CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
INVESTIGATION OF LASER VEHICLE COLLISION AVOIDANCE SYSTEH
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Science in
Engineering
by
James Ben Farb
January, 1975
California State University, Northridge
January, 1975
ii
My sincere
Hashimoto for his
ap~~ecietion
to Professor Ichiro
encouragement~
eo:nsl.deration, advioe 1
and support throughout the formulation of this Nor!r.
I wish also to
tha~~
Professor Edmund S. Gillespie
and Professor Gary .T. Hardeman for their valuable comments
that contribut8d to the thoroughness of the thesis.
Finally, I would like to express my gratitude to my
colleagues at Hughes Aircraft 5 Warren Burd,
Dennis Grantham, and Thomas Miotke, for their many helpful
technical suggestions.
iij.
To Liliane) ·;,..ri th love, for her pe:!:'severance in
attending to cur
t~;o
children 1 and foJ:• her infinite
patience in spite of my prolonged periods of absenteeism
in pursuit of timely a.nd adequate completion of this
paper.
iv
Preface
ziii
Abstract
xiv
Chapter 1.
=
...1
Introduction
Chapter 2 - Metherr.atical Hodel of Freeway Traffic
Flow·
2.0
Scope
2.1
The
3
Car-.:b'ollcwing Model
3
Chapter J _, General Description of Vehicle
Collision Avoidance System
3~0
Scope
7
3.1
System Mathematical Model
7
3.1.1
Separation Distance Behreen Vehicles
8
3.1. 2
Measured Separatj.on Distance Between
8
Vehicles
3.1.3
Foll.m;ring Vehicle Relative Speed
9
J.1.4
System Vehicle Ca.:r• Follm'ling Law
9
3.1.5
Discussion of the System Car Following
10
Law
3.1.5.1
Case I:
3.1.5.2
Case II:
Steady State Case R
= dk
Measured Separation
10
11
Distance is Greater than Desired
Separation Distance
3.1.5.3
Case III:
Measured Separation
Distance is Less than Desired
Separation Distance
v
11
Discurssion of Figu:c<? 3-:L
).1.6
3 .. 1.6.2
!1
Sig;.'lal Processor - Speed Co:ntrollel"
11
Actual Vehicle Speed
12
3.2
General System Requirements
12
3-3
General Sensor .Requirements
17
3.-4
Automatic versus the Semi-Automatic
18
System
3o5
Tracking Distance Criteria
20
3.6 Vehicle Collision Avoidance System
21
3.6.1
General Overall Description
2:1.
).6~2
The Basic Tracking Plan
22
3. 6. 2 .1
Tracking the Car Ahead.
22
3.6.2.2
Tracking the Car Bchi.nd Following
24
Vehicle
3.6.2.3
Tracking the Cars on the Right and
Lei't Side
3.6.3
Initiating and Shutdown of the System
25
).6.4
Console Description
2.5
3.7 Reflector Description
28
).8
29
Sensor-Reflector Tracking
J.8.1
System Description
3.8.2
Tracking Problems
29
3.8.2.1
Tracking in Curves
30
).8.2.2
Road Dips and Bumps
30
J.8.2.J
Grades
31
vi
~
.J~
...
8 -~~··
? 4
Yehiclcs not Traveling i:r.:t the Center·
31
of the Lane
3.8.2.5
3~9
3.10
Possible False Reflections
Safety Requirements
Self Test Requirements
31
?. ..
.....t.
Chapter 4 - Laser Propagation Study
4.0
Introduction
32
4.1
Basic Assumptions of the Study
32
1~.2
Description of the Medium
33
l~.
3 Scattering Conditions
33
4.4 Rayleigh Scattering
33
4.5 Mie Scattering Theory
37
4.5.1
Introduction
37
4.5.2
Partj.cle Crossections for Extinction,
37
Scattering, and Absorption
4.5.3 Efficiency Factors
37
4.5.4 Scattering Amplitude Functi.on
39
4.5.5 The Nie Solution
4.5.5.1
The Results of the Nie Solution
41
4.6 Extinction Coefficient
42
4.7 Solution of the Scattering Equation
44
4.9
47
Optical Propagation of Laser Light in
the Medium
4.10 Laser Survey
48
vii
4.11 !Jism:ssion of the Resultz
48
Chapter 5 - Conclusions
61
Bibliography
64
viii
~'able
3-1
De:fini tion of Te:•ms
14
Table 4-1
Solid State Lasers -
Table 4-2
Solid State Lasers - CW Operation
Table
I•
~r-
Pul~ed
Operation
3 Semiconductor Lasers
Table 4-4
53
53
54
Tunable Lasers
55
Table
l~-5
Gas Lasers - Pulsed Operation
56
Table
L~-6
Gas Lasers - CW Operation
57
ix
Separation Distance
5
F'igure 3-1
System f1athem.atical Model Block Diagram
13
Figure 3- ').....
