1. Introduction

A major advantage of biomedical polarimetry is the relatively minimal instrumentation required for operation compared to other optical and non-optical imaging modalities [1]. Technologies promoting non-contact or minimally invasive detection of pathologies using polarized light has been a major area of interest in the field for this reason. Development of polarimetric endoscopes [2–4] and laparoscopes [5] has emerged as a clinical application area where polarized light can play a large role in improving the standard of care. Incorporating polarized light sensing into these minimally invasive probes can allow for detection of local changes in collagen architecture without the use of exogenous contrast agents [2]. These technologies have shown to be particularly useful in the detection of a variety of cancers [6,7]. Both Mueller and Stokes polarimetric endoscopes exist, but division-of-focal plane Stokes endoscopes are among the simplest to implement as there does not need to be any change in the input polarized light nor an external polarization state analyzer [2–4,6–8].

When performing endoscopic procedures, the operator is limited in the total intensity of light that they can use to avoid excessive heat generation that can lead to undesired tissue damage [9]. Since the upper ceiling of light intensity is limited in “low light” applications such as endoscopy, outcomes of imaging modalities must be able to maintain robustness over a relatively lower signal-to-noise ratio than during ex vivo scenarios. Further, these in vivo polarimetric endoscopic applications are nearly always based on reflected light. Previously, Iannucci et al. described reflectance mode-based division-of-focal-plane (DoFP) Stokes imaging as inherently noisier than transmission mode-based imaging due to the collection of primarily backscattered photons [10]. Therefore, it is important to understand how low SNR affects DoFP Stokes polarimetry outcomes such as DoLP and AoP to aid in potential clinical translation of the technique to endoscopic scenarios.

In 2010, Perkins and Gruev demonstrated theoretical and experimental noise performance of the first three Stokes parameters (${S_0}$, ${S_1}$, ${S_2}$) when acquiring images with a DoFP polarimeter [11]. These methodologies were recently extended to investigate noise propagation through the common polarimetric outcomes of DoLP and AoP [12]. Through theoretical modeling and experimental validation, it was shown that the SNR of DoLP and AoP are dependent on both the incident light intensity and the DoLP of the light itself. However, the experimental validation of these outcomes was performed using idealized optical elements and not biological tissues. As the DoLP of light reflected by a tissue can change based on the underlying collagenous extracellular matrix properties, these findings indicate that signal integrity will depend not only on the optical properties of the incident light, but also of the structural properties of the tissue being imaged.

Therefore, it is essential to understand how noise propagates in outcomes of reflectance mode DoFP Stokes imaging across tissues of different microstructures to accurately interpret DoLP and AoP when imaging biological tissues. In this study, we aimed to evaluate the SNR in DoLP and AoP when imaging collagen hydrogel tissue phantoms of known, but differing, anisotropies across a gradient of incident light intensities. SNR information for polarimetric outcomes were extracted statically and compared to theoretical models of SNR presented previously [12]. SNR was also calculated during dynamic loading of tissue phantoms to assess the ability to discern differing magnitudes of dynamic microstructural realignment via DoLP and AoP at different noise levels. Finally, the relationship between DoLP and AoP signal accuracy and SNR or detected light was determined to elucidate the robustness of these outcomes when imaging different sample microstructures with varying light intensities.

2. Materials and methods

2.1 Tissue phantoms of varying collagen fiber alignment

Methods to produce tissue phantoms of varying collagen fiber alignment were identical to those previously described [10]. Briefly, a mixture of Type I collagen isolated from rat tail tendons and neonatal dermal human fibroblasts was generated and injection molded to create tissue phantoms of known and controlled collagen fiber alignment. Phantoms cast into cruciform molds exhibit (planar) isotropic collagen fiber organization in their centers (“Disorganized”), whereas phantoms cast in rectangular molds develop anisotropic fiber formation along the long axis of the rectangle (“Aligned”). A total of 12 tissue phantoms were generated per microstructure type (i.e., Disorganized vs. Aligned) for imaging in this study.

