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Differential optical polarization imaging in turbid media with different embedded objects
Optics Communications 241 (2004) 255–261 www.elsevier.com/locate/optcom
Differential optical polarization imaging in turbid media with different embedded objects Gang Yao
*
Department of Biological Engineering, University of Missouri-Columbia, 1406 E Rollins St. 249 Ag Eng. Bldg., 65211 MO, Columbia, USA Received 19 November 2003; received in revised form 30 June 2004; accepted 12 July 2004
Abstract A Monte Carlo modeling technique was developed to study subsurface polarization imaging of scattering media. Images of embedded absorption, scattering, and reflective objects were simulated with both linearly and circularly polarized incident light. Results indicated that different objects appeared differently in polarization-sensitive images. The effects of object depths on image contrast were also examined. 2004 Elsevier B.V. All rights reserved. Keywords: Polarization; Monte Carlo; Scattering media
1. Introduction Polarization gating has been applied as a simple way to enhance imaging contrast of scattering media [1–7]. This technology has been applied in many different fields such as material corrosion detection [1]; under water detection [2]; and medical imaging [5]. In turbid media, the incident polarization information is lost among multiply scattered photons, while it is partially preserved in weakly scattered light. Because photons from deep media tend to be scattered more than those from superfi*
Tel.: +1-573-8847529; fax: +1-573-8821115. E-mail address: [email protected].
cial depths, polarization techniques can thus be employed to selectively detect light from different depths inside the media [3]. The most often used technique is differential polarization detection, in which the cross-polarized signal is subtracted from co-polarized signal. A linearly polarized light is usually used in such a differential polarization imaging system. However, linearly polarized light and circularly polarized light propagate differently inside scattering media [8,9]. Therefore, different polarized light may provide better contrast in different scattering media. One of the fundamental tasks in polarization imaging is to interpret the image features. Optical contrast can originate from inhomogeneous
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.07.026
256
G. Yao / Optics Communications 241 (2004) 255–261
distributions of absorption, scattering, and reflection properties. In order to correctly interpret image features, it is important to understand how different optical objects manifest themselves in polarization sensitive images. We used a Monte Carlo technique to simulate polarization imaging in turbid media with different embedded objects. We compared images obtained with linearly and circularly polarized incident light. The effectiveness of differential polarization imaging on different types of objects was also studied. 2. Methods
CCD
The propagation of polarized light in turbid media is a complex process. Various parameters, such as the size, shape, and density of the scatterers as well as the polarization state of the incident light, all play important roles. Monte Carlo method with Stokes–Mueller formalism [10] has been used to simulate propagation of polarized light in turbid media. A semi-infinite turbid medium was used in our simulations. A laboratory coordinate system was defined as in Fig. 1. A laser beam of 2 cm in diameter was incident upon the scattering medium at 45 with the z axis. A CCD camera was focused on the sample surface and had an imaging area of 4 · 4 cm2. The simulation process has been described previously [10,12]. Basically, the Stokes vector and the
Incident light
Specular reflection
X
Y
Z Fig. 1. The laboratory coordinate system for the simulation.
