## Abstract

For high power-aperture lidar sounding of wide atmospheric dynamic ranges, as in middle-upper atmospheric probing, photomultiplier tubes’ (PMT) pulse pile-up effects and signal-induced noise (SIN) complicates the extraction of information from lidar return signal, especially from metal layers’ fluorescence signal. Pursuit for sophisticated description of metal layers’ characteristics at far range (80~130km) with one PMT of high quantum efficiency (QE) and good SNR, contradicts the requirements for signals of wide linear dynamic range (i.e. from approximate 10^{2} to 10^{8} counts/s). In this article, Substantial improvements on experimental simulation of Lidar signals affected by PMT are reported to evaluate the PMTs’ distortions in our High Power-Aperture Sodium LIDAR system. A new method for pile-up calibration is proposed by taking into account PMT and High Speed Data Acquisition Card as an Integrated Black-Box, as well as a new experimental method for identifying and removing SIN from the raw Lidar signals. Contradiction between the limited linear dynamic range of raw signal (55~80km) and requirements for wider acceptable linearity has been effectively solved, without complicating the current lidar system. Validity of these methods was demonstrated by applying calibrated data to retrieve atmospheric parameters (i.e. atmospheric density, temperature and sodium absolutely number density), in comparison with measurements of TIMED satellite and atmosphere model. Good agreements are obtained between results derived from calibrated signal and reference measurements where differences of atmosphere density, temperature are less than 5% in the stratosphere and less than 10K from 30km to mesosphere, respectively. Additionally, approximate 30% changes are shown in sodium concentration at its peak value. By means of the proposed methods to revert the true signal independent of detectors, authors approach a new balance between maintaining the linearity of adequate signal (20-110km) and guaranteeing good SNR (i.e. 10^{4}:1 around 90km) without debasing QE, in one single detecting channel. For the first time, PMT in photon-counting mode is independently applied to subtract reliable information of atmospheric parameters with wide acceptable linearity over an altitude range from stratosphere up to lower thermosphere (20-110km).

© 2013 OSA

## 1. Introduction

Due to the wide dynamic range of lidar return signal (from approximate 10^{2} to 10^{8} counts/s), photomultiplier tubes usually used to convert the faint light from far ranges to an electrical signal operate in photon-counting mode. Compared with analog mode, in which the PMT output is directly sampled, summed by means of a transient recorder able to give signal averages, in photon-counting mode the voltage output pulses are amplified and fed to a discriminator that separates the signal pulses from the noise pulses to enable high-precision measurement with a better signal-to-noise ratio in low light regime.

The ideal PMT output current is assumed to be linearly proportional to the input light intensity. However, the inability of the PMT to maintain a linear relationship between the incident photon flux and output current first becomes manifest at some threshold current level where the output is usually less than the expected value based on the linear response obtained at lower anode currents [1,2]. This effect, generally described as pulse pile-up, usually occurs whenever two or more pulses that would normally be counted individually arrive within too small an interval, only one count will actually be registered. Thus this occurring process tends to decrease the observed count rate [3].

In High Power-Aperture lidar system, as the size of upper atmospheric lidars is increasing and meanwhile researchers try to extend measurements into the thermosphere [4], high quantum efficiency (QE) of PMT is the preliminary concern for its capability to capture the faint return signal from far ranges. But it also means more significant pile-up distortion at lower altitude mainly due to such tubes’ either longer pulse width or limited electronic bandwidth, e.g., Hamamatsu H7421 series PMT tested in this article which offers high QE of ~40% at peak wavelength, has a pulsed width of 30ns, implying ~30MHz count rates. While its upper limit of count linearity is 1.5MHz and the pulse-pair resolution is 70ns, corresponding to 14MHz bandwidth, indicating that this tube’s pile-up effect mainly comes from electronic bandwidth. For those with lower QE but shorter width and wider bandwidth, e.g., Hamamatsu R3234 series PMT has a lower QE (~20%) but a much narrow pulse width of less than 10ns (corresponding to 100MHz counts rates) and 30ns pulse-pair resolution time (~30MHz bandwidth), the wider limitation of bandwidth may result in relative less pile-up effect in lower altitude, but apparently not as good SNR as PMTs of high QE obtain in the upper interesting area. Several groups have proposed some practical solutions by physically splitting the return signal among several channels with different techniques or with different sensitivities [5,6], good results (e.g., temperature statistical mean differences of 0.5K in the stratosphere and 2K in mesosphere) are obtained even if lidar systems are more sophisticated.

