Design and implementation of a portable colposcope Mueller matrix polarimeter

Abstract. Significance: Mueller matrix polarimetry can provide useful information about the function and structure of the extracellular matrix. A portable and low-cost system could facilitate the clinical assessment of cervical anomalies in low-resource settings. Aim: We introduce a low-cost snapshot Mueller matrix polarimeter that does not require external power, has no moving parts, and can acquire a full Mueller matrix in ∼1  s, to conduct a feasibility study for cervical imaging in the low-resource setting. Approach: A snapshot system based on two sets of Savart plates, a ring illuminator with polarizing elements (generating four polarization states), and one camera is introduced. Stokes vectors are formulated to recover the polarization properties of the sample. Then, using Mueller matrix decomposition, the depolarization and retardance information is extracted. Results: We report the results on 16 healthy individuals (out of 22 patients imaged), whose Pap smear showed no malignant findings from mobile clinics in rural region of Mysore, India. The depolarization and retardance information was in agreement with previous reports. Conclusions: We introduce an imaging system and conducted a feasibility study on healthy individuals. This work could futurely translate into diagnostic applications to provide a quantitative platform in the clinical environment (e.g., cervical cancer screening).

of the cervix that can be used during the cervical screening process to provide feedback by identifying probable pathologic areas. A pilot study introducing the potential clinical use of the device is presented. This work can translate to improving cervical cancer screening by providing a quantitative platform that is low cost and portable, which could in the future increase the diagnostic power of VIA and other screening modalities.

Methods
The snapshot Mueller Matrix polarimeter consists of two different elements: a polarization state generator (PSG) and a polarization state analyzer (PSA). The PSA is designed to have a field of view of 30 mm, operating wavelength of 633 nm, and a magnification of 0.5. In the PSA, Savart plates divide the light into four separate paths, each with intensities proportional to the polarization information of the object (Fig. 1). The four separate channels are recombined by an imaging lens onto the camera creating a spatial interference pattern.
The contrast of these fringe patterns is a function of the modulated transfer function of the optics and the polarization properties of the object (Fig. 2). To recover the polarization properties of the object, different reconstruction methods can be utilized. [45][46][47] In one method, a Fourier transform is performed on the image. Applying spatial filters and an inverse Fourier transform results in an image of the polarization information of the object. The process is described in detail elsewhere. 45,46 A second method, the sliding reconstruction approach, 47 is also used. Both methods require the acquisition of calibrations images: 0 deg and 45 deg linearly polarized beam for the Fourier method and 0 deg linearly polarized, 45 deg linearly polarized, and right circularly polarized for the sliding reconstruction method.  Our system consists of four calcite Savart plates 25 mm × 25 mm × 3.72 mm (United Crystals LLC) with 20/10 surface quality; parallelism less than 3 arc min and AR coating (angle of incidence 0 deg to 30 deg; R avg < 0.5% for wavelengths 500 to 800 nm). A ½ achromatic wave plate (Thorlabs Inc.), a 50 mm EFL imaging lens (MLV 50M1, Thorlabs Inc.), and a highsensitivity USB 3.0 complementary metal oxide semiconductor (CMOS) Cameras with Global Shutter (DCC3240C, Thorlabs Inc.) capable of 60 frames per second at full resolution 1280 pixels × 1024 pixels.
An image of the full system is shown in Fig. 3. Theoretically, this system can resolve spatial frequencies between 70 and 100 lp∕mm on the detector (Fig. 2). These frequencies correspond to features ranging from 20 to 30 μm on the object, which is well within the range needed to resolve the features of interest.
The snapshot system can acquire one full Stokes vector within one snapshot. Since we are interested in obtaining a full Mueller matrix, four different states of input polarizations are necessary. In previous work, three linear states (0 deg, 45 deg, and 90 deg to the reference plane and right circularly polarized) have been utilized and shown to be optimal. 48 The requirement of our system to be portable, computer controllable, and easy to use by non-experts has led to the choice of a preassembled set of light-emitting diode (LED) for our PSG (Fig. 4).
A NeoPixel Ring (Adafruit, New York) with 16 red, green, and blue LED with integrated drivers was used in this system. Four LEDs were chosen on the ring and were paired with a small diffuser and cellphone lenses. Overlapping spot size of 3 cm was then achieved at a distance of about 10 cm for each LED. The LEDs spectral bandwidth at the operating wavelength of 633 nm was 10 nm full width half max (FWHM). The LEDs were connected to an Arduino Mini and a custom driver was developed to control the board through MATLAB (MathWorks, Natick, Massachusetts). Given the small dimension of the Mini, it could be integrated into a cable.  A graphical user interface was designed in MATLAB to control acquisition and illumination. The program operates in two different modes. In focusing mode, all four LEDs are activated at half of their power setting and the camera acquires at 60 frames per second. Once appropriate focus onto the cervix is achieved, the acquisition mode begins by switching off all LEDs. Then, each LED is activated in sequence and after each activation, an image is acquired. Finally, the four images are combined into a stack and saved without any filtering or manipulation. Total acquisition time is about 1 s.
Data acquired with the system are analyzed in post-processing. Mueller matrix images are decomposed with a process illustrated by Lu and Chipman. 35 Retardation, depolarization, attenuation, and orientation images are created.

