Kohler-Polarization Sensor for Glint Removal in Water-Leaving Radiance Measurement

Abstract

High-precision hyperspectral remote sensing reflectance measurement of water bodies serves as the fundamental technical basis for accurately retrieving spatiotemporal distribution characteristics of water quality parameters, providing critical data support for dynamic monitoring of aquatic ecosystems and pollution source tracing. To address the critical issue of water surface glint interference significantly affecting measurement accuracy in aquatic remote sensing, this study innovatively developed a novel sensor system based on multi-field-of-view Kohler-polarization technology. The system incorporates three Kohler illumination lenses with exceptional surface uniformity exceeding 98.2%, effectively eliminating measurement errors caused by water surface brightness inhomogeneity. By integrating three core technologies—multi-field polarization measurement, skylight blocking, and high-precision radiometric calibration—into a single spectral measurement unit, the system achieves radiation measurement accuracy better than 3%, overcoming the limitations of traditional single-method glint suppression approaches. A glint removal efficiency (GRE) calculation model was established based on a skylight-blocked approach (SBA) and dual-band power function fitting to systematically evaluate glint suppression performance. Experimental results show that the system achieves GRE values of 93.1%, 84.9%, and 78.1% at ±3°, ±7°, and ±12° field-of-view angles, respectively, demonstrating that the ±3° configuration provides a 9.2% performance improvement over the ±7° configuration. Comparative analysis with dual-band power-law fitting reveals a GRE difference of 2.1% (93.1% vs. 95.2%) at ±3° field-of-view, while maintaining excellent consistency (ΔGRE < 3.2%) and goodness-of-fit (R² > 0.96) across all configurations. Shipborne experiments verified the system’s advantages in glint suppression (9.2%~15% improvement) and data reliability. This research provides crucial technical support for developing an integrated water remote sensing reflectance monitoring system combining in situ measurements, UAV platforms, and satellite observations, significantly enhancing the accuracy and reliability of ocean color remote sensing data.

1. Introduction

Against the backdrop of increasing global water scarcity and deteriorating ecological conditions, water environment protection has become a central concern for the international community. According to the UN World Water Development Report, approximately 2 billion people currently live in water-stressed regions, with water pollution further aggravating this crisis. In response, the Sustainable Development Goals (SDGs) explicitly mandate the “protection and restoration of water-related ecosystems”, setting 2030 targets for integrated water resources management and conservation. However, rapid urbanization, industrialization, and agricultural intensification have led to frequent aquatic ecological disturbances including algal blooms, black-odorous waters, eutrophication, red tides, oil spills, and wastewater discharges [1]. These phenomena have resulted in degraded aquatic ecosystem functionality and significant biodiversity loss, posing severe threats to sustainable water utilization and ecological security.

Within this context, close-range hyperspectral remote sensing has emerged as an essential methodology for calibrating and validating satellite/airborne ocean color data. The Global Climate Observing System (GCOS) requires water-leaving radiance (L_w) measurements to maintain less than 5% uncertainty for reliable climate variable monitoring. While System Vicarious Calibration (SVC) using field measurements can reduce satellite product uncertainties, the calibration accuracy fundamentally relies on the precision of field-acquired reflectance spectra [2]. This dependence has driven the evolution of field instrumentation from handheld devices to autonomous systems deployed across diverse platforms. However, a critical barrier persists: effective removal of sun and sky glint contamination from reflectance spectra [3,4]. Unlike laboratory conditions, field measurements must account for dynamic environmental variables including the following:

• Observation geometry.
• Solar elevation/azimuth angles.
• Cloud distribution patterns.
• Wind speed and direction.

The complex interdependence of these factors creates two fundamental challenges:

• Practical difficulties in comprehensive environmental parameter monitoring.
• Limitations in existing glint correction algorithms to handle natural variability.

Consequently, even with advanced autonomous systems, achieving GCOS-required uncertainty levels remains problematic when glint effects are improperly characterized. Although polarization measurement methods demonstrate significant theoretical advantages for water surface glint removal, their practical performance in aquatic remote sensing applications remains constrained by three critical factors: (1) Dynamic wave effects cause partial incident light rays within the observation field to deviate from the ideal Brewster angle, resulting in nonlinear distortion of the reflected light’s polarization characteristics. (2) During polarization modulation, the already weak water-leaving radiance signal (typically <10% of total incident light) undergoes further signal-to-noise ratio (SNR) degradation below the critical detection threshold after optical system attenuation. (3) Most importantly, current research lacks a systematic quantitative model for glint removal efficiency (GRE) in multi-field polarization sensors.

To address these challenges, this study focuses on “Kohler-polarization Sensor for Glint Removal in Water-Leaving Radiance Measurement” through innovative sensor design and algorithm optimization. This study aims to maximally suppress water surface glint interference through innovative polarization techniques, thereby enabling accurate characterization of glint effects and significant improvement in water-leaving radiance measurement precision, with the ultimate goal of acquiring high-accuracy aquatic remote sensing reflectance data.

