806–1808 (2002). [CrossRef]

26.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal to noise analysis,” Appl. Opt. 36, 75–92 (1997). [CrossRef] [PubMed]

27.

Y. Chen, X. Intes, S. Zhou, C. Mu, M. Holboke, A. G. Yodh, and B. Chance, “Detection sensitivity and optimization of phased array system,” Proc. SPIE 4250, 211–218 (2001). [CrossRef]

OCIS Codes
(170.3890) Medical optics and biotechnology : Medical optics instrumentation
(170.5280) Medical optics and biotechnology : Photon migration
(170.6920) Medical optics and biotechnology : Time-resolved imaging
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Research Papers

History
Original Manuscript: October 28, 2003
Revised Manuscript: December 8, 2003
Published: December 15, 2003

Citation
Nan Chen and Quing Zhu, "Time-resolved diffusive optical imaging using pseudo-random bit sequences," Opt. Express 11, 3445-3454 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-25-3445


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References

  1. B. Chance, �??Near-infrared (NIR) optical spectroscopy characterizes breast tissue hormonal and age status,�?? Academic Radiology 8, 209-210 (2001). [CrossRef] [PubMed]
  2. B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand and J. Butler, �??Non- Invasive in vivo characterization of breast tumors using photon migration spectroscopy,�?? Neoplasia 2, 26-40 (2000). [CrossRef] [PubMed]
  3. S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. M. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kashke, �??Frequency-domain optical mammography: Edge effect corrections,�?? Med. Phys. 23, 146-157 (1996). [CrossRef]
  4. T. L. Troy, D. L. Page, E. M. Sevick-Muraca, �??Optical properties of normal and diseased breast tissues: prognosis for optical mammography,�?? J. Biomed. Opt. 1, 342-355 (1996). [CrossRef] [PubMed]
  5. Q. Zhu, T. Durduran, M. Holboke, V. Ztziachristos, A. Yodh, �??An imager that combines near infrared diffusive light and ultrasound,�?? Optics letters 24, 1050-1052 (1999). [CrossRef]
  6. B. Chance, Z. Zhuang, C. UnAh, and L. Lipton, �??Cognition-activated low-frequency modulation of light absorption in human brain,�?? Proc. Natl. Acad. Sci. USA 90, 3770-3074 (1993). [CrossRef] [PubMed]
  7. D. A. Boas, T. Gaudette, G. Strangman, X. F. Cheng, J. J. A. Marota, J. B. Mandeville, �??The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics�?? Neuroimage 13, 76-90 (2001). [CrossRef] [PubMed]
  8. J. C. Hebden, A.Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, J. S. Wyatt, �??Three-dimensional optical tomography of the premature infant brain,�?? Phys. Med. Biol. 47, 4155-4166 (2002). [CrossRef] [PubMed]
  9. C. J. Aldrich, D. Dantona, J. A. D. Spencer, J. S. Wyatt, D. M. Peebles, D. T. Delpy, E. O. R. Reynolds, �??The Effect of Maternal pushing in fetal cerebral oxygenation and blood-volume during the 2nd stage of labor,�?? Brit. J. Obstet. Gynaec. 102, 448-453 (1995). [CrossRef] [PubMed]
  10. J. Beuthan, U. Netz, O. Minet, A. D. Klose, A. H. Hielscher, A. Scheel, J. Henniger, G. Muller, �??Light scattering study of rheumatoid arthritis,�?? Quantum Electronics 32, 945-952 (2002). [CrossRef]
  11. H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, J. F. Dunn, �??Near-infrared imaging in the small animal brain: optimization of fiber positions,�?? J. Biomed. Opt. 8, 102-110 (2003). [CrossRef] [PubMed]
  12. Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, S. H. Kurtzman, �??Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions: initial clinical results of 19 cases,�?? Neoplasia 5, 379-389 (2003). [PubMed]
  13. K. A. Kang, D. F. Bruley, J. M. Londono, B. Chance, �??Localization of a fluorescent object in highly scattering media via frequency response analysis of near infrared-time resolved spectroscopy spectra,�?? Ann. Biomed. Engr. 26, 138-145 (1998). [CrossRef]
  14. J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, �??Three-dimensional time-resolved optical tomography of a conical breast phantom,�?? Appl. Opt. 40, 3278-3287 (2001). [CrossRef]
  15. D. Grosenick, H. Wabnitz, H. Rinneberg, �??Time-resolved imaging of solid phantoms for optical mammography,�?? Appl. Opt. 36, 221-231 (1997). [CrossRef] [PubMed]
  16. W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, R. R. Alfano, �??Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,�?? Appl. Opt. 38, 4237-4246 (1999). [CrossRef]
  17. F. Gao, H. J. Zhao, Y. Yamada, �??Improvement of image quality in diffuse optical tomography by use of full time-resolved data,�?? Appl. Opt. 41, 778-791 (2002). [CrossRef] [PubMed]
  18. S. Behin-Ain, T. van Doorn, J. R. Patterson, �??Spatial resolution in fast time-resolved transillumination imaging: an indeterministic Monte Carlo approach,�?? Phys. Med. Biol. 47 2935-2945 (2002). [CrossRef] [PubMed]
  19. N. G. Chen, Q. Zhu, �??Optical Tomography with Early Arriving Photons: Sensitivity and Resolution Analysis,�?? Proc. SPIE 4250, 37-44 (2001). [CrossRef]
  20. G. W. Faris, M. Banks, �??Upconverting time gate for imaging through highly scattering media,�?? Opt. Lett. 19, 1813-1815 (1994). [CrossRef] [PubMed]
  21. R. Mahon, M. D. Duncan, L. L. Tankersley, J. Reintjes, �??Time-gated imaging through dense scatterers with a Raman amplifier,�?? Appl. Opt. 32, 7425-7433 (1993). [CrossRef] [PubMed]
  22. L. Wang, P. P. Ho, C. Liu, G. Zhang, A. A. Alfano, �??Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,�?? Science 253, 769-771 (1991). [CrossRef] [PubMed]
  23. F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, D. T. Delpy, �??A 32-channel time-resolved instrument for medical optical tomography,�?? Rev. Sci. Instrum. 71, 256-265 (2000). [CrossRef]
  24. H. Eda, Oda I, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, �??Multichannel time-resolved optical tomographic imaging system,�?? Rev. Sci. Instrum. 70, 3595-3602 (1999). [CrossRef]
  25. N. G. Chen, Q. Zhu, �??Time-resolved optical measurements with spread spectrum excitation,�?? Opt. Lett. 27, 1806-1808 (2002). [CrossRef]
  26. D. A. Boas, M. A. O�??Leary, B. Chance, and A. G. Yodh, �??Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal to noise analysis,�?? Appl. Opt. 36, 75-92 (1997). [CrossRef] [PubMed]
  27. Y. Chen, X. Intes, S. Zhou, C. Mu, M. Holboke, A. G. Yodh, B. Chance, �??Detection sensitivity and optimization of phased array system,�?? Proc. SPIE 4250, 211-218 (2001). [CrossRef]

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