A Sea Surface Roughness Retrieval Model Using Multi Angle, Passive, Visible Spectrum Remote Sensing Images: Simulation and Analysis

Abstract

Sea surface roughness (SSR) retrieval is a frontier topic in the field of ocean remote sensing, and SSR retrieval based on multi angle, passive, visible spectrum remote sensing images has been proven to have potential applications. Traditional multi angle retrieval models ignored the nonlinear relationship between radiation and digital signals, resulting in low accuracy in SSR retrieval using visible spectrum remote sensing images. Therefore, we analyze the transmission characteristics of signals and random noise in sea surface imaging, establish signals and noise transmission models for typical sea surface imaging visible spectrum remote sensing systems using Complementary Metal Oxide Semiconductor (CMOS) and Time Delay Integration-Charge Coupled Device (TDI-CCD) sensors, and propose a model for SSR retrieval using multi angle passive visible spectrum remote sensing images. The proposed model can effectively suppress the noise behavior in the imaging link and improve the accuracy of SSR retrieval. Simulation experiments show that when simulating the retrieval of multi angle visible spectrum images obtained using CMOS or TDI-CCD imaging systems with four SSR levels of 0.02, 0.03, 0.04, and 0.05, the proposed model relative errors using two angles are decreased by 4.0%, 2.7%, 2.3%, and 2.0% and 6.5%, 4.3%, 3.7%, and 3.2%, compared with the relative errors of the model without considering noise behavior, which are 7.0%, 6.7%, 7.8%, and 9.0% and 9.5%, 8.3%, 9.0%, and 10.2%. When using more fitting data, the relative errors of the model were decreased by 5.0%, 2.7%, 2.5%, and 2.0% and 7.0%, 5.0%, 4.3%, and 3.2%, compared with the relative errors of the model without considering noise behavior, which are 8.5%, 7.0%, 8.0%, and 9.4%, and 10.0%, 8.7%, 9.3%, and 10.0%.

1. Introduction

Sea surface roughness is an important physical parameter for studying the sea surface, and has important application value in fields such as oil spill observation [1,2], ocean dynamic observation [3,4,5], bathymetry [6,7], and sea ice observation [8,9,10], etc. Due to the complexity and randomness of sea surface fluctuations, it is difficult to directly measure SSR. Sea surface roughness is usually obtained using measured data (such as wind speed and other sea variables) and empirical formulas [11,12]. In recent years, active and passive ocean remote sensing methods such as microwave radar and optical imaging have been widely used to retrieve and analyze sea surface roughness and its related physical quantities.

Microwave radar is currently the main method for retrieving roughness and its related parameters through ocean remote sensing. It can be mainly divided into active and passive methods represented by the altimeter, reflectometer, scatterometer, synthetic aperture radar (SAR), and radiometer. The basic idea of using an altimeter to obtain sea surface roughness is to calculate changes in sea surface elevation and other data by receiving pulse echoes emitted by the altimeter, and then quantify sea surface roughness. In the past thirty years, satellite launch missions have continuously measured relevant data, and in recent years, new altimeters have gradually integrated SAR technology, which have high-precision sea surface imaging capabilities [13]. A reflectometer can receive signals reflected by navigation satellites from the sea surface and invert the roughness of the sea surface by analyzing the features [14,15]. Considering the direct relationship between sea surface roughness and radar backscattering signals, as roughness increases, scattering effects become stronger. Therefore, the relationship between backscattering coefficient and roughness can be established, and sea surface roughness calculation can be achieved. This is also the basic idea of microwave scatterometer for sea surface roughness retrieval [16,17]. Although the working principles of a synthetic aperture radar (SAR) and microwave scatterometer are different, their retrieval mechanisms have certain similarities. By measuring the backscattering signal of the sea surface, SAR generates high-resolution image data that characterizes the scattering intensity. The relationship between the image and the sea surface roughness can be established through the backscattering model, and the sea surface roughness information can be obtained. It is also the main method for conducting sea surface roughness retrieval and related research in recent years [18,19]. Based on typical methods such as the scatterometer and SAR, many studies have conducted in-depth research on how to accurately establish retrieval models, develop artificial intelligence algorithms, and so on. For example, Hwang et al. [20] proposed a method to obtain the short-scale properties of ocean surface roughness and wave breaking from Ku, C, and L band polarimetric sea returns, and the results can be used for quantitative evaluation of the ocean surface roughness spectral models. Iervolino et al. [21] proposed a new technique for estimating sea surface roughness parameters from SAR images by minimizing the absolute error between the Radar Cross Section of the sea surface measured on the SAR image and the expected RCS computed using the Kirchhoff approach within the Geometrical Optics solution. In addition, the roughness of the sea surface is directly related to environmental, dynamic and other parameters, so the sea surface roughness data obtained by SAR can also be used for the inversion of other parameters [22,23,24]. Unlike active detection methods such as the altimeter, reflectometer, scatterometer, and SAR, the radiometer belongs to passive remote sensing techniques. Its basic idea is that an increase in roughness will enhance the emissivity of the sea surface, leading to an increase in brightness temperature. Therefore, roughness information and related parameters can be inverted through brightness temperature data [25,26]. Although researchers have conducted many studies related to roughness retrieval using microwave remote sensing methods, there are still precision constraints such as low data resolution and high model complexity.

