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Shipborne single-photon fluorescence oceanic lidar: instrumentation and inversion

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Abstract

Laser-induced fluorescence (LIF) technology has been widely applied in remote sensing of aquatic phytoplankton. However, due to the weak fluorescence signal induced by laser excitation and the significant attenuation of laser in water, profiling detection becomes challenging. Moreover, it remains difficult to simultaneously retrieve the attenuation coefficient ($K_{lidar}^{mf}$) and the fluorescence volume scattering function at 180° (βf) through a single fluorescence lidar. To address these issues, a novel all-fiber fluorescence oceanic lidar is proposed, characterized by: 1) obtaining subsurface fluorescence profiles using single-photon detection technology, and 2) introducing the Klett inversion method for fluorescence lidar to simultaneously retrieve $K_{lidar}^{mf}$ and βf. According to theoretical analysis, the maximum relative error of βf for the chlorophyll concentration ranging from 0.01 mg/m3 to 10 mg/m3 within a water depth of 10 m is less than 20%, while the maximum relative error of $K_{lidar}^{mf}$ is less than 10%. Finally, the shipborne single-photon fluorescence lidar was deployed on the experimental vessel for continuous experiments of over 9 hours at fixed stations in the offshore area, validating its profiling detection capability. These results demonstrate the potential of lidar in profiling detection of aquatic phytoplankton, providing support for studying the dynamic changes and environmental responses of subsurface phytoplankton.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Marine phytoplankton are the most important primary producers in the ocean, initiating the flow of energy and cycling of matter in ecosystems, making them a primary focus of research in biological oceanography. Since the 1970s, a series of ocean color satellites have been launched, providing valuable phytoplankton products that have played a significant role in biological oceanography and global change studies, leading to an unprecedented understanding of global spatiotemporal variations in phytoplankton dynamics. These advancements have deepened our understanding of biological resource distribution, ecological processes, and phytoplankton diversity in large-scale marine ecosystems [1]. They have also provided valuable insights into global marine primary productivity [2], carbon storage capacity, and the mechanisms behind phytoplankton blooms and harmful algal blooms [3]. However, these measurements are limited to clear sky, day-light, high sun elevation angles, and are exponentially weighted toward the ocean surface. Fortunately, lidar has emerged as a stronger candidate due to its greater penetration depth, which is three times deeper than that of passive ocean color, and its ability to continuously profile water bodies day and night [4], position it as a crucial complement to passive ocean color [5].

In the field of lidar for remotely sensing phytoplankton, there are two main techniques: elastic oceanic lidar and laser-induced fluorescence lidar. Elastic lidar can obtain important parameters such as the backscattering coefficient (bbp) [6,7] and the light attenuation coefficient (Kd) [8] by analyzing the 180° volume scattering function (β), lidar attenuation coefficient ($K_{lidar}$), and polarization ratio (δ). Parameters related to phytoplankton, such as particulate organic carbon (POC) [9,10], phytoplankton carbon [11], and chlorophyll concentration (Chl) [12], can be derived using empirical formulas based on bbp, Kd, and δ. On the other hand, fluorescence lidar can directly monitor phytoplankton itself. However, despite the widespread use of fluorescence lidar systems in applications such as historical monuments [13], insect monitoring [14], and vegetation [15], there are still limitations in remote sensing monitoring of phytoplankton. This is mainly due to two reasons: Firstly, the fluorescence induced by laser in phytoplankton occurs in the red-light spectrum, with a central wavelength of ∼ 685 nm, where the light is heavily absorbed in water; secondly, the fluorescence backscattered signal is relatively weak compared to the elastic backscattered signal, so even with a high-power laser, only surface fluorescence information of the water body can be obtained [1621]. Fortunately, through the enhancement of detection sensitivity to the single-photon level, lidar technology has achieved the capability to profile weak signal energy under the constraints of low laser pulse energy and a small aperture telescope. Consequently, this technological advancement has found successful applications in various domains such as atmospheric studies [22], water Raman profiling [23], and standoff underwater oil detection [24]. Notably, the utilization of single-photon detection technology in fluorescence lidar has demonstrated its effectiveness in profiling and detecting weak fluorescence backscattered signals, as evidenced by Refs. [25,26].