Image Processing
Data analysis was performed primarily using the Fourier reconstruction method. A second methodology known as sliding reconstruction method was also explored. Both methods are illustrated below.

Fourier reconstruction
In this reconstruction method, the fringe coded image is Fourier transformed 49 and the extracted amplitudes and phases are used to determine the Stokes parameters.
Solving for the FFT of the output signal [Eq. (1)], a set of spatially independent values each carrying polarization information is observed. Many examples of this approach with ideal input Stokes vectors can be found in the literature. 45,46,50,51 Here, we focus on a United States Air Force 1951 (USAF) target. Some of the artifacts associated with the methodology, such as errors in reconstruction in the presence of edges, can be noted in Fig. 5, e.g., S 3 reconstructed shows traces of the target meanwhile S 3 ideal does not.
The intensity I of the interference pattern relates to the incident Stokes vectors according to the following equation: 52 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 3 8 6 (1) Ω is the frequency of the spatial modulation, λ is the wavelength, Δ is the sheer distance of the Savart plates, and f is the focal length of the lens closer to the camera. This image I is shown in Fig. 6(a) together with its two-dimensional Fourier transform [ Fig. 6 The spatial position of the four Stokes element vector is known and depends on the source wavelength, the thickness of the Savart plates, and the focal length of the imaging lens. A filter can be designed to extract the Stokes parameters in the Fourier domain for each state of polarization. This application utilizes three Gaussian filters to extract Stokes vectors S 0 , S 1 , and S 23 , which is applied to the interferogram in Fig. 6(b). The Gaussian filters and effect of the filter bandwidth in relation to the Stokes vector output can be seen in Fig. 7. The filtered image is then inverse Fourier transformed and normalized.
The normalization utilizes two reference images: 0 (S ref0 ) and 45 deg (S ref45 ) linear polarizations. The reference images must undergo the same reconstruction process as previously mentioned. The final Stokes vectors, after reconstruction and normalization, will be as shown in Eqs. 2(a)-2(d).
; t e m p : i n t r a l i n k -; e 0 0 2 b ; 1 1 6 ; 6 8 8 ; t e m p : i n t r a l i n k -; e 0 0 2 c ; 1 1 6 ; 6 5 2 ; t e m p : i n t r a l i n k -; e 0 0 2 d ; 1 1 6 ; 6 1 6 The effect of the filter on the image is shown in Fig. 7.

Sliding reconstruction
A second approach to reconstruction, the sliding reconstruction method, was introduced by Murali 47 and does not rely on Fourier analysis but on direct matching of the interference pattern. The light intensity exiting the Savart plates can be written as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 5 0 7 Oðx; yÞ ¼ S 0 ðx; yÞ where Oðx; yÞ is the intensity of the light, S 0 ðx; yÞ; S 1 ðx; yÞ; S 2 ðx; yÞ; S 3 ðx; yÞ are the Stokes components of the light entering the crystals, and F 0 ðx; yÞ; F 1 ðx; yÞ; F 2 ðx; yÞ; F 3 ðx; yÞ form the first row of the Mueller matrix elements. The Stokes components are estimated over the entire image. A unit cell, a 3 × 3 kernel in this case, is moved by one pixel either along the column or row. To compensate for multiple pixel calculations, the average value of the multiple reconstructions of the Stokes component is taken. Three reference images are needed for this reconstruction method: 0 (S ref0 ), 45 deg (S ref45 ), and right-hand circular (S refRHC ). The reconstruction using the sliding reconstruction method can be observed in Fig. 8.
The Stokes vectors produced using the reconstructions were used to populate the Mueller matrix in order to perform the MMD. This process has been extensively explained elsewhere. 35,42,48

