## Contrast improvement by selecting ballistic-photons using polarization gating |

Optics Express, Vol. 18, Issue 23, pp. 23746-23755 (2010)

http://dx.doi.org/10.1364/OE.18.023746

Acrobat PDF (2396 KB)

### Abstract

In this paper a new approach to improve contrast in optical subsurface imaging is presented. The method is based on time-resolved reflectance and selection of ballistic photons using polarization gating. Numerical studies with a statistical Monte Carlo method also reveal that weakly scattered diffuse photons can be eliminated by employing a small aperture and that the contrast improvement strongly depends on the single-scattering phase function. A possible experimental setup is discussed in the conclusions.

© 2010 Optical Society of America

## 1. Introduction

4. X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. **29**, 2773–2775 (2004). [CrossRef] [PubMed]

1. A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-Resolved Reflectance at Null Source-Detector Separation: Improving Contrast and Resolution in Diffuse Optical Imaging,” Phys. Rev. Lett. **95**, 078101 (2005). [CrossRef] [PubMed]

*g*> 0.7). For each test case the intensity, the

*V*-component of the Stokes vector, the reached depth and the contrast are shown as functions of time-of-flight.

## 2. Governing equations

**I**(

**x**,

**s**,

*λ*,

*t*) is solved with the Monte Carlo method implemented in our code Scatter3D [

**?**, 12

12. P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A **24**, 2206–2219 (2007). [CrossRef]

15. M. Šormaz, T. Stamm, and P. Jenny, “Influence of linear birefringence in the computation of scattering phase functions,” J. Biomed. Opt. **15**, 055010 (2010). [CrossRef] [PubMed]

**x**,

**s**is the propagation direction,

*λ*the wavelength and

*t*the time. The vectors

**s**and

**s**′ form a so-called scattering plane, for which the single-scattering Mueller matrix

**M**(

**s**,

**s**′) is defined. Extinction and scattering coefficients are denoted by

*γ*and

_{t}*γ*, respectively. A single scattering event requires rotation of the Stokes vector

_{s}**I**= [

*I Q U V*]

*into the scattering plane and its multiplication with the 4 × 4 single-scattering Mueller matrix (see Fig. 1). The components of the Stokes vector are defined as*

^{T}*E*and

_{l}*E*are the complex parts of the phasors

_{r}**E**

*=*

_{l}**a**

*(−*

_{l}exp*iωt*–

*iδ*

_{0}) and

**E**

*=*

_{r}**a**

*(−*

_{r}exp*iωt*–

*iδ*

_{0}–

*iδ*). Here,

**E**

*and*

_{l}**E**

*are the parallel and perpendicular components of the electric field vector with respect to the scattering plane. The phase difference between*

_{r}**E**

*and*

_{r}**E**

*is denoted by*

_{l}*δ*,

*a*= |

_{l}**a**

*| and*

_{l}*a*= |

_{r}**a**

*| are the amplitudes of*

_{r}**E**

*and*

_{l}**E**

*,*

_{r}*ω*= 2

*πc*/

*λ*is the frequency and

*δ*

_{0}is the phase of

**E**

*at t=0 (*

_{l}*c*is the speed of light).

16. M. Xu, “Electric field Monte Carlo simulation of polarized light propagating in turbid media,” Opt. Express **12**, 6530–6539 (2004). [CrossRef] [PubMed]

*E*=

_{l}*a*(−

_{l}exp*iωt*–

*iδ*

_{0}) and

*E*=

_{r}*a*(−

_{r}exp*iωt*–

*iδ*

_{0}–

*iδ*) are changed according to where

*ϕ*(azimuth angle) is the clockwise rotation angle around the pre-scattering propagation trajectory and

*θ*is the polar scattering angle defined as shown in Fig. 1. Note that

*S*

_{1}and

*S*

_{2}in Eq. (3) are computed by the Lorenz-Mie theory and the detailed description of their computation can be found in [14

14. M. Šormaz, T. Stamm, and P. Jenny, “Stochastic modeling of polarized light scattering using a Monte Carlo-based stencil method,” J. Opt. Soc. Am. A **27**, 1100–1110 (2010). [CrossRef]

*I*has to be preserved (without absorption), i.e.