Another effect many researchers [7–12] have observed in Lidar measurement is that anode output shows a nonzero residual signal with a slow exponential decay when a PMT is subjected to a high-intensity light pulse. The faint return from far ranges is overcome by the noise induced by the signal from close ranges, leading to a systematic overestimation of the far range returns, which changes with the distance. This tail has long been recognized as signal-induced noise [7,8]. Sources of SIN may be ascribed to charging effects between dynodes and to deexcitation of photocathode electrons trapped in metastable states with long decay times [9].

Different modeling methods [8,13] have been used to subtract SIN from lower-detecting lidar signal (e.g., stratospheric aerosol lidar or differential absorption lidar). However, due to the lack of experimental basis in accord with sodium Lidar acquisition process and sophisticated simulation, the complexity of the data analysis increased and the universality of the methods was debatable to apply in sodium lidar system. In contrast, by subtracting a model backscattered signal constructed by normalizing the atmosphere model to the experimental data at certain altitudes from real backscattered signal, a general estimate of SIN can be obtain and subtracted by a quadratic fit calculated from a certain altitude to the end of the signal [6]. Other methods used a mechanical chopper to prevent pulse pile-up and SIN by physically blocking the near-field intense light [14]. To our experience, a single mechanical shutter seems to be far from enough for data processing in our High Power-Aperture Sodium Lidar, because the PMT pile-up height is up to 55km, implying it would be too much wastage of signal by physically blocking. In particular, choppers blocking the intense low-altitude returns may NOT be effective to prevent the linearity of sodium fluorescence signals at upper-altitude from nonlinearity.

In our High Power-Aperture Sodium LIDAR system enrolled in the Meridian Space weather Monitoring Project [15], developed by National Space Science Centre (NSSC) State Key Laboratory of Space Weather, high power pulsed laser beam (50mj@589nm) is transmitted into atmosphere, while a large aperture telescope (~100cm) and high sensitivity PMT in photo-counting mode are used to receive lower backscattering signals at far ranges (~110km). This implies a strong near-field Rayleigh and Mie return may cause particularly obvious pile-up and signal-induced noise that distort the return signal. These distortions often result in significant errors in retrieving atmospheric parameters [7–12], especially in the concentrations of atmospheric metal species measured by sodium lidar.

Our intention in this paper is to propose an experimental method for quantitative evaluating the input-output relationship of tested acquisition system, while trying to approximate the actual return signal before distortion by retrieving it from the input-output response functions either deduced from ideal linear PMT model or fitted from experimental results respectively. A new experimental assembly is designed to investigate the behavior of PMTs operating in photon-counting mode, by considering the PMT and high speed Data-acquisition card as an Integrated Black-Box. Due to an equal varying step of optical density (OD), although the output is distorted by the Integrate Black-box, the distorting level should be certain under certain induced intensity (i.e. certain combination of ND filters). It simplifies the complexities of detailed inner systematic courses between PMT and acquisition card as a meaningfully overall input-output relationship that reduces variables and uncertainties to ensure reliable conclusions. We test its reliability by using our H7421 series photomultipliers for example.

Authors also describe an improved sophisticated simulation of SIN based on laboratory experiments, and propose a new experimental method for SIN deduction by quantitatively evaluating SIN accumulation on each lidar data point, deduced from each approximate SIN elements. We intend to apply above methods in saving and calibrating data acquired by the High Power-Aperture Lidar systems, especially for those with single detecting channel.

The organization of this paper is as follows: Section 2 describes the improved experimental assembly, based on which, conclusions from experiments can be applied in Lidar data acquisition well. In Section 3 analysis of the response function obtained from experimental results is presented to point out a new standpoint for pile-up calibration. In Section 4 fine structure of SIN in Lidar signals is investigated while a hypothesis is given to adjust the experimental parameters for SIN sophisticated approximation. According to the accumulation amounts of SIN, relative role of pile-up and SIN to the distortion of our lidar signal is assessed and discussed. Validity of these methods was demonstrated by using calibrated data to retrieve atmospheric density, temperature and sodium absolutely number density, in comparation with reference measurements in Section 5. Finally, conclusions are made in Section 6.