Optical remote sensing technology has the advantages of high data resolution and convenient data acquisition, which can complement microwave remote sensing. In recent years, research on retrieving SSR and its related physical quantities based on optical remote sensing methods is widely emerging in the field of ocean detection. The basic idea is to establish a quantitative relationship model between sea surface optical images/optical characteristics and sea surface roughness parameters or related physical parameters, such as the following: Based on the Cox and Munk [27] model, Burdyugov et al. [28] analyzed the relationship between the observed brightness of the sea and the information about the root mean square slope and its spatial variations, and recorded the surface development of interval waves by a series of numerical presumptions of photographic images of the Black Sea. Kudryavtsev et al. [1] proposed a method for retrieving and analyzing fine spatial variations in the sea surface roughness using sun glitter images, and applied this method to the analysis of oil spill scenes using MODIS and MERIS sun glitter image data. Many indirect studies on wind speed, water depth, etc. [6,29], can also provide theoretical support for roughness retrieval. Among these optical remote sensing retrieval methods, using multi angle image data to retrieve sea surface roughness and related parameters is a highly anticipated new approach. Rascle et al. [30,31] used airborne multiple angle data to observe roughness and retrieve the current gradient direction at the front. They also used airborne and satellite data of different scales to observe roughness and retrieve the current gradient magnitude and scale. Zhang et al. [32] proposed a model for estimating SSR at the pixel scale using multi angle sun glitter images. Mosadegh et al. [33] designed a data processing system for sea ice surface roughness, which is based on multi angle imaging spectroradiometer imagery. Recent studies have shown that using multi angle, passive, visible spectrum remote sensing images to retrieve SSR has potential applications. However, we found that most of these studies did not analyze the differences between digital signals and radiation signals. When using imaging data, the noise generated during the signal transmission of the imaging system can lead to a nonlinear relationship between radiation and digital signals, which restricts the accuracy of SSR retrieval.

Based on the above statement, we conduct the following work in this article: (1) Model the signals and noise transmission models of two typical visible spectrum remote sensing systems based on Complementary Metal Oxide Semiconductor (CMOS) and Time Delay Integration-Charge Coupled Device (TDI-CCD) for sea surface imaging. (2) Propose a model for SSR retrieval using multi angle visible spectrum remote sensing images, which considers the random noise behavior during the imaging process. (3) Simulate the model accuracy at different SSR levels, and analyze the interference of noise, angle selection and sensor parameter uncertainty to verify the superiority of the model.

The article is organized as follows. Section 2 introduces the sea surface imaging model and the proposed SSR retrieval model. Section 3 introduces data preparation and SSR retrieval results. Section 4 discusses the interference of noise, angle, and sensor parameters on SSR retrieval results. Section 5 draws conclusions.

2. Proposed Model

According to the basic principles of optical remote sensing imaging, if we want to use digital images to retrieve SSR, we must clarify how the optical signals representing SSR are converted into digital images. Therefore, we need to first establish a forward model for sea surface imaging, and then derive the reverse model for SSR retrieval.

2.1. Sea Surface Imaging Model

Assuming the solar zenith angle is θ_s, the solar azimuth angle is φ_s, the view zenith angle is θ_o, and the view azimuth angle is φ_o. We can use the Cox–Munk model [27] to analyze the tilt angle of the reflection facet:

$${\theta }_n=\arccos {\displaystyle \frac{cos{\theta }_s+cos{\theta }_o}{2\cdot cos\beta }}$$

(1)

$$\beta ={\displaystyle \frac{\arccos [cos{\theta }_{s}cos{\theta }_o+sin{\theta }_{s}sin{\theta }_{o}cos\left({\phi }_s-{\phi }_o\right)]}{2}}$$

(2)

We establish the probability density function of the wave slopes according to [23]:

$$p({\sigma }^2,\beta )={\displaystyle \frac{\exp (-\frac{{\tan }^2\beta }{{\sigma }^2})}{\pi \cdot {\sigma }^2}}$$

(3)

where σ² denotes SSR, which is a function of wind speed w, ${\sigma }^2=0.003+0.00512\cdot w$.

Considering that the proportion of water-leaving radiation to the total sea surface radiation signal is relatively small and its contribution to the signal and noise is limited, it can be regarded as an error fluctuation or removed through measurement. Therefore, the modeling process of this article ignores the water-leaving radiation, and the optical signal that can be captured by remote sensing imaging systems is as follows:

$$E_o={\displaystyle \frac{E\cdot t\cdot \rho \cdot p({\sigma }^2,\beta )}{4\cdot \cos {\theta }_o\cdot {\cos }^4{\theta }_n}}$$

(4)

where E denotes the solar irradiance, t denotes the downwelling direct transmittance, ρ denotes the Fresnel reflection coefficient. E_o is transmitted to the imaging sensor after passing through the optical system and attenuated to the following:

$$E_{sensor}={\displaystyle \frac{\pi \cdot {\tau }_o\cdot E_o}{4F^2}}$$

(5)

where τ_o denotes the transmittance of the optical system, and F denotes the F-Number (f/#) of the optical system.

For different sensors, the process of converting optical signals into electrical signals is different. We use the most common types of optical sensors (CMOS and TDI-CCD) in remote sensing systems as examples for analysis. For CMOS, we model signal electrons N_{s_cmos} and Noise Electrons N_{n_cmos} according to the typical working principle as follows:

$$N_{s\_cmos}={\displaystyle \frac{E_{sensor}\cdot \eta \cdot T_e\cdot \lambda \cdot {\mu }^2}{h\cdot c}}$$

(6)

$$N_{n\_cmos}=\sqrt{{\sigma }_{shot}^2+{\sigma }_{dark}^2+{\sigma }_{rms}^2}$$

(7)

where η denotes quantum efficiency, T_e denotes exposure time, λ denotes the central wavelength, μ denotes the pixel size of CMOS sensor, h is the Planck constant, c is the speed of light. σ_shot, σ_dark, σ_rms represents the equivalent electrons of shot noise, dark current noise, and readout noise, respectively. σ_dark, σ_rms are basic parameters of imaging systems, which can be obtained using laboratory measurements for cameras without prior knowledge. σ_shot is related to the number of signal electrons, and can be simulated by performing square root operation on the calculated or captured signal electron values N_{s_cmos}.

The total electrons N_cmos of the CMOS imaging system is as follows:

$$N_{cmos}=N_{s\_cmos}+N_{n\_cmos}$$

(8)

For TDI-CCD, we model signal electrons N_{s_tdiccd} and Noise Electrons N_{n_tdiccd} according to the typical working principle:

$$N_{s\_tdiccd}={\displaystyle \frac{E_{sensor}\cdot R\cdot T_{\mathrm{int}}\cdot M\cdot {\zeta }_{transfer}}{M_{\max }\cdot C}}$$

(9)

$$N_{n\_tdiccd}={\displaystyle \sum _{i=1}^M\sqrt{M{\sigma }_{shot}^2+M{\sigma }_{dark}^2+M{\sigma }_{rms}^2}}$$

(10)

where R denotes the average spectral responsivity, M denotes the integration stage, M_max denotes the maximum integration stage, C denotes the charge conversion factor, and ζ_transfer denotes the total charge transfer efficiency.

