Korean Journal of Optics and Photonics (한국광학회지)

Optical Society of Korea (한국광학회)
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Signal-to-noise Ratio in Time- and Frequency-domain Photoacoustic Measurements by Different Frequency Filtering

주파수 필터링 함수에 따른 시간 및 주파수 영역 광음향 측정에 대한 신호 대 잡음비 분석

  • Kang, DongYel (School of Basic Sciences, College of Engineering, Hanbat National University)
  • 강동열 (한밭대학교 공과대학 기초과학부)
  • Received : 2019.01.09
  • Accepted : 2019.03.18
  • Published : 2019.04.25
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Abstract

We investigate the signal-to-noise ratios (SNRs) of time-domain (i.e. pulsed illumination) and frequency-domain (i.e. chirped illumination) photoacoustic signals measured by a spherically focused ultrasound transducer for spherical absorbers. The simulation results show that the time-domain photoacoustic SNR is higher than that of frequency-domain photoacoustic signals, as reported in the previous literature. We understand the reason for this SNR gap between the two measurement modes by analyzing photoacoustic-signal spectra, considering the incident beam energy controlled by the maximum permissible exposure. As the result of this approach, we find that filtering off the DC term in the chirped signal's spectrum improves frequency-domain photoacoustic SNRs by up to approximately 5 dB. In particular, it is observed that photoacoustic SNRs are highly sensitive to an upper-frequency value of frequency filtering functions, and the optimal upper-frequency values maximizing the SNR are different in time- and frequency-domain photoacoustic measurements.

구면 초점 초음파 측정기에 의해 구형의 광 흡수체로부터 측정된 시간(즉, 펄스 형태 광원) 및 주파수 영역(즉, 처프 형태 광원) 광음향 신호의 신호 대 잡음비(signal-to-noise ratio)를 이론 및 시뮬레이션으로 분석하였다. 이전 문헌과 마찬가지로 시간 영역 광음향 측정에 의한 신호 대 잡음비 값이 주파수 영역 광음향 측정의 경우보다 더 높았는데 이 근본적인 이유를 최대허용노광량(maximum permissible exposure)에 따른 광원의 세기와 주파수 필터링을 통한 두 측정 모드의 광음향 스펙트럼들에 대한 분석을 통해 이해하였다. 또한, 분석의 결과로서 주파수 영역 광음향의 처프 형태 광원에 대한 정합 필터링에 더해 DC 스펙트럼 부분을 제거하니 신호 대 잡음비가 5 dB 정도 상승하는 것을 발견하였다. 특히, 주파수 필터 함수의 주파수 상한 값의 변화에 따라 신호대 잡음비 값이 급격하게 변동하였는데 신호 대 잡음비가 최대가 되는 주파수 상한 값이 두 광음향 측정 모드에서 서로 다르게 나타남을 관찰하였다.

Keywords

KGHHBU_2019_v30n2_48_f0001.png 이미지

Fig. 2. Photoacoustic measurement configuration for K-wave toolbox simulation. The inset: sectional image of the absorbing sphere. (b) Spatial photoacoustic spectra for 3 mm and 1.5 mm diameter absorbing spheres in (a) simulated by K-wave toolbox.

KGHHBU_2019_v30n2_48_f0002.png 이미지

Fig. 5. Variation of SNRs for photoacoustic signals from a 3 mm absorbing sphere to the upper frequency values of (a) the rectangular filter in time-domain photoacoustic measurement and (b) the matched filtered chirp with a rectangular filter in frequency-domain photoacoustic measurement.

KGHHBU_2019_v30n2_48_f0003.png 이미지

Fig. 6. Variation of SNRs for photoacoustic signals from a 1.5 mm absorbing sphere to the upper frequency values of (a) the rectangular filter in time-domain photoacoustic measurement and (b) the matched filtered chirp with a rectangular filter in frequency-domain photoacoustic measurement.

KGHHBU_2019_v30n2_48_f0004.png 이미지

Fig. 1. (a) Simulated ultrasound transducer’s transfer function from the simple modeling of Eq. (14). (b) Spectra of matched filtered chirp and Rect function filtering in frequency- and time-domain photoacoustic measurements, respectively.

KGHHBU_2019_v30n2_48_f0005.png 이미지

Fig. 3. (a) Time-domain and (b) frequency-domain photoacoustic SNRs calculated based on brute-force simulations and the theoretical equation, which are indicated as superscripts, b1, b2, and t in the legends.

KGHHBU_2019_v30n2_48_f0006.png 이미지

Fig. 4. (a) Frequency-domain photoacoustic signal’s SNR improved by additionally filtering off the DC terms in the matched filtered chirp spectrum. (b) Comparison of SNRs between time- and frequency-domain photoacoustic measurements before and after additionally applying a rectangular (Rect) filter to matched filtered chirp.

