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Optics and Lasers in Engineering 44 (2006) 779– 796
Simple approach to predict APD/PMT lidar
detector performance under sky background
using dimensionless parametrization
Ravil Agishev
a,b,
, Barry Gross
b
, Fred Moshary
b
,
Alexander Gilerson
b
, Samir Ahmed
b
a
Kazan State Technical University, 10, K.Marx Street, Kazan, Tatarstan 420111, Russian Federation
b
NOAA-CREST Center, City College of the City University of New York, Convent Avenue & 138th Street,
New York, NY 10031, USA
Received 24 April 2005; received in revised form 20 July 2005; accepted 27 July 2005
Available online 26 September 2005
Abstract
In this paper, we developed a simple approach to predict the APD/PMT (avalanche
photodiode/photomultiplier) lidar detector performance in the presence of residual skylight
background. By normalizing all relevant photodetector noise sources to the quantum noise, we
obtain quantitative expressions for the degradation of the signal-to-noise ratio (SNR), the
increasing threshold sensitivity of and decreasing lidar operation range. To apply the
formalism to any lidar photodetectors operating in the ultra violet, visible and near-infrared
spectral regions and to perform a comparative analysis of PMT and APD capabilities as the
best photodetectors for ultra-violet (UV), visible (Vis) and near infra-red (NIR) lidar, we
utilize a set of spectral characteristics that are built from an envelope of individual PMT and
APD component responses. On this basis, the general analysis of system performance under
intense background conditions is developed, and practical recommendations on detector use
for each spectral region are given. The dimensionless formalism and the generalized detector
ARTICLE IN PRESS
0143-8166/$ - see front matter r2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.optlaseng.2005.07.010
Corresponding author. Kazan State Technical University, 10 K. Marx Street, Kazan, Tatarstan
420111, Russian Federation. Tel./fax: +7 843 2 310 044.
E-mail address: ravil_agishev@mail.ru (R. Agishev).
spectral models used allows our analysis to be applied to nearly any lidar receiver operating
over very different signal/background situations.
r2005 Elsevier Ltd. All rights reserved.
Keywords: Laser remote sensing; Lidar; Photodetector; PMT; APD; Sky background radiation;
Dimensionless parametrization
1. Introduction
Remote sensing technology using electro-optic methods as instruments of
environmental monitoring has undergone intense development. In particular, lidar
technology which uses active optical pulses to explore the distribution of aerosols
and gases has been extremely useful [1–4]. Since most lidars operate at wavelengths
within the spectral range of the solar spectrum, lidar performances are often
influenced by strong daylight background illumination. Therefore, high precision
measurements of weak lidar echo-signals (e.g. Raman lidar) can be very difficult to
obtain especially in the presence of sky background light [2,4–8].
The sky background reduces the precision of lidar measurements and limits the
usable operating range, thereby reducing the capabilities of lidar for the remote
sensing of the atmosphere. Further, under intense background conditions,
traditional methods of spectral, spatial and time selection of signals may be
insufficient to obtain the desired SNR [2,5–11] and may even saturate the detector.
The conventional approach to analyze the relation between lidar echo-signals,
external backgrounds and internal noise has been actively discussed in the literature
[1–16] and is based on the use of rigorous and detailed models of photodetectors
[5,9,12–16]. This requires taking into account a large number of specific component
parameters for different lidar photodetectors.
To illustrate this, the detailed description of the signal-to-noise ratio (SNR) can be
written as follows [15]:
SNR ¼r¼Is
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2qDf½ðIsþIbþIdÞFþILþð4kTDfF A=RLM2Þþð¯
I2
A=M2Þ
q,
(1)
where I
s
,I
b
and I
d
are the echo-signal, background, and dark currents of the
photodetector for internal gain coefficient M¼1, qis the charge of electron, Dfis
the receiver transmission band, Fis the coefficient of noise magnification during
internal amplification (i.e. an excess noise factor), I
L
is the surface leakage current,
2qDf½ðIsþIbþIdÞFþILis the mean-square value of a shot-noise current, kis the
Boltzmann’s constant, Tis the effective noise temperature, F
A
is the amplifier noise
coefficient, R
L
is the resistance equivalent to output resistance of photodetector,
loading resistor and subsequent amplifier, IT¼2kT =RLqF is the thermal noise
current referred to the input, ¯
IAis the amplifier noise current.
