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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1129517</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2023.1129517</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Study of multispectral polarization imaging in sea fog environment</article-title>
<alt-title alt-title-type="left-running-head">Fu et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2023.1129517">10.3389/fphy.2023.1129517</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Fu</surname>
<given-names>Qiang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1989840/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yang</surname>
<given-names>Wei</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Si</surname>
<given-names>Linlin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Meng</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Yue</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Luo</surname>
<given-names>Kaiming</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhan</surname>
<given-names>Juntong</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1676976/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Su</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>National and Local Joint Engineering Research Center of Space Optoelectronics Technology</institution>, <institution>Changchun University of Science and Technology</institution>, <addr-line>Changchun</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>College of Opto-Electronic Engineering</institution>, <institution>Changchun University of Science and Technology</institution>, <addr-line>Changchun</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/981545/overview">Ben-Xin Wang</ext-link>, Jiangnan University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1891385/overview">Yao Hu</ext-link>, Beijing Institute of Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2012138/overview">Yi Ma</ext-link>, Ministry of Natural Resources, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Qiang Fu, <email>cust_fuqiang@163.com</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Optics and Photonics, a section of the journal Frontiers in Physics</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>19</day>
<month>01</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>11</volume>
<elocation-id>1129517</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>10</day>
<month>01</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Fu, Yang, Si, Zhang, Zhang, Luo, Zhan and Zhang.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Fu, Yang, Si, Zhang, Zhang, Luo, Zhan and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Marine exploration has become a popular field of concern and research all over the world. The impact of sea fog on ocean exploration is very great, and how to carry out accurate identification of targets in the sea fog environment is a problem we urgently need to solve. In this paper, we simulated and analyzed the particle distribution characteristics of the sea fog layer by using the principle of Mie scattering, designed a spectral polarization imaging system by using Liquid Crystal Variable Retarder (LCVR) and Liquid Crystal Tunable Filter (LCTF) according to the principle of spectral spectroscopy and polarization imaging, conducted calibration experiments on liquid crystal tunable filter, and carried out experiments on visibility, wavelength and imaging distance that affect the experimental results of polarization imaging of sea fog environment. The experimental results show that the polarization decreases with the increase of imaging distance; in the typical visibility (5&#xa0;km for light fog, 0.5&#xa0;km for medium fog and 0.05&#xa0;km for dense fog), the higher the visibility, the higher the polarization; for the typical wavelengths of visible light (450&#xa0;nm, 530&#xa0;nm and 670&#xa0;nm), the polarization increase with the increase of wavelength.</p>
</abstract>
<kwd-group>
<kwd>polarization image</kwd>
<kwd>multispectral</kwd>
<kwd>sea fog environment</kwd>
<kwd>target identification</kwd>
<kwd>marine exploration</kwd>
</kwd-group>
<contract-num rid="cn001">61890963 61890960 62127813</contract-num>
