A liquid crystal variable retarder (LCVR) was used for polarization imaging, and the related imaging principle is shown in Figure 2. Two LCVRs were used; the transmission of the polarization prism was perpendicular to the optical axis of LCVR1, and the polarization prism was at an angle of 45° to the optical axis of LCVR2. The LCVR mainly changes the phase difference between the two orthogonal polarization components of the measured light wave, which is equivalent to the role of a waveplate in an optical device.

When a vertical beam of monochromatic line-polarized light is flashed through the LCVR, it is divided into two vibrational components, namely, slow and fast, with an equal phase and amplitude. Figure 3 illustrates the concept of the LCVR liquid crystal polarization modulation.

These two components can be expressed as follows. E f = E 0 cos ⁡ θ = E s = E 0 sin ⁡ θ = 2 2 E 0 (2)

Where E 0 is the amplitude of the monochromatic line polarized light; E f is the amplitude of the polarized light vibrating along the fast axis; and E s is the amplitude of the polarized light vibrating along the slow axis. Eq. 2 indicates that the two vertical components produce a phase difference of 90° when the side is emitted from the liquid crystal phase delay.

1) When a voltage is applied such that the phase delay of the LCVR is λ / 4 , the two quadrature components are modulated by the LCVR to produce a phase difference of π / 2 between the component propagating along the fast axis and the component propagating along the slow axis, which can be expressed as follows [14]. E f = 2 2 E 0 sin τ + δ E s = 2 2 E 0 sin ⁡ τ (3)

A left-handed circularly polarized light is obtained when these two components are combined.

2) When the applied voltage causes the phase delay of LCVR to be 3λ/4, the component located in the slow axis propagates slightly faster, and a phase difference of 3π/2 is generated between the component propagating along the slow axis and component propagating along the fast axis. This can be expressed as follows. E f = 2 2 E 0 sin ⁡ τ E s = 2 2 E 0 sin τ + δ (4)

A right-handed circularly polarized light is obtained when these two components are combined.

By analogy, when the driving voltage is applied such that the phase delay of the LCVR is λ / 2 and λ , the phase difference between the components propagating along the fast and slow axes are π and 0, respectively. When these two orthogonal components are combined, a 0° and 90° linearly polarized light can be obtained.

This imaging approach utilizes a voltage-controlled liquid crystal phase retarder to collect the Stokes parameters without the mechanical rotation of the polarization instrument. This imaging technique has a low reaction time and high precision.

From Figure 4A, it can be seen that the specific process of two-dimensional wavelet decomposition is as follows: first, one-dimensional wavelet decomposition is performed on the one-dimensional data constituting each row in the image, and then one-dimensional wavelet decomposition is done on the one-dimensional data in each column of the low and high frequency information formed by the decomposition, and finally four sub-band images are obtained: c j − 1 、 d j − 1 1 、 d j − 1 2 and d j − 1 3 . where c j − 1 is obtained by row low-pass and column low-pass, so it contains the low-frequency approximation information of the image; d j − 1 1 is obtained by row low-pass and column high-pass, often denoted as d j − 1 L H (L denotes low-pass filtering, H denotes high-pass filtering), which corresponds to the high-frequency component in the vertical direction, i.e., the horizontal edge detail information; d j − 1 2 is obtained by row high-pass and column low-pass, denoted as d j − 1 H L , which corresponds to the high-frequency component in the horizontal direction, i.e., the vertical edge detail information. d j − 1 3 is obtained by row high-pass and column high-pass, denoted as d j − 1 H H , and contains the high-frequency component in the focusing direction, i.e., the diagonal edge detail information [15, 16].

