1

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

2

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

3

Range Gate Limited Imaging

Laser Radar Performance Analysis

4

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

5

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 ==

6

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

7

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

8

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

9

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

10

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 =

11

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

12

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

=××

=×

=−

13

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

14

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

15

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

16

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

17

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

18

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

19

Flood Simulation

Tides, Dikes and Flooding

20

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

21

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

22

3D Scanners

Pan/Prism Scanner Pan/Tilt Scanner

Imaging

Hue encoded helicopter image

23

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

24

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

25

Image Comparison

3D Perspective Movie

26

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

27

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

28

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

29

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.

30

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

31

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

32

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 ≈

33

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

34

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.

35

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

36

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

37

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

38

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

39

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