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R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796780
In turn, the signal current I
s
is equal to ðIs¼ÞZqlPs=hc, where Zis the quantum
efficiency of the photodetector, his the Planck’s constant, lis the wavelength, cis the
light velocity, P
s
is the received lidar signal power, that, in the single scattering
approximation, can be obtained from the lidar equation as follows:
Psðl;RÞ¼A0P0T2
atmðl;RÞR2,P
0
is the transmitted pulse power, A
0
is the
instrumental constant, T
atm
is the atmospheric transmission coefficient, Ris the
current range.
Finally, the background current is obtained from the expression Ib¼ZqlPb=hc.
The background radiation power, Pb, can be written as [5,8] Pb¼BlArODlx0, where
Blis the spectral radiance of the zone of the sky falling in the receiver filed of view,
A
r
the effective area of the optical receiving system, Ois the field-of-view solid angle,
Dlis the spectral width of the optical bandpass filter in the receiving system, and x0is
the optical receiver transmittivity.
It is clear that such a micro-model leads to significant difficulties when attempting
to analyze the detection capabilities limits and to select the optimum photodetector
for a given application under a wide variety of operating conditions.
The purpose of the present paper is to analyze and predict, from a unified
framework of dimensionless SNR parametrization and generalized PMT and APD
models, the background-response performance of lidar photodetectors, to estimate
and predict the threshold power degradation and operation range reduction for
given background conditions, to optimize the detection technology for different
spectral domains and signal-background levels, and to assist lidar researchers in
selecting a photodetector most appropriate for a given measurement.
This is done by the introduction of dimensionless lidar signals and noises, which
are normalized to the photodetector’s quantum noise level that determines the
maximum achievable signal-to-noise ratio. This dimensionless parametrization
allows a generalized theoretical analysis and numerical modeling of the sky
background influence that can be applied to any lidar photodetector. Within this
formalism, we introduce the dimensionless U-parameter which can estimate the
degradation of the receiver threshold sensitivity caused by any background level.
Then, we show that the U-parameter allows us to predict the operating range
reduction under intense sky background conditions.
To conduct a quantitative comparative analysis and mathematical modeling of
different detector technologies, we introduce ‘‘generalized’’ PMTs and APDs
response functions, which are modeled from ‘‘collective’’ spectral characteristics
(see Section 4 for details) allowing us to make useful comparisons over the entire
near ultra violet, visible and near infrared regions. This approach helps to explore to
what extent the use of a given photodetector over a selected spectral range under
given background spectral noise is sufficient for a given SNR threshold.
Analytical and computer modeling results obtained within this framework allowed
us to generalize the tendencies of the sky background influence on lidar performance
degradation and to provide useful design rules on the choice of different
photodetectors over a chosen spectral range under differing background conditions.
Since the rules are in a highly parameterized form, these results may be applied to a
wide set of lidar photodetectors.
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R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 781
In our recent work [11] we already discussed, from other points of view, some
features of role played by background noise in lidar systems. We introduced a
dimensionless spatial filtering efficiency criterion to be able to compare different
lidar instruments under intense external backgrounds conditions and to estimate
quantitatively their stability against sky background radiation. We showed a low
efficiency of the external backgrounds spatial filtration in traditional lidar systems
and gave recommendations how to improve the existing systems and to choose the
best approach. However, the general issues concerning detector performance over
the entire spectral and background conditions that can be encountered were not
examined.
2. Influence of background on SNR for a general lidar photodetector
Frequently, for elastic lidars with moderate pulse energies, and for all Raman lidar
applications, the most important factor that limits the detection of weak signals in
daytime is the sky background. Lidar applications need to deal with the detection of
weak pulse signals, wide passbands of the receiving subsystem, and potentially
intense sky background.
