1. Introduction

Multispectral polarimetric imaging is a powerful sensing technique that offers multimodal detection capability. This technique collects the 2D spatial intensity of a scene at multiple spectral bands, while also offering broadband polarization images [1]. The spectral and polarization domain of the image unveil important information about the captured target related to its chemical and geometrical nature, respectively. This is highly beneficial in a variety of applications such as biomedical imaging (in-vivo inner tissue characterization for early disease diagnostics) [2–4], atmospheric monitoring (characterizing aerosols for climate modeling) [5], agriculture (distinguishing healthy from contaminated sunflower leaves) [6], and computer vision (object separation) [7].

Many species in nature, including dragonflies [8,9], cephalopods [10], and stomatopods [11], leverage spectral and polarization sensing to acquire evolutionary advantages. Among these examples, the retinal complexity of the mantis shrimps is unrivaled. These marine crustaceans are characterized by their highly sophisticated compound eyes that feature a variety of optical elements to manipulate and detect light. For instance, some of the stomatopods in the Gonodactyloidea and Lysiosquilloidea super-families have up to 16 distinct photoreceptors. Of these, 12 are dedicated to color vision, with spectral sensitivity ranging from deep ultraviolet to far-red [12–14]. Furthermore, they feature a mixture of static and dynamic polarization vision analogous to division of time (DoT) and division of focal plane (DoFP) polarimetry [15,16]. What is even more remarkable is that one of their retinular cells, namely the R-8 cell, acts as an achromatic quarter-wave retarder, allowing sensitivity to circular polarization states [17]. Finally, the stomatopod’s eye offers three rotational degrees of freedom [15,18], of which the torsional rotation enabled the modulation and detection of polarized light with maximum efficiency [15].

Several bio-inspired image sensors have been reported in the literature that incorporate either multispectral imaging, polarization imaging, or both. These include sensors inspired by the cephalopod [19], dragonfly [20–24], and mantis shrimp [25–28]. Tanida et al. proposed a compound three-color imaging system, known as TOMBO, that utilized a micro-lens array and Bayer filters to achieve three color sensing [20,21]. One drawback of this system lies in the use of Bayer filters, which are impacted by signal crosstalk between the different color filters. Also, it is prone to sampling artifacts, demand a larger sensor size, and reduce the spatial resolution due to demosaicing. The techniques in [22–24] introduced minor modifications to the TOMBO (either add more color filters or change the micro-lens design) and suffer from the same drawbacks. Additionally, Refs. [26,28] reported sensors inspired by mantis shrimp. The first incorporated a three-color Foveon sensor together with DoFP polarimetry whereas the second utilized a 3×3 superpixel, which consists of 5 nominal color filters and 4 polarizers with unique orientations. While both techniques provide simultaneous spectral and polarization imaging, they exhibit several shortcomings, including (i) color crosstalk, (ii) limited to 3 color sensing (Foveon); and (iii) spatial sampling artifacts.

We have previously reported a stomatopod-inspired multispectral and polarization (SIMPOL) detector [29] that can overcome main limitations of the current state-of-the-art image sensors. The design was based on alternating layers of organic photovoltaic (OPV) cells and folded retarders (FRs) cascaded in series along the same optical axis. This scheme leverages the OPV’s semitransparency and anisotropic absorption to tandem polarimetric and spectral sensing. Moreover, the design exploited the excellent chromatic retardation control of PRs to enable a highly versatile color filtering approach. This enabled any arbitrary spectral profile to be absorbed by the polarization-sensitive OPV (P-OPV) detectors through polarization interference, a mechanism analogous to folded Solc filters. By cascading multiple OPV detectors and FR films along the same optical axis, all polarimetric and spectral information can be acquired simultaneously in a single pixel. This obviates the need for a super-pixel or a large FPA to accommodate all spectral and polarization information and avoids errors due to spatial misregistration and demosaicing. Additionally, since multiple OPV layers can be easily stacked in tandem, this enables more than 3 colors to be detected. Finally, the FR films can provide a narrow-band spectral profile with controllable sidelobe levels and free spectral range (FSR). This enabled the suppression of color crosstalk.

