Oceanographic lidar represents an active remote sensing technology that can satisfy the requirements of three-dimensional telemetry and profiling of the oceanic environment^[1]. In comparison with conventional passive ocean color remote sensing, oceanographic lidar possesses the capability to effectively penetrate the ocean mixed layer, thereby facilitating the acquisition of the optical properties of the subsurface ocean^[2–4]. Furthermore, spaceborne oceanic lidar compensates for the limitations of passive optical detection in nighttime and high-latitude regions^[5–7].

Airborne oceanic lidar systems emit laser pulses that traverse the atmosphere and penetrate the air-sea interface before entering the seawater. These pulses are subsequently scattered by water molecules and particulate matter, with a portion of the backscattered signal received by the lidar system. By analyzing changes in the echo signal, it is possible to directly or indirectly obtain information on particulate backscattering coefficients^[8,9], chlorophyll concentration^[4,10], and the absorption coefficients of chromophoric dissolved organic matter (CDOM)^[11]. In recent years, oceanographic lidar has been widely applied in studies related to particulate organic carbon (POC)^[5,12], net primary productivity and biomass^[13], subsurface chlorophyll maximum layers^[14–16], and the diel vertical migration of marine zooplankton^[17].

The dynamic range and linear response region of the received signal in airborne oceanic lidar are limited. When the laser incidence direction aligns with the normal vector of the sea surface and small wave facet, specular reflection causes the sea surface echo signal to be several orders of magnitude higher than that of the subsurface layer, which occupies a large portion of the detector’s dynamic range. Excessive input signals can lead to saturation and after-pulse effects in detectors such as photomultiplier tubes (PMTs), resulting in nonlinear responses and increasing errors in water parameter inversion^[18–20]. Ensuring a wide dynamic range and linear response is a critical consideration in the development of spaceborne oceanic lidar systems.

In the context of oceanographic lidar systems, the off-nadir angle of laser emission, pulse width, and the refraction of the laser beam on a rough sea surface have been shown to induce variations in the sea surface echo signal^[21]. To mitigate the intensity of the sea surface echo, the laser can be tilted at a specific angle into the water for detection. Spaceborne lidar systems, which are orbiting hundreds of kilometers above the sea surface, generate a laser footprint that is often tens of meters in diameter. A larger laser tilt angle can affect the pulse broadening and ranging performance of the receiver^[22–24]. Menzies et al. utilized the lidar in-space technology experiment (LITE) to assess the sea surface reflection intensity at varying incidence angles under different sea surface wind speeds, culminating in the proposal of a sea surface reflection model^[25]. Bufton et al.^[26] employed airborne oceanic lidar (AOL) to obtain sea surface backscattering data within 15° of the nadir angle. However, due to limitations in the dynamic range of the receiver, the uncertainty of the backscatter signal increased at larger off-nadir angles. Li et al.^[27] utilized the ALADIN-A2D airborne lidar system to measure sea surface reflectance at a 355 nm ultraviolet wavelength, with aircraft roll and pitch variations at a few finite angles. It was highlighted by the same authors that subsurface reflection was significant for medium-high off-nadir angles (greater than 15°).

Research using the CALIOP system has indicated that different off-nadir angles also affect cloud measurements in the atmosphere. To avoid specular reflection from horizontally oriented ice crystals, the CALIOP off-nadir angle was changed from 0.3° to 3°^[28]. At this angle, the ocean surface attenuated backscatter is approximately 30 times stronger than the subsurface counterpart^[29,30]. This significant disparity complicates the distinction between subsurface and surface backscatter^[31,32]. To accurately measure subsurface backscatter, the CALIOP lidar was tilted forward by 30° from the nadir on July 17, 2014, by CNES and NASA. This caused the sea surface signal to weaken by more than two orders of magnitude^[29,33].

Existing studies mostly use atmospheric lidar and are limited to the measurement and analysis of sea surface echo signals at one or a few off-nadir angles. However, there has not yet been a systematic quantitative analysis specifically targeting ocean lidar and the variations in sea surface echo signals with different off-nadir angles.

We used an airborne oceanic lidar system to conduct measurements in the South China Sea with varying roll angles. The goal was to investigate the changes in sea surface echo signals under different laser off-nadir angles and to compare the simulation results with actual measurements. This allowed us to optimize and clarify the relationship between the laser off-nadir angle and signal intensity.