Anisotropic and Ex Vivo Biological Samples
The portable colposcope was first tested with optical elements of known Mueller matrices (air, linear polarizers) as well as an extruded silicone phantom and an ex vivo porcine cervix before being used in a pilot study in Mysore, India. The extruded silicone phantom consisted of a silicone strip with visible striations along the same direction. This sample has known polarimetric properties and is often used for device validation. 53 The material's transparency allows for minimal polarization information loss, due to its low absorption and scattering. The polarimetric system was also tested with an ex vivo paraffin-embedded porcine cervix-the embedding process can be found in detail elsewhere. 42 The porcine cervix has a circumferentially aligned collagen structure around the os, similar to the human cervix, and therefore exhibits similar polarimetric properties. 42 A Mueller matrix system utilized in a previous study was also used to validate our newly developed apparatus. 42

Clinical Deployment
The evaluation of our system on healthy patients study was added to an ongoing screening protocol in a mobile clinic in Mysore, India. Patients were recruited among the ones coming for gynecological evaluation and Papanicolaou (Pap smear) testing. An IRB protocol (IRB-17-0181) was approved by Florida International University Institutional Review Board as well as the Public Health Research Institute of India's Institution Ethics Review Board (2016-20-08-34) and informed consent was obtained from all subjects. A total of 22 study participants were recruited. Eligibility criteria included: (1) age ≥ 18 years, (2) willing to undergo imaging, and (3) having the capacity to undergo informed consent process. Participants were screened for eligibility via chart review at the time of appointment. All eligible women were provided information about cervical cancer, study risks, and benefits. A brief data collection instrument was used to collect sociodemographic and medical information about each participant.
After recruitment, the patients underwent a standard gynecological exam that included a cervical inspection. For this purpose, a speculum was utilized to dilate the vaginal canal and access the cervix. Two strategies were devised for cervical visualization and positioning of the system for imaging. First, the system was mounted on a portable tripod that could be easily moved in front of the patient once the speculum was inserted. Second, the acquisition program was projected onto the screen of an iPhone 6 connected to the tripod. This was done with a commercially available app called Duet. This strategy is similar to having an eyepiece on a colposcope and allowed the system user to see and position the Savart system more efficiently rather than diverting his/her attention to a computer screen. The system was self-powered and required short acquisition time (∼1 s). The overall imaging portion of the study took about 10 min per patient. Little training was required in order to implement device deployment (less than 15 min). Finally, post-imaging, patients were administered the Pap smear.

Results
The error of the portable device was measured by taking the Mueller matrix of air. Figure 9 shows the Mueller matrix image of air obtained in transmission (light source positioned facing the PSA) displaying a typical unit matrix behavior. The total error in these images was well below 5%, but some structural error is perceivable in the images.
The system was then tested with a silicone phantom. The phantom's uniformity makes it a reliable target to validate the MMI system. The phantom was positioned at different orientations with respect to the system's reference frame. Figure 10 displays the extruded silicone phantom shifted 22 deg from the reference frame. On the left [ Fig. 10(a)], the raw image with the interferometric pattern can be seen in gray with the colored region of interest highlighted. The image on the right [ Fig. 10(b)] shows the calculated angles (α), which were in agreement with the positioning of the phantom.
To understand the portable colposcope's response to biological samples, the ex vivo paraffinembedded porcine cervix was imaged. The zone of interest, which is the area between the os and the outer layer of the cervix, was determined by choosing a region of interest in the mid-section of the cervix. The os and the outer cervix have longitudinally aligned collagen and therefore are excluded from the polarimetric evaluation.  Biological samples are strongly depolarizing due to their high scattering and absorbing nature. The polarized light interaction with collagen crosslinks also cause high retardance. Highlighting the zone of interest, we can observe a high level of depolarization (MD ave ¼ 0.96) and retardance (MR ave ¼ 26 deg) exhibited by the porcine cervix [Figs. 11(a)-11(c)], as we had expected. The depolarization is quantified from 0 to 1, going from low to high, respectively. The retardance is measured from 0 deg to 90 deg. Figures 11(d) and 11(e) portray the distribution of depolarization and retardance, respectively, which shows a similar outcome to what has been reported by Chue-Sang et al. 42 for the paraffin-embedded porcine cervix.
The portable colposcope was further tested in a clinical pilot where in vivo human imaging took place. The average age of women imaged was 35 AE 8 years old. Of the 22 patients imaged, six were deemed unsatisfactory due to image quality and therefore have been excluded from the resulting analysis. The remaining 16 patients received clinical assessments summarized in Table 1. Three patient images and corresponding MMDs are reported in Fig. 12. The zone of interest is highlighted superimposed over the raw images (a)-(c). The three cervices show a high level of depolarization (d)-(f) and retardance (g)-(i), as expected of healthy tissue.
The region of interest along the circumferential zone can be seen superimposed in the raw images (Fig. 12). The devices exhibit high depolarization and retardance values, as have been reported for healthy cervix tissue.
A summary of all the 16 patients imaged is displayed in Fig. 13. A region of interest has been selected to derive the depolarization and retardance information. The data have been color-coded in reference with Table 1 to aid in understanding of the polarimetric behavior compared to the clinical evaluation.
The 16 cervices showed a trend of high (median > 0.78) depolarization with the exception of patient 1, which had a polyp. The collagen structure in polyps differs from normal stroma, which was perceived by a lower depolarization value, as has been previously described by others. 54 The retardance (measured in deg) is visualized as high (red) and low (green), with a threshold of 25 deg-approach was first introduced by Rehbinder et al. 39 The retardance values had an overall high trend (median >29 deg), with the exception of patient 13 and 14.