local coordinates of each incident photon packet were traced statistically. At each scattering event, the incoming Stokes vector of the photon packet was first transformed into the scattering plane through a rotation operator and then converted by S0 ¼ MðhÞS;
ð1Þ
where S is the Stokes vector before scattering, but it is re-defined in the scattering plane; S 0 is the Stokes vector of the scattered photon; h is the polar scattering angle; and M is the single-scattering Mueller matrix given by the Mie theory. Geometrical computations were performed to decide if a photon intersects an embedded object. The Stokes vectors of all the output-photon packets were transformed to the laboratory coordinate system and then accumulated to obtain the final Stokes vector. The co-polarization and cross-polarization components can be calculated from the Stokes vectors as follows: S0 þ S1 S0 S1 ; H cr ¼ ; 2 2 S0 þ S3 S0 S3 Rco ¼ ; Rcr ¼ ; 2 2
H co ¼
ð2Þ
where Hco and Hcr are co-polarization images and cross-polarization images acquired with horizontal-linearly (H) polarized incident light; Rco and Rcr are co-polarization images and cross-polarization images acquired with right-circularly (R) polarized incident light; S0, S1, S2, and S3 are the four components of the output Stokes vector. The background scattering medium was modeled as a suspension of small spherical particles in water. The particle had a 1.0 lm radius with refractive index of 1.57; its volume concentration was 0.205%. This concentration corresponds to a scattering coefficient of 40 cm1. The calculated anisotropy was 0.91. The absorption property was modeled with added pure dye with absorption coefficient of 0.1 cm1. The wavelength of the incident light was 543 nm. The refractive index of the scattering medium was 1.33. The incident light illuminated the sample surface at an angle of 45. Only the backscattered photons exiting the sample within less than 30 (relative to z axis) were recorded. Therefore, the specular reflected light at air-solution interface did not contribute to the image. A
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a higher absorption coefficient of 1.0 cm1. Each image is displayed with its own color map to enhance the image contrast. The size of each image is 4 · 4 cm2. In Fig. 2, the object center is located at 0.25 cm below the surface. The patterns of the reflection Mueller matrix are different from those reported previously [11,12]. The butterfly-like patterns were averaged out because a broad incident beam was used instead of a pencil beam. The absorption object appears in dark pixels because less light comes from its location. As the object depth increases, the image becomes blurred because the photons passing through the object lose spatial information. The images acquired with a linearly polarized light are very similar to those acquired with circularly polarized light. In addition, the co-polarized and cross-polarized images are similar to nonpolarized images because the absorption object does not change the polarization state of the incident light. Fig. 3(a) shows that imaging contrast decreases as the object depth increases. The image contrast
small object was buried underneath the scattering medium. The object was a parallelepiped with a size of 0.3 · 0.3 · 0.4 cm3 in x, y, and z axis (Fig. 1). Different optical properties were assigned to the object in order to study their effects on the resulting polarization sensitive images.
3. Results Absorption is one of the most often encountered contrast mechanisms in optical imaging. It happens when the object has a different absorption coefficient than the surrounding media. In biomedical imaging, absorption contrast is important for tumor detection because tumor tissues usually have higher blood content which leads to a higher absorption at wavelengths such as 550 nm. Fig. 2 shows the polarization images of a turbid medium with a buried absorption object. The object has the same refractive index (1.33) and scattering coefficient (40 cm1) as the background medium, but
Fig. 2. Polarization imaging of an absorption object. H: horizontal-linearly polarized incident light; R: right-circularly polarized incident light; 0: nonpolarized imaging; co: co-polarized imaging; cr: cross-polarized imaging.
0.040
0.08 Hco Hcr Rco Rcr
0.07
0.05 0.04 0.03
0.025 0.020 0.015
0.02
0.010
0.01
0.005
0.00 0.24 (a)
0.030 Contrast
Contrast
0.06
0.26
0.28 0.30 0.32 Depth (mm)
0.34
Rco-Rcr Hco
0.035
0.000 0.24
0.36 (b)
0.26
0.28 0.30 0.32 Depth (mm)
Fig. 3. Imaging contrast of an absorption object versus the object depths.
0.34
0.36
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was calculated as jIobj Ibj/(Iobj + Ib), where Ib is the background intensity retrieved from pixels outside the object and Iobj is the object intensity retrieved from the object center in the image. Because algebraic operations that were used to derive differential polarized images may produce negative values, those images were scaled to positive territory before contrast calculation. The images were low-pass filtered to smooth the noise. The results indicate that the image contrast obtained with cross-polarized light is similar to that obtained with co-polarized light. It is usually considered that multiply scattered light has randomized polarization state. Therefore, the subtraction of the cross-polarized light from co-polarized light can effectively reduce the multiply scattered light. However for absorption objects, the contrast values obtained with co-polarized light and cross-polarized light are very close to each other, and the differential polarization image obtained with Ico Icr does not improve the contrast (Fig. 3(b)). For linearly polarized incident light, the contrast values for Hco Hcr images were not shown in Fig. 3(b) because the object was not discernable. In general, the image contrast also depends on the absorption coefficient of the object. An object with higher absorption coefficient has higher contrast. Reflective object is another important contrast mechanism in optical imaging. It originates from the refractive index difference between different components inside scattering media. It is the major contrast mechanism for underwater detection of metal objects. Fig. 4 shows the reflection polarization images of a turbid medium with a buried reflection object. A mirror (100% reflection at all object surfaces) was used in the simulation. Light is reflected at the object surface using reflection law. All other parameters are the same as before.
