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Abstract
In this paper, a new prototypical Scheimpflug lidar capable of detecting the aerosol extinction coefficient and vertical atmospheric transmittance at 1 km above the ground is described. The lidar system operates at 532 nm and can be used to detect aerosol extinction coefficients throughout an entire day. Then, the vertical atmospheric transmittance can be determined from the extinction coefficients with the equation of numerical integration in this area. CCD flat fielding of the image data is used to mitigate the effects of pixel sensitivity variation. An efficient method of two-dimensional wavelet transform according to a local threshold value has been proposed to reduce the Gaussian white noise in the lidar signal. Furthermore, a new iteration method of backscattering ratio based on genetic algorithm is presented to calculate the aerosol extinction coefficient and vertical atmospheric transmittance. Some simulations are performed to reduce the different levels of noise in the simulated signal in order to test the precision of the de-noising method and inversion algorithm. The simulation result shows that the root-mean-square errors of extinction coefficients are all less than 0.02 km−1, and that the relative errors of the atmospheric transmittance between the model and inversion data are below 0.56% for all cases. The feasibility of the instrument and the inversion algorithm have also been verified by an optical experiment. The average relative errors of aerosol extinction coefficients between the Scheimpflug lidar and the conventional backscattering elastic lidar are 3.54% and 2.79% in the full overlap heights of two time points, respectively. This work opens up new possibilities of using a small-scale Scheimpflug lidar system for the remote sensing of atmospheric aerosols.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As light travels through the atmosphere, it is progressively attenuated due to scattering and absorption. At the light wavelength of 532 nm, the absorption due to molecules and aerosols are negligible, hence, the atmospheric extinction can be considered to be due to scattering only. The molecular extinction can be determined from a model [1]. Plotting the atmospheric extinction distribution over both altitude and time offers valuable information for the study. Lidar, as a laser-based active remote sensing technique, capable of high temporal-spatial resolution measurement, has been extensively used to study atmospheric aerosols [2, 3]. The lidar system that is generally employed has a monostatic configuration, in which the transmitter and detector are placed in a single location [4, 5]. The detection height of the standard monostatic lidar can reach dozens of kilometers, thus, it is able to monitor the dynamic changes of the aerosols in the upper troposphere and lower stratosphere [6]. However, a standard monostatic lidar system is not able to measure close range backscattering signals due to the incomplete overlap between the transmitter and the receiver [7–9]. In general, the data acquired in the incomplete overlap region of the lidar can be modified by either theoretical or experimental methods [10, 11]. There are some assumptions in these studies that inevitably affect the results.
However, the overlap problem can be solved by altering the monostatic configuration to a bistatic frame that divides the detector from the laser by a baseline. Thus, bistatic lidar systems provide a complementary method for near-surface atmospheric monitoring. Meki et al. [12] used a bistatic imaging lidar system with a charge-coupled-device (CCD) camera detector and lens with fields of view of approximately 12° to observe the aerosols within several hundred meters near the surface. Barnes et al. [13, 14] constructed a CCD-based bistatic lidar with a geometry, in which the entire laser beam is imaged with a wide-angle lens onto a CCD camera, thus overcoming the problems of incomplete overlap region and dynamic range. The main distinction is that the latter design of wide-angle optics is able to image the entire laser beam. Obviously, digital image processing can be used to reduce the noise component in these instruments. There are some problems in these studies as well. For example, the baseline between the transmitter and receiver is equal to 158 m in Barnes’s study, therefore, the entire system is not convenient to physically carry, and it is not easy to do an experiment in the field. Recently, Brydegaard et al. [15] proposed using lidar following the Scheimpflug principle for atmospheric fauna sounding. Then, the Scheimpflug lidar system was employed by Mei et al. [16, 17] for atmospheric oxygen molecule detection and atmospheric aerosol monitoring over several kilometers of height, benefiting from the high power continuous-wave laser diodes that have become available in recent years. Most important is that the Scheimpflug lidar technique can be regarded as a monostatic lidar system because of the features of the Scheimpflug principle.
In particular, a small-scale Scheimpflug lidar system with a cooled CCD camera detector was designed to image the laser beam in the near surface with a baseline of 0.48 m, and it can also be considered a monostatic system based on previous studies [16,17]. The inversion algorithm presented in this paper is based on the relationship between the boundary value and range-square-corrected signal that is derived from the elastic scattering lidar equation. Using this relationship as a criterion, a boundary value can be determined in the lower troposphere with an iteration algorithm. The aerosol extinction coefficient profile is retrieved with the boundary value determined by using a modified method introduced in this paper. For lower atmosphere research, the advantages of this Scheimpflug lidar are due to its outstanding height resolution in the critical near surface, the small dynamic range required, and the simple and inexpensive detection optics [13]. To demonstrate the potential of using the small-scale Scheimpflug lidar for atmospheric remote sensing, aerosol monitoring measurements are presented and investigated in detail.
