## Scattering noise estimation of range-gated imaging system in turbid condition |

Optics Express, Vol. 18, Issue 20, pp. 21147-21154 (2010)

http://dx.doi.org/10.1364/OE.18.021147

Acrobat PDF (1115 KB)

### Abstract

The range-gated imaging systems are reliable underwater imaging system with the capability to minimize backscattering effect from turbid media. The tail-gating technique has been developed to fine tune the signal to backscattering ratio and hence improve the gated image quality. However, the tail-gating technique has limited image quality enhancement in high turbidity levels. In this paper, we developed a numerical model of range-gated underwater imaging system for near target in turbid medium. The simulation results matched the experimental work favorably. Further investigation using this numerical model shows that the multiple scattering components of the backscattering noise dominate for propagation length larger than 4.2 Attenuation Length (AL). This has limited the enhancement of tail-gating technique in high turbidity conditions.

© 2010 OSA

## 1. Introduction

3. C. Tan, A. Sluzek, and G. Seet, “Model of gated imaging in turbid media,” Opt. Eng. **44**, 116002 (2005). [CrossRef]

3. C. Tan, A. Sluzek, and G. Seet, “Model of gated imaging in turbid media,” Opt. Eng. **44**, 116002 (2005). [CrossRef]

5. E. A. McLean, H. R. Burris Jr, and M. P. Strand, “Short pulse range gated optical imaging in turbid water,” Appl. Opt. **34**(21), 4343–4351 (1995). [CrossRef] [PubMed]

11. C. S. Tan, G. L. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. **43**(9), 995–1009 (2005). [CrossRef]

6. R. Esposito, S. De Nicola, M. Brambilla, A. Pifferi, L. Spinelli, and M. Lepore, “Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions,” Opt. Express **16**(22), 17667–17681 (2008). [CrossRef] [PubMed]

12. D. M. He and G. L. Seet, “Underwater LIDAR imaging in highly turbid waters, ocean optics of remote sensing and underwater imaging,” Proc. SPIE **4488**, 71–81 (2002). [CrossRef]

13. J. M. Grace, P. E. Nebolsine, D. R. Snyder, N. E. Howard, and J. R. Long, “Integration of a high-speed repetitively pulsed laser with a high-speed CCD camera,” Proc. SPIE **3642**, 133–141 (1999). [CrossRef]

## 2. Light components of reflected image temporal profile (RITP)

14. F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. comparison with Monte Carlo results,” Appl. Opt. **36**(19), 4600–4612 (1997). [CrossRef] [PubMed]

15. A. D. Kim and A. Ishimaru, “Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. **37**(22), 5313–5319 (1998). [CrossRef]

11. C. S. Tan, G. L. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. **43**(9), 995–1009 (2005). [CrossRef]

8. L. R. Bissonnette, “Multiple scattering Lidar equation,” Appl. Opt. **35**(33), 6449–6465 (1996). [CrossRef] [PubMed]

16. L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. **41**(30), 6307–6324 (2002). [CrossRef] [PubMed]

*P(t)*, received at any time instance from scattering medium can be described as

*P*contains the single and multiple backscattering noise from turbid medium excluding target reflected photons within the receiver field of view (FOV).

_{BSN}(t)*P*contains the direct or forward scattered target reflected photons within the FOV (which is the desired signal in range-gated imaging system).

_{S}(t)*P*contains the target reflected photons within the FOV which have suffered multiple scattering such that the target information is lost.

_{SMM}(t)*P*] is initiated at the entrance of the medium and dissipated to produce a “tail” due to its attenuated energy and optical ringing effects [17]. The target signal [

_{BSN}(t)*P*] and signal scattered noise [

_{S}(t)*P*] contain photons from the target. On the way back to the receiver, they superimpose with the backscattering noise [

_{SMM}(t)*P*]. In order to quantify the signal to noise ratio, the photons return to the receiver are further classified into 18 groups based on their history [1]. Equation (1) is further divided based on this classification, namely:

_{BSN}(t)*P*represents the photons that reach the target surface after multiple scattering, reflect and return to the receiver with some forward scattering. Thus,

_{MTG}(t)*P*will be the later part of RITP signal compared to

_{MTG}(t)*P*.