## 2. Experimental assembly

#### 2.1 Schematic diagram

A schematic diagram of experimental arrangement is shown in Fig. 1. A T-1 3/4 590nm light emitting diode (LED) driven by an Arbitrary Function Generator provides light pulses of different period and width. The LED is placed in the focus of a converging lens, modulated by two Iris Diaphragms to ensure uniform illumination over the PMT photocathode. A set of neutral density (ND) filters fixed in lens tubes is used to vary the light intensity linearly over about six orders of magnitude. All optical components (i.e. Collimating Lens, ND Filters, Narrowband Filters, effective illumination area of PMT) are enclosed and fixed in High Precision coaxial optical lens tubes, where the dispersed signals are coupled to the PMT by means of optical fibers, ensuring a high degree of collimation. Both LED stabilization and intensity drift were monitored by a Digital Oscilloscope Tektronix DPO2024 in advance of each step, with a Biased Si Detector coupled with a 50Ω terminator for best frequency response.

The tested H7421 series photomultipliers (HAMAMATS Ltd., JAP) applied in our sodium fluorescence Lidar systems due to its high sensitivity on wavelength from 300nm to700nm are photon counting head devices containing a metal package photomultiplier tube with a GaAsP/GaAs photocathode and a thermoelectric cooler. The thermoelectric cooler reduces thermal noise generated from the photocathode which also offers high quantum efficiency (QE 40% at peak wavelength), allowing measurement to be made with a good SNR (i.e. 10^{4}:1 around 90km) even at very low light levels. For each pulse, the output signal of the PMT is amplified by preamplifier which has fixed threshold of 1.4001V and fed to a comparator and pulse discriminator shaper that separates the signal pulses from the noise pulse to enable high-precision measurement. The output TTL-shaped pulses are then transmitted to a 150 MHz bandwidth Ortec Multi-Channel-Scaler PCI card, providing time scan of counting rate. The signals are accumulated and averaged over 1000~10000 light pulse shots and the acquisition bin width is set to 100ns~1.28us, both depending on experimental focus.

#### 2.2 Experimental innovation

Two additional Graduated Ring-Activated Iris Diaphragms offering an additional laser-engraved scale, which indicates the actual diameter of the iris in millimeters to within ± 0.5 mm, can modulate the optical paths to ensure reproducibility of uniform illumination over the PMT photocathode. This fundamentally is critical to prove the input-output curve of tested PMT.

Two Function Generators were set. The second one, instead of DG535 Digital Delay/Pulse Generator (Stanford Research Systems Inc., USA), trigger the LED-driven Function Generator to vary illumination delay at will. It also provides pinpoint accuracy to tell the rising edge of square luminous pulse varying with intensity, as well as its falling edge to locate the SIN tails.

Except for a LED as the impulse-like light source and an Extra Function Generator, other instruments are arranged identically as the actual data acquisition process in our High Power-Aperture Sodium LIDAR system (i.e. Narrowband Filters, High Precision coaxial optical lens tubes, optical fibers importing). These make conclusions from experiments portable in actual lidar data processing.

## 3. Tests of data acquisition system’s response function to apply in pile-up calibration

#### 3.1 Methodology

The overall behavior of the Integrated Black-Box can be divided into two situations: Linear response area and non-linear response area. Due to an equal varying step of OD, although the output is distorted by the Integrate Black-box, the distorting level should be certain under certain intensity (i.e. certain combination of ND filters). Based on which, one can track the true input signal by retrieving it from the input-output response functions either deduced from ideal linear PMT model or fitted from experimental results respectively.

The key to choose which function should be used is to identify the upper limit of linearity by scanning the overall response curves from very weak count rate (~0.2MHz) to relative larger rate (~30MHz) under proportionally varied combinations of ND filters. Additionally, Authors would not want to drive the PMT too far into even blind area in case of damages, but definitely cover the wide dynamic range of measured lidar signal by prior estimating its maximum count rate (~20MHz).

#### 3.2 Tests of linear response

Vary the combinations of ND Filters in proportion from PMT’s linear dynamic range to nonlinear dynamic range under fixed intensity of induced square luminous pulses, as well as pulse width and prr (1.28us width, 30Hz prr, averaged over 1000 shots), to estimate the overall behavior of tested system, especially where the departure from linearity begins. The ideal PMT model should appear an identically linear relationship between the input and output signals, which expressed as:

^{0.1}in our case, as the minimum resolution of ND Filters suit is OD0.1. QE is the quantum efficiency of tested PMT.