In this paper, we build on our previous work demonstrating a more compact detector architecture system with full Stokes polarimetry and enhanced radiometric performance. This is achieved by introducing two fundamental modifications to the design. First, we focus on miniaturizing the sensor size by employing liquid crystal polymer (LCP) multi-twist retarders (MTRs) in place of the FRs. These MTRs can also provide chromatic retardation control while offering two additional advantages. The thickness of the twisted liquid crystal (LC) is typically a few microns thick; approximately two orders thinner than the FRs used in the prior system [29]. For multiple stacked layers, this makes a substantial difference in device size. Moreover, MTRs offer a simple, yet flexible fabrication process in that multiple LCP layers are aligned automatically based on a single alignment layer. This results in a monolithic film with a continuously varying optic axis. Secondly, the system radiometric performance is improved and full Stokes polarimetry is achieved by replacing one of the P-OPV layers with a rotating achromatic quarter-wave plate (AQWP). Despite a loss of the snapshot advantage, the introduction of the AQWP enables full polarimetric sensing and results in either more light throughput into the last detector or more spectral channels.

Experimental results demonstrate the sensor’s ability to detect full Stokes polarimetry, with an average root mean square (RMS) error of 2.16%, and to detect three distinct color channels, with a full width at half maximum (FWHM) spectral resolution up to 81 nm, all acquired simultaneously along the same optical axis. The signal-to-noise ratio (SNR) of the OPV devices are also provided with values ranging from 34 to 45 dB.

2. Operating principle

The LC-based SIMPOL sensor resembles the structural and functional units of the mantis shrimp’s compound eyes and how these organisms manipulate and detect light, both spectrally and polarimetrically. Both structures incorporate stacked spectral and polarization elements that alternates, in series, along the same optical axis. Additionally, both structures leverage depth-based sensing to extract multiple polarimetric and spectral information sequentially. Figure 1 provides a side-by-side comparison between the mantis shrimp visual system and the LC-based SIMPOL sensor. A picture of the peacock mantis shrimp, is provided in Fig. 1(a), displaying the capability of these species to rotate their eyes in all three degrees of freedom; pitch (up-down), yaw (side-to-side), and torsion (rotation about the visual axis). The yaw and pitch eye’s movements have been previously shown to be useful in gaze stabilization and enhancing the field of view [18]. More importantly, the torsional rotation enables mantis shrimps to modulate and detect polarized light with maximum efficiency [15]. Figure 1(b) illustrates an anterior view of the stomatopod’s apposition eye. The eye is divided into three main sections: the ventral hemisphere (VH), dorsal hemisphere (DH), and a narrow layer called the mid-band (MB), consisting of 6 distinct rows [30]. Each section comprises thousands of optical units known as ommatidia, which differ in types, specializations, and functionalities, particularly those located in the MB. For instance, some ommatidia are sensitive to linearly or circularly polarized light, while others are not [16]. Some are sensitive to red or far-red light while others are sensitive to deep-blue or ultraviolet light [31]. As an example, Fig. 1(c) displays a single ommatidium from row 3 of the MB of Odontodactylus Scyllarus. It consists of three primary parts; (i) a cornea, (ii) a crystalline cone, and (iii) a receptor region (Rhabdom) that guides light to the photoreceptor cells. As light enters the rhabdom, it traverses a series of vertically stacked photo-sensitive ratinular cells (R1-8). In this particular example, the R8 cell contains pigments that are sensitive to 301 nm light [14], the distally placed (shallower) R1-7 cells contain color filter with peak wavelengths around 610 nm [31], and the proximally placed (deeper) R1-7 cells are sensitive to 660 nm [31]. In the entire MB section, there exist 12 unique photoreceptors, with color sensitivity spanning UV to far-red. These receptors are equally divided across the first 4 rows of the MB layer. The last 2 rows of the MB are also known to be sensitive to circularly polarized light due to the R8 cell acting like an AQWP [17]. It is also worth noting that the rhabdom contains stacks of well-ordered microvilli in alternating orthogonal bands [15]. These are responsible for the mantis shrimp’s polarization vision. Light entering the cornea is focused via the crystalline cone into the rhabdom and is chromatically filtered and polarized by the vertically-stacked R-cells in a sequential manner.