In Fig. 4, the object center is located at 0.30 cm below the surface. The reflective object appears quite differently comparing to the absorption object. The object shows as a bright spot in nonpolarized images (H0 and R0) because of the reflection at the object surface. The linearly polarized light reserves its polarization state after being reflected from the object, while the circularly polarized light transforms its polarization to an orthogonal state. This difference causes the different appearance of the object in images acquired with H-incident and R-incident light. For example, the signal from the object is higher than background signals in co-polarized H-incident image, while it is smaller than background signals in a co-polarized R-incident image. Fig. 5 shows the image contrast at different object depths. In Fig. 5(a), the image obtained with cross-polarized R-incident light (Rcr) has significantly better contrast than all other polarization images. Hcr images had the lowest contrast and the object was not discernable below 0.4 cm object depth. For both R- and H-incident light, because the co-polarized images and cross-polarized images had distinct patterns, the differential polarized images had significantly enhanced contrast (Fig. 5(b)). The image contrast decays almost exponentially with the object depth. The contrast of differential polarization image with R-incident light decreases faster than that with H-incident light for object depths larger than 0.375 cm, where the object surface was at 7· of the mean-free-path. At a larger object depth, the contrast of the differential polarization image with H-incident light (Hco Hcr) is the best. In addition to absorption and reflection, optical scattering is also an important contrast mechanism in optical imaging. It can originate from scattersÕ
Fig. 4. Polarization images of a reflective object. The legends are the same as in Fig. 2.
G. Yao / Optics Communications 241 (2004) 255–261
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1 1.0
Contrast
Contrast
0.8 0.1
0.01 0.20
Hco Hcr Rco Rcr 0.25
(a)
0.6 0.4 0.2
0.30
0.35
0.40
0.45
0.0 0.20
0.50
Depth (mm)
Hco- Hcr Rco- Rcr Rcr 0.25
0.30
0.35
0.40
0.45
0.50
Depth (mm)
(b)
Fig. 5. Imaging contrast of a reflection object versus the object depths.
Fig. 6. Polarization imaging of a scattering object. The legends are the same as in Fig. 2.
density and size heterogeneity. For biomedical applications, there are many studies [14] indicating cancerous tissues have different scattering properties due to cell morphological changes. Fig. 6 shows polarization images obtained from embedded scattering objects. In Fig. 6, the object is
located at 0.25 cm below the surface. The object has the same reflective index (1.33) and absorption coefficient (0.1 cm1) as the background medium, but a higher scattering coefficient of 120 cm1. The object signal in Fig. 6 is higher than the background signal because the backscattered light
0.10
0.075 0.070
0.08 Contrast
0.065 Contrast
Rco - Rcr Rcr
Hco Hcr Rco Rcr
0.060 0.055 0.050
0.06 0.04
0.045 0.040 0.24 (a)
0.26
0.28
0.30
Depth (mm)
0.32
0.34
0.02 0.24
0.36 (b)
0.26
0.28
0.30
Depth (mm)
Fig. 7. Imaging contrast of a scattering object versus the object depths.
0.32
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0.36
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is stronger at the object. Similar to the reflective object, image obtained with cross-polarized R-incident light (Rcr) has better contrast than other polarization images (Fig. 7(a)). It is also better than the differential polarization images (Fig. 7(b)). A difference between a scattering object and a reflective object is that the light from the scattering object can be depolarized because of multiple scattering events. This can explain why the object is not discernable in differential linearly polarized images.
