1. Introduction

Electromagnetic waves exhibit three fundamental properties: intensity, wavelength, and polarization. While certain animals, such as reptiles and birds, can perceive polarization information, humans, like other mammals, are limited in their ability to perceive the intensity and wavelength of electromagnetic waves. Polarization imaging systems are essential for acquiring polarization information [1]. Polarimetric imaging involves polarization analysis of electromagnetic waves from a scene. The extracted polarization information offers valuable features, including object surface smoothness [2], three-dimensional information [3], and material composition [4]. Polarization information is typically conveyed through metrics such as polarization degree and angle [5]. Polarization imaging has diverse applications, including anti-jamming target detection [6], 3D reconstruction [7], and image defogging [8], highlighting its broad utility in various fields.

The DoFP polarization imaging detection technology is progressively emerging as the mainstream method for polarization detection, primarily owing to its real-time imaging capabilities. In this technology, sensors utilize micropolarization arrays, as illustrated in Fig. 1. Four linear polarizers oriented at 0°, 45°, 90°, and 135°were organized into groups of four pixels, forming a superpixel structure. While this structure effectively addresses the kinematic artifacts inherent in time-split scanning devices, it introduces field-of-view errors [9]. Modern DoFP cameras employ advanced demosaicing methods to mitigate these errors, resulting in a successful compensation for field-of-view errors and commendable results [10–14].

 

Fig. 1. Schematic diagram of a micropolarization array sensor.

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The infrared DoFP detector employs a linear polarizer to capture the first three Stokes vectors of incoming electromagnetic waves. This crucial step facilitates the reconstruction of the degree of line polarization and angle information within the scene. However, like traditional detectors, infrared DoFP detectors are susceptible to factors such as manufacturing material defects and unstable production process control. This results in inhomogeneity across infrared focal plane arrays (FPA), were signals from different pixels under identical radiant illumination exhibit variations. To address this inhomogeneity, researchers have proposed several correction algorithms to mitigate the associated noise in infrared focal planes, resulting in practical improvements in overall performance [15–18].

Polarization detectors integrate linear polarizers onto FPA, such as the short-wave polarization detector from the Shanghai Institute of Technology and Physics of the Chinese Academy of Sciences (SITP), an MPA comprising a superpixel-structured sub-wavelength aluminum grating [19] is integrated into the InGaAs focal plane array. While this structure achieves a high extinction ratio, the DoFP's non-uniformity is more intricate than that of conventional infrared focal planes, owing to factors such as grating transmittance and extinction ratio [20].

Researchers have developed several non-uniformity correction algorithms to mitigate the non-uniformity of DoFP polarization detectors and enhance the accuracy of scene polarization detection. These include calibration-based and scene-based correction methods. Calibration-based correction methods include the single-pixel correction algorithm and the superpixel correction algorithm proposed by Powell et al. [21]. The single-pixel correction method employs the analytical vectors of a single pixel for correction, whereas the superpixel correction method utilizes the ideal analytical matrix to derive the correction matrix. Building upon the superpixel correction method, Chen et al. [22] introduced the neighboring superpixel correction method, which corrects each pixel based on four overlapping superpixels at that specific location. In departure from the ideal analysis matrix, Zhang et al. [23] proposed an average analysis matrix correction method. Zheng et al. [24] presented a matrix correction method that achieved direct mapping from the image pixels to the polarization degrees. Feng et al. [25] introduced a model that characterizes the response of polarized image elements along with a corresponding correction method. Hathan et al. [26] proposed a straightforward polarization camera correction method that is independent of the light intensity of the input, relying on measurements at four different angles to calculate the features for each pixel. Ding et al. [27] proposed a calibration method that uses a standard light source. Yin et al. [28] considered the depolarization characteristics of optical systems and proposed a method for response and polarization corrections. Lane et al. [29] defined quantization errors in the quality of polarization measurements using a superpixel correction method. Chi et al. [30] proposed a calibration method for multispectral DoFP detectors.

Wang et al. [31] introduced a nonuniformity correction algorithm based on scene polarization redundancy estimation. This method involves calculating the polarization redundancy estimation from the scene image, analyzing differences in pixel statistical characteristics, and deriving updated gain correction coefficients.

In a study by Giménez et al. [32], it was found that the relatively straightforward superpixel correction method exhibited an effective performance within calibration-based correction methods. In contrast, other derived methods do not offer significant advantages.

