05Lec - Active Imaging Sensors.pdf
Transcript of 05Lec - Active Imaging Sensors.pdf
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TIME OF FLIGHT IMAGING
TIME OF FLIGHT IMAGING
Differences between Beamwidth and Pulsewidth/ Range Gate ImagingBeamwidth Limited Imaging
Push Broom Airborne Laser ScannersCollision Avoidance Laser Scanners3D Pan/Tilt and Pan/Prism Laser Scanner3D Mirror Millimetre Wave Radar ScannerPulsed Time of Flight Laser Analysis
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Measurement Modes
Beamwidth LimitedGood for complex surfacesResolution limited to the beamwidth spot sizeSlow processGood for narrow beam lasers
Range Gate LimitedRestricted to flat areasCross-range resolution determined by beam widthRange resolution determined by the gate sizeFast processGood for wide beam radars
Each range gate generates a unique pixel in the radar image
Beamwidth Limited Imaging
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Range Gate Limited Imaging
Laser Radar Performance Analysis
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Power Density on the Target
( ) 22 44
4 BWI R
PSθππ
π=
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
The power density at the target assuming an isotropic radiator
Power Density Back at the Receiver
The backscatter coefficient dependent on the target material etc.
The area of the beam footprint on the target assuming that the target is larger than the beam
( )( ) 2
222 2
144
44 R
RRPS BW
BWR π
ρθπθππ
π=
The reflected power is scattered equally over the forward hemisphere of 2πsteradians
Note: If the target is a retro reflector thenρ can be much larger than 1 to compensate for the assumption that the target scatters equally over 2π steradians
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Received Power
( )( ) oBW
BWA
RR
RPS τ
πρθπ
θππ
π 22
22 21
444
4=
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
2RPAS o
πρτ
=
Simplifies to
Target Smaller than the BeamIn 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
For optical systems the 1/e = 0.367 power level is used to define the beamwidth which equates to the following
242
2
BW
o
RPA
Sθπστ
=
DDBWλλθ ≈=
05.1ADBW 4
2
2
22 πλλθ ==
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Range Equation for Small Targets
Substituting for the beamwidth θBW the received power is given by the following formula
W243
28λπστ
RPA
S o=
Laser ReceiversDirect detection laser receivers convert the received laser echo directly into a voltage or current using a PIN diode or avalanche photodiode
Heterodyne receivers down-convert the received signal using a stable laser local oscillator Low frequency signals can then be amplified and filtered to enhance detection probability
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Photovoltaic DetectorsPhotovoltaic effect consists of the generation of a potential difference as a consequence of the absorption of radiationThe 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 interfacesFor a material with a conversion efficiency η, the average current (amps) produced by a light beam with optical power, P is as follows
As the output current is proportional to the input power, this is a square lawdetector
A hfePi η
=
Silicon
Photodiode TypesPIN Photodiode
P-Intrinsic (lightly doped)-N structureDepleted region made as large as possible to minimise recombinationResponsivity 0.5 to 1 A/W
Avalanche PhotodiodeElectrons and holes released by absorbed photons accelerate and strike neutral atoms freeing more “secondary” carriersResponsivity 0.5 to 100 A/WNeed high voltage (up to 300V for Si) and are temperature sensitiveMore complex circuitry, and less reliable than PINs
PIN Photodiode
Avalanche Photodiode
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Photodiode CharacteristicsCan 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
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Noise Level of a Direct Detection ReceiverThe receiver noise level for a direct detection laser radar can be related to the specific detectivity of the detector D* using the following formula
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
*)( 2/1
DfA
N dΔ=
Noise Level of an Heterodyne ReceiverThe noise spectral density of an ideal receiver comprising both thermal and photon noise is given by the following
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)
hfe
hff kThf +−
=1
)( /ψ
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Noise Power Spectral Density
hff =)(μ
kTf =)(γ
Noise Power Spectral DensityFor microwave radars, the noise power density is determined by the thermal noise floor γ(f) = kTIn the infrared, the noise power density is determined primarily by the photon noise μ(f) = hfThe noise level of an heterodyne receiver can therefore be written as
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)
ηhfBN =
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Cross section of Glint TargetsGlint targets represent returns from corner reflectors or normal surfaces (such as the ground) where there is a single dominant scattererReturns are generally fairly constant from pulse to pulseThe laser radar cross section for a square corner reflector is given by the following formula
Where: σ - Cross section (m2)D – Side of the reflector (m)
2
4
34λπσ D
=
Signal to Noise Ratio
Pd and Pfa
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ExampleAn 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 densityIs 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-reflectorIf 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
So the diameter will be
d = RθBW = 3.844x108x22.3x10-6 = 8556m
The power density of the signal on the moonAfoot = πd2/4 = 57.5x106 m2
SI = P/Afoot = 500/57.5x106 = 8.7μW/m2
radDBW μλθ 3.22
5.0106.1005.105.1 6
=××
=×
=−
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Example (continued)The power density back on the earth from the retro reflector
The effective cross section of the retro-reflector is