The total electrons N_tdiccd of the TDI-CCD imaging system can be expressed as follows:

$$N_{tdiccd}=N_{s\_tdiccd}+N_{n\_tdiccd}$$

(11)

Using the total electrons, the digital signal value of a CMOS or TDI-CCD imaging system can be modeled as follows:

$$DN={\displaystyle \frac{N_{sensor}\cdot 2^n}{N_{fullwell}}}$$

(12)

where DN denotes the output digital signal value, N_sensor denotes the total electrons of the sensor, n denotes the quantization bit, N_fullwell denotes the full well capacity.

Referring to the above process, we establish a relationship model between SSR and digital signals for typical CMOS and TDI-CCD imaging systems, and this model contains random noise.

2.2. SSR Retrieval Model

When two imaging systems capture images at the same time or one imaging system continuously captures images within a short time interval, SSR can be considered constant. According to (12), the digital signals of the images obtained from two different observation angles can be expressed as follows:

$$D{N}_1={\displaystyle \frac{\frac{C_{set}\cdot \exp (-\frac{{\tan }^2{\beta }_1}{{\sigma }^2})}{{\sigma }^2\cdot \cos {\theta }_{o1}\cdot {\cos }^4{\theta }_{n1}}+N_{n1}}{N_{fullwell}}}\cdot 2^n$$

(13)

$$D{N}_2={\displaystyle \frac{\frac{C_{set}\cdot \exp (-\frac{{\tan }^2{\beta }_2}{{\sigma }^2})}{{\sigma }^2\cdot \cos {\theta }_{o2}\cdot {\cos }^4{\theta }_{n2}}+N_{n2}}{N_{fullwell}}}\cdot 2^n$$

(14)

where subscripts 1 and 2 denote the parameters observed from two angles, N_n1 and N_n2 denote the random noise obtained using (7) or (10) based on σ_shot, σ_dark, σ_rms specified in the manual or measured. Since shot noise and dark current noise follow Poisson distribution characteristics, and readout noise follows Gaussian distribution characteristics, Poisson–Gaussian distribution can be chosen for noise fitting. C_set denotes a set of fixed parameters for a CMOS or TDI-CCD sensor:

$$C_{set\_cmos}={\displaystyle \frac{{\tau }_o\cdot E\cdot t\cdot \rho \cdot \eta \cdot T_e\cdot \lambda \cdot {\mu }^2}{16F^2\cdot h\cdot c}}$$

(15)

$$C_{set\_tdiccd}={\displaystyle \frac{{\tau }_o\cdot R\cdot T_{\mathrm{int}}\cdot M\cdot {\zeta }_{transfer}\cdot E\cdot t\cdot \rho }{16F^2\cdot M_{\max }\cdot C}}$$

(16)

According to (13) and (14), we can calculate the relationship between the ratio of two angle digital signals, which is a function of SSR:

$${\displaystyle \frac{D{N}_1\cdot N_{fullwell}/2^n-N_{n1}}{D{N}_2\cdot N_{fullwell}/2^n-N_{n2}}}=\exp ({\displaystyle \frac{{\tan }^2{\beta }_2-{\tan }^2{\beta }_1}{{\sigma }^2}})\cdot {\displaystyle \frac{\cos {\theta }_{o2}\cdot {\cos }^4{\theta }_{n2}}{\cos {\theta }_{o1}\cdot {\cos }^4{\theta }_{n1}}}$$

(17)

According to (17), we can establish the following SSR retrieval model:

$${\sigma }^2=<{\displaystyle \frac{{\tan }^2{\beta }_2-{\tan }^2{\beta }_1}{\ln \frac{(\frac{N_{fullwell}\cdot D{N}_1}{2^n}-N_{n1})\cdot \cos {\theta }_{o1}\cdot {\cos }^4{\beta }_1}{(\frac{N_{fullwell}\cdot D{N}_2}{2^n}-N_{n2})\cdot \cos {\theta }_{o2}\cdot {\cos }^4{\beta }_2}}}>$$

(18)

where < > represents calculating the spatial average value.

When there are two or more imaging angles, the SSR retrieval result can be obtained for every two angles. Calculate the fitted mean line for all SSRs to identify retrieval data within the 95% confidence interval. Then calculate the fitted mean line within the confidence interval and obtain the final retrieval result. Then use least squares regression to fit the data within the confidence interval and obtain the final retrieval result.

3. Results

3.1. Data Preparation

In order to accurately analyze and compare the SSR retrieval performance, we simulated sea surface images with fixed SSR levels as the reference data. Using the water-tank experiment scenario as a simulation scenario, assuming the solar radiation E is 10 W/m², the downwelling direct transmittance t is 0.9, the optical system transmittance τ_o is 0.9, the F-Number of optical system is 6, and the CMOS and TDI-CCD sensor parameters are shown in

Table 1. Parameters of CMOS sensor.

Symbol	Parameter	Value
η	Quantum efficiency	0.6
μ	Pixel size	5 μm
Te	Exposure time	2 ms
Nfullwell	Full well capacity	10,000
n	Quantization bit	10

and

Table 2. Parameters of TDI-CCD sensor.

Symbol	Parameter	Value
R	Average spectral responsivity	100,000
Tint	Integration time	0.3 ms
M	Integration stage	32
Mmax	Maximum integration stage	96
C	Charge conversion factor	0.00001
ζtransfer	Total charge transfer efficiency	1
Nfullwell	Full well capacity	100,000
n	Quantization bit	10

. The captured passive visible spectrum images with different angles (as shown in Figure 1) are simulated as multi angle data for SSR retrieval.

