**2. LIDAR atmospheric sensing**

LIDAR remote sensing of the atmosphere represents a complex activity joining together a variety of experimental equipments, measurement techniques, analytical methods, theoretical approaches, etc. Lidar sensing process includes the following principal stages:


The interpreted results from the lidar sensing can be used by different authorities (governmental, local, etc.) for decision making.

#### **2.1 General lidar block-schematic**

Regardless of the mentioned above diversity of lidars, there are some basic components common for all the systems, such as transmitter, receiver, and acquisition subsystems. A general block-diagram of a lidar is presented in Fig.1. One of the main parts of the lidar is the laser transmitter emitting pulsed radiation of appropriate power, spectral, spatial, and temporal characteristics. The laser beam is transmitted into the atmosphere by an optomechanical set-up. The latter comprises a set of optical elements (mirrors, splitters, etc.) for laser beam transportation and time-synchronization, an expanding telescope for minimising the output beam divergence, and mechanical mounts with precise translation and rotation mechanisms for beam steering and lidar adjustment.

The lidar receiver consists of optical receiving part and photo-electronic blocks. Backscattered radiation is collected by a telescope. Refractive and reflective telescopes of different types (Cassegrain, Newtonian, Schmidt, etc.), size, and configurations are typically used. A changeable properly-shaped and sized field-stop diaphragm, placed near the focal

using them in the lidar remote sensing of the atmosphere (Sec.4). Then, in Sec.5, a number of experimental results on lidar atmospheric sensing, obtained with these systems are presented. Reported are measurements focused on evaluations and range resolved profiling of a defined set of important optical characteristics of the atmospheric aerosol, such as backscattering and extinction coefficients, Ångström exponent, etc., as averaged over time so in their temporal evolution. This is in view of the close relation of these characteristics to the spatial distribution, concentration, size parameters, and dynamics of the atmospheric aerosol content. Also, the use of lidars for ecological measurements and detection of hidden aerosol pollution transport by lidar mapping, including the trans-border pollution transport over the Danube River, is shown. Special consideration is given to applications concerning remote sensing of different atmospheric phenomena such as volcanic ash and Saharan dust, to parallel observations with space-borne lidars, etc. In Sec.6, the role of multi-wavelength aerosol lidar probing in the mid-visible and near infrared (IR) ranges is underlined, as a powerful and reliable approach for atmospheric observations providing accurate rangeresolved profiling of valuable atmospheric parameters with high spatial and temporal

LIDAR remote sensing of the atmosphere represents a complex activity joining together a variety of experimental equipments, measurement techniques, analytical methods, theoretical approaches, etc. Lidar sensing process includes the following principal stages:

The interpreted results from the lidar sensing can be used by different authorities

Regardless of the mentioned above diversity of lidars, there are some basic components common for all the systems, such as transmitter, receiver, and acquisition subsystems. A general block-diagram of a lidar is presented in Fig.1. One of the main parts of the lidar is the laser transmitter emitting pulsed radiation of appropriate power, spectral, spatial, and temporal characteristics. The laser beam is transmitted into the atmosphere by an optomechanical set-up. The latter comprises a set of optical elements (mirrors, splitters, etc.) for laser beam transportation and time-synchronization, an expanding telescope for minimising the output beam divergence, and mechanical mounts with precise translation and rotation

The lidar receiver consists of optical receiving part and photo-electronic blocks. Backscattered radiation is collected by a telescope. Refractive and reflective telescopes of different types (Cassegrain, Newtonian, Schmidt, etc.), size, and configurations are typically used. A changeable properly-shaped and sized field-stop diaphragm, placed near the focal

resolution.

**2. LIDAR atmospheric sensing** 

Emitting pulsed radiation into atmosphere;

Lidar signal conversion and preprocessing;

(governmental, local, etc.) for decision making.

mechanisms for beam steering and lidar adjustment.

**2.1 General lidar block-schematic** 

Receiving, detection, and recording of backscattered lidar signals;

Displaying, visualization, analysis and interpretation of obtained results.

Data processing and profiling of major parameters of interest;

point of the telescope, provides angular spatial filtering of the backscattered radiation, forming by this manner the telescope's field of view in conformity with the laser beam divergence. An important part of the multiwavelength lidar receivers is the optical module for wavelength- and/or polarization separation and discrimination. It represents an optical assembly containing dichroic beam-splitters forming the lidar spectral channels for initial wavelength separation of the backscattered laser radiation. Narrow bandpass (1-3 nm FWHM) interference filters are usually placed in each of the spectral channels, providing the main fine spectral selection of the corresponding wavelengths and suppressing the solar radiation background, especially in day-time measurements. Residuals from the other laser wavelengths are further suppressed by using additional spectrally-selective optical elements (e.g. edgepass filters), leading to final transmission of less than 10-4% in the blocking spectral regions. As a result, a good enough signal-to-noise ratio is normally achieved, allowing reliable detection of weak lidar signals and, hence, reaching high altitudes of lidar sounding. Lidar spectral channels can be equipped for measurement of the depolarization ratio of aerosol backscatter on defined wavelengths as it is important for aerosol particle shape characterization.

Fig. 1. General block diagram of a lidar system.