To generalize the signalþbackground analysis to all values of received echo-
signals, external backgrounds and internal noises, all sources, irrespective of their
nature, are normalized to the quantum noise which determines the maximum
achievable limit of SNR. This allows us to estimate influence of any noise factor as
an excess noise in relation to the shot noise.
The signal-to-noise ratio at the output of a generalized system of direct
photodetection can be presented as follows [2]:
r¼Ps
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2hcDfF=ZlÞðPsþPbÞþðNEPÞ2Df
q, (2)
where noise equivalent power (NEP) is the equivalent power of internal noise of the
photodetector independent of signal and background, per unit of frequency.
Using as a criterion that the minimum detected power occurs at r¼1, where the
signal equals the internal noise, for weak signals (Ps5NEP2lZ=2hcF ) and no
background noise (Pb¼0), the minimum detected power is given as
Pn¼NEP Df1=2. In the quantum noise limit, for a photodetector having the
excess noise factor F, the minimum detected power determined is given as
Pq¼2hc F Df=lZ. (3)
The quantum noise power P
q
provides a useful scale to judge the power levels of
both signal and background since they both depend on the same factor of excess
noise F, transmission band Df, wavelength l, and quantum efficiency Z.
Defining normalized parameters CsPs=Pq;CbPb=Pq;CnPn=Pq, different
operating regimes will be defined from weak C51 to strong Cb1. When carrying
out the theoretical analysis and computer modeling, the following variability in the
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R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796782
key parameters of the lidar receiving and transmitting subsystems, the echo-signals
and the background radiation are given in Table 1. Variations in the APD and PMT
parameters are presented in Table 3 (Section 4.1).
Estimations of the variations in the normalized background and internal noise,
depending on the receiver frequency passband, are presented in Fig. 1. For PMTs,
the normalized internal noise is within the limits 101pCPMT
np103while for APDs
3101pCAPD
np3103and the normalized background power for both PMTs and
APDs is bounded as 3 103pCbp3103.
Eq. (2) can be rewritten as
r2¼C2
s
CsþCbþC2
n
. (4)
Then such an equation for Cscan be written as
C2
sr2Csr2ðCbþC2
nÞ¼0,
resulting in a normalized threshold signal power Pt=Pqfor a given S=Nlevel r:
Cmin
sPt=Pq¼1
2r21þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ4
r2ðCbþC2
nÞ
s
!
. (5)
Introducing the dimensionless parameter Uas the ratio of photodetector threshold
powers P
t
and P
t0
, which are obtained in the presence and absence of the
background noise, we have
UPt=Pt0 ¼Cmin
s
Cmin
sðCb¼0Þ¼
1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þð4=r2ÞC2
nð1þðCb=C2
nÞÞ
q1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þð4=r2ÞC2
n
q, (6)
it is easy to assess quantitatively the extent of performance degradation. Therefore,
U-parameter represents an excess noise factor that determines the influence of the
external background noise (Fig. 2).
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Table 1
Lidar system and parameter variations
Lidar parameters
Wavelengths range l¼3:0107;y,1.1 10
6
m
Transmitter pulse power P0¼106;y,3 10
8
W
Telescope area Ar¼102;y,10
1
m
2
Solid angle of view O¼106;y,10
5
sterad
Interference filter bandpass Dl¼31010;y,3 10
9
m
Optics transmission x0¼0:2;y,0.4
Receiver pass-band Df¼106;y,10
9
Hz
Operation parameters
Operation range R¼102;y,5 10
4
m
Sky background brightness Bl¼106;y,3 10
8
W/m
2
sterad m
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 783
In particular, for any lidar type and configuration, the influence of the sky
background is completely determined by U-parameter, which can be considered as
the factor of the excess noise caused by background. Quantitatively, the fractional
decrease of the lidar sensitivity due to the background is equal to the U-parameter.
As follows from Eq. (6) and illustrated in Fig. 2, the ‘‘noisy’’ photodetectors are
less sensitive to the external background influence.