4. Discussion The images obtained with linearly and circularly polarized light are different because light with different polarization states propagates differently in scattering media. Fig. 8 plots the ratio of detected cross-polarized light and co-polarized light as a function of the maximal probing depth. For linearly polarized incident light, the cross-polarized component is less than the co-polarized component at small depths. And they are equal to each other at a large depth where the light polarization has been totally randomized. The total backscattered cross-polarized light is slightly smaller than co-polarized light because the photons backscattered at small depths contribute more to the copolarized signal. For the scattering medium used, there are about 5% more co-polarized photons. 1.2 1.0
Ico/Icr
0.8 0.6 0.4 R - polarized H - polarized
0.2 0.0 0.0
0.5
1.0 Depth (cm)
1.5
2.0
Fig. 8. Ratio of cross-polarized photons (Icr) and co-polarized photons (Ico) versus the maximal probing depth.
For circularly polarized incident light, the curve also shows two distinct regions. This is slightly different from the three regions described before [13] because the cross-polarized photons that are directly backscattered depend on the incident angles. Initially, the contribution from co-polarized light is dominant. Then at large depths (>1.5 cm in the example), there are equal amounts of co-polarized light and cross-polarized light. The fact that co-polarized photons are dominant is often referred to as ‘‘polarization memory’’. In highly forward scattering media (g is close to 1.0), according to Mie scattering, the helicity of a circularly polarized light can only be changed by large angle scattering. The polarization memory effect is the result of multiple small angle forward scattering events [15]. As observed in Fig. 8, the polarization state of a linearly polarized incident light is randomized at a faster rate than that of a circularly polarized incident light. This is because each scattering event rotates the photonÕs reference plane even for small angle forward scatterings. The rotation of the reference frame changes the linear polarization direction. On the other hand, the change of the reference plane does not change the helicity of a circularly polarized light. As polarization detection will have no merit if the output light has randomized polarization states, circularly polarized light can probe deeper objects with better contrast than linearly polarized light. For circularly polarized incident light, the cross-polarization image usually has better contrast than co-polarization image. As shown in Fig. 8, many co-polarized photons from background media may not interact with the object at all. Their contributions reduce the image contrast obtained. Compared with the background medium, pure absorption or scattering objects have no significant effects on the polarization states of the incident photons. This may explain why differential polarization images cannot improve the image contrast for such objects. For a reflective object, the detected photons that are reflected at the object surface experience less scattering events. Therefore, for linearly polarized incident light, it tends to keep its linear polarization states, while for circularly polarized light, it will gain and keep the cross-polarization states. This
G. Yao / Optics Communications 241 (2004) 255–261
is why differential polarization images have better contrast for reflective objects as shown in Fig. 4. 5. Conclusion A Monte Carlo technique was employed to simulate the polarization imaging in scattering media. The contrast values of different embedded objects were compared. The results showed that differential polarization imaging cannot enhance the contrast of pure absorption or scattering objects. But it is useful for reflective objects. The image contrast obtained from cross-polarized R-incident light is better than that from H-incident light in most of the scenarios. Furthermore, different types of objects have different appearance in the polarization sensitive images, which provides a potential way to identify the object types. It must be pointed out that these results are obtained by using Mie scattering model for spherical particles. Different scattering models may produce different results. In addition, other polarization effects, such as birefringence, are not considered in the simulation. Nevertheless, these simulation results can help us understand the effects of object types in polarization imaging, which is important for image interpretation and feature extraction. It will also be helpful for applications that need to image a specific kind of optical target.
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Acknowledgement This work was supported in part by a Research Board Grant from University of Missouri system.