*F*(

*θ*,

*ϕ*) in Eq. (3) is defined in [16

16. M. Xu, “Electric field Monte Carlo simulation of polarized light propagating in turbid media,” Opt. Express **12**, 6530–6539 (2004). [CrossRef] [PubMed]

*E*and

_{l}*E*at any time for any scattering plane.

_{r}## 3. Simulation setup and materials

*R*= 2.5mm is coaxial with the laser beam and source-detector separation is

*ρ*= 0. Outgoing photons with all deflection angles from the surface normal were considered and in all test cases the center of the considered spherical inhomogeneity was placed on the line along the laser beam at different depths (

*z*= 3mm and

*z*= 5mm).

*d*= 1000nm embedded in silicon with

*n*= 1.404. The particles in phantom 1 are

_{si}*TiO*spheres with

*n*= 2.609 designed to mimic human tissue and in phantom 2 polystyrene spheres with

_{pa}*n*= 1.59 are considered. The illumination is a near-infrared laser light with

_{pa}*λ*= 780nm perpendicularly incident on the scattering medium (propagation along the positive

*z*-direction). The Stokes vector [see Eq. (2)] of incident light is

**I**= [1 0 0 1]

*. The background medium has the same scattering coefficient as the spherical inhomogeneity (*

^{T}*μ*= 10cm

_{s}^{−1}), but different absorption coefficients, i.e.

*μ*= 0.2cm

_{a,bg}^{−1}for the background medium and

*μ*= 0.5cm

_{a,target}^{−1}for the inhomogeneity. Matched refractive indices of phantoms and surrounding medium were used. To compute the single-scattering phase functions, which have anisotropy factors of

*g*≈ 0.72 and

*g*≈ 0.92 for the phantoms 1 and 2, respectively, the Lorenz-Mie theory was employed. For an easier overview Table 1 presents all considered test cases.

## 4. Results

*D*= 1mm is located at

*z*= 3mm. The results are shown in Fig. 3.

*V*-components of the Stokes vector shown in Fig. 3(b) differ significantly and the standard deviations are large in both cases indicating the potential for contrast improvement using polarization filtering. In Fig. 3(c) the reached depth is shown as a function of time-of-flight and it can be observed that it is larger for test case 2 compared to test case 1, which is due to the more anisotropic single-scattering phase function resulting in less corrugated photon trajectories. As a consequence, the contrast where

*I*and

*I*

_{0}are the detected intensities with and without spherical inhomogeneity, respectively, is larger for test case 2 than for test case 1 [Fig. 3(d)]. Note that the distance

*l*

_{1}in Fig. 2 is approximately represented by the speed of light times half the time-of-flight for which

*C*[see Eq. (4)] in Fig. 3(d) starts to rise, while

*l*

_{2}is approximately equal to the speed of light times half the time-of-flight corresponding to the contrast peak. Obviously it is possible to estimate depth and size of the target from the contrast curve, while zero source-detector separation leads to the best possible localization in the

*xy*-plane. Figure 4 shows the standard deviations of the photon trajectories (distances between scattering positions and the axis of the incident laser beam) conditional on time-of-flight and

*V*-component of the Stokes vector.

*V*-value tend have a larger standard deviation. Employing polarization filtering, photons with corrugated trajectories can be eliminated, which improves the signal-to-noise ratio and consequentially the contrast. Similar results were obtained for phantom 1 as well. The 3D histogram shown in Fig. 5 gives a closer look at the amount of detected photons within a certain time-of-flight and

*V*range.

*V*-values above −0.5, which is consistent with the ”bump” in Fig. 3(b) at a times-of-flight around 20ps. Compared to diffuse photons, the deflection angles

*α*from the surface normal tend to be smaller for detected photons with more or less straight trajectories. In order to see that, the outgoing angles of the detected photons (for phantom 2) are shown in Fig. 6 as a function of time-of-flight and

*V*-value. Furthermore, from the histogram in Fig. 5 and the results in Fig. 6 it becomes obvious that a large portion of weakly scattered diffuse photons can be removed by only accepting photons with

*α*≤ 30°.

*D*= 1mm and center at

*z*= 5mm is considered, while polarization filtering was only applied for test case 4, i.e. photons with

*V*∉ [−1, −0.7] were rejected. Results are shown in Fig. 7.

