## High-speed camera with real time processing for frequency domain imaging |

Biomedical Optics Express, Vol. 2, Issue 7, pp. 1931-1945 (2011)

http://dx.doi.org/10.1364/BOE.2.001931

Acrobat PDF (2048 KB)

### Abstract

We describe a high-speed camera system for frequency domain imaging suitable for applications such as in vivo diffuse optical imaging and fluorescence lifetime imaging. 14-bit images are acquired at 2 gigapixels per second and analyzed with real-time pipeline processing using field programmable gate arrays (FPGAs). Performance of the camera system has been tested both for RF-modulated laser imaging in combination with a gain-modulated image intensifier and a simpler system based upon an LED light source. System amplitude and phase noise are measured and compared against theoretical expressions in the shot noise limit presented for different frequency domain configurations. We show the camera itself is capable of shot noise limited performance for amplitude and phase in as little as 3 ms, and when used in combination with the intensifier the noise levels are nearly shot noise limited. The best phase noise in a single pixel is 0.04 degrees for a 1 s integration time.

© 2011 OSA

## 1. Introduction

1. B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. **69**(10), 3457–3481 (1998). [CrossRef]

^{4}), which means that a frequency domain system can achieve better temporal resolution than a time domain system with the same bandwidth. The two primary applications of frequency domain imaging are diffuse imaging in vivo and fluorescence lifetime imaging. For diffuse optical imaging, the time-resolved measurements are used to separate the contributions of scatter and absorption, hence improving the ability to recover information on concentrations of endogenous chromophores such as hemoglobin concentrations and hemoglobin oxygenation. For fluorescence lifetime imaging, the lifetime information can be used to provide information on the environment of the emitting fluorophor such as pH, oxygen concentrations, or ion concentrations through fluorescence quenching, molecular reorientation, or proximity of neighboring chromophores through fluorescence resonance energy transfer (FRET). The phase noise is often the critical performance criterion for these applications.

2. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. **195**(2), 330–351 (1991). [CrossRef] [PubMed]

6. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express **11**(21), 2717–2729 (2003). [CrossRef] [PubMed]

7. A. B. Thompson and E. M. Sevick-Muraca, “Near-infrared fluorescence contrast-enhanced imaging with intensified charge-coupled device homodyne detection: measurement precision and accuracy,” J. Biomed. Opt. **8**(1), 111–120 (2003). [CrossRef] [PubMed]

11. R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. **71**(3), 201–213 (2008). [CrossRef] [PubMed]

7. A. B. Thompson and E. M. Sevick-Muraca, “Near-infrared fluorescence contrast-enhanced imaging with intensified charge-coupled device homodyne detection: measurement precision and accuracy,” J. Biomed. Opt. **8**(1), 111–120 (2003). [CrossRef] [PubMed]

9. T. French, J. Maier, and E. Gratton, “Frequency domain imaging of thick tissues using a CCD,” Proc. SPIE **1640**, 254–261 (1992). [CrossRef]

10. J. R. Lakowicz and K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. **62**(7), 1727–1734 (1991). [CrossRef]

11. R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. **71**(3), 201–213 (2008). [CrossRef] [PubMed]

12. K. Zhang and J. U. Kang, “Real-time intraoperative 4D full-range FD-OCT based on the dual graphics processing units architecture for microsurgery guidance,” Biomed. Opt. Express **2**(4), 764–770 (2011). [CrossRef] [PubMed]

13. A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging **28**(9), 1468–1472 (2009). [CrossRef] [PubMed]

## 2. Instrumentation

### 2.1. Camera and data processing

*X*and

*Y,*as well as the DC level,

*D*, for each pixel. After the data processing, the two FPGA processors stream the data to the BenNUEY motherboard, which concatenates the data and outputs it to the PC through the 64-bit PCI interface.

