Abstract

Using a Green’s function solution to the photoacoustic wave equation, we compare intensity-modulated continuous-wave (CW) lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications. Assuming the same transducer is used in both cases, we show that the axial resolution is identical and is determined by the transducer and material properties of the object. We derive a simple formula relating the signal-to-noise ratios (SNRs) of the two imaging systems that only depends on the fluence of each pulse and the time-bandwidth product of the chirp pulse. We also compare the SNR of the two systems assuming the fluence is limited by the American National Standards Institute (ANSI) laser safety guidelines for skin. We find that the SNR is about 20 dB to 30 dB larger for pulsed laser systems for reasonable values of the parameters. However, CW diode lasers have the advantage of being compact and relatively inexpensive, which may outweigh the lower SNR in many applications.

© 2010 OSA

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References

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  1. C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
    [CrossRef] [PubMed]
  2. Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
    [CrossRef] [PubMed]
  3. Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
    [CrossRef] [PubMed]
  4. S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” J. Biomed. Opt. 11(4), 044006 (2006).
    [CrossRef] [PubMed]
  5. S. A. Telenkov and A. Mandelis, “Fourier-domain methodology for depth-selective photothermoacoustic imaging of tissue chromophores,” Eur. Phys. J. Spec. Top. 153(1), 443–448 (2008).
    [CrossRef]
  6. S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
    [CrossRef]
  7. S. A. Telenkov and A. Mandelis, “Photothermoacoustic imaging of biological tissues: maximum depth characterization comparison of time and frequency-domain measurements,” J. Biomed. Opt. 14(4), 044025 (2009).
    [CrossRef] [PubMed]
  8. H. H. Barrett, and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, NJ, 2004).
  9. C. E. Cook, and M. Bernfeld, Radar Signals: An Introduction to Theory and Application (Academic, New York, NY, 1967).
  10. R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
    [CrossRef] [PubMed]
  11. L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008).
    [CrossRef]
  12. Laser Institute of America, American National Standard for Safe Use of Lasers ANSI Z136.1–2007 (American National Standards Institute, Orlando, FL, 2007).

2009 (3)

C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
[CrossRef] [PubMed]

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

S. A. Telenkov and A. Mandelis, “Photothermoacoustic imaging of biological tissues: maximum depth characterization comparison of time and frequency-domain measurements,” J. Biomed. Opt. 14(4), 044025 (2009).
[CrossRef] [PubMed]

2008 (2)

S. A. Telenkov and A. Mandelis, “Fourier-domain methodology for depth-selective photothermoacoustic imaging of tissue chromophores,” Eur. Phys. J. Spec. Top. 153(1), 443–448 (2008).
[CrossRef]

L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008).
[CrossRef]

2006 (1)

S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” J. Biomed. Opt. 11(4), 044006 (2006).
[CrossRef] [PubMed]

2005 (1)

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

2004 (1)

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

1995 (1)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Appledorn, C. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Fan, Y.

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

Fang, Y. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Forcht, M.

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

Kruger, R. A.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Lashkari, B.

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

Li, C.

C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
[CrossRef] [PubMed]

Liu, P.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Mandelis, A.

S. A. Telenkov and A. Mandelis, “Photothermoacoustic imaging of biological tissues: maximum depth characterization comparison of time and frequency-domain measurements,” J. Biomed. Opt. 14(4), 044025 (2009).
[CrossRef] [PubMed]

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

S. A. Telenkov and A. Mandelis, “Fourier-domain methodology for depth-selective photothermoacoustic imaging of tissue chromophores,” Eur. Phys. J. Spec. Top. 153(1), 443–448 (2008).
[CrossRef]

S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” J. Biomed. Opt. 11(4), 044006 (2006).
[CrossRef] [PubMed]

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

Spirou, G.

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

Telenkov, S.

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

Telenkov, S. A.

