## Photoacoustic tomography imaging based on a 4f acoustic lens imaging system

Optics Express, Vol. 15, Issue 8, pp. 4966-4976 (2007)

http://dx.doi.org/10.1364/OE.15.004966

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### Abstract

The theory of photoacoustic tomography (PAT) imaging using a 4f acoustic lens imaging system has been investigated, and the theoretical results show that a 4f acoustic lens has the ability of imaging and guarantees axial and lateral unit magnification of image. A system, a 4f acoustic lens imaging system combining with time-resolved technique, is developed to acquire PAT images. The 4f acoustic lens is able to image initial photoacoustic (PA) pressure distribution, which exactly resembles the absorption distribution, onto an imaging plane. Combining with time-resolved technique, the linear transducer array is adopted to acquire the PA pressure distribution to reconstruct the PAT images. Experimental results demonstrate that the system is able to obtain PAT images and the images contrast sharply with their backgrounds.

© 2007 Optical Society of America

## 1. Introduction

1. X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. H. Wang, “Non-invasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. **21**, 803–806 (2003). [CrossRef] [PubMed]

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

15. J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-time three-dimensional optoacoustic imaging using an acoustic lens system,” Appl. Phys. Lett. **85**, 846–848 (2004). [CrossRef]

## 2. Theoretical model

### 2.1. Principle of 4f acoustic lens imaging

_{1}and L

_{2}is combined, the front focal plane of the lens L

_{1}is the object plane O, the image is inputted from this plane. The back focal plane of the lens L

_{2}is the imaging plane I, the image is outputted from this plane. The confocal plane is named the transform plane T. The system is named for short the OTI imaging system. When the object is illuminated by laser, the ultrasonic signals induced from the object plane can be considered as coherent signals, the whole OTI imaging system is coherent imaging system. According to Abbe theory of image formation, the imaging process of the system will be discussed as follows.

*P*(

_{O}*x*,

*y*, on the transform plane

*t*(

*u*,

*v*) =1, so

*P*

_{2}(

*u*,

*v*) =

*P*

_{1}(

*u*,

*v*) , that is

*P*(

_{T}*u*,

*v*) ; on the imaging plane, the amplitude of acoustic pressure is

*P*(

_{I}*x*′,

*y*′) . As Fig. 2 shows, the transforms of acoustic pressure-amplitude are Fourier transforms in the process of two Fraunhofer diffractions.

*x*′,

*y*′ means the image is inverted.

### 2.2. The lateral magnification and the axial magnification of the imaging system

*α*is the lateral magnification of the imaging system,

*β*is the axial magnification,

*f*is the object focal length,

*f*′ is the image focal length,

*n*′ is the refractivity of medium in object space, and

*n*is the refractivity of medium in image space. If the medium in object space is same to the image space, the formula (6) can be simplified as

*β*= ±1 .In the 4f imaging system,

*α*= 1 because of

*β*= -1, the image of a cube is also a cube. Therefore, the 4f acoustic imaging system guarantees axial and lateral unit magnification of the images, a displacement of the object plane by a distance Δ

*Z*results in a displacement of the corresponding focused image plane by a distance Δ

*Z*, just as Fig. 3 shows. In addition, the acoustic lens has the property of long focal depth, which means that the distance Δ

*Z*of the image plane of the lateral magnification

*α*= 1 will be long, about 1–2cm. And it can be described by [17

17. W. Wan, R. S. Liang, Z. L. Tang, Z. X. Chen, H. C. Zhang, and Y. H. He, “The imaging property of photoacoustic Fourier imaging and tomography using an acoustic lens imaging system,” J. Appl. Phys. **101**, 063103 1–7 (2007). [CrossRef]

*f*is the focal length of an acoustic lens,

*a*is the radius of the acoustic lens, and

*λ*is the wavelength of sound.

## 3. Imaging system and method

## 4. Experimental results and discussion

### 4.1. Two-dimensional (2D) PAT imaging

### 4.2. The resolution of the imaging system

### 4.3. The imaging property of the acoustic lens on axis

*v*is the acoustic velocity, and Δ

*t*is the time difference of two PA signals reached the detector.