However, a challenge remains in inferring two unknown parameters, the fluorescence lidar attenuation coefficient ($K_{lidar}^{mf}$), and the fluorescence volume scattering function at 180 ° (βf), from a single measurement after obtaining the profile data from the fluorescence lidar. To address this problem, recent research has proposed a method of adding a Raman channel of water alongside the fluorescence channel. This approach reduces the differential lidar attenuation coefficient and enables the use of perturbation methods to invert βf [26,27]. In this study, we verified that the Klett inversion method can be used to simultaneously obtain βf and $K_{lidar}^{mf}$ by studying the power-law relationship between βf and $K_{lidar}^{mf}$ in fluorescence lidar. Furthermore, we investigated that the quantum yield of phytoplankton (Φc) has no effect on the power-law terms of these two parameters, further validating the feasibility of using the Klett inversion method [28]. Through theoretical analysis, we confirmed the accuracy of this method for inverting these two parameters. Additionally, by utilizing the relationship between beam attenuation coefficient (cmf) and $K_{lidar}^{mf}$ established using a Monte Carlo (MC) simulation, as well as the relationship between βf and phytoplankton absorption coefficients (aph), the fluorescence lidar can simultaneously obtain cmf and aph. Note that the cmf, which signifies the rate at which light is absorbed and scattered in seawater, is crucial for estimating parameters such as POC in the water column. Finally, we conducted a 9-hour field experiment in an offshore area to verify the effectiveness of this method.

The article is organized as follows. We first introduce the all-fiber single-photon fluorescence lidar technology, followed by the methodology, including the study of the power-law relationship between βf and $K_{lidar}^{mf}$. Next, we analyze the error distribution through theoretical analysis. Finally, we present the results of a field experiment to validate the robustness and feasibility of the algorithm and lidar system.

2. Single-photon fluorescence lidar

As shown in Fig. 1, the single-photon fluorescence lidar system consists of three subsystems: a 532 nm picosecond pulse laser, a telescope, and a detection and data acquisition system. The transmitter of this lidar system utilizes a fiber-based picosecond pulse laser based on the master oscillator power amplifier (MOPA) architecture, with the seed light being a single longitudinal mode picosecond 1064 nm laser. The seed laser is amplified by a single-mode ytterbium-doped fiber amplifier (SM-YDFA) and a high-power ytterbium-doped fiber amplifier (HP-YDFA), and then the lithium borate crystal (LBO) converts the fundamental frequency 1064 nm laser to a 532 nm laser. Additionally, the residual fundamental 1064 nm light is separated using a dichroic mirror (DM). Finally, the generated 532 nm laser has a pulse width of 501 ps, a repetition frequency of 1 MHz, an output average power of 1.0 W, a divergence angle of 0.5 mrad, and a spectral width of 0.04 nm.

 figure: Fig. 1.

Fig. 1. (a) Optical layout of the single-photon fluorescence lidar. SM-YDFA: single-mode ytterbium-doped fiber amplifier; HP-YDFA: high-power ytterbium-doped fiber amplifier; L: lens; LBO: lithium borate; DM: dichroic mirror; MMF: multimode fiber; SPCM: single photon counting module; Detection & AQ: detection and data acquisition system; TDC: time-to-digital converter; FG: function generator; PC: personal computer. (b) Internal photo of the single-photon fluorescence lidar. (c) Photo of the single-photon fluorescence lidar.

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 figure: Fig. 2.

Fig. 2. Flowchart of the inversion process.

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The laser incident on the water interacts with the phytoplankton in the water, inducing fluorescence. Among them, the induced fluorescence backscattering signal is coupled into a 105 µm multimode fiber (MMF) through a numerical aperture (NA) 0.22. This coupling is achieved using an achromatic lens (Thorlabs RC12FC) with a focal length of 50.8 mm and an effective aperture of 22.4 mm, resulting in a narrow field of view of approximately 2.1 mrad. As shown in Fig. 1, the lidar system adopts a design with separate transmitter and receiver, with a distance of approximately 30 mm between the laser transmitter and the receiving lens, and the geometric overlap factor reaches 100% at a distance of about 7 m. In this work, the lidar is deployed on a ship with a distance of approximately 10 m from the water surface, so the geometric overlap factor of the water backscattered signal is 100% in the subsequent data inversion process.

To isolate the strong 532 nm elastic backscattered signal and extract the nearby 685 nm fluorescence signal, three fluorescence filter slices with a central wavelength of 685 nm and a bandwidth (full width at half maximum) of 10 nm are serially connected in front of the optical telescope. These filters provide a total isolation of 150 dB for the 532 nm elastic signal, and the total transmittance of the three filter slices is greater than 50%. It should be noted that due to the wide spectral width of the laser-induced phytoplankton fluorescence, a larger bandwidth can enhance the reception of fluorescence backscattering signals and improve signal-to-noise ratio (SNR). However, due to the use of a highly sensitive single-photon detector and background noise interference (such as signal lights on the research vessel and moonlight), a wider bandwidth results in stronger background noise. A wider bandwidth can also lead to interference from fluorescence signals induced by other substances (such as oil). Therefore, a bandwidth of 10 nm was chosen in this study. When the background noise on the platform is low and the fluorescence signals induced by negligible other substances, it is possible to consider using fluorescence filters with a larger bandwidth.

Finally, the extracted fluorescence backscattering signal is detected using a free-running single photon counting module (SPCM: Excelitas SPCM-AQRH-15), continuously counting individual photons without being constrained by specific time intervals or synchronization to external signals. The detection efficiency of the SPCM is 62% at 685 nm, with a dark count of 50 counts per second (cps). In addition, a self-developed time-to-digital converter (TDC) with a resolution of 500 ps is used to accurately capture the time information of the fluorescence backscattered photons [25]. The electronic module employs a self-built function generator (FG) implemented on a field-programmable gate array (FPGA) to generate precise control signals for the laser and TDC.

