Abstract

In this paper the use of pulse shaping in photoacoustic (PA) measurements is presented. The benefits of this approach are demonstrated by utilizing it for optimization of either the responsivity or the sensitivity of PA measurements. The optimization is based on the observation that the temporal properties of the PA effect can be represented as a linear system which can be fully characterized by its impulse response. Accordingly, the response of the PA system to an input optical pulse, whose instantaneous power is arbitrarily shaped, can be analytically predicted via a convolution between the pulse envelope and the PA impulse response. Additionally, the same formalism can be used to show that the response of the PA system to a pulse whose instantaneous power is a reversed version of the impulse response, i.e. a matched pulse, would exhibit optimal peak amplitude when compared with all other pulses with the same energy. Pulses can also be designed to optimize the sensitivity of the measurement to a variation in a specific system parameter. The use of the matched pulses can improve SNR and enable a reduction in the total optical energy required for obtaining a detectable signal. This may be important for applications where the optical power is restricted or for dynamical measurements where long integration times are prohibited. To implement this new approach, a novel PA optical setup which enabled synthesis of excitation waveforms with arbitrary temporal envelopes was constructed. The setup was based on a tunable laser source, operating in the near-IR range, and an external electro-optic modulator. Using this setup, our approach for system characterization and response prediction was tested and the superiority of the matched pulses over other common types of pulses of equal energy was demonstrated.

© 2009 Optical Society of America

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  1. J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
    [CrossRef] [PubMed]
  2. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
    [CrossRef] [PubMed]
  3. A. C. Tam, "Applications of PA sensing techniques," Rev. Mod. Phys. 58, 381-431 (1986).
    [CrossRef]
  4. H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982)
    [CrossRef]
  5. G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
    [CrossRef] [PubMed]
  6. R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
    [CrossRef] [PubMed]
  7. E. Bergman, A. Sheinfeld, S. Gilead, and A. Eyal, "The use of optical waveform synthesis in photoacoustic measurements" in Proc. IEEE 25th convention in Israel, 585-588 (2008).
  8. K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
    [CrossRef] [PubMed]
  9. A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
    [CrossRef] [PubMed]
  10. Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
    [CrossRef]
  11. J. G. Proakis, Digital Communications, 4th Edition (McGraw-Hill, 2001), Chap. 5.

2005

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

2004

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

2003

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

1995

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

1993

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

1991

G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
[CrossRef] [PubMed]

1986

A. C. Tam, "Applications of PA sensing techniques," Rev. Mod. Phys. 58, 381-431 (1986).
[CrossRef]

1984

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

1982

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982)
[CrossRef]

Appledorn, C. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

Beard, P.

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

Brandau, D. T.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Chen, Q.

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

Christison, G. B.

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

Delpy, D.

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

Diebold, G. J.

G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
[CrossRef] [PubMed]

Elwell, C.

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

Fang, Y. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

Harmatz, D.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Hodgson, P.

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

Horsch, J. G.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Khan, M. I.

G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
[CrossRef] [PubMed]

Kruger, R. A.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

Ku, G.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Lai, H. M.

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982)
[CrossRef]

Laufer, J.G.

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

Lawson, E. Q.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Liu, P.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

MacKenzie, H. A.

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

Middaugh, C. R.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Pang, Y.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Quan, K. M.

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

Sadler, A. J.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

Stoica, G.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Sun, T.

G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
[CrossRef] [PubMed]

Tam, A. C.

A. C. Tam, "Applications of PA sensing techniques," Rev. Mod. Phys. 58, 381-431 (1986).
[CrossRef]

Wang, L.V.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Wang, X.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

Xie, X.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Xing, D.

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

Young, K

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982)
[CrossRef]

Zeng, Y. G.

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

Anal. Biochem.

A. J. Sadler, J. G. Horsch, E. Q. Lawson, D. Harmatz, D. T. Brandau, and C. R. Middaugh, "Near-infrared photoacoustic spectroscopy of proteins," Anal. Biochem. 138, 44-51 (1984).
[CrossRef] [PubMed]

J. Acoust. Soc. Am.

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982)
[CrossRef]

Med. Phys.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995).
[CrossRef] [PubMed]

Nat. Biotechnol.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L.V. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003).
[CrossRef] [PubMed]

Phys. Med.

Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004).
[CrossRef]

Phys. Med. Biol.

J.G. Laufer, C. Elwell, D. Delpy, and P. Beard, "In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution," Phys. Med. Biol. 50, 4409-4428 (2005).
[CrossRef] [PubMed]

K. M. Quan, G. B. Christison, H. A. MacKenzie, and P. Hodgson, "Glucose determination by a pulsed photoacoustic technique: an experimental study using a gelatin-based tissue phantom," Phys. Med. Biol. 38, 1911-1922 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. J. Diebold, T. Sun, and M. I. Khan, "Photoacoustic monopole radiation in one, two and three dimensions," Phys. Rev. Lett. 67, 3384-3387 (1991).
[CrossRef] [PubMed]

Rev. Mod. Phys.

A. C. Tam, "Applications of PA sensing techniques," Rev. Mod. Phys. 58, 381-431 (1986).
[CrossRef]

Other

E. Bergman, A. Sheinfeld, S. Gilead, and A. Eyal, "The use of optical waveform synthesis in photoacoustic measurements" in Proc. IEEE 25th convention in Israel, 585-588 (2008).

J. G. Proakis, Digital Communications, 4th Edition (McGraw-Hill, 2001), Chap. 5.

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Figures (11)

Fig. 1.
Fig. 1.

A PA experimental setup enabling the use of pulses with arbitrary envelopes

Fig. 2.
Fig. 2.

A step input (pink) and the corresponding PA step response (blue).

Fig. 3.
Fig. 3.

A truncated time-reversed impulse response. This waveform was fed to the AWG to produce an enhanced PA response.

Fig. 4.
Fig. 4.

The measured (blue) and predicted (pink) PA response to a matched pulse.

Fig. 5.
Fig. 5.

The measured (black) and predicted (red) PA response to a Gaussian input (blue) with FWHM width of 1.4μsec .

Fig. 6.
Fig. 6.

The peak response of Gaussian (analytical calculation – blue line, experimental data – red circles) and square (numerical calculation – black line, experimental data – green squares) pulses as a function of their widths (the width of the Gaussian pulse is defined to be its FWHM):

Fig. 7.
Fig. 7.

The measured PA response of the matched pulse (blue), the optimal Gaussian pulse with FWHM=1.13μsec (black) and the optimal square pulse with time duration = 1.29μsec (dotted pink).

Fig. 8.
Fig. 8.

Normalized PA responses versus water concentration in Ethanol-Water mixture: matched pulse at t=T (red), optimal Gaussian pulse at t=T max_G (blue), optimal square pulse at t=T max_S (black).

Fig. 9.
Fig. 9.

Standard deviation of the local extrema of the PA response vs. their mean amplitudes. Both values were calculated over 50 samples and normalized by the maximum peak value. The corresponding correlation coefficient was found to be -0.05.

Fig. 10.
Fig. 10.

Three examples of the PA step response taken with intermissions of 5 minutes between them. The insets demonstrate the increased mismatch between the responses at times approaching the trailing edge of the response.

Fig. 11.
Fig. 11.

Calculation of the peak PA response to truncated pulses as a function of truncation time. The blue plot represents a stable system where there is a perfect match between the truncated pulse and the impulse response. All other plots (pink, green, red and cyan) are examples of responses of the system to a non-perfectly matched pulse.

Equations (7)

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

1 c 2 2 p ( r , t ) t 2 2 p ( r , t ) = αβ C p I ( r , t ) t
p ( r , t ) = H ( r , t ) * f ( t ) = H ( r , t τ ) f ( τ ) d τ
1 c 2 2 H ( r , t ) t 2 2 H ( r , t ) = αβ C p g ( r ) d d t [ δ ( t ) ]
p ( r , t , ρ ) ρ = H ( r , t , ρ ) ρ * f ( t )
f trun ( t , T ̃ ) = { a H ( r meas , T ̃ t ) 0 t T ̃ < T 0 elsewhere
p trun ( r meas , T ̃ ) = a 0 T ̃ H ( r meas , τ ) 2 d τ
p trun ( r meas , T ̃ ) p ( r meas , T ) = 0 T ̃ H ( r meas , τ ) 2 d τ 0 T H ( r meas , τ ) 2 d τ

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