3.2. SSR Retrieval

Analyze the performance of retrieving SSR using two angle visible spectrum images. Select the simulated SSR and corresponding wind speed shown in

Table 3. SSR retrieved using two angle visible spectrum images.

Wind Speed	Simulated SSR	Retrieved SSR
		CMOS	TDI-CCD
3.33 m/s	0.02	0.0206	0.0206
5.27 m/s	0.03	0.0312	0.0312
7.22 m/s	0.04	0.0422	0.0421
9.18 m/s	0.05	0.0535	0.0535

, assuming a solar zenith angle of 30°, a solar azimuth angle of 270°, and the view azimuth angle is 45°, the first view zenith angle is 20°, and the second view zenith angle is 40°. Images are captured using CMOS and TDI-CCD imaging systems, respectively, and the retrieved SSR results are shown in Table 3.

It can be seen from Table 3 that when the simulated SSR levels are 0.02, 0.03, 0.04, and 0.05, the relative errors of SSRs retrieved using CMOS imaging system are 3.0%, 4.0%, 5.5%, and 7.0%, respectively, and the relative errors of SSRs retrieved using TDI-CCD imaging system are 3.0%, 4.0%, 5.3%, and 7.0%, respectively. The difference between SSR results retrieved using CMOS imaging systems and TDI-CCD imaging systems is very small, and it is mainly caused by the difference in the number of random noise electrons. The pattern of both types of imaging systems is that as the roughness increases, the relative error of retrieval SSR increases.

Analyze the performance of retrieving SSRs using images with multi (more than 2) angles. Assuming the solar zenith angle is 30°, the solar azimuth angle is 270° and the view azimuth angle is 45°. We use a set of view zenith angles (20°, 25°, 30°, 35°, 40°, and 45°) to simulate the adjustment of pitch angle in remote sensing imaging. By combining every two view zenith angles, 15 pairs of images and 15 retrieval SSRs can be obtained. Calculate the fitted mean line of 15 SSRs, and then calculate the fitted mean line of SSRs within the 95% confidence interval to obtain the final SSR fitting value (as shown in Figure 2).

It can be seen from Figure 2 that there are differences in the values of SSR retrieved from different view angles. Based on the analysis of the simulated image, we found that when the retrieval error is large, the degradation of image details is significant, indicating weak signals in the image and significant noise behavior. By fitting the data within the confidence interval twice, we can effectively avoid results with significant errors. When the simulated SSR levels are 0.02, 0.03, 0.04, and 0.05, the relative errors of SSRs retrieved using CMOS imaging system are 3.5%, 4.3%, 5.5%, and 7.4%, respectively, and the relative errors of SSRs retrieved using TDI-CCD imaging system are 3.0%, 3.7%, 5.0%, and 6.8%, respectively. Similarly to the two angle retrieval method, multi angle retrieval still shows a trend of error increasing with the increase in SSR.

3.3. Simulation Application Results

Simulate the application scenario according to Section 3.1. and retrieve SSRs in application scenario. References [34,35] and other literature, combined with simulation and measured data in weak target signal application scenarios, assuming the solar radiation E is 150 W/m², the downwelling direct transmittance t is 0.4. To ensure no pixel saturation, the CMOS exposure time and TDI-CCD integration time are set to 0.3 ms and 0.05 ms, respectively, and all other parameters remain unchanged. Two angle visible spectrum images and multi angle visible spectrum images were used for SSR retrieval, and the angles selection and fitting method were consistent with Section 3.2. The retrieved SSR results are shown in

Table 4. SSR retrieved using two angle visible spectrum images in application scenario.

Wind Speed	Simulated SSR	Retrieved SSR
		CMOS	TDI-CCD
3.33 m/s	0.02	0.0206	0.0206
5.27 m/s	0.03	0.0312	0.0312
7.22 m/s	0.04	0.0422	0.0421
9.18 m/s	0.05	0.0535	0.0534

and Figure 3.

It can be seen from Table 4 and Figure 3 that for application scenario, when using two angle visible spectral images for SSR retrieval, the relative errors of SSRs retrieved using CMOS imaging system are 3.0%, 4.0%, 5.5%, and 7.0%, respectively, and the relative errors of SSRs retrieved using TDI-CCD imaging system are 3.0%, 4.0%, 5.3%, and 6.8%, respectively. The SSR retrieval results obtained by fitting 15 pairs of images and 15 retrieval SSRs show that the relative errors of SSRs retrieved using CMOS imaging system are 3.5%, 4.3%, 5.5%, and 7.6%, respectively, and the relative errors of SSRs retrieved using TDI-CCD imaging system are 2.5%, 3.7%, 5.0%, and 6.4%, respectively. From the data comparison results of Table 3 and Table 4, Figure 2 and Figure 3, it can also be seen that the proposed method has similar retrieval accuracy for different scenario data.

4. Discussion

Due to the direct interference of noise behavior on the SSR retrieval results in this article, compared with the application scenario, the noise characteristics of the water-tank experiment scenario are more significant, which is suitable for analyzing model performance. Therefore, in this section, we use water-tank experiment scenario data to conduct SSR retrieval discussion.

4.1. Noise Analysis

We analyzed the interference of noise on the SSR retrieval results. When there is no noise behavior, (18) can be written as follows:

$${\sigma }^2=<{\displaystyle \frac{{\tan }^2{\beta }_2-{\tan }^2{\beta }_1}{\ln \frac{D{N}_1\cdot \cos {\theta }_{o1}\cdot {\cos }^4{\beta }_1}{D{N}_2\cdot \cos {\theta }_{o2}\cdot {\cos }^4{\beta }_2}}}>$$

(19)

According to (19), the results of using image digital signals to retrieve SSR are the same as the results of using radiation to retrieve SSR. Compare the results of (18) and (19). Using the parameters in Table 3 and Figure 2, the results of using two angle images to retrieve SSR without noise behavior are shown in

Table 5. SSR retrieval using two angle visible spectrum images without noise behavior.