3. Methodology

3.1 Formula derivation

The backscatter profile of the fluorescence lidar through a fluorescence filter can be expressed as the convolution (${\otimes}$) of the backscatter profile [29] and the filter, as follows:

$${P_f}({\lambda _f},{\sigma _f},z) = \frac{{{B_f} \cdot {Q_f}(z)}}{{{{(n \cdot H + z)}^2}}} \cdot {\beta _f}({\lambda _f},z) \otimes g({\lambda _f},{\sigma _f}) \cdot \textrm{exp} \left\{ { - \int_0^z {[{K_{lidar}^m(y) + K_{lidar}^f(y)} ]dy} } \right\}, $$
where Pf represents the water fluorescence backscattered signal at a depth of z, given an emitted laser wavelength (λL) of 532 nm and a fluorescence wavelength (λf) of 685 nm; H represents the height at which the lidar is positioned above the water surface, which is 10 m in this case; n represents the refractive index indicator of the water; Bf is a constant that includes lidar parameters independent of depth, such as the output laser power, quantum efficiency of the detector, and transmittance of the optical transceiver system; Qf (z) represents geometric overlap factor; βf represents the volume scattering function at 180° for chlorophyll fluorescence at a wavelength of 685 nm; g(λf, σf) represents the transmittance function of a custom-made fluorescence filter, which can be approximated as a Gaussian function with a center wavelength of λf and a bandwidth of σf; $K_{lidar}^m$ represents the attenuation coefficient of the lidar at 532 nm; $K_{lidar}^f$ represents the attenuation coefficient of the lidar at 685 nm.

Taking the natural logarithm of the backscattered signal squared depth yields:

$$S({\lambda _f},{\sigma _f},z) = \ln [{{P_f}({\lambda_f},{\sigma_f},z) \cdot {{(n \cdot H + z)}^2}} ], $$
$$S({\lambda _f},{\sigma _f},{z_0}) = \ln [{{P_f}({\lambda_f},{\sigma_f},{z_0}) \cdot {{(n \cdot H + {z_0})}^2}} ], $$
where z0 is the depth of the first point of signal. By making the difference between Eq. (2) and Eq. (3), we can get:
$$\begin{aligned} S({\lambda _f},{\sigma _f},z) - S({\lambda _f},{\sigma _f},{z_0}) &= \ln \left[ {\frac{{{P_f}({\lambda_f},{\sigma_f},z) \cdot {{(n \cdot H + z)}^2}}}{{{P_f}({\lambda_f},{\sigma_f},{z_0}) \cdot {{(n \cdot H + {z_0})}^2}}}} \right]\\ &= \ln \left[ {\frac{{{\beta_f}({\lambda_f},z) \otimes g({\lambda_f},{\sigma_f})}}{{{\beta_f}({\lambda_f},{z_0}) \otimes g({\lambda_f},{\sigma_f})}}} \right] - \int_{{z_0}}^z {K_{lidar}^{mf}(y)dy} \end{aligned}, $$
where $K_{lidar}^{mf}$ (z) = $K_{lidar}^m$ (z)+ $K_{lidar}^f$ (z).

Theoretical analysis suggests that when the ${{d\beta } / {dz}} < 1.6 \cdot {10^{ - 9}}$, the retrieved error of βf is within 20%, and the Klett method is not required. Then, $K_{lidar}^{mf}$ (z) can be determined by solving Eq. (4) using the slope method [30]:

$$K_{lidar}^{mf}(z) ={-} \frac{{dS({\lambda _f},{\sigma _f},z)}}{{dz}} ={-} \frac{{d\{{\ln [{{P_f}({\lambda_f},{\sigma_f},z) \cdot {{(n \cdot H + z)}^2}} ]} \}}}{{dz}}, $$

However, if the water is inhomogeneous (${{d\beta } / {dz \ge 1.6 \cdot {{10}^{ - 9}}}}$), it becomes necessary to assume regarding the relationship between βf and $K_{lidar}^{mf}$ in order to solve for the unknown quantity in Eq. (4). After analysis, which will be further elaborated, βf and $K_{lidar}^{mf}$ approximately satisfy the following power law relationship:

$${\beta _f}({\lambda _f},z) = const \cdot {[{K_{lidar}^{mf}(z)} ]^k}, $$
where const is a constant and k is the power exponent. After that, by differentiating Eq. (4) we can get:
$$\begin{aligned} \frac{{dS({\lambda _f},{\sigma _f},z)}}{{dz}} &= \frac{1}{{{\beta _f}({\lambda _f},z)}} \cdot \frac{{d[{{\beta_f}({\lambda_f},z)} ]}}{{dz}} - K_{lidar}^{mf}(z)\\ &= \frac{k}{{K_{lidar}^{mf}(z)}} \cdot \frac{{d[{K_{lidar}^{mf}(z)} ]}}{{dz}} - K_{lidar}^{mf}(z) \end{aligned}. $$