2. Related Works

The above-water remote sensing reflectance (R_rs) at wavelength λ is defined as the ratio of water-leaving radiance (L_w) to downwelling irradiance (E_d(0⁺, λ)) at the water surface [5,6]:

$${\mathrm{R}}_{\mathrm{rs}}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{w}}(\mathrm{\lambda })}{{\mathrm{E}}_{\mathrm{d}}(0^{+},\mathrm{\lambda })}},$$

(1)

When measuring water-leaving radiance, the contribution of bottom-reflected light from sediments can be neglected depending primarily on water depth and optical transparency [7,8]. Here, we focus on analyzing the radiation components at the air–water interface under conditions where bottom reflectance is negligible. As illustrated in Figure 1, when an above-water sensor is positioned at an azimuth angle φ and a zenith angle θ, the total radiance L_u received by the sensor can be expressed as follows [9]:

$${\mathrm{L}}_{\mathrm{u}}(\mathrm{\lambda },\mathrm{\theta },\mathrm{\phi })={\mathrm{L}}_{\mathrm{w}}(\mathrm{\lambda },\mathrm{\theta },\mathrm{\phi })+{\mathrm{L}}_{\mathrm{SN}}(\mathrm{\lambda },\mathrm{\theta },\mathrm{\phi })+{\mathrm{L}}_{\mathrm{g}}(\mathrm{\lambda },\mathrm{\theta },\mathrm{\phi }),$$

(2)

where L_w is the water-leaving radiance, L_SN is the reflected sky radiance at the water surface, and L_g is the reflected direct solar radiance at the water surface.

Water-leaving radiance is essentially the backscattered light from water bodies and exhibits unpolarized characteristics. In stark contrast, water surface glint (including reflected direct sunlight and skylight) demonstrates significant polarization properties [10,11,12]. The degree of polarization, a physical quantity characterizing the polarization state of light, is defined as the ratio of linearly polarized light intensity to the total light intensity [13,14]:

$$\mathrm{P}=\left|{\displaystyle \frac{{\mathrm{I}}_{\perp }-{\mathrm{I}}_{\mathsf{\parallel }}}{{\mathrm{I}}_{\perp }+{\mathrm{I}}_{\mathsf{\parallel }}}}\right|,$$

(3)

In the equations, I_⊥ denotes the intensity of reflected light with the electric field vector perpendicular to the plane of incidence, while I_∥ represents the intensity with the electric field vector parallel to the plane of incidence.

Based on further analysis of the degree of polarization function according to Fresnel’s law [13], and given that light intensity is proportional to the square of the electric field amplitude, the expression for the degree of polarization is as follows:

$$\mathrm{P}=\left|{\displaystyle \frac{{\mathrm{E}}_{\perp }^2\frac{{\sin }^2(\mathrm{\alpha }-\mathsf{\beta })}{{\sin }^2(\mathrm{\alpha }+\mathrm{\beta })}-{\mathrm{E}}_{\mathsf{\parallel }}^2\frac{{\mathrm{tg}}^2(\mathrm{\alpha }-\mathrm{\beta })}{{\mathrm{tg}}^2(\mathrm{\alpha }+\mathrm{\beta })}}{{\mathrm{E}}_{\perp }^2\frac{{\sin }^2(\mathrm{\alpha }-\mathrm{\beta })}{{\sin }^2(\mathrm{\alpha }+\mathrm{\beta })}{+\mathrm{E}}_{\mathsf{\parallel }}^2\frac{{\mathrm{tg}}^2(\mathrm{\alpha }-\mathrm{\beta })}{{\mathrm{tg}}^2(\mathrm{\alpha }+\mathrm{\beta })}}}\right|,$$

(4)

In the equation, E_⊥ represents the perpendicular component of the incident light’s electric field vector relative to the plane of incidence, E_∥ denotes the parallel component, α is the incidence angle, and β is the refraction angle. When dealing with unpolarized incident light (E_⊥ = E_∥), the degree of polarization can be expressed by eliminating the refraction angle through the refractive index n as follows:

$$\mathrm{P}={\displaystyle \frac{2\sin \mathrm{\alpha }\mathrm{tg}\mathrm{\alpha }\sqrt{{\mathrm{N}}^2-{\sin }^2\mathrm{\alpha }}}{{\mathrm{N}}^2-{\sin }^2\mathrm{\alpha }+{\sin }^2\mathrm{\alpha }{\mathrm{tg}}^2\mathrm{\alpha }}},$$

(5)

For pure water with a refractive index of 1.33, when the incidence angle reaches 53.1°, the polarization function attains its extremum, at which point the reflected light becomes completely linearly polarized [15]. This specific angle is known as the Brewster angle. As the incidence angle increases gradually from 0°, the polarization degree of the reflected light first increases, reaches its maximum at the Brewster angle, and then decreases. Consequently, the closer the incidence angle approaches the Brewster angle, the more pronounced the linear polarization characteristics of the reflected light become. Based on this theoretical framework, the polarized characteristics of water surface glint can be effectively separated. When the sensor’s observation angle is set at 53.1°, the light entering the instrument’s field-of-view (FOV) exhibits strong linear polarization characteristics [16,17]. By installing a polarizer (typically a linear polarizing filter) at the sensor’s front end and aligning its transmission axis perpendicular to the vibration direction of the reflected light, the polarized component of surface glint can be effectively suppressed. This method significantly reduces interference from water surface glint in water-leaving radiance measurements, thereby improving the accuracy of aquatic remote sensing reflectance measurements.