Wind Speed	Simulated SSR	Retrieved SSR
		CMOS	TDI-CCD
3.33 m/s	0.02	0.0214	0.0219
5.27 m/s	0.03	0.0320	0.0325
7.22 m/s	0.04	0.0431	0.0436
9.18 m/s	0.05	0.0545	0.0551

. The comparison of the results of using multi angle visible spectrum images to retrieve and fit SSR is shown in Figure 4.

It can be seen from Table 5 that when the simulated SSR values are 0.02, 0.03, 0.04, and 0.05, according to (19) and using two angle images retrieval method, the relative errors of retrieved SSRs using CMOS imaging system are 7.0%, 6.7%, 7.8%, and 9.0%, respectively, and the relative errors of retrieved SSRs using TDI-CCD imaging system are 9.5%, 8.3%, 9.0%, and 10.2%, respectively. Compared with the results in Table 3, the relative errors retrieved using CMOS imaging system decreased by 4.0%, 2.7%, 2.3%, and 2.0%, while the relative errors retrieved using TDI-CCD imaging system decreased by 6.5%, 4.3%, 3.7%, and 3.2% after introducing noise behavior.

It can be seen from Figure 4 that when using multi angle visible spectrum images retrieval method, the retrieval accuracy of the fitted SSRs according to (18) is higher than that according to (19). When the simulated SSR values are 0.02, 0.03, 0.04, and 0.05, the relative errors of fitted SSRs using CMOS imaging system are 8.5%, 7.0%, 8.0%, and 9.4%, and the relative errors of fitted SSRs using TDI-CCD imaging system are 10.0%, 8.7%, 9.3%, and 10.0% according to (19). The relative errors retrieved using CMOS imaging system decreased by 5.0%, 2.7%, 2.5%, and 2.0%, while the relative errors retrieved using TDI-CCD imaging system decreased by 7.0%, 5.0%, 4.3%, and 3.2%.

Simulation experiment results for noise analysis show that as the simulated SSR increases, the difference in relative error of retrieved SSR before and after introducing noise interference tends to decrease. Introducing noise behavior into the multi angle SSR retrieval model can effectively improve retrieval accuracy.

It should be pointed out that the data analyzed in this article is image data obtained by CMOS or TDI-CCD sensors. The characteristic of these data is that random noise accumulates on the original signal, which also affects the consistent positive bias characteristics of our SSR retrieval results. Although the retrieval accuracy of the fitted SSR using (18) is higher than that of the SSR based on (19), the randomness of noise still leads to deviations between the retrieval results and the simulated SSR.

Analyze the interference of different noise levels on model accuracy. Using simulated SSR of 0.02 as an example for discussion. For TDI-CCD and CMOS sensors, assuming that the lighting conditions and imaging parameters in Section 3.1. remain unchanged, and the shot noise remains unchanged, we artificially increase the calculated values of readout noise and dark current noise by two, three, and four times, and represent these four noise levels as N_dr1, N_dr2, N_dr3, and N_dr4. The retrieved SSRs under different noise levels were calculated using both two angle and multi angle methods, and the results are shown in

Table 6. SSR retrieval using different levels of dark current and readout noise.

Simulated SSR	Noise Level	Retrieved SSR (Using Two Angles)		Retrieved SSR (Using Multi Angles)
		CMOS	TDI-CCD	CMOS	TDI-CCD
0.02	Ndr1	0.0206	0.0206	0.0207	0.0206
	Ndr2	0.0206	0.0206	0.0208	0.0206
	Ndr3	0.0206	0.0206	0.0208	0.0206
	Ndr4	0.0206	0.0206	0.0209	0.0207

. It can be seen from Table 6 that there is not much difference in the accuracy of SSR retrieval for four different noise levels, and the retrieval results using two view zenith angles of 20° and 40° are approximately consistent. The results retrieved from the other two angles showed no significant difference. However, there are cases where the signal-to-noise ratio of imaging at certain angles is low, and the increase in noise causes certain retrieval bias, resulting in a decrease in the retrieval accuracy of multi angle fitting. Overall, the increase in dark current and readout noise will lead to a certain decrease in retrieval accuracy, but the overall results are still better than the model results without considering noise behavior.

Keep the calculated values of readout noise and dark current noise unchanged, and change the solar radiation value to affect the level of shot noise. Using four solar radiation levels of 5 W/m², 10 W/m², 15 W/m², and 20 W/m², the corresponding noise levels were represented as N_s1, N_s2, N_s3, and N_s4 for SSR retrieval. The results are shown in

Table 7. SSR retrieval using different levels of shot noise.

Simulated SSR	Noise Level	Retrieved SSR (Using Two Angles)		Retrieved SSR (Using Multi Angles)
		CMOS	TDI-CCD	CMOS	TDI-CCD
0.02	Ns1	0.0206	0.0206	0.0209	0.0206
	Ns2	0.0206	0.0206	0.0207	0.0206
	Ns3	0.0206	0.0206	0.0206	0.0205
	Ns4	0.0206	0.0206	0.0206	0.0205

. It can be seen from Table 7 that when using two view zenith angles of 20° and 40° for retrieval, the approximate results of SSR are consistent. When using multi angle fitting to retrieve results, different levels of noise can lead to differences in retrieval accuracy. Among the four selected noise levels, the lower the solar radiation, the lower the SSR retrieval accuracy. Although an increase in solar radiation brings more shot noise, the number of signal electrons also increases, and the decrease in the proportion of noise keeps the retrieval accuracy stable and improves at some angles. Overall, under different levels of noise, the performance of the SSR retrieval model is still better than that without considering noise behavior. In summary, the proposed model has a certain degree of robustness to different levels of noise.

4.2. Angle Analysis

Sensitivity analysis was conducted on the impact of view zenith angles on SSR retrieval accuracy. Firstly, we fitted SSRs using different numbers of view zenith angles to analyze their impact on the SSR fitted accuracy.