*X*and

*Y*quadratures are calculated as the correlation between each pixel data value and cosine and sine waveforms according to the equations

*S*(t) =

*S*[1 +

_{DC}*m*

_{1}cost(

*ωt*+

*α*)] is the optical signal and

*S*is the DC signal on a given pixel in counts per second. A third value, the accumulated DC value,

_{DC}*D*=

*S*, is calculated by summing the pixel counts without a sinusoid multiplier. Three 16-bit words are stored for each pixel representing the accumulated DC value,

_{DC}nΔt*D*, and the two quadratures,

*X*and

*Y*. Calculation of the correlations of Eq. (1) do not require storage of the individual signals at each time point

*S*(

*nΔt*), only the running summation of the product of the pixel counts and the sinusoid. The FPGA discards the rest of the image data, converting gigabytes of image data to 8 Mb/image for 800x600 pixels, each 16 bits deep. The FPGA boards were specified primarily based on the data transfer rates and onboard memory. The 8 Rocket I/O inputs support 212.5 MB/s per channel for total bandwidth of 1700 MB/s. The adjacent bus between the BenData-II and the two BenDATA-WS boards supports 64-bit inputs at 66 MHz for a total of 1056 MB/s for both paths. The smaller data rate of the two (1056 MB/s) supports 16 bit processing of full camera frames at 1000 frames/s or 8-bit images at 2000 frames/s. Each BenDATA-WS provides up to 24 MB wide ZBT SRAM for a total of 48 MB, exceeding the maximum storage of 24 MB for the three images – the DC image and the two AC quadrature images.

*A*, and phase,

*ϕ*, are calculated according to Eq. (2) and Eq. (3)

### 2.2 RF electronics

_{rms}, which is applied to the image intensifier photocathode through a bias tee. The low frequency image (1-333 Hz) signal is created by the heterodyne mixing of the 100 MHz and 100+ MHz signal, which produces the low frequency signal and a high frequency signal at 200 MHz. The 200 MHz is filtered by the phosphor screen in the image intensifier, which acts as a low pass filter. The low frequency signal is projected onto the phosphor screen, which is captured by the high-speed camera.

## 3. System performance

### 3.1 Assessment of phase precision and linearity

### 3.2 Results of system linearity

*α*, following the notation in the Appendix) or the correlation (detection) waveform,

*γ*, for 4 frames per cycle. This is believed to be due to nonlinearity of the DAQ-driven LED power, which leads to a different apparent phase depending the exact phase,

*α*, of the sinusoid when the light level is produced. This effect can be avoided by using more frames per cycle or presumably though generation of a voltage waveform that corrects for the LED nonlinearity. When the nonlinearity is avoided, the residual is 0.02 or better for the LED and 1 s integration time and ~0.3 for the intensifier. All of the data in Tables 3 and 4 use variation of the detection waveform phase,

*γ*, for which there is no nonlinearity and no linearity bias. The final parameter in Tables 2-4 is the variation in phase across the image (phase in image). This value is on the order of 0.1 degree for the LED and an integration time T = 1 s, but drops to around 0.5-1 degree for T < = 10 ms. The laser/intensifier has worse performance, or 0.9 degree for T = 1 s.

### 3.3 Results of system precision

^{5}counts for 1000 frames) out of a maximum of 2

^{14}counts for the 14-bit images.

### 3.4 AC/DC amplitude results

*m*

_{1}and

*m*

_{2}from Table 1. For the direct detection (LED) experiments this ratio is

*m*

_{1}/2 = 0.3, which matches the measured amplitude ratio of 0.3. For the heterodyne with dc offset (laser) experiments, the ratio is

*m*

_{1}

*m*

_{2}/4 = 0.0875, which agrees well with the large amplitude ratio of 0.1 from Fig. 7. Thus these measurements also match theoretical calculations.

### 3.5 LED 3 frames per cycle noise results

## 4. Conclusions

*α*, have slightly worse linearity characteristics, presumably due to source intensity nonlinearities.