3. The Design and Calibration of the System

The overall design of system is illustrated in Figure 2, primarily consisting of core components such as the spectral measurement unit, the fore-optics irradiance probe, and the multi-configuration fore-optics radiance probes. To meet the requirements of portability and lightweight design, the system employs a Czerny–Turner spectrograph as the spectral detection unit. By precisely shaping the fiber bundle, the coupling efficiency between the fiber bundle and the spectrograph slit is maximized, thereby enhancing the SNR of the instrument. The fore-optics irradiance probe utilizes an upward-facing cosine corrector, ensuring accurate response to incident light from various angles and enabling precise measurement of downwelling irradiance within the hemispherical space. The fore-optics radiance probes for water-leaving radiance measurement are designed in two configurations: a combination of Kohler illumination lens and polarizer (polarized probe) and a combination of Kohler illumination lens and conical baffle (SBA probe). The Kohler illumination lens, serving as a homogenizing optical system, effectively eliminates the impact of uneven surface brightness distribution on measurement results, ensuring uniform reception of target radiation. During measurement, the radiation signals received by the fore-optics system are transmitted through the circular input end of the fiber bundle and enter the spectrograph slit via the square output end. Inside the spectrograph, the collimating lens, plane grating, and focusing lens disperse and focus the light, while the detector precisely captures the optical signals at each wavelength. Finally, the spectral data are displayed and stored in real-time via the host computer.

Based on the overall system design and the technical parameters of water color remote sensing detectors both domestically and internationally, the specific technical indicators of the system are proposed as shown in

Table 1. Technical specifications of system.

Parameter	Specification
Spectral Range	350–900 nm
Spectral Resolution	3 nm
Wavelength Accuracy	±0.5 nm
Downwelling Irradiance (Ed)	FOV: 180° Cosine Error: <5% (0–60°)
Water-Leaving Radiance (Lw)	FOV: ±3°; ±7°; ±12° Nadir Viewing Angle: 53°
Signal-to-Noise Ratio (SNR)	400 @550–900 nm 200 @Other Wavelengths
Uniformity of Halogen Light System	95%
Radiometric Accuracy	3% (k = 1)
Water Surface Glint Removal Rate	90%

.

3.1. Specific Design and Test Methodology

Considering the requirements for device stability, measurement accuracy, cost control, and compact size, this study selects the high-sensitivity fiber optic spectrometer Maya2000Pro from Ocean Optics. When equipped with a 100 μm × 1 mm slit, the spectrometer achieves a spectral resolution of 3 nm. To optimize the spot shape, a reshaped fiber bundle with a multi-core, dual-end configuration is employed: the fiber bundle features a single-core outer diameter of 110 μm, with nine cores arranged in parallel to match the slit length, and a single-core inner diameter of 100 μm to match the slit width. This design enhances the filling factor of the spectrometer’s entrance slit, thereby improving the system’s energy utilization efficiency.

The fore-optics irradiance probe of the system utilizes the CCSA2 cosine corrector from Thorlabs. The cosine response characteristics of the irradiance probe were tested using a rotary stage and a spectral irradiance standard lamp [18]. First, the distance between the center of the standard lamp target and the plane center of the irradiance probe was precisely adjusted to 500 mm using a micrometer and an optical rail. A laser line level was employed to ensure that both were at the same horizontal height. Subsequently, the rotary stage was rotated clockwise and counterclockwise by the same angle, and the two sets of values output by the spectrometer were recorded. The angle of the rotary stage was adjusted so that the output value was the average of the two recorded values, at which point the filament center of the standard lamp was aligned with the normal direction of the irradiance probe.

The radiance probe utilizes a Kohler illumination lens [19] to constrain the sensor’s FOV, offering the following key advantages: (1) This structure significantly enhances the energy density of the spot on the image plane, thereby increasing the radiant energy entering the spectrometer slit. This effectively reduces integration time, improves the instrument’s SNR, and enhances the efficiency of field measurements. Additionally, it minimizes errors caused by minor target variations during the measurement cycle. (2) The Kohler illumination lens provides excellent homogenization, ensuring that light spots from different field regions nearly overlap on the image plane. This guarantees that targets with uneven surface brightness distributions are uniformly received by the system during field measurements, further improving the reliability of the measurement results [20].

As shown in Figure 3, the Kohler illumination front optical system consists of objective lens L1 and field lens L2. In the figure, θ represents the half-field angle, U is the angle between the chief ray of the edge field and the optical axis, α denotes the angle between the edge ray and the optical axis, ƒ and ƒ’ are the focal lengths of the objective and field lenses, respectively, D is the entrance pupil diameter, and d is the image height. The geometric relationships are defined as follows:

$$f\cdot tan\theta =f^{\prime }\cdot \tan U$$

(6)

$$\tan \alpha ={\displaystyle \frac{d}{2f^{\prime }}}={\displaystyle \frac{D}{2f}}$$

(7)

To improve energy efficiency, U should be aligned with the numerical aperture angle of the optical fiber bundle.

$$\mathrm{U}=\arcsin (NA)=21.7°$$

(8)

This study designed and optimized three sets of Kohler illumination lenses with field angles of ±3°, ±7°, and ±12°, respectively, for integration into subsequent multi-configuration radiance probes. To enhance the uniformity of the spot on the image plane, a two-lens field lens group was employed. Additionally, the overall optimization was performed in ZEMAX by controlling the angle between the chief ray of the marginal field and the optical axis to be no more than 21.7°, ensuring compatibility with the numerical aperture of the fiber. Figure 4 presents the final optimization results of the three sets of Kohler illumination lenses, while

Table 2. Parameter table for three sets of Kohler illumination lenses.