Assuming the solar zenith angle is 30°, the solar azimuth angle is 270° and the view azimuth angle is 45°. We use combinations of three view zenith angles, four view zenith angles, and five view zenith angles to calculate and analyze SSRs. Among them, six representative combinations of three view zenith angles were selected, namely (20°, 30°, 40°), (25°, 35°, 45°), (20°, 25°, 30°), (25°, 30°, 35°), (30°, 35°, 40°), and (35°, 40°, 45°). By combining every two view zenith angles, three pairs of images and three retrieval SSRs can be obtained. Six representative combinations of four view zenith angles were selected, namely (20°, 25°, 30°, 35°), (25°, 30°, 35°, 40°), (30°, 35°, 40°, 45°), (20°, 25°, 40°, 45°), (20°, 25°, 30°, 40°), and (20°, 30°, 40°, 45°). By combining every two view zenith angles, six pairs of images and six retrieval SSRs can be obtained. Six representative combinations of five view zenith angles were selected, namely (20°, 25°, 30°, 35°, 40°), (20°, 30°, 35°, 40°, 45°), (20°, 25°, 35°, 40°, 45°), (20°, 25°, 30°, 40°, 45°), (20°, 25°, 30°, 35°, 45°), and (25°, 30°, 35°, 40°, 45°). By combining every two view zenith angles, 10 pairs of images and 10 retrieval SSRs can be obtained. The fitting operation was performed on the SSR retrieval results obtained from image pairs at different angles, and fitted SSRs using different numbers of angles are shown in Figure 5. Calculate the mean and standard deviation of fitted SSRs at different numbers of angles, as shown in

Table 8. Mean and standard deviation of fitted SSRs using different numbers of angles (CMOS).

Number	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	Mean	Std	Mean	Std	Mean	Std	Mean	Std
3	0.0208	3.8859 × 10−4	0.0316	7.0828 × 10−4	0.0427	9.7245 × 10−4	0.0545	0.0015
4	0.0207	8.1650 × 10−5	0.0313	1.6733 × 10−4	0.0423	3.7238 × 10−4	0.0539	7.4207 × 10−4
5	0.0207	5.1640 × 10−5	0.0313	6.3246 × 10−5	0.0423	2.0656 × 10−4	0.0536	2.1370 × 10−4

and

Table 9. Mean and standard deviation of fitted SSRs using different numbers of angles (TDI-CCD).

Number	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	Mean	Std	Mean	Std	Mean	Std	Mean	Std
3	0.0206	1.9408 × 10−4	0.0313	4.1673 × 10−4	0.0423	7.9162 × 10−4	0.0539	0.0015
4	0.0206	8.3666 × 10−5	0.0311	1.2247 × 10−4	0.0420	2.5033 × 10−4	0.0534	4.1191 × 10−4
5	0.0206	5.1640 × 10−5	0.0311	9.8319 × 10−5	0.0420	1.6330 × 10−4	0.0533	1.9664 × 10−4

.

From Figure 5 and Table 8 and Table 9, it can be seen that the selection of the number of view zenith angles has a certain impact on the results of our model, whether for CMOS or TDI-CCD. The more view zenith angles selected, the more stable the fitted SSR data obtained. The reason for the above pattern is due to the relatively large errors in SSR values retrieved from individual angles before fitting. When the number of angles is insufficient, the SSR retrieval results with large errors will interfere with the final fitting results. When the number of angles increases, the fitting method adopted in this article can effectively avoid the interference of outliers and maintain stable fitting accuracy to the maximum extent. When the sea surface roughness level increases, the retrieval error will increase, and a smaller number of view zenith angles may cause significant errors. For example, when the simulated SSR is 0.05, the standard deviation of SSRs fitted with three angles reaches 0.0015. When the three view zenith angles are (20°, 25°, 30°), the fitted SSR is 0.0574. When adding one angle to (20°, 25°, 30°, 35°), the fitted SSR increases to 0.0550. And when adding another angle to (20°, 25°, 30°, 35°, 40°), the fitted SSR increases to 0.0538. Therefore, for higher levels of sea surface roughness, using more angles to fit SSR can achieve better retrieval accuracy and stability.

Using different numbers of retrieved SSRs for SSR fitting, and analyze their impact on fitting accuracy. From the SSR retrieval results obtained from 15 view zenith angles (20°, 25°, 30°, 35°, 40°, 45°), 3~14 sets (including 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14) of data from different view zenith angles were randomly selected for SSR fitting. The fitting operation was repeated 10 times for each set, and the data used in each repeated experiment was inconsistent. The fitted SSRs with different numbers of retrieved SSRs are shown in Figure 6 and Figure 7. Analyze the fitted SSRs in Figure 6 and Figure 7, and the mean and standard deviation of fitted SSRs using different numbers of retrieved SSRs are shown in

Table 10. Mean and standard deviation of fitted SSRs using different numbers of retrieved SSRs (CMOS).

Number	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	Mean	Std	Mean	Std	Mean	Std	Mean	Std
3	0.0208	3.2735 × 10−4	0.0317	5.6683 × 10−4	0.0426	6.6292 × 10−4	0.0543	7.1090 × 10−4
4	0.0208	2.8491 × 10−4	0.0314	3.3649 × 10−4	0.0425	4.1362 × 10−4	0.0547	5.1105 × 10−4
5	0.0206	1.1270 × 10−4	0.0312	9.2832 × 10−5	0.0421	1.6876 × 10−4	0.0536	3.6272 × 10−4
6	0.0206	8.1507 × 10−5	0.0312	9.6452 × 10−5	0.0422	2.4870 × 10−4	0.0536	3.6788 × 10−4
7	0.0206	6.0777 × 10−5	0.0312	1.3246 × 10−4	0.0423	2.1404 × 10−4	0.0536	2.2404 × 10−4
8	0.0207	4.0914 × 10−5	0.0312	7.7275 × 10−5	0.0422	1.8431 × 10−4	0.0536	2.4339 × 10−4
9	0.0207	6.5264 × 10−5	0.0313	5.9143 × 10−5	0.0422	1.4107 × 10−4	0.0536	2.5683 × 10−4
10	0.0207	5.4573 × 10−5	0.0312	1.4729 × 10−5	0.0423	1.8891 × 10−4	0.0536	1.0619 × 10−4
11	0.0207	5.7051 × 10−5	0.0313	6.5933 × 10−5	0.0423	1.4650 × 10−4	0.0536	1.4172 × 10−4
12	0.0207	5.3545 × 10−5	0.0313	3.4202 × 10−5	0.0422	7.3500 × 10−5	0.0536	1.4568 × 10−4
13	0.0206	2.3675 × 10−5	0.0313	4.6944 × 10−5	0.0422	6.2344 × 10−5	0.0537	8.7450 × 10−5
14	0.0207	1.2421 × 10−5	0.0313	1.1609 × 10−5	0.0422	5.0399 × 10−5	0.0537	5.7833 × 10−5

and

Table 11. Mean and standard deviation of fitted SSRs using different numbers of retrieved SSRs (TDI-CCD).

