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TIME OF FLIGHT IMAGING
Differences between Beamwidth and
Pulsewidth/ Range Gate Imaging
„ Beamwidth Limited Imaging
„
… Push
Broom Airborne Laser Scanners
… Collision Avoidance Laser Scanners
… 3D Pan/Tilt and Pan/Prism Laser Scanner
… 3D Mirror Millimetre Wave Radar Scanner
… Pulsed Time of Flight Laser Analysis
1
Measurement Modes
„
Beamwidth Limited
…
…
…
…
„
Range Gate Limited
…
…
…
Each range gate generates a
unique pixel in the radar image
Good for complex surfaces
Resolution limited to the
beamwidth spot size
Slow process
Good for narrow beam lasers
…
…
Restricted to flat areas
Cross-range resolution
determined by beam width
Range resolution determined by
the gate size
Fast process
Good for wide beam radars
Beamwidth Limited Imaging
2
Range Gate Limited Imaging
Laser Radar Performance Analysis
3
Power Density on the Target
The power density at
the target assuming
an isotropic radiator
SI =
Modified by the collimating
effect of the lens used to
direct the beam. It is the ratio
of the beam angle in
steradians to that of the full
sphere
4π
P
2
4πR 2 (π 4 )θ BW
Power Density Back at the Receiver
The area of the beam
footprint on the target
assuming that the target
is larger than the beam
SR =
The backscatter
coefficient
dependent on the
target material etc.
The reflected power is
scattered equally over the
forward hemisphere of 2π
steradians
4π
P
π
(Rθ BW )2 ρ 1 2
2
2
4πR (π 4 )θ BW 4
2πR
Note: If the target is a retro reflector then
ρ can be much larger than 1 to
compensate for the assumption that the
target scatters equally over 2π steradians
4
Received Power
The received power
that is intercepted by
a lens with area A
The optical efficiency
of the laser chain from
the front aperture of
the lens
π
P
4π
1
2
(
)
R
θ
ρ
Aτ o
BW
2
4
4πR 2 (π 4 )θ BW
2πR 2
S=
Simplifies to
S=
PAτ o ρ
πR 2
Target Smaller than the Beam
„
In the unlikely event that the laser beam is wider than the
target diameter, then the target terms should be
substituted by the laser radar cross section σ
S=
„
2 PAστ o
2
π 2 R 4θ BW
For optical systems the 1/e = 0.367 power level is used
to define the beamwidth which equates to the following
θ BW
1.05λ λ
=
≈
D
D
θ BW =
2
λ2
D2
=
λ2π
4A
5
Range Equation for Small Targets
„
Substituting for the beamwidth θBW the received power is
given by the following formula
8PA 2στ o
S= 3 4 2
π R λ
W
Laser Receivers
„
Direct detection laser receivers
convert the received laser
echo directly into a voltage or
current using a PIN diode or
avalanche photodiode
„
Heterodyne receivers downconvert the received signal
using a stable laser local
oscillator
Low frequency signals can
then be amplified and filtered
to enhance detection
probability
„
6
Photovoltaic Detectors
„
„
„
„
Photovoltaic effect consists of the generation of a potential difference as a
consequence of the absorption of radiation
The primary effect is photo-ionisation, or the production of hole-electron
pairs that can migrate to a region where charge separation can occur.
