Abstract

Quantitative imaging of optical properties of biological tissues with high resolution has been a long-sought-after goal of many research groups. Photoacoustic imaging is a hybrid bio-optical imaging technique offering optical absorption contrast with ultrasonic spatial resolution. While photoacoustic methods offer significant promise for high-resolution optical imaging, quantification has thus far proved challenging. In this paper, a noniterative reconstruction technique for producing quantitative photoacoustic images of absorption perturbations is introduced for the case when the optical properties of the turbid background are known and when multiple optical illumination locations are used. Through theoretical developments and computational examples it is demonstrated that multiple-optical-source photoacoustic imaging can produce quantitative optical absorption reconstructions. The combination of optical and photoacoustic measurements is shown to yield improved reconstruction stability.

© 2010 Optical Society of America

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  1. A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).
  2. G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88, 1624–1631(2000).
    [CrossRef]
  3. M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. Z. Yuan and H. B. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88 (2006).
    [CrossRef]
  7. J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
    [CrossRef]
  8. T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
    [CrossRef]
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    [CrossRef]
  14. A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
    [CrossRef] [PubMed]
  15. G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” arXiv 0910.2503 (2009)
  16. R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
    [CrossRef]
  17. J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
    [CrossRef] [PubMed]
  18. M. H. Xu and L. H. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
    [CrossRef]
  19. L. V. Wang, Biomedical Optics: Principles and Imaging(Wiley, 2007).

2009 (6)

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography,” Philos. Trans. R. Soc. London Ser. A 367, 3043–3054 (2009).
[CrossRef]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[CrossRef] [PubMed]

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (3)

B. T. Cox, S. R. Arridge, K. P. Kostli, and P. C. Beard, “Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method,” Appl. Opt. 45, 1866–1875 (2006).
[CrossRef] [PubMed]

M. H. Xu and L. H. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

Z. Yuan and H. B. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88 (2006).
[CrossRef]

2005 (2)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[CrossRef]

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

2000 (1)

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88, 1624–1631(2000).
[CrossRef]

1997 (1)

1996 (1)

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Arridge, S. R.

Bagchi, S.

Bal, G.

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” arXiv 0910.2503 (2009)

Banerjee, B.

Beard, P. C.

Chen, X.

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

Chen, X. H.

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

Cox, B. T.

Englmeier, K. H.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

Frenz, M.

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

Hejazi, M.

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

Jacques, S. L.

Jaeger, M.

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

Jetzfellner, T.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

Jiang, H.

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography,” Philos. Trans. R. Soc. London Ser. A 367, 3043–3054 (2009).
[CrossRef]

Jiang, H. B.

Jiang, Y.

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

Karabutov, A. A.

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Kostli, K. P.

Letokhov, V. S.

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Mathewson, K.

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

Niederhauser, J. J.

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

Ntziachristos, V.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[CrossRef] [PubMed]

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[CrossRef]

Oraevsky, A. A.

Paltauf, G.

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88, 1624–1631(2000).
[CrossRef]

Podymova, N. B.

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Ranasinghesagara, J.

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

Ranasinghesagara, J. C.

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

Razansky, D.

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[CrossRef] [PubMed]

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

Ripoll, J.

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[CrossRef]

Rosenthal, A.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[CrossRef] [PubMed]

Roy, D.

Schmidt-Kloiber, H.

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88, 1624–1631(2000).
[CrossRef]

Schulz, R.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

Tittel, F. K.

Uhlmann, G.

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” arXiv 0910.2503 (2009)

Vasu, R. M.

Wang, L. H. V.

M. H. Xu and L. H. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

Wang, L. V.

L. V. Wang, Biomedical Optics: Principles and Imaging(Wiley, 2007).

Wang, Q.

Xu, M. H.

M. H. Xu and L. H. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

Yin, L.

Yuan, Z.

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography,” Philos. Trans. R. Soc. London Ser. A 367, 3043–3054 (2009).
[CrossRef]

Z. Yuan, Q. Wang, and H. B. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media by photoacoustic tomography coupled with diffusion equation based regularized Newton method,” Opt. Express 15, 18076–18081 (2007).
[CrossRef] [PubMed]

Z. Yuan and H. B. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88 (2006).
[CrossRef]

Zemp, R. J.

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

Zhang, Q. Z.

Appl. Opt. (2)

Appl. Phys. B (1)

A. A. Karabutov, N. B. Podymova, and V. S. Letokhov, “Time-resolved laser optoacoustic tomography of inhomogeneous media,” Appl. Phys. B 63, 545–563 (1996).

Appl. Phys. Lett. (2)

Z. Yuan and H. B. Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous media,” Appl. Phys. Lett. 88 (2006).
[CrossRef]

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K. H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett. 95, 013703 (2009).
[CrossRef]

IEEE Trans. Med. Imaging (1)

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88, 1624–1631(2000).
[CrossRef]

J. Biomed. Opt. (2)

M. Jaeger, J. J. Niederhauser, M. Hejazi, and M. Frenz, “Diffraction-free acoustic detection for optoacoustic depth profiling of tissue using an optically transparent polyvinylidene flouride pressure transducer operated in backward and forward mode,” J. Biomed. Opt. 10 (2005).
[CrossRef] [PubMed]

