2.1.

Stokes Vector

Polarization is the orientation of a light wave, which includes linear, elliptical, and circular states. The polarization state of light is formalized using a $4\times 1$ Stokes vector $\mathbf{S}$ as

Each of the Stokes vector parameters corresponds to the relationship between two orthogonal states of polarization. Using a Cartesian reference frame, an incident beam of light can be defined in a wave equation in terms of horizontal $X$ and vertical $Y$ axis components, while propagating in the $Z$ direction. $S_0$ is the total intensity of light and can be calculated as sum of any two orthogonal components. $S_1$ is the difference in intensity between horizontal and vertical linearly polarized components, $S_2$ is the difference in intensity between linear polarized components $+45\mathrm{deg}$ and $-45\mathrm{deg}$ from the horizontal, and $S_3$ is the difference in intensity between right- and left-hand circular polarized components.

The Stokes parameters can be quantitatively described using six different intensity measurements taken with ideal polarization filters: $I_{\mathrm{H}}$ (horizontal, linear), $I_{\mathrm{V}}$ (vertical, linear), $I_{\mathrm{P}}$ ($+45\mathrm{deg}$, linear), $I_{\mathrm{M}}$ ($-45\mathrm{deg}$, linear), $I_{\mathrm{R}}$ (right-hand circular), and $I_{\mathrm{L}}$ (left-hand circular). These relationships are shown in Eq. (2) which defines the Stokes parameters:

Note that the formalism described here for circular and elliptical polarization is from the perspective of the source. For ease of analysis, the Stokes vector is often normalized such that each Stokes parameter is divided by $S_0$. This brings $S_0$ to 1 while correspondingly reducing the other parameters.

As demonstrated by Collett,¹⁹ the Stokes vector can be derived with only four measurements using a single circular polarizer at different rotations. A linear polarizer followed by a quarter-wave plate, with the polarizer’s transmission axis at 45 deg from the waveplate’s fast axis, can act as a linear polarized filter when receiving light from the polarizer side and a right-hand circular polarized filter when receiving light from the waveplate side. This combined filter can be rotated and flipped successively to act as the above-mentioned $I_V,I_P,I_M$, and $I_R$ filters, and from these measurements the complete Stokes vector can be calculated since the sum of any two orthogonal polarization components are equal as in Eq. (3). This relationship and subsequent derivation of the Stokes vector in four parameters are shown in Eq. (4):

This technique of using a single circular polarizer sequentially can also be applied to using four identical filters and four detectors simultaneously, which underlies the polarization methodology for the probe in this study. The inclusion of four filters eliminates the need for mechanical rotation of a filter and allows for a one-shot measurement as opposed to multiple serial measurements.

We can determine depolarization by calculating the DOP from the Stokes vector, defined through Eq. (5). DOP is a value between $S_0$ and 0, and for a normalized Stokes vector the DOP is a percentage value of uniform polarized content within a given wave packet:

2.2.

Stokes Polarimetry Probe

Measurements in this study were taken by a handheld Stokes polarimetry probe, the design of which has been previously reported.^18,20 Briefly, the probe fires a laser diode with known polarization at the skin and measures the backscattered light that returns.

The laser diode has a peak wavelength of 663 nm (ThorLabs HL6545MG). It is collimated to a diameter of 1 mm, and each measurement is taken through a 1-ms exposure. The incident power on the skin is 63 mW, which is within exposure limitations while also offering a backscattered signal with a detectable intensity. This short exposure also helps to lessen the effect of movement artifacts on the output. For this study, the laser’s initial polarization was set to being linear and right-hand circular. Linear polarization was set using a wire-grid linear polarizer (ThorLabs WP12L-VIS) with the transmission axis set to a reference 0 deg. Circular polarization was set by adding a quarter-waveplate film (Bolder Vision Optik) after the wire-grid polarizer with the fast axis set placed at 45 deg from the reference.

The backscattered light is collected by four photodiodes equipped with film polarizing filters (Bolder Vision Optik) to measure a complete Stokes vector, using the Collett method as described in Sec. 2. The photodiodes (ThorLabs FDS100) have an active area of $3.6\mathrm{mm}\times 3.6\mathrm{mm}$. They are symmetrically placed radially around the source, and oriented parallel to the target plane under the assumption that the backscattered field is uniform for each photodiode. The measurements of the four photodiodes are averaged over the duration of the laser pulse, and then combined to generate a Stokes vector.