2.2 Reflectance-mode quantitative polarized light imaging (rQPLI)

The DoFP Stokes polarimetric method used in this study is referred to as reflectance-mode quantitative polarized light imaging (rQPLI). rQPLI methods are identical to those previously described [10]. Briefly, a white LED fiber optic light source passes through a right-handed circular polarizing film and illuminates the sample of interest from 30° above the sample normal. The DoFP polarimeter [13–15] is mounted above and normal to the sample. Polarization imaging data is acquired at 20 frames per second. From the raw polarization imaging data, the first three Stokes parameters (${S_0}$, ${S_1}$, ${S_2}$) are extracted on a pixelwise basis for every frame. From these parameters, two main outcomes are calculated: the degree of linear polarization (DoLP) and the angle of polarization (AoP). The DoLP is a unitless measurement from 0 to 1 that indicates the strength, or anisotropy, of collagen fiber alignment. The AoP provides a measure of the orientation of collagen fibers from 0 to 180°.

2.3 Mechanical testing and variation of incident light intensity

Tissue phantoms of both anisotropies were subjected to simultaneous rQPLI and dynamic mechanical testing on a planar biaxial loading system (TestResources, Shakopee, MN). All phantoms underwent a 0.1 N preload on all arms, were held in position for approximately 5 seconds, and subjected to 10 cycles of uniaxial (Aligned) or strip biaxial (stretched along only one axis of the cruciform shape) (Disorganized) strain to 1.25, 2.5, or 3.75% at 1 Hz.

For each strain amplitude, samples were imaged at each of seven varying light intensities (named R1 to R7, where increasing numbers indicate higher light intensity). Incident light intensity was altered by changing the power of the LED light source to one of seven built-in settings. The increasing gradient in incident light on the sample was validated by measuring light intensity at the plane of the sample using a luxmeter (LX1330B, Dr. Meter) for each of the incident LED light power settings (Fig. 1(A)). Light intensities at the plane of the sample were analyzed by one-way ANOVA where p < 0.05 was interpreted as statistically significant.

 

Fig. 1. Validation of progressively increasing gradient of incident and reflected light. (A) Luxmeter-measured light intensity at the plane of the sample for each light intensity setting. (One-way ANOVA, * indicates p < 0.05; mean ± SD) (B) Photon Transfer Curve (noise variance versus average effective output signal) for calculation of sensor conversion gain. DN = Digital Number. (C) Photon incident on sensor after reflecting from samples. (Two-way ANOVA, Factors: Light Intensity, Microstructure, * indicates p < 0.05; mean ± SD)

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The amount of photons incident on the sensor after reflecting from the tissue of interest was also quantified and validated to be a progressively increasing gradient (Fig. 1(B)-(C)). To calculate number of detected photons, a photon transfer curve was calculated for the sensor to determine the conversion gain, or constant value which converts the number of photons incident on a pixel to the output digital value [12,16]. A wide beam, white LED light source was positioned at a distance of 24” and directed at a smooth reflective viewing screen at a constant 300 Lux at the illumination surface. Sets (n = 11) of 500 images (25 s x 20 fps) were acquired of the illuminated surface with the exposure time varying from 5 ms to 55 ms at 5 ms increments. An additional set of images was taken with no illumination to calculate the dark current. At each exposure time, the average signal and noise variance were calculated, and the average signal minus the dark current was plotted against the noise variance (Fig. 1(B)). Using methods described previously [12,16], the slope of the linear portion of data describing the conversion gain, k, was computed as 0.2586 Digital Number (DN)/e^-. Assuming 100% quantum efficiency of the sensor (1 e^-/photon), this value is equivalent to 0.2586 DN/photon. This assumption was identical to that made in the experimental protocol of Chen et al. [12]. Photons incident on the sensor was then calculated pixelwise within the region of interest (ROI) bounding the sample prior to the start of mechanical loading, which was manually identified after image acquisition. Each pixel’s raw digital value was converted to incident photons by multiplication with the sensor conversion gain, k, and then averaged (Fig. 1(C)). Incident photon measurements were analyzed via two-way ANOVA with fixed effects of tissue microstructure and light intensity where p < 0.05 was statistically significant.

