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Lidar performance prediction by dimensionless SNR-parameterization
Ravil R. Agishev *a,b, Barry Gross b, Adolfo Comeron c
aKazan State Technical University, 10, K.Marx St., Kazan, Tatarstan 420111, Russia
b City College of the City University of New York, 140 St. & Convent Ave., New York, NY 10031, USA
c Polytechnic University of Catalonia, 1-3, Jordi Girona, Barcelona 08034, Spain
ABSTRACT
A general methodology for evaluating the capabilities of a general lidar system encompassing both backscatter (elastic and
Raman lidar) and topographic targets is presented. By introducing a well defined atmospheric reference medium and by
individually examining and decomposing the contribution of lidar system parameters including lidar transmitter power, fields
of view, receiver noise, atmospheric conditions, and sky background on the signal-to-noise-ratio (SNR), we obtain a simple
dimensionless parameterization of the lidar system. Using this parameterization, numerical simulations are carried out to
determine achievable lidar performance including operation range, minimum detectable gas concentration etc.
Key words: lidar, elastic lidar, Raman lidar, lidar performance prediction, signal-to-noise parametrization.
1. INTRODUCTION
Lidar designs vary widely1-8 depending on the specific application, available hardware components, and experience of
the developers. While simple qualitative design issues such as the use of a more powerful laser transmitter, a larger
aperture receiving telescope, and/or more sensitive photodetectors will obviously achieve a greater operation range,
better retrieval accuracy etc., cost constraints often limit such designs. To conduct quantitative tradeoff studies, a
significant number of instrumental parameters and external environmental factors must be taken into account and it is
often not clear from this representation how each system and/or environmental parameter can quantitatively affect the
ultimate performance.
Analysis of lidar performance is traditionally based on examination of the signal-to-noise ratio (SNR) at the
photodetector output1,2,4-7,9-12. While the comprehensive nature of the SNR criterion makes it a very useful tool for
assessing a given lidar system10,11, it is also a weak point12,13 because it obscures the impact of the different components.
For example, an increase or reduction of SNR can be caused not only by the scattering efficiency of the target under
study but also by changes in "weather" conditions for signal propagation1,6,7,11, by change of background conditions12,13,
or by other factors. If the influence of the different factors cannot be evaluated individually, it is difficult to evaluate
subsystem or overall system measurement capabilities13.
From these considerations, it is clear that a universal parameterization over many lidar technologies can be very useful
as a design and assessment tool. In the absence of such an approach, system developers use rather complex analytical
expressions and empirical formulas, which are often applicable only for a very narrow range of parameters and specific
experimental setups1,6,15.
The purpose of the present work is to develop criteria that can be widely used to evaluate a broad range of lidar system
capabilities for a variety of lidar remote sensing applications, and based on these criteria develop a methodology for
selection of appropriate lidar system parameters for a specific application. To do this, it is necessary to choose a
reference atmospheric state that will serve as a basis for comparison and evolve an appropriate parameterization scheme
for expressing lidar system parameters in a generalized manner that can be applied to differing systems.
_____________
* ravil_agishev@mail.ru, tel/fax.: +7-843-231-0244
Remote Sensing of Clouds and the Atmosphere X, edited by Klaus Schäfer, Adolfo Comerón,
James R. Slusser, Richard H. Picard, Michel R. Carleer, Nicolaos Sifakis,
Proc. of SPIE Vol. 5979, 59791G, (2005) · 0277-786X/05/$15 · doi: 10.1117/12.627569
Proc. of SPIE Vol. 5979 59791G-1
2. PARAMETRIZATION OF THE LIDAR SIGNAL-TO-NOISE RATIO
2.1. Molecular atmosphere as measurement reference
We propose that the most useful reference atmosphere is the standard molecular atmosphere whose parameters are well
characterized. In particular, at 0550
ref nm
λλ
≡= , the extinction coefficient of the molecular atmosphere under standard
conditions and at sea level is α0 =0.0116 km-1 and the backscatter-to-extinction ratio of the molecular
atmosphere 3/(8 )
m
b
π
=.
Using this reference has several advantages:
- Comparison of lidar returns under a common reference in the absence of atmospheric variability provides the most
direct comparison of lidar capability.
- Comparison of lidar returns from an arbitrary atmospheric target normalized to the reference molecular atmosphere
gives the most direct estimate of the measurement sensitivity.