 

Fig. 1. (a) Image of a mantis shrimp. Photo Credit: Michael Bok, Lund University. (b) Anterior view of the stomatopods eye. [29] (c) A single ommatidium structure, (d) The LC-based SIMPOL sensor structure. (e) Structure of a single multi-twist retarder

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It should be noted that a single ommatidium of the mantis shrimp eyes can only detect a maximum of three color channels. Additionally, some ommatidia are polarization-sensitive, while others are not. Conversely, a single-pixel (ommatidium) of our SIMPOL sensor can detect as many color channels as desired, only limited by the amount of light incident on the last detector layer in the stack. For a given application that specifies a minimum SNR, one can determine the number of color channels that can be detected in a single pixel. Additionally, unlike the ommatidia of mantis shrimp, all pixels in the SIMPOL sensor can be made polarization-sensitive. This results in an efficient compact sensor design, as opposed to DoFP-based sensors, Bayer-based sensors, or a combination of both.

Figure 1(d) depicts the structure of the LC-based SIMPOL sensor. A rotating AQWP modulator is placed at the entrance of the pixel, followed by 4 P-OPV cells (OPV0 – OPV3) that alternate with 3 LC-based MTR units (MTR1 – MTR3) in series. The OPVs’ anisotropy is obtained by aligning the polymer backbone chains uniaxially along the plane of the film [32,33]. In the current configuration of Fig. 1(d), all OPV cells have their transmission axes parallel to the x-axis. OPV0 is used exclusively for polarization sensing, while OPV1 – OPV3 are dedicated for spectral sensing. We leveraged the torsional eye rotation of the mantis shrimp, together with an AQWP-like R8 cell, to enable full Stokes polarimetry. As shown in Fig. 1(d), the polarization states of light are first modulated by a rotating AQWP and then analyzed and detected simultaneously by OPV0. This is analogous, in principle, to a DoT rotating retarder, fixed analyzer polarimeter. Depending on the transmittance and absorptance properties of OPV0, part of the light is absorbed, while the rest is transmitted (assuming negligible OPV reflectance). The transmitted polarized light traverses the first MTR. As illustrated in the inset of Fig. 1(e), each MTR unit consists of M stacked liquid crystal polymer (LCP) layers of a thickness ($d$) and fast axis ($\phi $). The LCP films’ fast axes are controlled automatically using a single alignment layer, in that one layer is self-aligned based on the pattern of the previous layer [34]. These MTRs are used to rotate the transmitted polarized light chromatically [35–38]. As light traverses the MTR, the light’s polarization state for in-band light is rotated by 90°, enabling OPV1 to absorb it, while out-of-band light undergoes no rotation, enabling OPV1 to transmit it to subsequent OPV detectors. Through this spectrally dependent polarization interference, the OPV can preferentially absorb specific colors. This process is repeated within a tandem series of OPVs and MTRs, with different OPVs optimally tuned to absorb different wavelengths. The center-band wavelength and the absorbed spectral profile can be controlled by optimizing 2 $M$+1 degrees of freedom. These parameters include M twist angles ($\phi $), M layer thicknesses ($d$), and the start angle (${\phi _0}$) that is set by the uniform alignment layer as shown in 1 (e). A comparison between our LC-based SIMPOL sensor and the ommatidia of the mantis shrimp reveals several structural and functional similarities; including: (1) the OPV polymer chains are analogous to the microvilli, (2) the MTRs are analogous to the pigmented cells, (3) the AQWP is analogous to the R8 cell, (4) the torsional rotation of the mantis shrimp eye is analogous to the rotation of the AQWP (5) OPV1 – OPV3 are analogous to the R-cells and (6) both structures consist of stacked elements.. All these features are efficiently realized in a single-pixel sensor structure.

3. Theoretical system model

Here we explore the LC-based SIMPOL design tradespace in terms of its polarimetric, spectral, and radiometric performances. Complete derivations of the mathematical equations are also presented in Supplement 1.

3.1 Polarimetric performance

Referring to Fig. 1(d), a broadband light passes through an AQWP, with fast axis oriented at an azimuth angle denoted by $\theta$, and is then partially absorbed by OPV0. The intensity detected by OPV0 is given by