Spectrally selected optical lidar signals are detected and converted to electrical ones by using highly-sensitive photodetectors such as photomultipliers, avalanche photodiodes, and CCD-cameras. Further, the received signals enter the acquisition system which provides sampling and pre-processing of raw signals to standard lidar data. The acquisition system is designed to operate in either analog or photon-counting modes, depending on the lidar type, laser pulse energy, measurement tasks, etc. The acquired lidar profiles are stored and

LIDAR Atmospheric Sensing by Metal Vapor and Nd:YAG Lasers 349

at a reference range *r*0 are known, the lidar can be calibrated with these boundary conditions to determine the calibration constant *P*0*C*. Then the solution of Eq.(5) can be written as

2

0 0 2

procedure negative values for the denominator and, consequently, for

2

 *<sup>r</sup>* and max max 

<sup>2</sup> max max <sup>2</sup>

compared to the molecular backscatter coefficient, i.e.

*r*

2

The molecular atmospheric backscattering coefficient

0 0

*a*(*r*0) or extinction

sense that small errors in the determination of

 

max max

 

*r r*

 

() ()

 

However, the aerosol backscattering

introducing max max ( ) *a a* 

can rewrite Eq.(6) as follows:

() ()

 

*r r*

*a m*

*r r*

*a m*

backscattering

0 0

*Pr r S P S S dd*

*a*(*r*) and extinction

( ) exp 2 ( ) ( )

*Prr S r S d*

( ) 2 ( ) ( ) exp 2 ( ) ( ') ' () ()

 

*<sup>a</sup> a mm r r a m*

model of Standard atmosphere or calculated using meteorological data from a radiosonde.

*Sa*(*r*)], remain to be determined as two unknown variables from the values of one variable – the so-called range corrected signal *P*(*r*)*r*2, obtained from the lidar measurement. This is not possible without using additional information about at least one of the unknown variables. When choosing the reference range *r*0 near to the ground (and to the lidar), the aerosol

integrate Eq.(6) and retrieve the atmospheric backscattering coefficient profile. Unfortunately, there exists a mathematical instability in the calculations following Eq.(6) in

measured range corrected signal *P*(*r*)*r*2, start to produce in few steps of integration

problem, Klett (Klett, 1981) and Fernald (Fernald, 1984) proposed an inverse integration of Eq.(6), starting from the far end of the lidar sounding path. Applying this idea and

> 

( ) 2 ( ) ( ) exp 2 ( ) ( ') '

 

*<sup>a</sup> am m <sup>r</sup> a m*

The reference range *rmax* is chosen so that the aerosol backscatter coefficient is negligible

atmospheric conditions are observed in the upper troposphere. Thus, we can attach the upper backscattering value to the value of the molecular backscattering and calculate the backscatter profile in backward direction by Eq.(7), using the measured range-corrected lidar signal. Determination of the reference range *rmax* is a problem for some atmospheric conditions as cloudy atmosphere, intensive background, etc. (see Sec.6). This algorithm is now widely applicable in practice, assuming also invariant value for the aerosol lidar ratio *Sa*=const along the laser beam path in the atmosphere. The exact value of this constant is determined depending on the laser wavelength and also on *a priori* assumptions about the type of the observed aerosols. The influence of the assumption for constant aerosol lidar ratio on the results of calculated profiles of atmospheric backscattering coefficient is studied

max max

*r r*

*Pr r S P S S dd*

( ) exp 2 ( ) ( )

*Prr S r S d*

max

 

*a*(*rmax*)<<

*r am m <sup>r</sup>*

0

 

*<sup>a</sup>*(*r*0) can be measured independently. After that, we can

*m m* ( ) *r* , where *rmax* is the maximal distance, we

 

 

*<sup>m</sup>*(*rmax*). Normally such

*r a mm <sup>r</sup>*

 

*<sup>a</sup>*(*r*0) at the reference distance *r*<sup>0</sup>or in the

*<sup>a</sup>*(*r*). To solve this

. (7)

 

*<sup>m</sup>*(*r*) can be determined from the

*<sup>a</sup>*(*r*) [or the aerosol lidar ratio

. (6)

follow:

processed by specialized retrieving algorithms and software. The controlling and timing electronics provides the overall lidar operation.

#### **2.2 Lidar equation**

Basic aerosol parameters derived from lidar data are the aerosol backscattering and extinction coefficients. Theoretical models for retrieving their range profiles from raw lidar data are based on solving of so-called lidar equation describing the relation between the received range-resolved backscattered optical radiation power and atmospheric and system parameters. For a single-scattering elastic backscatter lidar (measuring backscattered light at the same wavelength as the sensing laser wavelength ) the power *P*(*r*), detected at a time *t* after the instant of pulse emission, is written as:

$$P(r) = P\_0 \frac{c\tau}{2} A\varepsilon \frac{\gamma(r)}{r^2} \beta(r) \exp\left[-2\int\_0^r a(\rho)d\rho\right],\tag{1}$$

where *r*=*ct*/2 is the distance along the laser beam path, *P*0 is the average power of a single laser pulse, is the pulse duration, *A* is the area of the primary receiving optics, is the overall system efficiency, *(r)* and *(r)* are the backscattering and extinction coefficients, respectively, at wavelength . The term *(r)* describes the overlap between the laser beam and the receiver field of view, being equal to 1 for ranges of complete overlap. To solve the lidar equation (1), it is useful to split the backscatter and extinction in molecular and aerosol terms:

$$
\beta(r) = \beta\_a(r) + \beta\_m(r) \; ; \quad \alpha(r) = \alpha\_a(r) + \alpha\_m(r) \; . \tag{2}
$$

