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Christian Doppler LaboratorySpatial Data from Laser Scanning and
Remote Sensing
Waveform Analysis Techniques in Airborne Laser Scanning
Wolfgang Wagner
2
3
Why Digitising the Waveform?
BathymetryMeasurement of depth in shallow, coastal watersComplex echo due to scattering and spreading of pulse at air-water boundary, within water column and the seafloorDepth can not be reliably estimated in real time during data acquisition ⇒ waveform-digitisation
Large-footprint Vegetation LidarWhen the laser footprint is large, the echo from vegetated areas iscomplexAirborne (e.g. LVIS) and spaceborne (e.g. GLAS) have waveform-digitising capabilities
4
Topographic ALS
Topographic ALS have a small footprint and high pulse repetitionfrequency (PRF)
Required for collecting a high number of geometrically well defined terrain echoesNumber of echoes typically small, even over vegetated terrain
1 echo: 50-80 %2 echoes: 20-30 %3 echoes: < 10 %4 echoes are more: < 1 %
So why small-footprint, high-PRF ALS with waveform-digitisation?» Riegl LMS-Q560» TopEye Mark II» Optech ALTM 3100 with waveform-digitiser» Leica ALS50» TopoSys Falcon III
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Goals of Waveform Analysis?
Get more echoes than for first/last pulse ALSPersson et al. 2005
Adjust algorithms according to the task, e.g. adapt rangedetection algorithms
Jutzi and Stilla (2003), Wagner et al. (2004)Use additional attributes, i.e. echo amplitude and echo width for classification purposes
Terrain/off-terrain echoes (Doneus and Briese 2006)Coniferous/deciduous trees (Reitberger et al. 2006)
Physical understandingMeasurement process depicted in its entire complexity
6
Gaussian Decomposition
Decompose the waveform into a series of Gaussian pulsesNon-linear optimisation techniques, e.g. Levenberg-MarquardtRequire, in general, initial parameter estimates
Number of echoes, range, amplitude, widthNon-Gaussian functions can be used
534 535 536 537 538 539 540 541 5420
5
10
15
20
25
Distance (m)
Am
plitu
de
Laser pulseGaussian model
Range
Amplitude
Echo width
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Pulse Detection
For range determination different pulse detection methods can beusedMethods
thresholdcentre of gravitymaximumzero crossingconstant fraction
0 3 6 9 12 15 18distance (m)
0 20 40 60 80 100 120
-0.5
0
0.5
1
1.5
2
time (ns)
sign
al a
mpl
itude
← emitted pulse
cross section →
← reflected pulse
estimated travel time
zero crossingmaximumcenter of gravitythresholdconst. frac.
Emitted pulse Echo Si
gnal
Am
plitu
de
Target
Estimated travel time
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Numerical Experiments – Roof 45°
7.5 9 10.5 12 13.5 15 16.5 180
0.1
0.2
0.3
0.4
distance (m)
d σ
50 60 70 80 90 100 110 1200
0.5
1
1.5
2
time (ns)
sign
al a
mpl
itude
zero crossingmaximumcenter of gravitythresholdconst. frac.
Scattering propertiesof a tilted roof
GeneratedWaveform
For 1 m footprint difference in range estimates between detectors was > 30 cm
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Pulse Detection using ASDF
Average Square Difference Function (ASDF) technique
Correlation techniqueNoise is reduced but extra computational effortDetection still necessary
thresholds arbitrary
Sensor-Waveform
Echo Waveform
( ) ( )[ ]∑=
+−=n
kASDF kTxkTxR
1
221)( ττ
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Performance of ASDF Method
1 2 3 4 >= 5
M ax-Detection 58,08 32,20 7,73 1,08 0,09ASDF (Gaussian Pulse) 66,23 21,09 9,22 1,81 0,18ASDF (M ean Reference Pulse) 65,89 20,65 9,74 2,01 0,24
Method # detected echoes (%)
• Problems with laser ringing were reduced• More higher-order echoes were detected
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Scattering TheoryCohen-Tannoudji et al. (1977)
( )ϕθσ ,⋅ΩΦ= ddn
dn … number of scattered particlesΦ … incoming flux (number of particles per unit time and area)dΩ … solid angleσ(θ,ϕ) … differential cross section in direction (θ,ϕ)
dΩ
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Quantum Mechanics
Wave function ΨProbability amplitude of the particle's presence
Differential cross section
( ) ( )r
eferikr
rkir
ϕθ ,+→Ψ∞→ vvv
Incident plane waveScattered spherical wave
Far-field approximation
( ) ( ) 2,, ϕθϕθσ f=
Scattering amplitude
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Scattering of Electromagnetic Waves
Electric field vector E
Radar backscattering cross section
Ishimaru (1978)
( ) ( )r
eeikr
ikr
si iofeEErE ri ˆ,ˆˆ ˆ +→+=∞→
( ) ( )222
ˆ,ˆlimˆ,ˆ ioEE
io fr
i
s
r==
∞→σ
( )ii,ˆ4 −= πσσ b
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Radar Equation I
Wagner, W., A. Ullrich, V. Ducic, T. Melzer, N. Studnicka (2006) Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner, ISPRS Journal of Photogrammetry and Remote Sensing, 60(2), 100-112.