2.4 Experimental SNR evaluation

As described previously [10], qualitative DoLP and AoP color maps were generated to visualize the qualitative effect of noise on signal integrity at each light intensity. At each light intensity, the average signal and noise were calculated as the mean and standard deviation (STD), respectively, for the first 100 frames after preload but before commencement of dynamic testing for both DoLP and AoP (Fig. 2). The ratio of signal (mean) and noise (STD) was then calculated as that pixel’s SNR. This process was repeated pixelwise and then the sample’s SNR was calculated as the average across all pixels within the ROI.

 

Fig. 2. SNR calculation workflow visualization. Signal and noise were calculated over the first 100 frames per pixel. The SNR was then calculated pixelwise and averaged across the ROI for each sample.

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2.5 Theoretical SNR calculations

As explored and validated in Chen et al. [12], derivation of equations for the SNR of DoLP (Eq. (1)) and AoP (Eq. (2)) can be expressed as:

It is important to note that the $\textrm{SN}{\textrm{R}_{\textrm{DoLP}}}$ is dependent on AoP as seen in Eq. (1). When solving for the SNR expressions using the above parameters, the surface theoretical solutions for $\textrm{SN}{\textrm{R}_{\textrm{DoLP}}}$ and $\textrm{SN}{\textrm{R}_{\textrm{AoP}}}$ as a function of I and AoP can be seen in Fig. 3.

 

Fig. 3. Solutions to $\textrm{SN}{\textrm{R}_{\textrm{DoLP}}}$ (Eq. (1)) as a function of AoP and I. Values for I and DoLP were chosen to match experimental parameters of (A) Disorganized phantoms (DoLP = 0.14) and (B) Aligned phantoms (DoLP = 0.28).

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The $\textrm{SN}{\textrm{R}_{\textrm{DoLP}}}$ changes with AoP in a sinusoidal manner that is dependent on the magnitude of the DoLP. However, in the range of DoLP and I values considered in this study (DoLP < 0.3, I < 2000 photons), the $\textrm{SN}{\textrm{R}_{\textrm{DoLP}}}$ does not fluctuate across the entire AoP range more than ∼1 dB (Fig. 3(B)). As our main objective was to evaluate the effect of DoLP on SNR of AoP and DoLP, and this negligible effect of AoP on SNR was demonstrated across the range of interest for this study (DoLP < 0.3, I < 2000 photons), an AoP value of 45$^\circ $ was chosen for simplicity such that Eq. (1) reduces to:

2.6 SNR during dynamic realignment

In addition to the static SNR evaluation, we also aimed to evaluate the sensitivity of rQPLI in detecting dynamic realignment across the range of incident light intensities. During the dynamic loading portion of the mechanical loading protocol, phantoms were subjected to 10 cycles of uniaxial (Aligned) or strip biaxial (Disorganized) strain to 1.25, 2.5, or 3.75% at 1 Hz. Three magnitudes were chosen to induce progressively increasing changes in strain birefringence to the phantoms.

Like the calculation of static SNR, the dynamic SNR was calculated on a pixelwise basis and then averaged across all pixels within the specified ROI. ROIs were defined framewise to account for the dynamically changing sample area during mechanical loading via a custom MATLAB code. The intersection between (1) a user-defined polygon that outlined the sample, and (2) a grayscale threshold that segmented the sample from the background was used to generate the sample-spanning region for each frame.

For each sample, the average change in DoLP or AoP was calculated across all 10 cycles of loading as the “peak-to-peak” DoLP or AoP. This value was normalized to the noise from Section 2.4 to compute a metric of the imposed dynamic “signal” to the overall noise. These “dynamic SNR” values for each QPLI outcome and microstructure type were statistically analyzed using a two-way ANOVA with fixed effects of light intensity and strain amplitude with post hoc Tukey’s HSD where p < 0.05 was statistically significant.