The backscattered light that emerges from the tissue forms a polarization speckle field due to the interference within the backscattered partially coherent light. This field expands conically,²¹ and the photodiode detectors are placed far enough away (10 cm) to allow for the collection of a uniform speckle field. The detectors measure the spatial average intensity of this speckle pattern, with the Stokes vector and DOP measurements being derived from this average intensity, which is indicative of the bulk polarization behavior. In as of yet unpublished validation testing, the device demonstrated 1.1% standard error in DOP measurements of ideal polarized light. This is attributed to probe misalignment errors and nonideal circular polarizing film. The probe requires an equal intensity of light to reach each of the photodiodes for accurate polarization measurements. There is also a slight incompatibility between polarizing film intended for monochromatic light and the multispectral profile of a laser diode. These errors were determined to be minor enough to not significantly affect DOP measurements and future iterations of this device will improve upon these errors. In addition, full imaging and spatial analysis of polarization speckle patterns, as opposed to the average measured here, may offer additional information and will be the focus of ongoing study.

The probe head is shown in Fig. 1. The conical front of the probe is placed and sized to ensure that the detectors are fixed 10 cm away from the target site, and the interior is coated in antireflective velvet. This head is connected to a circuit and a computer for data collection. The software is programmed in a National Instruments LabVIEW system.

Fig. 1

(a) Illustration of the Stokes polarimetry probe head components, including (1) conical front piece, (2) laser diode and collimator, (3) parts to hold polarizing film, and (4) photodiodes. (b) Photo of the probe in hand.

2.3.

Skin Phantoms

The rough color phantoms in this study were constructed as per a previously published recipe.²² Roughness was controlled by curing the resin mixture over a metal roughness comparator (Microshurf #334 comparator, Rubert+Co Ltd., Cheadle, United Kingdom) with seven rough surfaces. The root-mean-square roughness $Rq$ values, ranging from 1 to $64\mu \mathrm{m}$, were within the order of previously reported human skin roughness.^23–26 The phantom roughness was confirmed by a WYKO NT2000 optical profilometer (Veeco, Tucson, Arizona) with vertical resolution of $0.05\mu \mathrm{m}$, lateral resolution of $0.5\mu \mathrm{m}$, and standard error of 10%. Each phantom contains seven zones of different surface roughnesses, of which six were tested by the Stokes polarimetry probe: 2.2, 4.5, 9, 18, 34, and $68\mu \mathrm{m}$.

The matrix of the phantoms was constructed using Smooth-On brand MoldMax 10T silicone which came as a viscous resin, accompanied by a curative that causes the silicone to cure at room temperature. Silc-pig silicone pigments (Smooth-On, Inc.) were added as absorbing particles. These liquid pigments came in nine colors and create a homogeneous colored solution when mixed with silicone resin; human skin color can be replicated using the proper combination and concentration of pigments. The reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$ and absorption coefficient ${\mu }_{\mathrm{a}}$ of the phantoms were determined using a red diode laser (B&WTek Flex, 5 mW, $\lambda =663\mathrm{nm}$) according to the integration sphere approach,²⁷ while a ballistic photon detection technique²² and the inverse adding-doubling software from the Oregon Medical Laser Center were applied to calculate the anisotropy $g$ of the phantoms.²⁸ Table 1 shows the properties of the four rough color phantoms P1 through P4 with distinct optical properties. Phantoms P1 and P4 had different ${\mu }_{\mathrm{a}}$ values (0.284 and $0.094{\mathrm{mm}}^{-1}$), although their ${\mu }_{\mathrm{s}}^{\prime }$ values (0.507 and $0.549{\mathrm{mm}}^{-1}$) are similar. There is a good separation in ${\mu }_{\mathrm{s}}^{\prime }$ for P2 and P4 (1.285 and $0.549{\mathrm{cm}}^{-1}$), although their ${\mu }_{\mathrm{a}}$ are indistinguishable ($0.085\pm 0.016$ and $0.094\pm 0.018{\mathrm{cm}}^{-1}$). The ${\mu }_{\mathrm{s}}^{\prime }$ of P3, $0.780{\mathrm{cm}}^{-1}$, was in between the values for P2 and P4. On the other hand, the anisotropy $g$ values for all four phantoms were similar. Table 1 also reports published optical properties for normal skin, the benign lesion SK, BCC, SCC, and MM.^29,30 The phantoms’ absorption is in line with the published values; however, scattering tends to be lower than the published values.

