Cancerous and healthy human colon samples have been analyzed ex-vivo using a multispectral imaging Mueller polarimeter operated in the visible (from 500 to 700 nm) in a backscattering configuration with diffuse light illumination. Three samples of Liberkühn colon adenocarcinomas have been studied: common, mucinous and treated by radiochemotherapy. For each sample, several specific zones have been chosen, based on their visual staging and polarimetric responses, which have been correlated to the histology of the corresponding cuts. The most relevant polarimetric images are those quantifying the depolarization for incident linearly polarized light. The measured depolarization depends on several factors, namely the presence or absence of tumor, its exophytic (budding) or endophytic (penetrating) nature, its thickness (its degree of ulceration) and its level of penetration in deeper layers (submucosa, muscularis externa and serosa). The cellular density, the concentration of stroma, the presence or absence of mucus and the light penetration depth, which increases with wavelength, are also relevant parameters. Our data indicate that the tissues with the lowest and highest depolarizing powers are respectively mucus-free tumoral tissue with high cellular density and healthy serosa, while healthy submucosa, muscularis externa as well as mucinous tumor probably feature intermediate values. Moreover, the specimen coming from a patient treated successfully with radiochemotherapy exhibited a uniform polarimetric response typical of healthy tissue even in the initially pathological zone. These results demonstrate that multi-spectral Mueller imaging can provide useful contrasts to quickly stage human colon cancer ex-vivo and to distinguish between different histological variants of tumor.
©2011 Optical Society of America
Cancer development is characterized by different stages: the uncontrolled cellular growth on healthy tissue first, then the invasion and destruction of underlying tissues and eventually the spread to other locations in the body via the lymph or the blood (metastasis).
Currently the most radical treatment of cancer with a curative purpose is surgery, provided that the disease is detected at early stages. Typically, after surgery the pathologist realizes the histological examination of the surgical sample and defines the staging of the cancer. This is a tedious work which typically involves the examination of many slides with a microscope and requires a lot of time and professional skills. However, proper cancer staging is very important for the choice of the appropriate medical treatment after surgery to increase the patient survival time. Optical techniques, being quite fast and inexpensive, are of particular potential interest to improve the efficiency of the staging procedure.
Generally the interaction of incident light with biological tissues can be described by elastic light scattering and absorption. The absorption and scattering coefficients (µ a and µ s, respectively), the anisotropy factor (g) and the indices of refraction of all tissue components (n i) are the fundamental parameters which determine the optical response of the tissue. Cancer development introduces biochemical and morphological modifications that change these parameters and, consequently, the scattering and absorption properties of the analyzed tissue. Thus, the measurement of optical parameters may allow differentiating the healthy from cancerous zones of the same sample when this difference is not directly observable by conventional imaging techniques, and particularly at early stages of cancer development.
The measurement of the angular distribution of light intensity, spectroscopic diffuse reflectance or degree of polarization of the backscattered or transmitted light can help to distinguish between healthy and abnormal zones of the tissue, both in vivo and ex vivo.
In vitro the optical properties of human healthy and adenomatous colon mucosa/submucosa and muscle layer/chorion were investigated by Wei et al  using integrating sphere techniques. The observed differences in optical properties demonstrate that optical methods can be used for cancer diagnostics.
There is an emerging interest in the applications of polarized light for biomedical diagnostics. Blood glucose sensing with polarized light that is based on the optical activity of glucose was demonstrated [2–4]. Hielscher et al.  showed that the polarimetric analysis of the light backscattered from cell suspensions can be used to distinguish cancerous from healthy cells. Wang and Yang  realized a polarization-sensitive optical coherence tomographic system and demonstrated that this new approach reveals some tissue structures not perceptible with standard optical tomography. Orthogonal state contrast imaging  and Mueller matrix imaging techniques [8,9] were explored as potential diagnostic tools for various dermatological diseases. The spectral fiber-optic system which measured both polarized and unpolarized light transport properties of tissue was used for in vivo detection of cancerous and precancerous lesions of the cervix .
The photons propagating in biological tissues lose their polarization information because of multiple scattering. The vector radiative transfer equation (VRTE) describes the propagation of polarized light in scattering media. Monte Carlo techniques have been widely used to solve VRTE [11–14]. The development of a proper optical model, including the size and concentration of the scatterers, their distribution and refractive indices, the number of different layers, the absorption coefficients and possibly other parameters is an essential step for the numerical modeling of polarized light propagation in biological tissues.