Thus, the upper limit of linearity in tested PMT can be evaluated from the output signal starting to deviate from linear relationship, which in our case is 1.5 × 10^{6} counts/s (equivalent to 1920 counts under 1.28us bin width, averaged 1000 shots), according to the H7421 series Manual, as well as the experimental results proved in Fig. 2. Photo-counting mode proved to be accurate and linearly reliable up to a counts of 1920 counts, below which, Eq. (1) can describe H7421’s response well; while for higher rates, bandwidth limitation and several kinds of induced noise originated in PMT electronics [16,17], e.g., gain variations, baseline shift and some regenerative processes, will distort the linearity and degraded the measurement.

#### 3.3 Tests of non-linear response

Due to an equal varying step of OD, although the output is distorted by the Integrate Black-box, the distorting level should be certain under certain intensity (i.e. certain combination of ND filters), based on which one can track the should-be input signal by extending the ideal linear relations into nonlinear area with Eq. (1). Thus, when starting to deviate from linearity, nonlinear input-output relationship can be captured and fitted by using a least squares fit method as empirical exponential functions, through the difference between the ideal/true input signal (Y-axis) and its corresponding measured/distorted output signal (X-axis) in Fig. 2. Therefore, an exclusive input-output response curve of tested acquisition system under certain bin width and averaged shots can be extracted and fitted as two empirical exponential functions:

where ${N}_{input}$is the true number of input signal, which has been evaluated by the ideal linear model represented by Eq. (1), $N\text{'}$ is measured output signal in nonlinear dynamic range. The coefficients of Eq. (2) are given by Table 1, as well as the corresponding acquisition parameters.The fit of the nonlinear response resulting from Eq. (2) is presented in Fig. 2 by a red solid line. 28 dots represent 28 combinations of ND filters, varying with an equal step of OD 0.1. Each dot represents an inversion relationship between the ideal/true input signal given by Eq. (1) and the measured value of output signal averaged though 1.28us pulse width. The fitting curve fails in the very first hundreds of counts, but after ${N}_{L}$ it fit the points well. Below${N}_{L}$, tested system is capable to maintain a linear relationship well, described by Eq. (1). Therefore, Eq. (1) and Eq. (2) should combine together to evaluate the actual input signal, delimited by the upper limit of count linearity${N}_{L}$.

## 4. SIN modeling hypothesis to apply in SIN calibration

#### 4.1 Methodology

By the analysis of SIN fine structure, Finite Element Method (FEM) is used to simulate the atmospheric induced sources of 10ns width by square signal of 1.28us width. Then linear interpolation is applied to extract SIN corresponding to each data point of lidar signal from finite experimental data. Finally, SIN overall accumulative effect summed from sophisticated approximation of individual SIN element is evaluated and expressed as functions.

Sophisticated experimental foundation enables us to approximate the actual induced signal of 10ns width in atmosphere, by modulating the experimental square induced signal of 1.28us width and then subdividing the return signal curve with Finite Element Method (FEM). The choice for induced pulse width should base on an important consideration: The trade-off between the normal operating range of LED and the narrow elements for more sophisticated FEM approximation. Additionally, narrow acquisition bin (100ns in our cases) should be chosen for better description of SIN tails after the shorter induced pulse ends. Once the SIN curve has been clearly described, the counts under bin width of 100ns can be converted to those under actual lidar acquisition bin width (1.28us) by a count rate-counts relation:

where ${N}_{rate}$ is the measured count rate, ${N}_{1}$,${N}_{2}$ are the measured counts under different bin width $bi{n}_{1}$,$bi{n}_{2}$ and different average shots ${S}_{1}$, ${S}_{2}$.Then, authors extract the SIN tails from limited experimental data, labeled by its associated induced intensity to create a three-dimensional array of Intensity-SIN-Time relation. As the experimental induced signals have wider dynamic range by prior estimation, each data point of lidar signal can extract its associated SIN tails from the database, by locating its corresponding proximate upper-lower interval of experimental induced intensity to apply linear interpolation. Finally, an expression of SIN accumulation on measured lidar signal is deduced to apply in calibration. These above methods of evaluating SIN overall accumulative effect by sophisticated approximation of individual SIN element are described in details in the following subsections.