_{DTD}(t)*P*and

_{BSN}(t)*P*increase proportionally, while

_{SMM}(t)*P*is reduced under increased scattering conditions. For near target turbid seawater and narrow FOV, Walker et al. [18

_{S}(t)18. R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. **38**(12), 2384–2397 (1999). [CrossRef]

*P*) might be higher than

_{SMM}(t)*P*for higher attenuation length (higher turbidity level) and wider FOV condition when the multi path time is significant.

_{BSN}(t)*P*will be considered in higher attenuation length in section 4. In order to differentiate the interval of RITP which contains target signal (target irradiance pulse) from other temporal region without

_{SMM}(t)*P*, we describe this specific interval with

_{S}(t)*P*as Actual RITP.

_{S}(t)## 3. Backscattering noise within RITP analysis

*P*which starts at

_{o}(t)*t*= 0 and ends at

*t*The kernel of evolution integral function

_{0}.*S*is the TPSF of each component (from

_{i}(r)*i*= DBD, direct-backscattering-direct, to

*i*= MBM, multiple scattering-backscattering-multiple scattering), and

*v*= speed of light in the medium. Equation (6) is adopted in this work for range-gated imaging system. For a laser pulse sent to an underwater target in turbid condition, the photons are assumed to have constant speed and traveling through virtual linear distance,

*r*=

*vt*/2. The returning pulse length will be stretched due to the longer photon transportation path in multiple scattering process, where <

*t*> represent the mean multi-path time. If the emitted laser pulse with temporal profile,

*P*hits an opaque target, and all the energy is either absorbed or reflected at the target, then the convolution process of backscattering effect will terminate at target distance,

_{0}(t),*r*. We established here a formulation to explain this phenomenon, a fixed upper-boundary condition due to the opaque target is introduced. We rewrite Eq. (6) as

_{0}*t*> ≈0; then

*P*= 0 for

_{i}(t)*t*>(2

*r*/

_{0}*v*+

*t*). This formulation describes the backscattering noise as a function of TPSF of the medium, outgoing pulse profile, pulse length

_{0}*t*, and time

_{0}*t*. Direct interpretation of this function is proportional to the outgoing power

*P*and

_{0}(t)*S*. However, it is also affected by the fixed upper-limit at

_{i}(r)*t*>(2

*r*/

_{0}*v*+

*t*), assuming that v(

_{0}*t-t*approaches (2

_{0})/2*r*/

_{0}*v*+

*t*),

_{0}*P*reduces. Based on Eq. (7), the backscattering noise is reduced at the tail end of RITP compared to the front of Actual RITP [11

_{BSN}(t)11. C. S. Tan, G. L. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. **43**(9), 995–1009 (2005). [CrossRef]

*P*etc, are believed to have higher contributions to the total backscattering noise. In order to demonstrate the dominant effects of multiple scattering photon noises, we experiment the tail-gating condition as shown in Fig. 1 and 2 to higher level turbidity.

_{DBM,}, P_{GBM}, P_{MTM}## 4. The Results of Multiple Scattering Noise versus Target Signals

18. R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. **38**(12), 2384–2397 (1999). [CrossRef]

*ζ*=

*r*+

_{o}*v*/2, and ⊗ represents the convolution of

_{t}*P*and

_{target}(ζ)*P*over

_{o}(t)*t*. In this paper,

*P*is simulated. It represents the total impulse response function of each

_{target}(ζ)*P*component (

_{S}(t)*P*, indexed from DTD to MTG).

_{i}’(t)*P*in Eq. (9) contains highly scattered reflected photons that have lost the original target reflection properties (such as location, orientation of the photon) .