Antonelli et al.  demonstrated that cancerous zones at early stages of development are less depolarizing than surrounding healthy tissue for human colon and proposed an initial model to explain the experimental results using Monte Carlo techniques.
In this paper we demonstrate that multi-spectral Mueller polarimetry imaging may provide useful contrasts to distinguish between the different histological types of human colon cancers and their stages of development. The next section of the paper describes the experimental set-up and the samples used for the measurements. It also briefly describes the anatomy of healthy human colon tissue and the colon cancer development. The results of polarimetric imaging of three ex-vivo samples are presented and discussed in the third section of the manuscript. Section 4 concludes the paper.
2.1 The experimental setup
The multi-spectral imaging Mueller polarimeter used in this study is an upgraded version of the instrument described earlier [16,17]. A halogen lamp is used to illuminate the sample. The polarization of the incident light beam is modulated using a Polarization State Generator (PSG) which consists of a linear polarizer and two nematic liquid crystals with fixed axes and variable retardations. The backscattering light is analyzed with a Polarization State Analyzer (PSA) made of the same elements as the PSG, assembled in the reverse order. The observation window can be changed from 4 to 25cm2 using a system of lenses and the wavelength can be chosen between 500 and 700 nm in steps of 50 nm by using 20 nm bandpass interference filters.
2.2 Healthy colon tissue structure and cancer development
Healthy colon tissue has an ordered microscopic structure. We can distinguish between different tissue layers, starting from the innermost layer: the mucosa, the submucosa, the muscularis externa (formed by circular muscular tissue and longitudinal muscular tissue), the pericolic tissue and the serosa (see Fig. 1 ).
The mucosa itself is composed of two layers: a one-cell layer of epithelial tissue and the lamina propria. The light incident on the colon sample first interacts with the epithelial tissue (about 25 µm thick). The light beam penetrating into the lamina propria is scattered by the sub-cellular particles and by a loose network of fine collagen fibres . A network of capillaries organized in a honeycomb-like structure around the mucosal glands is present in the lamina propria. Hence, the haemoglobin contained in the blood causes the absorption of the light in the visible wavelength range . Between mucosa and submucosa there is a thin layer of smooth muscle named muscularis mucosa .
The submucosa is formed almost entirely by a dense network of collagen fibres that are larger compared to those within mucosa [18–21]. It also contains large blood vessels . Muscularis externa is formed by elongated fibres, organized in two different layers: the circular and longitudinal muscular tissues. The fibres of the former are orthogonal to the colon axis while the fibres of the latter are parallel to this axis. Blood vessels are also present. The light penetrating into the muscularis externa is thus scattered by the fibres and absorbed by the haemoglobin contained in the large blood vessels . Pericolic tissue is formed largely by fat. Finally serosa encloses the colon tube and contains the cells producing a lubricating fluid for the reduction of friction from muscle movement. As pericolic tissue and serosa contain much less haemoglobin than the inner layers, their light absorption coefficient is also much lower. The thickness of the various layers may vary from sample to sample.
Biochemical and morphological modifications of the cells, uncontrolled cellular growth and the development of an inter-cellular substance supporting the abnormal cells growth (the stroma) characterize the development of colon cancer.
The development of colon cancer can be summarized in two steps (see Fig. 2 ). Initially an uncontrolled growth of the epithelial cells occurs, with a consequent increase of the epithelial layer thickness and an invasion of the mucosa layer down to the muscularis mucosa. This first stage of the disease is named carcinoma in situ (Tis). Usually, at this stage the cancer appears as a uniformly exophytic/budding cellular growth with predominantly intraluminal aspect (see Fig. 2b). The abnormal cells are confined to the mucosa layer and muscularis mucosa.
The penetration of abnormal cells in deeper colon layers begins on the second step. The lesion is named T1 when the submucosa is invaded, T2 when the abnormal cells spread into the muscularis externa and T3 when the tumor spreads into the pericolic tissue or serosa. Finally the lesion is named T4 when cancer spreads to other organs or structures.