- Comparison of the reference signal to those signals generated under different atmospheric states (high aerosol loading
etc) along the lidar path provides a direct measure of the effects of atmospheric transmission on the measurement
capabilities.
As a reference signal we choose an echo-signal Ps0 obtained from an elastic lidar received from a reference range R0 (this
range can be thought of as a natural length scale which may or may not have any particular significance to the system in
question) at λ0=550 nm under standard molecular atmosphere conditions. In this case,
Ps0(λ0,R0) = ½ c τp βπ0(λ0,α0) Ar R0
-2 P0(λ0) ξ(λ0) T0
2(λ0,R0) (1)
where c is the light velocity, τp is the laser pulse duration, βπ0 is the backscattering coefficient for molecular atmosphere
(βπ0 = (3/8π)⋅α0), Ar is the receiver effective area, R0 is the reference range, P0 is the transmitted pulse power, ξ is the
optical efficiency of lidar, and the path transmittance T0(λ0,R0) = exp[-α0(λ0) R0].
2.2. Decomposition of lidar signal-to-noise ratio
Since the total SNR is not useful in comparing different lidar classes, we focus on decomposing the signal-to-noise ratio
into several factors, each factor being connected to a particular aspect of the lidar system and/or the measurement
medium. To begin, the power of the echo-signal received from a range R has the following form:
PsX(λL,λX,R) = KX(λL,λX,R) P0(λL) ξ(λL,λX) Tfw(λL,R) Tbw(λX,R) (2)
where the subscript symbol X defines the lidar type:
1. X=BS for backscattering lidar
2. X=Ram for Raman lidar
3. X=Top for lidar with a topographic target.
Here PsX is the echo-signal power received at wavelength λX for range R, ξ(λL,λX) is the overall transmittance of
transmit and receive optics, Tfw is the atmospheric transmission in the forward direction at the laser wavelength λL, and
Tbw is the atmospheric transmission of the atmosphere in the backward direction at the echo-signal wavelength λX (only
for Raman systems is λL ≠ λX). In turn
KX (λL,λX,R) = ½ c τp Ar(λX)βπ(λL,λX,R)R-2
with βπ(λL,λX,R) the backscatter coefficient at R for incident wavelength λL and backscattered wavelength λX .
To develop the parameterization we define the input signal-to-noise ratio ΨX as the ratio of the received signal power to
a prescribed minimum or threshold power in the form:
Proc. of SPIE Vol. 5979 59791G-2
1
0
00
sX sX s
X
tst
PPP
U
PPP
−
Ψ≡ = (3)
where Pt is the photodetector threshold power, which is the power required to achieve a minimum prescribed signal-to-
noise ratio at the lidar photoreceiver output, Pt0 is the threshold power in the absence of sky background and U is the
background factor describing the increase of the photodetector threshold due to the sky background. The photodetector
threshold power is given as the product
Pt = Pt0 U (4)
A description of the background factor U is given in section 3.4.
2.3. Echo-signal power normalized to reference signal for different lidars
To evaluate Eq. (3), we need to determine the effective ratio KEfX of an echo-signal of any type of lidar PsX to the reference
echo-signal Ps0. It is easy to see from eqn. (2) that, in general,:
KEfX = PsX(λL,λX,R) / Ps0(λ,λ0,R0) = (KX / KBS0) [Tfw(λL,R) Tbw(λX,R) / T0
2(λ0,R0)] (5)
Taking into account Eqns. (2) and (5), the specific values of the PsX/Ps0 ratios for different lidars are as follows:
X=BS molecular: KEfBSm = [αm(λL)/α0(λ0)] [T(λL,R)/T0(λ0,R0)]2r-2
X=BS aerosol: KEfBSa = {[βπa(λL)+βπm(λL)] / βπ0(λ0)} [T(λL,R)/ T0(λ0,R0)] 2 r-2 6b)
(6)
X=Raman: KEfRam = [βπR(λR) / βπ0(λ0)] [Tfw(λL,R)Tbw(λR,R)/T0
2 (λ0,R0)] r-2 (6c)
X=Topographic: KEfTop =(ρaAr/πR2) [T(λL,R)/T0(λ0,R0)]2 / ½cτpβπ0ArR0
-2 = [(2ρa/πcτp)/βπ0(λ0)] [T(λL,R)/T0(λ0,R0)]2r-2
( d)
where αm and βπm indicate molecular extinction and backscatter coefficient respectively, βπa stands for aerosol
backscatter coefficient, r = R/R0 is the normalized lidar range and ρa is the backscatter albedo of the topographic target.