2. Principles and methods
2.1 Scheimpflug lidar principles
Figure 1 is a schematic of the Scheimpflug lidar. The laser transmits in the vertical direction, and the receiver is separated from the laser by a baseline D. The CCD is set at an elevation angle ϒ. The light interacts with the air molecules and aerosols in the direction of the scattering angle θ, and a part of the scattered light can be collected by the optics and imaged onto a CCD. The return signal is shown as the recorded counts. The energy Er made up of the photon counts is detected by a pixel with the field of view dθ that occurred at height z and range r from the CCD camera. The analysis here assumes that the field of view of a pixel is constant. The pixel number 1 corresponds to the closest measurement distance z0.
The energy Er is expressed as [14]:
where A is the effective area of the receiving telescope, Tz the atmospheric transmittance from the laser to the height z, Tr the atmospheric transmittance from the height z along the slant path r to the camera, and βa(z) and βm(z) are the backscattering coefficients for aerosols and molecules at altitude z, respectively. dz is the altitude resolution and K the lidar constant. For the lidar optics used in this study, D = 0.48 m and f = 0.2 m. Two models of particles in Hefei [18] are used to simulate the phase function relationship between the backscattering and other scattering degrees. The parameters of these two models are listed in Table 1. N0 is the total number of particles in per unit volume of air. The parameters rgm and ϵgm are the characteristic parameters that describe the log-normal distribution denoted the geometric mean radius and geometric standard deviation, respectively.
Table 1. Two models of particles in Hefei
Then, these parameters are inputted into the software [19] and the phase function at angles between 0° and 180° are obtained. The simulation result is shown in Fig. 2. The minimum scattering angle detected by the system is 178.6°. This result suggests that under these circumstances the ratios of the phase functions at other degrees to the phase function at 180° are almost equal to 1. Thus, the lidar signal collected by the system can be regarded as backscattering, and this result matches the feature of the Scheimpflug lidar described above. Therefore, Eq. (1) becomes:
In Eq. (2), where d is the width of the pixel and α is the atmospheric extinction coefficient, including the contributions of the aerosol (αa) and molecule (αm). The height resolution of the Scheimpflug lidar is better in the lower atmosphere, where there is a focus of attention. The data in this area have superior resolution, while this area suffers from the problem of incomplete overlap in conventional lidar systems [10]. Detailed specifications of the instruments described in this paper are presented in Table 2. Here, a continuous-wave laser is used in order to avoid the complex timing synchronization and to obtain larger average power.
Fig. 2 Specific value between collecting light and backscattering light with scattering angle increase.
Table 2. Instrument parameters
2.2 Image preprocessing
Owing to the response of each pixel being different under the same condition, noise is introduced on the image. The noise is called fixed pattern noise (FPN), which consists of dark current non-uniformity and photon-response non-uniformity (PRNU). In order to make the images closer to the actual situation, the CCD flat fielding of the image data is used to mitigate the effects of pixel sensitivity variation and chip illumination variation [20]. Flat fielding images are taken by exposing the CCD to diffuse light from a uniform light. Random Gaussian noise still exists in the images after performing the CCD flat fielding. Owing to the high frequency of the Gaussian noise and the low signal frequency, an efficient method of two-dimensional wavelet transform according to a local threshold is presented to reduce the Gaussian white noise in the lidar signal [21]. The high-frequency noise is suppressed by the procedure of decomposition and reconstruction accordingly, and the de-noising image is obtained. The process of the two-dimensional wavelet decomposition with two layers is shown in Fig. 3.
In the figure, the parameters of h and p represent the pixel numbers in the horizontal direction and perpendicular direction, respectively. cA, cH, cV, and cD denote the approximate coefficient, detail coefficient in the horizontal direction, detail coefficient in the vertical direction, and detail coefficient in the diagonal direction, respectively, and the subscript of these coefficients represents the level of the decomposition layer. The image de-noising method is based on the adjustment of the approximate coefficient and the detail coefficient in the process of the wavelet transform decomposition. In this paper, the threshold value can be computed utilizing the following equation [22]:
where δ denotes the deviation of noise and n is the length of the image signal. In summary, the following steps can be used to reduce the noise in the lidar signal [21]:Step 1: The flat field image data is decomposed with N layers according to wavelet transformation after a correct wavelet function and decomposition layer number N are selected.