This charge separation usually occurs at a potential barrier between two
layers of solid material. These can include semiconductor PN junctions and
metal-semiconductor interfaces
For a material with a conversion efficiency η, the average current (amps)
produced by a light beam with optical power, P is as follows
i=
ηeP
hf
A
Silicon
„
As the output current is proportional to the input power, this is a square law
detector
Photodiode Types
„
PIN Photodiode
…
…
…
„
P-Intrinsic (lightly doped)-N structure
Depleted region made as large as
possible to minimise recombination
Responsivity 0.5 to 1 A/W
Avalanche Photodiode
…
…
…
…
PIN Photodiode
Electrons and holes released by
absorbed photons accelerate and
strike neutral atoms freeing more
“secondary” carriers
Responsivity 0.5 to 100 A/W
Need high voltage (up to 300V for Si)
and are temperature sensitive
More complex circuitry, and less
reliable than PINs
Avalanche Photodiode
7
Photodiode Characteristics
„
„
„
Can be configured as a current-to-voltage converter where the
relationship between P and ip tracks the current axis (V=0) (red line)
Alternatively the diode produces a voltage across its terminals when
operated into a high resistance (green line)
io refers to the dark current which flows in the absence of any light
and is attributed to thermal generation of hole-electron pairs
Operating Ranges of Some IR Detectors and
Transmission Characteristics of the Atmosphere
8
Noise Level of a Direct Detection Receiver
„
The receiver noise level for a direct detection laser radar
can be related to the specific detectivity of the detector
D* using the following formula
( Ad Δf )1 / 2
N=
D*
W
where: N – Noise level (W)
Ad – Detector area (cm2)
Δf – Receiver bandwidth (Hz)
D* - Detectivity (cm-Hz1/2W-1) (see Fig 3.7 for D*)
„
This is often listed in the specifications for photodiodes
as the dark current and is typically of the order of 1nA
Noise Level of an Heterodyne Receiver
„
The noise spectral density of an ideal receiver
comprising both thermal and photon noise is given by
the following
ψ(f ) =
hf
e
hf / kT
−1
+ hf
where: Ψ(f) – Spectral density (W/Hz)
h – Plank’s Constant 6.6256x10-34 (Ws2 )
f – Frequency (Hz)
k – Boltzmann Constant 1.38x10-23 (Ws/K)
T – Absolute Temperature (K)
9
Noise Power Spectral Density
μ ( f ) = hf
γ ( f ) = kT
Noise Power Spectral Density
„
„
„
For microwave radars, the noise power density is
determined by the thermal noise floor γ(f) = kT
In the infrared, the noise power density is determined
primarily by the photon noise μ(f) = hf
The noise level of an heterodyne receiver can therefore
be written as
N=
hfB
η
where: N – Noise level (W)
η - Quantum efficiency (0.3 to 0.5) (how many photons are
required to produce one photo-electron)
B – Receiver bandwidth (Hz)
10
Cross section of Glint Targets
„
„
„
Glint targets represent returns from corner reflectors or
normal surfaces (such as the ground) where there is a
single dominant scatterer
Returns are generally fairly constant from pulse to pulse
The laser radar cross section for a square corner
reflector is given by the following formula
4πD 4
σ =
3λ2
Where: σ - Cross section (m2)
D – Side of the reflector (m)
Signal to Noise
Ratio
Pd and Pfa
11
Example
„
An earth bound CO2 laser operating at a wavelength of
10.6μm radiates through a collimating lens with a
diameter of 500mm. If it produces 500W pulses with a
duration of 0.1s
…
…
…
…
…
What would the diameter of the footprint be on the moon
Ignoring atmospheric effects what would the power density on
the moon be in W/m2
A retro-reflector with a diameter of 10cm and a reflectivity of
0.99 reflects some of the power back to earth. What is the
received power density
Is the reflected power density from the moons surface back on
the earth (backscatter ρ = 0.2 ) larger or smaller than that
returned by the retro-reflector
If an heterodyne receiver uses the same size lens, what is the
single pulse signal to noise ratio that we could expect
Example (continued)
„
The diameter of the footprint on the moon
…
…
The mean distance to the moon is 384400km
The 1/e beamwidth is
θ BW =
…
1.05 × λ 1.05 ×10.6 ×10−6
=
= 22.3μrad
D
0.5
So the diameter will be
d = RθBW = 3.844x108x22.3x10-6 = 8556m
„
The power density of the signal on the moon
Afoot = πd2/4 = 57.5x106 m2
SI = P/Afoot = 500/57.5x106 = 8.7μW/m2
12
Example (continued)
„
The power density back on the earth from the retro
reflector
…
The effective cross section of the retro-reflector is
σ = 0.99
…
4πD 4
4π × 0.14
=
0
.