The airborne dual-wavelength ocean lidar system, developed by the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences^[34], was used in this flight experiment. The laser pulse energy of the system is 2 mJ at 486 nm and 5 mJ at 532 nm. The system has four receiving channels: 486 nm high and low gain and 532 nm high and low gain; for more detailed system parameters, please refer to Ref. [34]. Due to the problem of signal saturation at the sea surface caused by low flight altitude in the presence of low clouds, the 486 and 532 nm low-gain channels are used for data analysis in this study. To optimize the detection performance while matching the laser footprint dimensions and field of view (FOV) characteristics of spaceborne lidars in orbit, and reduce signal fluctuation caused by local sea surface roughness, a 5 mrad laser beam divergence and 28 mrad receiver FOV were implemented. The laser pulse width of this lidar system is 2.5 ns with a sampling rate of 1 GHz, with each profile containing 2000 bins. The distance resolution is Δz=c0·τ/(2n), where c0=3×108 is the speed of light, τ=1ns is the sampling time resolution, and n=1.34 is the refractive index of water relative to air at 486.1 nm, which in air and water is 0.15 and 0.11 m, respectively.

The installation of the system inside the aircraft is shown in Fig. 1(a). The laser emission axis is perpendicular to the flight direction and forms an angle of θ=15° with the nadir direction (pointing to the left side of the aircraft). The reference coordinates for the roll or tilt of the aircraft are shown in Fig. 1(b). Therefore, the actual off-nadir angle of the lidar is equivalent to the roll angle plus 15°.

During maneuvers such as circling and turning, the roll of the aircraft will cause the off-nadir angle of the laser to vary so that it can adjust and change between 0° and 35° as it hits the sea surface.

The sea surface echo signal is principally associated with the backscatter coefficient of the sea surface. The total backscatter coefficient from the sea surface can be divided into three components: the backscatter from the whitecaps (γwc)^[35], the backscatter from the sea surface (γs)^[30,36], and the backscatter from the water column immediately beneath the sea surface (γu)^[37,38]. The total backscatter coefficient (γ) from the sea surface can be expressed as^[27,39]γ=ks·γwc+(1−ks)γs+γu,(1)where ks represents the whitecap coverage, which is related to the sea surface wind speed v^[40,41]: ks=2.95×10−6v3.75.(2)

The backscatter coefficient of whitecaps, γwc, is given by^[35]γwc=Rwcπcosθ.(3)

The effective reflectance of whitecaps, Rwc, is approximately 0.4. The backscatter coefficient from the sea surface, γs, is given by^[30,36]γs=ρ4πσ2cos4θexp(−tan2θ2σ2).(4)

The backscatter coefficient γs is a function of wind speed v and off-nadir angle θ, and ρ is the Fresnel reflection coefficient, approximately 0.0209. The mean square slope σ2 of the sea surface is related to the sea surface wind speed ν and can be expressed as^[42]{σ2=0.0146v,v<7m/sσ2=0.003+0.00512v,7m/s≤v≤13.3m/sσ2=0.138lgv−0.084v,v>13.3m/s.(5)

The backscatter coefficient from the water column immediately beneath the sea surface, γu, is given by^[37,38]γu=(1−Rwc)R0πcosθ,(6)where R0 represents the equivalent subsurface reflectance. The variation in ocean turbidity dictates the value of R0, which typically ranges from 0.008 to 0.02.^[37].

As demonstrated in Fig. 2, the sea surface backscatter coefficient for different wind speeds and off-nadir angles is calculated by combining Eqs. (1)–(6). When the laser pulse contacts the sea surface, specular reflection occurs, and the reflected signal is stronger for smaller off-nadir angles. For a given wind speed, the backscatter coefficient exhibits a decreasing trend with the increase in off-nadir angle.

The experimental area is located in the South China Sea (110.60°E–110.80°E, 17.81°N–17.87°N), as illustrated in Fig. 3(a). The flight experiment was conducted over a two-day period from May 17 to May 18, 2024. To eliminate the interference of solar background light on the echo signal, all experimental trials were conducted during nighttime. On May 17, 2024, the aircraft conducted the first flight experiment, with the counterclockwise flight path depicted in Fig. 3(b).

The aircraft completed 20 circles flown in the designated experimental area during the first flight, with 19 circles flown in a counterclockwise direction and maintaining a consistent altitude of approximately 415 m. The final circle was flown in a clockwise direction at an altitude of about 320 m, approximately 100 m lower than during the counterclockwise flight, with a time difference of approximately 2 h. According to the MERRA-2 hourly instantaneous two-dimensional data product^[43], the average sea surface wind speed was approximately 7.2 m/s. Further documentation and information on accessing MERRA-2 data can be found in Ref. [44].