Generally, the tumor proliferation into deeper colon layers is accompanied by surface ulceration (a decrease of tissue thickness due to the loss of its superficial part) of the cancerous zone. Sometimes the ulceration and the penetration processes do not progress with the same speed. Histological examination of typical surgical samples show that during the second step of cancer growth a strong penetration of abnormal cells in deeper layers may occur, with either deep (Fig. 2c-e) or shallow ulceration (Fig. 2f-h) on the surface.
Carcinomas may also be exophytic/budding with predominantly intraluminal growth or endophytic/ulcerative with predominantly diffusely infiltrative intramural growth. The overlap of both types is quite common. The macroscopic aspects and the microscopic features of colon cancer are influenced by the phase of tumor development at the time of cancer detection. Mueller polarimetric imaging of cancerous colon shows that cancerous zone at the first step of development (Fig. 2b) is less depolarizing than the surrounding healthy tissue . In this paper we demonstrate that the polarimetric signatures of cancer on more advanced stages are more complex.
3. Results and discussion
3.1 General features
In this section we present the results of our studies of three colon samples with different macroscopic and microscopic features. The surgical samples of colon tube are first open along the longitudinal direction and then fixed on flat support.
The experimental Mueller matrices of images of the samples are essentially diagonal, where only the M22, M33 and M44 do not vanish. In other words, the colon tissue behaves as a partial depolarizer. Moreover, for both cancerous and healthy zones, we observe that5], for healthy and cancerous cell suspensions, and by Sankaran et al. , who studied the polarimetric response of a variety of tissues (fat, tendon, arterial wall, myocardium, blood) in transmission configuration. Only the whole blood preserved better the circular polarization of transmitted light in their experiments.
The Mueller matrix images of any given sample taken at 500, 550, 600, 650, 700 nm exhibit depolarization which increases with the wavelength. This general trend is certainly due to the decrease of absorption caused by haemoglobin and, consequently, to the increase of the average number of scattering events suffered by the photons eventually detected.
3.2 The first specimen of colon: Lieberkühn adenocarcinoma
The first sample under study is a 60 mm diameter Lieberkühn adenocarcinoma, which occupied 90% of the colon circumference. The photo of the sample is shown in Fig. 3a . The analyzed region includes the interface between cancerous and healthy tissues (the latter being indicated by letter H). Two macroscopically different zones can be distinguished in the abnormal part. The first zone separating the cancerous part from the healthy one presents an exophytic/budding growth with predominantly intraluminal aspect (indicated with letter B). The second, inner zone is the one presenting an endophytic/ulcerative growth with predominantly intramural aspect (indicated with letter U).
As described earlier, the increase of thickness in zone B is caused by an uncontrolled cellular growth. In this zone the cancerous cells are confined to the most superficial tissue layers. Conversely, in the ulcerated zone U the cancer penetrates into deeper layers destroying the more superficial ones with a consequent reduction of colon wall thickness.
The polarimetric images of this sample (diagonal element M22 of Mueller matrix) taken at different wavelengths are shown in Fig. 3b-f. At 500 and 550 nm both ulcerated and budding cancerous zones depolarize less than the healthy tissue. In contrast, at 600, 650 and 700 nm at first sight the ulcerated zone appears rather similar to the healthy tissue while the exophytic zone remains less depolarizing. However, careful examination of Figs. 3d-f shows that at these wavelengths the depolarization is not homogeneous in the ulcerated zone: part 3 seems almost identical to the healthy zone H while part 2 is less depolarizing and more similar to the part 1 in the exophytic zone B.
Figure 4a is a photo of the same sample, shifted to the left in the field of view. The cancerous part now covers three quarters of the image on the left side. A biopsy was taken in the part A (the region is delimited by the dotted curve), where all the layers above pericolic tissue were intentionally removed. This part is clearly more depolarizing than both the healthy and ulcerated zones for all investigated wavelengths (Fig. 4b-f).
We now correlate these results to the histology of each zone shown in Fig. 5 .
Histological examination of the part 1 of zone B (Fig. 5a) shows that the cancer is confined to the mucosa layer whose thickness has increased up to about 6 mm, while submucosa (SM), circular muscularis (C) and the underlying layers are intact (stage Tis). Within the cancerous layer T we observe an increase of cellular density and vascularisation, with a very low concentration of stroma.