99
3λ2
3 × 10.6 × 10 − 6
(
)
2
= 3.7 × 10 6 m 2 = 65.7 dBm 2
So the power density back on earth is found by applying the
range equation
SR =
2 Pσ
2 × 500 × 3.7 × 106
=
2
4
π 2 R 4θ BW
π 2 × 3.844 × 108 22.3 × 10− 6
(
)(
)
2
= 3.45 × 10 −17 W / m 2
Example (continued)
„
The power density back on earth from the signal
reflected from the surface of the moon
SR =
„
Pρ
500 × 0.2
=
2
πR π 3.844 × 108
(
)
2
= 2.15 × 10 −16 W / m 2
Which is 10x higher than that obtained from the retro
reflector
13
Example (continued)
„
What is the signal to noise ratio
…
The matched filter bandwidth
β = 1/τ = 10Hz
…
The noise floor is determined by photon noise and a detector
with a quantum efficiency of 0.5
N=
hfβ
η
=
hcβ
ηλ
=
6.625 × 10 −34 × 3 × 108 × 10
= 3.75 × 10 −19 W
−6
0.5 × 10.6 × 10
…
For an optical efficiency of 100%, the received signal power is
the product of the power density and the lens aperture
S = SRπd2/4 = 2.15x10-16x0.196 = 4.21x10-17 W
…
So the SNR is
S/N = 112 (20.5dB)
Fine Range
Measurement
„
„
„
„
„
Coarse time is measured using a
digital clock which is stopped
when the echo pulse exceeds a
fixed threshold
Samples of the direct pulse and
the delayed pulse voltages are
made at the following clock
leading edge
A delay line discriminator
determines the pulse position with
respect to this leading edge
The clock count and the
discriminator output are added to
determine the true range
Accurate to a fraction of the pulse
length
Received
Pulse
Vthresh
Clock
Last
count
N
Stop
counting
Enable
S&H
Vdir
Vdel
Delayed pulse
Direct pulse
Sample
and
Hold
Vdir - Vdel
ΔR = -------------Vdir + Vdel
Range = K x Count(N) + J x ΔR + Offset
14
Push Broom Scanners
ƒRotating prism scans the laser beam at
right angles to the direction of travel
ƒBetween 2000 and 8000 laser pulses
are generated every second
ƒBecause the ground is rough, some
power is reflected back to the receiver
ƒBy registering the forward motion of the
aircraft using GPS/INS and the beam
angle, a 2D raster is produced
ƒRange and /or reflected signal
amplitude are logged to produce an
image of the ground
Scanner Unit
Operational Principle
Surface Models
„
A digital image is a rectangular
array of cells where each cell
contains a single value
…
…
„
Topological images are produced
when height information is stored
Reflectivity images are produced
when echo amplitude is stored
Though the points measured
usually have a non-linear spacing,
the cells in the image are generally
placed at the vertices of a regular
grid to facilitate processing
15
Digital Model Definitions
„
„
„
Digital Elevation Model (DEM):
A continuous mathematical
representation describing the
shape of the surface of the
earth as a function of latitude
and longitude
Digital Surface Model (DSM):
Defines the air/surface
interface it includes trees,
buildings etc.
Digital Terrain Model (DTM):
Reflects the pure terrain
information as it is represented
on contour maps. Usually
produced by filtering the raw
DSM data as shown
Digital Landscapes
„
„
Digital surface models with additional information like
colour and texture that produce a more realistic (or
effective) representation
Both DEM’s and DSM’s are considered to be 2½ D
representations as they contain only a single elevation
value, whereas in reality each point may contain a
multitude of surfaces
…
…
…
Tree canopy
Building roof
Ground
16
Image Analysis
„
The fine structure of the pulse echo yields information
about the vertical structure of the surface
…
…
…
…
„
„
Roughness
Height and shape of manmade objects
Tree canopy height
Tree canopy density
Reflectivity properties can be analysed to produce
images similar to those available from infrared cameras
(albeit with lower resolution)
Most DTMs are made in conjunction with high resolution
passive multi-spectral images that rely on external
sources of lighting
Transformed Topological Image
17
Intensity, Hugh
Saturation (IHS)
Image
„
„
Elevation determines the
colour (hue)
Reflectivity determines the
brightness (intensity)
Building Topology
„
„
Individual buildings can be