_{SMM}(t)21. S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. **67**(1), 23–32 (1998). [CrossRef] [PubMed]

**43**(9), 995–1009 (2005). [CrossRef]

20. I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H. J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. **36**(25), 6529–6538 (1997). [CrossRef]

22. L. G. Henyey and G. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. **93**, 70–83 (1941). [CrossRef]

23. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. **37**(31), 7392–7400 (1998). [CrossRef]

^{0}half angle from the camera position respectively.

^{0}from the optical axis). The records are separated at time domain (0.1 ns step) when the photons are directly reflected by the target. The multiple scattering photons are those photon noises that have reflected back from the target and have scattered more than 2 times after the photons return to the FOV. In this case, the differentiation of the ballistic photons and multiple scattering noises are clearly separated.

## 5. Conclusion

## Acknowledgments

## References and links

1. | B. A. Swartz, “Laser range gated underwater imaging advances,” IEEE J. Ocean Eng. |

2. | H. Sakai, J. Akizono, S. Yasumura, and Y. Takahashi, “Underwater laser viewing system and its application”, in Proceeding of IEEE Conference on Underwater Technology (Institute of Electrical and Electronics Engineers, New York, 161–167 (1988). |

3. | C. Tan, A. Sluzek, and G. Seet, “Model of gated imaging in turbid media,” Opt. Eng. |

4. | N. H. Witherspoon, and J. H. Holloway, Jr., “Feasibility testing of a range gated laser illuminated underwater imaging system”, in |

5. | E. A. McLean, H. R. Burris Jr, and M. P. Strand, “Short pulse range gated optical imaging in turbid water,” Appl. Opt. |

6. | R. Esposito, S. De Nicola, M. Brambilla, A. Pifferi, L. Spinelli, and M. Lepore, “Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions,” Opt. Express |

7. | A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express |

8. | L. R. Bissonnette, “Multiple scattering Lidar equation,” Appl. Opt. |

9. | E. P. Zege, I. L. Katsev, A. S. Prikhach, and G. D. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic LIDAR return”, in Proceedings of International Conference Current Problems in Optics of Natural Waters (D. S. Rozhdestvensky Optical Society), 255–260 (2001). |

10. | F. Falk, and R. Lange, “Solution method for the LIDAR equation”, in LIDAR for Remote Sensing, Richard J. Becherer and Christian Werner, eds., Proc. SPIE |

11. | C. S. Tan, G. L. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. |

12. | D. M. He and G. L. Seet, “Underwater LIDAR imaging in highly turbid waters, ocean optics of remote sensing and underwater imaging,” Proc. SPIE |

13. | J. M. Grace, P. E. Nebolsine, D. R. Snyder, N. E. Howard, and J. R. Long, “Integration of a high-speed repetitively pulsed laser with a high-speed CCD camera,” Proc. SPIE |

14. | F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. comparison with Monte Carlo results,” Appl. Opt. |

15. | A. D. Kim and A. Ishimaru, “Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. |

16. | L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. |

17. | G. D. Gilbert, and M. H. North, “Studies of optical ringing in seawater,” in Ocean Optics XII, Jules S. Jaffe, ed., Proc. SPIE |

18. | R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. |

19. | C. S. Tan, G. L. Seet, and A. Sluzek, “Practical quantitative assessment of imaging system in turbid water using a modified fidelity index,” in Visual Information Processing XII, Z. Rahman et al., Proc. SPIE |

20. | I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H. J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. |

21. | S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. |

22. | L. G. Henyey and G. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. |

23. | A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. |

24. | C. D. Mobley, |

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(280.0280) Remote sensing and sensors : Remote sensing and sensors

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: May 25, 2010

Revised Manuscript: August 11, 2010

Manuscript Accepted: September 3, 2010

Published: September 22, 2010

**Citation**

ChingSeong Tan, Gerald Seet, Andrzej Sluzek, Xin Wang, Chai Tong Yuen, Chen Yep Fam, and Hin Yong Wong, "Scattering noise estimation of range-gated imaging system in turbid condition," Opt. Express **18**, 21147-21154 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21147