The goal of polarization correction consists of two aspects: first, to ensure a uniform response of uniformly incident unpolarized light; and second, for incident light with the same polarization state, the calculated polarization state should be at the same level. Many existing correction methods primarily focus on high-polarization scenarios, often neglecting the influence of integration time changes on correction effectiveness. This study addresses these challenges by establishing radiometric and polarization calibration models for the DoFP pixels. The pixel response model analyzed the impact of different integration time on the polarization detector. The proposed calibration method caters to short-wave infrared polarization detectors and accommodates changes in the integration time. This method decomposes the analytical vector of the DoFP detector into the average polarization responsivity and unit analytical vector, enabling separate corrections. It diminishes reliance on polarization channel constraints, accommodating unpolarized and highly polarized scenarios, while demonstrating robustness across different integration times.

2. Principle of non-uniformity generation in DoFP detectors

2.1 DoFP detector imaging principle

The short-wave infrared polarization detector [19] is a polarization-sensitive pixel imaging sensor. Its superpixel structure facilitates the capture of incident polarized light, which is represented by the Stokes vector S.

A DoFP detector arranged in a superpixel structure cannot obtain circularly polarized light and, therefore, cannot obtain ${S_3}$. However, a DoFP detector arranged with a superpixel structure is optimal for system signal-to-noise ratio maximization and system error minimization [33].

The degree of linear polarization (DoLP) and angle of linear polarization (AoLP) of the incident light can be reconstructed from the Stokes vector, as shown in Eqs. (2) and (3), respectively:

2.2 DoFP imaging mathematical model

The scene incident light ${S_{in}}$ was modulated by the MPA and then irradiated onto the FPA to obtain ${S_{out}}$, as shown in Fig. 2. MPA is a non-ideal linear polarizer, also known as a diattenuator [26], and a Mueller matrix ${M_f}$ can represent the optical properties of a diattenuator device:

 

Fig. 2. DoFP camera imaging schematic.

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In Eq. (5), q is the maximum transmittance of the micropolarizer and r is the minimum transmittance of the micropolarizer. Hence, A is the average transmittance and D is the diattenuation coefficient. In Eq. (4), $\alpha$ is the direction of the polarization transmission of the micropolarizer.

When the polarizer was ideal, the maximum transmittance of the diattenuation device was $q = 1$ and the minimum transmittance was $r = 0$. Therefore, the ideal polarizers are $A = 1/2$ and $D = 1$. The Mueller matrix of the ideal polarizer is ${M_{ideal}}$:

Therefore, the final stokes vector incident on the FPA in DoFP is ${S_{out}}$,

However, the FPA of the DoFP detector responds only to light intensity; therefore, the actual amount of radiation projected onto the focal plane is L,

Assuming a linear relationship between the pixel value of the shortwave image element and the amount of radiation, the pixel value I of the actual image element is:

${A_f} = \left[ {\begin{array}{{cccc}} {{A_0}}&{{A_1}}&{{A_2}}&{{A_3}} \end{array}} \right]$ is an analytical vector that was described by Powell et al. [21]. ${A_0} = g \cdot A$ is the product of the focal plane gain coefficient, the average transmittance, and the average polarization responsivity of the polarized image element. ${A_1} = {A_0} \cdot D\cos (2\alpha )$, ${A_2} = {A_0} \cdot D\sin (2\alpha )$ and ${A_3} = 0$. Equation (10) shows that if the incident light ${S_{in}}$ of the scene is homogeneous, there are four primary sources of non-uniformity in the image I, which are ${A_0}$, D, $\alpha$, and d. The non-uniformity of ${A_0}$ is MPA and FPA coupling. D and $\alpha$ are the results of defects in the manufacturing process of miniature polarization arrays.

To analyze the non-uniformity of the DoFP detector, it is essential to develop both a radiative calibration model and a polarization calibration model for DoFP, as illustrated in Fig. 3. An ideal polarizer and blackbody are placed in front of the DoFP detector so that the incident light of the DoFP camera is polarized. The ${S_{in}}$ produced by the blackbody is uniform, unpolarized light, and thus, ${S_{in}} = {\left[ {\begin{array}{{cccc}} {{S_0}}&0&0&0 \end{array}} \right]^T}$. ${S_0}$ is the uniform radiation L emitted by a blackbody. At this point, the pixel value ${I_p}$ of the polarization pixel should be

 

Fig. 3. DoFP detector calibration model, (a) polarization calibration model, (b) radiometric calibration model.

