PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2016
767
The Influence of Elliptical Gaussian Laser Beam
on Inversion of Terrain Information for Satellite
Laser Altimeter
Zhou Hui, Li Song, and Yang Chi
Abstract
The transmitted laser mode of Geosciences Laser Altime-
ter System (GLAS) is a significant factor in determining the
received pulse waveforms, which are used for inversing target
information. The inversion algorithms in the scientific liter-
ature are based on the assumption that the transmitted laser
is circular Gaussian. The practical laser pattern of
GLAS
is not
circularly symmetric, but elliptical Gaussian. The received
pulse shape will contain a bias, which would cause an error
in the inversion information. In this paper, we describe new
theoretical models about received pulse signal and inversion
errors of range, surface slope and roughness. We present the
results of waveforms shape and inversion errors for three
representative terrains with different surface slope and rough-
ness. The results show that the maximal inversion errors of
range, surface slope, and roughness will reach 24.25 cm, 8.82°
and 4.58 m, respectively, which cannot be negligible. There-
fore, the inversion information should be reevaluated and
amended depending on the type of terrain.
Introduction
Satellite laser altimeter provides a method to obtain the topo-
graphic mapping of the Earth, Moon, Mars and other planets
from several hundred kilometers. By measuring the round-
trip flight time of laser pulse, combined with position and
attitude of satellite platform, target surface elevation can be
determined at centimeter to decimeter precision level (Flood
et al
., 2001). Therefore, more countries and researchers have
been making great efforts on the development and application
of satellite laser altimeter.
The National Aeronautics and Space Administration
(NASA) is one of the institutions who made successful
progress on satellite laser altimeter. During the past 20 years,
NASA researchers have developed four space laser altimeter
systems (Sun
et al
., 2013), which are the Mars Obiter Laser
Altimeter (
MOLA
) (Smith
et al
., 2001), Geoscience Laser Altim-
eter System (
GLAS
) (Zwally
et al
., 2002; Wang
et al
., 2011), the
Mercury Laser Altimeter (
MLA
) (Solomon
et al
., 2007), and the
Lunar Orbital Laser Altimeter (
LOLA
) (Zuber
et al
., 2007). Of
these systems, the
GLAS
receiver has the function in sampled
the received pulse waveforms by using a waveform recorder
at 1
GHz
. By the means of processing and analyzing of wave-
forms, the target’s information including not only the range,
but also the surface slope, roughness, and reflectance can be
inversed. Carabajal and Harding (2006), Neuenschwander
et
al
. (2008), Rosette
et al
. (2011), Garcia
et al
. (2012), Hayashi
et
al
. (2013), and Wang
et al
. (2013) have described the appli-
cation of
GLAS
data in calculating the tree height, cover and
relief. Parrish
et al
. (2011) applied the waveform processing
algorithms to extract range. Moreover, several researchers
have estimated the surface slope and roughness according
to the pulse width of waveform (Huang
et al
., 2012; Li
et al
.,
2012; Shi
et al
., 2013; Mahoney
et al
., 2014; Poole, 2015).
As a matter of fact, the received pulse signal is influenced
by spatial and temporal distribution of transmitted laser
pulse, cloud, and target surface profile (Filin
et al
., 2000;
North
et al
., 2010). The inversion theories in most scientific
literatures above are based on the classical mathematical
expressions given by Gardner (Gardner, 1992). It was assumed
that the spatial distribution of transmitted laser pulse was a
circular Gaussian beam. Thus, if the spatial distribution has
been changed, the inversion results of the target information
will have some errors.
During the practical working process of the laser altim-
eter, with the impact of the spatial distribution and other
parameters of pumping source, the laser mode usually does
not satisfy the circular Gaussian. The
GLAS
receiver captured
the actual laser spot pattern for different campaigns, which
showed that laser pulse followed the elliptical Gaussian
distribution (Abshire
et al
., 2005). Therefore, the difference of
inversion results about target between circular Gaussian beam
and elliptical Gaussian beam should be analyzed comprehen-
sively.
In this paper, the mathematical expression of the received
pulse signal will be deduced for the elliptical Gaussian beam.
For various relief terrains, the temporal moments of received
pulse signal will be expressed and the variety of waveform’s
modes between the circular Gaussian beam and the elliptical
Gaussian beam will be analyzed. Moreover, the influence of
elliptical Gaussian beam on the range error, surface slope, and
roughness will be discussed in detail. The methods in this
paper are applicable to laser altimeter systems with elliptical
Gaussian beam if the ellipticity of beam patterns is available,
and the results contribute to the correction and evaluation of
terrestrial inversion information.
Mathematical Model of Received Pulse Signal
According to the measurement principle of satellite laser
altimeter, if only the atmospheric attenuation effect was con-
sidered, for the target with Lambertian surface, the received
pulse signal power can be expressed as (Gardner, 1982):
p t
T A
E R
I x y f t
R
c
h x y
c
x y
cR
r d a
r
( )
=
(
)
− +
(
)
+
+
η η ρ ϕ
2
0
2
2
2
2 2
cos
,
,
dxdy
Σ
∫∫
. (1)
Electronic Information School, Wuhan University, Geospa-
tial Information Collaborative Innovation Center, Luojia
,
Wuchang District, Wuhan, Hubei Province, China, 430072
(
).
Photogrammetric Engineering & Remote Sensing
Vol. 82, No. 10, October 2016, pp. 767–685.
0099-1112/16/767–685
© 2016 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.82.10.677