The particular limiting expressions for the U-parameter, which measures the
decrease in S/N due to the increased noise components for the case r¼1 are
presented in Table 2 and Fig. 3.
As one can see, the approximation U
1
leads to overestimation of the background
impact, and the applicability of both curves U
1
and U
2
is limited by very low-noise
photodetectors.
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Fig. 1. Variations of background and internal noise power depending on the receiver passband.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796784
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Fig. 2. Photodetector threshold sensitivity degradation due to external background.
Table 2
U-parameter of lidar
General case PqbPn PbbPqbPnPb¼0
1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ4ðCbþC2
nÞ
q
1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ4C2
n
q
1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ4ðCbþC2
nÞ
q2
1þ2ffiffiffiffiffiffi
Cb
p
2ffiffiffiffiffiffi
Cb
p1
Fig. 3. Comparison of different approximations of the external background influence.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 785
3. Reduction of lidar operating range under intense background conditions
To estimate the reduction of lidar operating range under intense sky background
conditions, we write the lidar echo-signal power P
s
as CsPs=Pq¼A=R2Pq(Ais
the proportionality factor) by neglecting for simplification the signal extinction in a
relatively transparent atmosphere and taking into account only its geometrical
extinction that is proportional to a range squared. Therefore, Eq. (4) has the form
r2¼A2
R4P2
qðA=R2PqþCbþC2
nÞ(7)
from which it is easy to obtain the expression for the reduction of lidar operating
range under intense sky background conditions:
rbRb
R0¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þð4=r2ÞC2
nð1þðCb=C2
nÞÞ
q1
ð1þðCb=C2
nÞÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þð4=r2ÞC2
n
q1
v
u
u
u
u
t
. (8)
The ratio rbis in a form when it depends only on dimensionless powers of the
background and internal noise, for a given SNR level. This representation allows us
to quickly predict the reduction of the lidar operation range on the basis of Cb,Cn
alone as illustrated in Fig. 4.
As seen in Fig. 3, a level of the lidar operation range reduction increases when the
internal noise levels are smaller. In particular, combining Eqs. (6) and (8), r
b
,andU
are simply connected through
rb¼U1=2. (9)
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Fig. 4. Reduction of the lidar operating range due to the sky background for photodetectors with different
internal noise levels (r¼1).
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796786
Of course, other atmospheric affects would complicate the analysis of relations
between r
b
and U.
From Eq. (9) another physical interpretation of the system parameter Ubecomes
clear: its inverted numerical value defines a square of a normalized operation range
of lidar when taking into account only the geometrical extinction of the echo-signal.
4. Use of generalized APD and PMT models to estimate and generalize the lidar
photodetectors spectral behavior caused by the sky background
4.1. Definition of generalized photodetector models
Most modern lidars operate at near-UV, visible and near-IR spectral regions
which correspond to the highest levels of sky background radiation. To better
understand the issues for detection technologies in these spectral bands, we will use
‘‘generalized’’ spectral efficiency models for both PMTs and silicon APDs. These
models are simply defined as the limiting efficiency values obtained from a
compendium of commercial detectors. In essence, while no single detector will match
the limiting model over all wavelengths, a commercial sensor will exist and have the
model efficiency for any particular wavelength. Based on this compendium of
commercial PMTs and APDs, we obtain in Fig. 5 the spectral representation of the
generalized photodetector’s quantum efficiency relevant to the parameters of
individual real-life devices given in Table 3.
For the ‘‘generalized’’ PMT’s quantum efficiency ZðlÞwe use the limiting envelope
of the quantum efficiency curves of real-life PMTs with different types of
photocathodes. For the APD, in the spectral region 1:0mmplp1:1mm,we took
into consideration the availability of improved silicon APD quantum yields and
included them into Table 3.
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Fig. 5. Quantum efficiency and K0-parameter of generalized PMT and silicon APD vs. wavelength.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 787
From the point of view of the approach we are using here, the exact values of
parameters Z,I
d
,M,Fdo not play a key role, and, in general, they can be corrected
as needed.