Step 2: The detail coefficients from layer 1 to layer N can be quantified by different threshold values of every decomposition layer based on the local threshold method.
Step 3: The de-noising data image can be reconstructed via inverse wavelet transformation after the approximate coefficient of the Nth layer and all detail coefficients quantified above are selected.
De-noising data images can be analyzed by applying a beam finding rule that fits a function making up a Gaussian plus a constant to the data in the direction perpendicular to the beam propagating direction at each height [14]:
where x is the pixel number from the best-fit curve along the perpendicular line, A0 the height of the Gaussian curve, A1 the center location of the beam, and A2 the width of the Gaussian. The laser beam intensity at each height can be expressed by the area of the Gaussian curve, and the value corresponds to . The constant A3 is the background count at each height.2.3 Inversion method
The relationship between pixel position and distance can be obtained from Ref [16]. In this paper, the pixel-distance and the resolution-distance relationship with the specific parts of our lidar system are shown in Figs. 4(a) and 4(b), respectively. In particular, the relationship needs a calibration procedure by detecting the backscattering signal counts from an object with the known range. There is a dome that is exactly 500 m from our laboratory, and the beam is focused on it at 805 pixels. As discussed in Ref [17], the pixel-distance relationship can be calibrated from the distant object. The range-resolved atmospheric backscattering is measured by the camera in the image plane, and the counts detected by a pixel with dθ represent the volume imaged by the receiver. The height imaged in each pixel is not equal and expands with increasing height because of the geometrical relationship. The lidar equation proves that the sampling distance is proportional to the square of distance. Thus, the typical dependence of the square of the distance inherent in conventional backscattering lidar signals is cancelled out. This will result in the low requirements of the dynamic range in the lidar system, and also has the best height resolution on the surface ground [17].
To solve the problem of the height resolution degrading considerably at upper heights, a method that carried out the normalization process followed by an interpolation scheme was applied. Finally, the signal with fixed height resolution was obtained. Thus, the traditional inversion methods can be used to obtain the atmospheric parameters. In this paper, the transmittance was calculated based on Eq. (5). Therefore, it is important to retrieve the extinction coefficient. The aerosol extinction coefficient can be calculated in terms of the lidar backscattering signal according to the Fernald inversion algorithm [23]. In this inversion algorithm, the general principle of data handling is counted on the hypothesis of a horizontally uniform atmosphere with constant scattering features at every height. The detection height designed in the lidar system is 1 km, so the clear atmospheric condition is difficult to satisfy. Many methods have been proposed to deal with this drawback, which is a concern for many researchers. In particular, the boundary value method is widely used [4]. The initial assumption in this method is that there is a restricted region in which the relative aerosol loading is least within the lidar detection height. Thus, it is important to determine the boundary value while handling the extracted data. Chen et al. [24] applied the iteration method of the backscattering ratio (IMBR) to find the boundary value. In this method, the ratio of the total backscatter to molecular backscatter, which is represented as the backscatter ratio R, is important to analyze lidar aerosol data:
The IMBR is combined with the genetic algorithm (GA) to invert the aerosol extinction coefficient. The GA is a global search optimal algorithm that achieves the global optimum by simulating the natural evolutionary process. However, the disadvantages of this algorithm are that it needs a larger population and genetic algebra in order to obtain the global optimal solution. The value of scattering ratio ranges from 1 to 3 [24]. In this paper, the GA is used to find an initial value of R in the range of 1-3 for the IMBR [25]. Thus, βa can be determined from Eq. (8). If the aerosol extinction-to-backscatter ratio is assumed to be 50 sr, αa can also be obtained. It can obtain a nonlinear equation between the return signal and the boundary value of the extinction coefficient according to the lidar equation. The nonlinear equation used in this study can be expressed as:
where z0, zc, α, and τ are the initial height, reference height, extinction coefficient, and optical depth, respectively. The value of α(zc) is able to be adjusted by changing R(λ, z) until the stopping criteria condition is met. Two parameters are defined, U equal to the left-hand side of this equation and V equal to the right-hand side. Then, the relative error of these two parameters can be written as:In this paper, a stopping criterion of 5% is given to the iterative program when the RE is smaller than the criterion. The crucial characteristic of this method is the employment of an iterative program that makes it feasible to inspect the signal profile and obtain a lowest aerosol-loaded region.