Table 1

Bulk optical properties of phantoms and skin lesions at λ=663  nm.

3.1.

Skin Phantom Measurements

For each of the roughness zones on the skin phantoms, the Stokes polarimetry probe measured the DOP of backscattered light for both linear (${\mathrm{DOP}}_{\mathrm{L}}$) and circular (${\mathrm{DOP}}_{\mathrm{C}}$) input polarizations. These measurements of DOP versus roughness are reported in Fig. 2, including trend lines. Consistent with previous studies of depolarization and roughness,¹⁷ increasing roughness has a stronger depolarizing effect.

Fig. 2

DOP versus phantom roughness with trend lines for (a) linear and (b) circular input polarizations. Trend lines shown for P1, P2, and P4.

Figure 2 shows the relationship between DOP and surface roughness, the trend of which can be modeled with a log function $\mathrm{DOP}=m·\log (R)+C$. The parameters $m$ and $C$ are constants determined by optical properties and $R$ is the surface roughness. The parameter $m$ is indicative of the trendline’s curvature, with higher absolute values indicating a greater slope that represents higher sensitivity to roughness. The parameter $C$ indicates the relative height of the curve and relates to the overall DOP. Comparing the trend lines between the ${\mathrm{DOP}}_{\mathrm{L}}$ and ${\mathrm{DOP}}_{\mathrm{C}}$ results, the average $m$ of the trendlines is $-0.078$ for ${\mathrm{DOP}}_{\mathrm{L}}$ and $-0.098$ for ${\mathrm{DOP}}_{\mathrm{C}}$, suggesting that ${\mathrm{DOP}}_{\mathrm{C}}$ is more sensitive to roughness than ${\mathrm{DOP}}_{\mathrm{L}}$. In addition, circular polarized light is more strongly depolarized by the phantoms than linear polarized light at each roughness as indicated by the mean $C$ of the trend lines, 0.58 for ${\mathrm{DOP}}_{\mathrm{L}}$ and 0.53 for ${\mathrm{DOP}}_{\mathrm{C}}$.

Also by inspecting these trendlines, the curves followed by each phantom appear to differentiate by the parameter $C$. This difference between phantoms is likely due to their different optical properties independent of roughness. This finding reflects polarimetric sensitivity to volume scattering and absorption, which are therefore important to measure as these are the properties that would differ more between cancerous and benign lesions than surface roughness.

3.2.

Clinical Evaluation of Skin Lesions In Vivo

This pilot clinical trial was performed with volunteer patients at the Vancouver General Hospital Skin Care Centre in Vancouver, Canada. The study was approved the University of British Columbia research ethical board, H06-70281. We measured 69 lesions in vivo across 47 patients. Lesions were identified by a dermatologist, and if suspected to be cancerous, their diagnoses were confirmed through histological analysis following a biopsy. Lesions were grouped into seven categories: MM, benign nevus (BN), BCC, seborrheic keratosis (SK), SCC, actinic keratosis (AK), and other benign lesions (OB). The nevi were atypical on observation and biopsied on suspicion of cancer. The OB category included dermatofibroma, lentigo, neurofibroma, cherry angioma, and scar tissue. Each lesion was measured, and the ${\mathrm{DOP}}_{\mathrm{L}}$ and ${\mathrm{DOP}}_{\mathrm{C}}$ were calculated for each.

The five lesions in the OB category were omitted from analysis, as it contains a variety of individual lesion types that should not be analyzed together. In addition, lesions were also excluded from averaging due to device malfunction errors such as the mislabeling of input polarization, or probe misalignment leading to nonuniformity between the four photodiodes. For linear polarized input light, 1 BCC was excluded for this reason. For circular polarized input light, five lesions were excluded: 1 BCC, 1 SK, 2 SCC, and 1 AK. Finally, the probe was constructed take measurements from a normal direction to the lesion surface, and measurements taken from body sites that were not relatively flat, such as the ear and nose, were also excluded. Four data points were excluded for both input polarizations for this reason: 1 BN, 2 BCC, and 1 SCC. This protocol filtered the results down to a total of 59 lesion measurements with linear polarized input light and 55 lesion measurements with circular polarized input light. The final counts are shown in Table 2, which also summarizes the mean and standard error of the collected measurements of all tested lesion types. Figure 3 visualizes this data and to demonstrate the effect of roughness on DOP in these measurements the lesions are sorted in order of mean roughness from smoothest to roughest. The roughness values were determined through a study of lesion roughness using the depolarization ratio.³¹ The report on the thorough analysis of mean surface roughness and skin lesion types is under preparation. For this paper, we used only the relative ranks of lesion roughness, such as MM tending to have the smoothest surface and AK tending to have the roughest among the studied lesion types. These rankings agree with the common notion of roughness among most dermatologists.