resolved to an accuracy of
between 0.5 and 2m
Can resolve
…
…
…
Individual building footprints
Building height
Roof shape
18
Flood Simulation
Tides, Dikes
and Flooding
19
Sea Bottom Profiling
„
„
„
„
„
„
„
„
„
Laser Airborne Depth Sounder (LADS
Mk II)
Laser altimeter measures aircraft
height
GPS/INS measures aircraft position
Blue-green laser firing 900 pulses/s
measures the water depth to 70m
Sounding density 2m x 2m
Position accuracy <5m CEP 95%
Swathe width 240m
Coverage 64 sq km/hr
Direct link to NOAA satellite allow the
system to avoid areas of turbidity
Light Penetration Through Water
20
LADS Sea-Bottom Profile
LADS Aircraft over Sydney
Sow and Pigs Reef and the Western Channel
2D Laser Scanners for Collision Avoidance and
Navigation
Laser Scanner
Laser Scan While Driving
21
3D Scanners
Pan/Prism Scanner
Pan/Tilt Scanner
Imaging
Hue encoded helicopter image
22
CAD-CAM Rapid Prototyping
CAM Model
Original
Volume Estimation
Combine to form a
point cloud image
Target
Scan the target from
different positions
Resample onto a uniform grid
and calculate the volume
23
Reverse Engineering
Millimetre Wave Radar Mirror Scanner
„
„
„
Laser performance is degraded in
bad weather or in dust and smoke
An alternative is to use millimetre
wave radar even though the
angular resolution is lower
Radar has the advantage of
illuminating multiple targets within
the beam simultaneously
…
…
„
Increases update rate
Foliage penetration and evaluation
Typical specifications
…
…
…
Range resolution 25cm
Beamwidth 1°
Scan rate >1Hz
24
Image Comparison
3D Perspective Movie
25
Pulsewidth Limited Imaging
„
„
Includes 2D Ultrasound
Imaging and Radar Imaging
This method will be dealt with
in detail in the chapters on
Phased Arrays and Synthetic
Aperture Radar
26
Acoustic Microscopy
„
The
Scanning
Acoustic
Microscope (SAM) produces
images by scanning a
focussed beam of acoustic
energy (sound) across a
sample to measure its
elastic properties
Magnification
Low
Medium
High
Acoustic image of
the interior of a
plastic potted IC
Tracking insect Swarms
27
The Problem
„
„
To understand the behaviour of swarms of insects is a
crucial step in the process of minimising the devastation
caused by these pests during their relentless advance
across the land.
Previous attempts to track individual insects have been
both expensive and time consuming as they involved
tagging individuals with small wireless beacons and then
pinpointing their position periodically using radio location
devices and GPS.
The Solution
„
„
„
„
Design an alternative, less
manpower intensive and more
effective method of tracking
both individual, and groups of
insects as follows:
A number of insects are
captured and each tagged with
a small patch of an efficient
retro-reflective material.
A laser based push-broom
scanner is developed to
pinpoint the range and scan
angle
In conjunction with a helicopter
or fixed-wing aircraft fitted with
a GPS/INS, pinpoint the
positions of the tagged locusts.
Helicopter with
push-broom scanner
Detail of Locust
with Retroreflector
Locust Swarm
28
Laser Specifications
„
Scanner Requirements
…
…
„
Operational height
Swathe width
h = 1000m
x = >1000m
Laser Specifications
…
…
…
…
…
…
…
Wavelength
Average power
Pulsewidth
PRF
Beam divergence
Tx Aperture
Rx Aperture
Pp =
λ = 905nm +/-5nm (near infrared)
Pave = 2mW (eye safe?)
τ = 20ns
fp = 10kHz
θb = 2mrad
dtx = 50mm diameter
drx = 50mm diameter
2 × 10-3
Pave
=
= 10W
τ . f p 20 × 10-9 × 104
System Block Diagram
„
„
„
„
A faceted mirror rotates at high
speed and scans the laser beam
across the ground.
Reflections from the
retroreflectors on the locusts and
returns from the ground are
detected by the receiver and
digitised.
A processor determines the
position of each retroreflector from
the measured range and angle of
the beam in conjunction with the
instantaneous position and
attitude of the aircraft as
measured by the GPS and Inertial
Measurement Unit (IMU).
The data can be stored on an
onboard hard drive (HD) or
communicated the the ground
through a wireless modem.