<contract-sponsor id="cn001">National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100001809</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Due to the serious scattering effect of chaotic media such as tiny particles and soluble organic matter suspended in sea fog on light waves, light-intensity information is scattered and absorbed by aerosol particles with a high concentration of sea salt suspended over the sea surface during atmospheric transmission, resulting in faster light attenuation during transmission, making the background scattered light superimposed on the target light to form noise [<xref ref-type="bibr" rid="B1">1</xref>&#x2013;<xref ref-type="bibr" rid="B3">3</xref>]. Therefore, maritime scenes are more susceptible to chaotic environments than non-maritime scenes, making imaging appear with more complex target backgrounds, blurred effects, large coverage of detailed information, and a significant decrease in contrast [<xref ref-type="bibr" rid="B4">4</xref>&#x2013;<xref ref-type="bibr" rid="B6">6</xref>], which directly affects the accuracy of analysis and judgment of the imaging content. Therefore, along with the increasing attention and more rapid development of spectral polarization imaging technology, the technology has continued to advance the development of imaging technology, which is important for the study of clear target imaging, images containing a high amount of information, and high imaging contrast and clarity.</p>
<p>In the sea fog environment, polarization imaging experiments are easily affected by the sea fog particles suspended over the sea surface, the visible light imaging effect is gray, and low contrast, so detecting the reflected intensity information of the target, can not effectively identify the target. Polarized light has a better fog-transparent ability, and compared with traditional optical imaging methods, polarized imaging techniques can acquire target characteristics at longer distances and highlight the features of the target in complex backgrounds, and polarized images also have advantages such as high signal-to-noise ratio [<xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B8">8</xref>]. However, the amount of energy absorbed by different wavelengths of light is also very different, and the polarization properties of light can be used to obtain multi-wavelength polarization in complex sea fog environments, and the study of polarization imaging techniques in appropriate wavelengths can provide technical support for the detection of targets in complex sea fog environments.</p>
</sec>
<sec id="s2">
<title>2 Characterization of multilayer particle distribution in a complex environment of sea fog</title>
<p>The particle scale distribution of the sea fog layer is subject to a combination of geographical, weather and time factors, and the droplet particles are usually described by the most widely used gamma distribution model [<xref ref-type="bibr" rid="B9">9</xref>].<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>a</mml:mi>
<mml:msup>
<mml:mi>r</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>b</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is the number of droplet particles per unit volume per unit radius (in <inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>&#x3bc;</mml:mi>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>), r is the droplet particle radius, and <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> are the shape parameters of the droplet spectrum, respectively, related to the water content W (in <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> ) and the visibility V (in <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) [<xref ref-type="bibr" rid="B10">10</xref>], denoted as<disp-formula id="e2">
<mml:math id="m8">
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>9.781</mml:mn>
<mml:mrow>
<mml:msup>
<mml:mi>V</mml:mi>
<mml:mn>6</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>W</mml:mi>
<mml:mn>5</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mn>0</mml:mn>
<mml:mn>15</mml:mn>
</mml:msup>
<mml:mo>,</mml:mo>
<mml:mi>b</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1.304</mml:mn>
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mn>0</mml:mn>
<mml:mn>4</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>In the sea fog environment, the advective fog has a larger range and heavier concentration. For advective fog, water content and visibility have the following relationships<disp-formula id="e3">
<mml:math id="m9">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>18.35</mml:mn>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1.43</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.0156</mml:mn>
<mml:msup>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1.43</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>Then the relationship between the particle size distribution of sea mist and visibility can be obtained<disp-formula id="e4">
<mml:math id="m10">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.059</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mn>0</mml:mn>
<mml:mn>7</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>V</mml:mi>
<mml:mn>1.15</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>r</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>0.8359</mml:mn>
<mml:msup>
<mml:mi>V</mml:mi>
<mml:mn>0.43</mml:mn>