Table 2

Clinical trial results summary: each lesion type, the number of cases measured, and mean DOP for both input polarizations.

Fig. 3

Mean DOP measurements for skin lesion types. The order of lesions types is based on the ranking of skin lesion roughness.

The most striking observation in these results is the greater mean ${\mathrm{DOP}}_{\mathrm{L}}$ and ${\mathrm{DOP}}_{\mathrm{C}}$ for melanoma over any other lesions. Noting the standard errors, the measured mean ${\mathrm{DOP}}_{\mathrm{L}}$ for MM ($0.46\pm 0.09$) and BN ($0.31\pm 0.06$) are distinguishable by a small margin, while the measured mean ${\mathrm{DOP}}_{\mathrm{C}}$ for MM ($0.45\pm 0.10$) stands clearly separate from BN ($0.18\pm 0.03$). For both input polarizations, MM is distinguishable from the mean DOP values of all other lesions combined. In clinical practice, melanoma is identified as smoother than other skin lesions, which may be the predominant reason for this difference. Another relevant observation is the pattern across all lesions that the ${\mathrm{DOP}}_{\mathrm{C}}$ is lower than the ${\mathrm{DOP}}_{\mathrm{L}}$, and the difference between the two may communicate a relevant measurement. These findings are the basis for further investigations into the effect of skin lesions on polarized light.

4.1.

Trial Limitations

The Stokes polarimetry probe was designed with compact size and cost-effectiveness in mind. While testing on skin phantoms in a controlled setting yielded reasonable results, clinical testing revealed that a more robust polarimetric measurement system will be required. For example, parallel alignment of the detector plane to the target surface is especially crucial to ensure symmetry among the four free-space detectors, and this is disrupted by probe misalignment due to any possible angled orientation with respect to the lesion. Designing a more rigorous alignment method in the probe or including measurement checks for alignment errors will be necessary. Reducing the impact of error caused by field nonuniformity could potentially be improved using a different four-filter scheme. As proposed by Hsu et al.,³² taking four measurements in equidistant polarization states using elliptical polarizers will better balance against errors.

The skin phantoms measured in this study replicate the roughness and absorption properties of skin lesions and were found to have consistently lower scattering coefficients. This was intentional, as surface roughness has the predominant effect on DOP. Creating phantoms to additionally replicate the scattering properties of skin is a nontrivial task and may be the subject of future study.

The clinical trial presented here was a proof of principle field test of the probe and the potential utility of DOP measurements. While the difference in DOP for melanoma is notable, a low number of melanoma and nevus lesions were measured, and this is too small a sample size to perform a valid statistical significance test. More extensive clinical testing in the future, with a greater number of lesions and an updated device, will be required to validate a clinical claim.

4.2.

Conclusions

The DOP is shown to be a potentially useful diagnostic property to identify melanoma among other types of skin lesions. A one-shot Stokes polarimetry probe was used to analyze the polarimetric properties of skin lesions in vivo by measuring the Stokes parameters of backscattered laser light in both linear and circular initial polarization.

Through trials on rough skin phantoms, it was demonstrated that there is a correlation between backscattered DOP and skin roughness. This correlation exists for both linear and circular input polarization and was found to be a more sensitive metric using circular polarized input. In addition, the optical properties of the skin phantom’s volume such as absorption and scattering allowed for the differentiation of skin phantoms through DOP independent of surface roughness. In a pilot clinical trial where a variety of cancerous and benign skin lesions were tested in vivo, it was found that the DOP for melanoma lesions was measured to be greater than that of other lesions. This separation is greater for circular polarized input light, and it is likely that circular polarized light’s greater sensitivity to surface roughness contributes to this result. In addition, skin lesions appear to have a stronger depolarizing effect on circular polarized light than linear polarized light, as demonstrated by a lower mean DOP for circular polarized input light across all lesion types evaluated.