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### References

- B. A. Swartz, “Laser range gated underwater imaging advances,” IEEE J. Ocean Eng. 19, 722–727 (1994).
- H. Sakai, J. Akizono, S. Yasumura, and Y. Takahashi, “Underwater laser viewing system and its application”, in Proceeding of IEEE Conference on Underwater Technology (Institute of Electrical and Electronics Engineers, New York, 161–167 (1988).
- C. Tan, A. Sluzek, and G. Seet, “Model of gated imaging in turbid media,” Opt. Eng. 44, 116002 (2005). [CrossRef]
- N. H. Witherspoon, and J. H. Holloway, Jr., “Feasibility testing of a range gated laser illuminated underwater imaging system”, in Ocean Optics X, Richard W. Spinrad, ed., Proc. SPIE 1302, 414 – 420 (1990).
- E. A. McLean, H. R. Burris, and M. P. Strand, “Short pulse range gated optical imaging in turbid water,” Appl. Opt. 34(21), 4343–4351 (1995). [CrossRef] [PubMed]
- R. Esposito, S. De Nicola, M. Brambilla, A. Pifferi, L. Spinelli, and M. Lepore, “Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions,” Opt. Express 16(22), 17667–17681 (2008). [CrossRef] [PubMed]
- A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express 16(17), 13188–13202 (2008). [CrossRef] [PubMed]
- L. R. Bissonnette, “Multiple scattering Lidar equation,” Appl. Opt. 35(33), 6449–6465 (1996). [CrossRef] [PubMed]
- E. P. Zege, I. L. Katsev, A. S. Prikhach, and G. D. Ludbrook, “Computer simulation with regard to pulse stretching for oceanic LIDAR return”, in Proceedings of International Conference Current Problems in Optics of Natural Waters (D. S. Rozhdestvensky Optical Society), 255–260 (2001).
- F. Falk, and R. Lange, “Solution method for the LIDAR equation”, in LIDAR for Remote Sensing, Richard J. Becherer and Christian Werner, eds., Proc. SPIE 1714, 303–308 (1992).
- C. S. Tan, G. L. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005). [CrossRef]
- D. M. He and G. L. Seet, ““Underwater LIDAR imaging in highly turbid waters”, Ocean Optics of Remote Sensing and Underwater Imaging,” Proc. SPIE 4488, 71–81 (2002). [CrossRef]
- J. M. Grace, P. E. Nebolsine, D. R. Snyder, N. E. Howard, and J. R. Long, “Integration of a high-speed repetitively pulsed laser with a high-speed CCD camera,” Proc. SPIE 3642, 133–141 (1999). [CrossRef]
- F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36(19), 4600–4612 (1997). [CrossRef] [PubMed]
- A. D. Kim and A. Ishimaru, “Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. 37(22), 5313–5319 (1998). [CrossRef]
- L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. 41(30), 6307–6324 (2002). [CrossRef] [PubMed]
- G. D. Gilbert, and M. H. North, “Studies of optical ringing in seawater”, in Ocean Optics XII, Jules S. Jaffe, ed., Proc. SPIE 2258, 472–479 (1994).
- R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38(12), 2384–2397 (1999). [CrossRef]
- C. S. Tan, G. L. Seet, and A. Sluzek, “Practical quantitative assessment of imaging system in turbid water using a modified fidelity index,” in Visual Information Processing XII, Z. Rahman et al., Proc. SPIE 5108, 51–62 (2003).
- I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H. J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36(25), 6529–6538 (1997). [CrossRef]
- S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol. 67(1), 23–32 (1998). [CrossRef] [PubMed]
- L. G. Henyey and G. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
- A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37(31), 7392–7400 (1998). [CrossRef]
- D. Curtis, Mobley, “Light and water, radiative transfer in natural water”, Academic Press, 1994.

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