#### 4.2 SIN characteristics: to decide SIN expression and suitable parameters of induced pulse

Same experimental arrangement is used to investigate SIN temporal behavior corresponding to the actual H7421-MCS acquisition process after the induced pulse end. For a better view of the coherence between SIN behavior and the induced signal, we change the induced square light into 100us pulse width, 30 HZ prr, averaged over 5000 shots, varying with relative stronger intensity. The empirical expression that fits the temporal behavior best consist of two decreasing exponential functions:

In particular, as the dependences of SIN characteristics on intensity and duration of induced signals shown in Figs. 3(a) and 3(b), it strongly indicates that experimental results to be applied for SIN deduction in lidar signal should base on actual lidar acquisition parameters, which is 1.28us bin width, 30HZ prr, 1000 averaged shots in our case. Therefore we adjust the induced pulsed light to actual acquisition parameters to acquire other sets of data for further analysis in subsequent Sections.

#### 4.3 Fine structure of SIN in lidar measurement & FEM approximation

As the lidar transmit-receive process shown in Figs. 4 and 5, the real lidar backscattering echo is actually continuous with 10ns pulse width, 30HZ prr, equivalent to that of laser pulse. The fine structure of SIN shown in Fig. 5 implies that each atmospheric return signal with 10ns width causes a tail accumulating on the actual signal that is the basic element of SIN. Notice that the MCS-PCI card records the continuous return signals with 10ns width as a function of time on 1.28us bins, averaged over 1000 shots, using sum mode for signal averaging.

In Fig. 6(a), the exponentiall**y** decaying lidar return signals with 10ns pulse width, 30HZ prr are modeled and subdivided by induced square pulses of 1.28us width. In Fig. 6(b), errors between the decaying signals and simulated square pulses given by the dashed line are acceptable, as the variation of atmospheric return signal on the Y-axis is negligible, corresponding to the altitude change of only 192m on the X-axis.

#### 4.4 Linear interpolation: to extract SIN tails corresponding to each data point of lidar signal from experimental Intensity-SIN-Time database

The luminous intensity varied by ND Filters was NOT continuous, and the combinations of ND Filters are finite, we cannot obtain SIN tails corresponding to each lidar return signal, i.e. 1024 data points acquired by MCS card in lidar return signal, compared with only 56 experimental data points to cover the similar dynamic range of lidar signal. Hence, linear interpolation was used to obtain the continuous one-to-one relationship between the lidar return signals and their SIN tails. For an measured lidar signal x located in its proximate experimental signal interval $({x}_{n-1},{x}_{n-2})$, the value of each SIN corresponding to $x$ is given by

Thus, according to the sum principle of MCS-PCI card acquisition process shown in Fig. 5, SIN overall accumulative effect ${N}_{SIN}$ on a certain data point $n$, corresponding to a time moment*T*is given by

#### 4.5 Relative role of pulse pile-up and SIN to the distortion of lidar signal

The ratio of SIN to lidar raw signal is shown in Fig. 7(a), as well as the relative roles of SIN and pulse pile-up to the distortion of lidar signal is assessed in Fig. 7(b). SIN has significant influences on the near-filed raw signal (~10 times at 15km) revealed in Fig. 7(a), due to the accumulative process shown in Fig. (5). However, SIN decrease rapidly from 30km (~11%) to 80km (1%), implying SIN induced by Rayleigh backscattering at mid-altitude has a negligible residual decay (less than 2 photons) to distort the sodium florescence backscattering signal. SIN accumulative effect on sodium layer (~12% at 90km) is similar to that of 30km, but negligible at altitude above 110km (~1%) according to the red straight marks. That strongly indicates the shape of sodium backscattering signal would be affected by SIN rather in vertical than in horizontal in the tested H7421-MCS acquisition system applied in our actual lidar detection.

