高斯光束特性对激光雷达测量精度的影响深度探讨
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本文主要探讨了高斯光束在激光雷达测量中的重要性，特别是在多普勒测风激光雷达中广泛应用的Fabry-Perot Etalon (FPE) 鉴频器的作用及其特性对测量精度的影响。高斯光束的传播特性，如光束质量因数 \( M_2 \) 和输出激光扩束器（MBE）的放大率，显著地决定了激光雷达回波的发散角，这是衡量光束在空间分布上的关键参数。
首先，发散角的变化直接影响到雷达系统的角度分辨率和远场性能。质量因数 \( M_2 \) 越低，光束越集中，发散角越小，但在实际应用中，为了保证足够的探测范围，往往需要使用MBE来增大光束的扩散，这可能导致发散角在远场中增大，从而影响系统的灵敏度和精度。此外，MBE的放大率也是一个关键因素，它决定着激光雷达能否在不同距离上保持稳定的探测能力。
文章特别关注了FPE在风速测量中的响应敏感性，因为FPE作为频率分辨元件，它的稳定性和选择性对激光雷达的频率测量至关重要。随着高度的增加，由于光束发散，FPE的传输特性可能会发生变化，这可能造成系统在远场中的响应变弱，导致风速测量误差相对稳定但整体精度下降。
在近场中，由于FPE的不稳定性，特别是对于质量因数较低和MBE放大率较高的激光，必须进行系统校准，以抵消这些传播特性带来的影响。这包括对光束扩散、FPE响应以及测量噪声等因素的补偿，以确保在各种环境条件下都能实现准确的风速测量。
研究通过数值结果展示了这些影响，并强调了在设计和优化激光雷达系统时，需要充分考虑高斯光束的传播特性，以达到最佳的测量效果。本文的关键词包括风力雷达、Fabry-Perot Etalon、光束质量因数、扩束器放大率、发散角、多普勒效应以及近场和远场性能。
这篇论文为理解和减小由高斯光束传播特性引起的激光雷达测量误差提供了深入的理论分析和技术指导，对提高多普勒测风激光雷达的性能具有重要的实用价值。
Please
cite
this
article
in
press
as:
Y.
Wang,
et
al.,
Analysis
of
measurement
error
of
wind
lidar
caused
by
propagation
properties
of
Gaussian
beam.
Optik
-
Int.
J.
Light
Electron
Opt.
(2011),
doi:10.1016/j.ijleo.2011.07.062
ARTICLE IN PRESS
G Model
IJLEO-51781;
No.
of
Pages
4
Optik
xxx
(2011)
xxx–xxx
Contents
lists
available
at
SciVerse
ScienceDirect
Optik
jo
ur
n
al
homepage:
www.elsevier.de/ijleo
Analysis
of
measurement
error
of
wind
lidar
caused
by
propagation
properties
of
Gaussian
beam
Yufeng
Wang,
Dengxin
Hua
∗
,
Li
Wang,
Qing
Yan,
Zhirong
Zhou,
Shichun
Li
School
of
Mechanical
and
Precision
Instrument
Engineering,
Xi’an
University
of
Technology,
Xi’an
710048,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
2
March
2011
Accepted
22
July
2011
Available
online
xxx
Keywords:
Wind
lidar
Fabry–Perot
Etalon
Beam
quality
factor
Magnification
of
beam
expander
a
b
s
t
r
a
c
t
The
Fabry–Perot
Etalon
(FPE)
is
widely
used
in
Doppler
wind
lidar
as
frequency
discriminator
and
its
performance
is
certainly
affected
by
the
propagation
properties
of
Gaussian
beam.
The
divergence
angle
of
lidar
returns
affected
by
the
quality
factor
M
2
and
magnification
of
beam
expander
(MBE)
of
outgoing
laser
is
firstly
discussed.
Also,
the
corresponding
sensitivity
of
system
on
wind
velocity
is
analyzed.
The
numerical
results
show
that
the
divergence
angle
of
lidar
returns
and
FPE
transmission
varied
with
height,
the
resulting
sensitivity
of
system
is
decreased
and
the
wind
velocity
error
is
relatively
steady
in
the
far
field.