2.7 Relating SNR and illumination to DoLP and AoP measurement accuracy

When using rQPLI to image biological samples in low light conditions, knowing how resilient the outcome measures of DoLP and AoP are to low SNR is important when optimizing imaging conditions. For this reason, the impact of SNR and detected photons on the measurement accuracy of the DoLP and AoP were assessed. We employed a robust statistical pipeline to minimize technical variability and maximize accuracy of predictive outcomes. Linear mixed models (LMM) were developed using JMP (SAS, Cary, NC, USA) to statistically account for random effects associated with sample variability while determining fixed effects of microstructure and light intensity on outcome measures. The model was used to predict the least square means and standard error of baseline DoLP, baseline AoP, SNR DoLP, and SNR AoP for each microstructure and light intensity combination, while accounting for random effects of sample variability. These LMM-predicted means rather than the arithmetic means were used as the input for this analysis. The LMM-predicted baseline DoLP or AoP for each light intensity was then used with the corresponding ground truth to calculate the percent error for that microstructure (Aligned or Disorganized) and light intensity setting (R1-R7). The ground truth for this analysis was defined as the LMM-predicted least square mean baseline DoLP or AoP at R7 for each microstructure type. Based on this definition of ground truth, the percent error for all samples at R7 was assumed to be 0. For each outcome measure and microstructure, the percent error was plotted against the corresponding predicted SNRs for each light intensity level. Additionally, the percent error was plotted against the empirically determined photons detected as shown in Fig. 1(C).

The data were then analyzed using a non-linear regression fit to a single-phase exponential decay model using GraphPad Prism 10 (San Diego, CA, USA). For each regression, the half-life (t_1/2) and goodness of fit (R²) were extracted. The t_1/2 is the technical reciprocal of the curve’s decay constant $\tau $ and represents the amount of the independent variable (i.e., SNR, in dB, or light detected, in photons) that is required to reduce the dependent variable (i.e., percent error) by half.

3. Results

3.1 Validation of light intensity gradient

Generation of a progressively increasing gradient of light at the plane of the sample was verified via direct luxmeter readings, with values ranging between 10.2 ± 0.9 and 104.0 ± 9.4 Lux from R1 to R7 (p < 0.05). (Figure 1(A)) Additionally, a gradient in incident photons on the sensor after sample reflection was verified by calculating the number of detected photons within the region of interest of the sample (p < 0.05); these values ranged between 76.5 ± 17.2 and 1647.8 ± 236.4 photons from R1 to R7 in Disorganized samples and between 94.2 ± 23.1 and 1640.7 ± 139.1 photons from R1 to R7 in Aligned samples. (Figure 1(C)).

3.2 Qualitative evaluation of varied light intensity on QPLI outcomes

Qualitative color maps of DoLP and AoP were generated for phantoms of both microstructures across all light intensities (Fig. 4). At R1, the DoLP signal was completely consumed by noise. Without any a priori knowledge of the underlying microstructure, the DoLP color maps would have been completely indistinguishable from one another. Additionally, the noise seems to have artificially introduced higher values of DoLP into the signal at lower light levels. The expected distribution of DoLP appeared to emerge around R3-4, with the color maps from R4-R7 qualitatively appearing to have the same quality of signal in both microstructure types. In the Aligned case, it seemed as if the signal emerged from the noise at or around R3, earlier than the Disorganized case.

 

Fig. 4. Representative color maps of DoLP and AoP for tissue phantoms of Aligned and Disorganized microstructures at varying incident light intensities.

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Considering AoP values, the noise did not completely consume the signal at R1 to the same degree as the DoLP color maps. In fact, the highly uniform orientation of the Aligned gel emerged through the noise at R1 and was quite clear at R2. This trend was similar in the Disorganized case but took until R3 to reach the same signal integrity as the Aligned case.