As a case in point, Fig. 4(a) illustrates the flight altitude of the fifth circle of counterclockwise flight, while Figs. 4(b)–4(d) depict the aircraft’s three attitude angles: heading, pitch, and roll, respectively. The original lidar profile data along the flight path are shown in Fig. 4(e). When the roll angle reaches approximately −20°, corresponding to an actual off-nadir angle of −5°, sea surface echo signal saturation occurs. A comparison of the off-nadir angle and the original lidar data distribution clearly demonstrates that as the off-nadir angle increases, the number of photons in the sea surface echo signal decreases significantly.

The original data from this flight were processed for sea surface position alignment, and the underwater distance was corrected to vertical depth according to the off-nadir angle. For off-nadir angles ranging from 0° to 35°, single-profile echo signals were extracted and compared every 5°, as shown in Figs. 5(a) and 5(b). It is evident that as the off-nadir angle increases from 0° to 35°, the sea surface echo signal diminishes by two to three orders of magnitude. The 532 nm low-gain channel can validate the conclusions derived from the 486 nm low-gain channel, and the results obtained from both channels exhibit strong consistency, with the results illustrated in Figs. 5(a) and 5(d). Furthermore, an increase in the off-nadir angle of the laser entry into the water results in the signal experiencing depth aliasing within the same detection depth bin. This is influenced by both sea surface scattering and water column scattering beneath the surface. The broadening of the sea surface signal in the depth direction becomes more significant.

A similar analysis was performed on the data collected during the clockwise flight, with the results illustrated in Fig. 5(b). Due to the aircraft’s flight attitude, the 0° off-nadir angle was not formed and recorded. Therefore, the analysis was restricted to the single-profile echo signals from 5° to 35°. As the off-nadir angle increases from 5° to 35°, the sea surface echo signal decreases by two to three orders of magnitude, which is consistent with the phenomenon and results observed during counterclockwise flight.

By comparing the green profile signal at 5° in Figs. 5(a) and 5(b), it can be seen that due to the decrease in flight altitude, saturation of the detector even happens at bigger off-nadir angles.

On May 18, 2024, the second flight experiment was conducted, during which the average sea surface wind speed was approximately 2.1 m/s and the flight altitude increased to around 510 m. As demonstrated in Fig. 5(c), the sea surface echo signal pattern was consistent with the results from the first day, leading to the same conclusion as that derived from the calculations in Fig. 2. Specifically, with a decrease in sea surface wind speed, the sea surface echo signal increased at the same off-nadir angle. A comparison of Figs. 5(a) and 5(c) reveals that when the sea surface wind speed is lower, the decrease in the sea surface echo signal as the off-nadir angle increases from 0° to 35° is less pronounced than when the wind speed is higher. Comparative analysis of Figs. 5(a), 5(b), and 5(c) reveals that sea surface return signals intensify under lower wind speeds, with particularly greater saturation depths observed at 0° incident angle. In subsequent figures, waveform analyses default to the 486 nm low-gain channel unless otherwise specified.

To reduce the influence of a rough sea surface, system instability, and aircraft motion on the backscatter signal at different off-nadir angles, 1000 profiles (the laser repetition frequency is 100 Hz, 1000 profiles corresponding to a flight distance of about 700 m; corresponding time is 10 s) were averaged within a ±0.25° range for each off-nadir angle. We assume that the sea conditions will remain basically unchanged in this period and region. For instance, for an off-nadir angle of 10°, the range of 9.75° to 10.25° was used. The results are shown in Fig. 6. As the off-nadir angle increases from 0° to 35°, the sea surface echo signal decreases by two to three orders of magnitude, a phenomenon that is analogous to the results observed for single-profile measurements. Between 0° and 10°, a stronger sea surface echo signal results in signal saturation. However, as the off-nadir angle increases, the saturation effect significantly diminishes. Between 15° and 35°, no such signal saturation was observed. Furthermore, an increase in the off-nadir angle results in depth aliasing of signals within the same detection depth bin, attributable to the combined effects of sea surface backscattering and subsurface water backscattering. Consequently, this phenomenon induces a significant broadening of the sea surface signal in the depth direction.