3. Numerical simulations
In this section, the numerical simulations are used to verify the performance of the above-mentioned methods, including flat fielding, de-noising, signal extraction, and inversion. The performance indicators are represented by the root-mean-square error (RMSE) of the extinction coefficient and the relative error between the model transmittance and retrieved transmittance. The ideal curves of the lidar signal and the extinction coefficient used in the simulations are shown in Fig. 5.
The simulations are divided into four parts with different levels of noise. A lidar image is simulated, and noise added into the image. The variance of the noise photons is 400, 800, 1200, and 1600 in Figs. 6(a)-6(d), respectively. As shown in the figure, when the noise level is higher, the volatility of intensity involved in the pixels that are perpendicular to the direction of the laser also becomes greater. However, there is a significant smoothing of the volatility in these four circumstances after using the two-dimensional wavelet transform method to reduce the noise. In this process, the wavelet function of sym4 is adopted to execute the wavelet transform decomposition with a layer of 3. The symlet family is adopted due to its better de-noising function. Eventually, the noise is almost filtered, and the background signal tends to be close to the level of the average background. The signal-to-noise ratios (SNRs) and the SNR enhancement factor for four noise levels are calculated, and the results are listed in Table 3. It is obvious that the SNR enhancement factor has some degrees of improvement in almost all cases. Only in the first case, in which the noise level is low, does the de-noising method have no significant effect. Therefore, the de-noising method is feasible.
Fig. 6 (a), (b), (c), and (d) are noised and de-noising signals under different noise levels with counts of 400, 800,1200, and 1600 in the row direction, respectively.
Table 3. SNRs and the enhancement factor for four cases studied
When all of the above procedures are done for the lidar signals, the aerosol extinction coefficient in 1 km range can be retrieved by the combined GA-IMBR method. To supply a further explanation of the validity of the algorithm, 30 continuous conditions were managed to calculate the RMSE for error analysis because of the randomness of the algorithm. RMSE denotes for the residual between the inverse and true values of the aerosol extinction coefficient expressed as [25]:
The results are shown in Figs. 7(a)–7(d), in which the dashed blue line represents the simulated model data and the red line represents the extinction coefficient retrieved from the model data. For altitudes under 1 km, the RMSEs of the extinction coefficients are all less than 0.02 km−1 when the GA-IMBR method was applied. Moreover, the line of model extinction is almost in the scope of error bars that are calculated by 30 successive cases. These results prove the validity of the method. Its advantage lies in the fact that it does not need to be done one by one before it reaches the stopping criteria.
Fig. 7 Extinction coefficient retrieval profiles with error bars and corresponding to RMSEs based on 30 successive cases under different noise levels (a) 400 counts; (b) 800 counts; (c) 1200 counts; (d) 1600 counts.
The transmittance can be calculated with Eq. (5). Figure 8 shows the comparison result between the model transmittance and the retrieved transmittance. The relative errors between the model and retrieved transmittance of the four noise levels plotted in the figure are 0.011%, 0.307%, 0.556%, and 0.522%, respectively. These results show that the relative errors are all below 0.56%, thus proving that the algorithm presented above is feasible.
4. Measurements and results
In order to prove the efficiency of the proposed inversion algorithm experimentally, continuous observations of the vertical atmospheric transmittance were carried out on the campus of the Anhui Institute of Optics and Fine Mechanics of Chinese Academy of Sciences (31.901°N, 117.169°E). The experiment started at 19:00 on 17 July 2017 and ended at 22:30 on 18 July 2017. The vertical and time resolutions of the measurements are 5 m and 1 min, respectively. The lidar system consists of a CW Nd:YAG laser that was transmitted in the vertical direction and a cooled CCD camera detector with an interference filter that was placed 0.48 m away from the laser. The parameters of the instruments are listed in Table 2. The signal counts are computed from the proportion under Gaussian curve fitting, as mentioned above. The final lidar signal curves are obtained from the signal counts after linear interpolation and noise subtraction, as discussed in Section 2.2. Two typical backscattering lidar signals are presented in Figs. 9(a) and 9(b), which shows that the backscattering signal changes markedly within the detection height.
Fig. 9 Corrected signals corresponding to height profiles (a) measured at 21:00 on 18 July 2017; (b) measured at 22:00 on 18 July 2017.