After the image is wavelet transformed, the low-frequency sub-band coefficients still reflect the average energy of the image, and the high-frequency sub-band coefficients reflect the detail information of the image such as edges and textures in different directions. The fusion is performed by using the criterion of weighted average of low-frequency coefficients and the coefficients of high-frequency coefficients are selected to have the largest absolute value, which focuses on fusing the high-frequency parts containing significant details of the images and helps to improve the visual effect of the fused images and retain the significant detail information in the source images. Let the coefficients c A , d A j E 、 c B , d B j E be obtained from the source images A and B after J-layer wavelet decomposition, and the corresponding coefficients of the fused image F are c F , d F j E . Where, c A , d A j E denotes the low-frequency scale coefficients of image X at layer J, and c B , d B j E denotes the high-frequency wavelet coefficients in the direction of layer J of image X.

The weighted average fusion criterion for the low frequency sub-bands is a F m , n = 1 2 c A m , n + c B m , n (5) where m , n denotes the position of the low-frequency sub-band coefficients.

The indoor simulation system device was used to simulate sea fog and non-sea fog environments; an optical imaging experiment was performed in this environment, known as the sea fog box, as shown in Figure 5. The majority of the control section of the sea fog chamber consists of four main components: a sea fog generating device, stirring device, intake and exhaust device, and measuring and detecting equipment.

The detection window may be a concentration monitoring, aerosol particle size detection, visibility detection device, temperature and humidity detection device, power supply cable interface, or interface for other equipment cables. A water mist generator pipe intake, illumination device, and exhaust port were mounted on top of the box. The bottom of the box provides access to the smoke generator pipeline entrance, mixing fan mouth, and two spare detection windows.

Aerosols are also considered as sea fog arising from seawater through evaporation that forms marine aerosols in the atmosphere. Therefore, in this study, seawater was artificially sprayed through an ultrasonic atomizer device to the sea fog box as salt spray to simulate the sea fog environment. Considering the manufactured seawater, the ratio of water to sea salt was 1:2.99 at a temperature of 25°C. Therefore, artificial sea salt particles were purchased, and artificial seawater was rationed according to the aforementioned ratio. The imaging experimental steps are listed as follows.

1) Experimental imaging platform construction: The salt spray in the sea fog box was used as the medium, lighting in the sea fog box was turned on, and optical imaging platform was built outside the sea fog box, as shown in Figure 6.

For comparison with salt spray media imaging, a water mist imaging comparison experiment is conducted here. This experiment simulates water mist under ideal conditions, and the main component of this aerosol is water. The artificial seawater in the water tank is emptied and cleaned, and the water tank is filled with an appropriate amount of pure water to spray water mist into the sea mist tank, and the above experimental steps 1) to 5) are repeated.

Since the indoor polarization imaging experiments were conducted with different concentrations of salt spray and water mist environment as the medium, it was seen that it was crucial to get equal concentration values of salt spray and water mist in a smooth situation. Due to the restricted experimental conditions, it is not possible to obtain information about the medium concentration directly through the instrument, so this experiment is conducted to measure the medium concentration by measuring the light intensity of the incident light and the light intensity of the outgoing light.

During the experiment, the medium concentration has instability, so the concentration of each medium obtained at different fog filling times can be characterized by the optical thickness. The Beer-Lambe law shows that when light is incident into a homogeneous medium, the relationship between the incident light intensity and the outgoing light intensity is as follows. I = I 0 exp − μ g L = I 0 exp − τ (6)

Where I 0 is the incident light intensity, I is the incident light intensity, μ g is the extinction coefficient, L is the thickness of the medium, and τ = μ g L is the optical thickness, where the extinction coefficient is related to the concentration of the absorbing medium [21]. It can be expressed as follows. μ g = ρ C g = ρ π r 0 2 Q g (7)

In the above equation, Q g is the extinction factor, ρ is the concentration of the medium through which the laser passes in the transmission process, π r 0 2 is the absorption cross section of the medium particles, r 0 is the particle radius, and the particle size is basically equal in the same medium. Substituting Eq 7 into Eq 6, the following equation can be obtained T = I / I 0 = exp − τ = exp − ρ π r 0 2 Q g L (8)

In the case of constant particle size, the media thickness L value also remains constant, and the right side π r 0 2 Q g L also remains constant, and from the above Eq 8, we can learn that the media concentration ρ is proportional to the optical thickness τ , so it is feasible to use the optical thickness to characterize the media concentration. Based on the above conclusion, the optical transmittance T is calculated and the corresponding optical thickness τ is derived using Eq. 8.