So the power density back on earth is found by applying the range equation
( )226
26
4
2
47.65107.3
106.103
1.0499.03
499.0 dBmmD=×=
××
×==
−
πλπσ
( ) ( )217
26482
6
242 /1045.3103.2210844.3
107.350022 mWRPS
BWR
−
−×=
×××
×××==πθπ
σ
Example (continued)The power density back on earth from the signal reflected from the surface of the moon
Which is 10x higher than that obtained from the retro reflector
( )216
282 /1015.210844.3
2.0500 mWR
PSR−×=
×
×==ππ
ρ
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Example (continued)What is the signal to noise ratio
The matched filter bandwidthβ = 1/τ = 10Hz
The noise floor is determined by photon noise and a detector with a quantum efficiency of 0.5
For an optical efficiency of 100%, the received signal power is the product of the power density and the lens apertureS = SRπd2/4 = 2.15x10-16x0.196 = 4.21x10-17 W
So the SNR is S/N = 112 (20.5dB)
WhchfN 196
8341075.3
106.105.01010310625.6 −
−
−×=
××××××
===ηλβ
ηβ
Fine Range Measurement
Coarse time is measured using a digital clock which is stopped when the echo pulse exceeds a fixed thresholdSamples of the direct pulse and the delayed pulse voltages are made at the following clock leading edgeA delay line discriminator determines the pulse position with respect to this leading edgeThe clock count and the discriminator output are added to determine the true rangeAccurate to a fraction of the pulse length
ReceivedPulse
Vthresh
Clock
Stopcounting
EnableS&H
Lastcount
N
Delayed pulseDirect pulse
Vdir
Vdel
SampleandHold
ΔR = --------------Vdir - Vdel
Vdir + Vdel
Range = K x Count(N) + J x ΔR + Offset
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Push Broom ScannersRotating prism scans the laser beam at
right angles to the direction of travelBetween 2000 and 8000 laser pulses
are generated every secondBecause the ground is rough, some
power is reflected back to the receiverBy registering the forward motion of the
aircraft using GPS/INS and the beam angle, a 2D raster is producedRange and /or reflected signal
amplitude are logged to produce an image of the ground
Scanner Unit Operational Principle
Surface ModelsA digital image is a rectangular array of cells where each cell contains a single value
Topological images are produced when height information is storedReflectivity 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
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Digital Model DefinitionsDigital Elevation Model (DEM): A continuous mathematical representation describing the shape of the surface of the earth as a function of latitude and longitudeDigital 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 LandscapesDigital surface models with additional information like colour and texture that produce a more realistic (or effective) representationBoth 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 canopyBuilding roofGround
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Image AnalysisThe fine structure of the pulse echo yields information about the vertical structure of the surface
RoughnessHeight and shape of manmade objectsTree canopy heightTree 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
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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 2mCan resolve
Individual building footprintsBuilding heightRoof shape
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Flood Simulation
Tides, Dikes and Flooding
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Sea Bottom ProfilingLaser Airborne Depth Sounder (LADS Mk II)Laser altimeter measures aircraft heightGPS/INS measures aircraft positionBlue-green laser firing 900 pulses/s measures the water depth to 70mSounding density 2m x 2m Position accuracy <5m CEP 95%Swathe width 240mCoverage 64 sq km/hrDirect link to NOAA satellite allow the system to avoid areas of turbidity
Light Penetration Through Water
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LADS Sea-Bottom Profile
Sow and Pigs Reef and the Western Channel
LADS Aircraft over Sydney
2D Laser Scanners for Collision Avoidance and Navigation
Laser Scanner
Laser Scan While Driving
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3D Scanners
Pan/Prism Scanner Pan/Tilt Scanner
Imaging
Hue encoded helicopter image
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CAD-CAM Rapid Prototyping
Original
CAM Model
Volume Estimation
Target
Scan the target from different positions
Combine to form a point cloud image
Resample onto a uniform grid and calculate the volume
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Reverse Engineering
Millimetre Wave Radar Mirror ScannerLaser performance is degraded in bad weather or in dust and smokeAn alternative is to use millimetre wave radar even though the angular resolution is lowerRadar has the advantage of illuminating multiple targets within the beam simultaneously
Increases update rateFoliage penetration and evaluation
Typical specificationsRange resolution 25cmBeamwidth 1°Scan rate >1Hz
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Image Comparison
3D Perspective Movie
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Pulsewidth Limited Imaging
Includes 2D Ultrasound Imaging and Radar ImagingThis method will be dealt with in detail in the chapters on Phased Arrays and Synthetic Aperture Radar
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Acoustic MicroscopyThe Scanning Acoustic Microscope (SAM) produces images by scanning a focussed beam of acoustic energy (sound) across a sample to measure its elastic properties
Acoustic image of the interior of a plastic potted IC
Magnification
Low
Medium
High
Tracking insect Swarms
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The ProblemTo 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 SolutionDesign 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 angleIn conjunction with a helicopter or fixed-wing aircraft fitted with a GPS/INS, pinpoint the positions of the tagged locusts.