4.2. APD/PMT signal-to-noise ratio analysis
The basic criteria to assess the system sensitivity for weak optical signals are the
signal-to-noise ratio and the minimum detected signal. As before, it is convenient to
write the SNR in terms of the specific noise sources of each photodetector according
to Eqs. (2) and (4).
The minimum detected signal current of the photodetector having no internal
magnification (M¼1), for SNR ¼r¼1, is given by Iq¼2qDfF and is closely
connected with Pq. This is a universal parameter of the photodetector (once the
photodetector’s type is chosen, i.e. the factor of noise Fand the receiver frequency
passband Dfare known). In turn, I
q
describes the potentially achievable SNR value.
Rewriting Eq. (1) in view of Eq. (3) for the quantum noise power gives
SNR ¼r¼
Ps
Pq
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ps
PqþPb
PqþId
Iq1þIL
IdFþITFA
IdM2þ¯
I2
A
IqIdM2
r
and in terms of the dimensionless C-parameters:
SNR ¼r¼Cs
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CsþCbþYd1þIL
IdFþITFA
IdM2þ¯
I2
A
IqIAdM2
r. (10)
For the PMT as a lidar photodetector, the thermal noise is negligible due to the
very high internal gain (M¼105;y,10
7
). Furthermore, for a broadband pulsed
lidar, the Schottky noise of both the signal and background dominates, the
photodetector dark current is usually very low, and the surface leakage current, the
thermal noise current and the amplifier noise current are negligible.
The general Eq. (10) is then simplified as follows:
SNRPMT ¼CPMT
s
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CPMT
sþCPMT
bþYPMT
d
q, (11)
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Table 3
Parameters variations of hypothetical photodetector models
Parameter Variation limits considered
APD PMT
Dark current (Id,A) 10
9
,y,10
8
10
10
,y,10
9
Internal gain (M) 20,y,200 10
5
,y,10
7
Excess noise factor (F)5,y,10 1.2,y,1.5
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796788
where YPMT
d¼IPMT
d=IPMT
q. For the APD, the internal gain is usually much less than
for PMT (20oMo200), and the APD dark current is higher. Further, the APD has
a much greater (4–10 times) excess noise factor and is subject to greater thermal
noise effects than PMTs [14,15]. In this case Eq. (10) results in
SNRAPD ¼CAPD
s
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CAPD
sþCAPD
bþYAPD
d1þIL
FAPDIAPD
dþIAPD
TFA
IAPD
dM2
APD þ¯
I2
A
M2
APDIAPD
dIAPD
q
s,
(12)
where YAPD
d¼IAPD
d=IAPD
q. As in the case of PMTs, due to the internal
amplification, thermal noise is usually much less than the shot noise of signal and
background. Since internal amplification M430, the thermal noise and noise of the
amplifier often can be neglected.
Dependences of SNR for the ‘‘generalized PMT and APD models’’ for different
levels of signal and background power at 600 nm are shown in Fig. 5. Here the
parameter
K0ðlÞ¼FPMT
FAPD
ZAPDðlÞ
ZPMTðlÞ(13)
is equal to 1 (Fig. 4). This condition is of particular importance since it represents the
ratio of APD and PMT quantum noise powers and is equal to the theoretical
SNR assuming all internal noise sources in expression are identical for both APD
and PMT and therefore, we may clearly extract the signal and background
contributions.
As follows from Fig. 6, for weak lidar signals (0oCso1), in the absence of the
background light, the PMT’s signal/noise ratio is much higher than for the APD’s
for signal power values up to Cs¼1. With increased background intensity, however,
the photomultiplier noise dramatically increases and PMT loses its advantage over
the APD.
5. Comparative analysis of the effects of background noise to SNR for ‘‘generalized’’
PMT and APD detectors
In this section, a complete spectral analysis for the ‘‘generalized APD and PMT
model’’ for variable sky background conditions is examined.
