Waveform Analysis Techniques - Aalto · 4 Topographic ALS Topographic ALS have a small footprint...

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

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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

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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.

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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!

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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

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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

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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.

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Simple Models

iii

i AρπσΩ

=4

∑=

=N

iit

1

σσ

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Single and MultipleEchoes

Single echo

Multiple echoes

Laseri AA =

∑ ∑

∑

= =

=

Ω==

=

N

ii

N

ii

iit

N

iLaseri

A

AA

1 1

1

4

ρπσσ

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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

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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

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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

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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