</mml:msup>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>If we assume that the sea surface fog layer consists of dense fog, medium fog and light fog respectively, and the typical visibility is 0.05&#xa0;km, 0.5&#xa0;km, and 5&#xa0;km respectively, the particle size distribution of dense sea fog, medium sea fog and light sea fog can be obtained respectively by substituting into Eq. <xref ref-type="disp-formula" rid="e4">4</xref>, as shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. The mode radii of three different concentrations of dense sea fog, medium sea fog and light sea fog satisfying the Gamma distribution are 8.676&#xa0;&#x3bc;m, 3.223&#xa0;&#x3bc;m, and 1.198&#xa0;&#x3bc;m, respectively.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Solution process of vector radiation transmission equation based on RT3.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g001.tif"/>
</fig>
<p>As can be seen from <xref ref-type="fig" rid="F1">Figure 1</xref>, the relationship between the corresponding mode radius and particle size distribution varies for different visibility levels. The mode radius is between 0 and 1&#xa0;&#x3bc;m, where the larger the visibility, the more the particle size distribution of sea spray particles and the larger the rising rate. The mode radius is between 0 and 3&#xa0;&#x3bc;m, followed by the visibility of 0.5&#xa0;km when the sea spray particle size distribution is more and rises faster; finally, when the visibility is 0.05&#xa0;km, the mode radius is between 0 and 9&#xa0;&#x3bc;m, the sea spray particle size distribution is more, and the trend is rising.</p>
<p>When the die radius &#x3e;1&#xa0;&#x3bc;m and visibility is 5&#xa0;km, the particle size distribution decreases rapidly with the increase of die radius, and when the die radius reaches 6&#xa0;&#x3bc;m, the sea mist particle distribution disappears; when the die radius &#x3e;3&#xa0;&#x3bc;m and visibility is 0.5&#xa0;km, the particle size distribution decreases slowly with the increase of die radius, and when the die radius reaches 16&#xa0;&#x3bc;m, the sea mist particle distribution disappears; when the die radius &#x3e;9&#xa0;&#x3bc;m and When the visibility is 0.05&#xa0;km, the particle size distribution decreases slowly with the increase of the die radius, and the decreasing speed is slower than the first two, and the corresponding sea spray particle size distribution still exists when the die radius &#x3e;24&#xa0;&#x3bc;m.</p>
</sec>
<sec id="s3">
<title>3 Experiment</title>
<sec id="s3-1">
<title>3.1 Experimental principle</title>
<sec id="s3-1-1">
<title>3.1.1 Principle of liquid crystal tunable filter</title>
<p>The structure of the Liquid Crystal Tunable Filter (LCTF) is shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. The incident light passing through the LCTF crystal will form two coherent polarized beams, o-light and e-light, and the two beams will interfere to achieve transmission at a specific wavelength [<xref ref-type="bibr" rid="B11">11</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>], and the intensity of the interference light coming out of the detector is<disp-formula id="e5">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">sin</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2061;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>&#x3b1;</mml:mi>
<mml:msup>
<mml:mi mathvariant="italic">sin</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>Where a denotes the incident light amplitude, <inline-formula id="inf7">
<mml:math id="m12">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the angle between the fast axis of the crystal and the detector, and <inline-formula id="inf8">
<mml:math id="m13">
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the phase delay<disp-formula id="e6">
<mml:math id="m14">
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>Where <inline-formula id="inf9">
<mml:math id="m15">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the wavelength, <inline-formula id="inf10">
<mml:math id="m16">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the refractive index, and the crystal thickness is <inline-formula id="inf11">
<mml:math id="m17">
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. It can be seen that the light intensity changes with <inline-formula id="inf12">
<mml:math id="m18">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and there is a great value of light intensity at a specific wavelength.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Schematic diagram of LCTF structure.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g002.tif"/>
</fig>
</sec>
<sec id="s3-1-2">
<title>3.1.2 Principle of liquid crystal variable retarder</title>
<p>Liquid Crystal Variable Retarders (LCVR) are optical devices made based on the fact that anisotropic liquid crystal molecules with uniaxial birefringence properties are susceptible to deflection by electric and magnetic fields [<xref ref-type="bibr" rid="B18">18</xref>&#x2013;<xref ref-type="bibr" rid="B21">21</xref>], thus causing the phase of the incident light wave to be modulated.</p>