Number	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	Mean	Std	Mean	Std	Mean	Std	Mean	Std
3	0.0207	1.4778 × 10−4	0.0314	3.2478 × 10−4	0.0423	6.3247 × 10−4	0.0541	0.0011
4	0.0206	5.9861 × 10−5	0.0313	2.3010 × 10−4	0.0424	4.8005 × 10−4	0.0543	9.7426 × 10−4
5	0.0206	3.5449 × 10−5	0.0311	9.0433 × 10−5	0.0420	1.7525 × 10−4	0.0533	2.7884 × 10−4
6	0.0206	4.5829 × 10−5	0.0311	6.6299 × 10−5	0.0420	7.0836 × 10−5	0.0533	1.9248 × 10−4
7	0.0206	3.7060 × 10−5	0.0311	8.6631 × 10−5	0.0420	9.1541 × 10−5	0.0533	2.2198 × 10−4
8	0.0206	3.5973 × 10−5	0.0311	6.8055 × 10−5	0.0420	9.2337 × 10−5	0.0533	1.9020 × 10−4
9	0.0206	3.7391 × 10−5	0.0311	3.8127 × 10−5	0.0420	8.2369 × 10−5	0.0534	1.8317 × 10−4
10	0.0206	2.9527 × 10−5	0.0311	4.3751 × 10−5	0.0420	8.0293 × 10−5	0.0533	1.2457 × 10−4
11	0.0206	2.0656 × 10−5	0.0311	3.0005 × 10−5	0.0420	7.8606 × 10−5	0.0534	1.3065 × 10−4
12	0.0206	2.3284 × 10−5	0.0311	3.5420 × 10−5	0.0421	5.4439 × 10−5	0.0533	1.1975 × 10−4
13	0.0206	6.8601 × 10−6	0.0311	1.5908 × 10−5	0.0420	2.9310 × 10−5	0.0533	7.5533 × 10−5
14	0.0206	1.5028 × 10−5	0.0311	8.6066 × 10−6	0.0420	2.1517 × 10−5	0.0534	5.1976 × 10−5

.

From Figure 6 and Figure 7, and Table 10 and Table 11, it can be seen that the numbers of retrieved SSRs have a certain impact on the results of our method, whether for CMOS or TDI-CCD. Consistent with the empirical pattern of data fitting, the more retrieved SSRs there are, the better the stability of fitting SSRs. When the number of retrieved SSRs is few, there may be results with a small mean but a large standard deviation, which means that when one of the fitted SSR values is taken as the retrieval result, there may be a significant error in that value. However, when the number of angles increases, the fitting method used in this article can effectively avoid the interference of outliers and maintain the maximum stability of fitting accuracy. However, when there are a large number of retrieved SSRs, the error value is relatively controllable. From the ratio of the standard deviation to its mean, when randomly using five or more sets of retrieved SSRs for data fitting, the impact of error is relatively small. When the simulated SSR is 0.05, the standard deviation is on the order of 3.0000 × 10⁻⁴ or below. It should be pointed out that the results in Figure 6 and Figure 7, Table 10 and Table 11 are statistical values obtained through 10 rounds of random sampling. The mean and standard deviation obtained here may differ from the results in Figure 5 and Table 8 and Table 9. The results in Figure 5 and Table 8 and Table 9 are special cases of the results in Figure 6 and Figure 7 and Table 10 and Table 11.

In addition, a comparison of the data in Table 10 and Table 11 shows that the standard deviation of TDI-CCD is smaller than that of CMOS, mainly due to the higher signal-to-noise ratio of TDI-CCD after multiple noise accumulations. However, when the retrieved SSRs are 3 and 4, the data shows that the standard deviation of CMOS seems to be smaller. The main reason for this pattern is that the data used in each repeated experiment needs to be consistent, while the retrieved SSRs of TDI-CCD have the same values in many angles, which leads to fewer selectable angle combinations and an increase in standard deviation.

In summary, whether using different numbers of angles or different numbers of retrieved SSRs, the model can exhibit better stability when using more fitting data. However, in practical applications, it is more difficult to obtain images from more angles, so it is necessary to make a reasonable selection of the number of fitting data based on an acceptable range of error.

4.3. Sensor Parameter Analysis

Local and global sensitivity analysis were conducted to quantify how parameter uncertainties impact SSR retrieval. The key parameters and their uncertainties considered for CMOS and TDI-CCD sensors are shown in

Table 12. Key parameters and their uncertainty range of CMOS sensor.

Symbol	Parameter	Value	Uncertainty Range
F	F-Number	6	±10%
τo	Optical system transmittance	0.9	±10%
η	Quantum efficiency	0.6	±10%
Nfullwell	Full well capacity	10,000	±10%

and

Table 13. Key parameters and their uncertainty range of TDI-CCD sensor.

Symbol	Parameter	Value	Uncertainty Range
F	F-Number	6	±10%
τo	Optical system transmittance	0.9	±10%
R	Average spectral responsivity	100,000	±10%
C	Charge conversion factor	0.00001	±10%
ζtransfer	Total charge transfer efficiency	1	−10%
Nfullwell	Full well capacity	100,000	±10%

. It should be noted that in order to quantify the impact of parameter uncertainty on the proposed model, we added 10% uncertainty to all key parameters. However, in practical applications, the baseline values and uncertainties of relevant parameters may differ, so calculations can be made based on the specific parameter values of the detector.