FOV	Lens Name	Front Surface Radius of Curvature (mm)	Back Surface Radius of Curvature (mm)	Thickness (mm)
±3°	Objective Lens	61.0	−61.0	4.7
	Field Lens 1	14.7	−33.4	3.0
	Field Lens 2	13.9	−23.2	3.0
±7°	Objective Lens	25.2	−25.2	3.4
	Field Lens 1	14.2	−18.2	3.0
	Field Lens 2	11.4	−21.8	3.0
±12°	Objective Lens	30.4	−30.4	3.1
	Field Lens 1	34.6	−19.7	3.0
	Field Lens 2	18.8	−45.5	3.0

provides a detailed list of the optical parameters of the optimized lens configurations.

The ray trace diagrams of the three sets of Kohler illumination lenses are shown in Figure 5. These diagrams provide a visual representation of the light distribution on the image plane, including the size and shape of the spots. This helps analyze the propagation effects of light at different field angles and evaluate the system’s performance and the homogenization effect of the Kohler illumination lenses under various fields-of-view. In the three lens configurations, the spots formed by incident light from different field angles fall within circular regions with diameters of 5.4 mm, 6.2 mm, and 8.6 mm, respectively, fully covering the spectrometer’s entrance slit.

To further evaluate the uniformity of the spots on the image plane for the three sets of Kohler illumination lenses, the optical design results were converted into three-dimensional solid models and imported into L software for simulation. As shown in Figure 6, surface light sources with divergence angles of 3°, 7°, and 12° were setup for simulation analysis to ensure that the light sources adequately cover the entire FOV.

The simulation results of the spot uniformity are shown in Figure 7, where the color gradient visually represents the energy distribution within the spot area. The spot uniformity is quantitatively calculated based on the following equation, where Emax represents the maximum radiance value within the circular region, and Emin represents the minimum radiance value.

$$\mathrm{u}=1-{\displaystyle \frac{{\mathrm{E}}_{\max }-{\mathrm{E}}_{\min }}{{\mathrm{E}}_{\max }+{\mathrm{E}}_{\min }}},$$

(9)

The calculation results demonstrate that the three sets of Kohler illumination lenses exhibit excellent surface uniformity, with uniformity values all exceeding 98.2%. This effectively eliminates measurement errors introduced by surface brightness non-uniformity during water-leaving radiance measurements.

The Kohler illumination lenses need to be further equipped with conical baffles and linear polarizing elements, respectively, to meet the hardware requirements for polarization-based measurements and skylight blocking approach (SBA) measurements.

A broadband wire-grid polarizer WP25M-UB1 with an acceptance angle of ±20° was selected to eliminate polarized water surface glint. The working principle of the wire-grid polarizer is based on selective transmission: its surface consists of periodically aligned parallel metallic nanowires with spacing smaller than the incident light wavelength. When unpolarized light is incident, the electric field component parallel to the wire direction excites free-electron oscillations in the metallic wires, causing reflection or absorption; whereas the perpendicular electric field component transmits directly due to ineffective coupling. This anisotropic response separates the incident light into transmitted linearly polarized light (with vibration direction perpendicular to the wires) and reflected/absorbed polarized components. The same screw-in polarization lens is combined with the aforementioned three sets of Kohler lens groups to construct polarization probes with different field-of-view angles. The polarizer is fixed inside the sleeve via front and rear retaining rings, while the internal thread at the rear end of the sleeve mates with the external thread at the front end of the Kohler lens. During on-site measurements, the transmission axis direction can be adjusted by rotating the outer wall of the sleeve to ensure it lies within the observation plane. This design not only reduces system integration costs but also avoids measurement errors caused by inherent differences in the characteristics of various polarizers.

The design of the conical baffle aims to prevent surface glint from entering the FOV of the radiance probe during observation while ensuring the probe’s normal operation. Therefore, the following aspects need to be considered during the design process:

(1) Minimizing Instrument Self-Shadowing Effects: Since the self-shadowing caused by the conical baffle on the water surface disrupts the underwater light field distribution, resulting in measured water-leaving radiance values lower than the true values, and the interference from self-shadowing is proportional to the size of the baffle, the baffle must be designed to be compact.

(2) Avoiding Baffle Interference with the Instrument’s FOV: The lens group connected to the baffle uses a Kohler illumination lens with a FOV of ±7°. Thus, the baffle’s shape must match the lens’s FOV to avoid interference. The baffle is designed as a conical shape with openings at both ends, where the lower opening diameter D_d, upper opening diameter D_u, and height H must satisfy the following relationship:

$${\mathrm{D}}_{\mathrm{d}}\ge {\mathrm{D}}_{\mathrm{u}}+2\times \mathrm{H}\times \tan 7^{°},$$

(10)

(3) Preventing Reflection Interference: The inner and outer surfaces of the baffle are coated with matte black material to avoid surface reflections that could disrupt the underwater light field during field measurements.