<p>The basic principle of phase regulation in LCVR is shown in <xref ref-type="fig" rid="F3">Figure 3</xref> [<xref ref-type="bibr" rid="B22">22</xref>], where two transparent glasses are used as the upper and lower substrates, and Indium Tin Oxide is plated on the inner side of the substrate as the electrode so that the external signal is applied to the liquid crystal through the electrode. To pre-orient, the liquid crystal molecule pointing, an orientation film, usually polyimide, is also coated on the Indium Tin Oxide electrodes, which are encapsulated with liquid crystal spacers infused in between. When the driving voltage <inline-formula id="inf13">
<mml:math id="m19">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is loaded on the LCVR (<inline-formula id="inf14">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the liquid crystal threshold voltage), as shown in <xref ref-type="fig" rid="F3">Figure 3A</xref>, the long axis of the stretched anisotropic liquid crystal molecules is parallel to the substrate under the anchoring effect of the orientation film, and the long axis of the liquid crystal molecules is equivalent to the optical axis of a uniaxial crystal; when the driving voltage <inline-formula id="inf15">
<mml:math id="m21">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is loaded on the LCVR, the long axis of the liquid crystal molecules will follow the direction of the electric field under the action of the electric field as shown in <xref ref-type="fig" rid="F3">Figure 3B</xref>, and the long axis of the liquid crystal molecules will be deflected along the electric field direction under the action of the electric field, which is equivalent to the deflection of the optical axis.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Principle diagram of Liquid Crystal Variable Retarder modulation. <bold>(A)</bold> <inline-formula id="inf16">
<mml:math id="m22">
<mml:mrow>
<mml:mi mathvariant="bold-italic">U</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">U</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(B)</bold> <inline-formula id="inf17">
<mml:math id="m23">
<mml:mrow>
<mml:mi mathvariant="bold-italic">U</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">U</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g003.tif"/>
</fig>
<p>The relationship between the deflection angle &#x3b8; of the optical axis and the driving voltage U is<disp-formula id="e7">
<mml:math id="m24">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="{" close="" separators="&#x7c;">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi mathvariant="italic">arctan</mml:mi>
<mml:mrow>
<mml:mfenced open="{" close="}" separators="&#x7c;">
<mml:mrow>
<mml:mi mathvariant="italic">exp</mml:mi>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="&#x7c;">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mi>M</mml:mi>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>where <inline-formula id="inf18">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the threshold voltage and <inline-formula id="inf19">
<mml:math id="m26">
<mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, M are constants [<xref ref-type="bibr" rid="B23">23</xref>]. Due to the deflection of the long axis of the molecule, the angle <inline-formula id="inf20">
<mml:math id="m27">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> between the light vector K and the optical axis changes for the incident light wave, and the refractive index of e-light will change according to the birefringence property of anisotropic crystals. The refractive index of the e-light equation is<disp-formula id="e8">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi>n</mml:mi>
<mml:mn>0</mml:mn>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:msubsup>
<mml:mi mathvariant="italic">sin</mml:mi>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2061;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:msubsup>
<mml:mi mathvariant="italic">cos</mml:mi>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac bevelled="true">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:msup>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>Therefore, the phase delay of the modulated light through the Liquid Crystal Variable Retarder is<disp-formula id="e9">
<mml:math id="m29">
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>n</mml:mi>
</mml:mrow>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msup>