In the part 2 of ulcerated zone U (Fig. 5b) the cancer destroyed the mucosa (M), submucosa (SM), and circular muscularis (C) layers, and penetrated the longitudinal muscularis (L) and pericolic (P) layers (stage T3). We again observe a high cellular density and more vascularisation compared to the healthy zone. The thickness of the cancerous layer T is about 6 mm. The concentration of stroma is low (but not quite as low as in the previous zone).
The histology of the part 3 of ulcerated zone U (Fig. 5c) shows that the cancer has destroyed both the mucosa and submucosa and is now confined to the circular muscularis layer (stage T2). The longitudinal muscularis layer (L) and pericolic tissue (P) are intact. In the cancerous layer T we again observe an increase of cellular density and vascularisation with respect to the healthy zone, and a very low density of stroma.
Finally the histological examination of the part A (Fig. 5d) confirms that mucosa (M), submucosa (SM), circular muscularis (C) and longitudinal muscularis (L) layers were removed. The cancer had spread into a superficial zone of pericolic tissue (P). The thickness of cancerous layer remaining above the serosa after the biopsy is about 1 mm. Again, in this layer the cellular density is increased with respect to normal tissue. Moreover, the concentration of stroma is definitely higher than that observed in the parts 1, 2 and 3.
We interpret these data as follows. First, as the budding zone B is always less depolarizing compared to all other parts, we are naturally led to the conclusion that the cancerous tissue with high cellular density and vascularisation typical of this region depolarizes less than the other tissues, a characteristic which is certainly connected with the enhancement of light scattering due to cell nuclei and blood vessels. This interpretation is further supported by the evolution of polarimetric images with wavelength shown in Fig. 3. In the green part of the spectrum (at 500 and 550 nm) both the B and U zones appear as less depolarizing than healthy tissue, while this is no longer true at 600 nm and above. This trend is certainly due to the increase of the light penetration depth with increasing wavelengths from the green to the red due to the decrease of the absorption by haemoglobin. At 500 and 550 nm the backscattered light has probably predominantly interacted with the most superficial layers, which consist of cancerous tissue over all B and U zones, though with variable thickness. On the other hand, with red light the signal may be dominated by scattering in the cancerous layer only where this layer is sufficiently thick, which is certainly the case in the part 1 (or part 2, to a slightly lesser extent). Conversely, in the regions where the cancerous layer is thin, like in the part 3, this layer is hardly “seen” by the red light, which is backscattered essentially in the muscularis, pericolic and, to a lesser extent, the serosa layers, resulting in a polarimetric response close to that of healthy tissue.
We now discuss the origin of the strong depolarization observed in the part A at all wavelengths. As described above in this part the serosa is covered only by a thin layer of cancerous tissue with some stroma. The influence of this thin tissue is likely to be small at all but the shortest wavelengths, resulting in a predominant contribution of the serosa in the detected backscattered light. Preliminary measurements realized on a sample of serosa alone indeed indicate that this weakly absorbing tissue is very strongly depolarizing one.
To summarize, the development of colon cancer is characterized by increased cellular density, modified morphological characteristics of the cells, increased vascularisation, formation of stroma and destruction of the natural order of tissue. The polarimetric images of a sample of common Liberkühn adenocarcinoma suggest that the polarization response in the abnormal zone is predominantly determined by the thickness of cancerous layer, and secondarily by the nature of the underlying tissues, with a significant increase in depolarization when only the serosa is left beneath a thin layer of cancerous tissue.
3.3 The second specimen of colon: Lieberkühn adenocarcinoma, common and mucinous
The photo of second specimen of colon is shown in Fig. 6a . It was prepared the same way as the first sample and it presents a 40 mm diameter Lieberkühn adenocarcinoma. As in the previous case, healthy (H), budding (B) and endophytic ulcerated (U) zones are readily identified on the photo.
As in the first sample, the budding zone B displays the lowest depolarization at all wavelengths. At 500 and 550 nm the ulcerated zone U looks homogeneous, but, in contrast with the previous case, this zone exhibits a stronger depolarization than that of zone B. At 600, 650 and 700 nm zone U is characterized by a spatially inhomogeneous polarization response: the part 2 depolarizes more than zone B but less than part 3, which behaves essentially as the healthy zone H (Fig. 6e-g) (like the part 3 of the previous sample).
