Warsaw University of Technology

Institute of Aeronautics and Applied Mechanics

Department of Automation and Aeronautical Systems

2014

Presented By : Sumit Singh

M.Sc Aerospace Engineering

Supervised By : Professor

Janusz Narkiewicz D.Sc, Ph.D

1/13/2014

Laser Scanner - Principle of Operation, Application in Navigation

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List of Symbols = Area, illuminated by the laser beam

c = Speed of light

D = Beam diameter at its source

Dr = Aperture diameter of the receiver

LASER = Light Amplification by the Stimulated Emission of Radiation

n = Index of refraction

nsys = system transmission factor

natm = Atmospheric transmission factor

Pr = Power of radar

Pt = transmitted power

R = Total time in second case of calculation

S = Distance

T = Total time in first case of calculation

t = Time

v = Frequency of light

= Angle of incidence

t = Laser width

= wavelength of light

= angle of light emitted by a laser medium with a single mirror

= Cross-section of the target

= Scattering angle of the target

= Intensity distribution of a beam

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Table of Contents List of Symbols ........................................................................................................................................ 2

1. Introduction ........................................................................................................................................ 4

2. Basic Theory of Laser Scanner............................................................................................................. 5

2.1 Light ............................................................................................................................................... 5

2.2 Light Propagation .......................................................................................................................... 6

2.3 Building a LASER ............................................................................................................................ 7

2.3.1 Population Inversion .............................................................................................................. 7

2.3.2 Light Amplification ................................................................................................................. 7

2.3.3 Beam Characteristics .............................................................................................................. 8

2.3.4 Wavelength ............................................................................................................................ 8

2.3.5 Laser Types ............................................................................................................................. 9

3. Principle of Operation ......................................................................................................................... 9

3.1 Time of Flight ................................................................................................................................ 9

3.2 Triangulation ............................................................................................................................... 10

3.3 Principle of operation of an Airborne Laser Scanner .................................................................. 11

3.4 Block Diagram of an Airborne Laser Scan System ....................................................................... 12

4. Application ........................................................................................................................................ 13

4.1 General Application .................................................................................................................... 13

4.2 Airborne Laser Scanning intensity data correction ..................................................................... 13

5. Problem and Solution ....................................................................................................................... 15

5.1 Assumptions ................................................................................................................................ 15

5.2 Diagram of the problem .............................................................................................................. 15

6. Algorithms ......................................................................................................................................... 16

6.1 Flow Chart ................................................................................................................................... 16

7. MATLAB Script ................................................................................................................................... 17

7.1 Problem Solutions ....................................................................................................................... 17

8. Conclusion ......................................................................................................................................... 18

9. List of References .............................................................................................................................. 19

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1. Introduction

Laser scanning is basically a method of high accuracy mapping or reality

capture. Laser scanner is the device which precisely records three dimensional

information of a real object or environment. Laser scanner has two related but

separate meaning.

i. Controlled deflection of laser beams.

ii. controlled steering of laser beams followed by a distance measurement.

There are different types of scanner in the market but they work on the same basic

principle. A laser scanner emits rapidly pulsing or continuous laser beams. As it

emits the beam the scanner automatically rotates around its vertical axis, and a

rapidly spinning or oscillating mirror also moves the beam up and down, resulting in

a systematic sweeping of the beam over an area. When the beams hit an object

some of its energy bounces back to its scanner, where if the returned energy signal

is strong enough the sensor detects it. The inbuilt timer calculates the distance from

the scanner to the object.

Image-1 (Pulsing laser beams) Image-2 (Oscillating laser beams)

There are more to 3-D scanning than measuring distance. For each distance

measurement additional critical data is recorded including the corresponding

horizontal angle of the rotating laser and the corresponding vertical angle of the

moving mirror. The scanner automatically combines these to calculate a 3-D (X,Y,Z)

co-ordinates position for each point. The resulting scan is a set of 3-D co-ordinate

measurements. It's a detailed 3-D representation of the scene often called 'Point

Cloud'.

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2. Basic Theory of Laser Scanner

2.1 Light

In an atom the nucleus based electrons occupy certain orbits revolving around

the proton. When some energy is added to the atom electron jumps to a new orbit

away from the nucleus. Alternatively when an electron jumps closer to a nucleus the

atom releases energy. One of the most convenient way to release energy is as a

quantum of electromagnetic energy, a Photon. The energy carried by the photon is

equal to the transition energy. Photons of different wavelengths carries different

energy. The control of photon emission is critical for laser. There are two types of

photon emission.

i. Spontaneous

ii. Stimulated

Spontaneous Emission - This type of emission occurs all by itself and is the source

of virtually all light we see in nature, such as: the sun, the stars, the television

monitor, the fluorescent bulb. In the spontaneous emission if the electrons of an

atom are in an energy level above the lowest possible energy level then they can

drop down to a lower energy level, releasing energy often in form of light without

outside intervention.