## Appendix A: Measurement uncertainties from shot noise for frequency domain measurements

*X*and

*Y*as they would be represented on the polar plane. These can be determined from the real and imaginary parts of Fourier transformed data or from cosine and sine correlations. The modulated (AC) amplitude

*A*and phase

*ϕ*are given by Eqs. (2) and (3) above. Standard error propagation using Eqs. (2) and (3) gives the dimensionless expressions for the coefficient of variation in the AC amplitude and phase uncertainty [Eq. (4) and Eq. (5)]

*σ*and

_{X}^{2}*σ*are the variances in

_{Y}^{2}*X*and

*Y*, and

*σ*is the covariance in

_{XY}*X*and

*Y*. In the following we will consider only the case where the noise is determined by shot noise, which constitutes a fundamental limit governed by the number of detected photons, except with methods such as squeezed light [15

15. D. F. Walls, “Squeezed states of light,” Nature **306**(5939), 141–146 (1983). [CrossRef]

6. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express **11**(21), 2717–2729 (2003). [CrossRef] [PubMed]

16. X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. **46**(10), 1624–1632 (2007). [CrossRef] [PubMed]

17. T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. **7**(4), 643–649 (2002). [CrossRef] [PubMed]

*ω*

_{1}, phase,

*α,*and modulation efficiency,

*m*

_{1}, then

*N*

_{Δ}

*, the average number of photoelectrons produced in a measurement time Δ*

_{t}*t*centered at time

*t*is

*m*

_{1 }≤ 1. Note that the dc level

*i*/

_{dc}*q*Δ

*t*includes all dc light whether from the frequency domain light source or background light, whereas the modulated light (

*i*Δ

_{dc}*t*/

*q*)

*m*

_{1}cos(

*ω*

_{1}

*t*+

*α*)] is predominantly from the frequency domain light source. For shot noise, the average fluctuation in this value is

*E*(

*t*) includes a factor to convert electrons to a measurable value such as volts or counts. A single quadrature

*X*is found by correlation of the signal from Eq. (8) with a cosine function according to

*Y*, and the DC,

*D*, are the same as Eq. (10) except with

*C*(

*t*) replaced by

*S*(

*t*) and 1, respectively.

*C*(

*t*) and

*S*(

*t*) are of the general form cos(

*ωt*+

*γ*) and sin(

*ωt*+

*γ*). Although we write the expressions for the two quadratures as correlations, the following analysis is valid for calculation of the quadratures through Fourier transforms as well because the two correlations for

*X*and

*Y*are identical to the real and imaginary parts of the Fourier transform, with the exception of a constant multiplier. The constant multiplier does not affect the dimensionless noise expressions in Eqs. (4) and (5).

*C*(

*t*) or

*S*(

*t*). We write the summed variance as an integral according to

*σ*,

_{Y}^{2}*σ*and

_{D}^{2}*σ*are the same as Eq. (11) except that [

_{XY}*C*(

*t*)]

^{2}is replaced with [

*S*(

*t*)]

^{2}, 1, and

*C*(

*t*)

*S*(

*t*) respectively. This analysis is valid regardless of whether the experiment is better described by an integral such as Eqs. (10), or by summations such as in Eq. (1); i.e., by either continuous or discrete correlations or Fourier transforms.

*E*(

*t*),

*C*(

*t*), and

*S*(

*t*), which are given in Table 6 . The AC may be separated from the DC using filters prior to electronic demodulation and digitization of the signal (Cases 1A and 1B) or the AC and DC may be digitized together (Cases 2A and 2B). The homodyne methods perform demodulation in one step to determine the quadratures

*X*and

*Y,*such as performing RF mixing with an I/Q demodulator to produce two DC quadratures (Case 1A) or demodulation computationally following digitization (Case 2A). Heterodyne methods perform demodulation in two steps with a first mixing step reducing an RF frequency

*ω*

_{1}to a lower (intermediate) frequency |

*ω*

_{1}-

*ω*

_{2}| and a second step to determine the quadratures

*X*and

*Y*. Measurements with a photomultiplier typically perform the heterodyne and digitization of the AC separately from the DC (Case 1B), while measurements using an image intensifier perform the heterodyne without AC/DC separation and digitize AC and DC together (Case 2B).