3.3 Comparison of theoretical and experimental SNR

Next, considering the quantification of the experimental SNR, DoLP SNR ranged between 3.0 ± 0.2 and 10.3 ± 0.7 dB for R1 to R7 light intensities in Aligned samples and between 3.0 ± 0.2 and 7.0 ± 1.2 dB for R1 to R7 light intensities in Disorganized samples (Fig. 5(A)). AoP SNR ranged between 6.5 ± 0.4 and 15.9 ± 0.2 dB for R1 to R7 in Aligned samples and between 2.7 ± 0.6 and 8.9 ± 1.5 dB for R1 to R7 in Disorganized samples (Fig. 5(B)).

 

Fig. 5. Overlaid theoretical and experimentally determined SNR of (A) DoLP and (B) AoP of tissue phantoms of varying microstructures. Theoretical SNR represents solutions to Eq. (2) & (3) over the following variables: DoLP was input as each microstructure’s “ground truth” (mean DoLP at R7 ± STD), and I was defined as the range of incident photons that was experimentally tested (1–2000 photons; Fig. 1(C)). The experimental light intensity setting (R1-7) was converted to photons (Fig. 1(A) and (B)) and plotted against the expected range of theoretical values; plotted as mean SNR ± STD.

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The baseline DoLP of each microstructure at R7 was the ground truth used to solve Eqs. (2) and (3) (Aligned 0.28 ± 0.10; Disorganized 0.14 ± 0.03). In these theoretical solutions, the higher baseline DoLP of the Aligned phantoms resulted in a larger SNR in both AoP and DoLP across all light intensities. (Fig. 5) Additionally, the magnitude of the SNR in AoP was larger across light intensities than that of their respective DoLP SNR counterparts. Increasing the number of incident photons increased the SNR of all phantoms, regardless of microstructure. There was a high degree of congruence between the experimental results and the theoretical solutions, both in magnitude and trend.

3.4 Dynamic SNR

The average peak-to-peak change in DoLP and AoP over 10 cycles of loading across all pixels within the ROI was normalized to the amount of baseline noise to calculate the “dynamic SNR” for each microstructure, light intensity, and strain magnitude (Fig. 6). This value conceptually represents how large the imposed change in the outcome parameter due to loading was in comparison to the baseline noise at that light intensity. The ability to discern statistically significant differences between strain magnitudes was assessed to determine if there was sufficient signal integrity at each specific light intensity to monitor dynamic realignment changes.

 

Fig. 6. Average peak-to-peak change to noise ratio (dynamic SNR) in (A,B) DoLP and (C,D) AoP for (A,C) Aligned and (B,D) Disorganized tissue phantoms. (Two-way ANOVA, Factors: Light Intensity, Microstructure, * indicates p < 0.05; mean ± SD)

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For the DoLP, there were significant differences in dynamic SNR between strain magnitudes beginning at R3 in the Aligned phantoms and R4 in the Disorganized phantoms. In the AoP, this emergence only occurred at brighter light intensities, with significant differences emerging at R5 for the Aligned phantoms and R6 for the Disorganized phantoms. AoP had larger values for dynamic SNR overall when compared to DoLP. Additionally, in both AoP and DoLP, Aligned phantoms had larger values for dynamic SNR than Disorganized counterparts. Dynamic SNR increased with increasing light intensity for all microstructures and outcomes.

3.5 DoLP and AoP accuracy across tested SNRs

The percent error of DoLP and AoP from baseline was calculated for both tissue phantom microstructure types across all light intensities tested using a linear mixed model to predict the least square means and plotted against their corresponding SNRs (Fig. 7(A)-(B)). The percent error in DoLP decreased from 154.5 ± 8.1% to 3.4 ± 8.1% for Disorganized samples at R1 to R6. Similarly, DoLP percent error decreased from 63.5 ± 8.9% to 0.4 ± 8.9% for Aligned samples at R1 and R6. For AoP, the percent error ranged from 5.9 ± 2.8% to 0.8 ± 2.6% for Disorganized and 4.1 ± 0.8% and 0.2 ± 0.7% for Aligned at R1 and R6, respectively.