A simulation was conducted to visualize the Stokes parameters’ modulation path across the Poincaré sphere, which represents a 3-D polarization space. Simulation parameters included an AQWP’s azimuth angle sampled from $0^\circ $ to $180^\circ $ in $3^\circ $ increment and two different OPV models: (i) OPV with ideal diattenuation i.e. ${D_{A0}} = 1$ and (ii) OPV with non-ideal diattenuation ${D_{A0}} = 0.78$. We also assumed on-axis indecent light, and negligible crosstalk polarization terms. The simulation’s results are depicted in Fig. 2. Although the Stokes parameters of the two OPV models trace similar paths along the Poincaré sphere, the polarization efficiency of the non-ideal OPV decreased by a factor of 0.78 compared to the ideal OPV detector. Additionally, notice that the use of AQWP as the polarization modulator is optimal for ${S_1}$ and ${S_3}$ parameters. Equal modulation amplitudes of the Stokes parameters can be obtained using a modulator with a retardance of 127$^\circ $ instead of 90$^\circ $ [39]. The Stokes parameters in Eq. (1) can be reconstructed using a minimum of four different AQWP orientations by solving four simultaneous equations. However, this will not yield an accurate reconstruction in practice, due to the presence of crosstalk polarization terms in addition to off-axis light which results in a change to ${D_{A0}}$. Thus, to fully reconstruct the Stokes parameters, one can apply either the data reduction matrix (DRM) method [40] to multiple intensity recordings at different azimuth angles, or utilize Fourier analyses technique to the polarimetric signals [41].

 

Fig. 2. Modulation of the Stokes parameters in the Poincaré Sphere for ideal OPV (blue line, red stars) and non-ideal OPV (yellow line, green squares).

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3.2 Spectral performance

Next, we analyze the spectral performance of the LC-based SIMPOL sensor. The portion of the transmitted light through OPV0 enters the multispectral sensor which consists of three stacked MTR-OPV pairs. Each MTR enables specific spectral band to be absorbed by its OPV pair through spectrally-dependent polarization rotation. Assuming negligible polarimetric crosstalk coefficients (see Eq. S3 in Supplement 1), the fraction of optical power absorbed by the n ^th OPV can be expressed as

It was shown in [36,37] that a Solc filter’s spectral response, given $N$ retarders, could be closely emulated by an MTR with $M = 2N - 1$ LCP layers. This assumes that the Solc’s retarder parameters (layer thicknesses and fast axis orientations) are converted to their equivalent MTR parameters (${d_m}$ and ${\phi _m}$). The design we implemented here is based on alternating achiral-chiral LCP layers [37]. The odd layers are all achiral (uniaxial), exhibiting no twist angle $({\phi _{m,odd}} = 0)$ and are relatively thick in order to provide the required birefringence for the desired color filtering. Conversely, the even layers are all chiral, exhibiting a finite twist angle, and are relatively thin. Based on this design, we simulated three color filters MTR1, MTR2, and MTR3, that were configured to optimally absorb light at wavelengths 454 nm (blue), 532 nm (green), and 635 nm (red), respectively. The design parameters for these colors are provided in Table S1 in Supplement 1. Both the blue and red filters consisted of 3 LCP layers and matched the 2 layers of the Solc fold and Solc fan configurations, respectively. Conversely, the green filter comprised 5 LCP layers and matched the 3 layers of the Solc fold configuration.

Figure 3(a) depicts the simulated individual transmission spectra of MTR1, MTR2, and MTR3 when they are placed between two ideal linear polarizers. MTR1 and MTR2 were placed between two crossed polarizers whereas MTR3 was placed between two parallel polarizers. The FWHM spectral resolution of MTR1, MTR2, and MTR3 was calculated to be 65 nm, 118 nm, and 136 nm, respectively. The FWHM can be further reduced by increasing the number of LCP layers within a given MTR filter.

 

Fig. 3. (a) Modeled transmission spectra of the MTR, (b,c) Modeled absorption spectra of P-OPV cells with different diattenuation values, (d-f) The spectral contrast of OPV1, OPV2 and OPV3 for different diattenuation and T_x values.