*V*is much smaller for test case 4 due to polarization filtering [see Fig. 7(b)]. Since the average trajectories of the polarization filtered photons (test case 4) are less corrugated, the reached depths are slightly larger for the same time-of-flight compared to test case 3 [see Fig. 7(c)]. Consequently, a better contrast can be detected for test case 4 due to improved signal-to-noise ratio [see Fig. 7(d)]. Note that the contrast curve for test case 4 declines for larger times-of-flight and eventually reaches zero. This is due to the coaxial setup of laser and detector and the V-shaped photon trajectories. For large times-of-flight the same reflection angle as that of trajectory

*t*

_{2}in Fig. 2 leads to elimination for deeper penetrations. The same simulation setup as for the test cases 3 and 4 was used for the test cases 5 and 6, but phantom 1 instead of phantom 2 was considered. The results are plotted in Fig. 8.

*g*, i.e. a larger

*g*-value leads to less corrugated trajectories and consequentially in larger contrast. On the other hand, smaller

*g*-values result in more diffuse photon scattering and thus polarization filtering has a higher impact. Figures 9(a) and 9(b) depict the reconstructed inclusions based on the contrast curves for test cases 5 and 6, respectively. The abscissa represents the scanning direction (

*x*-axis) and the ordinate the depth (

*z*-axis; the dimensions of both axes are in mm). The grayscale value represents the slope of the contrast curve showing that polarization gating leads to significant contrast improvements. A slope of the contrast curves is calculated as a difference between contrast values in two neighbor time bins divided by its width which is equal to 1; i.e. time bins of 1ps were used in all presented results. Thus the grayscale values in Fig. 9 are one order of magnitude lower than the contrast values in Fig. 8(d). For larger depths (

*z*= 10mm and

*D*= 2mm), in phantom 1 the polarization information gets lost and no contrast improvement can be achieved, while in phantom 2 a small contrast improvement is achieved and the peak contrast value is of the same order of magnitude as in the test cases 3 and 4. Next, the contrast curves with and without polarization gating were computed using phantom 2 and inclusion with D=2mm placed at depth of 15mm. The contrast values are one order of magnitude smaller compared to those in Fig. 7 and no contrast improvement was achieved using polarization gating. However, in this simulation a low signal-to-noise ratio is reported.

## 5. Conclusions

4. X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. **29**, 2773–2775 (2004). [CrossRef] [PubMed]

*V*-component of the Stokes vector monotonically increases with time-of-flight, the detected signal obtained by converting elliptically polarized backscattered light into linearly polarized light can be conditioned on the penetration depth. Obviously, such an approach is slower and more expensive than simpler ones, where all light with flipped helicity is detected [4

4. X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. **29**, 2773–2775 (2004). [CrossRef] [PubMed]

*V*-component as a function of time-of-flight (for a given phantom and illumination), the contrast curve could be obtained without measurements in the time domain avoiding the use of an expensive streak camera. Therefore it is sufficient to measure the change only once for each commonly used phantom and illumination wavelength and it is possible to use the obtained curves for future imaging experiments, since in both phantoms the V-value of detected ballistic-photons (photons detected using polarization gating) monotonically changes with the time-of-flight and thereby uniquely determines their penetration depth. In all our simulation studies the incident laser light was circularly polarized and the anisotropy factor

*g*was greater than 0.7 (which is the case for most biological tissues). Note that larger anisotropy factors lead to higher contrast values, but the improvement due to polarization filtering is greater for smaller

*g*values.

## Acknowledgments

## References and links

1. | A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-Resolved Reflectance at Null Source-Detector Separation: Improving Contrast and Resolution in Diffuse Optical Imaging,” Phys. Rev. Lett. |

2. | S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. |

3. | S. G. Demos, H. B. Radousky, and R. R. Alfano, “Deep subsurface imaging in tissues using spectral and polarization filtering,” Opt. Express |

4. | X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. |

5. | S. A. Kartazayeva, X. Ni, and R. R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. |

6. | R. Nothdurft and G. Yao, “Expression of target optical properties in subsurface polarization-gated imaging,” Opt. Express |

7. | Y. Liu, Y.L. Kim, X. Li, and V. Backman, “Investigation of depth selectivity of polarization gating for tissue characterization,” Opt. Express |

8. | A.D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. |

9. | W. Cai, X. Ni, S.K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E |

10. | A. D. Kim and M. Moscoso, “Backscattering of beams by forward-peaked scattering media,” Opt. Lett. |