 

Fig. 7. Percent error of DoLP and AoP as a function of (A-B) SNR and (E-F) detected photons during rQPLI. (C-D, G-H) Corresponding half-life (t_1/2) in dB (C-D) and photons (G-H) and goodness-of-fit (R²) parameters were extracted for each regression. (A-B) Data points are mean +/- SEM of percent error and SNR generated from linear mixed model (LMM) predictions. (E-F) Data points are mean +/- SEM of percent error mean from LMM and detected photons determined empirically in Fig. 1(C). Lines are best fit results of nonlinear regression to an exponential decay model of the data.

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A nonlinear regression was performed to mathematically describe the relationship between percent error and SNR as a single-phase exponential decay (Fig. 7(A)-(B)). This description reached a goodness of fit (R²) > 0.74 for each microstructure and outcome measure (Fig. 7(C)-(D)). From each regression line, a “half-life” (t_1/2) was extracted to describe the increase of SNR (in dB) required to reduce the error in that particular outcome metric by half (Fig. 7(C)-(D)).Within each outcome measure, the t_1/2 for both microstructures were similar, but was greater overall for the AoP (Aligned = 1.31, Disorganized = 1.45) than DoLP (Aligned = 0.34, Disorganized 0.31).

Percent error of DoLP and AoP was also plotted against the number of detected photons and non-linear regression was performed (Fig. 7(E)-(F)). This analysis was performed via the same pipeline as the comparison between percent error and SNR in Fig. 7(A)-(D). For the description of percent error versus detected photons, the regression reached a R² > 0.92 for each microstructure and outcome measure. A t_1/2 (in photons) describing the amount of additional detected photons required to reduce the percent error by half was also extracted (Fig. 7(G)-(H)). Similar to SNR, the t_1/2 in photons was smaller for DoLP (Aligned = 62.0 photons, Disorganized = 74.3 photons) than AoP (Aligned = 215.9 photons, Disorganized = 518.0 photons).

4. Discussion

In this study, the signal-to-noise ratio of DoLP and AoP during rQPLI was explored through imaging of biological tissue phantoms of varied anisotropies at graded light intensities. Tissues of known, controlled fiber alignment were fabricated and successfully subjected to a range of incident light intensities resulting in an increasing gradient of detected photons on the surface of the polarization sensor after interaction with the tissues.

Based on the SNR equations of both DoLP and AoP derived from error propagation techniques in previous studies [12], we expected SNR to be dependent not only on the incident light intensity, but also the baseline DoLP of the sample. Since the DoLP represents the strength of collagen fiber alignment, this has been shown to be a measurement of the structural anisotropy of a tissue of interest [2]. Therefore, the SNR of these polarization measurements, and the SNR response as a function of light intensity, should vary based a sample’s collagen fiber alignment or structural anisotropy. We confirmed this qualitatively in QPLI color maps (Fig. 4), theoretical solutions to the SNR equations, experimental evaluation of SNR during imaging of biological tissue phantoms (Fig. 5), and in evaluating SNR associated with dynamic realignment (Fig. 6). SNR was substantially higher across all light intensities in both DoLP and AoP when imaging Aligned phantoms compared to Disorganized counterparts.

Further, these data show that AoP may be more resilient to the noise floor at lower light than DoLP. The magnitude of AoP SNR was consistently larger both theoretically and experimentally when comparing different microstructures as well as in evaluation of dynamic SNR. DoLP SNR was roughly the same between Aligned and Disorganized at low light intensities (R1-R4, Figs. 5,6). At lower light levels (e.g., R1), it was impossible to qualitatively distinguish between microstructures based on the strength of alignment (DoLP) (Fig. 4) and the signal was effectively lost below the noise floor. Interestingly, noise from low light imaging may have artificially inflated DoLP values (Fig. 4). Qualitative obscuring was only present at the lowest light intensities (R1-R2) when considering the orientation of fibers (AoP) (Figs. 4,5).

When considering dynamic changes in the AoP (Fig. 6), we expected less of an overall change to the AoP values themselves during dynamic loading than the DoLP. Loading induces strain birefringence within tissue phantoms, and as such this should induce a greater change in DoLP magnitude (which is proportional to the tissue birefringence) than AoP magnitude (which provides information about fiber orientation). Therefore, when evaluating statistically significant difference between strain magnitudes, differences associated with the AoP do not emerge until brighter light intensities even given the higher dynamic SNR.