Integrating the above three requirements, a conical baffle was designed, with the physical prototype shown in Figure 8. The baffle has a height of 78 mm, an upper opening diameter of 12 mm, and a lower opening diameter of 32 mm, resulting in a wall inclination angle of approximately 7.3°, slightly larger than the half-field angle of the front Kohler illumination lens to avoid interference with the instrument’s FOV. Both the front and rear surfaces are coated with matte black material to prevent reflection interference. The entire assembly is supported by a handheld black pole positioned above the water, fixing the waterline at the midpoint of the baffle so that the lower port of the baffle is submerged in water while the Kohler illumination lens remains in the air medium. Compared to buoy-based deployment methods, the handheld black pole solution addresses the issue of real-time changes in instrument floating posture during measurements while avoiding the impact of buoy body shadows and reflected light on the underwater light field.

The signal-to-noise ratio (SNR) is one of the core performance metrics in radiometric measurements, used to quantify the relative intensity of the target signal compared to background noise [21,22]. To ensure that the experimental test conditions can realistically reflect the radiation signal intensity in actual measurement scenarios, as shown in Figure 9, a 1 m integrating sphere set at 1/64 attenuation is used as the radiance measurement target, while a spectral irradiance standard lamp is used as the irradiance measurement target. To ensure the stability of the light sources, they were sufficiently preheated before the experiment, with a warm-up time set to 40 min. The integration time for radiance measurements is set to 200 ms, and for irradiance measurements, it is set to 50 ms, which is consistent with the integration times used in actual field experiments.

To minimize the impact of random errors, 20 sets of target signal and dark noise data were collected for each measurement mode, which will be used for subsequent SNR calculations. The SNR is calculated based on the ratio of the mean value of the net signal to its standard deviation, as expressed by the following formula:

$$\mathrm{SNR}\left(\mathrm{\lambda }\right)={\displaystyle \frac{\overline{\mathrm{DN}\left(\mathrm{\lambda }\right)}}{\mathsf{\sigma }\left(\mathrm{DN}\right(\mathrm{\lambda }\left)\right)}},$$

(11)

In the formula, $\overline{\mathrm{DN}\left(\mathrm{\lambda }\right)}$ represents the mean value of the net signal after removing dark noise, and $\mathsf{\sigma }\left(\mathrm{DN}\right(\mathrm{\lambda }\left)\right)$ represents the standard deviation of the net signal.

3.2. Laboratory Radiometric Calibration

If an integrating sphere is used as the light source for radiance calibration, a high-precision spectrometer is required to indirectly measure its radiance [23]. However, the spectrometer’s inherent measurement uncertainty is relatively large, adding steps to the standard value transfer process and introducing additional error sources, which significantly increases the uncertainty of the radiometric calibration. Therefore, this study employs a lamp-plate system for radiance calibration [24]. Figure 10 shows the irradiance and radiance responsivity curves.

The uncertainty of the spectral irradiance of the standard lamp is provided by its calibration report, with the maximum value taken as 1.2% (k = 1); the uncertainty of the BRDF of the standard diffuse reflector is provided by the test report from the metrology institute, with an uncertainty value of 1% (k = 1); the distance between the standard lamp and the diffuse reflector is constrained by a precision rail, with a displacement accuracy better than 0.1 mm, and the target distance is 500 mm, resulting in a distance uncertainty of 0.4%; the number of integration cycles for each set of measurement signals is set to 20, meaning 20 repeated samples, and its uncertainty is calculated [25]. The individual uncertainty components and the final combined uncertainty values for the radiometric calibration are listed in

Table 3. Uncertainty component table for radiometric calibration (k = 1).

Uncertainty Sources	Radiance Calibration Uncertainty Value (%)	Irradiance Calibration Uncertainty Value (%)
Standard Lamp Spectral Irradiance Uncertainty	1.2	1.2
Diffuse Reflector BRDF Uncertainty	1.0	-
Distance Uncertainty	0.4	0.4
Wavelength Calibration Uncertainty	0.5	0.5
Measurement Repeatability	0.8	0.6
Combined Uncertainty	1.9	1.5

. The combined uncertainty for radiance calibration is 1.9% (k = 1), and for irradiance calibration, it is 1.5% (k = 1). Based on the formula for calculating water remote sensing reflectance, its relative combined uncertainty is 2.42% (k = 1).

4. Field Experiments and Results

4.1. Field Experiments

Located on the western foothills of the eastern mountainous region in Jilin Province, Songhua Lake sits in the upper reaches of the Songhua River, approximately 14 km southeast of Jilin City. As a multi-purpose hydraulic complex, the lake plays vital roles in drinking water supply, hydroelectric power generation, flood control and irrigation, navigation, aquaculture, and eco-tourism (see Figure 11 for precise location). Serving as a crucial water source for both Jilin City and Changchun City, Songhua Lake has been the subject of numerous remote sensing studies in recent years focusing on the retrieval and monitoring of chlorophyll-a concentration and suspended matter content. However, quantitative evaluation of water surface glint suppression efficacy in optical remote sensing remains relatively understudied—a critical factor that directly affects the accuracy of remote sensing data inversion.