Block Diagram of the Vehicle Collision
23
~,ignre
2-1
Avoidro1ce System
Figure 3-3
Vehicle Collision Avoidance System
27
· Console Display
Figure
l}-1
Geometry of Rayleigh Scattering
3.5
Figure
4-~2
Mie Scattering Diagram
38
~
Figure 4-3
v~
versus
Figure 4-4
Y-4-~
Jt,igUI'e 4-5
'{~
Figure 4-6
Composite Graph
Figm:•e 4-7
·y~
Figu.re 5-1
v-~
.
for a = 5 microns
49
versus )-..
for a = 25 microns
.50
versus
for a =
50 microns
51
)\
52
versus )-.
Measured
60
versus ~
for a = 80 microns
63
X
i .
l,IS1J..1 01" ABBREVIATIONS
Symbol
Name
Micron
fo
Neodymium
Nd
Yttrium Aluminum Garnet
YAG
Doubled
Dbld
Gallium Aluminum Arsenic
GaA1As
Gallium Aluminum
GaAl
Nitrogen
N2
Argon
Ar
Transversly Excited Atmosphere
TEA
Transversly Excited
TE
Lithium Oxide
Li03
Carbon Dioxide
C02
Hydrogen Fluoride
HF
Carbon I1onoxide
co
Nitrogen Oxide
N20
Hydrogen Carbon Nitrogen
HCN
Water
H20
Neon
Ne
Hellium-Cadmium
He-Cd
Xenon
Xe
Krypton
Kr
Hellium-Neon
He-Ne
Argon/Krypton
Ar/Kr
xi
I!IST OF ABBHEVIA!J..'IONS
Name
Symbol
Hellium-Seleniurn
He ....se
Continuous Wave
cw
Cadmium Tellurim
CdTe
xii
PREFACE
The topic chosen for this paper was selected with
bm purposes in :nind:
1. To create a comprehensive
document wm•thy of presentation as a significant effort
for partial satisfaction of requirements for a Master of
Science in Engineering degree, and 2. To present an
adequate amount of information regarding the subject
system so that this paper may be used as an accurate
engineering document.
xiii
ABSTRAC'l'
INVESTIGA'I'ION OF LASER VEHICLE COJ...LISION AVOIDANCE SYSTEM
by
James Ben Farb
Master of Science in Engineering
t.Tanuary 1 197.5
The paper investigates the possibility of developing
an automatic vehicle collision avoidance system for autos
traveling on a freeway i:n dense fog.
The collision
avoidance system is comprised of two major components:
1. Speed. Cruise Contr·o1, and 2. A Laser Tracker.
With the
use of the value of "driver selected speed" from the Speed
Cruise Control, and range and range-·rate data from the
laser tracker, the system will automatically maintain a
safe separation distance between following vehicles.
First, a mathematical model was developed to describe
the empirical observation that a form of
11
t'lave phenomenon 11
exists in a long line of vehicles traveling on a highway.
The theory derived to analyze highway traffic movement
was a car-following model based on modern mathematical
technj.ques.
A model for the collision avoidance system
xiv
- was then postulated using-the above-method..
The necessary general requirements for the overall
system, sensor, reflector:; and tracking distance criteria
'\'iere then determined.
Then an examination of automatic
versus the semiautomatic system was rr.ade.
Based on the
above requirements a general description of the vehicle
collision avoidance system is presented along with a
detailed discussion of the basic tracking
plan~
The
reflector-sensor tracking problem is evaluated from which
self test requirements are then determined.
Next, a study was perf'ormecl to determine if it was
possible to propagate laser light through fog.
results of the study were:
The
1. Light is scattered at a
constant value and is independent of k'iavelength until fog
droplet radius equals the laser
~"Javelength,
and 2. The
amount ·of scattering is negligible when the value of laser
wavelength equals ten times the fog droplet radius.