S. A. Telenkov and A. Mandelis, “Photothermoacoustic imaging of biological tissues: maximum depth characterization comparison of time and frequency-domain measurements,” J. Biomed. Opt. 14(4), 044025 (2009).
[CrossRef] [PubMed]

S. A. Telenkov and A. Mandelis, “Fourier-domain methodology for depth-selective photothermoacoustic imaging of tissue chromophores,” Eur. Phys. J. Spec. Top. 153(1), 443–448 (2008).
[CrossRef]

S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” J. Biomed. Opt. 11(4), 044006 (2006).
[CrossRef] [PubMed]

Vitkin, I. A.

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

Wang, L. V.

C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
[CrossRef] [PubMed]

L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008).
[CrossRef]

Whelan, W. M.

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Eur. Phys. J. Spec. Top. (1)

S. A. Telenkov and A. Mandelis, “Fourier-domain methodology for depth-selective photothermoacoustic imaging of tissue chromophores,” Eur. Phys. J. Spec. Top. 153(1), 443–448 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008).
[CrossRef]

J. Acoust. Soc. Am. (1)

Y. Fan, A. Mandelis, G. Spirou, and I. A. Vitkin, “Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment,” J. Acoust. Soc. Am. 116(6), 3523–3533 (2004).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

S. Telenkov, A. Mandelis, B. Lashkari, and M. Forcht, “Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues,” J. Appl. Phys. 105(10), 102029 (2009).
[CrossRef]

J. Biomed. Opt. (2)

S. A. Telenkov and A. Mandelis, “Photothermoacoustic imaging of biological tissues: maximum depth characterization comparison of time and frequency-domain measurements,” J. Biomed. Opt. 14(4), 044025 (2009).
[CrossRef] [PubMed]

S. A. Telenkov and A. Mandelis, “Fourier-domain biophotoacoustic subsurface depth selective amplitude and phase imaging of turbid phantoms and biological tissue,” J. Biomed. Opt. 11(4), 044006 (2006).
[CrossRef] [PubMed]

Med. Phys. (1)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Y. Fan, A. Mandelis, G. Spirou, I. A. Vitkin, and W. M. Whelan, “Laser photothermoacoustic heterodyned lock-in depth profilometry in turbid tissue phantoms,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051908 (2005).
[CrossRef] [PubMed]

Other (3)

H. H. Barrett, and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, NJ, 2004).

C. E. Cook, and M. Bernfeld, Radar Signals: An Introduction to Theory and Application (Academic, New York, NY, 1967).

Laser Institute of America, American National Standard for Safe Use of Lasers ANSI Z136.1–2007 (American National Standards Institute, Orlando, FL, 2007).

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Figures (4)

Fig. 1.
Fig. 1.

(a) The spectrum and (b) time signal, compressed by applying a matched filter, for a chirp signal with f 0 = 3 MHz and bT = 4 MHz.

Fig. 2.
Fig. 2.

Illustration of coordinate system and geometry of absorber.

Fig. 3.
Fig. 3.

Pressure at a distance of 3 cm for a 10 ns pulse excitation. The temporal profiles of each of the pressure pulses are almost exact replicas of the laser pulse for the parameters chosen.

Fig. 4.
Fig. 4.

The optimum repetition rates for a short pulse and a 1 ms chirp pulse.

Equations (33)