5.1. General considerations
First, we look to calculate the ratio between the APD and PMT SNR’s:
Kr¼SNRAPD=SNRPMT .
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R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 789
From (11) and (12), the ratio is in general given as
KP¼CAPD
s
CPMT
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CPMT
sþCPMT
bþYPMT
d
CAPD
sþCAPD
bþYAPD
d1þIL
FAPDIAPD
dþIAPD
TFA
M2
APDIAPD
dþI2
A
M2
APDIAPD
dIAPD
q
v
u
u
u
t
¼K0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CPMT
sþCPMT
bþYPMT
d
CAPD
sþCAPD
bþydYPMT
d
FPMT
FAPD 1þYAPD
add
s,ð14Þ
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Fig. 6. SNR for ‘‘generalized’’ APD and PMT for different signal+background superpositions at
l¼600 nm.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796790
where
YAPD
add ¼IL
ðFAPDIAPD
dÞþIAPD
TFA
ðM2
APDIAPD
dÞþI2
A
ðM2
APDIAPD
dIAPD
qÞ
is the factor describing the additional APD-related noises (i.e. currents of the surface
leakage, the thermal noise and the amplifier noise) in comparison with PMT.
We consider two extreme cases.
(1) Weak echo-signal+background superposition: CsþCb¼ðPsþPbÞ=Pq51.
Then
KP¼K0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
YPMT
d=YAPD
d
ð1þYAPD
add Þ
s¼K0ffiffiffi
x
p5K0, (15)
since as a rule YPMT
d=YAPD
d¼IPMT
dFAPD=IAPD
dFPMT51 and usually
0:1oYAPD
add o10.
Therefore, the APD/PMT signal-to-noise ratios quotient for weak signals and back-
grounds is determined by the factor K0ðlÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðIPMT
dFAPD =IAPD
dFPMT Þ=ð1þYAPD
add Þ
q.
(2) Strong echo-signal+background superposition: CsþCb¼ðPsþPbÞ=Pqb1.
Then
KP¼K0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðPsþPb=PPMT
qÞ=ðPsþPb=PAPD
qÞ
q¼ffiffiffiffiffiffiffiffiffiffiffiffi
K0ðlÞ
p(16)
because ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PAPD
q=PPMT
q
q¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðFPMT=FAPD ÞðZAPD =ZPMTÞ
p. Therefore, the APD/PMT
signal-to-noise ratios quotient is described completely by ffiffiffiffiffiffiffiffiffiffiffiffi
K0ðlÞ
p.
5.2. Influence of residual skylight background and impact of ‘‘noisy’’ APDs
The spectral profiles of the expressions K0ðlÞffiffiffi
x
pfrom Eq. (15) and ffiffiffiffiffiffiffiffiffiffiffiffi
K0ðlÞ
pfrom
Eq. (16) are illustrated in Fig. 7.
It is easy to see that as the term x¼ðYPMT
d=YAPD
dÞ=ð1þYAPD
add Þdecreases (noisier
APDs), the wider the wavelength range where the PMT performance outperforms
the APD (i.e. where K0ðlÞffiffiffi
x
po1Þ.
We should note that the curve K0ðlÞffiffiffi
x
pfor x¼1 is not a practical case and
it is shown in Fig. 7 only for comparison. This curve corresponds to a
theoretical assumption that all internal noise sources are identical for both APD
and PMT.
This general behavior is also true in the presence of sky background. The spectral
dependence of the APD/PMT–SNR quotient for different normalized background
powers and different levels of the additional APD noise are shown in Fig. 8. As seen
from the curves KpðlÞin Fig. 8a, for all values of the Y
add
-parameter describing the
extra APD noise in comparison with PMT, the quotient curves KpðlÞfall below
K0ðlÞwhich is determined by the quantum efficiency and excess noise factor of
chosen APDs and PMTs according to Eq. (13), thereby increasing the spectral region
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R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 791
where the PMT outperforms the APD. As illustrated in Fig. 8a, the PMT
outperforms the ‘‘noisy’’ APD (Yadd ¼10) for modest background conditions up to
l41mm.