References [1] J.H. Ali, W.B. Wang, P.P. Ho, R.R. Alfano, Opt. Lett. 25 (2000) 1303. [2] G.W. Kattawar, M.J. Rakovic, Appl. Opt. 38 (1999) 6431. [3] S.G. Demos, R.R. Alfano, Appl. Opt. 36 (1997) 150. [4] S.G. Demos, H.B. Radousky, R.R. Alfano, Opt. Express 7 (2000) 23. [5] S.L. Jacques, J.R. Roman, K. Lee, Lasers Sur. Med. 26 (2000) 119. [6] J.S. Baba, J.R. Chung, A.H. DeLaughter, B.D. Cameron, G.L. Cote, J. Biomed. Opt. 7 (2002) 341. [7] S.P. Morgan, I.M. Stockford, Opt. Lett. 28 (2003) 114. [8] V. Sankaran, M.J. Everett, D.J. Maitland, Joseph T. Walsh Jr., Opt. Lett. 24 (1999) 1044. [9] V. Sankaran, J.T. Walsh, D.J. Maitland, J. Biomed. Opt. 7 (2002) 300. [10] G. Yao, L.-H. Wang, Opt. Express 7 (2000) 198. [11] B.D. Cameron, M.J. Rakovic, M. Mehrubeoglu, G.W. Kattawar, S. Rastegar, L.V. Wang, G.L. Cote, Opt. Lett. 23 (1998) 485. [12] S. Bartel, A.H. Hielscher, Appl. Opt. 39 (2000) 1580. [13] I.M. Stockford, S.P. Morgan, P.C.Y. Chang, J.G. Walker, J. Biomed. Opt. 7 (2002) 313. [14] M. Canpolat, J.R. Mourant, Appl. Opt. 40 (2001) 3792. [15] A.D. Kim, M. Moscoso, Opt. Lett. 27 (2002) 1589.
Differential optical polarization imaging in turbid media with different embedded objects Gang Yao
*
Department of Biological Engineering, University of Missouri-Columbia, 1406 E Rollins St. 249 Ag Eng. Bldg., 65211 MO, Columbia, USA Received 19 November 2003; received in revised form 30 June 2004; accepted 12 July 2004
Abstract A Monte Carlo modeling technique was developed to study subsurface polarization imaging of scattering media. Images of embedded absorption, scattering, and reflective objects were simulated with both linearly and circularly polarized incident light. Results indicated that different objects appeared differently in polarization-sensitive images. The effects of object depths on image contrast were also examined. 2004 Elsevier B.V. All rights reserved. Keywords: Polarization; Monte Carlo; Scattering media
1. Introduction Polarization gating has been applied as a simple way to enhance imaging contrast of scattering media [1–7]. This technology has been applied in many different fields such as material corrosion detection [1]; under water detection [2]; and medical imaging [5]. In turbid media, the incident polarization information is lost among multiply scattered photons, while it is partially preserved in weakly scattered light. Because photons from deep media tend to be scattered more than those from superfi*
Tel.: +1-573-8847529; fax: +1-573-8821115. E-mail address: [email protected].
cial depths, polarization techniques can thus be employed to selectively detect light from different depths inside the media [3]. The most often used technique is differential polarization detection, in which the cross-polarized signal is subtracted from co-polarized signal. A linearly polarized light is usually used in such a differential polarization imaging system. However, linearly polarized light and circularly polarized light propagate differently inside scattering media [8,9]. Therefore, different polarized light may provide better contrast in different scattering media. One of the fundamental tasks in polarization imaging is to interpret the image features. Optical contrast can originate from inhomogeneous
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.07.026
256
G. Yao / Optics Communications 241 (2004) 255–261
distributions of absorption, scattering, and reflection properties. In order to correctly interpret image features, it is important to understand how different optical objects manifest themselves in polarization sensitive images. We used a Monte Carlo technique to simulate polarization imaging in turbid media with different embedded objects. We compared images obtained with linearly and circularly polarized incident light. The effectiveness of differential polarization imaging on different types of objects was also studied. 2. Methods
CCD
The propagation of polarized light in turbid media is a complex process. Various parameters, such as the size, shape, and density of the scatterers as well as the polarization state of the incident light, all play important roles. Monte Carlo method with Stokes–Mueller formalism [10] has been used to simulate propagation of polarized light in turbid media. A semi-infinite turbid medium was used in our simulations. A laboratory coordinate system was defined as in Fig. 1. A laser beam of 2 cm in diameter was incident upon the scattering medium at 45 with the z axis. A CCD camera was focused on the sample surface and had an imaging area of 4 · 4 cm2. The simulation process has been described previously [10,12]. Basically, the Stokes vector and the
Incident light
Specular reflection
X
Y
Z Fig. 1. The laboratory coordinate system for the simulation.