The experiment followed a standardized field measurement procedure. First, the instrument was preheated for 20 min to ensure stability. Subsequently, multi-angle radiometric measurements were conducted using Kohler-polarized sensors with field-of-view angles of ±3°, ±7°, and ±12°. In situ measurements were performed using the sky radiance obstruction method. The experiment was strictly conducted under clear and mostly cloud-free weather conditions (cloud cover < 20%), with each measurement cycle controlled within 10 min. Simultaneously, a downward irradiance probe was used every 10 min to measure the water surface downwelling irradiance, eliminating the influence of solar radiation fluctuations on the measurement results. Throughout the experiment, a portable anemometer was employed to monitor the water surface wind speed in real-time (accuracy ±0.2 m/s), ensuring that the evaluation of glint suppression performance was not affected by changes in water surface waves. Figure 12 comprehensively documents the experimental field setup.

The Sky Glint Blocking Approach (SBA) utilizes an optimally designed baffle to effectively prevent both sun glint reflections and sky diffuse light from entering the spectrometer slit, ensuring that the spectrometer exclusively captures water-leaving radiance [26]. Consequently, SBA enables direct measurement of water-leaving radiance.

The signal acquisition process is fully controlled by Ocean View spectral acquisition software, with main parameter settings including integration time optimization, measurement curve quantity setting (20 spectra per single measurement), and data storage path configuration. All raw spectral data must undergo strict quality control procedures, with specific implementation schemes as follows [27,28,29,30]: (1) Wind speed assessment: If the wind speed exceeds the preset threshold (5 m/s), which may cause increased water surface fluctuations and affect measurement accuracy, data collection should be suspended or the data should be labeled as low quality. (2) Cloud cover assessment: When cloud cover is determined to be excessive, it may lead to unstable downwelling irradiance, affecting the calculation of remote sensing reflectance. (3) The 3σ criterion: Based on statistical principles, by calculating the mean and standard deviation of the dataset, data points that deviate from the mean by more than three times the standard deviation are quantitatively identified and removed as outliers. (4) Multi-source data consistency check: Compare water-leaving radiance data obtained by different measurement methods (polarization method and skylight blocking method) to evaluate their consistency. If data from one method significantly deviates from others, the cause should be analyzed and a decision should be made whether to exclude it.

4.2. Test Results of System

The cosine response characteristic is shown in Figure 13, achieving a cosine response error of less than 3% within a ±40° range. As the angle increases, the error gradually rises, remaining below 5% at approximately ±60° and below 8% at around ±75°.

Figure 14 shows the SNR test results. From the figure, it can be observed that the SNR curves for radiance and irradiance measurements are largely consistent, indicating that the instrument exhibits high consistency in performance during both radiance and irradiance measurements. Within the 560–900 nm wavelength range, the SNR is generally better than 400, meeting the measurement requirements. However, the SNR in the ultraviolet (UV) band is significantly lower, primarily due to the insufficient radiant energy of the laboratory’s 3000 K blackbody source in the UV band, which fails to fully activate the instrument’s detection capabilities. In actual field measurements, the sun serves as the primary light source, and its UV band radiation intensity is significantly higher than that of the laboratory source. Therefore, there is a discrepancy between the laboratory test results and the actual performance. This result suggests that while laboratory test results provide valuable reference for assessing the instrument’s performance, they need to be comprehensively validated with field measurement data.

4.3. Measurement Results of Downwelling Irradiance at Water Surface

This study employs the Coefficient of Variation (CV) to assess the relative variability of irradiance data before and after each experimental set [31]. The calculation formula for CV is as follows:

$$\mathrm{CV}={\displaystyle \frac{\mathrm{\sigma }}{\mathrm{\mu }}}\times 100\%,$$

(12)

In the equation, σ represents the standard deviation of the two sets of irradiance data, and μ denotes the mean value of the two sets of irradiance data.

Two sets of data with relatively large variations in downwelling surface irradiance were selected for comparative analysis. Here, ${\mathrm{E}}_{\mathrm{d}}^{{\mathrm{t}}_1}$ and ${\mathrm{E}}_{\mathrm{d}}^{{\mathrm{t}}_2}$ represent the irradiance values at the start and end times of the first experimental set, respectively, while ${\mathrm{E}}_{\mathrm{d}}^{{\mathrm{t}}_3}$ and ${\mathrm{E}}_{\mathrm{d}}^{{\mathrm{t}}_4}$ correspond to the irradiance values at the start and end times of the second experimental set. Based on these data, Equation (14) was employed to calculate the relative CV of irradiance before and after the two experimental sets, thereby quantifying the characteristics of irradiance variation. The results are shown in Figure 15.

4.4. Cross Validation of Satellite Data

Equivalent spectral simulations of R_rs^PMHRS and R_rs^ASD were conducted using Sentinel-2B’s spectral response functions. These simulations were then compared with Sentinel-2B data corrected by FLAASH for modeling analysis. The results are depicted in Figure 16, where the correlation coefficient (R²) between the equivalently transformed R_rs^PMHRS and satellite data (R² = 0.926) surpasses that of R_rs^ASD and satellite data (R² = 0.90).