*t*= 8.21×10

^{-5}

*s*-7.65×10

^{-5}

*s*, = 5.6×10

^{-6}

*s*, = 5.6μ

*s*, and

*v*= 1.49

*mm*/μ

*s*, so

*D*=

*v*∙Δ

*t*= 1.49×5.6

*mm*= 8.344(

*mm*). The distance between the two object planes is about 15mm in polymethylmethacrylate, so it must be transformed to the distance in solution. The transforming relation is

*d*=

*s*/

*n*, where s is the distance between the two object planes,

*n*is a relative refraction index, and

^{17}

*τ*is the temporal impulse width of PA signals and

*v*is the velocity of PA signals in the biological tissue. In general,

*v*is a constant, thus DR is determined by

*τ*, where

*τ*relates to the response characteristic of the detector.

## 5. Conclusion

## Acknowledgments

## References and links

1. | X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. H. Wang, “Non-invasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. |

2. | R. J. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, and W. Steenbergen, “Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis,” Opt. Express |

3. | R. G. M. Kolkman, J. H. G. M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, and T. G. van Leeuwen, “Photoacoustic determination of blood vessel diameter,” Phys. Med. Biol. |

4. | A. Oraesky, A. Karabutov, V. S. Solomatin, E. V. Savateeva, V. G. Andreev, Z. Gatalica, H. Singh, and R. Y. D. Fleming, “Laser optoacoustic imaging of breast cancer in vivo,” Proc. SPIE |

5. | C. G. A. Hoelen, F. F. M. de Mul, R. Pongers, and A. Dekker, “Three-dimensional photoacoustic imaging of blood vessels in tissue,” Opt. Lett. |

6. | K. Geng, W. Xueding, X. Xueyi, S. George, and W. Lihong, “Imaging of tumor angiogenesis in rat brains in vivo by photoacoustic tomography,” Appl. Opt , |

7. | K. H. Song, G. Stoica, and L H. V. Wang, “In vivo three-dimensional photoacoustic tomography of a whole mouse head,” Opt. Lett. |

8. | X. D. Wang, X. Y. Xie, G. Ku, L. H. Wang, and G. Stoica, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. |

9. | R. A. Kruger, P. Y. Liu, Y. C. Fang, and C. R. Appledom, “Photoacoustic ultrasound (PAUS)-Reconstruction tomography,” Med. Phys. |

10. | M. H. Xu and L. H. Wang, “Time-Domain Reconstruction for Thermoacoustic Tomography in a Spherical Geometry,” IEEE Trans. Med. Imag. |

11. | K. P. KÖstli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. |

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

13. | B. Z. Yin, D. Xing, Y. Wang, Y. G. Zeng, Y. Tan, and Q. Chen, “Fast photoacoustic imaging system based on 320-element linear transducer array,” Phys . Med . Biol. |

14. | D. W. Yang, D. Xing, H. M. Gu, Y. Tan, and L. M. Zeng, “Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm,” Appl. Phys. Lett. |

15. | J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-time three-dimensional optoacoustic imaging using an acoustic lens system,” Appl. Phys. Lett. |

16. | Z. X. Chen, Z. L tang, W. Wan, and Y. H. He, “Photoacoustic tomography imaging based on an acoustic lens imaging system,” Acta. Phys. Sin. |

17. | W. Wan, R. S. Liang, Z. L. Tang, Z. X. Chen, H. C. Zhang, and Y. H. He, “The imaging property of photoacoustic Fourier imaging and tomography using an acoustic lens imaging system,” J. Appl. Phys. |

**OCIS Codes**

(170.0110) Medical optics and biotechnology : Imaging systems

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.5120) Medical optics and biotechnology : Photoacoustic imaging