In Eq.(2) and further, the subscripts "*a*" and "*m*" stand for aerosol and molecular terms, respectively. We also assume negligible atmospheric absorption at a wavelength and *(r)* = 1. In next step we introduce the aerosol extinction-to-backscatter lidar ratio *Sa*(*r*) as:

$$S\_a(r) = \alpha\_a(r) / \beta\_a(r) \tag{3}$$

by analogy with the molecular extinction-to-backscatter ratio:

$$S\_m = \alpha\_m(r) / \beta\_m(r) = 8\pi / 3\,\text{.}\tag{4}$$

*Sa*(*r*) depends on range *r* through the size distribution, shape, and chemical composition of the aerosol particles. Substituting Eqs.(2) in Eq.(1), and bearing in mind Eqs.(3) and (4) , we obtain:

$$\begin{aligned} &P(r)r^2 \exp\left\{-2\int\_0^r \left[S\_a(\rho) - S\_m\right]\beta\_m(\rho)d\rho\right\} = \\ &= P\_0 \mathbb{C}\left[\beta\_a(r) + \beta\_m(r)\right] \exp\left\{-2\int\_0^r \left[\beta\_a(\rho) + \beta\_m(\rho)\right]S\_a(\rho)d\rho\right\}.\tag{5} \end{aligned} \tag{5}$$

In Eq.(5) the constant *C*=*Ac*/2 (so-called lidar constant) covers all system parameters. Next, following the steps described in Weitkamp, (2005), we take the logarithm of both sides of Eq.(5) and differentiate it with respect to *r*. Finally a differential equation of Bernoulli type is obtained. In a case when the values *a*(*r*0) of aerosol and *<sup>m</sup>*(*r*0) of molecular backscattering

processed by specialized retrieving algorithms and software. The controlling and timing

Basic aerosol parameters derived from lidar data are the aerosol backscattering and extinction coefficients. Theoretical models for retrieving their range profiles from raw lidar data are based on solving of so-called lidar equation describing the relation between the received range-resolved backscattered optical radiation power and atmospheric and system parameters. For a single-scattering elastic backscatter lidar (measuring backscattered light at

> <sup>0</sup> <sup>2</sup> <sup>0</sup> ( ) ( ) ( )exp 2 ( ) <sup>2</sup> *c r <sup>r</sup> Pr P A r <sup>d</sup> r*

where *r*=*ct*/2 is the distance along the laser beam path, *P*0 is the average power of a single

and the receiver field of view, being equal to 1 for ranges of complete overlap. To solve the lidar equation (1), it is useful to split the backscatter and extinction in molecular and aerosol

In Eq.(2) and further, the subscripts "*a*" and "*m*" stand for aerosol and molecular terms, respectively. We also assume negligible atmospheric absorption at a wavelength

*(r)* = 1. In next step we introduce the aerosol extinction-to-backscatter lidar ratio *Sa*(*r*) as:

*S rr mm m* 

*a mm*

( ) ( )/ ( ) *Sr r r a aa* 

 ( )/ ( ) 8 /3 

*a*(*r*0) of aerosol and

 

 

/2 (so-called lidar constant) covers all system parameters.

( ) ( ) exp 2 ( ) ( ) ( )

*r a m a ma*

 

*PC r r S d*

Next, following the steps described in Weitkamp, (2005), we take the logarithm of both sides of Eq.(5) and differentiate it with respect to *r*. Finally a differential equation of Bernoulli type

*Sa*(*r*) depends on range *r* through the size distribution, shape, and chemical composition of the aerosol particles. Substituting Eqs.(2) in Eq.(1), and bearing in mind Eqs.(3) and (4) , we

is the pulse duration, *A* is the area of the primary receiving optics,

 *a m* ; () () () 

 

 

. The term

() () ()

 

 *rr r* 

by analogy with the molecular extinction-to-backscatter ratio:

0

*r*

( ) exp 2 ( ) ( )

*Prr S S d*

<sup>0</sup> <sup>0</sup>

 

 *rr r* 

 

) the power *P*(*r*), detected at a time *t*

, (1)

*a m* . (2)

(3)

. (4)

*(r)* are the backscattering and extinction coefficients,

*(r)* describes the overlap between the laser beam

is the

> and

. (5)

*<sup>m</sup>*(*r*0) of molecular backscattering

electronics provides the overall lidar operation.

the same wavelength as the sensing laser wavelength

*(r)* and

2

In Eq.(5) the constant *C*=*A*

is obtained. In a case when the values

> *c*

after the instant of pulse emission, is written as:

**2.2 Lidar equation** 

laser pulse,

terms:

obtain:

overall system efficiency,

respectively, at wavelength

at a reference range *r*0 are known, the lidar can be calibrated with these boundary conditions to determine the calibration constant *P*0*C*. Then the solution of Eq.(5) can be written as follow:

$$\begin{split} \beta\_{a}(r) &= -\beta\_{m}(r) \\ &+ \frac{P(r)r^{2}\exp\left\{-2\left[S\_{a}(r) - S\_{m}\right]\int\_{r\_{0}}^{r} \beta\_{m}(\rho)d\rho\right\}}{\beta\_{a}(r\_{0}) + \beta\_{m}(r\_{0})} - 2\int\_{r\_{0}}^{r} S\_{a}(\rho)P(\rho)\rho^{2}\exp\left\{-2\left[S\_{a}(\rho) - S\_{m}\right]\int\_{r\_{0}}^{\rho} \beta\_{m}(\rho')d\rho'\right\}d\rho} \end{split} \tag{6}$$

The molecular atmospheric backscattering coefficient *<sup>m</sup>*(*r*) can be determined from the model of Standard atmosphere or calculated using meteorological data from a radiosonde. However, the aerosol backscattering *a*(*r*) and extinction *<sup>a</sup>*(*r*) [or the aerosol lidar ratio *Sa*(*r*)], remain to be determined as two unknown variables from the values of one variable – the so-called range corrected signal *P*(*r*)*r*2, obtained from the lidar measurement. This is not possible without using additional information about at least one of the unknown variables. When choosing the reference range *r*0 near to the ground (and to the lidar), the aerosol backscattering *a*(*r*0) or extinction *<sup>a</sup>*(*r*0) can be measured independently. After that, we can integrate Eq.(6) and retrieve the atmospheric backscattering coefficient profile. Unfortunately, there exists a mathematical instability in the calculations following Eq.(6) in sense that small errors in the determination of *<sup>a</sup>*(*r*0) at the reference distance *r*<sup>0</sup>or in the measured range corrected signal *P*(*r*)*r*2, start to produce in few steps of integration procedure negative values for the denominator and, consequently, for *<sup>a</sup>*(*r*). To solve this problem, Klett (Klett, 1981) and Fernald (Fernald, 1984) proposed an inverse integration of Eq.(6), starting from the far end of the lidar sounding path. Applying this idea and introducing max max ( ) *a a <sup>r</sup>* and max max *m m* ( ) *r* , where *rmax* is the maximal distance, we can rewrite Eq.(6) as follows:

$$\begin{split} \beta\_{a}(r) &= -\beta\_{m}(r) \\ P(r)r^{2} &\exp\left\{-2\left[S\_{a}(r) - S\_{m}\right]\right\}\_{r}^{r\_{\text{max}}} \beta\_{m}(\rho) d\rho \Big\} \\ &+ \frac{P(r\_{\text{max}})r\_{\text{max}}^{2}}{\beta\_{a}^{\text{max}} + \beta\_{m}^{\text{max}}} + 2\Big[\int\_{r}^{r\_{\text{max}}} S\_{a}(\rho)P(\rho)\rho^{2} \exp\left\{-2\left[S\_{a}(\rho) - S\_{m}\right]\right\}\_{\rho}^{r\_{\text{max}}} \beta\_{m}(\rho^{\text{s}}) d\rho^{\text{s}}\right] d\rho \end{split} \tag{7}$$

The reference range *rmax* is chosen so that the aerosol backscatter coefficient is negligible compared to the molecular backscatter coefficient, i.e. *a*(*rmax*)<<*<sup>m</sup>*(*rmax*). Normally such atmospheric conditions are observed in the upper troposphere. Thus, we can attach the upper backscattering value to the value of the molecular backscattering and calculate the backscatter profile in backward direction by Eq.(7), using the measured range-corrected lidar signal. Determination of the reference range *rmax* is a problem for some atmospheric conditions as cloudy atmosphere, intensive background, etc. (see Sec.6). This algorithm is now widely applicable in practice, assuming also invariant value for the aerosol lidar ratio *Sa*=const along the laser beam path in the atmosphere. The exact value of this constant is determined depending on the laser wavelength and also on *a priori* assumptions about the type of the observed aerosols. The influence of the assumption for constant aerosol lidar ratio on the results of calculated profiles of atmospheric backscattering coefficient is studied

LIDAR Atmospheric Sensing by Metal Vapor and Nd:YAG Lasers 351

~ () *Gk kk <sup>q</sup> h t t dt*

where *q* is the electron charge. The SEP arrival times are expressed by *tk*=*tphe,k*+*tpd*+*tk*, where *tpd* is the mean time delay and *tk* are the centered time delay fluctuations or the jitter (transit

The parameters of *hk*(*t*-*tk*) dramatically affect the photoreceiving process. It becomes impossible to measure the photoelectron arrival times at the photon detector output. It is due mainly to limitations imposed by the processing electronics. The temporal structure of the output current *Iout*(*t*) provides successive extraction of the optical information from the flow of SEPs at the output in definite number of cases, strongly depending on the optical intensity. Four basic regimes (modes) of photodetection are typically recognized, requiring specific approaches to be applied in developing optical receivers and corresponding acquisition techniques. An approximate criterion for distinguishing these regimes is the

diodes of electronic circuits after the photon detector (discriminators, amplifiers, etc). The dead time prevents the registration of two successive SEPs, separated by time intervals,

photodection modes (ordered by increasing of optical intensity) are as follows: single quantum (SQ) mode; photon counting (PC) mode; overlapping (OV) mode; and analog

In the so-called SQ mode, the time intervals between adjacent SEPs are quite larger than the dead time and, thus, the probability for appearance of adjacent SEPs, separated by intervals

arrival times of SEPs. Unfortunately, photon rates in this mode are very low, resulting in intolerably long accumulation times in many applications including the lidar sensing.