References

  1. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999). https://doi.org/10.1088/0266-5611/15/2/022
  2. D. Kang and M. A. Kupinski, "Figure of merit for task-based assessment of frequency-domain diffusive imaging," Opt. Lett. 38, 235-237 (2013). https://doi.org/10.1364/OL.38.000235
  3. L. V. Wang and S. Hu, "Photoacoustic tomography: In vivo imaging from organelles to organs," Science 335, 1458-1462 (2012). https://doi.org/10.1126/science.1216210
  4. P. Beard, "Biomedical photoacoustic imaging: A review," Interface Focus 1, 602-631 (2011). https://doi.org/10.1098/rsfs.2011.0028
  5. E. M. Strohm, M. J. Moore, and M. C. Kolios, "Single cell photoacoustic microscopy: A review," IEEE J. Sel. Topics Quantum Electron. 22, 6801215 (2016).
  6. Y. Zhou, J. Yao, and L. V. Wang, "Tutorial on photoacoustic tomography," J. Biomed. Opt. 21, 061007 (2016). https://doi.org/10.1117/1.JBO.21.6.061007
  7. C. Li and L. V. Wang, "Photoacoustic tomography and sensing in biomedicine," Phys. Med. Biol. 54, R59-R97 (2009). https://doi.org/10.1088/0031-9155/54/19/R01
  8. K. Konstantin and L. V. Wang, "Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser," J. Biomed. Opt. 13, 024006 (2008). https://doi.org/10.1117/1.2904965
  9. S. Kellnberger, N. C. Deliolanis, D. Queiros, G. Sergiadis, and V. Ntziachristos, "In vivo frequency domain optoacoustic tomography," Opt. Lett. 37, 3423-3425 (2012). https://doi.org/10.1364/OL.37.003423
  10. S. Telenkov, A. Mandelis, B. Lashkari, and F. Michael, "Frequency-domain photothermoacoustics: Alternative imaging modality of biological tissues," J. Appl. Phys. 105, 102029 (2009). https://doi.org/10.1063/1.3116136
  11. S. Telenkov and A. Mandelis, "Signal-to-noise analysis of biomedical photoacoustic measurements in time and frequency domains," Rev. Sci. Instrum. 81, 124901 (2010). https://doi.org/10.1063/1.3505113
  12. B. Lashkari and A. Mandelis, "Comparison between pulsed laser and frequency-domain photoacoustic modalities: Signal-to-noise ratio, contrast, resolution, and maximum depth detectivity," Rev. Sci. Instrum. 82, 094903 (2011). https://doi.org/10.1063/1.3632117
  13. L. Yang, B. Lashkari, J. W. Y. Tan, and A. Mandelis, "Photoacoustic and ultrasound imaging of cancellous bone tissue," J. Biomed. Opt. 20, 076016 (2015). https://doi.org/10.1117/1.JBO.20.7.076016
  14. J. Yao and L. V. Wang, "Sensitivity of photoacoustic microscopy," Photoacoustics 2, 87-101 (2014). https://doi.org/10.1016/j.pacs.2014.04.002
  15. A. Petschke and P. J. La Riviere, "Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications," Biomed. Opt. Express 1, 1188-1195 (2010). https://doi.org/10.1364/BOE.1.001188
  16. G. Langer, B. Buchegger, J. Jacak, T. A. Klar, and T. Berer, "Frequency domain photoacoustic and fluorescence microscopy," Biomed. Opt. Express 7, 1-11 (2016). https://doi.org/10.1364/BOE.7.000001
  17. B. Lashkari and A. Mandelis, "Photoacoustic radar imaging signal-to-noise ratio, contrast, and resolution enhancement using nonlinear chirp modulation Bahman," Opt. Lett. 35, 1623-1625 (2010). https://doi.org/10.1364/OL.35.001623
  18. B. Lashkari and A. Mandelis, "Linear frequency modulation photoacoustic radar: Optimal bandwidth and signal-to-noise ratio for frequency-domain imaging of turbid media," J. Acoust. Soc. Am. 130, 1313-1324 (2011). https://doi.org/10.1121/1.3605290
  19. J. Goodman, Statistical Optics (Wiley, 2000).
  20. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).
  21. American National Standard for the Safe Use of Lasers, ANSI Z136.1-2014, Laser Institute of America, Orlando, FL (2014).
  22. D. Leedom, G. Matthaei, and R. Krimholtz, "New equivalent circuits for elementary piezoelectric transducers," Electron. Lett. 6, 398-399 (1970). https://doi.org/10.1049/el:19700280
  23. G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart and Winston, 1957).
  24. J. Wang, T. Liu, S. Jiao, R. Chen, Q. Zhou, K. K. Shung, L. V. Wang, and H. F. Zhang, "Saturation effect in functional photoacoustic imaging," J. Biomed. Opt. 15, 021317 (2010). https://doi.org/10.1117/1.3333549
  25. C. E. Cook and M. Bernfeld, Radar signals; an introduction to theory and application (Artech house, Inc. 1993).
  26. B. T. Cox and P. Beard, "Fast calculation of pulsed photoacoustic fields in fluids using k-space methods," J. Acoust. Soc. Am. 117, 3616-3627 (2005). https://doi.org/10.1121/1.1920227
  27. B. E. Treeby and B. T. Cox, "k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields," J Biomed. Opt. 15, 021314 (2010). https://doi.org/10.1117/1.3360308
  28. D. Kang, B. Lashkari, and A. Mandelis, "Photoacoustic resonance by spatial filtering of focused ultrasound transducers," Opt. Lett. 42, 655-658 (2017). https://doi.org/10.1364/OL.42.000655