<mml:mi mathvariant="italic">cos</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>Where d is the thickness of the liquid crystal layer, and according to Eqs <xref ref-type="disp-formula" rid="e7">7</xref>, <xref ref-type="disp-formula" rid="e8">8</xref>, the refractive index of e-light differs at different places of the liquid crystal layer under the same driving voltage [<xref ref-type="bibr" rid="B24">24</xref>], thus making it imprecise to calculate the Liquid Crystal Variable Retarder phase delay using the theoretical equation [<xref ref-type="bibr" rid="B25">25</xref>], so the integration of Eq. <xref ref-type="disp-formula" rid="e9">9</xref> is<disp-formula id="e10">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>V</mml:mi>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mfrac>
<mml:msubsup>
<mml:mo>&#x222b;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mi>d</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>Where <inline-formula id="inf21">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>V</mml:mi>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the phase delay of the LCVR. In an LCVR at a fixed voltage, the magnitude of phase delay is inversely related to the wavelength [<xref ref-type="bibr" rid="B26">26</xref>], the shorter the wavelength, the larger the amount of phase delay; the longer the wavelength, the smaller the amount of phase delay; at a fixed wavelength, the phase delay is positively related to the voltage, the larger the voltage the larger the phase delay.</p>
<p>The LCVR is a polarization optical device based on the fact that anisotropic liquid crystal molecules with uniaxial birefringence are easily deflected by electric and magnetic fields, thus modulating the phase of the incident light wave. Therefore, it is widely used in optical communication, optical information processing and polarization spectrum imaging.</p>
</sec>
</sec>
<sec id="s3-2">
<title>3.2 Experimental setup and parameters of each setup</title>
<p>The visible light polarization imaging system is shown in <xref ref-type="fig" rid="F4">Figure 4</xref>, where LCVR stands for Liquid Crystal Variable Retarder. LCTF stands for Liquid Crystal Tunable Filter. LCTF divides visible light into different wavelengths and produces light with different polarization states by changing the angle between the 2 LCVRs and imaging them. Literature 17 absorption spectra from individual textile fibers using LCTF, literature 21 developed a 400&#x2013;1700&#xa0;nm spectral polarization imager, and literature 26 developed a full Stokes parametric spectral polarization imager. None of the above articles have studied the factors affecting polarization imaging in depth, and the present device uses LCTF and LCVR to experiment and analyze the important factors affecting polarization imaging.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Spectral polarization imaging experimental setup.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g004.tif"/>
</fig>
<p>The parameters of each instrument are shown in the following table. <xref ref-type="table" rid="T1">Table 1</xref> shows the parameters of the visible light camera, <xref ref-type="table" rid="T2">Table 2</xref> shows the parameters of the Liquid Crystal Tunable Filter, and <xref ref-type="table" rid="T3">Table 3</xref> shows the parameters of the Liquid Crystal Variable Retarder.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Visible light camera Parameters.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Visible light cameras</th>
<th align="center">Parameters</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Brand</td>
<td align="center">IMPERX</td>
</tr>
<tr>
<td align="center">Model</td>
<td align="center">GEV-B1410C-SC000</td>
</tr>
<tr>
<td align="center">Data Interface</td>
<td align="center">GigE, PoE</td>
</tr>
<tr>
<td align="center">Frame rate</td>
<td align="center">30&#xa0;fps</td>
</tr>
<tr>
<td align="center">Chip Model</td>
<td align="center">Sony ICX285</td>
</tr>
<tr>
<td align="center">Resolution</td>
<td align="center">1,360 &#xd7; 1,024</td>
</tr>
<tr>
<td align="center">Pixel size</td>
<td align="center">6.45&#xa0;&#x3bc;m</td>
</tr>
<tr>
<td align="center">Minimum S/N ratio</td>
<td align="center">60&#xa0;dB</td>
</tr>
<tr>
<td align="center">Chip type</td>
<td align="center">CCD</td>
</tr>
<tr>
<td align="center">Size</td>
<td align="center">46&#xa0;mm &#xd7; 46&#xa0;mm x TBD</td>
</tr>
<tr>
<td align="center">Operating temperature</td>
<td align="center">&#x2212;40&#xb0;C&#x2013;85&#xb0;C</td>
</tr>
<tr>
<td align="center">Supply voltage</td>
<td align="center">12&#xa0;V DC</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Liquid crystal tunable filter parameters.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Liquid crystal tunable filter</th>
<th align="center">Parameters</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Brand</td>
<td align="center">Kurios<sup>&#xae;</sup>
</td>
</tr>
<tr>
<td align="center">Model</td>
<td align="center">KURIOS-XL1 (/M)</td>
</tr>
<tr>
<td align="center">Wavelength range</td>
<td align="center">430&#x2013;730&#xa0;nm</td>