The photon counting is realized by conversion of SEPs into corresponding normalized electric pulses of standard amplitude (NSEPs) (photocounts). This transformation just causes the dead time effects. The normalized pulses are then counted (within some defined sampling intervals *t*) by standard electronic circuits. To count the normalized SEPs (i.e., to count photons) they have to be resolved in time. It is evident that minimum time intervals

tolerable instantaneous photon count rate *R*NSEP (in number of NSEPs per second) can be

receivers in order to provide linear dependence of the counted NSEPs on the input optical intensity. The NSEPs are described by Poisson statistics as it is for the input photon flux. The dynamic range of PC receiver is very high. At higher intensities it is limited by the above

limitation here is the tolerable data accumulation (measurement) time. For these reasons the

*pd* of the photon detector.

*pd*]. Its appearance is due to the carrier restoration processes in transistors and

*dead*, causing nonlinearities in the detection process. The quoted above

*dead*, is minimized. This condition provides the measurement of individual

*dead* ~1. However, there are no limitations at low intensities. The only

*dead* are more preferable to be satisfied in photon counting

time spread) of the photon detector. The mean time width

*pd*~/

number of photoevents (or SEPs) per the photon counter dead time

between the adjacent SEPs have to be longer than the dead time

effects of photoevents, a part of input SEPs will not be counted, if (*R*NSEP)max

estimated approximately by the condition (*R*NSEP)max

receiving frequency bandwidth

*dead*

shorter than

mode (see Fig.2).

of the order of

why the values of (*R*NSEP)max

PC mode is widely used in modern lidar systems.

condition (*R*NSEP)max

, (10)

*pd* of the SEPs defines the

*dead*. Because of the time grouping

*dead*. The maximum

*dead* ~ 1. That is

*dead* [as a rule

and described in Böckman et al., 2004. The backscattering profiles are calculated from numerical models of lidar returns in two stages: once using constant *Sa*(*r*), and second – with variable profile of *Sa*(*r*). As shown, the errors in the calculated aerosol backscatter profiles due to the variance of the aerosol lidar ratio at different atmospheric conditions could reach 25-30%. The conclusion thrusts on the strong recommendation to use all available *a priori* information about the atmospheric conditions and the observed aerosols to apply an adequate variable aerosol lidar ratio in lidar determination of the aerosol backscatter profiles.

#### **2.3 Photon detection methods in lidar sensing**

Photon detection (using photomultipliers, photodiodes, etc.) is a key operation in optical devices, including lidars (Gagliardi & Karp, 1976). The understanding of photon detection processes is of essential importance for the development and performance of the lidar. This process is described by the probability for a photoelectron emission, which is proportional to the square of the envelope of the classical electromagnetic field (the optical field intensity) on the photosensitive surface. The transformation of optical field into a photoelectron flux is a quantum process. The output photoelectron current is a random temporal process, corresponding to the random photon absorption by independent quantum systems of the photocathode and to the photoelectron emission. The concept for the randomness of the photoelectron current is always valid for the stochastic or determined optical fields. The output photoelectron current *Iphe*(*t*) is described mathematically by a superposition of -pulses, each corresponding to a single process of photoelectron emission or

$$I\_{phe}(t) \sim \sum\_{k=1}^{N(0,t)} \delta(t - t\_{phe,k}) \, \prime \tag{8}$$

where *k*=1,…,*N*(0,*t*) are the successive photoelectron numbers, *N*(0,*t*) is the total number of photoelectrons and *tphe,k* are the so-called photoelectron arrival times. As seen, the information, carried by the optical field after the photodetection, is contained in the arrival times of photons (or photoelectrons). As the probability of photoelectron emission depends on the optical intensity, the increase of optical energy causes an increase of the number of photoelectrons per unit time and thus, decreasing the time intervals between adjacent photoelectrons. This is the so-called effect of photoelectron time-grouping, depending on the instant optical intensity. The optical field is transformed into a photoelectron flux of timedependent intensity. Measuring the arrival times *tphe,k* of all photoelectrons one could, in principle, extract the whole information carried by the optical field.