While the true input signal before distortion should be even stronger than measurement, by which SIN is actually induced. The relative role of SIN and pulse pile-up to the distortion should be assessed by a relation of${N}_{SIN}/\Delta {N}_{pile-up}$, where the absolute distorting value $\Delta {N}_{pile-up}$is given by$({N}_{measured}\cdot \phi -{N}_{measured})$. Red mark in Fig. 7(b) delimits the preponderance of SIN, hence the relative roles are evaluated by dividing the dynamic range of lidar signal into five periods, as listed in Table 3. The turbulence below 30km is mainly ascribed to the coherence between the separated transmit-receive systems and the considerable pile-up distortion in lower altitude. The random distribution of dots either between 65km and 75km (linear range) or above 115km (background) are resulted from both negligible ${N}_{SIN}$and $\Delta {N}_{pile-up}$, meanwhile the Y-axis was transfered to logarithm coordinates. The alternate domination of SIN in the distortion indicates that real lidar signal even if decreasing rapidly they continuously induce SIN at each time that are sum up.

## 5. Results and discussions

#### 5.1 Raw signal after pile-up & SIN calibration

As shown in Fig. 8, the raw return signals have been calibrated by Eq. (8). Differences between the red line and black line indicate the stronger the return signal is, the more photons it earns after calibration. Non-linear response distorts the raw signal even up to 55km, while above 55km good linearity appears, implying SIN starting to take the leading role in distortion, by reaching its peak at 60km, i.e. a ratio of 1000% to $\Delta {N}_{pile-up}$, equivalent to ~6 counts according to Figs. 7(a) and 7(b). Distortions among sodium layer are also significant (~300 counts@85km) that probably means splitting channels may have limited role in calibrating signal from metal layer (85km~110km), but to choose different PMTs with lower QE and much narrow pulse width. In contrast, authors have tried to approach a new balance between maintaining the linearity of adequate signal and guaranteeing good SNR without debasing QE, by means of the proposed methods to revert the true signal independent of detectors.

The first step we designed to examine the validity of proposed methods was to compare atmosphere densities derived from calibrated signals with those from signal of full-range linearity, as the latter can be considered as a standard without distortions. According to the mentioned upper limit of count linearity, we decrease the pulsed power of laser beam from 50mj@589nm to nearly 1mj, to ensure the acceptable linearity of wide dynamic range, which is shown as black solid line in Fig. 9(a). Assuming atmosphere density has no perturbation in such short time interval (about 10 minutes), we recover the pulsed power to original level (50mj@589nm) to acquire a normal profile which has been calibrated and shown as red line.

Figure 9(b) shows good agreement between the atmosphere densities derived from calibrated signal (red line) and full-scale linear signal (black line), especially at altitude where serious nonlinearity has been calibrated, i.e. from 25km to 45km. Differences to black line are less than 5%, while the estimated error due to photons’ Poisson distribution is ± 15%@40km. Therefore the validity of proposed methods can be preliminary proved and clearly identified from the potential instrumental variation of other reference measurements, and of particular importance from the errors induced by the method of temperature retrieval [18].

#### 5.2 Atmosphere density & temperature calibration

Comparison of atmosphere parameters derived from calibrated lidar signals to *TIMED* satellite and atmosphere model are shown in Figs. 10 and 11, respectively for density and temperature. Black solid lines represent profiles derived from non-calibrated lidar signal; green solid lines are profiles after calibration. Good agreements can be seen from Figs. 10(a) and 10(b) that density differences are less than 5% between the green line and reference lines above 30 km, while the black lines shows more than 100% difference deviating from reference lines.

For temperature retrieval, theories to determine density fluctuations and temperature from the Rayleigh-scatter signals are straightforward in concept but subtle in practice. The useful range of measurements is typically between 30 and 100 km. Below 30 km aerosols should be taken into account for their additional scattering that cannot be independently estimated to permit separation of the Rayleigh-scatter component, which explain the disagreement among the altitude range from the surface to 25 km [19], especially in the temperature retrieval below 30km as shown in Figs. 11(a) and 11(b). This indicates, at least in our case, the principles of pile-up and SIN calibrations are applicable to calibrate systematic distortion, for accurate measurements of atmosphere parameters above 30km, i.e. differences to *TIMED* results are less than ± 10K from 30km to 65km. While below 30km, we were not able to calculate the aerosol spectrum by means of our sodium lidar system.