The above nonlinear ordinary differential equation has a basic structure, namely Bernoulli equation. Based on the Klett method [28], the inversion result of $K_{lidar}^{mf}$ can be concluded as:

$$K_{lidar}^{mf}(z) = \frac{{2 \cdot \textrm{exp} \{{{{[{S({\lambda_f},{\sigma_f},z) - S({\lambda_f},{\sigma_f},{z_m})} ]} / k}} \}}}{{{{\left[ {\frac{{K_{lidar}^{mf}({z_m})}}{2}} \right]}^{ - 1}} + \frac{2}{k}\int_z^{{z_m}} {\textrm{exp} \{{{{[{S({\lambda_f},{\sigma_f},y) - S({\lambda_f},{\sigma_f},{z_m})} ]} / k}} \}dy} }}, $$

After obtaining $K_{lidar}^{mf}$, βf can be obtained based on Eq. (6). To provide a clearer representation of the inversion process, a flowchart is illustrated in Fig. 2.

3.2 Relationship between βf and$K_{lidar}^{mf}$

Based on the above analysis, it is evident that the Klett method requires a power-law relationship between βf and $K_{lidar}^{mf}$. Firstly, βf can be expressed as follows [31]:

$${\beta _f}({\lambda _f},\textrm{Chl}) = {a_{ph}}({{\lambda_L},\textrm{Chl}} ){\Phi _c}\frac{{{\lambda _L}}}{{{\lambda _f}}}{h_c}({\lambda _f})\frac{1}{{4\pi }}, $$
where Φc is the quantum yield of chlorophyll fluorescence, which is affected by factors such as light, nutrients and temperature; hc is the normalized emission wavelength function of chlorophyll fluorescence, which can be expressed using a model [32], aph(λL, Chl) is the chlorophyll fluorescence absorption coefficient at an excitation wavelength of 532 nm, the theoretical model can be used to calculate it as follows [33]:
$${a_{ph}}({\lambda _L},\textrm{Chl}) = 0.0113 \cdot \textrm{Ch}{\textrm{l}^{0.871}}. $$

According to Eq. (9,10), the relationship between βf and Chl can be established.

The inherent optical properties (IOPs) of the water are modeled as follows:

$$a(\lambda ,\textrm{Chl}) = {a_w}(\lambda ) + 0.06A(\lambda ) \cdot \textrm{Ch}{\textrm{l}^{0.65}} + {a_y}(\lambda ,\textrm{Chl}), $$
$$b(\lambda ,\textrm{Chl}) = {b_w}(\lambda ) + {b_p}(\lambda ,\textrm{Chl}), $$
$$c(\lambda ,\textrm{Chl}) = a(\lambda ,\textrm{Chl}) + b(\lambda ,\textrm{Chl}), $$
where a, b and c are absorption coefficient, scattering coefficient and beam attenuation coefficient respectively, aw is the absorption coefficient of pure seawater [34], A is the normalized spectral absorption values of phytoplankton pigments [34], ay is the absorption coefficient of yellow substance [35], bw is the scattering coefficient of pure water [36]; bp is the particulate scattering coefficient [37] and the details are shown in Table 2. cmf is the sum of beam attenuation coefficient at 532 nm and 685 nm, that is:
$${c_{mf}}({\textrm{Chl}} )= c({\lambda _m},\textrm{Chl}) + c({\lambda _f},\textrm{Chl})$$

Therefore, the relationship between cmf and Chl can be established based on Eq. (1114). Then, the relationship between βf and cmf can be established through Chl. However, it is necessary to establish the relationship between cmf and $K_{lidar}^{mf}$ first before establishing the relationship between βf and $K_{lidar}^{mf}$.

Subsequently, the relationship between $K_{lidar}^{mf}$ and the IOPs of the water is established. Due to the fact that this relationship is influenced by both the hardware parameters of the lidar system and the IOPs of the water, determining this relationship requires the use of the MC simulation. MC simulation is widely recognized as a crucial tool for simulating complex processes and has been extensively employed in simulating the backscattered signal of oceanic lidars [38]. In this study, a brief introduction to MC-based simulation of backscattered signals is provided without delving into specific details. For a more comprehensive understanding of the simulation process, it is recommended to refer to a recent article [39].