Based
on a discussion of the results the conclusions are:
1. The system is not feasible with present technology,
and 2. Fog consists of large spherical droplets which
result in the scattering of light that is essentially
independent of wavelength.
XV
Introd.uc:tion
A survey of the literattire (8) (11) 1 revealed two
basic systems for automobile collision avoidance.
first system contained. a
~ad.ar
seeker.
The
After a target
is detected, the system is able to maintain a safe
separation distance
bet~'leen
follmving vehicles by
activating the brakes ru1d accelerator.
The system had
two major problems:
1. High susceptibility to false targets.
2. Inability to acquire a target in a cur·ve.
The second system also used a. radar tracker.
Each
car is required to have a passive reflector that would
reflect the second harmonic of the transmitted radar signal.
The major problems with this system were:
1. Inability to acquire a target in a. cuPve.
2. The system depended on the vehicle operator
to take the necessary corrective action.
In addition, both of the above described systems l'.rere not
tested under adverse weather conditions.
In this text, the optical approach is investigated to
determine \vhether a laser· can be used as the seeker of an
automatic vehicle collision avoidance system.
In
Chapter 3 a general description of this system is presented.
1.
(8) (11):
Reference numbers listed in bibliography.
1
After the system description is introduced, an a.'Yl.alysis
is conclucted. to determine if the las"'ilr' seeker is pra<Jtical.
The analysis should includ.e a consideration of the
following:
1. Scattering
2. Absorption
J.
Required laser power output
l.J..
Circuit response time
5. Required electromechanical device
reaction time
6. Required minimum received signal
strength at the sensor
7. Environment
An initial survey showed that, of the above, scattering
~ras
the most severe problem, because fog droplet radii
can be greater than or equal to laser \'lavelength.
Chapter 4 performs the study to determine if laser light
can propagate through dense fog.
In Chapter 5 conclusions
are determined based on the investigation conducted in
Chapter 4.
Prior to proceeding with the above, a mathematical
model of freeway traffic flow is developed.
a typical freeway.
This model
· CHAP'rER 2···
Mathematical :Hodel of Freeway Traffi.c F'low
2.0
SCOPE.
Chapter 2 is a development of a mathematical
model of traffic flow on a typical freeway.
The
technique used to analyze highway traffic movement ·is a
car-following model based on the theory developed by
L. A. Pipes (4).
Through the development of the
mathematical model of freeway traffic flow the following
parameters are determined:
1.
How does traffic basically flow on the
freeway.
2.
What are the mathematical expressions that
define traffic movement.
J.
Items 1 and 2 will determine how the
electronic system must function in order for
the driver of a car to "see" through the fog
while driving on the freewa;y.
The derived mathematical model defines:
2.1
1.
Distance of separation of following vehicles.
2.
The Car-Following Law.
THE CAR-FOLLOWING I10DEL.
Consider a straight road
with a line of n identical vehicles following each other.
Assume that the road coincides with the x-axis of an
x-y coordinate system.
of the lead car to be x 0
kth car xk+l •
At time t designate the position
the second car x 1 , and the
Now define the separation distance, dk ,
,
J
4
-between the xk and xk+l car to be (See ·Figure· 2.-._1).
( 2-1)
The distance between cars can also be thought of in the
follow·ing manner:
Every driver on the f'rem-Tay normally
maintains a following separation distance that is directly
I
proportional to the speed of the car, xk+ 1 , plus a
constant distance, S, of separation that existed between
cars at standstill.
Thus
or
(2-2)
where
T =Constant= 1.023 seconds per California Code.
Equating the tv;o expressions for dk contained in
Equations 2-1 and 2-2 results in
,
dk = xk - xk+1 = Txk+l + S
(2-3)
Next, postulate (Reference 4)
The above postulated equation is satisfied when the
quantity ~k= 0.
The condition, ~k= 0, occurs under
steady-state conditions of constant following vehicle
velocity.
However, under normal driving conditions, the
5
t
X
X
k-1
Separation Distru1ce
Figure 2-1
6
dynamic case, there are certain transients where the
driver tries to maintain a safe
follm·r~ng
d.is tance.
Driver
"II
response is finite a.:nd the acceleration of the car, xk+l ,
needed to maintain the fixed separation distance is a
function of the square of driver response.
response is represented by the term W0
•
Driver
\-1 0 is a
measure of the degree of uanticipation" or "response
frequency" of various drivers.
An increase in W0
corresponds to increasing the natural response frequency of
the driver.