From analysis of the above expressions, each case can be factored in the form
PsX / Ps0 = Qx W2 r-2
where the explicit representations of Qx and W appear in sections (3.2) and (3.3).
3. LIDAR PARAMETER INTERPRETATION
Combining the explicit signal ratios obtained in equation (6) with the general decomposition of
X
Ψ in equation (3)
shows that the signal to noise ratio can be decomposed into the following dimensionless parameterization
ψX = V Qx W2 U-1 r-2, (7)
Thus, the SNR at the lidar photodetector is given as a product of five independent dimensionless parameters, each of which
follows from a different source.
3.1 V-parameter
In Eq. (7), V is defined as the ratio of the echo-signal power Ps0 received from the reference range R0 for the reference
atmosphere to the threshold power Pt0 in the absence of background noise:
Proc. of SPIE Vol. 5979 59791G-3
V = Ps0/Pt0 (8)
Pt0 can be expressed as14
2
2
022
4
12 1 1 n
t out q
out q
P
PP P
ρρ
⎛⎞
⎜⎟
=++
⎜⎟
⎝⎠
, with out
ρ
the prescribed (agreed on) output signal-to-noise
ratio, n
P the power of the internal noise of the photoreceiver referred to the photodetector input, and q
P the power
characterizing the quantum limit of the photoreceiver sensitivity. In turn n
PNEPf
=
∆ and 2/
qX
PhcfF
η
λ
=∆ , with
NEP the photoreceiver noise equivalent power not depending on signal and background power, f∆ the photoreceiver
electrical bandwidth, h Planck’s constant,
F
the photodetector excess-noise ratio, and
η
the photodetector quantum
efficiency.
The V-parameter can be interpreted as a universal parameter describing the energetic potential of the lidar instrument:
()
0
0000
2
0
13
exp 2 /
28
p
rt
Pc
VRAP
R
τ
ααξ
π
⎛⎞
=−
⎜⎟
⎝⎠ (9)
As it is seen from Eq. (9), to calculate the V-parameter for existing or proposed lidar instruments, it is only necessary to
know the receiving and transmitting subsystems parameters, and the optical parameters of a standard molecular
atmosphere.
According to Eq. (9), due to wide variations of lidar instrument parameters for different lidar types (P0, τp, Ar, ξ, NEP, ∆f),
the value of V-parameter can change by several orders of magnitude.
It is easy to see that large values of V lead to better operation performance of the lidar, but such values correspond to more
expensive electro-optical components.
3.2. QX-parameter
While the V parameter probes the effect of transmitter and receiver operation on a reference atmosphere, backscatter
magnitudes are included in the QX-parameter which simply describes the backscatter efficiency of an arbitrary species to
the molecular reference. For different types of lidar, the QX-parameter can be written as follows:
for a molecular backscattering lidar: 0
000
() ()
(, ) () ()
mm
BSm
m
Q
π
π
β
λαλ
λλ
β
λαλ
==
for aerosol backscattering lidar 0
000
() () () () ()
(, ) () ()
amaamm
BS
mm
bb
Qb
ππ
π
β
λβλ λαλ αλ
λλ βλ αλ
++
==
for Raman lidar 0
00 00
(, )/ (, )/
()
(,) () ()/ ()
gRLR gRLR
RR
Ram R
mmm m
Nd d Nd d
QNd d b
π
π
σ
λλ σ λλ
βλ
λλ βλ σλ αλ
Ω
Ω
== =
Ω
for lidar with a topographic target:
[
]
000
(, ) 2 /[ ()] / ()
Top a p m a m
Qc R
ππ
λ
λρπτβλρπβλ
==∆
where a
α
indicates extinction coefficient, /
aaa
b
π
β
α
=
, /3/(8)
mmm
b
π
β
απ
=
= are the lidar ratios for aerosol and
molecular atmosphere respectively,
g
N is the molecular concentration of the species producing the Raman backscatter,
(, )/
RLR
dd
σ
λλ
Ω is the differential Raman backscatter cross-section of the species molecule, m
N is the molecular
concentration of the reference atmosphere, 0
()/
m
dd
σ
λ
Ω
is the effective elastic differential backscatter cross-section of the
“average” molecule in the reference atmosphere, and ∆R = cτp/2 is the potentially achievable range resolution.