Stimulated Emission - In such type of emission generally electrons are in higher

energy level. The excited atoms are forced to release their energy in form of light.

The provoked emission of light has the same wavelength and is precisely in phase

with the photon that generated it. In simple word the photon that hits the atom

generates another identical photon, which in turn stimulate another photon emission.

This is how the starter photon creates a cascade of stimulated emission which is

called LASER (Light Amplification by the Stimulated Emission of Radiation).

Image-3 (Cascade of stimulated emission)

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2.2 Light Propagation

The application of laser is closely related to the behaviour of light as it travels

through various material. When light is transmitted through solids, liquids, or gasses

the following propagation of light takes place.

i. Refraction - The part of the light projecting on the surface propagates

through the material. the beam of light changes direction at the point of

entrance to the new medium. Such phenomena is known as refraction.

ii. Reflectance - Part of the light falling on the surface is reflected back from the

surface.

iii. Absorption - Part of the light projecting on the surface is absorbed as it

propagates through material. The electromagnetic beam usually is converted

into heat.

iv. Scattering - In such case light gets diffused in many directions as light

projects on random distribution surfaces (like smoke or fog particles).

v. Polarization - The plane of oscillation of the light beam may change when

light projects on the surface.

Different materials creates different kinds of propagation. Reflectance and Refraction

are the two important light propagation. Refraction is directly related to the speed of

light as it travels through various material. In vacuum light travels faster 300,000

km/s. But when it travels through any material the velocity comes down to 299,920

km/s. Index of refraction (n) is an important measure to be taken into account which

is :

=

The index of refraction is always higher than 1. The wavelength of light is , the

frequency of light wave is v, and the velocity by which the light travels is c. And the

relation between these parameter can be described as =

. The frequency (v) of

light wave as it travels through different media as the velocity and wavelength

changes : =

. As the light passes through one transparent

medium to another transparent medium (air to water) the ray of light bends. The

angle of this light wave bending is called refraction, which is directly related to the

index of refraction. When the light wave passes through and gets back from the first

material the reverse refraction takes place. Reflectance also changes the travelling

direction of light. There are two types of refraction a) Specular b) Diffuse.

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2.3 Building a LASER

2.3.1 Population Inversion

The very basic of stimulated light emission is that the majority of light has to

be in high energy state, unfortunately this high energy state is not the default state

under thermodynamic equilibrium. That's why a prerequisite for Light Amplification by

the Stimulated Emission of Radiation (LASER) is that the distribution of light atoms

be altered so that more atoms become excited to emit energy and where the number

of excited atoms are more than low energy atoms which are ready to absorb energy.

This process of altering the energy distribution within atoms, making sure that most

of the atoms is in high energy state, is known as Population Inversion.

The basic step of creating popular inversion is by selecting the atoms and excite

them to a particular energy level. Light and electron techniques are the most

common technique for laser excitation. Population inversion often creates sublevels

of high and low energy level, which helps to form a multiline laser (multiple

simultaneous wavelengths). By the population inversion the laser medium gets

excited when it is hit by a photon and produces stimulated light.

2.3.2 Light Amplification

A starter photon triggers a cascade stimulated emission when a population of

laser material is inverted. The magnitude of cascading effect is proportional to the

distance light travels through the laser material. In order to build a bright laser light

the light has to travel long distance that is why an elongated rod of a laser material

can be used for bright light, to intensify the beam mirrors are placed in the path of

the laser light before it exits for the laser medium. The figure below shows the basic

principle of the laser rod operation.

Image-4 (Stimulated emission in a Laser rod)

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The formation of narrow laser beam is caused by the oscillation of light in a laser

cavity. The radius of the beam depends on the length, the light has travelled with in

the laser medium. Light emitted by a laser medium with no mirror can be defined by

an angle .

= Sin1( dn

2l ) (1)

Where, d = rod diameter, n = index of refraction of the laser material, l = length or

cavity of the rod.

Light emitted by a laser medium with a single mirror can be defined by an angle .

= Sin1( dn

4l ) (2)

2.3.3 Beam Characteristics

Across the laser beam the distribution of light is not uniform. Normally the

intensity of the laser beam is less in the sides and it is more bright in the middle.