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$L$ can be calculated from the Planck’s law and Stephen-Boltzmann’s law:

When the incident light of the DoFP detector was unpolarized, as shown in Fig. 3(b), Eq. (11) is degraded because the incident light loses the modulation of the ideal polarizer, and the pixel value ${I_f}$ of the polarized pixel is

According to Eqs. (10), (11), and (13), ${A_0}$ the D, $\alpha$, and d of the DoFP detector image element can be calculated based on the blackbody temperature and the rotation angle of the ideal polarizer.

Figure 4 shows the four primary sources that affect the non-uniformity of the DoFP detector. Figure 4(d) shows the relative angle of $\alpha$ with pixel (127,127) as a reference.

 

Fig. 4. DoFP detector non-uniformity diagram, (a) average polarization responsivity ${A_0}$, (b) dark offset d, (c) diattenuation coefficient D, (d) the direction of polarization transmission of the micropolarizer $\alpha$.

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2.3 Effect of integration time on DoFP response

Integration time is an essential parameter of the infrared DoFP detector, which can directly affect the gain coefficient g and dark offset d of the infrared focal plane converted from radiation to an electrical signal, which then affects ${A_0}$, which also affects the polarization response of the DoFP detector ${I_p}$ and the radiation response ${I_f}$. By the structure shown in Fig. 3(a), change the integration time t of the DoFP camera and the angle $\theta$ of the ideal polarizer, and set the temperature of the blackbody as ${{\rm T}_d}$ so that the radiation outgoing degree is ${L_d}$ to obtain Eq. (14):

${I_p}(\theta ,t)$ is the pixel value of the polarization response, ${A_0}(t)$ is the ${A_0}$ that changes with the integration time, and $d(t)$ is the d that changes with the integration time. According to the structure shown in Fig. 3(b), the DoFP camera integration time t and blackbody temperature T to get ${I_f}(T,t)$

Figures 5(a) and (b) show the detector image-element response curves plotted using Eqs. (14) and (15), and four integration time (1, 2, 3, and 4 ms) were selected to set the DoFP camera to collect data. From Fig. 5(a) and (b), the variation in the integration time can significantly affect the radiance response and polarization response of the DoFP detector. The variation in the integration time almost does not change the phase of the polarization response curve; therefore, it does not change the diattenuation coefficient of the DoFP and the transmission angle of the MPA.

 

Fig. 5. Image response curves of the DoFP detector, (a) the polarization response ${I_p}(\theta ,t)$, (b) the radiant response ${I_f}(T,t)$, (c) the polarization response divided by the integration time ${I^{\prime}_p}(\theta ,t)$, (d) the radiant response divided by the integration time ${I^{\prime}_f}(T,t)$.

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As shown in Fig. 5, when the integration time increases by 1 ms, the polarization response increases by ${d_p}$ and the radiation response increases by ${d_f}$; this observation suggesting that when the integration time changes by t, the pixel value changes by $k \cdot t$, therefore, we assume that ${A_0}(t)$ changes linearly:

We divide ${I_p}(\theta ,t)$ and ${I_f}(\theta ,t)$ by the integration time t, eliminating the effect of the integration time t on ${A_0}(t)$, and obtain ${I^{\prime}_p}(\theta ,t)$ and ${I^{\prime}_f}(T,t)$:

Plots of ${I^{\prime}_p}(\theta ,t)$ and ${I^{\prime}_f}(T,t)$ are shown in Fig. 5(c) and (d). In Fig. 5(c) and (d), the radiance and polarization response curves with different integration time are significantly different only for $d^{\prime}(t)$ on the y-axis. In summary, integration time affects the ${A_0}$ and d of the DoFP detector. In contrast, D and $\alpha$ are unaffected by integration time, which is also consistent with the physical meaning of these four parameters. After dividing the DoFP pixel response by the integration time t, ${A_0}(t)$ transforms into k, causing the pixel to be exclusively influenced by $d^{\prime}(t)$. Consequently, accurate estimation of $d^{\prime}(t)$ is imperative for effectively mitigating non-uniformity noise in the DoFP detector.

The DoFP integration time was set from 1 ms to 6 ms at 0.2 ms intervals. As shown in Fig. 6(a), the $d^{\prime}(t)$ is a distinct monotonic curve. Figure 6(b) illustrates $\ln [d^{\prime}(t)]$, which shows a clear linear relationship:

 

Fig. 6. Four images A, B, C, and D are randomly selected at the DoFP detector Curve, (a) $d^{\prime}(t)$, (b) $\ln [d^{\prime}(t)]$.