Sample calculations results of the values of QX for different types of lidars and for different intervening atmospheres for
a range of Qx-parameter magnitudes are given in Table 1.
Proc. of SPIE Vol. 5979 59791G-4
Elastic lidar Raman lidar
LIDAR TYPE Topographic
lidar Aerosol atmosphere Molecular atmosphere N2 H
20
Range of Qx-parameter 102…104 100...102 10-1...101 10-5...10-3 10-7...10-5
Table 1. Typical ranges of QX-parameter
3.3. W-parameter
The third factor in Eq. (7) is a normalized atmospheric component W2 that is determined by the transparency ratio of the
atmosphere state and the standard molecular atmosphere. The normalized transparency along the sounding path is defined
differently for elastic and Raman lidars:
00 0
00 0 0
(, ) (, )
(,) exp 1
(, )
RaLmL
L
BS
L
RR
TR dR
WR
TR R
αλα λ
λα
λα
⎛⎞
′′
⎡
⎤
′
+
==− −
⎜⎟
⎢
⎥
⎜⎟
⎣
⎦
⎝⎠
∫ (10)
() ()
00 0
00 0 00
(,) (,) ,(,)(,),
1
exp 1
(, ) 2
R
fW L bW R aLmLaRmR
Ram
TRTR RRR R
dR
WR
TR R
λλ αλαλαλαλ
α
λα
⎧⎫
′′′ ′
+++
⎡
⎤
′
⎪⎪
==− −
⎨⎬
⎢
⎥
⎪⎪
⎣
⎦
⎩⎭
∫ (11)
For homogeneous atmospheres, the W-parameter can be expressed as:
00 0
00
exp 1 exp 1
am am
BS
WRr r
αα αα
ατ
αα
⎡
⎤⎡ ⎤
⎛⎞⎛⎞
++
=− −=− −
⎢
⎥⎢ ⎥
⎜⎟⎜⎟
⎢
⎥⎢ ⎥
⎝⎠⎝⎠
⎣
⎦⎣ ⎦
(12)
with 000
R
τ
α
=.
W is a direct measure of the degradation of the lidar performance due to the attenuation along the beam path which
increases both as a function of the extinction coefficient of the aerosol and the range parameter r.
When sounding scattering media, the W-parameter characterizes the optical “weather” along the path. For absorbing
media, the W-parameter includes the absorber concentrations of the trace constituents under investigation that were
considered in Ref. 14.
3.4. U-parameter
Frequently for aerosol lidars with moderate pulse energies, or in Raman lidar applications, the most important factor
that limits the detection of weak signals in daytime is the background sky radiation. The fourth factor of Eq. (7)
describes the influence of the background clutter on the sensitivity threshold of the lidar photodetector.
The U-parameter is defined as the ratio of the photodetector threshold powers Pt and Pt0 defined in the presence and
absence of the background noise respectively:
2
22
02
22
4
11
/
4
11
bn
q
out q
tt
n
out q
PP
PP
UPP
P
P
ρ
ρ
⎛⎞
++ +
⎜⎟
⎜⎟
⎝⎠
≡=
++
(13)
The U-parameter is the excess noise factor quantifying the influence of the background noise.
From fig. 1, which illustrates the background factor (U) behavior, the smaller the internal noise of the photodetector, the
greater the influence of the external background. When background power increases, the threshold power increases
resulting in a decreased operation range, increased minimum detectable concentration, etc.
In cases where Pb≈Pq>>Pn, the U parameter becomes a universal function of background to shot noise
Proc. of SPIE Vol. 5979 59791G-5
0.01 0.1 IID 100 1000
b1 Pq
Fig.1. Illustration of the photodetector threshold sensitivity worsened by background clutter.
3.5. r-parameter
Finally, the fifth term in Eq. (7) is the normalized range-factor r = R/R0, that compares the current range R to the
reference range R0. This parameter should be interpreted only as a scale parameter which must be agreed on when
intercomparing different lidars and should be fixed to a universal value for intercomparisons.
