## The use of pulse synthesis for optimization of photoacoustic measurements

Optics Express, Vol. 17, Issue 9, pp. 7328-7338 (2009)

http://dx.doi.org/10.1364/OE.17.007328

Acrobat PDF (283 KB)

### 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

## 1. Introduction

1. J.G. Laufer, C. Elwell, 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]

## 2. Theory

*p*(

**,**

*r**t*) , in a liquid medium, can be described by the following wave equation [4

4. H. M. Lai and K Young, “Theory of the pulsed optoacoustic technique,” J. Acoust. Soc. Am. **72**, 2000–2007 (1982) [CrossRef]

*c*is the sound velocity,

*β*is the volumetric thermal expansion coefficient,

*C*is the specific heat,

_{p}*α*is the absorption coefficient and

*I*(

*,*

**r***t*) is the intensity of the impinging light.

*I*(

*,*

**r***t*) =

*g*(

*) ·*

**r***f*(

*t*), where

*g*(

*) describes the spatial distribution of the intensity and*

**r***f*(

*t*) describes the temporal modulation. Using the separated form of the intensity and the linearity of the PA equation, it is possible to express the solution to Eq. (1) as:

*H*(

*,*

**r***t*) , the PA impulse response, satisfies:

*H*(

*,*

**r***t*) , is completely determined by the medium parameters, the spatial distribution of the optical intensity and the boundary conditions. Furthermore, once

*H*(

*,*

**r***t*) is measured at a given point in space,

**r**_{meas}, it is possible to analytically predict the response of the PA measurement system, at this position, to any other optical excitation pulse via the convolution in Eq. (2). In case of a homogeneous medium it is possible to use a Green function to solve the wave equation, in which case the impulse response can be calculated analytically, as was shown by Kruger

*et al*[6

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]

*et al*[10

10. Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. **49**, 3117–3124 (2004). [CrossRef]

*f*(

*t*) =

*a∂H*(

**r**_{meas},

*T*-

*t*,

*ρ*)/

*∂ρ*maximizes

*∂ρ*(

**r**_{meas},

*t*,

*ρ*)/

*∂ρ*and ensures optimal sensitivity to variations in

*ρ*. The use of this approach for optimizing the sensitivity of a PA setup for variations of the concentration of water inside an Ethanol-water mixture, is experimentally demonstrated in sec. 3-4.

*H*(

**r**_{meas},

*t*) that will affect the magnitude of the response. As shown in sec. 5, in our experimental setup the effect of environmental instabilities on

*H*(

**r**_{meas},

*t*) was

*f*

_{trun}(

*t*,

*T*̃) in Eq. (2) and then setting

*t*=

*T*̃:

*T*̃ and the maximum response is obtained when

*T*̃

*=*

_{optimal}*T*. It is shown in sec. 5, however, that measurement instabilities may moderate this improvement and in some cases they can even lead to a decrease in the response for pulses longer than some

*T*̃

*<*

_{optimal}*T*.

## 3. The experimental setup and the measurement method

## 4. Experimental results – PA impulse response and pulse pre-shaping

*f*

_{trun}(

*t*,

*T*̃), truncated to

*T*̃ = 40μ sec, was produced from the derivative of the step response in accord with Eq. (4) (Fig. (3)).

*t*> 25

*μ*sec is due to the truncation of the impulse response.

*μ*sec and optimal Gaussian pulse FWHM is 1.13

*μ*sec. Figure (7) shows the measured PA responses to the matched pulse and to the optimal Gaussian and square pulses. The advantage of using a matched pulse, which yielded a factor of two improvement in the peak amplitude compared with the other pulses, is clearly seen. Note the similarity between the responses to the optimal square and Gaussian pulses. This is attributed to the limited bandwidth of the system which caused a filtering of the high frequency components of the response to the square pulse.

*(*

_{c}H**r**,

*T*-

*t*,

*C*) ≈

*H*(

**r**,

*T*-

*t*,10%) -

*H*(

**r**,

*T*-

*t*,20%) =

*f*

_{10–20}(

*t*) (

*C*denotes concentration). In addition, we used the measured impulse responses to predict the responses to Gaussian and square pulses and to numerically find the parameters of the Gaussian and square pulses that maximize the sensitivity to local variations in water concentration. This was done in the same method described for the first experiment, however here the convolution was done with the impulse derivative approximation

*f*

_{10–20}(

*t*) rather than the impulse response. The FWHM of the optimal Gaussian pulse was found to be 1.036