15
Radar Equation II
σηηβπ atmsys
t
rtr R
DPP 24
2
4=
Pr ... Received power (Wm-2)Pt ... Transmitted power (Wm-2)Dr ... Diameter of receiver aperture (m)R ... Range (m)βt ... Beam divergence (rad)ηSYS ... system transmission factorηatm ... atmospheric transmission factorσ ... Backscatter cross section (m2)Γ(t) … Receiver impulse function
)()()(4
)(1
24
2
tttPR
DtP
N
iit
ti
atmsysrr Γ∗′∗=∑
=
σβπηη
Static Description:
Time-Dependent Description:
Laser Pulse Receiver
Cross section of i-th targetNumber of targets
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Gaussian Solution
Combined effect of transmitter and receiver electronics can be described by Gaussian function
Gaussian scatterers
( ) ( ) ( ) 2
2
2ˆ sst
t eStSttP−
==Γ∗
Riegl LMS-Q560
( )( )
2
2
2ˆ i
i
stt
ii et−
−
=′ σσ( )
iistt
ii sdte i
i
σπσσ ˆ2ˆ2
2
2 ==−
−∞
∞−∫
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Backscattered Waveform
For Gaussian scatterers the backscattered waveform is described by a series of Gaussian pulses
Pulse width
Pulse strength
( )
∑=
−−
=N
i
stt
irip
i
ePtP1
2 2,
2
ˆ)(
22, isip sss +=
ip
si
ti
atmsysri s
sSR
DP
,24
2ˆ
4ˆ σ
βπηη
=
ipir
st
sPP
sSP
,ˆ
ˆ
→
→
Looks like the static radar equation!
18
Cross Section from Waveform through Calibration
CalibrationSeparate constant and variable parametersUse of external reference targets
ipiipratmsys
ti sPR
sSD ,4
2
2ˆ
ˆ4
⋅=ηηπβσ
from Gaussian decomposition
iP̂
ips ,
iR
19
Calibration
Estimating the cross section of homogeneous targets with a Riegl "Reflectometer"
Riegl Reflectometer
Incidence Angle
Mea
sure
d R
efle
ctiv
ity
Reflectivity of 63,5 Spectralon target using different reference targets
Master Thesis Hubert Lehner, in cooperation with FGI
20
Waveform Parameters
a) Orthophotob) Digital Surface Modelc) Ranged) Amplitudee) Echo widthf) Backscatter cross section
Wagner, W., M. Hollaus, C. Briese, and V. Ducic (2007). 3D vegetation mapping using full-waveform airborne laser scanners. Manuscript submitted to the International Journal of Remote Sensing.
21
Simple Models
iii
i AρπσΩ
=4
∑=
=N
iit
1
σσ
22
Single and MultipleEchoes
Single echo
Multiple echoes
Laseri AA =
∑ ∑
∑
= =
=
Ω==
=
N
ii
N
ii
iit
N
iLaseri
A
AA
1 1
1
4
ρπσσ
23
Improve DTM Filtering with Waveform Parameters
DSM Classified Non-Terrain Echoes
DTM without Waveform DTM with Waveform
Short vegetation issometimes not properlyfiltered using justgeometric information
24
Conclusions
Waveform-digitisation allows linking ALS to scattering theoryWaveform analysis and calibration techniques should be applied together for estimating the 3D cross section
3D cross section visualisation of Schönbrunn palace and park in Vienna
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3D Point Cloud Representation of Cross Section
Cross Section
Cross Section
Spatial extent of scattereris ignored. An additionalattribute (echo width) is needed.
Standard representation of ALS data
26
Voxel Space Representation of Cross Section
Cross Section
Cross Section
May be useful for advanced modelling efforts,e.g. ray tracing simulations within vegetation canopies
27
Challenges ahead of us
Master large size of waveform data setsData base managementFast processing routines
Understand the impact of selecting different waveform analysis techniquesDevelop theoretically sound, yet practical solution for calibration problemImprove our physical understanding of the measurement process
Predict impacts of changing ALS configurationsFurther develop applications of waveform-digitising ALSDevelop scattering theory for ALS