Different effects in photon detectors prevent the extraction of the entire information from the received optical radiation. The output current *Iout*(*t*) can be expressed now in the form:

$$I\_{out}(t) \sim \sum\_{k=1}^{N(0,t)} h\_k(t - t\_k) \, , \tag{9}$$

where *hk*(*t*-*tk*) are the output pulse functions of finite duration, depending on the photon detector parameters. They are usually called single electron pulses (SEPs) or photoevents. The SEPs are of fluctuating shapes, amplitudes, and arrival times *tk*. The electric charge *Gk* of an individual *k*-th SEP is a fluctuating variable, depending mainly on the processes of the secondary emission. It is given by

and described in Böckman et al., 2004. The backscattering profiles are calculated from numerical models of lidar returns in two stages: once using constant *Sa*(*r*), and second – with variable profile of *Sa*(*r*). As shown, the errors in the calculated aerosol backscatter profiles due to the variance of the aerosol lidar ratio at different atmospheric conditions could reach 25-30%. The conclusion thrusts on the strong recommendation to use all available *a priori* information about the atmospheric conditions and the observed aerosols to apply an adequate variable aerosol lidar ratio in lidar determination of the aerosol backscatter

Photon detection (using photomultipliers, photodiodes, etc.) is a key operation in optical devices, including lidars (Gagliardi & Karp, 1976). The understanding of photon detection processes is of essential importance for the development and performance of the lidar. This process is described by the probability for a photoelectron emission, which is proportional to the square of the envelope of the classical electromagnetic field (the optical field intensity) on the photosensitive surface. The transformation of optical field into a photoelectron flux is a quantum process. The output photoelectron current is a random temporal process, corresponding to the random photon absorption by independent quantum systems of the photocathode and to the photoelectron emission. The concept for the randomness of the photoelectron current is always valid for the stochastic or determined optical fields. The output photoelectron current *Iphe*(*t*) is described mathematically by a superposition of

> (0, ) , <sup>1</sup> ( )~ ( ) *N t phe phe k <sup>k</sup> I t tt*

where *k*=1,…,*N*(0,*t*) are the successive photoelectron numbers, *N*(0,*t*) is the total number of photoelectrons and *tphe,k* are the so-called photoelectron arrival times. As seen, the information, carried by the optical field after the photodetection, is contained in the arrival times of photons (or photoelectrons). As the probability of photoelectron emission depends on the optical intensity, the increase of optical energy causes an increase of the number of photoelectrons per unit time and thus, decreasing the time intervals between adjacent photoelectrons. This is the so-called effect of photoelectron time-grouping, depending on the instant optical intensity. The optical field is transformed into a photoelectron flux of timedependent intensity. Measuring the arrival times *tphe,k* of all photoelectrons one could, in

Different effects in photon detectors prevent the extraction of the entire information from the received optical radiation. The output current *Iout*(*t*) can be expressed now in the form:

> (0, ) <sup>1</sup> <sup>~</sup> *N t*

where *hk*(*t*-*tk*) are the output pulse functions of finite duration, depending on the photon detector parameters. They are usually called single electron pulses (SEPs) or photoevents. The SEPs are of fluctuating shapes, amplitudes, and arrival times *tk*. The electric charge *Gk* of an individual *k*-th SEP is a fluctuating variable, depending mainly on the processes of the

, (8)

*out k k <sup>k</sup> I t htt* , (9)


principle, extract the whole information carried by the optical field.

secondary emission. It is given by

profiles.

**2.3 Photon detection methods in lidar sensing** 

$$G\_k \sim q \int\_{-\infty}^{\infty} h\_k(t - t\_k) dt \,, \tag{10}$$

where *q* is the electron charge. The SEP arrival times are expressed by *tk*=*tphe,k*+*tpd*+*tk*, where *tpd* is the mean time delay and *tk* are the centered time delay fluctuations or the jitter (transit time spread) of the photon detector. The mean time width *pd* of the SEPs defines the receiving frequency bandwidth *pd*~/*pd* of the photon detector.

The parameters of *hk*(*t*-*tk*) dramatically affect the photoreceiving process. It becomes impossible to measure the photoelectron arrival times at the photon detector output. It is due mainly to limitations imposed by the processing electronics. The temporal structure of the output current *Iout*(*t*) provides successive extraction of the optical information from the flow of SEPs at the output in definite number of cases, strongly depending on the optical intensity. Four basic regimes (modes) of photodetection are typically recognized, requiring specific approaches to be applied in developing optical receivers and corresponding acquisition techniques. An approximate criterion for distinguishing these regimes is the number of photoevents (or SEPs) per the photon counter dead time *dead* [as a rule *deadpd*]. Its appearance is due to the carrier restoration processes in transistors and diodes of electronic circuits after the photon detector (discriminators, amplifiers, etc). The dead time prevents the registration of two successive SEPs, separated by time intervals, shorter than *dead*, causing nonlinearities in the detection process. The quoted above photodection modes (ordered by increasing of optical intensity) are as follows: single quantum (SQ) mode; photon counting (PC) mode; overlapping (OV) mode; and analog mode (see Fig.2).

In the so-called SQ mode, the time intervals between adjacent SEPs are quite larger than the dead time and, thus, the probability for appearance of adjacent SEPs, separated by intervals of the order of *dead*, is minimized. This condition provides the measurement of individual arrival times of SEPs. Unfortunately, photon rates in this mode are very low, resulting in intolerably long accumulation times in many applications including the lidar sensing.