The above formula shows that only the incident light intensity and the outgoing light intensity can be obtained to calculate the optical thickness of each medium, the experimental process of light intensity measurement is shown in Figure 8. In the indoor experimental process, the fog filling time can be controlled to obtain to different concentrations of the medium environment. First, through the ultrasonic atomizer to the sea box body spray salt spray and wait for the medium to fill the sea fog box, in order to ensure that the received laser power range in the optical power meter range, a beam of laser through the attenuation piece for attenuation, by adjusting the attenuation piece to make the laser output power of 5 mW at the transmitting end, and record the incident light intensity, and then the laser through the sea fog box body and in the box under the action of the internal uniform medium Then the laser passes through the sea fog box and scattering phenomenon occurs under the action of uniform medium inside the box, and finally reaches the receiving end, and again uses the optical power meter at the receiving end to measure the outgoing light in order to get the value of the outgoing light intensity in the continuous stable environment.

In the previous experiment, the medium entered a stable condition for approximately 5–10 min after being filled with salt spray. When the incident light intensity was the same, an optical power meter was used to measure the incident light intensity value through the medium under various fog-filling times. Five groups of salt fog were filled, and the corresponding outgoing light intensity values were recorded to calculate the light transmission rate and optical thickness. To minimize excessive errors, the average value was determined via five separate trials. Table 2 presents the relationship between the salt-spray filling time, light transmission rate, and optical thickness.

To characterize the low and high concentrations of the medium in the sea fog box, indoor tests were chosen when the optical thickness was 0.27 and 2.9. Controlling the water mist filling time to achieve the same optical thickness as the salt mist produced in a water–mist environment. The model of a tank was chosen as the subject of the multiband polarization imaging study. Figure 9 depicts multiband pictures of the salt mist environment, where (a)–(c) represent the medium environment with a low concentration, and (d)–(f) represent the medium environment with a high concentration.

Figure 10 presents the multi-band images of the water mist environment, where (a)–(c) indicate low-concentration media and (d)–(f) indicate high-concentration media environments.

For this experiment, five polarization imaging sessions were performed, the degree of polarization (DOP) data of the corresponding intensity and polarization images were obtained, and the results were averaged for data analysis. The experimental results are shown in Figure 11.

As indicated by the histogram, the DOP of the polarization image decreased when the concentration of the medium was high. This is because the DOP of the polarization image decreases as the concentration increases as the polarized light appears to be significantly depolarized owing to multiple scattering. The largest DOP of the polarimetric image occurred at a wavelength of 670 nm, thus indicating that the image includes a considerable quantity of polarization information, and the observational effect was enhanced. This is because at various concentrations, the absorption and scattering of light waves by water mist particles in the 530 nm band have a greater impact, thereby resulting in a higher penetration rate of water mist particles in this band, which improves the imaging effect and clarifies the edge contour.

Figure 12 shows the polarization fusion image based on two-dimensional discrete wavelet transform; where a) is the multi-band polarization fusion image in low concentration salt mist medium environment, b) is the multi-band polarization fusion image in high concentration salt mist environment, c) is the multi-band polarization fusion image in low concentration water mist medium environment, and d) is the multi-band polarization fusion image in high concentration water mist environment.

The analysis in Table 3 shows that the polarization image fusion method based on the two-dimensional discrete wavelet transform can make the image eliminate noise to a large extent, improve image contrast, and retain some high-frequency details and texture information in the image while recovering the image. The practice shows that the method has good robustness to low signal-to-noise ratio.