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Different simulations of the tandem SIMPOL configuration are depicted in Fig. 3(b, c) showcasing the effect of varying the OPV cells’ transmission diattenuation (${D_T}$), defined in Eq. (S7) in Supplement 1. In particular, we considered 6 different configurations. The first configuration represents the ideal case where all the OPVs in the stack have an ideal diattenuation of 1. The remaining 5 configurations consider non-ideal OPV cells with uniform diattenuation of 0.9 (dashed lines) and 0.8 (dotted lines) in Fig. 3(b), and 0.6 (solid lines), 0.4 (dashed lines) and 0.2 (dotted lines) in Fig. 3(c). We observe three notable features of the SIMPOL sensor, in which two features are intrinsic to the device’s tandem nature. First, we notice a tapering amplitude effect caused by the non-ideal transmission characteristics of the OPV cells. This effect limits the number of detected spectral bands within a single SIMPOL device. Second, we notice a relative decrease in the FWHM spectral resolution of the detected spectral bands. This effect is also inherent to the tandem nature of the device and can be advantageous for some applications. Lastly, we notice that the filters’ contrast of the three MTRs decreases by decreasing the OPVs’ diattenuation. Here, we define the filter’s contrast as follows:

In addition to reduced color contrast, spectral crosstalk increases in each OPV cell. Thus, it is desirable to use OPV cells with high diattenuation to enable better color isolation and improved contrast. We calculated the filter’s contrast for each OPV cell given various combinations of ${T_x}$ and ${D_T}$ as provided in Fig. 3(d-f). To achieve a filter contrast greater than 50% across all the OPV cells, one may design the cells to have ${T_x} = 0.8$ and ${D_T} = 0.8$.

These simulation results demonstrate the power of chromatic retardation control in enabling a versatile spectral detection scheme. Similar to the FR design in our previous work [29], the MTR can be integrated with OPV cells to achieve multispectral sensing in a stacked detector device. Although the MTR requires more layers than the Solc to achieve a similar spectral performance, its total physical thickness remains considerably smaller than its equivalent Solc (almost by a factor of 100) enabling a more compact design. This is because the MTR exhibits stronger birefringence as per Eq. (S12) in Supplement 1 compared to a typical retarder made from polymer material (plastic), which in turn enables a smaller thickness while providing a similar retardation control.

3.3 Radiometric performance

We theoretically quantified the signal-to-noise ratio (SNR) of the LC-based SIMPOL sensor. To emulate our experimental setup, the output photocurrent of each OPV cell was modelled using a switched-integrator circuit (Burr-Brown ACF2101), as shown in Fig. 4(a). This circuit served to convert an input current to an output voltage. Additionally, we assumed each OPV operated in photovoltaic mode (under 0 V bias) and exhibited a responsivity as illustrated in Fig. 4(b).

 

Fig. 4. (a) OPV and ACF2101 circuit models, and (b) Modeled OPV responsivity

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The generated photocurrent from each OPV can be expressed as

For the noise analysis, we assumed that the device was dominated by two fundamental noise sources, namely Johnson-Nyquist and shot noise (including both signal and dark current contributions). Similar to the signal photocurrent, the shot noise can be calculated at the output of the integrator circuit as follows

In addition to the detector’s intrinsic shot noise, the Johnson noise from the ACF2101 switched integrator is given by

The SNR (in decibel) can then be calculated as

Simulations were then carried out with all parameters configured to match the experimental configurations. The parameters used in the simulation included $F = 1,{A_{\det }} = 0.25\,\textrm{c}{\textrm{m}^\textrm{2}},$ a dark current density of ${10^{ - 7}}\,\textrm{mA/c}{\textrm{m}^\textrm{2}}\,({i_{dark}} = 0.25 \times {10^{ - 10}}\,\textrm{A}),$ a modeled responsivity as displayed in Fig. 4(b), a detector’s terminal capacitance ${C_t} = 50\textrm{pF}$(estimated from the dielectric constants of the polymers used to fabricate our OPV devices [44]), and a shunt resistance ${R_{sh}} = 400\textrm{k}\Omega, \tau = 16.7\,\textrm{ms},{C_f} = 100\,\textrm{pF},\,\,{R_f} = 167\,\textrm{M}\Omega,\,\Delta f = 30\textrm{Hz},\,\,\textrm{and}$ $T = 298\textrm{K}\textrm{.}$ In addition, the RMS noise of ${v_{\textrm{op - amp}}}\,\textrm{and }{v_q}$ were set to $({1 + {{{C_t}} / {{C_f}}}} )\times 10\mu \textrm{V}$ and $10\mu \textrm{V}$, respectively, which are consistent with the theoretical values provided in [45].