</tr>
<tr>
<td align="center">Bandwidth</td>
<td align="center">10&#xa0;nm@550&#xa0;nm</td>
</tr>
<tr>
<td align="center">Switching speed</td>
<td align="center">&#x3c;70&#xa0;m</td>
</tr>
<tr>
<td align="center">Light passing aperture</td>
<td align="center">35&#xa0;mm</td>
</tr>
<tr>
<td align="center">Polarization transmittance</td>
<td align="center">17%@550&#xa0;nm</td>
</tr>
<tr>
<td align="center">Field of view</td>
<td align="center">&#xb1;6&#xb0;</td>
</tr>
<tr>
<td align="center">Minimum growth step</td>
<td align="center">1&#xa0;nm</td>
</tr>
<tr>
<td align="center">Operating temperature</td>
<td align="center">0&#xb0;C&#x2013;40&#xb0;C</td>
</tr>
<tr>
<td align="center">Damage Threshold</td>
<td align="center">0.1&#xa0;J/cm2</td>
</tr>
<tr>
<td align="center">Size</td>
<td align="left">79.0&#xa0;mm &#xd7; 79.0&#xa0;mm x 60.5&#xa0;mm (3.11&#x2033;&#xd7; 3.11&#x2033;x 2.38&#x2033;)</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Liquid crystal variable retarder parameters.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Liquid crystal variable retarder</th>
<th align="center">Parameters</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Brand</td>
<td align="center">Thorlabs</td>
</tr>
<tr>
<td align="center">Model</td>
<td align="center">LCC1423-A</td>
</tr>
<tr>
<td align="center">Wavelength range</td>
<td align="center">357&#x2013;700&#xa0;nm</td>
</tr>
<tr>
<td align="center">Light passing aperture</td>
<td align="center">20&#xa0;mm</td>
</tr>
<tr>
<td align="center">Delay amount</td>
<td align="center">0&#xa0;nm-&#x3bb;</td>
</tr>
<tr>
<td align="center">Minimum delay compensation</td>
<td align="center">0&#xa0;nm</td>
</tr>
<tr>
<td align="center">Switching speed</td>
<td align="center">39.4&#xa0;m/310&#x3bc;s@25.6&#xb0;C</td>
</tr>
<tr>
<td align="center">Damage Threshold</td>
<td align="center">2.04&#xa0;J/cm<sup>2</sup>
</td>
</tr>
<tr>
<td align="center">Delay uniformity</td>
<td align="center">&#x3c;&#x3bb;/20</td>
</tr>
<tr>
<td align="center">Operating temperature</td>
<td align="center">&#x2212;20&#xb0;C&#x2013;45&#xb0;C</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3-3">
<title>3.3 Liquid crystal variable retarder characteristic curve calibration experiment</title>
<p>The phase delay of the Liquid Crystal Variable Retarder (LCVR) is determined by the voltage applied to the liquid crystal, and we need to measure the voltage delay characteristics of the liquid crystal variable phase delayers used in the experiments. The LCVR made with anisotropic nematic liquid crystal molecules has a uniaxial birefringence effect, and when an external voltage is applied to the liquid crystal, the long axis of the liquid crystal molecules rotates at a different inclination angle due to the different electric field strengths. This changes the optical axis of the liquid crystal compared with the time when the electric field is not applied so that the light passing through the liquid crystal is modulated. The phase delay of LCVR The phase delay of LCVR is related to the applied driving voltage, and the LCVR phase delay characteristics are tested by the optical intensity method. The site of phase delay characteristics tested by the light intensity method is shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. Where LCVR stands for Liquid Crystal Variable Retarder.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>The site of phase delay characteristics tested by the light intensity method.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g005.tif"/>
</fig>
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<label>(13)</label>
</disp-formula>Then the relationship between the outgoing light intensity I and the amount of phase delay <inline-formula id="inf35">
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<label>(14)</label>
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</inline-formula> is the maximum light intensity value of the outgoing light.</p>
<p>The measured LCVR drive voltage versus phase delay amount characteristic curve is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>, where the horizontal coordinate represents the LCVR drive voltage and the vertical coordinate represents the phase delay amount.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Liquid Crystal Variable Retarder phase delay characteristic curve.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g006.tif"/>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Experiments on the effect of different visibility on polarization imaging</title>