#### 5.3 Sodium number density calibration

The mesospheric sodium layer is generally confined to the region between 80 and 150 km with a peak near 90km where its density ranges from approximate l0^{3}~l0^{4} cm^{−1} [20]. Sodium lidar employ sodium fluorescence in the mesopause region for sounding of the middle and upper atmosphere [21]. As the backscattering signal intensity of sodium layer is equivalent to that of 30km, the similar distortion caused by acquisition system may also occur in the sodium layer signal. Figure 12 shows sodium number densities at their peak values around 90km have significant difference between calibrated signal and raw signal, which reaches about 700 cm^{−3}. Removal of pulse pile-up and SIN result in more reasonable sodium concentrations at far ranges, which also has major implications for sodium Doppler wind-temperature lidars where measurements are made at multiple frequencies (and hence signal levels with different levels of distortion) that are then analyzed in terms of ratios. Significant differences of sodium number density imply distortions may not be ignored for their impact on the climatology and characteristics research of sodium layer.

#### 5.4 Discussions

In the upper interesting area, the fluorescence signals of metal layer suffer from the similar distortion as Rayleigh backscattering induced at mid-altitude shown in Figs. 8 and 12. Normal solutions as running with a chopper and thus block the intense low-altitude returns seems to be inadequate to prevent the linearity of sodium fluorescence signals at upper-altitude from nonlinearity, as well as the electronic gated PMT. Even though the PMT was gated off, the photocathode was still exposed to the intense near-field backscattering signals, which will saturate the photocathode and creates a cloud of electrons near photocathode. When PMT is gated on later, the SIN and lidar signal will mix together. Despite the gating process protects the secondary amplifying elements of PMT from blind or damage, gating the PMT does not help to eliminate SIN.

Coupling of different channels with different lidars [5] or with different sensitivities [6] have been proved to be an effective solution, even if lidar systems are more sophisticated and imposes more stringent requirements on the choice of detectors (i.e. PMTs of analog mode or of photon-counting mode in different channels, and furthermore the trade-off between QE and pulse pile-up). In contrast, our standpoint for the contradiction between extending the measurements range of good SNR with one PMT of high QE and maintaining the linearity of adequate signal, is to ensure good SNR as high as possible, while trying to approach the actual return signal before distortion, by retrieving it from the input-output response functions obtained by proposed methods. It reduces the complexities of quantitatively evaluating detectors’ performance varied with different altitudes by recover the true input signal. Each acquisition system can obtain its exclusive input-output response curve under identical lidar operating parameters, through our modular experimental assembly. In theory, each PMT in photon-counting mode can be applied to subtract the reliable profiles of atmospheric parameters with wide acceptable linearity over an altitude range from stratosphere up to lower thermosphere.

It should be noted that, although our methods have expand the acceptable linearity and provide a theoretically universal calibration for PMT suffered from pile-up and SIN, the accuracy of atmospheric profiles derived from calibrated signal (i.e. differences of atmosphere density, temperature are less than 5% in the stratosphere and less than 10K from 30km to mesosphere respectively) is not as ideal as that obtained by signal combinations (i.e. Potassium resonance lidar and RMR lidar are combined together [5], leaving a reliable continues temperature profile from 1 to 105km, where errors are less than 1K near 90km and less that 1K at the bottom respectively), or by nonlinearity corrections with channel comparison [6], i.e. temperature statistical mean differences of 0.5K in the stratosphere and 2K in mesosphere. That may be ascribed to either the potential errors induced by proposed methods, or the spatial-temporal coincidence between the reference satellite and our lidar, which need to be further identified in future work.

## 6. Conclusions

We have proposed two practical methods for treating lidar signals affected by Pile-up and SIN respectively. Our solutions could have substantial improvements on measurements of our high Power-Aperture sodium fluorescence lidar, as well as expand its linear dynamic range, by experimental modeling and calibrating pile-up and SIN under the identical Lidar acquisition parameters. The major methods are (1) by considering PMT and Data Acquisition Card as a Integrated Black-Box, one can easily approximate the true input signal before distortion, by retrieving it from the input-output response relationship either deduced from ideal linear PMT model or fitted from experimental results respectively; (2) by the analysis of SIN fine structure, FEM method is used to simulate the atmospheric induced sources of 10ns width by square signal of 1.28us width. Then linear interpolation is applied to extract SIN corresponding to each data point of lidar signal from finite experimental data. Finally, SIN overall accumulative effect summed up from sophisticated approximation of individual SIN element is evaluated and expressed as Eq. (6).