11. | K. G. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express |

12. | P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A |

13. | M. Šormaz, T. Stamm, S. Mourad, and P. Jenny, “Stochastic modeling of light scattering with fluorescence using a Monte Carlo-based multiscale approach,” J. Opt. Soc. Am. A |

14. | M. Šormaz, T. Stamm, and P. Jenny, “Stochastic modeling of polarized light scattering using a Monte Carlo-based stencil method,” J. Opt. Soc. Am. A |

15. | M. Šormaz, T. Stamm, and P. Jenny, “Influence of linear birefringence in the computation of scattering phase functions,” J. Biomed. Opt. |

16. | M. Xu, “Electric field Monte Carlo simulation of polarized light propagating in turbid media,” Opt. Express |

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

(120.5700) Instrumentation, measurement, and metrology : Reflection

(260.5430) Physical optics : Polarization

(290.4210) Scattering : Multiple scattering

(320.7100) Ultrafast optics : Ultrafast measurements

(110.0113) Imaging systems : Imaging through turbid media

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: August 20, 2010

Revised Manuscript: September 16, 2010

Manuscript Accepted: October 24, 2010

Published: October 27, 2010

**Virtual Issues**

Vol. 6, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Miloš Šormaz and Patrick Jenny, "Contrast improvement by selecting ballistic-photons using polarization gating," Opt. Express **18**, 23746-23755 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-23-23746

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### References

- A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, "Time-Resolved Reflectance at Null Source-Detector Separation: Improving Contrast and Resolution in Diffuse Optical Imaging," Phys. Rev. Lett. 95, 078101 (2005). [CrossRef] [PubMed]
- S. G. Demos, and R. R. Alfano, "Optical polarization imaging," Appl. Opt. 36, 150-155 (1997). [CrossRef] [PubMed]
- S. G. Demos, H. B. Radousky, and R. R. Alfano, "Deep subsurface imaging in tissues using spectral and polarization filtering," Opt. Express 7, 23-28 (2000). [CrossRef] [PubMed]
- X. Ni, and R. R. Alfano, "Time-resolved backscattering of circularly and linearly polarized light in a turbid medium," Opt. Lett. 29, 2773-2775 (2004). [CrossRef] [PubMed]
- S. A. Kartazayeva, X. Ni, and R. R. Alfano, "Backscattering target detection in a turbid medium by use of circularly and linearly polarized light," Opt. Lett. 30, 1168-1170 (2005). [CrossRef] [PubMed]
- R. Nothdurft, and G. Yao, "Expression of target optical properties in subsurface polarization-gated imaging," Opt. Express 13, 4185-4195 (2005). [CrossRef] [PubMed]
- Y. Liu, Y. L. Kim, X. Li, and V. Backman, "Investigation of depth selectivity of polarization gating for tissue characterization," Opt. Express 13, 601-611 (2005). [CrossRef] [PubMed]
- A. D. Kim, and M. Moscoso, "Backscattering of circularly polarized pulses," Opt. Lett. 27, 1589-1591 (2002). [CrossRef]
- W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, "Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media," Phys. Rev. E 74, 056605 (2006). [CrossRef]
- A. D. Kim, and M. Moscoso, "Backscattering of beams by forward-peaked scattering media," Opt. Lett. 29, 74-76 (2004). [CrossRef] [PubMed]
- K. G. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, "Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media," Opt. Express 13, 7954-7969 (2005). [CrossRef] [PubMed]
- P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, "Computing light statistics in heterogeneous media based on a mass weighted probability density function method," J. Opt. Soc. Am. A 24, 2206-2219 (2007). [CrossRef]
- M. Šormaz, T. Stamm, S. Mourad, and P. Jenny, "Stochastic modeling of light scattering with fluorescence using a Monte Carlo-based multiscale approach," J. Opt. Soc. Am. A 26, 1403-1413 (2009). [CrossRef]
- M. Šormaz, T. Stamm, and P. Jenny, "Stochastic modeling of polarized light scattering using a Monte Carlo-based stencil method," J. Opt. Soc. Am. A 27, 1100-1110 (2010). [CrossRef]
- M. Šormaz, T. Stamm, and P. Jenny, "Influence of linear birefringence in the computation of scattering phase functions," J. Biomed. Opt. 15, 055010 (2010). [CrossRef] [PubMed]
- M. Xu, "Electric field Monte Carlo simulation of polarized light propagating in turbid media," Opt. Express 12, 6530-6539 (2004). [CrossRef] [PubMed]

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