local coordinates of each incident photon packet were traced statistically. At each scattering event, the incoming Stokes vector of the photon packet was first transformed into the scattering plane through a rotation operator and then converted by S0 ¼ MðhÞS;
ð1Þ
where S is the Stokes vector before scattering, but it is re-defined in the scattering plane; S 0 is the Stokes vector of the scattered photon; h is the polar scattering angle; and M is the single-scattering Mueller matrix given by the Mie theory. Geometrical computations were performed to decide if a photon intersects an embedded object. The Stokes vectors of all the output-photon packets were transformed to the laboratory coordinate system and then accumulated to obtain the final Stokes vector. The co-polarization and cross-polarization components can be calculated from the Stokes vectors as follows: S0 þ S1 S0 S1 ; H cr ¼ ; 2 2 S0 þ S3 S0 S3 Rco ¼ ; Rcr ¼ ; 2 2
H co ¼
ð2Þ
where Hco and Hcr are co-polarization images and cross-polarization images acquired with horizontal-linearly (H) polarized incident light; Rco and Rcr are co-polarization images and cross-polarization images acquired with right-circularly (R) polarized incident light; S0, S1, S2, and S3 are the four components of the output Stokes vector. The background scattering medium was modeled as a suspension of small spherical particles in water. The particle had a 1.0 lm radius with refractive index of 1.57; its volume concentration was 0.205%. This concentration corresponds to a scattering coefficient of 40 cm1. The calculated anisotropy was 0.91. The absorption property was modeled with added pure dye with absorption coefficient of 0.1 cm1. The wavelength of the incident light was 543 nm. The refractive index of the scattering medium was 1.33. The incident light illuminated the sample surface at an angle of 45. Only the backscattered photons exiting the sample within less than 30 (relative to z axis) were recorded. Therefore, the specular reflected light at air-solution interface did not contribute to the image. A
G. Yao / Optics Communications 241 (2004) 255–261
257
a higher absorption coefficient of 1.0 cm1. Each image is displayed with its own color map to enhance the image contrast. The size of each image is 4 · 4 cm2. In Fig. 2, the object center is located at 0.25 cm below the surface. The patterns of the reflection Mueller matrix are different from those reported previously [11,12]. The butterfly-like patterns were averaged out because a broad incident beam was used instead of a pencil beam. The absorption object appears in dark pixels because less light comes from its location. As the object depth increases, the image becomes blurred because the photons passing through the object lose spatial information. The images acquired with a linearly polarized light are very similar to those acquired with circularly polarized light. In addition, the co-polarized and cross-polarized images are similar to nonpolarized images because the absorption object does not change the polarization state of the incident light. Fig. 3(a) shows that imaging contrast decreases as the object depth increases. The image contrast
small object was buried underneath the scattering medium. The object was a parallelepiped with a size of 0.3 · 0.3 · 0.4 cm3 in x, y, and z axis (Fig. 1). Different optical properties were assigned to the object in order to study their effects on the resulting polarization sensitive images.
3. Results Absorption is one of the most often encountered contrast mechanisms in optical imaging. It happens when the object has a different absorption coefficient than the surrounding media. In biomedical imaging, absorption contrast is important for tumor detection because tumor tissues usually have higher blood content which leads to a higher absorption at wavelengths such as 550 nm. Fig. 2 shows the polarization images of a turbid medium with a buried absorption object. The object has the same refractive index (1.33) and scattering coefficient (40 cm1) as the background medium, but
Fig. 2. Polarization imaging of an absorption object. H: horizontal-linearly polarized incident light; R: right-circularly polarized incident light; 0: nonpolarized imaging; co: co-polarized imaging; cr: cross-polarized imaging.
0.040
0.08 Hco Hcr Rco Rcr
0.07
0.05 0.04 0.03
0.025 0.020 0.015
0.02
0.010
0.01
0.005
0.00 0.24 (a)
0.030 Contrast
Contrast
0.06
0.26
0.28 0.30 0.32 Depth (mm)
0.34
Rco-Rcr Hco
0.035
0.000 0.24
0.36 (b)
0.26
0.28 0.30 0.32 Depth (mm)
Fig. 3. Imaging contrast of an absorption object versus the object depths.