Consequently,
for
the
wind
lidar
using
FPE
as
frequency
discriminator,
it
is
supposed
that
the
outgoing
laser
with
both
lower
beam
quality
factor
M
2
and
higher
MBE
are
requested,
in
particularly,
the
system
calibration
due
to
FPE
instability
must
be
considered
in
the
near
field.
©
2011
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
Laser
radar
or
lidar
has
become
one
of
powerful
tools
for
atmo-
spheric
remote
sensing
and
has
been
widely
applied
in
many
fields
such
as
laser
atmospheric
transmission,
aerosol
radiation,
global
climate
prediction,
and
atmospheric
environment
because
of
its
priority
in
high
temporal
and
spatial
resolution
[1,2].
And
since
the
behind
of
19th
century,
FPE
has
been
largely
used
in
metrol-
ogy
and
spectroscopy
as
a
precision
optics
tool.
Especially,
FPE
has
been
used
as
one
of
important
spectroscopic
devices
in
atmospheric
temperature,
wind
measurement
lidar
and
high
spectral
resolution
lidar
[3–7].
Relevant
researches
have
been
carried
out
on
FPE
used
in
Doppler
wind
lidar
as
frequency
discriminator,
which
analyzes
the
Doppler
frequency
shift
from
the
atmospheric
aerosol
movement
by
wind
[7,8].
Recent
studies
indicate
that
such
factors
as
the
inci-
dence
angle
and
beam
divergence,
beam
shape
and
its
intensity
distribution
have
effect
on
FPE
transmission
curve
in
single-
or
dual-FPE
wind
lidar
systems
[9–11].
The
measurement
error
of
sys-
tem
is
currently
discussed
by
Signal-to-Noise
Ratio
(SNR)
under
the
condition
that
the
sensitivity
of
FPE
is
assumed
as
a
constant.
Also,
it
has
been
found
that
from
the
long-term
experiments
the
resolution
and
stabilization
of
FPE
directly
affects
the
measurement
accuracy
of
the
wind
lidar
system
[11,12].
In
this
paper,
a
Doppler
wind
lidar,
which
applied
a
FPE
as
frequency
discriminator,
is
selected
as
research
item,
and
the
∗
Corresponding
author.
E-mail
address:
dengxinhua@xaut.edu.cn
(D.
Hua).
measurement
error
of
wind
velocity
caused
by
propagation
prop-
erties
of
Gaussian
beam,
corresponding
to
the
beam
quality
factor
M
2
and
MBE
are
discussed.
The
numerical
results
indicate
that
the
beam
divergence
of
lidar
returns
depended
largely
on
height,
thus
affects
greatly
the
properties
of
FPE.
The
sensitivity
of
system
due
to
the
beam
divergence
is
firstly
discussed
and
the
wind
velocity
error
is
also
analyzed.
This
work
is
expected
to
supply
numeri-
cal
foundation
for
the
lidar
system
which
uses
FPE
as
frequency
discriminator.
2.
Analysis
of
FPE
Based
on
multi-beam
interference
theory,
the
transmission
function
of
FPE
t
(v)
can
be
expressed
as
t(,
)
=
1
−
L
1
−
R
2
1
1
+
(4F
2
/
2
)
sin
2
[(2dn
0
/c)
cos()]
(1)
where
L
is
the
light
loss
by
FPE,
R
the
reflectivity
of
the
reflecting
surface,
n
0
the
refractive
index
of
medium
of
flats,
d
the
distance
of
flats,
c
the
velocity
of
light,
the
frequency
of
light,
the
angle
of
incidence,
and
F
is
the
fineness
of
FPE.
Considering
practical
optical
system
where
the
incident
beam
on
FPE
is
commonly
non-paralleled
and
non-zero
divergence,
if
the
lateral
distribution
of
the
light
energy
is
uniform,
the
transmission
function
of
FPE,
where
beam
divergence
expects
to
max
,
can
be
denoted
in
polar
coordinates:
T()
=
max
/2
0
h()
×
2
×
r()
×
t(,
)f
d
max
/2
0
h()
×
2
×
r()f
d
(2)
0030-4026/$
–
see
front
matter
©
2011
Elsevier
GmbH.
All
rights
reserved.
doi:10.1016/j.ijleo.2011.07.062
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