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Using Eq. (20), $d^{\prime}(t)$ can be estimated; consequently, the influence of the dark offset on the DoFP detector can be mitigated based on the integration time.

3. Non-uniformity correction method

Conventional DoFP detectors are usually corrected for non-uniformity using the superpixel correction method [21], which uses an analytical matrix to solve the correction matrix. The traditional superpixel correction method relies on mutual constraints among the four channels of the DoFP. In the case of high polarization, the superpixels can be well constrained to each other (e.g., the polarization of the incident light is one, as shown in Fig. 3(a)); however, in the case of very low scene polarization (e.g., the polarization of the incident light is 0 in Fig. 3(b)), the superpixel correction method tends not to achieve a relatively good correction effect.

This study introduces a two-stage nonuniformity correction approach for DoFP. Initially, the analysis vector ${A_f}$ in the DoFP imaging model is decomposed into k and ${A^{\prime}_f}$ for specific corrections. In the first stage, by leveraging the radiometric calibration model, the detector's response to the integration time and dark migration is rectified. The correction of k for each pixel was performed based solely on the radiation response of that individual pixel. In the second stage, according to the polarization calibration model, D and $\alpha$ were unaffected by the integral time change. Consequently, the unit analysis vector of DoFP is employed for polarization correction, effectively eliminating non-uniformities in D and $\alpha$ contingent upon the mutual constraints of the superpixels.

3.1 Radiometric correction model

For the DoFP detector, the radiative correction removes the dark offset of the pixel while making the k of each pixel consistent per unit integration time, which ultimately results in the DoFP responding to the same grayscale for each pixel for incident uniform unpolarized light.

3.2 Polarization correction model

Radiometric correction corrects each pixel's k to ${k_{ideal}}$ and removes each pixel's dark offset, and must be corrected for D and $\alpha$. The usual practice is to perform this using the superpixel correction method, but we have corrected each pixel for k so that ${{\rm I}^{\prime}_p}(\theta )$ is

Use the least squares that fit ${I^{\prime}_p}(\theta )$ and then solve for each pixel ${A^{\prime}_f}$. The superpixel, shown in Fig. 1, has a unit analysis matrix ${A^{\prime}_{sp}}$,

For superpixels, the non-uniformity correction is

Figure 2 illustrates the arrangement of four superpixels centered around a single pixel. Consequently, a single pixel could be corrected four times. Therefore, after four calibrations for a single pixel, an average was obtained to derive the final calibration result.

4. Experimental results

4.1 Experimental setup

The non-uniformity correction algorithm was tested by acquiring uniform images according to the device shown in Fig. 3(a) and (b). The light source required for short-wave DoFP detector calibration was a high-temperature blackbody. In this study, a high-temperature blackbody with a working range of 0–400 °C was used as an unpolarized light source. The ideal polarizer is Thorlabs WP50L-UB, with polarized wavelengths from 250 nm to 4 µm and extinction ratios of up to 10,000:1. The high-precision rotating platform was a Thorlabs Model BSC 101. This study uses a short-wave DoFP detector [19] developed by the Shanghai Institute of Technical Physics, Chinese Academy of Sciences, and the pixel response band is 0.9um∼1.7um. The detector has $320 \times 256$ pixels, each of which has 14 bits.

First, the device shown in Fig. 3(a) was used to collect images taken at two different temperatures and rotated at 18 different angles at four integration time. The device shown in Fig. 3(b) was then used to collect images taken at 12 different temperatures by setting the DoFP detector at four different integration time. Each image was sampled 256 times to reduce the effect of time noise on the results. At the time of data acquisition, the maximum intensity was set as high as possible with the pixel unsaturated and then decreased by 10 °C each time. The rotating platform rotated by 18 angles, starting at 0° and increasing by 10°. In the experiment, we filled the field of view of the DoFP detector with the outgoing blackbody radiation so that the distance of blackbody radiation to the focal plane of the detector was as equal as possible.

4.2 Correction analysis

To elucidate the distinctive features and benefits of our proposed algorithm, we compared it with existing methods, including superpixel correction (Superpixel) [21], adjacent superpixel correction (A-superpixel) [22], average analysis matrix correction (A-matrix) [23], and Yin’s method [28]. This analysis focused on the correction parameter calculated using data collected under a 4 ms integration time. Subsequently, various correction algorithms were tested using datasets obtained at different integration time to assess their performance and to highlight the effectiveness of the algorithm in diverse scenarios.