<p>For light fog (visibility 5&#xa0;km), medium fog (visibility 0.5&#xa0;km) and dense fog (0.05&#xa0;km) three typical visibility conditions to carry out polarization imaging experiments, imaging of a building 4&#xa0;km away, the experimental results are as follows, <xref ref-type="fig" rid="F7">Figure 7</xref> shows the intensity image under different visibility, <xref ref-type="fig" rid="F9">Figure 9</xref> shows the polarization image under different visibility.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Intensity and Polarization images at different visibility levels. <bold>(A)</bold> Intensity image (visibility 5&#xa0;km) <bold>(B)</bold> Intensity image (visibility 0.5&#xa0;km) <bold>(C)</bold> Intensity image (0.05&#xa0;km) <bold>(D)</bold> Polarization image (visibility 5&#xa0;km) <bold>(E)</bold> Polarization image (visibility 0.5&#xa0;km) <bold>(F)</bold> Polarization image (0.05&#xa0;km).</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g007.tif"/>
</fig>
<p>The histogram of contrast between the intensity image and the polarization image is shown in <xref ref-type="fig" rid="F8">Figure 8</xref>.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Histogram of contrast between intensity image and polarization image.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g008.tif"/>
</fig>
<p>As can be seen from <xref ref-type="fig" rid="F8">Figure 8</xref>, the contrast ratio of the intensity image is 5.5% and the contrast ratio of polarization is 7.6% at the visibility of 5&#xa0;km, which is 1.38 times better; the contrast ratio of the intensity image is 4.4% and the contrast ratio of polarization is 6.3% at the visibility of 0.5&#xa0;km, which is 1.43 times better; the contrast ratio of intensity image is 2.3% and the contrast ratio of polarization at the visibility of 0.05&#xa0;km is 3.8%, an improvement of 1.65 times. The contrast of the polarized image is higher than that of the intensity image at all three visibility levels, which shows that the polarized image can effectively suppress stray light caused by atmospheric particle scattering and effectively improve the image contrast; as the visibility decreases, the image contrast of the polarized image decreases. As the average radius of particles increases when the visibility decreases, the particle concentration increases, which leads to more scattering, while the scattering effect between particles leads to depolarization, which reduces the polarization so that the polarization decreases gradually as the visibility decreases.</p>
</sec>
<sec id="s3-5">
<title>3.5 Experiment with the effect of different wavelengths on polarization imaging</title>
<p>To study the effect of different wavelengths on polarization imaging, we selected three wavelengths, 450&#xa0;nm, 530&#xa0;nm and 670&#xa0;nm, to carry out spectral polarization imaging experiments, imaging of a building 4&#xa0;km away, and the experimental results are as follows. <xref ref-type="fig" rid="F9">Figure 9</xref> shows the intensity polarization images of the three wavelengths.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Intensity and Polarization images of three wavelengths <bold>(A)</bold> 670&#xa0;nm Intensity image <bold>(B)</bold> 530&#xa0;nm Intensity image <bold>(C)</bold> 450&#xa0;nm Intensity image. <bold>(D)</bold> 670&#xa0;nm Polarization image <bold>(E)</bold> 530&#xa0;nm Polarization image <bold>(F)</bold> 450&#xa0;nm Polarization image.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g009.tif"/>
</fig>
<p>The histogram of contrast between the intensity image and the polarization image is shown in <xref ref-type="fig" rid="F10">Figure 10</xref>.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Intensity image and polarization image contrast histogram.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g010.tif"/>
</fig>
<p>As visualized in <xref ref-type="fig" rid="F9">Figure 9</xref>, the intensity image is blurred, the imaging gray value is high, a lot of information is covered, the contour details are not obvious enough, and the target edge information cannot be seen, which is due to the different absorption and scattering effects of sea fog particles on different wavelengths of light in the complex sea fog environment, resulting in more background noise during imaging. There is a significant difference in the grayscale values of the polarized images compared to the conventional intensity images.</p>
<p>
<xref ref-type="fig" rid="F10">Figure 10</xref> shows that at 670&#xa0;nm, the intensity image contrast is 8.1% and the polarization image contrast is 9.3%, an improvement of 1.15 times; at 530&#xa0;nm, the intensity image contrast is 7.0% and the polarization image contrast is 9.0%, an improvement of 1.29 times; at 450&#xa0;nm, the intensity image contrast is 6.4% and the polarization image contrast is 7.5%, a The improvement was 1.17 times. The image contrast of polarization imaging at all three wavelengths is higher than that of intensity images, and the image contrast decreases as the wavelength decreases. Among the three wavelengths, the difference between the target and the background is the largest at 670&#xa0;nm, which is more suitable for the observation of the target.</p>