Figures 10(a) and 10(b) show the retrieved aerosol extinction coefficients acquired by different instruments at 21:00 and 22:00 at local standard time. The molecular extinction coefficient used in the algorithm is calculated based on the following equations [1]:
Fig. 10 Aerosol extinction coefficient determined by conventional lidar and Scheimpflug lidar (a) measured at 21:00 on 18 July 2017; (b) measured at 22:00 on 18 July 2017.
For the inversion algorithm, the aerosol extinction-to-backscatter ratio is assumed to be 50 sr. The blue solid lines in Figs. 10(a) and 10(b) are the retrieved aerosol extinction coefficient profiles using the Scheimpflug lidar, and red dotted lines in Figs. 10(a) and 10(b) the aerosol extinction coefficient profiles from the conventional backscattering elastic lidar. From Fig. 10, one can see that between 0 and 0.6 km altitude the data retrieved from conventional backscattering elastic lidar are not adopted due to the fact that the overlap factor will affect the data. The red dotted lines show the data from the conventional backscattering elastic lidar with full overlap of a few hundred meters. The aerosol extinction coefficients measured by these two systems are well matched in the full overlap heights. The average relative errors of the aerosol extinction coefficients are 3.54% and 2.79% in the full overlap heights at two time points, respectively. In the close surface, the variation of the aerosol in the vertical structure cannot be measured by conventional backscattering elastic lidar due to the overlap factor, while the system described in this paper can reveal it. Therefore, the feasibility of our system and the proposed inversion algorithm is validated.
The derived range-square-corrected backscattering signals and the total extinction coefficients with height are shown for the time sequence in Figs. 11 and 12, respectively. There are hundreds of individual profiles forming the map with the time resolution of 1 min. A clear aerosol layer, as well as the variation of the aerosol height, can be observed in Figs. 12(a) and 12(b). Results reveal that atmospheric status at the ground layer changed greatly in a short period. The small-scale Scheimpflug lidar technique can be suited to detect the aerosol, especially for aerosol layers below 1 km, where the height resolution is the best.
Fig. 11 Time-range map of range-square-corrected backscattering signal (a) measured on 17 July 2017; (b) measured on 18 July 2017.
Fig. 12 Time-range map of atmospheric extinction coefficients (a) measured on 17 July 2017; (b) measured on 18 July 2017.
Although the atmospheric extinction coefficient under the circumstance of vertical-looking operation has been obtained, the ultimate goal is to obtain the vertical atmospheric transmittance. Therefore, the vertical atmospheric transmittance is calculated based on the principle of layered structure, the profiles of aerosol extinction coefficients, and the method of discrete numerical quadrature. The vertical atmospheric transmittances within the range of 1 km during two time periods are given in Figs. 13(a) and 13(b). The atmospheric transmittance tracks the time-range map extremely well, and proves the surface layer performance of the algorithm. The data of atmospheric transmittance are all over 0.8, which suggests that the weather during the period has a low level of aerosol.
Fig. 13 Atmospheric transmittance measured by Scheimpflug lidar (a) measured on 17 July 2017; (b) measured on 18 July 2017.
5. Discussion and conclusions
In summary, an algorithm combining the GA and the IMBR method was proposed for determining aerosol extinction profiles and vertical atmospheric transmittance inversion from the land surface up to 1 km with a small-scale Scheimpflug lidar. The algorithm does not need a boundary value that exists in the area far from the lidar operating range with only purely molecular scattering. The availability of the algorithm is substantiated by both simulations and experiments. Simulated results suggest the RMSEs between the model extinction profiles and the retrieved profiles from the model data are all below 0.02 km−1, and the relative errors in the atmospheric transmittance between model and inversion data are all below 0.56%. The measured aerosol extinction coefficients were also compared with conventional backscattering elastic lidar, and the average relative errors of the aerosol extinction coefficients between the two systems are 3.54% and 2.79% in the full overlap heights of two time points, respectively. This shows that the system design and algorithms are effective. The work presented in this paper is of great significance for studying the dynamic changes of aerosols in the atmosphere. Unfortunately, there is no comparison result of the transmittance between the lidar proposed in this paper and that acquired using other instruments. An unmanned aerial vehicle that carries a light source and flies to a location in the atmosphere and the intensity of the attenuated light can be collected on the ground. The ratio of the light energy received by the ground to the light energy emitted by the light source is the atmospheric transmittance measured by the direct method. This value can be used as a point of comparison in future studies.
Funding
Natural National Science Foundation of China (NSFC) (41405014).
Acknowledgments
The authors acknowledge teacher Zhenzhu Wang for providing aerosol extinction coefficients of the research-grade elastic lidar.
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