29
Maximum Angular Scan Rate
„
The angle subtended by a swathe width of x = 1000m from a
height of h = 1000m is
500
x/2
= 2 tan −1
= 53°
1000
h
θ s = 2 tan −1
„
„
„
Angle doubling suggests a 12 faceted mirror with 30° between
facets to generate a 60° scan swathe width
Need 50% overlap to ensure coverage. Hence, the beam should
scan 1mrad (half the beam divergence) between pulses.
The maximum angular scan rate is therefore determined by the
following
θ& =
„
θb
2
fp =
2 × 10-3
× 10000 = 10 rad/s
2
The beam scans through 60° (1.05 rad) in 1.05/10 = 0.105s
Maximum Allowable Forward Velocity
„
At a height of h = 1000m, the diameter of the footprint on the
ground is xf = θbh = 2m. Therefore to provide for the same 50%
overlap that was achieved for the cross-range scan, the aircraft
can advance by xf /2 = 1m in 0.105s, which equates to a forward
velocity of 9.5m/s
1
N+1
2
n
r Sca
Mirro
60deg
Aircraft
Motion
N
Beam Footprint
30
Footprint Area
„
The maximum operational range required of the laser is at an offset
angle of 30°. For h = 1000m, this corresponds to
1000
= 1155m
cos 30
rmax =
„
The spot size on the ground is will be slightly elliptical with a minor
axis diameter of
d min = rmaxθ b = 1155 × 2 × 10 -3 = 2.31m
„
and a major axis diameter of
rmaxθb 1155 × 2 × 10-3
=
= 2.66m
cos 30
0.866
d maj =
„
Making the total area of the footprint
Af =
πd min d maj
4
= 4.86m2
Laser Power Density on the Ground
„
The power density of the beam on the ground at the maximum
operational range is just the peak power divided by the footprint area
Si =
Pp
Af
=
10
= 2.06 W/m 2
4.86
31
Power Density of Retro Reflected Signals
Back at the Receiver
„
The total reflected power is the product of the incident power density,
Si and the patch area, Apat. Assuming that the reflected light is
scattered uniformly over the hemisphere, the power density back at
the camera is given by
S r = Si Apat .
„
„
1
2πR 2
Because the patch is retroreflective, when it is illuminated, the
simplest model is to assume that it becomes an antenna that is
diffraction limited by its aperture.
The gain of such an antenna is just the ratio of the power radiated in
a specific direction relative to the isotropic. The power density back
at the laser receiver will be
Retroreflective
patch 5x5mm
S r = Si Apat .
1
G pat
2πR 2
Relationship Between Gain and Aperture
„
The relationship between the aperture, Apat, and
the gain, Gpat, of a diffraction limited antenna is
G pat ≈
4πApat
λ2
32
Calculating the Retro Reflected Power
Density at the Receiver
„
Substituting for the gain
2
4πApat
S r = Si
„
λ
2
For a square retroreflective patch with dpat = 5mm, the formula
becomes
4
4πd pat
S r = Si
„
λ
2
1
2πR 2
The optical cross section, σ, is defined as the ratio by which the
power density at the receiver exceeds that of an isotropic scatterer.
Therefore
4
−3 4
σ=
„
1
2πR 2
4πd pat
λ
2
=
(
4π × 5 × 10
(905 × 10 )
)
−9 2
= 9526m 2
Making the equation
S rr = Siσ
1
1
= 2.06 × 9526 ×
= 2.34 × 10- 3 W/m 2
2
2πR
2π × 11552
Calculating the Backscattered Power
Density at the Receiver
„
The physical cross section of the footprint on the
ground is Af = 4.86m2 and the backscatter coefficient
ρ = 0.1 (see Table 3.1) which makes the backscattered
power density at the receiver
S rg = Si A f ρ .
1
1
= 2.06 × 4.86 × 0.1 ×
= 1.19 × 10 − 7 W/m 2
2
2πR
2π × 11552
33
Signal to Noise Ratio due to Laser
Backscatter from the Ground
„
The ratio of the power density at the receiver due to the
retroreflector and that of the ground backscatter
SNR = 10 log10
„
2.34 × 10 −3
S rr
= 10log10
= 42.9dB
1.19 × 10 − 7
S rg
This in more than adequate to ensure that the correct
signal is detected
Noise from the Sun
„
Over the full band from 300nm to 2500nm, the total
power density is obtained by determining the integral
under the curve. This is approximately 1000W/m2.