*μ*s and the optimal square pulse was 1.3

*μ*s long. The three pulses – the approximated impulse response derivative, the optimal Gaussian pulse and square pulse were fed to the AWG. As was described in sec. 2, when the optimal pulse is used it ensures maximum sensitivity of the response to variation in the perturbed parameter at a specific point in time which was denoted by

*T*. Figure (8) shows the normalized PA responses at

*t*=

*T*, for the approximated optimal pulse,

*f*

_{10–20}(

*t*), versus water concentration in the range where the derivative was obtained. Also shown are the normalized responses of the optimal Gaussian and square pulses at their optimal times

*T*

_{max_G}and

*T*

_{max_S}respectively. The superiority of the matched pulse is clearly seen. Note that the ability to produce the optimal Gaussian and square pulses is also a feature of our setup and that non-optimized Gaussian and square pulses will perform even worse.

## 5. Experimental results - noise and stability

*g*(

*) , and subject to the specific boundary conditions of the PA system. In realistic experimental situations, however, the PA system may be affected by environmental instabilities such as temperature variations, mechanical vibrations etc. which can lead to variations in its impulse response. These variations in the impulse response can cause a deviation of the predicted PA response from the measured response or suboptimal response to the “matched” pulse. The effect of environmental instabilities is demonstrated in Fig. (10). It shows 3 consecutive PA step responses that were recorded with intermissions of approximately 5 minutes. It can be seen that the effect of instabilities is more pronounced towards the trailing edge of the response than near the leading edge. In light of this observation, the use of truncated matched pulses was studied. According to Eq. (7), in ideal conditions the peak PA response is a monotonically increasing function of the truncation time*

**r***T*̃ , but due to instabilities, in realistic conditions this may no longer be true. This can be observed in Fig. (11), where calculated normalized peak responses are plotted as a function of the truncation time. These numerical estimations of matched-pulse responses were calculated from measured impulse responses with the use of Eq. (2). The blue plot represents a perfectly stable system. It was calculated by convolving an impulse response with its truncated and reversed versions. In all other plots the convolution is between the truncated matched pulse and an impulse response which was recorded between 5 to 30 minutes after the first impulse response which was used for the matched pulse synthesis. It can be seen that due to the instability of the impulse response the peak response is not optimal. Moreover, in some cases there exists a truncation time,

*T*̃

*<*

_{optimal}*T*, for which the peak response reaches a maximum and an additional increase in the truncation time leads to a decrease in the response rather than an increase. The analysis leading to Fig. (11) can be used in order to determine the optimal truncation time in a given PA setup.

## 6. Conclusions

## Acknowledgment

## References and links

1. | J.G. Laufer, C. Elwell, Delpy, and P. Beard, “In vitro measurements of absolute blood oxygen saturation using pulsed near-infrared photoacoustic spectroscopy: Accuracy and resolution,” Phys. Med. Biol. |

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. |

3. | A. C. Tam, “Applications of PA sensing techniques,” Rev. Mod. Phys. |

4. | H. M. Lai and K Young, “Theory of the pulsed optoacoustic technique,” J. Acoust. Soc. Am. |

5. | G. J. Diebold, T. Sun, and M. I. Khan, “Photoacoustic monopole radiation in one, two and three dimensions,” Phys. Rev. Lett. |

6. | R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacostic ultrasound - reconstruction tomography,” Med. Phys. |

7. | E. Bergman, A. Sheinfeld, S. Gilead, and A. Eyal, “The use of optical waveform synthesis in photoacoustic measurements” in |

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. |

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. |

10. | Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. |

11. | J. G. Proakis, |

**OCIS Codes**

(170.5120) Medical optics and biotechnology : Photoacoustic imaging

(300.1030) Spectroscopy : Absorption

(300.6430) Spectroscopy : Spectroscopy, photothermal

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: December 15, 2008

Revised Manuscript: February 19, 2009

Manuscript Accepted: March 16, 2009

Published: April 20, 2009

**Virtual Issues**

Vol. 4, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Adi Sheinfeld, Elad Bergman, Sharon Gilead, and Avishay Eyal, "The use of pulse synthesis for optimization of photoacoustic measurements," Opt. Express **17**, 7328-7338 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-9-7328

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### References

- 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]
- 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]
- A. C. Tam, "Applications of PA sensing techniques," Rev. Mod. Phys. 58, 381-431 (1986). [CrossRef]
- H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982) [CrossRef]
- 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]
- R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, "Photoacostic ultrasound - reconstruction tomography," Med. Phys. 22, 1605-1609 (1995). [CrossRef] [PubMed]
- 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).
- 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]
- 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]
- Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. 49, 3117-3124 (2004). [CrossRef]
- J. G. Proakis, Digital Communications, 4th Edition (McGraw-Hill, 2001), Chap. 5.

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