Thus, the acceleration needed to maintain a
safe separation distance is directly proportional to
driver response;
and the postulated following vehicle accelerat:i.on needed
to maintain the safe separation distance is (Reference 4)
and (Reference 4)
(2-5)
k
= 0,
Equation 2-5 is the Car-Following Law.
1, 2, ••• (n-1)
CHAPTER 3
General Description of' Vehicle Collj.sion Avoidance System
J.O
SCOPE.
This chapter describes, in general terms, the
basic.features of the Vehicle Collision Avoidance System.
Throughout the remainder of this paper the Vehicle
Collision Avoidance System (VCAS) will be referred to as
the "system" or liVCAS 11 •
plan.
Introduced is the basic tracking
This section discusses the following three topics:
1.
System tracking of the vehicle in front of
the car
2.
System tracking of the vehicles around the
car
J.
System initiation and shutdown
In addition, general requirements and assumptions of the
overall system are speclfied.
A discussion of
semiautomatic versus an automatic system is conducted and
a choice made.
Tracking distance criteria is established
and a general discussion of tracking sensor requirements
is provided.
feature.
Also mentioned is the system Self Test
Before presenting the above mentioned topics, a
system mathematical model is constructed.
This model uses
the mathematical expressions derived in Chapter 2 to
J.l
SYSTEM MATHEMATICAL MODEL.
---
This section develops a
---
system mathematical model to describe the VCAS.
The (7)(9)
definition of a mathematical model is an equation.
7
The
8
·equation to· be developed is based on expressions from
Chapter 2.
A System Mathematical Model Block Diagram is
shov-m in Figura 3-1.
Table 3-1 defines the quantative
values in Figure 3-1.
3.1.1
SEPARATION DISTANCE BETtvEEN VEHICLES.
Based on a
survey of the literature (5) (6) the desired separation
distance, dk , between following vehicles is
dk
=
30 ll'eet + Vehicle speed in NPH
or
dk -- 30
+
( 3-1)
(2/3) vk+l
Where
Vk+l
=
Speed of the following vehicle
2/3
=
Conversion factor from feet/second
to f1PH
3.1. 2
MEASURED SEPARATION DISTANCE BET\vEEN
~HICLES.
The
VCAS system via the sensor measures the actual range, R
(in feet), between following vehicles.
This will differ
slightly from the true range, R 1 (in feet), due to minor
system measuring errors.
No'l'r, the system vTill try to
make
or for
R
=
R
~
dk
(3-2)
then
(3-3)
Thus, the system will tend to make R - dk approach zero,
9
and when R = dk the desired and. actual separation distance
has been achieved.
3.1.3 FOLLOWING VEHICLE HELATIVE SPEED.
In addition to
lead vehicle range, the sensor provides range-rate
,
The range-rate, R, is the relative
(feet/second) data.
speed of the lead vehicle with respect to the following
,
vehicle.
If R is positive the lead vehicle is moving
•
ahead and if R is negative the following vehicle is
gaining on the lead vehicle.
Thus
•
R ') 0
Lead vehicle
moving ahead
R
<
0
(3-4)
Following vehicle
gaining on lead
(3-5)
vehicle
R = 0
,
R 1 is the true range-rate.
.
}
Steady state case
(3-6)
•
R will differ slightly from
R 1 due to slight sensor measurement errors.
).1.4
SYSTEM VEHICLE CARFOLLOWING LAW.
In Chapter 2 the
car-following law was defined as
,
.
=
In this case W~ now represents the rapidity or reaction
10
time of the VCAS system to r·espo:nd to changes in lead
vehicle speed and separaticn distance.·
One expression in
Equation 3...;7 represents the measured separation distance, ·.
R (in feet), between the two following vehicles.
So, if
then
(3-8)
Equation 3-8 represents the measured separation distance
in feet..
The desired separation distance is dk ; so
(3-9)
Thus Equation 3-7 becomes
••
=
w§ [
R -
( TXk+l
+
J
s)
(3-10)
Equation 3-10 is the System Car Following Lavv.
3.1.5
DISCUSSION OF THE SYSTEIVI CAR FOLLOWING LA\.J.
Rewrite
Equation 3-10 as follows:
~
k+l
= w2o (R - dk)
( 3-11)
where
3.1.5.1
CASE I:
THE STEADY STATE CASE R
=
dk•
measured range and the desired range are equal.
the steady state case.