</sec>
<sec id="s3-6">
<title>3.6 Experiments on the effect of different imaging distances on polarization imaging</title>
<p>To study the effect of different imaging distances on polarization imaging, we selected 50&#xa0;m, 1.5&#xa0;km at the tower crane and 100&#xa0;m, 2.5&#xa0;km at the house to carry out spectral polarization imaging experiments, the experimental results are as follows, <xref ref-type="fig" rid="F11">Figure 11</xref> is the intensity image and polarization degree of the four imaging distances.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Intensity and Polarization images for different imaging distances <bold>(A)</bold> 50&#xa0;m Intensity image <bold>(B)</bold> 1.5&#xa0;km Intensity image <bold>(C)</bold> 100&#xa0;m Intensity image <bold>(D)</bold> 2.5&#xa0;km Intensity image <bold>(E)</bold> 50&#xa0;m Polarization image <bold>(F)</bold> 1.5&#xa0;km Polarization image <bold>(G)</bold> 100&#xa0;m Polarization image <bold>(H)</bold> 2.5&#xa0;km Polarization image.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g011.tif"/>
</fig>
<p>The histograms of the intensity image and polarization image contrast for different imaging distances are shown in <xref ref-type="fig" rid="F12">Figure 12</xref>.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Histogram of contrast between images with different imaging distance intensity and polarized images.</p>
</caption>
<graphic xlink:href="fphy-11-1129517-g012.tif"/>
</fig>
<p>As can be seen in <xref ref-type="fig" rid="F12">Figure 12</xref>, the intensity image contrast of the tower crane at 50&#xa0;m away is 22.5% and the polarization contrast is 55%, which is 2 times higher; the intensity image contrast of the tower crane at 1.5&#xa0;km away is 14% and the polarization contrast is 21.6%, which is 1.54 times higher; the intensity image contrast of the house at 100&#xa0;m away is 21.4% and the polarization contrast is 41%, which is 1.92 times higher; the intensity image contrast of the house at 2.5&#xa0;km away is 16.5% and the polarization contrast is 25.6%, which is 1.55 times higher. The contrast of the intensity image of the house 2.5&#xa0;km away was 16.5%, and the polarization contrast was 25.6%, which improved 1.55 times; the contrast of the polarization image was higher than that of the intensity image; for the same object, the contrast of both the intensity image and the polarization image decreased with the increase of the imaging distance.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>In this paper, we designed a multispectral polarization detection imaging system to study the effects of different visibility, different wavelengths and different imaging distances on the imaging effect. Because when the visibility decreases, increased particle concentration leads to more scattering, and the scattering effect between particles leads to depolarization, thus reducing the polarization, therefore, the polarization will gradually decrease with the decrease of visibility. Under the three wavelengths, the 670&#xa0;nm imaging effect is the best. The closer the imaging distance, the better the imaging effect. According to the calculated contrast, the polarized image has obvious advantages over conventional intensity imaging; the texture details that cannot be seen in the intensity imaging can be well seen in the polarized image. Therefore, when the polarization imaging detection technique is used to detect targets in a sea fog environment, the target contrast can be effectively improved. Polarization imaging can enrich target information, improve image quality and target detection accuracy, and can better analyze the polarized light information reflected from the object&#x2019;s surface, the roughness, texture and edge information of the target can be obtained, which can improve the recognition of the target and the contrast between the target and the background to a certain extent, which is very effective in target recognition in complex environments such as sea fog.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>Data curation, QF and YZ; formal analysis, LS and KL; investigation, JZ and SZ; methodology, QF; project administration, YZ and KL; resources, QF; software, WY and JZ; supervision, MZ and LS; validation, SZ; visualization, MZ and WY; writing&#x2014;original draft, QF; writing&#x2014;review and editing, WY All authors have read and agreed to the published version of the manuscript.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>National Natural Science Foundation of China (No. 61890963; No. 61890960; No. 62127813).</p>
</sec>
<ack>
<p>Thanks to the Natural Science Foundation of China for helping identify collaborators for this work.</p>
</ack>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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