The MC method is used to simulate the random trajectories of photon propagation in a specific medium. Both the step and direction are determined by the scattering and absorption properties of the medium. The step refers to the distance or interval traveled during each random sampling iteration, while the direction denotes the path taken by the photon. The MC method ignores the photon’s wave properties, and the propagation of laser signal in the water is acted as the combination of many photon trajectories. The attenuation of laser energy is determined by three factors: the absorption of medium, the scattering probability, and the probability distribution of the steps. Thus, the MC method is widely utilized to simulate the photon propagation trajectories and monitor the energy changes. To enhance the utilization efficiency of individual photons, a semi-analytic MC model is applied [39]. This model allows for the calculation of the expected energy value and position recording of each photon within the FOV of the telescope. Note that the key parameters of the fluorescence lidar have been listed in Table 1, and the hardware parameters used during the MC simulation process match those of the fluorescence lidar.

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Table 1. Key parameters of the fluorescence lidar system

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Table 2. The bio-optical models used in the MC simulation

In the simulations, a widely used Petzold phase function was adopted [40]. With a sampling length of 10 m and a sampling interval of 0.1 m, a total of 100 sampling points can be obtained. As shown in Fig. 3(a), the simulated fluorescence backscattering signal decays exponentially. To mitigate the effects of multiple scattering in the lidar backscatter signal, a small-aperture telescope with a narrow FOV is employed.

 figure: Fig. 3.

Fig. 3. (a) Simulate fluorescence backscattered signals (lines) and the percentage of multiple scattering (PMS) in the signals (scatters) for Chl ranging from 0.01 to 10 mg/m3 using the Petzold phase function [40]. (b) Relationships between $K_{lidar}^{mf}$ and cmf, where scatter represents the results of MC simulations, and the solid line represents the fitted results.

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As shown in Fig. 3(a), when the Chl is low, the percentage of multiple scattering (PMS), which includes secondary scattering and higher-order scattering, is low. Consequently, the lidar signal is predominantly governed by single scattering. However, as the Chl increases, the PMS increases. Afterwards, $K_{lidar}^{mf}$ at different Chl is obtained by selecting the original signal with a PMS less than 100% and using the slope method [23]. The relationship between $K_{lidar}^{mf}$ and cmf is presented in Fig. 3(b). Subsequently, a second-order polynomial is used to fit the relationship between $K_{lidar}^{mf}$ and cmf. The fitting results are shown in Fig. 3(b), with a high degree of correlation indicated by the R-Square (R2) value of 0.99. From Fig. 3(b), it can be observed that when Chl is low, $K_{lidar}^{mf}$ is approximately equal to cmf. As Chl increases, PMS increases, leading to an increasing difference between $K_{lidar}^{mf}$ and cmf. The conclusion is consistent with the finding that $K_{lidar}^{mf}$ tends to closely align with the cmf when the lidar backscattered signal is predominantly governed by quasi-single scattering, whereas the lidar attenuation coefficient is given by the Kd when the backscattered signal is primarily influenced by multi-scattering [41].

Subsequently, the relationship between cmf (comprising the beam attenuation coefficient at 532 nm and 685 nm) and $K_{lidar}^{mf}$ is established through the MC simulation. This relationship is depicted in Fig. 3(b) and can be expressed as follows:

$${c_{mf}} = 0.31 \cdot {(K_{lidar}^{mf})^2} + 0.71 \cdot K_{lidar}^{mf} + 0.04. $$

Existing models [31,3436] were utilized to establish separate relationships between βf and Chl, as well as between cmf and Chl. By considering Chl as the pivot, the relationship between βf and cmf was subsequently determined. Subsequently, based on Eq. (15), the relationship between βf and $K_{lidar}^{mf}$ can be established. According to the specified range (∼0.005-0.07) of Φc [42], Fig. 4 depicts the relationship between βf and $K_{lidar}^{mf}$ for different values of Φc (0.01, 0.03, 0.05, and 0.07), with the Chl ranging from 0.01 mg/m3 to 10 mg/m3. Notably, the power index k remains constant regardless of Φc. While const varies with Φc, it has been established in Section 3 that the value of const does not affect the inversion result. Hence, the Klett inversion algorithm can be applied, utilizing the power law relationship between βf and $K_{lidar}^{mf}$, where k is determined as 2.97.

 figure: Fig. 4.

Fig. 4. Relationship between βf and $K_{lidar}^{mf}$ for Φc values of 0.01, 0.03, 0.05, and 0.07. Among them, the solid line represents the relationship given by the empirical model, and the dashed line is the fitted result.

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4. Inversion error analysis

In this section, the errors caused by the inversion algorithm will be analyzed. It should be noted that this analysis exclusively focuses on the errors originating from the inversion algorithm, while excluding errors that arise from the SNR of the lidar backscattered signal. Four typical vertical distribution models of Chl will be used for analysis, representing the waters of North Benguela [43], North Western Shelf [44], surrounding Europe [45], and acidic lakes [46], respectively. The vertical distribution profiles of these four chlorophyll profiles are shown in Fig. 5.

 figure: Fig. 5.