(170.6920) Medical optics and biotechnology : Time-resolved imaging

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: February 26, 2007

Revised Manuscript: March 24, 2007

Manuscript Accepted: March 24, 2007

Published: April 9, 2007

**Virtual Issues**

Vol. 2, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Zhanxu Chen, Zhilie Tang, and Wei Wan, "Photoacoustic tomography imaging based on a 4f acoustic lens imaging system," Opt. Express **15**, 4966-4976 (2007)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-8-4966

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### References

- X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. H. Wang, "Non-invasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nat. Biotechnol. 21, 803-806 (2003). [CrossRef] [PubMed]
- R. J. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem and W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005). [CrossRef] [PubMed]
- R. G. M. Kolkman, J. H. G. M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen and T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 47454756 (2004). [CrossRef] [PubMed]
- A. Oraesky, A. Karabutov, V. S. Solomatin, E. V. Savateeva, V. G. Andreev, Z. Gatalica, H. Singh, and R. Y. D. Fleming, "Laser optoacoustic imaging of breast cancer in vivo," Proc. SPIE 4256, 12-22 (2001).
- C. G. A. Hoelen, F. F. M. de Mul, R. Pongers, and A. Dekker, "Three-dimensional photoacoustic imaging of blood vessels in tissue," Opt. Lett. 23, 648-650 (1998). [CrossRef]
- K. Geng, W. Xueding, X. Xueyi, S. George, and W. Lihong, "Imaging of tumor angiogenesis in rat brains in vivo by photoacoustic tomography," Appl. Opt., 44, 770-775 (2005). [CrossRef]
- K. H. Song, G. Stoica, and L. H. V. Wang, "In vivo three-dimensional photoacoustic tomography of a whole mouse head," Opt. Lett. 31, 2453-2455 (2006). [CrossRef] [PubMed]
- X. D. Wang, X. Y. Xie, G. Ku, and L. H. Wang, G. Stoica, "Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography," J. Biomed. Opt. 11, 024015 1-9 (2006). [CrossRef]
- R. A. Kruger, P. Y. Liu, Y. C. Fang, and C. R. Appledom, "Photoacoustic ultrasound (PAUS)-Reconstruction tomography," Med. Phys. 22, 1605-1609 (1995). [CrossRef] [PubMed]
- M. H. Xu, and L. H. Wang, "Time-Domain Reconstruction for Thermoacoustic Tomography in a Spherical Geometry," IEEE Trans. Med. Imag. 21, 814-822 (2002). [CrossRef]
- K. P. Köstli, and P. C. Beard, "Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response," Appl. Opt. 42, 1899-1908 (2003). [CrossRef] [PubMed]
- Y. Wang, D. Xing, Y. G. Zeng, and Q. Chen, "Photoacoustic imaging with deconvolution algorithm," Phys. Med. Biol. 49, 3117-3124 (2004). [CrossRef] [PubMed]
- B. Z. Yin, D. Xing, Y. Wang, Y. G. Zeng, Y. Tan, and Q. Chen, "Fast photoacoustic imaging system based on 320-element linear transducer array," Phys. Med. Biol. 49, 1339-1346 (2004). [CrossRef] [PubMed]
- D. W. Yang, D. Xing, H. M. Gu, Y. Tan, and L. M. Zeng, "Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm," Appl. Phys. Lett. 87, 194101 1-3 (2005). [CrossRef]
- J. J. Niederhauser, M. Jaeger, and M. Frenz, "Real-time three-dimensional optoacoustic imaging using an acoustic lens system," Appl. Phys. Lett. 85, 846-848 (2004). [CrossRef]
- Z. X. Chen, Z. L. tang, W. Wan, and Y. H. He, "Photoacoustic tomography imaging based on an acoustic lens imaging system," Acta.Phys. Sin. 55, 4365-4370 (2006).
- W. Wan, R. S. Liang, Z. L. Tang, Z. X. Chen, H. C. Zhang, and Y. H. He, "The imaging property of photoacoustic Fourier imaging and tomography using an acoustic lens imaging system," J. Appl. Phys. 101, 063103 1-7 (2007). [CrossRef]

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