34
Effect of Optical Filter
The specified wavelength for a typical laser range finder is stated
as 905+/-5nm. Hence an optical filter with a bandwidth of 10nm
would be sufficient. Such filters can be acquired from a number
of optics suppliers, and have the following specifications
Full width half max (FWHM)
λb = 10+/-2nm
Efficiency
τo = 0.7
„
„
„
For an incident flux of 0.6Wm-2nm-1 at λ = 905nm, the total power
density will be
„
Sis = 0.6λb = 6W/m 2
So the total power density back at the laser receiver is, once
again, determined by the area of the footprint on the ground, the
backscatter coefficient and the assumption of uniform scattering.
„
S rs = Sis A f ρ .
1
1
= 6 × 4.86 × 0.1 ×
= 3.47 × 10 − 7 W/m 2
2
2
2πR
2π × 1155
Signal to Noise Ratio due to backscatter
from the Sun
„
The ratio of the power density at the receiver due to the
retroreflector and that of the ground backscatter from
the sun
SNR = 10 log10
„
S rr
2.34 × 10−3
= 10log10
= 38.2dB
S rs
3.47 × 10− 7
This is slightly lower than the SNR from the laser
backscatter and so will define the SNR at the receiver
35
Power into the Receiver
„
„
The total power received is equal to the product of the power
density at the receiver, Srr, the receive lens aperture, Alens, and
the optical efficiency, τo.
Assume that the lens diameter is 50mm, which makes
Alens = 1.96×10-3 m2
Srr =2.34×10-3 W/m2 was determined earlier
τo = 0.7 from the specifications of the optical filter
Prec = S rr Alensτ o = 2.34 × 10 -3 × 1.96 × 10 −3 × 0.7 = 3.21 × 10 -6 W
Optics
Micro
Controller
Detection
Digital
Signal
Processor
Diode
Laser
Photo
Diode
Receiver
Optical
Filter
PIN Photodiode Characteristics
36
Photodiode Output
„
Note that the peak sensitivity (Responsivity) occurs at around 900nm
and is R = 0.53A/W. The maximum output current will therefore be
I rec = Prec R = 3.21 × 10-6 × 0.53 = 1.7 × 10-6 A
„
The signal to noise ratio is determined from the ratio of the received
current to Irec to the dark current Id
SNR = 20 log10
I rec
1.7 × 10−6
= 20log10
= 64.6dB
Io
10− 9
Current to Voltage Converter
„
„
Because it is more convenient to work with voltage, the output
current passes through an op-amp based current to voltage
converter before passing through a filter matched to the laser pulse
width.
The feedback resistor, R, is selected to produce a reasonable
output voltage. For example, by selecting R = 1MΩ, a peak voltage
of 1.7V would be produced for an input current pulse of 1.7μA
V+
Photodiode
R
i
+
Bandpass
Filter
Vo = iR
37
Matched Filter Effects
„
The transmitted pulsewidth is τ = 20ns, so the receiver bandwidth, β,
will be the reciprocal of that to a first approximation
β=
„
„
1
τ
=
1
= 50MHz
20 × 10− 9
An appropriately fast op amp would be required to drive the filter with
this short pulse
Assuming that the dark current comprises white noise which is
uniformly distributed over the 200MHz bandwidth of the photodiode,
then by placing a matched filter with a bandwidth of 50MHz at the
output, the SNR is improved by the ratio of the total bandwidth to the
filter bandwidth
200
= 70.6dB
10 50
SNR = 64.6 + 10 log
Effects of Square law Detector on input
SNR
„
It can be shown that the effective signal to noise ratio
out of a square law detector is also squared, so the
SNR of the retroreflector return compared to that from
the sun will increase from 38.2dB to 76.4dB
38
Conclusions
„
In this example, it can be seen that the retroreflective
return will easily be visible above the returns from the
backscattered laser signal, the backscatter from the
sun and the dark current. The signal to noise ratio of
64.6dB is limited by the photodiode dark current
Helicopter with
Strobe & Camera
Detail of Locust
with Retroreflector
Locust Swarm
39