The basis of the model proposed in this article is two angles model, therefore the retrieval results of the view zenith angles of 20° and 40° are used for analysis. Using the One-at-a-time method for local sensitivity analysis, the impact of single parameter uncertainty on SSR retrieval results was analyzed by calculating the SSR retrieval results corresponding to each parameter under +10% and −10% uncertainty. The relative error of SSR retrieval results (all results were calculated as absolute values) was used as the sensitivity indicator for evaluation. The local sensitivity analysis results for CMOS and TDI-CCD sensors are shown in

Table 14. SSR retrieval relative error with different parameter uncertainties using One-at-a-time method (CMOS).

Parameter	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	+10%	−10%	+10%	−10%	+10%	−10%	+10%	−10%
F	0.48%	0.39%	0.32%	0.25%	0.13%	0.18%	0.12%	0.12%
τo	0.17%	0.21%	0.11%	0.14%	0.08%	0.08%	0.05%	0.08%
η	0.18%	0.25%	0.07%	0.14%	0.07%	0.08%	0.04%	0.07%
Nfullwell	0.46%	0.44%	0.27%	0.28%	0.21%	0.20%	0.17%	0.18%

and

Table 15. SSR retrieval relative error with different parameter uncertainties using One-at-a-time method (TDI-CCD).

Parameter	SSR = 0.02		SSR = 0.03		SSR = 0.04		SSR = 0.05
	+10%	−10%	+10%	−10%	+10%	−10%	+10%	−10%
F	0.79%	0.63%	0.53%	0.38%	0.39%	0.34%	0.33%	0.29%
τo	0.30%	0.39%	0.20%	0.29%	0.19%	0.21%	0.14%	0.18%
R	0.32%	0.39%	0.19%	0.29%	0.20%	0.19%	0.13%	0.18%
C	0.37%	0.35%	0.24%	0.20%	0.16%	0.20%	0.16%	0.14%
ζtransfer	-	0.40%	-	0.28%	-	0.20%	-	0.17%
Nfullwell	0.70%	0.70%	0.48%	0.45%	0.36%	0.41%	0.30%	0.34%

, respectively.

It can be seen from Table 14 and Table 15 that using two view zenith angles of 20° and 40° for retrieval, for CMOS sensors, the error interference between F-Number and full well capacity is relatively large, while the error interference between optical system transmission and quantum efficiency is relatively small. For TDI-CCD sensors, the error interference between F-Number and full well capacity is relatively large, while the error interference between optical system transmittance, average spectral responsivity, charge conversion factor, and total charge transfer efficiency is relatively small. Overall, the uncertainty of parameters in both CMOS and TDI-CCD sensors can interfere with the accuracy of SSR retrieval. From the function of the proposed model, it can be seen that due to the randomness of noise, the interference of parameter uncertainty also has a certain degree of randomness, and the degree of interference is also related to the signal-to-noise ratio of the data used. Overall, under ±10% uncertainty, the relative error of SSR retrieval accuracy caused by a single parameter is within 0.80%.

We perform global sensitivity analysis using Monte Carlo method. We conducted 2000 random samplings within the uncertainty range of [−10%, +10%] to analyze the global interference of parameters uncertainty within ±10% on SSR retrieval results. The sensitivity indicators were evaluated based on the maximum relative error (all results were calculated in absolute value) and average relative error (all results were calculated in absolute value) of SSR retrieval results. The global sensitivity analysis results for CMOS and TDI-CCD sensors are shown in Figure 8.

It can be seen from Figure 8 that according to the simulation parameters we selected, for both CMOS and TDI-CCD sensors, the random sampling retrieval results within the uncertainty range of [−10%, +10%] show that the maximum relative error of SSR retrieval accuracy is within 1.40%, and the average relative error is within 0.70%. It should be pointed out that Table 14 and Table 15 and Figure 8 show a trend of decreasing relative error values in SSR retrieval results with increasing SSR. The main reason for this trend is that the calculation process of relative error is to divide the absolute error by the SSR baseline value. The larger the SSR value, the smaller the relative error.

5. Conclusions

In this article, we design a model for retrieving sea surface roughness based on multi angle passive visible spectrum images. The model considers the nonlinear relationship between radiation signals and digital signals caused by random noise in the remote sensing imaging system, and introduces it into the SSR retrieval process, which effectively improving the accuracy of SSR retrieval using multi angle images. The experimental results show that the proposed model exhibited higher accuracy in SSR retrieval at four SSR levels of 0.02, 0.03, 0.04, and 0.05 compared to the model without noise behavior. For CMOS imaging systems, the introduction of noise reduced the relative errors of SSR retrieval using two angle and multi angle methods by 4.0%, 2.7%, 2.3%, and 2.0%, and 5.0%, 2.7%, 2.5%, and 2.0%, respectively. For the TDI-CCD imaging system, introducing noise reduced the relative errors of SSR retrieval using two angle and multi angle methods by 6.5%, 4.3%, 3.7%, and 3.2%, and 7.0%, 5.0%, 4.3%, and 3.2%, respectively. And the model has a certain robustness to different levels of noise. Analysis of the model and data shows that for different numbers of angles or different numbers of retrieved SSRs, the more data fitted, the better the stability of the model. Fitting SSR values with five angles can improve by 6.27% compared to three angles, and the standard deviation of data fitting with more than five sets of retrieved SSRs is less than 3.0000 × 10⁻⁴. The uncertainty of sensor parameters can affect the model results. When the uncertainty of key parameters is ±10%, the relative error of SSR retrieval accuracy caused by a single local parameter is within 0.80%. The maximum relative error of SSR retrieval accuracy after random sampling of global parameters is within 1.40%, and the average relative error is within 0.70%. However, it should be pointed out that the results obtained in this article are based on the assumed camera parameters. For different CMOS and TDI-CCD sensors, their parameters and noise characteristics are different, and the SSR result values improved by the retrieval method in this article are different. Our current research data is simulation based, as it is difficult to obtain detailed parameters of remote sensing imaging systems, such as full well capacity, etc. In future research, we plan to design a camera specifically for experiments to obtain more measured experimental results.