Discussion
We have introduced a new snapshot Mueller matrix polarimeter capable of the fast acquisition of a full Mueller matrix. The imaging was performed in healthy cervices, where there were no cases of dysplasia. The results of the MMD support this clinical evaluation by showing a high   depolarization trend with an average depolarization value of 0.85, where the lowest value, 0.52, is displayed by region of interest with a polyp. This is in accordance with previously reported work, where a polyp changes the collagenous structure and therefore the polarimetric response. 37 The retardance shows an average of 44 deg, which is within the range found in literature for healthy cervices. Some non-uniformity of the retardance data can be due to the heterogeneity of the cervix as well as presence of artifacts such as specular reflection. The ability of MMI to identify differences in the collagen's polarimetric response by detecting the distinct depolarization response between the polyp and other healthy cervices shows how our portable system has the potential to be deployed for use in conjunction with routine cervical screening. The system is fully powered by a laptop computer and can be deployed in conditions where electrical outlets are not readily available. The cost of the system is also relatively low compared to current colposcopes (∼2000), with a limiting factor being the cost of the Savart plates (∼200). It is to be noted, however, that should the modality prove to be useful in sensing dysplastic lesions, higher production levels could be considered, lowering the overall production cost.
Further studies are necessary to truly determine the diagnostic power of this approach. One noted issue with the current system is the size of the illuminator and the ability of all illumination sources to reach the cervix without cutoff from the uterine walls. Six sets of patient images, out of the 22 patients imaged, were discarded due to absence of data on account of poor illumination from one or more polarization states. In older patients and women that have experienced multiple pregnancies, this effect could be more severe limiting the use of our apparatus. To minimize this effect, we are currently redesigning the illuminator to allow for more direct access to the cervix. A second issue noted is the development of artifacts in the Fourier-based analysis due to strong discontinuities in the inverse Fourier transform. When the regions of interest laid around those problematic regions, the second analysis (sliding reconstruction method) was utilized. Finally, another limiting factor was the loss of fringe contrast suffered in regions with high curvature. This, at times, limited the area that could be analyzed, and future work will focus on optimizing the imaging optics so that the entire cervix can be processed. Future studies will also be targeted toward testing the device's ability to detect malignancies in cervical tissues.

Conclusion
A feasibility study was conducted among healthy volunteers in Mysore, India. The results showed accordance with current literature about the depolarization and retardance behavior of healthy cervices. 32,37,39,44 Due to the dependence spatial interference pattern of the current methodology, there are limitations on the deployment and data analysis, as well as the limitation of non-realtime feedback. Recent advancement in polarization technology may lead to new direction of this research. Particularly, new cameras with integrated polarization capability (4-Directional Wire Grid Polarizer Array such as the Sony's IMX250MZR CMOS chip) may allow for fast acquisition of four linear states (horizontal, vertical, 45 deg polarization, and −45 deg polarization). This technology would allow at maximum the creation of a reduced Mueller matrix (i.e., not 4 × 4), requiring other data analysis techniques. In that regard, the proposed Savart method is still seen as superior as it offers the capability of capturing a full Mueller matrix.
In conclusion, we have developed a portable MMI system that can be deployed in the lowresource setting for cervical imaging. We believe that this type of imagery could improve the cervical screening assessment in the low-resource setting beyond the current procedures.

Disclosures
The authors have no relevant financial interests in this article and no potential conflicts of interest to disclose.