We first modeled the noise performance by varying the incident optical flux from $1 \times {10^{ - 9}}\,\textrm{to}\,\,\textrm{2}\textrm{.5} \times \textrm{1}{\textrm{0}^3}\,\textrm{mA/c}{\textrm{m}^\textrm{2}}.$ Fig. 5(a) depicts the thermal noise and shot noise contributions for each OPV cell. The thermal noise dominated the system up until $2.3 \times {10^{ - 4}}\textrm{mA/c}{\textrm{m}^\textrm{2}}$ with a constant value of $35\mu \textrm{V}$ independent of the incident optical power. Further increase in the optical flux resulted in linear increase in the shot noise forming a lower boundary limit to the SNR. Figure 5(b) depicts the signal and total noise for each OPV cell. The OPV signal voltage increased linearly with the input optical flux until approximately a value of $\textrm{1}{\textrm{0}^{ - 2}}\,\textrm{mW/c}{\textrm{m}^\textrm{2}}$, where it saturates due to reaching the full well capacity of the integrator circuit. Meanwhile, the shot noise kept increasing beyond the signal saturation value, which consequently degraded the SNR. The SNR performance of the LC-based SIMPOL system is depicted in Fig. 5(c). The maximum SNR was reached at the saturation point with a value of 98.9 dB. This value defines the dynamic range of the system. Beyond the saturation point the SNR degraded as the input optical flux increased. Note that in order to enable higher incident optical power $({\Phi > \,\textrm{1}{\textrm{0}^{ - 2}}\,\textrm{mW/c}{\textrm{m}^\textrm{2}}} )$ without saturation, one can adjust the circuit parameters, including the integration time and feedback capacitance.

 

Fig. 5. (a) Thermal and shot nosie modeling of OPV0-3 at different optical power density, (b) signal and total noise levels for OPV0-3 versus optical power density. Solid lines represent signal levels, dashed lines represent total noise levels, with black, blue, green and red colors representing OPV0, OPV1, OPV2 and OPV3, respectively. (c) SNR performance of OPV0-3 versus optical power density.

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4. Device fabrication and experimental results

Based on the MTR simulations given in Fig. 3(a), we fabricated three MTR filters with details on the fabrication methods (Fig. S1), design parameters (Table S2, S3) and experimental results (Fig. S2) provided in Section 4 of Supplement 1.

Additionally, the fabricated OPV devices for the LC-based SIMPOL were based on an inverted bulk heterojunction (BHJ) polymer semiconductor as depicted in Fig. 6(a). The photoactive layer (with overall thickness of 40 nm and area of 0.25 cm²) consisted of a polymer-polymer blend of PBnDT-FTAZ, as electron donor, and P(NDI2OD-T2), as electron acceptor [29]. These two polymers were selected as they exhibited complementary spectral absorption, enabling a broad spectral sensitivity from 350 nm to 800 nm. Polarization sensitivity was induced into the system by orienting the polymer backbone in the plane of the film using a mechanical rubbing process illustrated in Fig. 6(b). The detectors consisted of a 30 nm zinc oxide (ZnO) electron transport layer on indium tin oxide (ITO)-coated glass, followed by the active layer, then a 20 nm molybdenum trioxide (MoO3) hole transport layer, and finally a 10 nm Au semitransparent top electrode. The details of the fabrication process has been previously described [29].

 

Fig. 6. (a) The OPV device architecture. (b) High-temperature rubbing alignment technique (c) Responsivity of P-OPV cells under linearly polarized light. (d) Transmittances of P-OPV cells under linearly polarized light.

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The responsivity and transmittances of the OPV cells are depicted in Fig. 6(c) and (d), respectively, under 0 V bias with linearly polarized light incident parallel and perpendicular to the direction of polymer’s alignment. The peak responsivity is reach at around 540 nm with a value of $0.18\,\textrm{A/W}$. Additionally, a notable separation between T_x and T_y at 590–600 nm with a diattenuation of approximately 0.72. As stated previously, high diattenuation is required to improve the polarimetric efficiency and spectral contrast of the OPV cells.

We then incorporated these P-OPV devices together with our fabricated MTR filters to demonstrate a proof of concept of the system in Fig. 1(d). The different experimental setups and procedures are depicted in Fig. 7(a-d). The generated photocurrents from OPV0-3 were measured using ACF2101 low noise, charge integrator chip [46], which produce voltage that is related to the photocurrent by Eq. (5). The feedback capacitance and integration time were adjusted according to the experimental task and the incident optical power. The experimental procedures involved quantifying the polarimetric, spectral and radiometric performance of the LC-based SIMPOL. For the polarimeter part, which included the rotating AQWP and OPV0, we first performed polarimetric calibration to accurately determine the polarimeter’s analyzer vectors followed by data validation.