Helicopter withpush-broom scanner
Locust Swarm
Detail of Locustwith Retroreflector
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Laser SpecificationsScanner Requirements
Operational height h = 1000mSwathe width x = >1000m
Laser SpecificationsWavelength λ = 905nm +/-5nm (near infrared)Average power Pave = 2mW (eye safe?)Pulsewidth τ = 20nsPRF fp = 10kHzBeam divergence θb = 2mradTx Aperture dtx = 50mm diameterRx Aperture drx = 50mm diameter
10W 101020
102 . 49-
-3
=××
×==
p
avep f
PPτ
System Block DiagramA 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.
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Maximum Angular Scan RateThe angle subtended by a swathe width of x = 1000m from a height of h = 1000m is
Angle doubling suggests a 12 faceted mirror with 30° between facets to generate a 60° scan swathe widthNeed 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
The beam scans through 60° (1.05 rad) in 1.05/10 = 0.105s
°=== −− 53 1000500tan22/tan2 11
hx
sθ
rad/s 10 100002102
2
-3
=××
== pb fθθ&
Maximum Allowable Forward VelocityAt 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
AircraftMotion
Beam Footprint
1
2
N
N+1
Mirror Scan
60deg
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Footprint Area
The maximum operational range required of the laser is at an offset angle of 30°. For h = 1000m, this corresponds to
The spot size on the ground is will be slightly elliptical with a minor axis diameter of
and a major axis diameter of
Making the total area of the footprint
1155m 30cos
1000max ==r
2.31m 1021155 -3maxmin =××== brd θ
2.66m 0.866
1021155 30cos
-3max =
××== b
majrd θ
2min 4.86m 4
== majf
ddA
π
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
2 W/m2.06 4.8610 ===
f
pi A
PS
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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
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
221.R
ASS patir π=
patpatir GR
ASS 221.π
=
Retroreflectivepatch 5x5mm
Relationship Between Gain and Aperture
The relationship between the aperture, Apat, and the gain, Gpat, of a diffraction limited antenna is
2
4λπ pat
pat
AG ≈
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Calculating the Retro Reflected Power Density at the Receiver
Substituting for the gain
For a square retroreflective patch with dpat = 5mm, the formula becomes
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
Making the equation
22
2
214R
ASS pat
ir πλπ
=
22
4
214R
dSS pat
ir πλπ
=
( )( )
229
43
2
4
9526m 10905
1054 4
=×
××==
−
−πλπ
σ patd
23-22 W/m102.34
11552195262.06
21
×=×
××==ππ
σR
SS irr
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
2722 W/m1019.1
1155210.14.862.06
21. −×=
××××==
ππρ
RASS firg
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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
This in more than adequate to ensure that the correct signal is detected
42.9dB 1019.11034.210log log10 7
3
1010 =××
== −
−
rg
rr
SSSNR
Noise from the SunOver 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.
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Effect of Optical FilterThe 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 specificationsFull width half max (FWHM) λb = 10+/-2nmEfficiency τo = 0.7
For an incident flux of 0.6Wm-2nm-1 at λ = 905nm, the total power density will be
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.
26W/m 6.0 == bisS λ
2722 W/m1047.3
1155210.14.866
21. −×=
××××==
ππρ
RASS fisrs
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
This is slightly lower than the SNR from the laser backscatter and so will define the SNR at the receiver
38.2dB 1047.31034.210log log10 7
3
1010 =××
== −
−
rs
rr
SSSNR
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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 earlierτo = 0.7 from the specifications of the optical filter
W103.21 0.7101.96102.34 -63-3 ×=××××== −olensrrrec ASP τ
MicroController
Detection
DigitalSignal
Processor
DiodeLaser
PhotoDiode
Receiver
Optics
OpticalFilter
PIN Photodiode Characteristics
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Photodiode OutputNote that the peak sensitivity (Responsivity) occurs at around 900nm and is R = 0.53A/W. The maximum output current will therefore be
The signal to noise ratio is determined from the ratio of the received current to Irec to the dark current Id
A 101.7 0.53103.21 -6-6 ×=××== RPI recrec
64.6dB 10
107.120log log20 9
6
1010 =×
== −
−
o
rec
IISNR
Current to Voltage ConverterBecause 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+
-
+Bandpass
Filter
R
i
Vo = iR
Photodiode
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Matched Filter Effects
The transmitted pulsewidth is τ = 20ns, so the receiver bandwidth, β, will be the reciprocal of that to a first approximation
An appropriately fast op amp would be required to drive the filter with this short pulseAssuming 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
50MHz 102011
9 =×== −τ
β
70.6dB 50200log106.64
10=+=SNR
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
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ConclusionsIn this example, it can be seen that the retroreflectivereturn 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 withStrobe & Camera
Locust Swarm
Detail of Locustwith Retroreflector