4.5. Measurement Results of Water-Leaving Radiance

The measurement results of radiance from Kohler-polarized sensors with different fields-of-view and the SBA are shown in Figure 17. ${\mathrm{L}}_{\mathrm{w}}^{\mathrm{FOV}=\pm 3°}$, ${\mathrm{L}}_{\mathrm{w}}^{\mathrm{FOV}=\pm 7°}$, and ${\mathrm{L}}_{\mathrm{w}}^{\mathrm{FOV}=\pm 12°}$ represent the radiance measurements obtained by the three FOV radiance sensors under 0° polarization conditions, indicating the residual radiance after partial removal of surface glint. ${\mathrm{L}}_{\mathrm{u}}^{\mathrm{FOV}=\pm 3°}$, ${\mathrm{L}}_{\mathrm{u}}^{\mathrm{FOV}=\pm 7°}$, and ${\mathrm{L}}_{\mathrm{u}}^{\mathrm{FOV}=\pm 12°}$ denote the total water radiance measured by the three FOV radiance probes without polarization. ${\mathrm{L}}_{\mathrm{w}}^{\mathrm{SBA}}$ corresponds to the water-leaving radiance measured using the SBA method.

4.6. Results of GRE for Polarized Probes with Different Fields-of-View

To quantitatively analyze and evaluate the surface glint removal effectiveness of Kohler-polarized water-leaving radiance sensors with different fields-of-view, this study proposes a novel computational method for determining GRE. For clarity in presentation, this study defines the condition where the vibration direction of incident light is orthogonal to the transmission axis of the polarizing probe as 0° polarization. By, respectively, measuring the peak radiance values of target water bodies under 0° polarization ${\mathrm{L}}_{0°}$, total peak radiance without polarization ${\mathrm{L}}_{\mathrm{Non}-\mathrm{Polarized}}$, and peak water-leaving radiance using the SBA ${\mathrm{L}}_{\mathrm{SBA}}$, the corresponding GRE is calculated according to the following equation:

$$\mathrm{GRE}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{Non}-\mathrm{Polarized}}-{\mathrm{L}}_{0°}}{{\mathrm{L}}_{\mathrm{Non}-\mathrm{Polarized}}-{\mathrm{L}}_{\mathrm{SBA}}}},$$

(13)

The GRE calculated by this method represents the proportion of surface glint removed through polarization relative to the total surface glint. A GRE value approaching 1 indicates optimal glint removal performance, while a value nearing 0 signifies poor glint removal effectiveness. The calculated GRE for water-leaving radiance sensors with different Kohler-polarized fields-of-view is presented in

Table 4. The GRE computation results under different fields of view based on SBA.

FOV	Peak Radiance at 0° Polarization State (W·m⁻2·sr⁻¹·nm⁻¹)	Peak Radiance in Non-Polarized State (W·m⁻2·sr⁻¹·nm⁻¹)	Peak Radiance via SBA (W·m⁻2·sr⁻¹·nm⁻¹)	GRE (%)
±3°	1.08	1.35	1.06	93.1
±7°	1.11	1.37	1.06	83.9
±12°	1.13	1.38	1.06	78.1

.

4.7. Validation of GRE Based on Dual-Band Power Function Fitting

During field experiments, the instability of wind speed, observation angle errors of the sensor, and self-shadowing effects of the conical baffle may all affect the accuracy of GRE calculations. To evaluate result accuracy, this study utilizes measured spectral data from two bands (350–380 nm and 890–900 nm) for power-law fitting, with the fitting results representing the surface glint contribution [32]. The glint values derived from this fitting approach are then compared with those obtained through polarized measurement methods to validate both the effectiveness of the aforementioned GRE calculation method and the accuracy of its results.

The fitting results of the dual-band power function method are shown in Figure 18. In the figure, the red triangular area represents the reference bands, while the green dashed line indicates the fitting results, which quantify the contribution of surface glint to the final measured water remote sensing reflectance. By multiplying these results with the downwelling surface irradiance, the peak radiance of surface glint ${\mathrm{L}}_{\mathrm{glint}}$ can be derived, enabling the calculation of GRE. The GRE is computed as follows:

$$\mathrm{GRE}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{Non}-\mathrm{Polarized}}-{\mathrm{L}}_{0°}}{{\mathrm{L}}_{\mathrm{glint}}}},$$

(14)

The GRE computation results of the water-leaving radiance sensor under different fields of view were obtained by applying the dual-band power-law fitting results to Equation (14), as presented in

Table 5. The GRE computation results under different fields of view based on power-law fitting.

FOV	Peak Radiance at 0° Polarization State (W·m⁻2·sr⁻¹·nm⁻¹)	Peak Radiance in Non-Polarized State (W·m⁻2·sr⁻¹·nm⁻¹)	Peak Glint Radiance Derived from Power-law Fitting (W·m⁻2·sr⁻¹·nm⁻¹)	GRE (%)
±3°	1.08	1.35	0.284	95.1
±7°	1.11	1.37	0.296	87.8
±12°	1.13	1.38	0.310	80.6

.