0.34
0.36
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G. Yao / Optics Communications 241 (2004) 255–261
was calculated as jIobj Ibj/(Iobj + Ib), where Ib is the background intensity retrieved from pixels outside the object and Iobj is the object intensity retrieved from the object center in the image. Because algebraic operations that were used to derive differential polarized images may produce negative values, those images were scaled to positive territory before contrast calculation. The images were low-pass filtered to smooth the noise. The results indicate that the image contrast obtained with cross-polarized light is similar to that obtained with co-polarized light. It is usually considered that multiply scattered light has randomized polarization state. Therefore, the subtraction of the cross-polarized light from co-polarized light can effectively reduce the multiply scattered light. However for absorption objects, the contrast values obtained with co-polarized light and cross-polarized light are very close to each other, and the differential polarization image obtained with Ico Icr does not improve the contrast (Fig. 3(b)). For linearly polarized incident light, the contrast values for Hco Hcr images were not shown in Fig. 3(b) because the object was not discernable. In general, the image contrast also depends on the absorption coefficient of the object. An object with higher absorption coefficient has higher contrast. Reflective object is another important contrast mechanism in optical imaging. It originates from the refractive index difference between different components inside scattering media. It is the major contrast mechanism for underwater detection of metal objects. Fig. 4 shows the reflection polarization images of a turbid medium with a buried reflection object. A mirror (100% reflection at all object surfaces) was used in the simulation. Light is reflected at the object surface using reflection law. All other parameters are the same as before.
In Fig. 4, the object center is located at 0.30 cm below the surface. The reflective object appears quite differently comparing to the absorption object. The object shows as a bright spot in nonpolarized images (H0 and R0) because of the reflection at the object surface. The linearly polarized light reserves its polarization state after being reflected from the object, while the circularly polarized light transforms its polarization to an orthogonal state. This difference causes the different appearance of the object in images acquired with H-incident and R-incident light. For example, the signal from the object is higher than background signals in co-polarized H-incident image, while it is smaller than background signals in a co-polarized R-incident image. Fig. 5 shows the image contrast at different object depths. In Fig. 5(a), the image obtained with cross-polarized R-incident light (Rcr) has significantly better contrast than all other polarization images. Hcr images had the lowest contrast and the object was not discernable below 0.4 cm object depth. For both R- and H-incident light, because the co-polarized images and cross-polarized images had distinct patterns, the differential polarized images had significantly enhanced contrast (Fig. 5(b)). The image contrast decays almost exponentially with the object depth. The contrast of differential polarization image with R-incident light decreases faster than that with H-incident light for object depths larger than 0.375 cm, where the object surface was at 7· of the mean-free-path. At a larger object depth, the contrast of the differential polarization image with H-incident light (Hco Hcr) is the best. In addition to absorption and reflection, optical scattering is also an important contrast mechanism in optical imaging. It can originate from scattersÕ
Fig. 4. Polarization images of a reflective object. The legends are the same as in Fig. 2.
G. Yao / Optics Communications 241 (2004) 255–261
259
1 1.0
Contrast
Contrast
0.8 0.1
0.01 0.20
Hco Hcr Rco Rcr 0.25
(a)
0.6 0.4 0.2
0.30
0.35
0.40
0.45
0.0 0.20
0.50
Depth (mm)
Hco- Hcr Rco- Rcr Rcr 0.25
0.30
0.35
0.40
0.45
0.50
Depth (mm)
(b)
Fig. 5. Imaging contrast of a reflection object versus the object depths.
Fig. 6. Polarization imaging of a scattering object. The legends are the same as in Fig. 2.
density and size heterogeneity. For biomedical applications, there are many studies [14] indicating cancerous tissues have different scattering properties due to cell morphological changes. Fig. 6 shows polarization images obtained from embedded scattering objects. In Fig. 6, the object is
located at 0.25 cm below the surface. The object has the same reflective index (1.33) and absorption coefficient (0.1 cm1) as the background medium, but a higher scattering coefficient of 120 cm1. The object signal in Fig. 6 is higher than the background signal because the backscattered light
0.10
0.075 0.070
0.08 Contrast
0.065 Contrast
Rco - Rcr Rcr
Hco Hcr Rco Rcr
0.060 0.055 0.050
0.06 0.04
0.045 0.040 0.24 (a)
0.26
0.28
0.30
Depth (mm)
0.32
0.34
0.02 0.24
0.36 (b)
0.26
0.28
0.30
Depth (mm)
Fig. 7. Imaging contrast of a scattering object versus the object depths.