J. C. Ranasinghesagara, Y. Jiang, X.H. Chen, K. Mathewson, and R. J. Zemp, “Photoacoustic technique for assessing optical scattering properties of turbid media,” J. Biomed. Opt. 14, 040504 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (1)

Philos. Trans. R. Soc. London Ser. A (1)

Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography,” Philos. Trans. R. Soc. London Ser. A 367, 3043–3054 (2009).
[CrossRef]

Phys. Rev. E (1)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[CrossRef]

Proc. SPIE (1)

R. J. Zemp, J. Ranasinghesagara, Y. Jiang, X. Chen, and K. Mathewson, “A photoacoustic method for optical scattering measurements in turbid media,” Proc. SPIE 7177, 71770Q (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

M. H. Xu and L. H. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[CrossRef]

Other (2)

L. V. Wang, Biomedical Optics: Principles and Imaging(Wiley, 2007).

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” arXiv 0910.2503 (2009)

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Figures (3)

Fig. 1
Fig. 1

Simulated data illustrating the potential of multiple-illumination PAT for reconstructing absorption perturbations in the idealized case when there is no noise. (a) True 2D μ a distribution. Scale bar is in units of cm 1 . The reduced scattering coefficient of the background is taken as μ s = 10 cm 1 . (b) Simulated normalized Gru¨neisen parameter map. (c) Fluence due to source s 1 . (d) Fluence due to source s 2 . (e) Photoacoustic image normalized by the fluence distribution Φ 0 due to source s 1 , where Φ 0 is calculated under the assumption of a homogeneous medium. This is meant to estimate the absorption map. This zeroth-order estimate exhibits unacceptable errors. Some of these errors are due to fluence perturbations and some are due to bias of data due to spatially varying Gru¨neisen parameters. Units are cm 1 . (f) Absorption coefficient reconstructed using multiple-illumination PAT using four sources around the object. Units are cm 1 .

Fig. 2
Fig. 2

Figure illustrating reconstruction in the presence of noise. The true absorption distribution is shown in Fig. 1a. (a) Photoacoustic image normalized by the fluence distribution Φ 0 due to source s 1 , where Φ 0 is calculated under the assumption of a homogeneous medium. This is meant to estimate the absorption map. This zeroth-order estimate exhibits unacceptable errors and noise dominates where the fluence is weak. Units are cm 1 . (b) Reconstructed image of the optical absorption map using our first-order multiple-source photoacoustic inversion technique, Eq. (16), using four sources positioned around the object, as in Fig. 1. The reconstruction fails in the presence of such substantial noise. (c) Diffuse optical tomography reconstruction of the absorption parameter using only four sources but 80 detectors positioned circumferentially around the object. While this underdetermined problem produces erroneous reconstructions, combining these measurements with photoacoustic measurements using Eq. (19) produces a stable reconstruction, shown in (d). Units are cm 1 .

Fig. 3
Fig. 3

Singular values of the matrix Q used in the example of Figs. 1, 2, but with only two sources on the top separated by 8 mm (dotted curve) and four sources (solid curve): one on the top center, one in the center of each side, and one at the bottom. The added illumination locations and their choice of placement dramatically improve the matrix condition number. The dashed curve shows the singular value of the matrix in Eq. (19). This shows the additional stability imparted due to using optical and photoacoustic measurements.

Equations (21)

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

h ( r ) = μ a ( r ) Φ ( r ) ,
Φ ( r , t ) t + c μ a Φ ( r , t ) c · [ D Φ ( r , t ) ] = q ( r , t ) ,
μ eff 2 Φ 0 ( r ) 2 Φ 0 ( r ) = A c D δ ( r ) ,
[ k 2 + μ eff 2 ] Φ 0 ( k ) = A c D ,
Φ 0 ( r ) = A exp ( μ eff r ) 4 π c D r ,
Φ 0 ( r ) = A 2 π c D K 0 ( μ eff r ) ,
G 0 ( r , r ) = exp ( μ eff | r r | ) 4 π | r r | ,
G 0 ( r , r ) = 1 2 π K 0 ( μ eff | r r | ) ,
Φ ( r j , r s ) = Φ 0 ( r j , r s ) + Φ SC ( r j , r s ) ,
Φ SC ( r j , r s ) = δ μ a ( r ) D 0 G 0 ( r j , r ) Φ ( r , r s ) d r ,
Φ SC ( r j , r s ) = n W { i j } n a δ μ a ( r n ) ,
W { i j } n a = G 0 ( r j , r n ) Φ 0 ( r n , r s i ) Δ V / D 0 ,
Φ SC = W a δ μ a ,
h ^ i ( r j ) h ^ ( r j ) = Φ 0 ( r j , r s i ) + Φ SC ( r j , r s i ) Φ 0 ( r j , r s ) + Φ SC ( r j , r s ) .
n [ h ^ i ( r j ) W { j } n a h ^ ( r j ) W { i j } n a ] δ μ a ( r n ) = h ^ ( r j ) Φ 0 ( r j , r s i ) h ^ i ( r j ) Φ 0 ( r j , r s ) .
Q δ μ a = b ,
δ μ a = V Σ - 1 U T b = i u i T b σ i v i .
Φ SC = W DOT δ μ a ,
W { i j } n DOT = G 0 ( r d j , r n ) Φ 0 ( r n , r s i ) Δ V / D 0 ,
[ Q W DOT ] [ δ μ a ] = [ b Φ SC ] .
J = [ Φ μ a , Φ D ]

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