Several innovations on experimental assemble are made to ensure the experimental conclusions reliable and portable in actual lidar signal calibration, without that the fine structure of SIN and modeling hypothesis could not be able to calculate quantitatively. Of particular importance is a new standpoint of taking into account the PMT and High Speed Data Acquisition Card as a Integrated Black-Box, which simplifies the complexities of detailed inner systematic response between PMT and Multi-Channel Scaler Card as a meaningful input and output relationship from the data processing standpoint that reduces variables and uncertainties to ensure reliable conclusions.

The overall input-output relationship shown in Fig. 2 reveals that Eq. (2) fails in the very first hundreds of counts, but above ${N}_{L}$ it captures the nonlinearity well. Below${N}_{L}$, tested system is capable to maintain a linear relationship well, described by Eq. (1). Therefore, Eq. (1) and Eq. (2) should combine together to evaluate the actual input signal, delimited by the upper limit of count linearity${N}_{L}$.

For investigation on SIN temporal behavior after the 100us width inducing square pulse end, SIN was expressed as an empirical exponential function with a time constant ${\rm T}$and intercept ${\rm I}$. In particular, as SIN increase with the pulse width and induced intensity at all time, experimental conclusions and results for SIN deduction from actual lidar signal should base on lidar actual acquisition parameters (i.e. 1.28us bin width, 30HZ prr in our case).

Furthermore, Relative role of pulse pile-up and SIN to the distortion of lidar signal has been evaluated in Figs. 7(a) and 7(b), implying SIN induced by Rayleigh backscattering at mid-altitude (30-70km) has a negligible residual decay (less than 2 photons) to distort the sodium florescence signal at higher altitude (85-110km) in the tested H7421-MCS acquisition system applied in our actual lidar detection. Additionally, the shape of sodium florescence signal would be affected by SIN rather in vertical than in horizontal. The alternate domination of SIN in the distortion listed in Table 3 indicates that real lidar signal even if decreasing rapidly they continuously induce SIN at each time that are sum up.

Differences between the calibrated signal and raw signal in Fig. 8 indicate that in sodium lidar system, non-linearity distorts the raw signal even up to 55km, while above 55km good linearity appears, implying SIN starting to take the leading role in distortion, by reaching its peak at 60km, i.e. a ratio of 1000% to $\Delta {N}_{pile-up}$, equivalent to ~6 counts according to Figs. 7(a) and 7(b). Distortions among sodium layer are also significant (~300 counts@85km).

The validity of the proposed methods is demonstrated by the full-scale linear signal under very weak pulsed power, as well as by applying the calibrated signal to retrieve atmosphere parameters and mesospheric sodium number density, in comparation with satellite and atmosphere model. Good agreements are obtained between results derived from calibrated signal and reference measurements, where differences of atmosphere density, temperature are less than 5% in the stratosphere and less than 10K from 30km to mesosphere, respectively. Additionally, approximate 30% changes are shown in sodium concentration at its peak value. For the first time, PMT in photon-counting mode is independently applied to subtract reliable information of atmospheric parameters with wide acceptable linearity over an altitude range from stratosphere up to lower thermosphere (20-110km).

Authors have approached a new balance between maintaining the linearity of adequate signal and guaranteeing good SNR without debasing QE, by means of the proposed methods to revert the true signal independent of detectors. We successfully expand the acceptable linearity and provide a theoretically universal calibration for PMT suffered from pile-up and SIN. In this sense, authors believe that the proposed methods could combine with coupling of different channels to obtain more precise profiles of atmospheric perimeters and expand much wider dynamic ranges when our system updates to a Dual-Wavelength Upper-Detecting Lidar with multi-channels.

## Acknowledgment

Authors wish to acknowledge Prof. S.S. Gong and Prof. J.Y. Xu for various useful discussions and Prof. F.Q. Li for his help in experiments. We also sincerely acknowledge the Meridian Space weather Monitoring Project for their contributions to Lidar data acquisition. This work was supported by the Natural Science Foundation of China, under the Grant No. 41264006, No. 40905012 and No. 41174129. This research was also supported by the Specialized Research Fund for State Key Laboratories of China. We are grateful to the topical editor James Churnside and three anonymous referees for their help in evaluating this paper.

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