The photon counting is realized by conversion of SEPs into corresponding normalized electric pulses of standard amplitude (NSEPs) (photocounts). This transformation just causes the dead time effects. The normalized pulses are then counted (within some defined sampling intervals *t*) by standard electronic circuits. To count the normalized SEPs (i.e., to count photons) they have to be resolved in time. It is evident that minimum time intervals between the adjacent SEPs have to be longer than the dead time *dead*. The maximum tolerable instantaneous photon count rate *R*NSEP (in number of NSEPs per second) can be estimated approximately by the condition (*R*NSEP)max*dead*. Because of the time grouping effects of photoevents, a part of input SEPs will not be counted, if (*R*NSEP)max*dead* ~ 1. That is why the values of (*R*NSEP)max*dead* are more preferable to be satisfied in photon counting receivers in order to provide linear dependence of the counted NSEPs on the input optical intensity. The NSEPs are described by Poisson statistics as it is for the input photon flux. The dynamic range of PC receiver is very high. At higher intensities it is limited by the above condition (*R*NSEP)max*dead* ~1. However, there are no limitations at low intensities. The only limitation here is the tolerable data accumulation (measurement) time. For these reasons the PC mode is widely used in modern lidar systems.

LIDAR Atmospheric Sensing by Metal Vapor and Nd:YAG Lasers 353

measurement times are normally higher, due to the lower return intensities. In practice, the combined use of both regimes causes some problems as the gluing of both lidar profiles. The PC mode in lidar sensing can also be realized by lasers of lower pulsed power but at higher pulse repetition rates, providing high enough mean output power. In this case the above

Assuming Poisson statistics (Sec.2.3) for the photon detector output signal fluctuations, the probability *WN*(*<sup>r</sup>*) of detecting *N(r)* photons (or SEPs) from a distance *r* in PC and analog

( ) 1

number of detected photons (SEPs) per sampling interval by the expression

the total error balance of lidar measurements. Unfortunately, as it is clear from the lidar equation (Sec.2.2), a multitude of variables contribute to the total estimated error. In fact it is difficult to find an analytical expression for the errors of the calculated backscatter profiles by a classical way, differentiating the lidar equation. In the practice a roundabout approach is applied. It consists in two-step calculation of the backscatter coefficient profiles: i) using the measured values of the range corrected signal *P*(*r*)*r*2; ii) adding some estimated

*E*(*r*), where

The requirements for successful lidar atmospheric sensing impose strong limitations on the laser parameters as the pulse width, pulsed and mean powers, repetition frequency, operational wavelengths, stability, etc. That is why the number of laser types applied in lidars is limited. The Nd:YAG lasers are widely used in the most of lidar systems (Measures, 1984; Weitkamp, 2005) providing simultaneous sensing in analog and photon counting modes at typically 4 to 6 wavelengths (using harmonic generation techniques) in the IR, visible and near UV ranges (including Raman channels). Lasers emitting a set of basic wavelengths of proper parameters, say approximately equal output powers, are also of great importance for multiwave lidar atmospheric sensing. The use of such lasers can simplify the

The MV lasers eligible for lidar probing (in the sense of above requirements) are mainly lasing on two active media, namely copper (Cu) and gold (Au) vapors. They offer unique output parameters (Astadjov et al., 1988; Kim, 1991; Stoilov et al., 2000) attractive for development of lidars in the mid-visible range, capable to probe simultaneously the troposphere and stratosphere. These lasers emit pulses with mean power of up to 2 kW at relatively high repetition frequencies, normally ranging from 2 KHz to 100 KHz, depending on the laser type. The pulsed energy is substantially low (~0.1 mJ at 5-10 ns pulse duration). The combination of low pulse energy, high mean power, high repetition frequency and multiwavelength performance of MV lasers are their key advantages for application in lidar

*E*(*r*)

*<sup>N</sup>*(*r*) of lidar signals can be added for estimation of lower error limit and

. The contribution of Poisson noises with variance <sup>2</sup>

profile. If no other useful information is available to estimate strictly

( ) ( ) ( ( )!) exp( ( ) ) *N r W R t Nr R r t Nr N <sup>N</sup>* . (11)

*<sup>N</sup> r* is determined from the mean

*<sup>N</sup> r* is essential in

*<sup>E</sup>*(*r*), at least the

*<sup>N</sup>*(*r*) is the estimated deviation

requirements to PC mode can be satisfied.

deviation to the measured values *P*(*r*)*r*2

opto-mechanical lidar design.

 <sup>2</sup> *Rrt r N N* 

Poisson variance

modes for a sampling interval *t* at a mean rate *RN* is given by :

For Poisson distributed lidar signals the noise variance <sup>2</sup>

the error propagation along the backscatter calculus chain.

**3. Metal vapor and Nd:YAG lasers: Basic parameters** 

Fig. 2. Regimes of photon detection as a function of optical intensity.

The overlapping mode is typically recognized as a non-operational signal gap, where the performance of optical receivers is ineffective. In OV mode the output flow of SEPs (before the normalization) could be represented by a stochastic process, due to the random summation (at each moment) of a low number of SEPs of fluctuating individual charges, shapes, duration, and arrival times. The output current is not proportional to the optical intensity. The appearance of OV mode is due mainly to the electronics, when the photon counts are not resolved any more (due to the higher photon rates) in order to be counted. At the same time, due to the large fluctuations of the output amplitudes, signals could not be correctly sampled by analog-to-digital converters (ADCs). In OV mode the input optical intensity is higher than that in PC mode and this is why the OV mode is attractive for development of methods for providing the linear performance. Some novel techniques are reported (Stoyanov, 1997; Stoyanov et al., 2000). The analysis of OV mode is out of the scope of this chapter as it is not used in lidar sensing.

