1. Multi-footprint Airborne LiDAR Data in Forest Vegetation
Ilkka Korpela University of Helsinki
Background
Thesis: LiDAR data acquired in more than one scale, (using maximal footprint illumination), is informative of the illuminated and sampled vegetation structure.
Footprints of different size measure gaps of different size. The scattering profiles of wide and narrow beams differ. This may characterize for example the tree species (Fig. 0).
Challenges: Altering divergence. Reaching max allowed energy (J/m2) for large footprints.
Large footprint: Geometry weakens, Likelihood of penetration increases, Sampling degree increases (illuminated m2 for pulses/m2).
Small footprint: Intersection geometry is better, clumped scatterers attenuate the pulse, penetration of ‘intact pulses’, low sampling degree.
Maximal pulse energy: Transmitted peak power and total energy spreads across the footprint and the energy through the binocular aperture (m2) cannot exceed eye-safety limits on the ground.
Power received, Pr
Large surfaces:
Pr is linear w.r.t. output power Pt
Pr is inversely proportional to the square of divergence , which is compensated by A in (t), thus increase in footprint size does not influence Pr.
Linear and blob-like targets:
For same Pr and SNR, the needed Pt is proportional to the 1st and 2nd power of the footprint diameter ratio, e.g. 1.5 and 2.25 for (30 cm/20 cm) footprints.
Fig. 0. Scatterers and Gaps
Peak amplitude/intersection-area in ’top canopy’ % %
Large footprint
Small footprint
Area
Area
Effect of footprint size on the simulated (top) and real (bottom) WFs from birch crowns. The first 100 pulses that produced a DR echo more than 1.5 m above the ground were chosen. Footprint diameter in 1/e. The x axis shows the time (ns), and the y axis the amplitude (DN).
A. Hovi, I. Korpela Real and simulated waveform-recording LiDAR data in juvenile boreal forest vegetation. RSE 140, 665–678
TOP CANOPY
LOW CANOPY
GROUND
Backscatter cross-section
”Typical Waveforms”
AMPLITUDE
TIME
EXPERIMENTATION, CNTD .
Differences in relative change over footprint size
Conclusions
Relative WF-recording LiDAR radiometry was complex due to many instrument properties, solved using ’reverse-engineering’. E.g. the flight planning SW omitted the 0.2 dB/km atmospheric attenuation & low output power was unstable.
The responses in point height and WF attribute distributions vary with e.g. tree species and the stand developmental stage. How to harness is an open Q.
The SNR in the used data was well below the limits of eye-safety. The signatures in the joint distributions of WF attributes of multi-footprint pulses are likely stronger in maximum SNR data.
EXPERIMENTATION, Hyytiälä Finland
Leica ALS60, 1GHz waveform (WF) digitizer, 1064 nm
ALS60 receiver: photodiode/transimpedance ampli- fier, an AGC-circuit, signal splitter between DR circuits and a WF digitizer triggered by the DR echo #1.
Varying (20 dB, 1-100%) Pt was applied at heights of 500, 1000, 2000 and 2700 m. Similar SNR (except for ATM-losses, 0.2 dB/km) were achieved at all heights for larger-than-footprint targets (Fig. 1). Max Pt from 2700 m  1/e2 footprints of 11, 22, 44 and 59 cm. Transmitted pulses were 9- or 4-ns-long.
Receiver linearity w.r.t.power entering the aperture was tested, using multi-height acquisition with fixed transmitter and receiver properties. Non-linearities (±5%) were observed in weak and strong echoes (Fig. 2). Source? Received WFs slightly deformed by the signal-strength-dependent bandwidth of the receiver (impulse response). The 4-ns pulses had 67 ns FWHM (Fig. 4)
Receiver AGC-effects removed up to 90% of the between-pulse variance (automatic gain control) in homogenous targets. Influence of AGC is  dB.
Effect of the varying dm-scale surface texture was observed in different surfaces (Table 1). Basic noise of (peak) amplitude observations ~ 5%.
Table 2. Mean values and CV(%) of WF attributes in 3045-year old pure pi­ne, spruce and birch plots.
Footprint, cm
FWHM
RiSeTime
Peak Amplitude
Energy
11 Birch
1.51 (38)
1.35 (28)
66.1 (34)
1141 (19) 22
1.49 (38)
1.30 (25)
67.9 (30)
1163 (14) 44
1.68 (40)
1.51 (26)
58.7 (29)
1205 (13) 59
1.77 (39)
1.63 (25)
55.2 (28)
1235 (12)
11 Spruce
1.33 (40)
1.21 (26)
60.2 (33)
941 (20)
1.40 (41)
1.25 (28)
57.2 (32)
935 (16)
1.66 (47)
1.45 (30)
49.6 (34)
982 (15)
1.84 (47)
1.60 (30)
44.6 (33)
995 (15)
11 Pine
1.45 (37)
1.30 (27)
53.4 (30)
869 (16)
1.49 (35)
1.32 (24)
51.8 (25)
875 (12)
1.68 (34)
1.53 (23)
46.1 (22)
916 (10)
1.77 (37)
1.63 (23)
43.1 (25)
932 (13)
Fig. 2. Power thru aperture vs. amp-litude recorded. Illustration of a non-linear sensor response analyzed using multi-height LiDAR data:
Table 1. Coefficient of variation (CV, %) of peak amplitude in different surfaces listed in dec­reasing order of brightness.
Fig. 3. Relative peak amplitude of ground (single) returns below a pine canopy as a function of the pulse-trunk distance (m) at crown base. Negative distance corresponds to cases, in which the pulse 'intersected' the estimated crown perimeter. Footprint-gapsize relation is clear.
Surface
Footprint, cm 11 22 44 59
Hay, < 50 cm
7.0
5.8
4.6
3.6
Short grass
4.9
4.3
4.0
3.5
Mire surface
9.7
8.3
6.3
5.4
Fine sand
4.5
3.0
2.8
Asphalt, old
7.4
7.3
6.9
7.2
Asphalt, new
5.1
5.0
Gravel road
11.4
7.7
Bitumen
9.4
9.0
8.6
Fig. 4. Examples of weak and strong ref-lectors and the deformation of WF due to varying bandwidth of the receiver (depending on signal strength).
Fig. 1. Normalized mean amplitude values (BK reflectance ~0.050.45) of the four acquisit­ion heights in calibration surfaces. The 500-m (11 cm) data deviated in two cases more than 5%, due to strip-level variations of the low output power.