To quantify the performance of the different correction algorithms, we used the RMSE as a metric to precisely describe the performance of the correction algorithm.

We designate the image captured by the DoFP, following modulation of blackbody emission radiation by an ideal polarizer, as a polarized image. In contrast, the image captured by the DoFP without ideal polarizer modulation is termed unpolarized. By applying the five correction algorithms to the unpolarized image, with ${R_{ideal}}$ representing the mean value of the image, we calculated the RMSE based on the S0 image of DoFP, as illustrated in Table 1. Additionally, the DoLP and AoLP images lack valid values and are thus excluded from Table 1. The second to sixth columns show the RMSE values calculated using five different correction algorithms: the Superpixel correction method, A-superpixel correction method, A-matrix correction method, Yin's method, and the correction method proposed in this paper.

Table 1. Results of five correction algorithms applied to unpolarized images.

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As observed in Table 1, the Superpixel correction, A-superpixel correction, and A-matrix methods display limited correction efficacy for unpolarized light. This limitation is attributed to their reliance on mutual constraints between superpixels. In scenarios with low scene polarization, the effective establishment of these mutual constraint falters leads to a pronounced reduction in correction effectiveness. Yin’s method can effectively correct the non-polarization scene, but with a change in the integration time, the Yin method deteriorates rapidly. In contrast, the correction method proposed in this paper is very effective for non-polarized images and has the best robustness in the integration time range of 1–4 ms.

Table 2 presents the RMSE calculation results for various correction algorithms for the S0, DoLP, and AoLP images of DoFP. It is crucial to highlight that in our experiment, the ideal DoLP was set to 1, and the ideal AoLP corresponded to the rotation angle of the ideal polarizer. Upon careful examination of Table 2, the A-superpixel method stands out for its superior efficacy compared with the Superpixel method. This approach strategically employs four superpixels adjacent to one pixel for correction when addressing a single pixel. However, the A-matrix method exhibits suboptimal performance on AoLP and DoLP images because of the lack of an ideal analysis matrix. However, it achieved the lowest RMSE for the S0 images. Yin's method fails to provide good results when correcting polarized images, probably because it fails to strike a balance between response correction and polarization correction. Remarkably, the correction algorithm proposed in this study outperformed the other four methods on DoLP images, delivering lower RMSE values. The proposed method demonstrates a significant advantage even on AoLP images, especially within the integration time range of 3–1 ms. Additionally, our algorithm demonstrates outstanding stability amidst changes in integration time, consistently maintaining a high correction effect. The RMSE variation observed in the AoLP and DoLP images was notably lower than that of the Superpixel and A-superpixel algorithms.

Table 2. Results of five correction algorithms applied to polarized images.

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As shown in Tables 1 and 2, to enhance the adaptability of the algorithm across diverse scenarios, we opted to segregate the intensity and polarization correction of DoFP. This strategic choice renders our proposed algorithm more advantageous for reconstructing intensity information (S0) in unpolarized scenes, albeit with a slight reduction in accuracy for intensity information in polarized scenes. However, the proposed algorithm guarantees higher accuracy in polarization information (DoLP and AoLP) during second-stage correction in polarized scenes.

In Fig. 7, a 1 ms integration time measurement is used as an example to visually illustrate the impact of different correction algorithms on the polarization state measurement accuracy of the DoFP detector. Figure 7 depicts the outcomes of the five distinct correction algorithms in the polarization state measurement, including the ideal values. The horizontal coordinates in Fig. 7 refer to 100 randomly sampled test points. The correction results of the A-matrix method differed from the ideal value, indicating that the use of the average analysis matrix was less effective in correcting the polarized scene. The results of Yin's method are unstable. The Superpixel correction method, A-superpixel correction method, and the algorithm proposed in this paper closely approach ideal values. As indicated in Table 2, the proposed algorithm demonstrates minor errors in the polarization state measurement compared with other algorithms.

 

Fig. 7. Schematic diagram of polarization state measurement, (a) polarization angle measurement, (b) polarization degree measurement.

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In summary, the algorithm proposed in this paper demonstrates significant advantages over the other four algorithms for unpolarized images. Moreover, our algorithm outperforms the others in terms of accurately measuring the polarization state in polarized images.