The analog mode is a basic regime of optical receiving (together with PC mode), widely used in lidar sensing. Here the number of SEPs at the photon detector output typically exceeds 102-103. In this mode, the fluctuations of SEP parameters can be neglected because of the averaging over a large number of SEPs at each moment. The output current is an analog signal of amplitude proportional to the input intensity and can be directly sampled by ADCs. The noises in the output current typically also display Poisson statistics, but because of the larger number of photons within each sampling interval it is transformed into Gaussian one.

The analog and PC regimes of optical detection impose special requirements to the lasers, used in lidars. Say, the analog mode is typically used with high pulsed power, low repetition rate lasers (as Nd:YAG lasers). The Nd:YAG lidars are also used in PC mode for large distances for which the number of received photons dramatically decreases. Here the

Fig. 2. Regimes of photon detection as a function of optical intensity.

~0.1-1

Optical intensity scale in number of events (SEPs) per dead time

~102-103

of this chapter as it is not used in lidar sensing.

Gaussian one.

The overlapping mode is typically recognized as a non-operational signal gap, where the performance of optical receivers is ineffective. In OV mode the output flow of SEPs (before the normalization) could be represented by a stochastic process, due to the random summation (at each moment) of a low number of SEPs of fluctuating individual charges, shapes, duration, and arrival times. The output current is not proportional to the optical intensity. The appearance of OV mode is due mainly to the electronics, when the photon counts are not resolved any more (due to the higher photon rates) in order to be counted. At the same time, due to the large fluctuations of the output amplitudes, signals could not be correctly sampled by analog-to-digital converters (ADCs). In OV mode the input optical intensity is higher than that in PC mode and this is why the OV mode is attractive for development of methods for providing the linear performance. Some novel techniques are reported (Stoyanov, 1997; Stoyanov et al., 2000). The analysis of OV mode is out of the scope

**SINGLE QUANTUM MODE** 

**OVERLAPPING of SEPs - signal gap** 

**PHOTON COUNTING MODE** 

good lidar performance

**ANALOG MODE** 

good lidar performance

The analog mode is a basic regime of optical receiving (together with PC mode), widely used in lidar sensing. Here the number of SEPs at the photon detector output typically exceeds 102-103. In this mode, the fluctuations of SEP parameters can be neglected because of the averaging over a large number of SEPs at each moment. The output current is an analog signal of amplitude proportional to the input intensity and can be directly sampled by ADCs. The noises in the output current typically also display Poisson statistics, but because of the larger number of photons within each sampling interval it is transformed into

The analog and PC regimes of optical detection impose special requirements to the lasers, used in lidars. Say, the analog mode is typically used with high pulsed power, low repetition rate lasers (as Nd:YAG lasers). The Nd:YAG lidars are also used in PC mode for large distances for which the number of received photons dramatically decreases. Here the measurement times are normally higher, due to the lower return intensities. In practice, the combined use of both regimes causes some problems as the gluing of both lidar profiles. The PC mode in lidar sensing can also be realized by lasers of lower pulsed power but at higher pulse repetition rates, providing high enough mean output power. In this case the above requirements to PC mode can be satisfied.

Assuming Poisson statistics (Sec.2.3) for the photon detector output signal fluctuations, the probability *WN*(*<sup>r</sup>*) of detecting *N(r)* photons (or SEPs) from a distance *r* in PC and analog modes for a sampling interval *t* at a mean rate *RN* is given by :

$$\mathcal{W}\_{\mathcal{N}(r)} = \left(\mathcal{R}\_{\mathcal{N}} \Delta t\right)^{\mathcal{N}(r)} \left(\mathcal{N}(r)!\right)^{-1} \exp\left(-\mathcal{R}\_{\mathcal{N}}(r) \Delta t\right). \tag{11}$$

For Poisson distributed lidar signals the noise variance <sup>2</sup> *<sup>N</sup> r* is determined from the mean number of detected photons (SEPs) per sampling interval by the expression <sup>2</sup> *Rrt r N N* . The contribution of Poisson noises with variance <sup>2</sup> *<sup>N</sup> r* is essential in the total error balance of lidar measurements. Unfortunately, as it is clear from the lidar equation (Sec.2.2), a multitude of variables contribute to the total estimated error. In fact it is difficult to find an analytical expression for the errors of the calculated backscatter profiles by a classical way, differentiating the lidar equation. In the practice a roundabout approach is applied. It consists in two-step calculation of the backscatter coefficient profiles: i) using the measured values of the range corrected signal *P*(*r*)*r*2; ii) adding some estimated deviation to the measured values *P*(*r*)*r*2 *E*(*r*), where *E*(*r*)*<sup>N</sup>*(*r*) is the estimated deviation profile. If no other useful information is available to estimate strictly *<sup>E</sup>*(*r*), at least the Poisson variance *<sup>N</sup>*(*r*) of lidar signals can be added for estimation of lower error limit and the error propagation along the backscatter calculus chain.