Thus
The
This is
11
a."'ld
Vk+l = Constant
3.1.5.2
CASE II:
MEASURED SEPARATION DISTANCE IS
THAN DESIRED SEPARATION DISTANCE.
,,
->
Thus R
> dk
GREATE~
and
0
Here, the following vehicle is accelerating or maintaining
constant vehicle speed because the lead vehicle has
accelerated or is out of sensor range.
3.1.5.3
CASE III:
MEAStffiED SEPARATION DISTANCE IS LESS
THAN DESIRED SEPARATION DISTANCE.
,, <
X
k+l
·
If R
<:
~ then
0
In this case the following vehicle decelerates.
This
condition would arise if the lead vehicle slowed down or
a car cut in front of the following vehicle.
It is also not surprising that the System Car
Following Law is similar to the Freeway Car Following Law.
The reason being that the system being designed basically
obeys Equation 2-5 of Chapter 2.
3.1.6 DISCUSSION OF FIGURE 3-1.
The remainder of this
section is devoted to discussing some of the remaining
points of Figure 3-1.
3.1.6.1 SIGNAL PROCESSOR - SPEED CONTROLLER.
This part
of the model maintains vehicle speed based on the value
12
The Signal Processor generates the value V...,
.)
and causes the automobile speed -to be matched to the
combined value of
(3-12)
The V signal output from the Sigflal Processor is negative,
3
thus preventing v2 from becoming greater than vl (driver
selected speed).
3.1.6.2
ACTUAL VEHICLE SPEED.
The actual speed of the
• I
vehicle, xk+l
, may differ slightly from the speedometer
•
speed, xk+l'
due to slight system measurement errors.
Now, from Figure 3-1
r
(3-13)
=
,
uAP is the acceleration caused by movement of the
accelerator due to a deflection XAp•
,
This would occur if
uB is the deceleration caused by the pressure
being applied to the brakes by the brake actuation signal
EB.
This would occur if the measured range is greater
than the desired separation distance.
3.2
GENERAL SYSTEM REQUIREMENTS.
As mentioned in
Chapter 1, this paper applies to a vehicle collision
avoidance system for turnpike or freeway driving.
In
general, there are two conditions of highway driving:
1.
The steady state case
2.
The transient case
d
I
I SEPARATION
DES IRED
14
k
,
Vz
= xk+1
.
DISTANCE
SIGNAL
PROCESSOR
I ~VEHICLE
Xk+1
FOLLOWING
ICt
R
LAWS
~,
R
EB
v3t
R' ACTUAL
SENSOR
.
I
~ BRAKES
R'
I
t
~ ACCELERATOR
XAP
Vz
'
SEPARATION
DISTANCE
•
~
Vk
1
I UAP
•
I
-I
l
~
= xk+1
LEAD
VEHICLE
.
•
UB
t~
FOLLOWING
VEHICLE
SPEED
CONTROLLER
VEHICLE
l
" I
vk+1 = xk+1
I
u
Vk+1 =
~SPEEDOMETER
J
CABLE
• g
xk+1
J
SYSTEN HATHEMATICAL MODEL BLOCK DIAGRAM
Figure 3-1
,.....
\...)
14
Table 3-1
Definition of Terms
dk =Desired separation distance (ft).
Vk =Speed of the lead vehicle (ft/sec).
' = Actual
= ,xk+l
speed of the following
vehicle (ft/sec).
#
v2 = xk+l = Following vehicle speed as determined
by the speedometer ( ft/sec).
f
ik+l
Vt
::
" f
xk+l
Driver selected speed ( ft/sec).
v 3 =Commanded vehicle speed (ft/sec) •
.Xk+l
,
= Acceleration and deceleration of the
following vehicle needed to maintain a
safe separation distance between following
cars ( ft/sec2).
EB =Brake actuation signal (ft).
R = f'Ieasured range ( ft) •
R' =True measured range (ft).
,
R =Measured range-rate (ft/sec).
,
R' = True measured range-rate (ft/sec).
•
UB = Vehicle deceleration due to actuation of
~'
I
') \
the brakes \It;jSeC""'J•
I
XAP = Accelerator deflection (in).
•
uAP
= Vehicle accel0ration due to deflection of
accelerator caused by XAP (ft/sec2).
1 ,..
-::>
,Under steady state conditionE the
car-follo~ring
system-
requirements are:
1.
Each vehicle in a line of n identical
following cars travels at a steady state
velocity v
0
•
This implies that the
relative velocity between adjacent vehicles
is zero.