Fig. 5. Inversion errors under different vertical distributions of Chl. The sub-figures (a)-(d) show different Chl vertical distribution: (a) linearly increasing [43], (b) linearly decreasing [44], (c) unimodal with a single Gaussian distribution [45], and (d) bimodal with two Gaussian distribution [46]. Each sub-figure comprises three panels. The first panel displays the corresponding Chl vertical distribution; the second panel shows the distribution of Errorc and Errorβ; while the third panel displays the distribution of ErrorChl.

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To calculate the errors, firstly, it is needed to reconstruct the fluorescence backscattered signal. Based on the four vertical distribution models of Chl in Fig. 5, utilizing the bio-optical models of Eqs. (1113), the value of cmf is calculated. Then referring to the relationship between cmf and $K_{lidar}^{mf}$ of Eq. (15), the vertical profile of $K_{lidar}^{mf}$ can be obtained. In addition, according to the vertical distribution models of Chl and the empirical relationship of βf in Eq. (9), the vertical profile of βf can be acquired. Finally, based on the reconstruction of $K_{lidar}^{mf}$ and βf, along with the assumption of Bf, Pf can be reconstructed based on Eq. (1).

After obtaining the reconstructed signal, the inversion is performed using the iterative method mentioned in Section 3, the initial value of the iterative method is calculated by using the slope method on the farthest end of the signal. According to the assumed relationship in Eq. (6), combined with Fig. 4, the inversion result of $K_{lidar}^{mf}$ and βf can be obtained. By utilizing the relationship between cmf and $K_{lidar}^{mf}$ shown in Eq. (15), the vertical distribution profile of cmf can be obtained. Finally, based on the bio-optical models of Eq. (1113), the Chl vertical profile can be further inverted. After obtaining the inversion values, the respective deviations from the true values, denoted as Errorc (error for cmf), Errorβ (error for βf) and ErrorChl (error for Chl) can be calculated as follows:

$$Erro{r_c} = |{[{{c_{mf}}(z) - c_{mf}^{gt}(z)} ]/c_{mf}^{gt}(z)} |\times 100\%, $$
$$Erro{r_\beta } = |{[{{\beta_f}(z) - \beta_f^{gt}(z)} ]/\beta_f^{gt}(z)} |\times 100\%, $$
$$Erro{r_{\textrm{Chl}}} = |{[{\textrm{Chl}(z) - \textrm{Ch}{\textrm{l}^{gt}}(z)} ]/\textrm{Ch}{\textrm{l}^{gt}}(z)} |\times 100\%, $$
where, $c_{mf}^{gt}$, $\beta _f^{gt}$ and Chlgt are the true value of cmf, βf and Chl respectively.

Based on the aforementioned analysis, the Errorc, Errorβ and ErrorChl for the four different Chl distributions are shown in Fig. 5. As shown in Fig. 5(a) and Fig. 5(b), When Chl demonstrates a linear increase or decrease with a determined slope, Errorc, Errorβ and ErrorChl are relatively small, which are all below 10%. In the other two scenarios depicted in Fig. 5(c) and Fig. 5(d), where Chl exhibits a layered distribution ranging from 0.01 to 10 mg/ m3, Errorc, and ErrorChl are both below 15%, and although Errorβ is influenced by the assumed relationship, it remains below 20%.

5. Field experiment

To validate the effectiveness of the algorithm, the laser-induced fluorescence lidar was mounted on the R/V Experiment 3 of the Chinese Academy of Sciences. From October 10, 2023, 21:25 to October 11, 6:30, a continuous field experiment of over 9 hours was conducted at the location marked by the red pentagon in Fig. 6(a). The lidar was installed on the deck of the research vessel, positioned approximately 10 m above the water surface, and it emitted laser beams into the water at a zenith angle of 10 degrees.

 figure: Fig. 6.

Fig. 6. (a) The location of the lidar overlaid on a monthly averaged Chl map from an ocean color satellite. (b) Photograph of the lidar in operation. Chl data sourced from NASA MODIS standard monthly composite for October 2023.

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During the experiment, the fluorescence lidar accumulated photon counts every 40 s at depth intervals of 0.11 m. The spatial-temporal distribution of the logarithm of fluorescence photon count, ln(Pf), with a dynamic measurement range of approximately 30 dB, is depicted in Fig. 7(a), where the actual depth positions of photons were adjusted based on a zenith angle of 10 degrees. For the parameter inversion process, the initial value of $K_{lidar}^{mf}$ was obtained using the slope method, followed by the inversion of βf and $K_{lidar}^{mf}$ using the Klett method. The cmf profile was derived from the inverted $K_{lidar}^{mf}$ and the relationship established between cmf and $K_{lidar}^{mf}\; $ from Eq. (15) using the MC method. The cmf and βf profiles are shown in Fig. 7(b) and 7(c), respectively. Lastly, based on the biogeochemical model presented in Table 2, Chl was obtained through the inversion of cmf profile data, as shown in Fig. 7(d).

 figure: Fig. 7.