It is important to note that, in the absence of multiple scattering effects, the lidar echo signal can be expressed as^[6,45]$$\begin{gathered} N(z)=N0A(nH+z)2Tatm2Tsur2ηc0Δt2 \\ ×β(π,z)exp[−2∫0zα(z′)dz′], \end{gathered}$$(7)where N0 denotes the number of laser photons emitted, A represents the telescope’s receiver aperture area, n is the refractive index of seawater, H is the altitude of the aircraft platform, nH+z represents the refractive index corrected effective optical path, Tatm is the atmospheric transmission, Tsur is the sea surface transmission, η is the detection system efficiency, c0 is the speed of light, and c0Δt/2 is the sampling resolution. The β(π,z) is the 180° volume scattering function at depth z, representing the backscattering intensity per unit volume generated by particles/molecules in water, and is primarily governed by particulate matter properties (e.g., concentration, size, and morphology) and inherent optical properties of water. The α is the lidar attenuation coefficient. To quantify the effects of multiple scattering, we leveraged the lidar attenuation coefficient optimized through Monte Carlo simulations, with the fitting results as α=Kd+(c−Kd)exp(−0.85cD), where Kd is the water diffusion attenuation coefficient, c is the beam attenuation coefficient, and D is the laser footprint diameter.

Based on the lidar system parameters in Sec. 2, the echo photon counts for off-nadir angles ranging from 0° to 25° were simulated using Eq. (7) and then compared with airborne measurements. As shown in Figs. 7(a) and 7(b), significant saturation of the sea surface echo signal at 0° and 5° led to a substantial discrepancy between the airborne measurements and the simulation results at depths ranging from 0 to 3 m. However, at depths exceeding 3 m, the echo signals began to converge, leading to enhanced consistency in the results. As shown in Fig. 7(c), at an off-nadir angle of 10°, the saturation effect of the sea surface echo signal becomes less pronounced as the sea surface backscatter coefficient decreases. For depths greater than 2 m, the airborne and simulated results are in good agreement. As demonstrated in Figs. 7(d)–7(f), at off-nadir angles ranging from 15° to 25°, the laser pulse wavefront experiences substantial variations in the time required to enter the water, attributable to the augmented tilt angle. Due to the tilted incidence of the laser footprint on the water surface, the echo signal near the sea surface constitutes a spatially weighted superposition of returns from the air-water interface and several adjacent subsurface bins within a given time window. This results in varying degrees of depth-directional broadening of the sea surface signal. The observed discrepancies between airborne measurements and simulation results within the 0 to 4 m subsurface layer are primarily attributable to four interconnected factors: 1) after-pulse effects induced by intense surface echoes, 2) limitations in surface scattering modeling, 3) ignoring the contributions of multiple scattering, and 4) the diffusion from the uneven sea surface impinging upon the subsurface water column.

The ocean lidar echo signal at the sea surface N(0) can be expressed as N(0)=N0AH2Tatm2ηc0Δt2·γ.(8)

As demonstrated in Figs. 5 and 6, it can be concluded that the sea surface echo signal is the maximum value of the lidar signal profile. According to Eq. (8), the sea surface echo signal during fixed-altitude detection exhibits exclusive dependence on the sea surface backscatter coefficient γ, with other parameters maintaining constant values. The variation of the sea surface backscatter coefficient with an off-nadir angle can be used to validate the sea surface wind speed. Figure 8 illustrates that the sea surface echo signal curves from the first flight on May 17, 2024, across various off-nadir angles, correlate closely with the sea surface backscatter coefficient within the wind speed range of 6.2 to 8.2 m/s. This further validates that the sea surface wind speed in the current region is approximately 7 m/s. It is important to note that the sea surface echo signal curve is lower due to signal saturation at off-nadir angles of 0° to 5°. Some discrepancies between the sea surface echo signal curve and the sea surface backscatter coefficient curve exist, caused by factors such as wind speed measurement, spatiotemporal matching, and system instability.

In this airborne oceanic lidar experiment, when the aircraft platform was positioned at an altitude of approximately 500 m, a substantial number of photons generated by the sea surface echo signal resulted in receiver overload and saturation, particularly under near-vertical incidence conditions (e.g.,  0°–5°). When the off-nadir angle exceeds a certain threshold (e.g.,  15°–35°), the sea surface signal is susceptible to echo aliasing from different bins in the depth direction, leading to a reduction in vertical resolution and stretching of the laser footprint.

This, in turn, causes changes in the distribution of incident energy. Furthermore, as the off-nadir angle increases, variations in the sea surface roughness affect the subsurface water echo signal. A comprehensive consideration of these factors indicates that an off-nadir angle within 10° to 15° effectively avoids saturation of the sea surface echo signal during small-angle incidence while achieving the vertical resolution of less than 1 m. Due to the limitation of experimental conditions, we can only draw conclusions in the South China Sea and for two different wind speeds, and we cannot conduct a comprehensive survey of the global oceans. Future work will involve comprehensive field experiments across diverse marine environments, with particular emphasis on high-latitude regions and turbid water bodies, to enhance the robustness of our findings.