0.32
0.34
0.36
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is stronger at the object. Similar to the reflective object, image obtained with cross-polarized R-incident light (Rcr) has better contrast than other polarization images (Fig. 7(a)). It is also better than the differential polarization images (Fig. 7(b)). A difference between a scattering object and a reflective object is that the light from the scattering object can be depolarized because of multiple scattering events. This can explain why the object is not discernable in differential linearly polarized images.
4. Discussion The images obtained with linearly and circularly polarized light are different because light with different polarization states propagates differently in scattering media. Fig. 8 plots the ratio of detected cross-polarized light and co-polarized light as a function of the maximal probing depth. For linearly polarized incident light, the cross-polarized component is less than the co-polarized component at small depths. And they are equal to each other at a large depth where the light polarization has been totally randomized. The total backscattered cross-polarized light is slightly smaller than co-polarized light because the photons backscattered at small depths contribute more to the copolarized signal. For the scattering medium used, there are about 5% more co-polarized photons. 1.2 1.0
Ico/Icr
0.8 0.6 0.4 R - polarized H - polarized
0.2 0.0 0.0
0.5
1.0 Depth (cm)
1.5
2.0
Fig. 8. Ratio of cross-polarized photons (Icr) and co-polarized photons (Ico) versus the maximal probing depth.
For circularly polarized incident light, the curve also shows two distinct regions. This is slightly different from the three regions described before [13] because the cross-polarized photons that are directly backscattered depend on the incident angles. Initially, the contribution from co-polarized light is dominant. Then at large depths (>1.5 cm in the example), there are equal amounts of co-polarized light and cross-polarized light. The fact that co-polarized photons are dominant is often referred to as ‘‘polarization memory’’. In highly forward scattering media (g is close to 1.0), according to Mie scattering, the helicity of a circularly polarized light can only be changed by large angle scattering. The polarization memory effect is the result of multiple small angle forward scattering events [15]. As observed in Fig. 8, the polarization state of a linearly polarized incident light is randomized at a faster rate than that of a circularly polarized incident light. This is because each scattering event rotates the photonÕs reference plane even for small angle forward scatterings. The rotation of the reference frame changes the linear polarization direction. On the other hand, the change of the reference plane does not change the helicity of a circularly polarized light. As polarization detection will have no merit if the output light has randomized polarization states, circularly polarized light can probe deeper objects with better contrast than linearly polarized light. For circularly polarized incident light, the cross-polarization image usually has better contrast than co-polarization image. As shown in Fig. 8, many co-polarized photons from background media may not interact with the object at all. Their contributions reduce the image contrast obtained. Compared with the background medium, pure absorption or scattering objects have no significant effects on the polarization states of the incident photons. This may explain why differential polarization images cannot improve the image contrast for such objects. For a reflective object, the detected photons that are reflected at the object surface experience less scattering events. Therefore, for linearly polarized incident light, it tends to keep its linear polarization states, while for circularly polarized light, it will gain and keep the cross-polarization states. This
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is why differential polarization images have better contrast for reflective objects as shown in Fig. 4. 5. Conclusion A Monte Carlo technique was employed to simulate the polarization imaging in scattering media. The contrast values of different embedded objects were compared. The results showed that differential polarization imaging cannot enhance the contrast of pure absorption or scattering objects. But it is useful for reflective objects. The image contrast obtained from cross-polarized R-incident light is better than that from H-incident light in most of the scenarios. Furthermore, different types of objects have different appearance in the polarization sensitive images, which provides a potential way to identify the object types. It must be pointed out that these results are obtained by using Mie scattering model for spherical particles. Different scattering models may produce different results. In addition, other polarization effects, such as birefringence, are not considered in the simulation. Nevertheless, these simulation results can help us understand the effects of object types in polarization imaging, which is important for image interpretation and feature extraction. It will also be helpful for applications that need to image a specific kind of optical target.
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Acknowledgement This work was supported in part by a Research Board Grant from University of Missouri system.
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