4.3 Visual effect comparison

In the final phase, we implemented our correction algorithm on authentic DoFP polarization images, subjecting them to testing against five distinct correction techniques. To demonstrate better visualization, all the final images presented use the [34] method to reduce the field of view error, which does not affect the comparison of non-uniformity correction algorithms.

Figure 8 shows the original image taken by the DoFP camera, and Fig. 8(a) to (d) shows the images taken when the integration time is set at 1 ms to 4 ms, respectively.

 

Fig. 8. Real scene captured by DoFP camera, (a) 1 ms image, (b) 2 ms image, (c) 3 ms image, (d) 4 ms image.

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In Fig. 9, a series of DoLP images are presented. The rows correspond to images captured with the DoFP camera set at integration time ranging from 4 ms to 1 ms. Within each row, the columns represent the uncorrected images, those corrected using the Superpixel method, A-superpixel method, A-matrix method, Yin’s method, and the algorithm proposed in this paper, respectively. For visual clarity, a pseudo-color representation is employed in the display of the DoLP images.

 

Fig. 9. DoLP images of real scenes, (a) Uncalibrated, (b) Superpixel, (c) A-superpixel, (d) A-matrix, (e) Yin’s method, (f) Proposed.

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The analysis in Fig. 9 reveals a notably low degree of linear polarization in the uncorrected image. As the integration time decreases from 4 ms, the images corrected by the Superpixel correction method, A-superpixel correction method, and Yin’s method exhibit increasing noise. Notably, the A-superpixel correction method surpasses the Superpixel correction method, showing superior correction effects and heightened stability with changing integration time. While the A-matrix method demonstrates more stable correction effects than the first two methods, it comes at the cost of a lower calculated polarization. This observation aligns with the findings in Table 2, underscoring a critical limitation of the A-matrix method: its failure to employ the ideal analysis matrix for correction, resulting in an inability to rectify the micropolarization array in DoFP to the desired level. In stark contrast, the algorithm proposed in this paper excels in correction, displaying optimal performance and remarkable stability across integration time ranging from 4 to 1 ms.

Figure 10 shows the AoLP images following the same arrangement as in Fig. 9. Notably, the polarization angle is displayed across a range of −90° to 90°, representing the angle of scene-polarized light relative to the 0° channel of the MPA pixel. Figure 10 shows that fringe noise emerges in the uncorrected image as the integration time changes. The correction effects of the Superpixel, A-superpixel, A-matrix, and Yin’s methods mirror those observed in the DoLP images, deteriorating with decreasing integration time. Remarkably, under an integration time of 1 ms, the AoLP images from these four correction methods struggle to distinguish features such as the car tail in the image. By contrast, the algorithm proposed in this study maintained the most effective correction and remarkable stability.

 

Fig. 10. AoLP images of real scenes, (a) Uncalibrated, (b) Superpixel, (c) A-superpixel, (d) A-matrix, (e) Yin’s method, (f) Proposed.

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It is difficult to evaluate the image quality of authentic DoFP images, but this study used the accuracy of polarization measurement redundancy (APMR) [35] metrics to evaluate authentic DoFP images. APMR, which is based on physical information, presents the distinct advantage of evaluating the polarization image quality without requiring reference data.

Table 3 shows the average APMR obtained using different correction algorithms at integration time ranging from 4 ms to 1 ms. The algorithm proposed in this paper achieved the highest APMR in authentic DoFP images, which indicates its excellent correction effect.

Table 3. Average APMR of five correction algorithms for real DoFP images.

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5. Summarize

In this paper, we introduce a two-stage non-uniformity correction algorithm for short-wave infrared polarization detectors and present the theoretical framework of the new correction method. We discuss in detail the source of non-uniformity noise in DoFP detectors based on the DoFP detector imaging model, discuss the effect of integration time on the non-uniformity noise, and introduce a dark offset estimation algorithm to remove the effect of integration time on the non-uniformity of DoFP.

Our method decomposes the analysis vectors of DoFP pixels into average polarization response and unit analysis vectors, which are corrected using radiometric and polarization correction methods, respectively, so that the correction algorithm can be adapted to a broader range of scenes. We compared the proposed algorithm with the current mainstream algorithms in uniform images, and the experimental results showed that the proposed method can adapt to both unpolarized and polarized scenes and achieve optimal results in polarization measurement accuracy. Most importantly, the algorithm proposed in this study exhibits the best robustness when the integration time changes.