Abstract

A closed form solution for time-averaged modulated fluence rate is presented for acoustically modulated diffusive light propagation in a medium. The solution assumes that the component of modulated light flux in the direction of acoustic pressure variation is zero.

© 2009 Optical Society of America

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References

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  1. L. Wang, Phys. Rev. Lett. 87, 043903 (2001).
    [CrossRef] [PubMed]
  2. R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
    [CrossRef]
  3. E. Granot, A. Lev, Z. Kotler, B. G. Sfez, and H. Taitelbaum, J. Opt. Soc. Am. A 18, 1962 (2001).
    [CrossRef]
  4. M. L. Shendeleva, J. Opt. Soc. Am. A 21, 2464 (2004).
    [CrossRef]
  5. K. E. Oughstun and N. A. Cartwright, Opt. Express 11, 1546 (2003).
  6. P. Duchateau and D. W. Zachmann, Schaum's Outline of Theory and Problems of Partial Differential Equations (McGraw-Hill, 1986).

2004 (1)

2003 (1)

K. E. Oughstun and N. A. Cartwright, Opt. Express 11, 1546 (2003).

2001 (2)

Cartwright, N. A.

K. E. Oughstun and N. A. Cartwright, Opt. Express 11, 1546 (2003).

DiMarzio, C. A.

R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
[CrossRef]

Duchateau, P.

P. Duchateau and D. W. Zachmann, Schaum's Outline of Theory and Problems of Partial Differential Equations (McGraw-Hill, 1986).

Granot, E.

Kotler, Z.

Lev, A.

Murray, T. W.

R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
[CrossRef]

Oughstun, K. E.

K. E. Oughstun and N. A. Cartwright, Opt. Express 11, 1546 (2003).

Roy, R. A.

R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
[CrossRef]

Sfez, B. G.

Shendeleva, M. L.

Sui, L.

R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
[CrossRef]

Taitelbaum, H.

Wang, L.

L. Wang, Phys. Rev. Lett. 87, 043903 (2001).
[CrossRef] [PubMed]

Zachmann, D. W.

P. Duchateau and D. W. Zachmann, Schaum's Outline of Theory and Problems of Partial Differential Equations (McGraw-Hill, 1986).

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

Opt. Express (1)

K. E. Oughstun and N. A. Cartwright, Opt. Express 11, 1546 (2003).

Phys. Rev. Lett. (1)

L. Wang, Phys. Rev. Lett. 87, 043903 (2001).
[CrossRef] [PubMed]

Other (2)

R. A. Roy, L. Sui, C. A. DiMarzio, and T. W. Murray, in Third IEEE International Symposium on Biomedical Imaging (IEEE, 2006), pp. 1200.
[CrossRef]

P. Duchateau and D. W. Zachmann, Schaum's Outline of Theory and Problems of Partial Differential Equations (McGraw-Hill, 1986).

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Figures (2)

Fig. 1
Fig. 1

First eigenmode of time-averaged fluence rate of modulated light in a rectangular sheet with dimension, x [ 0 , 0.1 ] and y [ 0 , 0.2 ] . Each panel corresponds to one of three source locations as shown by black dots: (a) point source located at (0.002, 0), (b) (0.05, 0), and (c) (0.08, 0). Ultrasound is applied at y = 0.05 for all cases.

Fig. 2
Fig. 2

Sum of first 10 eigenmodes of time-averaged fluence rate of modulated light for the same geometry and source positions as in Fig. 1.

Equations (14)

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n c ϕ t D 2 ϕ + ϕ [ μ a 2 D ( | n | 2 n 2 2 n n ) ] = P sc δ ( x x s ) δ ( y y s ) u ( t ) 2 D n ( ϕ n ) ,
n 0 c ϕ t D 2 ϕ + ϕ [ μ a 2 D ( | n | 2 n 0 2 2 n n 0 ) ] = P sc δ ( x x s ) δ ( y y s ) u ( t ) 2 D n 0 ( ϕ n ) .
2 D ( | n | 2 n 0 2 2 n n 0 ) μ a
2 ϕ m ϕ m μ 2 eff = 2 n 0 [ ϕ m n + Φ ss ( n ) + Φ ss 2 ( n ) ] 4 n 0 2 ϕ ss ( n ( n ) ) P sc δ ( x x s ) δ ( y y s ) δ ( t ) D ,
2 ϕ ¯ m ϕ ¯ m μ 2 eff = f ¯ ( x , y ) ,
ϕ ¯ m = 2 T s 0 T s 2 ϕ m d t ,
f ¯ ( x , y ) = 4 n 0 T s [ ϕ ss 0 T s 2 ( n ) d t + ϕ ss 0 T s 2 2 ( n ) d t ] 8 n 0 2 T s ϕ ss 0 T s 2 ( n n ) d t ,
n = n 0 + G 0 e ( y y 0 ) 2 W 2 cos ( k s x ω s t ) ,
ϕ ¯ m ( x , y ) = r = 1 ϕ ¯ m r ( y ) Φ r ( x ) .
Φ r ( x ) = A sin ( λ r x ) ,
ϕ ¯ m r ( y ) λ r 2 ϕ ¯ m r ( y ) μ eff 2 ϕ ¯ m r ( y ) = f ¯ r ( y ) ,
f ¯ r ( y ) = 1 A 0 a f ¯ ( x , y ) Φ r ( x ) d x for r = 1 , 2 , .
ϕ ¯ m r ( y ) = 1 2 π π Ω r e Ω r | y η | f ¯ r ( η ) d η ,
ϕ ¯ m ( x , y ) = r = 1 1 2 A r Ω r 0 a e Ω r | y η | Φ r ( ξ ) f ¯ ( ξ , η ) d ξ d η .

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