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I chirp ( t ) = I 0 [ 1 + cos ( ω 0 t + π b t 2 ) ] rect ( t T ) ,
I ~ pos ( ω ) = I 0 2 2 π e i π b ( f f 0 ) 2 1 2 b T b 2 2 b ( f f 0 ) T b 2 2 b ( f f 0 ) e i π 2 ( t ) 2 d t ,
C ( x ) = 0 x cos ( π 2 t 2 ) d t
S ( x ) = 0 x sin ( π 2 t 2 ) d t
I ~ pos ( ω ) = I 0 2 2 π e i π b ( f f 0 ) 2 1 2 b [ C ( T b 2 2 b ( f f 0 ) ) + i S ( T b 2 2 b ( f f 0 ) )
C ( T b 2 2 b ( f f 0 ) ) iS ( T b 2 2 b ( f f 0 ) ) ] ,
I ~ pos ( ω ) I 0 2 2 π e i ( ω ω 0 ) 2 4 π b 1 2 b ( 1 + i ) rect ( ω ω 0 2 π b T ) .
I ~ neg ( ω ) I 0 2 2 π e i ( ω + ω 0 ) 2 4 π b 1 2 b ( 1 i ) rect ( ω + ω 0 2 π b T ) .
G ~ chirp ( ω ) = e i ( ω ω 0 ) 2 4 π b 1 i 2 rect ( ω ω 0 2 π b T ) + e i ( ω + ω 0 ) 2 4 π b 1 + i 2 rect ( ω + ω 0 2 π b T ) ,
I ~ fc ( ω ) = I 0 2 2 π 1 b [ rect ( ω ω 0 2 π b T ) + rect ( ω + ω 0 2 π b T ) ] .
I fc ( t ) = I 0 bT 2 sinc ( π b T t ) cos ( ω 0 t ) ,
T ( r , t ) t D T 2 T ( r , t ) = H ( r , t ) ρ C V ,
T ( r , t ) t = H ( r , t ) ρ C V .
( 2 1 ν s 2 2 t 2 ) p ( r , t ) = β κ ν s 2 2 T ( r , t ) t 2 ,
( 2 1 v s 2 2 t 2 ) p ( r , t ) = β C P H ( r , t ) t .
( 2 + k 2 ) p ~ ( r , ω ) = i ω β C P H ~ ( r , ω ) ,
p ~ ( r , ω ) = i ω β 4 π C P V e ik r r 0 r r 0 H ~ ( r 0 , ω ) d 3 r 0 .
p ~ ( r r 0 , ω ) = i ω β 4 π C P e ikr r V e ik r ̂ · r 0 H ~ ( r 0 , ω ) d 3 r 0 .
H ( x 0 , y 0 , z 0 , t ) = { χ μ e μ ( a 2 z 0 ) I ( t ) a 2 x 0 , y 0 , z 0 a 2 0 otherwise ,
p ~ ( ω ) = β χ μ v s a 2 4 π z C P I ~ ( ω ) ω ω i μ v s ( e i ω ( 2 z a 2 v s ) e μ a e i ω ( 2 z + a 2 v s ) ) ,
I pulse ( t ) = F 0 τ rect ( t τ ) ,
I ˜ pulse ( ω ) = F 0 2 π sinc ( ω τ 2 ) .
p pulse ( t ) = β χ μ v s a 2 F 0 4 π z τ C P [ e μ v s t 1 u ( t 1 ) e μ v s t 2 u ( t 2 ) e μ a e μ v s t 3 u ( t 3 ) + e μ a e μ v s t 4 u ( t 4 ) ] ,
S ˜ ( ω ) = A ˜ ( ω ) I ˜ ( ω ) T ˜ ( ω ) G ˜ ( ω ) ,
A ˜ ( ω ) = β χ μ v s a 2 4 π z C P ω ω i μ v s ( e i ω ( 2 z a 2 v s ) e μ a e i ω ( 2 z + a 2 v s ) ) .
S ˜ pulse ( ω ) = F 0 2 π A ˜ ( ω ) T ˜ ( ω ) [ rect ( ω ω 0 2 π Δ f ) + rect ( ω + ω 0 2 π Δ f ) ] ,
G ˜ pulse ( ω ) = rect ( ω ω 0 2 π Δ f ) + rect ( ω + ω 0 2 π Δ f )
S ˜ chirp ( ω ) = I 0 2 2 π 1 b A ˜ ( ω ) T ˜ ( ω ) [ rect ( ω ω 0 2 π Δ f ) + rect ( ω + ω 0 2 π Δ f ) ] .
N ˜ pulse ( ω ) = N ˜ chirp ( ω ) = N ˜ ( ω ) [ rect ( ω ω 0 2 π Δ f ) + rect ( ω + ω 0 2 π Δ f ) ] .
SNR chirp SNR pulse = I 0 T 2 F 0 b T 2 .
min { 20 C A { 1100 C A t 1 4 N τ t 10 s 200 C A t N τ t 10 s ,
min { 1100 C A T 1 4 { 1100 C A t 1 4 N T t 10 s 200 C A t N T t 10 s
SNR chirp SNR pulse = 55 2 T 3 8 Δ f .

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