However, it should be made clear that the effects of the ‘‘noisy’’ APD are less
significant as the level of background light is increased as seen in Figs. 8b–d.
5.3. Background influence for YAG– Nd-laser wavelengths
From the point of view of lidar aerosol remote sensing, it is of interest to single out
the harmonic wavelengths (355, 532 and 1064 nm) of the YAG–Nd-laser, which is
very frequently used as a lidar transmitter. From our general formalism, it is easy to
examine the K
p
behavior which depends on both the background and lidar signal
intensity. The responses are shown in Figs. 9a–c.
It should also be pointed out that for given echo-signal and background powers P
s
and P
b
at the detector input, the dimensionless ratios Cs¼Ps=Pqand Cb¼Pb=Pq
can vary depending on the receiver frequency bandwidth Df, because the quantum
noise power P
q
is proportional to Df. Therefore, the values of the dimensionless
parameters Csand Cbcan be very small (Cs;Cb51) for high frequency bands Df
but increases for intermediate Dfvalues. Therefore, a very wide dynamic range of Cs
and Cb(from Cs;Cb51toCs;Cbb1) should be taken into account in a complete
analysis.
In the UV-region (l¼355 nm), the PMT has a (5–10)-fold advantage over the
APD for weak signal+background superposition (Cs;Cb¼102;...;101). With
increased lidar signal and backgrounds, the SNR values for the PMT and APD
detectors gradually become closer and, according to the estimation (16), under
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Fig. 7. Spectral course of the APD/PMT signal-to-noise ratios related functions K0ðlÞffiffiffi
x
pand ffiffiffiffiffiffiffiffiffiffiffiffi
K0ðlÞ
p.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796792
strong background conditions (Cb410) their quotient approaches the saturation
level ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K0ðl¼355 nmÞ
p. In the green spectral region (l¼532 nm), the situation
is similar but with some modest improvement in the APD, which can be
estimated to be proportional to the enhancement factor seen at saturation of
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K0ð532 nmÞ=K0ð355 nmÞ
p41.
While the relative behavior is similar, the magnitude of the ratio is now greater
than 1 and hence the situation reverses in the IR-region. Therefore, even for weak
lidar echo-signals and backgrounds, the APD surpasses the PMT. Of course for
intense background, the advantage in SNR reaches the saturation value
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K0ðl¼1064 nmÞ
p.
At this point, we now consider the influence of the additional noise terms of the
APD on the SNR’s quotient. The KrðCbÞcurves, describing the ratio of APD/PMT
SNR at the YAG–Nd-laser wavelengths for different levels of the Y
add
-parameter,
are presented in Fig. 10. Here the Cbvalues can be considered as a superposition
CsþCb. For all curves, the full range the responses are shown; their borders set by
small (Yadd ¼0:1) and large (Yadd ¼10) values of the Y
add
-parameter.
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Fig. 8. Spectral dependences of the APD/PMT–SNR quotient at variations of normalized background
power taking into account the additional noise of APD. yd¼IAPD
d=IAPMT
d¼10.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 793
In general, the effect of the high-Y
add
-parameter APD’s is to decrease the SNR
ratio in the presence of small backgrounds while having little effect when the
background signal is strong. These results are quite intuitive but as can be seen, they
can have significant effects on the overall performance. For example, the conclusion
that in general the APD detector is better at 1064 needs revision when the ‘‘noisy’’
APD is considered.
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Fig. 9. Behavior of the SNR quotient for wavelengths of the YAG–Nd-laser under variable sky
backgrounds. yd¼IAPD
d=IAPMT
d¼10.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796794
6. Conclusions
In the present paper, we developed a simple approach to predict APD/PMT lidar
detector performance in presence the residual skylight background. By introducing
dimensionless signals and noises, we unified previous approaches to an analysis of
the influence of sky background noise on the signal-to-noise ratio and threshold
sensitivity of a given generalized lidar receiver. We also introduced a system
parameter Uand developed simple expressions with dimensionless variables
depending solely on the various signal and noise parameters to quantify the detector
threshold degradation as well as the reduction in operating range under variable sky
background conditions. It was shown that for any lidar receiver, the inverted
numerical value of the U-parameter defines a square of a normalized operation range
of lidar when taking into account only the geometrical extinction of the echo-signal.