4. APPLICATION OF THE GENERALIZED SYSTEM PARAMETERS
FOR ESTIMATIONS OF POTENTIAL CAPABILITIES OF LIDARS
The determination of lidar criteria for quantitative atmospheric sounding is based on the condition that the output SNR
exceeds a minimum value, for which a minimum threshold received echo-signal is requires. In Sects. 2 and 3, we used
the molecular atmosphere as a reference medium and decomposed the resultant SNR into a five-parameter expression.
In this section, the parameterization formalism will be applied to estimate lidar operation range independent of the
particular design principles used. This formalism can then be used to predict the potential performance of lidar for
remote sensing of different atmospheric objects using different lidar technologies under very different conditions of
optical "weather" and sky background.
4.1. Maximum operation range of lidar for horizontal sounding
Let us first consider horizontal sounding in the lower layers of the atmosphere. From Eq. (7), it is easy to determine the
normalized operation range assuming ψ = 1. The maximum operating range reduces to the solution of a nonlinear
equation:
()
max
1
maxmax )( rfUrWQVr x== − (14)
that can be solved. For the simplest case of sounding in a molecular atmosphere, where QX=1 and the W-parameter is
determined from Eqs. (10) and (15), this becomes much simpler:
1
max 0 0 max
0
exp 2 1rV Rr U
α
αα
−
⎡⎤
⎛⎞
=− −
⎢⎥
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(15)
To give the physical interpretation of the V-parameter, let’s assume α=α0 and Rmax>>R0. Then if the background
radiation is low (U = 1) and atmospheric optical densities α0R<<1, the maximum operation range reduces to
Vr =
max (16)
From here, the physical interpretation of the system parameter V becomes clear: its numerical value defines a square of
a normalized operation range of lidar for horizontal sounding at standard molecular atmosphere conditions (with
α0R<<1) in the absence of background noise.
Proc. of SPIE Vol. 5979 59791G-6
=
11111
- Q
=
=
=
= —
o P P — =
— — — = =
=
= —
o P P — =
— — — = =
=
=
=
=
4.2. Operational range of a real-world horizontal lidar
For horizontal sounding, allowing for a particularly easy representation of the intervening weather, the scattering
efficiency of a particular target (aerosol particulates, molecular, etc.) at range r is totally specified by its Qx-parameter
while the intervening medium (weather) is quantified by the W parameter. The dependence of the maximum operation
range rmax on the Qx-parameter for various optical conditions of the atmosphere obtained by numerical solution of Eq.
(14) are shown on Fig. 2. The range of the Qx-parameter used in our calculations corresponds to the reflected echo-
signals from a topographical target, backscatter from dense haze, backscatter from weak haze, molecular scattering, and
finally Raman scattering (Q-branch of vibrational-rotational spectrum of molecular nitrogen at concentration of 78%
and Q-branch of vibrational-rotational spectrum of water vapor at concentrations of 1 % and 1 ppm (Qx=104, 102, 101,
100, 10-4, 10-6, 10-10, accordingly). If the target is an extended body such as haze, it should be emphasized that the haze
below the range r is contained in the W parameter.
Fig. 2. Maximum operation range of lidar as a function of QX-parameter for the V-parameter values V=104 (left) and 107 (right) in absence of
background clutter. R0=1 km. Typical ranges of QX for different types of scattering are shown.
Curves of the maximum operation range versus optical weather conditions for different QX-parameters are illustrated in Fig.3.
Using the curves in Fig. 2 and Fig. 3, it is possible to estimate the operating range of lidar over many different target
and weather scenarios.
Fig. 3. Maximum operation range of lidar versus optical weather conditions
for various values of the Qx-parameter in the absence of background clutter. R0=1 km.
Proc. of SPIE Vol. 5979 59791G-7
= —
o P — =
— — — = =
= .
D -
' /= =
= .= — =
: kIIiiIIRI
= —
o P p — =
— — — P1 = =
= . ... II
Vfl AD
-%—LL--- —-N --
= II
-\---- -3vW -
-
\ \p[___
II —- L -
- _\______ —
i: \ Un
Dr--.i %-- = --
0
0 ___ III
In the above calculations, background noise was ignored but it is clear that increased background noise will degrade
lidar performance and considerably decrease the operation range of any lidar.
Since the case of most interest in assessing lidar performance is to consider the highest background noise and a fixed
data processing (shot-averaging) scheme, it is often more useful to incorporate the background noise and signal
processing into the equivalent V-parameter according.
1/2 1
equ
VVNU
−
=
with N the number of accumulated lidar returns.