Fig. 7. Field experiment results: (a) measured fluorescence backscattered signal presented as the natural logarithm of photon count, i.e., ln(Pf), accompanied by lidar-inverted (b) cmf, (c) βf, and (d) Chl, each including their respective time series at a depth of 1 m. Typical Chl vertical distributions at (e) October 10, 22:30, (f) October 11, 00:10, (g) October 11, 03:00.

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The results in Fig. 7(d) indicate that the Chl in the area mostly remains below 1 mg/m3, which is consistent with the results shown in Fig. 6(a) obtained from water color satellite remote sensing. Furthermore, from Fig. 7(b-d), it can be observed that the Chl in the 0-2 m depth range is generally higher than that in the 2-4 m depth range. The typical vertical distribution of chlorophyll is shown in Fig. 7(e-f), with the respective observation times being October 10 at 22:00, October 11 at 00:10, and October 11 at 03:00. Additionally, a low Chl is observed between 23:00 and 02:00, as indicated by the values at a depth of 1 m in the figure. This may be related to the feeding behavior of zooplankton during that period, although further investigation is needed to determine the exact reasons. Overall, laser-induced fluorescence lidar provides a new approach for subsurface phytoplankton detection, enabling the observation of dynamic changes in aquatic phytoplankton with high temporal and depth resolution.

6. Conclusion

In this study, we propose and demonstrate an algorithm that can accurately retrieve the profiles of βf and $K_{lidar}^{mf}$ from fluorescence oceanic lidar simultaneously. To the best of our knowledge, this is the first time that βf and $K_{lidar}^{mf}$ profiles have been retrieved simultaneously using single-photon fluorescence lidar. This provides a pathway to improve the capability of fluorescence lidar for phytoplankton detection by inverting aph based on βf and retrieving cmf based on $K_{lidar}^{mf}$.

In terms of hardware, the adoption of single-photon detection technology enables fluorescence lidar to obtain profiles of phytoplankton fluorescence signals, laying the foundation for simultaneous retrieval of βf and $K_{lidar}^{mf}$. In terms of algorithms, theoretical analysis verifies that the relationship between βf and $K_{lidar}^{mf}$ in our single-photon fluorescence lidar can be expressed by a power-law exponent, satisfying the conditions for using the Klett algorithm. In the process of establishing the relationship between βf and $K_{lidar}^{mf}$, the shipborne single-photon fluorescence lidar adopts a small beam laser and a small-aperture telescope, which tends to make $K_{lidar}^{mf}$ serve as the cmf of IOPs, facilitating the establishment of the relationship between βf and $K_{lidar}^{mf}$. The feasibility and effectiveness of the algorithm in fluorescence oceanic lidar are demonstrated through theoretical analysis and field experiments.

In future work, we will further validate the applicability of the relationship between βf and $K_{lidar}^{mf}$ under case 2 water conditions, as it was initially established based on case 1 water conditions. Additionally, a comprehensive comparison between fluorescence lidar measurements and in-situ data, as well as ocean color remote sensing results, will be conducted to optimize the algorithm. Regarding the hardware aspect of the lidar system, the broad fluorescence spectrum and the wide bandwidth of the fluorescence filter (10 nm) pose a challenge when employing single-photon detection, as they make the system susceptible to interference from solar radiation noise. To address this issue, the plan will be to integrate the miniaturized fluorescence lidar into underwater platforms, as demonstrated in our previous research [24,47,48]. This deployment will help eliminate interference arising from the air-sea interface and mitigate the impact of solar radiation noise on our detection capabilities. We believe that this work will be an important complement to color remote sensing of phytoplankton, deepening our understanding of the spatiotemporal distribution and dynamic changes of marine phytoplankton.

Funding

National Key Research and Development Program of China (2022YFB3901704); Blue Carbon Ecosystem Assessment, Restoration and Accounting: A Tencent supported project; Innovation Program for Quantum Science and Technology (No. 2021ZD0303102); Joint Funds of the National Natural Science Foundation of China (No. U2106210); Natural Science Foundation of Fujian Province (No. 2020J01026); Fujian Provincial Central Guided Local Science and Technology Development Special Project (2022L3078); MEL-RLAB Joint Fund for Marine Science & Technology Innovation.

Acknowledgments

The authors would like to thank Zhifeng Yang, Zhenwu Weng, and Zaifa Lin for their assistance in fluorescence lidar data acquisition.