Another characteristic of the beam is it's divergence which means the light spreads

out from the laser cavity. The angle of divergence , depends on the wavelength of

the laser , the beam diameter at its source is D.

Intensity distribution of a beam can be described by .

= Sin1(K

D ) (3)

K is a constant which depends on the distribution of light intensity in a cross section

of a laser beam.

2.3.4 Wavelength

Several factors are there which determine the wavelength of a laser emits.

The most important of them is the emitted laser wave length depends on the laser

material and its quantum properties. The wavelength of stimulated emission is

directly affected by the process of achieving popular inversion.

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2.3.5 Laser Types

According to the type of material used as a laser medium, a laser can be

divided into three different categories - 1) Gas Laser, 2) Solid - state Laser, 3)

Semiconductor Laser.

Laser Medium Main Wavelength

Other Wavelengths

Gas Helium-Cadmium vapour 441.6 nm 325 nm (UV)

Copper vapour 511 nm 578 nm

Solid-state Laser

Alexandraite 700-830 nm (IR) 325 nm (UV)

Erbium 1540 nm (IR) 850 nm (IR)

Semiconductor Laser

GaN/SiC 423 nm 405-425 nm

GaInPAs/GaAs 670-680 nm

3. Principle of Operation All of the measurement of distance of objects using the laser beam utilizes the

three basic attributes of laser light :

i. Clear light travels through straight lines.

ii. The velocity of light when travelling through space is known.

iii. The light produced by laser generally is a single wavelength light and that's

why it's easy to detect.

There are two traditional ways of measuring distance with laser :

i. Time-of-Flight.

ii. Triangulation.

3.1 Time of Flight

The principle behind this technique is to measure the total time (t) a laser

pulse takes to travel to an object and return to the receiver. Since the speed of light

(c) is known that's why it is possible to determine the distance travelled by the laser

pulse. Assuming the distance travelled is S, then the relation between distance

travelled, speed of light and time taken could be shown as following :

= (

2) (4)

In a Time -of-Flight (TOF) measurement system a scanner typically emits pulses of

laser electromagnetic radiation. The emitted pulse is focused, narrowed and pointed

at a targeted object. The object reflects part of the laser pulse electromagnetic

radiation back to the photosensitive sensor fixed on the scanner. An internal clock

measures the time take during the whole operation i.e. laser electromagnetic

radiation starting from the scanner and return back to the scanner after hitting by the

targeted object. A built-in microprocessor performs the aforementioned time-of-flight

measurements and reports the distance of the target object relative to the laser

scanner.

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Image-4 (Time-of-Flight Illustration)

In the Image-4 it can be seen that there is a little angle between laser emission and

reception but in reality it has negligible effect on the time-of-flight measurement. For

the high velocity of light it is possible to take thousands of measurements per

second. Multiple pulses are often used in a least square fitting to improve reliability.

Distance is then computed by comparing the phase shift between the emitted

wavelength and received laser pulse.

3.2 Triangulation

In such method two laser beams are used instead of one laser beam. There

are options to produce two laser beams 1) Using two laser scanner 2) splitting one

beam in two. The two beam intersect at the targeted object, the position of two laser

beam source is known. The angle formed at the intersection can be measured and

from this value it is possible to calculate the distance to the target object.

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3.3 Principle of operation of an Airborne Laser Scanner

Airborne laser scanner creates disk images of acquired 3-D data with the help

of many laser scanner combined with an attitude and position measurement system

on a platform mounted on an aircraft. The main goal of airborne laser scanner is to

take three dimensional data from earth's surface by taking the following

considerations into account -

1) Over large areas it is very time efficient for data acquisition.

2) In a common co-ordinate system the 3-D data registers automatically.

3) High accuracy and resolution of the registered data.

Normally an airborne laser scanning system comprises the following parts -

i. At least one laser scanner which offers full waveform echo digitalization and

provides a two dimensional line scan mode.

ii. A Global Navigation Satellite System (GNSS) which measures the attitude

and position of an aircraft with in the World Geodic System'84 (WGS84). At

least one terrestrial Global Positioning System (GPS) is mandatory in order to

acquire high quality GPS data.

iii. A software is normally used for monitoring of coverage and real time system

control.

iv. A software is also used to merge the scanned data with the position and the

orientation data of the scanning platform.

v. For the sensors a shock absorbing and rigid platform is necessary.