When using rQPLI to image biological samples, knowing how robust the outcome measures of DoLP and AoP are to error when the SNR is low (e.g., with inherently low light as in endoscopy, imaging disorganized tissues with a low baseline DoLP, etc.) is essential for accurate data interpretation. Further, we wanted to leverage our experimental design to derive a measure that can help inform how imaging conditions must change to improve outcome measure accuracy. By extracting a half-life for the regression curve fit to percent error versus SNR and detected light for each microstructure and outcome measure (Fig. 7), we saw that the increased resilience to noise observed in the AoP translated to an increased t_1/2. As the AoP had a smaller maximum error for both microstructure types over the light range tested (<6%), this increased half-life indicates that AoP requires a greater increase in dB or photons to reduce the error in half, as the error is already low to begin with. This is in contrast to the DoLP, which had a peak error of >150%. Therefore, as the DoLP is more error prone in low light, it has a lower half-life, meaning a smaller increase in SNR or collected photons will have a larger effect on outcome accuracy. However, the differences in half-lives between the microstructure types for each outcome were largely similar. These data indicate that regardless of microstructure, a increase in the SNR by 0.5 dB or 100 photons for DoLP and 1.5 dB or 600 photons for AoP should improve the accuracy of the respective metric by greater than 50%.

There were some assumptions in the evaluation of the theoretical model that should be addressed to contextualize the data. There was a dependence of DoLP SNR on AoP as addressed in Fig. 3. However, this effect was minimal in the range of DoLP values and light intensities probed experimentally. The assumption made to simplify the model may result in the small deviations observed between experimental and theoretical data (Fig. 5). We suspect that these models would further diverge if not considering the AoP of the light incident on the sensor if the DoLP was higher or if brighter light intensities were used. Incorporation of the effects of AoP is simpler in the case of the Aligned phantoms or in biological tissues like tendon, as the variance of fiber orientations is very low. However, this is a non-trivial task when considering the more varied distribution of fiber orientations in the center of the Disorganized phantoms. Finally, in the derivation of the theoretical SNR solutions from Chen et al. [12], the model is assumed to have negligible contribution from sensor readout noise, and instead is dominated by shot noise. This assumption is valid for “moderate” light conditions, greater than a few hundred photons as previously determined [12]. As we observed the largest discrepancy between the theoretical and experimental solutions to SNR of DoLP and AoP when 500 photons or less were detected, it is possible that readout noise is not negligible over this regime leading to this disparity.

Advances in polarization technology may serve to enhance the application areas of QPLI to more low light scenarios. For example, a logarithmic division-of-focal-plane polarimeter with an improved dynamic range has been recently developed and characterized to outperform standard DoFP sensors at low light levels [17]. Additionally, polarization-sensitive event-based sensors have recently been shown to improve the dynamic range over standard DoFP sensors so could emerge as a powerful tool in low light applications [18].

5. Conclusions

Overall, these data demonstrate important features to consider around noise propagation in outcomes when using polarized light to image biological tissues. The SNR of DoLP and AoP are both functions of DoLP, and, subsequently, tissue anisotropy. Because of this dependency, low light imaging of highly aligned tissue like tendon may be possible whereas visualization of the disorganized collagen microstructure of other tissues (e.g., skin, cancerous tissue) might not be visible through noise under the same sensor architecture and conditions of lighting. There is close agreement between theoretical models and experimental data indicating that models may be used to predict SNR in applications outside of those evaluated herein. Further, AoP values appeared to be more resilient to noise than DoLP, so may be of greater use in low light applications like endoscopy, particularly if the dynamic range in the sensor of interest is limited. Finally, we found that a modest increase in SNR or detected photons (0.5 and 1.5 dB or 100 and 600 photons for DoLP and AoP, respectively) should increase the accuracy of each metric by greater than half, a principle that can help guide optimization of imaging conditions when low light is inherently limited.