In this reduced representation, the dependence of the operating range resulting from the equivalent system parameter
Vequ=VN1/2U-1 are shown in Fig. 4. Note that the influence of the background factor is to reduce the V-parameter, while
averaging of echo-signals will increase the V parameter.
Fig. 4. Operation range vs. equivalent V-parameter for different values of Qx-parameter
at (αa+αm)/α0 =10 (a) and 100 (b). R0=1 km.
The results of calculations presented in Fig. 4 allow quantitative estimation of the influence of background and signal
averaging trade-offs. Note that the equivalent parameter Vequ can be used directly instead of V-parameter when
analyzing the achievable operation range rmax. For example, using Fig. 4 it is possible to determine the number of
averaged shots necessary to achieve the desired operational range.
5. ESTIMATION OF MINIMUM DETECTABLE VALUE OF QX-PARAMETER
AND MINIMUM DETECTABLE GAS CONCENTRATION
The target backscatter efficiency is directly related to the value of QX, so the determination of the minimum value of QX
for a given range r determines the minimum detectable target. To determine the lower limit of lidar sensitivity, we
equate the input signal-to-noise ratio in Eq. (7) to unity which results in:
V QX W2
U-1 r-2 = QXnorm W2r-2 =1
where for generality, a normalized QXnorm ≡ QXV/U is used. The dependence of the normalized parameter QXnorm as a
function of the operation range for different optical weather conditions are shown in Fig.5. From these curves, for given
or estimated values of V- and U-parameters, we can determine the minimum measurable value of QX.
Proc. of SPIE Vol. 5979 59791G-8
12 ______________________________ _____________
10
1010
QxV 100
U 106
IO
IOU
0.010.1 rID IOU
in-in4in3inn
Qin
XmIn I
0.1
0.01in3in4in5in_6in-,in3in3in_In
,rel 0.1
INgasfin0.01
in3
in4
in—S
in_6
in—,
V7 H
,iO3,/iO5 /1b71o9
V/..Y
'-7/Vt7/____
V,, . .
r
0.1 I10 100 0.1 10 100
Fig. 5. Minimum detectable value of the normalized parameter QXnorm = QXV/U
as a function of operation range for different optical weather conditions. R0=1 km.
Given the relevant backscatter cross-section of the target and the molecular reference, the lower limit of Qx allows us to
calculate the minimum retrievable volume concentration as:
min
min min
0
()/
(, )/
gas
rel m
gas Ram
mRamLR
Ndd
NQ
Nd d
σλ
σλλ
Ω
≡=
Ω
Illustrations of the minimum retrievable values of QXmin and Nrel
gasmin versus V and r parameters are shown in Fig. 6
assuming the gas under measurement is water vapor and that the Raman-backscattered radiation corresponds to the Q-
branch of its vibrational-rotational spectrum under a 355 nm incident wavelength ( 354.7
Lnm
λ
=, 407.5
Rnm
λ
=
,
30 2
(, )/ 6.210
Ram L R
dd cm
σλλ
−
Ω= × ). These curves can be used for the determination of the minimum necessary value of
V-parameter for a given range r or for the determination of maximum operating range to detect the desired species
concentration for a given V (or Vequ) parameter.
Fig. 6. Minimum retrievable value of parameter QX and minimum detectable gas concentration Nrel
gasmin as functions of operation
range for different values of V-parameter. Gas under measurement is water vapor. Raman cross section corresponds to Q-branch of
vibrational-rotational spectrum under 355 nm wavelength excitation. Optical weather condition is set at (αa+αm)/α0 =10. R0=1 km.
6. CONCLUSIONS
In this paper, a general method for the validation and performance comparison of various lidar systems is proposed. The
method is based on introducing a universal atmospheric reference medium and a decomposition of the total SNR into
Proc. of SPIE Vol. 5979 59791G-9
five dimensionless parameters representing the transmitter and receiver conditions, background noise, target efficiency,
atmospheric operation conditions and a scale length.
The main advantage of this approach is that it provides generalized, uniform and objective criteria for the evaluation of
a broad range of lidar types and systems (aerosol, Raman, DIAL), operating on different targets (backscatter or
topographic) and can be used within the lidar community to compare different instruments.
ACKNOWLEDGEMENTS
The authors acknowledge partial support of this work by grants from NOAA # NA17AE1625 and NASA # NCC-1-03009.
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