*N*=

*i*/

_{dc}T*q*. These expressions are valid when all of the oscillatory terms average to zero (well-sampled conditions). The covariance

*σ*is zero for well-sampled conditions. When the number of intervals is small or the integration range does not cover an integral number of cycles of the various difference frequencies, then the results will differ somewhat from the expressions in Table 8, as is described below for three measurements per cycle for Case 2A. Note that the expressions in Table 8 depends only

_{XY}*N*,

*m*

_{1}, and

*m*

_{2}. The gain or conversion factor

*G*cancels out.

*G*can be different for the AC and DC signals without affecting the dimensionless noise expressions.

*σ*/

_{D}*D*in Cases 1A, 2A, and 1B are all the same and equal to the expected expression for shot noise,

*N*

^{-1/2}. For Case 2B, the DC uncertainty increases by an additional factor of (1+

*m*

_{1}

^{2}/2)

^{1/2}relative to the signal, which arises because the signal sums linearly while the noise sums in quadrature, resulting in an increase of the noise relative to the signal. The dimensionless AC noise terms

*σ*and

_{ϕ}*σ*/

_{A}*A*are always larger than the dimensionless DC noise terms for two reasons. First, a non-unity modulation depth leads to a reduction in the AC signal relative to the DC signal while the noise is unaffected by the modulation depth, resulting in a net increase in the dimensionless AC noise by a factor of 1/

*m*

_{1}for Cases 1A/2A/1B or 1/(

*m*

_{1}

*m*

_{2}) for Case 2B. Second, each demodulation step leads to an increase in the dimensionless AC noise by a factor of 2

^{1/2}because the oscillatory sampling reduces both the AC signal and the AC variance by a factor of two relative to their nominal amplitudes, and the dimensionless noise scales with the square root of the variance. This leads to a net factor of 2

^{1/2}or 2 increase in the dimensionless AC noise for Cases 1A/2A or Case 1B, which have one and two demodulation steps, respectively. For case 2B the net increase is 2(2

^{1/2}) because the first demodulation step passes the full DC noise. Note that the dimensionless noise expressions for the two homodyne methods (Case 1A and Case 2A) are identical.

6. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express **11**(21), 2717–2729 (2003). [CrossRef] [PubMed]

*m*

_{2}only where ours has

*m*

_{2}

^{2}.

*τ*= 2

*π*/

*ω*

_{1}. Well-sampled conditions are exactly fulfilled even for a single period

*τ*for Cases 1A and 2A (and also Cases 1B and 2B provided low pass filtering removes the

*ω*

_{1}+

*ω*

_{2}frequency) or when there are n

*evenly spaced measurements per period*

_{p}*τ*(i.e., measurements are τ/n

*apart) and*

_{p}*n*≥ 4. Two measurements are sufficient to determine

_{p }*A*and

*ϕ*when the DC contribution to the measurements is zero, but not for evenly spaced measurements because only one quadrature is sampled. For

*n*=3 and even sample spacing, Eqs. (2), (3) and (10) are correct, but the expressions for the AC and phase noise parameters in Tables 7 and 8 are not valid because there is a correlation between the noise expression of Eq. (7) and the sampling spacing τ/3, and the terms with frequency 3

_{p}*ω*

_{1}resulting from Eq. (11) do not sum to zero. Correct AC noise expressions for

*n*=3 with even sample spacing for Cases 1A and 2A are shown in Table 9. The dimensionless phase and amplitude noise

_{p}*σ*and

_{ϕ}*σ*/

_{A}*A*depend on the phase of the light α when the measurements are performed, as verified experimentally in Figure 8.