5. Discussion

The measurement results reveal that both experimental sets exhibit consistent overall trends in irradiance before and after measurements, varying within ranges of 20 $\mathrm{\mu }W\cdot \mathrm{c}{\mathrm{m}}^{-2}\cdot \mathrm{n}{\mathrm{m}}^{-1}$~58 $\mathrm{\mu }W\cdot \mathrm{c}{\mathrm{m}}^{-2}\cdot \mathrm{n}{\mathrm{m}}^{-1}$ and 17 $\mathrm{\mu }W\cdot \mathrm{c}{\mathrm{m}}^{-2}\cdot \mathrm{n}{\mathrm{m}}^{-1}$~49 $\mathrm{\mu }W\cdot \mathrm{c}{\mathrm{m}}^{-2}\cdot \mathrm{n}{\mathrm{m}}^{-1}$, respectively. All CV values remain below 10%, with an average CV of approximately 4%. The study identifies dynamic cloud variations (including formation and movement) during measurements as the primary factor causing irradiance fluctuations. Additionally, instrument random noise contributes to CV values to some extent, particularly exhibiting more pronounced effects in weak signal regions at both short-wave and long-wave bands.

The radiance measurements obtained from the Kohler-polarized sensors with different fields-of-view and the Skylight-Blocked Approach (SBA) demonstrate that the results from the three polarized probes at 0° polarization state are significantly lower than the total water radiance measured without polarization and closely align with the SBA measurements. This effectively confirms the excellent glint suppression capability of the polarized probes on surface-reflected radiance in the total water signal. As the sensor’s FOV increases, the measured water-leaving radiance also increases, indicating a gradual reduction in GRE. This phenomenon primarily occurs because larger FOVs lead to an increased proportion of non-Brewster’s angle reflections in the total received light, which decreases the overall polarization degree of the light and consequently reduces the probe’s glint removal capability.

The calculation results of surface GRE for Kohler-polarized water-leaving radiance sensors with different fields-of-view demonstrate a clear decreasing trend in glint suppression performance with increasing FOV angles: GRE values decrease from 93.1% at ±3° FOV to 84.9% at ±7° FOV and further to 78.1% at ±12° FOV. Field measurements consistently show slightly higher GRE values than theoretical predictions due to self-shadowing effects in SBA measurements that cause underestimation of reference water-leaving radiance, thereby inflating calculated glint contributions. Comparative analysis with dual-band power-law fitting reveals GRE values of 93.1% versus 95.2% at ±3° FOV, 83.9% versus 87.8% at ±7° FOV, and 78.1% versus 80.6% at ±12° FOV, with discrepancies primarily attributed to SBA probe self-shadowing effects that depress reference measurements and power-law fitting uncertainties influenced by spectral band selection sensitivity (±2.5% variability), non-glint signal contamination, and angular dependence of glint spectral characteristics, while maintaining GRE consistency (ΔGRE < 3.2%) and fitting robustness (R² > 0.96) across all FOV configurations. The superior performance of this system was validated through ship-based measurement data. Future research will extend to the development of marine remote sensing reflectance measurement technologies to address the pressing demands of global climate change and marine ecosystem conservation. The system requires further optimization to overcome the distinctive challenges in marine measurement scenarios, including the implementation of corrosion-resistant materials and advanced optical designs to enhance operational robustness. Special emphasis will be placed on developing more sophisticated glint suppression techniques to mitigate interference from sea surface whitecaps. Furthermore, we will establish an integrated monitoring framework that synergizes UAV platforms, satellite remote sensing, and in situ underwater sensors to achieve efficient and precise measurement of marine remote sensing reflectance.

6. Conclusions

This study innovatively developed a water-leaving radiance sensor based on multi-field-of-view Kohler-polarization technology. To address the critical need for high-efficiency sun glint removal in aquatic remote sensing reflectance measurements, we integrated polarizers with Kohler-type homogenizing lenses into a co-dispersed spectral measurement unit, effectively suppressing glint interference. The designed optical system achieves exceptional uniformity of 98.2% and, when combined with high-precision radiometric calibration (uncertainty < 3%), ensures uniform and accurate reception of absolute radiance signals.

Quantitative evaluation of glint removal efficiency (GRE) from multi-angle polarization measurements provides crucial data for characterizing field performance and improving inland water reflectance measurement accuracy. Building upon instrument measurements, we proposed a novel GRE calculation model incorporating Skylight-Blocked Approach (SBA) and dual-band power function fitting to quantitatively assess GRE at different viewing angles. The model demonstrates that our Kohler-polarization sensor can effectively remove glint interference in inland water reflectance measurements, achieving over 93.1% glint suppression. Field validation at Songhua Lake, China, with cross-comparisons against ASD field instruments and Sentinel-2 satellite data, showed superior correlation between our system and satellite data (R² = 0.926) compared to ASD measurements (R² = 0.90). These results confirm the unique value of this research for hyperspectral reflectance measurements under complex illumination conditions, not only addressing current technical challenges in aquatic remote sensing but also establishing a critical foundation for developing next-generation high-precision water quality monitoring systems.