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3.4 Block Diagram of an Airborne Laser Scan System

System

Control

Airborne

Scanner

Shock absorbing rigid platform

IMU GPS

Antenna

Raw scan data Position and

attitude IMU/GPS

raw data

Terrestrial GPS-reference

network

GPS-reference network

raw data

Third party

IMU/GPS data

processing

software

Scan data

processing and

adjustment

Position and Attitude

Flight data in WGS84

Laser scan data in

WGS84

Airb

orne

Dat

a A

cqui

sitio

n

GP

S r

efe

ren

ce D

ata

Acq

uisi

tion

Dat

a P

roce

ssin

g

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4. Application

4.1 General Application

Nowadays laser technology is used in many areas starting from items we use

on daily basis. Instead of a needle to read data from a disk now days laser

technology is used to read data from a compact disk, such as music CDs. Bar code

scanner uses laser to illuminate barcodes to read special strips. Holograms are

produced by laser. Telecommunication data is transferred as a form of a pulsed laser

beams through fibre optic cables.

Laser is also used in corrective eye surgery which is achieved by quickly and

preciously burning the tissue of lens of the eye, correcting deformities that cause

myopia. By penetrating a laser deep into a tissue and coagulating a tissue area,

bleeding can be stopped. Harmful skin blemish are also removed by using laser

treatment. Laser is also used in spectrograph with the help of its controlled

wavelength and high resolution.

In military laser is also used to destroy short and medium range tactical missiles

with in the air before the missiles hit the ground. Military prefers laser as a defence

weapon for the capabilities of their fast retargeting an object by a speed of mach

velocities.

4.2 Airborne Laser Scanning intensity data correction

Airborne Laser Scanner (ALS) produces point cloud where each point cloud

has three coordinates (X,Y,Z) and which is determined using the following systems -

Global Navigation Satellite System (GNSS), Inertial measurement Unit (IMU) and

laser range finder. Laser scanning intensity values comprises number of photons

which are striking the detector, and they are recorded digitally. The intensity values

are also related to which comes back to the receiver. It is possible to use power

equation for radar as the basic physical operation is same for ALS and Radar.

Pr =PtDr

2

4R4t2 nsysnatm (5)

Where, Pr is the intensity or received power, Pt is the transmitted power, Dr is the

aperture diameter of the receiver, t is the laser width, nsys is system transmission

factor, natm is the atmospheric transmission factor, is the cross-section of the target. From the equation (5) it can easily be seen that the intensity or received

power is directly related to the power which has been transmitted, the atmospheric

and system transmission and the footprint of the laser beam.

The cross section of a laser beam can be explained with the equation below -

=4

(6)

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In the previous equation (6) is the scattering angle of the target, is reflectance of

the surface, is the area which is illuminated by the laser beam. can also be

written as a function of beam width and distance R, which is shown below -

=2

2

4 (7)

Substituting the value of from equation (7) to equation (6) one can obtain the following equation -

= 22cos () (8)

Substituting the value of into equation (5) one can obtain the following laser scanning intensity equation -

Pr =PtDr

2

4R2 nsysnatmcos() (9)

nsys is the optical transmission efficiency of any type of optical components in an

Airborne Laser Scanning (ALS) system. It is a constant value for certain ALS system

but may vary with different type of sensors. The Dr component also varies with

different type of sensors. The is an angle of incidence which is described as an angle between the surface normal and the incoming laser beam. The figure below

represents the Lambertian scattering of surface, topographic effect on angle of

incidence.

Image-5 (Topographic Effect)

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5. Problem and Solution A laser beam has to travel from point P1 to point P2. At the middle of both

points there is an obstacle circle. So the laser has to avoid the circular obstacle and

reach at point P2 from P1 and the total time elapsed during the whole process has to

be calculated.

5.1 Assumptions

Where distance between P1 and P2 is 100000 m, Diameter of the circle is

20000 m, Distance at first stopping point from P1 to S1 is (d1) = 30000 m. Distance

at second stopping point from S1 to S2 is (d2) = 22360.68 m (2 = 2 + 2),

Distance at third stopping point from S2 to S3 is (d3) = 22360.68 m. Distance at last

stopping point from S3 to P2 is (d4) = 30000 m. a = 20000 m, b = 10000 m.

Using the formula of Time of Flight =

2 the total time (T) taken by the laser to

travel from P1 to P2 has been calculated in Matlab. The Matlab script is given below.

Where S = distance, t = time, c = speed of light. Circular obstacle is an assumption.

5.2 Diagram of the problem

P1

P2

S1

S2

S3

a

b

F1

F2

k

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In the above diagram the time measurement has been calculated with the change in

distance at second time the first stopping point is F1 from P1 and the distance is

(m1) = (m4) = 20000 m, and distance from F1 to S2 is (m2) = 31622.7766 m = (m3).