## Acknowledgments

## References and links

1. | B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. |

2. | E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. |

3. | S. J. Madsen, E. R. Anderson, R. C. Haskell, and B. J. Tromberg, “Portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. |

4. | H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. |

5. | M. Gerken and G. W. Faris, “High-precision frequency-domain measurements of the optical properties of turbid media,” Opt. Lett. |

6. | V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express |

7. | A. B. Thompson and E. M. Sevick-Muraca, “Near-infrared fluorescence contrast-enhanced imaging with intensified charge-coupled device homodyne detection: measurement precision and accuracy,” J. Biomed. Opt. |

8. | S. V. Patwardhan and J. P. Culver, “Quantitative diffuse optical tomography for small animals using an ultrafast gated image intensifier,” J. Biomed. Opt. |

9. | T. French, J. Maier, and E. Gratton, “Frequency domain imaging of thick tissues using a CCD,” Proc. SPIE |

10. | J. R. Lakowicz and K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. |

11. | R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. |

12. | K. Zhang and J. U. Kang, “Real-time intraoperative 4D full-range FD-OCT based on the dual graphics processing units architecture for microsurgery guidance,” Biomed. Opt. Express |

13. | A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging |

14. | J. R. Janesick, “Scientific Charge-Coupled Devices,” (SPIE Press, Bellingham, Washington, 2001), pp. 101–105. |

15. | D. F. Walls, “Squeezed states of light,” Nature |

16. | X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. |

17. | T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. |

**OCIS Codes**

(170.0110) Medical optics and biotechnology : Imaging systems

(170.3650) Medical optics and biotechnology : Lifetime-based sensing

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.5280) Medical optics and biotechnology : Photon migration

(170.6920) Medical optics and biotechnology : Time-resolved imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: May 2, 2011

Revised Manuscript: June 13, 2011

Manuscript Accepted: June 13, 2011

Published: June 15, 2011

**Citation**

Victor Shia, David Watt, and Gregory W. Faris, "High-speed camera with real time processing for frequency domain imaging," Biomed. Opt. Express **2**, 1931-1945 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-7-1931

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### References

- B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69(10), 3457–3481 (1998). [CrossRef]
- E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195(2), 330–351 (1991). [CrossRef] [PubMed]
- S. J. Madsen, E. R. Anderson, R. C. Haskell, and B. J. Tromberg, “Portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19(23), 1934–1936 (1994). [CrossRef] [PubMed]
- H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20(20), 2128–2130 (1995). [CrossRef] [PubMed]
- M. Gerken and G. W. Faris, “High-precision frequency-domain measurements of the optical properties of turbid media,” Opt. Lett. 24(14), 930–932 (1999). [CrossRef] [PubMed]
- V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrumentation for near-infrared spectro-imaging of the human brain,” Opt. Express 11(21), 2717–2729 (2003). [CrossRef] [PubMed]
- A. B. Thompson and E. M. Sevick-Muraca, “Near-infrared fluorescence contrast-enhanced imaging with intensified charge-coupled device homodyne detection: measurement precision and accuracy,” J. Biomed. Opt. 8(1), 111–120 (2003). [CrossRef] [PubMed]
- S. V. Patwardhan and J. P. Culver, “Quantitative diffuse optical tomography for small animals using an ultrafast gated image intensifier,” J. Biomed. Opt. 13(1), 011009 (2008). [CrossRef] [PubMed]
- T. French, J. Maier, and E. Gratton, “Frequency domain imaging of thick tissues using a CCD,” Proc. SPIE 1640, 254–261 (1992). [CrossRef]
- J. R. Lakowicz and K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62(7), 1727–1734 (1991). [CrossRef]
- R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. 71(3), 201–213 (2008). [CrossRef] [PubMed]
- K. Zhang and J. U. Kang, “Real-time intraoperative 4D full-range FD-OCT based on the dual graphics processing units architecture for microsurgery guidance,” Biomed. Opt. Express 2(4), 764–770 (2011). [CrossRef] [PubMed]
- A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009). [CrossRef] [PubMed]
- J. R. Janesick, “Scientific Charge-Coupled Devices,” (SPIE Press, Bellingham, Washington, 2001), pp. 101–105.
- D. F. Walls, “Squeezed states of light,” Nature 306(5939), 141–146 (1983). [CrossRef]
- X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. 46(10), 1624–1632 (2007). [CrossRef] [PubMed]
- T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643–649 (2002). [CrossRef] [PubMed]

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