 

Fig. 7. Experimental setup of the LC-based SIMPOL sensor. (a) Polarimetric calibration, (b) polarimetric validation, (c) Spectral characterization and (d) SNR measurements

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The calibration was based on the DRM technique as described in Section 5 of Supplement 1. The benefit of this method is that all the parameters associated with the OPV cell, such as diattenuation, responsivity and reflectance are implicitly included in the measurement matrix. Thus, one can use this matrix to reconstruct the Stokes parameter directly from voltage measurements. Additionally, the DRM method intrinsically minimizes the polarimetric crosstalk and enables more accurate reconstruction of the Stokes parameters.

For validation, known polarization states were independently generated using three different polarization state generator configurations: (1) a polarizer with transmission axis oriented along the x-axis so as to generate the S₁ Stokes parameter, (2) a polarizer with transmission axis oriented at 45$^\circ $ from the x-axis so as to generate the S₂ Stokes parameter and (3) a polarizer oriented at 45$^\circ $ from the x-axis together with an AQWP at 0$^\circ $ so as to generate S₃. The spectral bandwidth of the AQWP (Bolder Vision – AQWP3) was from 400 to 750 nm with retardance of 0.25 ± 0.0025 wave from 450 to 715 nm. For each case, the light was modulated by the AQWP by rotating its fast axis from 0$^\circ $ to 180$^\circ $ in 5$^\circ $ increments and the light intensity was measured by OPV0 in the form of voltage. We removed the dark voltage offset from the measured data, then applied the DRM method (the measurement matrix in Eq. S15 in Supplement 1) to reconstruct the unknown Stokes parameters. Figure 8(a) shows the reconstructed Stokes parameters versus the theoretical Stokes parameters of S₁, S₂ and S₃. For each case, the RMSE was calculated and found to be 1.37% for S₁/S₀, 1.56% for S₂/S₀ and 3.55% for S₃/S₀. The average RMSE was also calculated to be 2.16%.

 

Fig. 8. (a) Reconstructed Measurements of the normalized Stokes parameters (blue circles) vs theoretical Stokes parameters (red solid line). (b) Measured spectral response of OPV1-3.

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For the SIMPOL spectral characterization experiment as shown in Fig. 7(c), we inserted the color sensor behind the polarimeter. The color sensor comprised of the entrance linear polarizer, 3 MTR color filters and 3 P-OPV cells. The transmission axes of LP and OPV0-2 were oriented along the x-axis, whereas the transmission axis of OPV3 was oriented along the y-axis. This configuration enabled the measured MTR spectral responses, depicted in Fig. S2 in Supplement 1, to be absorbed by the P-OPV cells rather than to be transmitted. To measure the OPVs’ spectral absorption profile, a scanning monochromator (Horiba - MicroHR) was used in conjunction with a Xenon-arc lamp. The light’s wavelength was then scanned from 400 nm to 780 nm in 5 nm increments and the output voltages of OPV1-3 were recorded. The OPV voltages were then converted to photocurrents using Eq. (5) and subsequently to absorbed intensities by using the responsivity and transmittance data provided in Fig. 6(c, d). The absorbed optical intensity was then normalized to the intensity incident on the OPV cells. The reconstructed OPV spectra are provided in Fig. 8(b) showing three distinct bands centered at 455 nm (OPV1), 535 nm (OPV2) and 640 nm (OPV3). The FWHM was measured to be 81 nm for OPV1, 117.4 nm for OPV2, and 150.7 nm for OPV3. Additionally, the color contrasts for OPV1, 2 and 3 were measured to be 39%, 31.8%, and 17.9%, respectively. While the measured results are analogous to the simulation results in Fig. 3(c), it is not directly possible to compare the two results due to the OPV cells exhibiting spectrally dependent T_x and T_y in practice. The filter contrast and efficiency can be further improved by using OPV cells with higher diattenuation.