Histological images of these three parts are shown in Fig. 7 . The budding zone (part 1, Fig. 7a) consists of common adenocarcinoma, similar to that of the first sample. The cancer is confined to the mucosa and presents a high cellular density, with a low density of stroma. No mucus is detected and the thickness of cancerous layer is about 7 mm.
In the part 2 of ulcerated zone U (Fig. 5b) the cancer penetrates down to the circular muscularis (C) layer, with a shallow ulceration on the surface. In this case two different variants of cancer are present. On the top we observe a common adenocarcinoma (similar to that of the first sample) confined to the mucosa and again characterized by high cellular density and vascularisation, low stroma density and shallow ulceration on the surface. The average thickness of this top layer T is about 2 mm. On the other hand, the cancer penetrating in deeper layers is a Mucinous adenocarcinoma characterized by the presence of pools of extracellular mucus. This different variant of cancer reaches the circular muscularis and it is about 7 mm thick.
Finally, in the part 3 of the ulcerated zone U, (Fig. 7c) the cancer has destroyed the mucosa (M), the submucosa (SM) and the circular muscularis (C) layers, penetrating the longitudinal muscularis (L). The upper layer of pericolic tissue (P) is invaded (stage T3). The cancerous layer has a thickness of about 3 mm. We observe a high cellular density and larger vascularisation compared to the healthy zone, with a low but visible concentration of stroma. Extracellular mucus is also present, but in smaller quantity compared to the mucinous adenocarcinoma seen in the part 2 of the same zone U.
The origin of the low depolarization, observed in the budding region B, is certainly the same as for the previous sample, due to the similarity of the tissue nature and thickness of the regions B of these samples.
The contrasts seen with green light suggest that the presence of mucus increases the depolarization power of tumoral tissue. Indeed, in the part 2 with the top layer T being free of mucus, but only 2 mm thick, the light probably interacts also with the top part of the mucinous adenocarcinoma, which may account for the larger depolarization with respect to that of part 1. In the part 3 the tumoral layer is 3 mm thick with significant amount of mucus. Provided that green light does not penetrate much below those 3 mm (a reasonable assumption), the parts 2 and 3 feature the same “components” - tissue without and with mucus. As a result, even though their spatial organization is different (superimposed or mixed) these components may eventually account for the similar optical response observed in the parts 2 and 3.
At 600, 650, 700 nm the light beam penetrates into deeper layers and the polarimetric response is determined by the contribution of both cancerous and healthy underlying layers. The response of part 2, which is intermediate between those of zones B and H, is certainly due to the replacement of the mucosa and submucosa by mucus-free and mucinous adenocarcinoma, which feature a depolarizing power intermediate between those of the mucus free cancer found in zone B and the healthy mucosa and submucosa present in zone H.
Finally, the similarity of the responses of the part 3 and zone H may come from a fortuitous compensation of two opposing trends: on the one hand, the replacement of healthy mucosa, submucosa and muscularis by tumoral tissue would decrease the depolarization, but on the other hand, the contribution of the heavily depolarizing pericolic tissue would increase the depolarization, due to the overall decrease of the thickness of the layers above it.
Thus the polarization signatures of the first and second samples exhibit similar trends. In case of low stroma density the polarimetric response is defined by the thickness of cancerous layer, the cellular density and the depth of light penetration. Moreover, multi-spectral analysis allows us to distinguish between the different microscopic structures of the first and the second samples and, in particular, to detect the presence of mucinous adenocarcinoma in the second sample. These results prove that Mueller matrix imaging technique may be sensitive to the nature of the cancer under study.
3.4 The third specimen of colon: adenocarcinoma after radiochemotherapy
The last analyzed sample is a cancerous colon from a patient treated with radio-chemotherapy. The endoscopic investigation before this treatment showed an adenocarcinoma probably penetrating muscularis externa. After the treatment the surgery was performed and the third sample was prepared the same way as the previous two. The photo of the third specimen of colon is shown in Fig. 8a . We observe the presence of an ulcerated zone of size 20 × 30 mm2 (RC on Fig. 8a). In this case the polarimetric images (see Fig. 8b-f) do not provide any contrast between the ulcerated and healthy zones at all wavelengths.