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. (a) Optical layout of the single-photon fluorescence lidar. SM-YDFA: single-mode ytterbium-doped fiber amplifier; HP-YDFA: high-power ytterbium-doped fiber amplifier; L: lens; LBO: lithium borate; DM: dichroic mirror; MMF: multimode fiber; SPCM: single photon counting module; Detection & AQ: detection and data acquisition system; TDC: time-to-digital converter; FG: function generator; PC: personal computer. (b) Internal photo of the single-photon fluorescence lidar. (c) Photo of the single-photon fluorescence lidar.
Fig. 2.
Fig. 2. Flowchart of the inversion process.
Fig. 3.
Fig. 3. (a) Simulate fluorescence backscattered signals (lines) and the percentage of multiple scattering (PMS) in the signals (scatters) for Chl ranging from 0.01 to 10 mg/m3 using the Petzold phase function [40]. (b) Relationships between $K_{lidar}^{mf}$ and cmf, where scatter represents the results of MC simulations, and the solid line represents the fitted results.
Fig. 4.
Fig. 4. Relationship between βf and $K_{lidar}^{mf}$ for Φc values of 0.01, 0.03, 0.05, and 0.07. Among them, the solid line represents the relationship given by the empirical model, and the dashed line is the fitted result.
Fig. 5.
Fig. 5. Inversion errors under different vertical distributions of Chl. The sub-figures (a)-(d) show different Chl vertical distribution: (a) linearly increasing [43], (b) linearly decreasing [44], (c) unimodal with a single Gaussian distribution [45], and (d) bimodal with two Gaussian distribution [46]. Each sub-figure comprises three panels. The first panel displays the corresponding Chl vertical distribution; the second panel shows the distribution of Errorc and Errorβ; while the third panel displays the distribution of ErrorChl.
Fig. 6.
Fig. 6. (a) The location of the lidar overlaid on a monthly averaged Chl map from an ocean color satellite. (b) Photograph of the lidar in operation. Chl data sourced from NASA MODIS standard monthly composite for October 2023.
Fig. 7.
Fig. 7. Field experiment results: (a) measured fluorescence backscattered signal presented as the natural logarithm of photon count, i.e., ln(Pf), accompanied by lidar-inverted (b) cmf, (c) βf, and (d) Chl, each including their respective time series at a depth of 1 m. Typical Chl vertical distributions at (e) October 10, 22:30, (f) October 11, 00:10, (g) October 11, 03:00.

Tables (2)

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Table 1. Key parameters of the fluorescence lidar system

Tables Icon

Table 2. The bio-optical models used in the MC simulation

Equations (18)

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P f ( λ f , σ f , z ) = B f Q f ( z ) ( n H + z ) 2 β f ( λ f , z ) g ( λ f , σ f ) exp { 0 z [ K l i d a r m ( y ) + K l i d a r f ( y ) ] d y } ,
S ( λ f , σ f , z ) = ln [ P f ( λ f , σ f , z ) ( n H + z ) 2 ] ,
S ( λ f , σ f , z 0 ) = ln [ P f ( λ f , σ f , z 0 ) ( n H + z 0 ) 2 ] ,
S ( λ f , σ f , z ) S ( λ f , σ f , z 0 ) = ln [ P f ( λ f , σ f , z ) ( n H + z ) 2 P f ( λ f , σ f , z 0 ) ( n H + z 0 ) 2 ] = ln [ β f ( λ f , z ) g ( λ f , σ f ) β f ( λ f , z 0 ) g ( λ f , σ f ) ] z 0 z K l i d a r m f ( y ) d y ,
K l i d a r m f ( z ) = d S ( λ f , σ f , z ) d z = d { ln [ P f ( λ f , σ f , z ) ( n H + z ) 2 ] } d z ,
β f ( λ f , z ) = c o n s t [ K l i d a r m f ( z ) ] k ,
d S ( λ f , σ f , z ) d z = 1 β f ( λ f , z ) d [ β f ( λ f , z ) ] d z K l i d a r m f ( z ) = k K l i d a r m f ( z ) d [ K l i d a r m f ( z ) ] d z K l i d a r m f ( z ) .
K l i d a r m f ( z ) = 2 exp { [ S ( λ f , σ f , z ) S ( λ f , σ f , z m ) ] / k } [ K l i d a r m f ( z m ) 2 ] 1 + 2 k z z m exp { [ S ( λ f , σ f , y ) S ( λ f , σ f , z m ) ] / k } d y ,
β f ( λ f , Chl ) = a p h ( λ L , Chl ) Φ c λ L λ f h c ( λ f ) 1 4 π ,
a p h ( λ L , Chl ) = 0.0113 Ch l 0.871 .
a ( λ , Chl ) = a w ( λ ) + 0.06 A ( λ ) Ch l 0.65 + a y ( λ , Chl ) ,
b ( λ , Chl ) = b w ( λ ) + b p ( λ , Chl ) ,
c ( λ , Chl ) = a ( λ , Chl ) + b ( λ , Chl ) ,
c m f ( Chl ) = c ( λ m , Chl ) + c ( λ f , Chl )
c m f = 0.31 ( K l i d a r m f ) 2 + 0.71 K l i d a r m f + 0.04.
E r r o r c = | [ c m f ( z ) c m f g t ( z ) ] / c m f g t ( z ) | × 100 % ,
E r r o r β = | [ β f ( z ) β f g t ( z ) ] / β f g t ( z ) | × 100 % ,
E r r o r Chl = | [ Chl ( z ) Ch l g t ( z ) ] / Ch l g t ( z ) | × 100 % ,
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