This allows lidarists easy prediction of the extent of the lidar operation range
reduction caused by the sky background.
In addition, by introducing a ‘‘generalized’’ spectral efficiency model for both
PMTs and APDs which is built from an envelope of individual component
responses, we performed a unified comparative analysis of the capabilities of typical
lidar photodetectors for selected spectral regions under a wide variety of possible
background noise levels. These generalized results can assist lidar researchers in
selecting a photodetector most appropriate for given measurements.
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Fig. 10. Variability of APD/PMT signal-to-noise ratios as a function of the normalized background
power at the wavelengths of YAG–Nd-laser for weak and strong additional APD noise factors.
yd¼IAPD
d=IAPMT
d¼10.
R. Agishev et al. / Optics and Lasers in Engineering 44 (2006) 779–796 795
Basing on dimensionless formalization introduced, we showed that for both the
UV and visible spectral regions, the generalized PMTs SNR surpasses the
generalized APDs SNR for all background conditions. In particular, the less the
introduced parameter x, depending on the ratio of the PMT and APD dark currents
and the additional APD noise, the wider the wavelengths range where the PMT
performance outperforms the APD. In the IR-region, we show that APD’s are
superior to PMT for all backgrounds with the best improvement (up to factor of 10)
occurring for strong background conditions. However, if we include some additional
noises present in ‘‘noisy’’ APD’s, it is possible that the PMT can outperform the
APD for modest background conditions.
Acknowledgements
The authors acknowledge partial support of this work by Grants from NOAA #
NA17AE1625 and NASA # NCC-1-03009.
References
[1] Hinkley E, editor. Laser monitoring of the atmosphere. Topics in Applied Physics, vol. 14. Berlin:
Springler; 1978.
[2] Measures R. Laser remote sensing: fundamentals and applications. New York: Wiley; 1994.
[3] Bosenberg J, Brassington D, Simon P, editors. Instrument development for atmospheric research and
monitoring: Lidar profiling, DOAS and TDLS. Berlin: Springer; 1997.
[4] Kovalev V, Eichinger W. Elastic lidar: theory, practice and analysis methods. New York: Wiley-Inter-
science; 2004.
[5] Ross M. Laser receivers. New York: Wiley; 1966.
[6] Agishev R. Protection from backgrounds in electro-optical systems of atmosphere monitoring.
Moscow: Mashinostroenie; 1994 [in Russian].
[7] Zuev V, Kaul B, Samokhvalov I. Laser sensing of industrial aerosol. Moscow: Nauka Press; 1996.
[8] Kopeika N. Background noise in optical communication systems. Proc. IEEE 1970;58(10):1365–84.
[9] Minkoff J. Signal processing fundamentals and applications for communications and sensing systems.
Norwood: Artech House; 2002.
[10] Yakushenkov Yu, Lukantsev V, Kolosov M. Methods of struggle against clutter in electro-optical
systems. Moscow: Radio i Svyaz; 1997 [in Russian].
[11] Agishev R, Comeron A. Spatial filtering efficiency of biaxial monostatic lidar: analysis and
applications. Appl Opt 2002;41(36):7516–21.
[12] Kingston R. Detection of optical and infrared radiation. Berlin: Springer; 1978.
[13] Arsenyev V, Davydov Yu. Receiving devices of optical range. Moscow: MAI-Press; 1992 [in Russian].
[14] Berkovskiy A, Gavanin V, Zaydel I. Vacuum photoelectronic devices. Moscow: Radio i Svyaz; 1998
[in Russian].
[15] Keiser G. Optical fiber communication. NY: McGraw-Hill; 2000.
[16] Osche G. Optical detection theory for laser applications. New York: Wiley; 2002.
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