The histology of three cuts taken in the parts 1, 2 and 3 of the RC zone defined in Fig. 8d is presented in Fig. 9 . For all three parts no residual cancerous proliferation is observed, a very encouraging result when correlated with the lack of polarimetric contrast between zone RC and healthy H zone. Fibrous scratches, sometimes calcified, are present within the submucosa and, in certain parts, the muscularis externa.
In the part 1 (Fig. 9a), all layers are intact. In the part 2 (Fig. 9b) the surface ulceration eliminated the mucosa layer. However, due to the fibrous tissue beneath the muscularis the overall thickness of the layers above the pericolic tissue is comparable to that of the part 1. In the part 3 (Fig. 9c) again all layers are intact, with the same overall thickness above the pericolic layer. The similarity of the polarimetric responses of all three parts of zone RC and of the healthy zone H may be explained by assuming that the polarimetric response is prevalently determined by the overall thickness of the layers above the pericolic tissue, which makes sense if all these layers (healthy mucosa, submucosa, muscularis and fibrosis) exhibit similar depolarization powers.
Healthy colon possesses an ordered and complex microscopic structure. The polarimetric response of healthy colon is the sum of contributions of its constituent layers (mucosa, submucosa, muscularis externa, pericolic tissue and serosa).
The proliferation of cancer destroys this natural order by an uncontrolled cellular growth, an increase of cellular density, morphological and biochemical mutations of the cells with possible secretion of mucus and development of an inter-cellular substance (stroma) which supports the cancerous cells growth.
The interaction of polarized light with cancerous and healthy zones is very different. The results of ex-vivo measurements of three surgical colon samples performed with a multi-spectral Mueller matrix imaging polarimeter show that the polarimetric signature of the sample is determined by the cellular density, the thickness of the cancerous layer, the degree of surface ulceration and the light penetration depth. When the thickness of the cancerous layer is large enough, the light interacts predominantly with this layer at all studied wavelengths. When its thickness is smaller, the light (with wavelength 600 nm and longer) penetrates deeper and interacts also with the healthy underlying layers.
Though still preliminary, our data show that multi-spectral Mueller matrix imaging polarimetry may provide enhanced contrasts to differentiate types of cancer (common and mucinous) and their stage of advancement and penetration, which are normally visible only with histological examination. Moreover this technique may also be useful to quickly verify the presence of residual cancer in colon samples treated using radiochemotherapy. Of course this “optical biopsy” is not likely to replace classical histology, but it may provide useful information to better manage the choice of the cut placements to be studied in more detail and thus improve the overall efficiency of the work of pathologists.
References and links
1. H.-J. Wei, D. Xing, J.-J. Lu, H.-M. Gu, G.-Y. Wu, and Y. Jin, “Determination of optical properties of normal and adenomatous human colon tissues in vitro using integrating sphere techniques,” World J. Gastroenterol. 11(16), 2413–2419 (2005). [PubMed]
3. Yu. Lo and T. Yu, “A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal,” Opt. Commun. 259(1), 40–48 (2006). [CrossRef]
5. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Exp.1, 441–453 (1997) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-1-13-441. [CrossRef]
6. G. Yao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography,” Opt. Lett. 24(8), 537–539 (1999). [CrossRef]
7. S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I (1–7) (2008). [CrossRef]
8. M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000). [CrossRef]
9. M. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001). [CrossRef]
10. J. R. Mourant, T. M. Powers, T. J. Bocklage, H. M. Greene, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering for the detection of cancerous and precancerous lesions of the cervix,” Appl. Opt. 48(10), D26–D35 (2009). [CrossRef] [PubMed]
11. S. Bartel and A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering mueller matrix for highly scattering media,” Appl. Opt. 39(10), 1580–1588 (2000). [CrossRef]
13. F. Jaillon and H. Saint-Jalmes, “Description and time reduction of a Monte Carlo code to simulate propagation of polarized light through scattering media,” Appl. Opt. 42(16), 3290–3296 (2003). [CrossRef] [PubMed]
14. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13(12), 4420–4438 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-12-4420. [CrossRef] [PubMed]
15. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18(10), 10200–10208 (2010). [CrossRef] [PubMed]
16. R. Ossikovski, C. Fallet, A. Pierangelo, and A. De Martino, “Experimental implementation and properties of Stokes nondiagonalizable depolarizing Mueller matrices,” Opt. Lett. 34(7), 974–976 (2009). [CrossRef] [PubMed]