As the

6. Algorithms

First of all using the Pythagorean formula 2 = 2 + 2), distance between

S1 and S2 then S2 and S3 has been calculated. Later using Time of Flight formula

=

2 time has been calculate. By adding each time the total time has been

calculated.

So, 1 = 2

=

2310^4

310^4= 2 10^(4) , in the same way all the other t2, t3, and

t4 has been calculated and added together to obtain the total elapsed time T, and r1,

r2, r3, r4 has been calculated and added together to obtain the total elapsed time R

for the time calculation with different distance.

6.1 Flow Chart

Input values of distances

d1, d2, d3, d4, m1, m2,

m3, m4

Application of formulas

2 = 2 + 2),

=

2 ,

Output values of times

t1, t2, t3, t4, T, r1, r2,

r3, r4, R

END

START

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7. MATLAB Script clc clear all %Distance between point P1 and P2 [meter] da = 10^5; %Distance between point P1 and first stopping point S1 and m1 [meter] d1 = 3*10^4; m1 = 2*10^4; %Distance between first stopping point S1/F1 and second stopping point S2

[meter] a = 2*10^4; k = 3*10^4; b = 10^4; d2 = sqrt(a^2+b^2); m2 = sqrt(k^2+b^2); %Distance between second stopping point S2 and third stopping point S3/F2

[meter] d3 = d2; m3 = m2; %Distance between third stopping point to point P2 [meter] d4 = d1; m4 = m1; %% Using Time of Flight formulation, calculating total time elapsed %Speed of light [meter/sec] c = 3*10^8; %Time taken to reach from point P1 TO S1/F1 [sec] t1 = (2*d1)/c r1 = (2*m1)/c %Time taken to reach from point S1/F1 to S2 [sec] t2 = (2*d2)/c r2 = (2*m2)/c %Time taken to reach from point S2 to S3/F2 [sec] t3 = (2*d3)/c r3 = (2*m3)/c %Time taken to reach from point S3/F2 to P2 [sec] t4 = (2*d4)/c r4 = (2*m4)/c %Total time elapsed to reach from point P1 to point P2 [sec] T = (t1+t2+t3+t4) R = (r1+r2+r3+r4)

7.1 Problem Solutions Case 1 Case 2

t1 [sec] t2 [sec] t3 [sec] t4 [sec] T [sec] r1 [sec] r2 [sec] r3 [sec] r4 [sec] R [sec] 2.0000e-004

1.4907e-004

1.4907e-004

2.0000e-004

6.9814e-004

1.3333e-004

2.1082e-004

2.1082e-004

1.3333e-004

6.8830e-004

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8. Conclusion After reviewing the above information on laser scanner it has been

understood that the total operation of laser scanner is dependent on laser and which

is dependent on the energy level of an atom. Propagation of light is very important is

laser scanning, different materials creates different kinds of propagation. In order to

build a bright laser light the light has to travel long distance that is why an elongated

rod of a laser material can be used for bright light, to intensify the beam mirrors are

placed in the path of the laser light before it exits for the laser medium. Time of flight

is the most common way to calculate distance between two objects, and where the

distance is known the time can be measured through this method, like the problem

which has been solved in the report. A starter photon triggers a cascade stimulated

emission when a population of laser material is inverted. By the oscillation of light in

a laser cavity the narrow laser in generally created. Across the laser beam the

distribution of light is not uniform. The most important of them is the emitted laser

wave length depends on the laser material and its quantum properties. The

wavelength of stimulated emission is directly affected by the process of achieving

popular inversion.

In the problem as the obstacle is a proper circle and it is situated at right middle of

both points P1 and P2 that is why it is easier to calculate the distance of the

divergence from point S1 (in first case) and from pint F1 (in second case). From the

calculated total time of the both cases it can be easily understood that if the laser

light divert from point F1 (according to the second case), then the laser light is taking

less time (R = 6.8830e-004 sec)to reach point P2 from Point P1 compared to the first

case of laser light divergence (T = 6.9814e-004 sec). This same method can be to

determine the distance between objects such as buildings, monuments, landscapes

etc, where time and speed of light shall be a known factor.

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9. List of References

1. http://repository.upenn.edu/cgi/viewcontent.cgi?article=1083&context=ci

s_reports

2. http://www.riegl.com/nc/products/principle-of-operation-

detail/poo/airborne-laser-scan-systems/

3. http://www.fig.net/pub/athens/papers/ts26/TS26_1_Schulz_Ingensand.p

df

4. http://www.fig.net/pub/athens/papers/ts26/TS26_1_Schulz_Ingensand.p

df