Finally, to quantify the radiometric performance of our LC-based SIMPOL sensor, we measured the SNR of the four OPV cells using the setup in Fig. 7(d). This was achieved by recording 100 consecutive voltage measurements for each OPV cell with light source turned on and 100 voltage measurements with the light source turned off. The voltage measurements were then subtracted pair by pair to obtain the baseline corrected voltage signals. The standard deviations of these baseline corrected voltages were calculated to obtain the voltage noise variance for each OPV. Moreover, the OPV voltage signals were calculated by taking the mean of the measurements. Finally, the SNR was calculated as the ratio of the signal power to the noise level using Eq. (8). The measurements are depicted in Fig. 9(a-d), which were obtained under input optical power of $0.94\,\textrm{mW}\textrm{.}$ The integrator circuit parameters were adjusted to an integration time of 1 ms and a feedback capacitance of 10100 pf in order to avoid voltage saturation.

 

Fig. 9. SNR measurements of OPV0-3

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The SNR for OPV0, 1, 2 and 3 were measured to be 45.4, 39.3, 38.8 and 34.4 dB, respectively. These experimental values are approximately 56 to 66 dB smaller than the theoretical SNR values provided in Fig. 5 (for the same voltage level). There were various experimental factors that could likely be the cause for the low SNR values relative to the theoretical values. First, our circuit model assumed near-ideal OPV characteristics with negligible series resistance, large shunt resistance (400 kΩ) and a terminal capacitance smaller than the feedback capacitance. Any deviation from these near-ideal values would increase the noise bandwidth $\Delta f$, which would subsequently result in a substantial increase in the thermal and shot noise levels. Secondly, our circuit model assumed the presence of only two noise factors. Any additional noise source may further limit the SNR performance (if it dominates the other noise sources at any given input optical power). The results in Fig. 9 indicate a total noise of 56-70 mV across the four OPV cells. This is approximately a factor of $2 \times {10^3}$ greater than the simulated thermal noise ($35\mu \textrm{V}$). Including this multiplication factor to the voltage ratio in Eq. (8) would cause the SNR to drop by 66 dB making the theoretical SNR values agree with the experimental results.

Overall, the polarimetric, spectral and radiometric results presented in Section 4 showcased the unique abilities of the LC-based SIMPOL sensor in delivering full Stokes polarimetry and multicolor sensing along a single optical axis while offering SNRs between 34.4 and 45.4 dB. The SIMPOL tandem design is a key feature that eliminates the spatial sampling artifacts present in DoFP-based color or polarization sensors, such as Bayer filters or SONY’s polarization cameras (e.g. IMX250MZR). Additionally, the ability of MTRs to provide excellent chromatic retardation control, while having a total thickness of a few microns, is particularly attractive in realizing compact sensors.

Although, in this paper, we demonstrated a free-space sensor, monolithically integrating the LCP and OPV devices could likely be achievable. This is because both materials have independently proven viable in realizing monolithic device architectures through a variety of roll-to-roll printing or coating techniques [47–52].

In addition to realizing a monolithic device, proceeding from a single pixel detector to a dense 2D pixelated sensor will be another important milestone. Here, we incorporated a passive readout circuit to measure the OPV signal; however, this method may not be suitable for a 2D image sensor and may exhibit unwanted electrical crosstalk between pixels, especially at low illumination [53]. Instead, an active-pixel sensor approach would be a more viable option, where one or more transistors control each pixel unit. Such an approach has been previously incorporated in organic semiconductors and has showcased high imaging performance [54,55]. These research advancements herald the possibility of seeing a variant of the LC-based SIMPOL design in future image sensor technologies.

5. Conclusion

A novel mantis shrimp-inspired polarization and spectral sensor has been presented. The sensor structure incorporates liquid crystal MTR elements together with polarization-sensitive organic detectors to offer spectral and polarimetric detection. The structure features ultra-thin components of the order of microns, dynamic color tuning, and full Stokes polarimetry. Experimental results demonstrate the sensor’s ability to detect full Stokes polarimetry, with average RMSE of 2.16%, and to detect three distinct color channels, with a FWHM spectral resolution up to 81 nm, all acquired simultaneously along the same optical axis with SNR ranging from 34 to 45 dB. Further improvement in the spectral resolution is possible by optimizing the liquid crystal parameters and increasing the number of twist layers. Moreover, further increase in the number of color channels can be realized by adding more detector and MTR layers. This sensor overcomes the inherent bottlenecks associated with DoFP-based Foveon sensors and can potentially enable polarization and hyperspectral sensing, with proper optimizations of the MTR and OPV layers.