2.
The separation distance,
~~
between
following cars is directly proportj.onal
to the steady state velocity v
0
and is
constantly maintained between following
vehicles.
If the line of following vehicles is subjected to a
perturbation in the flow of traffic due to a change in
lead vehicle velocity, the following requirements should
hold true:
1.
Each following vehicle must be locally
stable with respect to the car directly in
front.
2.
Any perturbations in the line of following
vehicles will become damped out as the
disturbance moves down the line of following
___ ,_..! _., --
Vt:;H.Lv..L.t:;i:>o
3.
The acceleration and deceleration forces of
the vehicle made to compensate for the,
perturbation must be limited to insure
passenger safety and must not exceed the
1.6
dynamic capabil:ittes of the vehicle.
A
survey of the li te;r-a ture ( 5) ( 6) specLfies
an ideal value of acceleration anQ
deceleration between .lg and .• 75g.
In addition, the following system requirements are
specified:
1.
It is assumed that all vehicles are
equipped with this system.
Thus, the VCAS
is a cooperative system.
2.
All cars traveling on the freei'lay will have
the VCAS on for system operation to be
attainable.
Finally, in addition to the above requirements, the
follow~ng
overall requirements are specified for the (10)
realization of an opt:i.mal car following system:
1.
All n identical following vehicles have
the same dynamics.
2.
All vehicles normally move in a single lane
of traffic.
3.
All vehicles in the line of following cars
operate normally under steady state
conditions and any motion perturbations
of the lead vehicle to the system are in
equilibrium around the steady state case.
4.
Any other disturbances affecting the motion
of the lirie of following vehicles (wind
gusts, etc.) are random in nature (Gaussian
1?
I
White Noise).
5.
The system must incorporate the so-called
11
Fail-Safe 11 feature.
Thus, a failure in·
the VCAS system will result in immediate
system shutdown and notification to the
driver of this new vehicle status.
6.
The system must be as fool proof as possible
to overcome human error.
3. 3
GENERAL SENSOR REQUIREriJENTS.
Based on a survey of the
literature, (6), (8), and (11), there are two types of
sensors available:
1.
Radar type sensors
2.
Optical type sensors
The radar systems tested to date are undesirable because
of two fundamental faults:
1.
Inability to acquire a target in a curve.
2.
Large suscepttbility to detection of false
targets.
The optical system was tested only under static conditions.
It was a proposed system that employed light emitti.ng
diodes but was never proven functional.
The remaining
optical system available but not used to date is the
laser.
A laser tracking system is capable of providing
range and range-rate data needed for collision avoidance.
It is proposed that the VCAS system will use this type of
optical tracker.
The laser tracking system will be
18
.referred herein as the "sensor".
General requirements
---·
for the optical sensor a y>o•
1.
Provide range a:nd range-rate data on
vehicles ahead \'Ihile ignoring false targets
such as overpasses, bridges, and side road
signs.
2·.
Most likely the vehicle ahead will have
no special optical markings to discriminate
them from false targets.
Thus, target
discrimination will be accomplished
through sensor beamwidth.
In addition to the above requirements, the following
overall requirement is specified to achieve an optimal
car following system;
Minimization of false alarms in
the optical tracking system is of prime importance if the
tracking system is ever to become a reality.
Otherwise,
users will lose faith in the system and either shut it off
or find some method of overriding the system.
3. 4
AUTOf1ATIQ. VI:RSUS THE SEMI-AUTOMATIC SYSTElVI.
The
VCAS system has a choice of two modes of operation:
1.
Semiautomatic
2.
Automatic
This section discusses both systems and then chooses from
which mode the VCAS system will be designed.
It is
assumed that the optical tracking system is the same for
both systems.
19
In the semiautomatic sy·stem the VCAS
~muld
rr..oni tor
the distance betl'l'een following cars, closing r::1.te, and
following vehicle ground speed.
A display \'l'ould be present
inside the vehicle on the dashboard.
Most likely the
display would advise the driver that a vehicle is ahead
and that a safe separation distance is being maintained.
If the separation distance becomes less than a
predetermined value, the driver would be advised by a_
blinking light accompanied by an alarm.
It would then be
u:P to the driver to slow down and resume a safe following
distance.
If the driver failed to heed the warning and
was about to collide with the car in front, the system
would then apply the brakes.
This action would either
prevent an accident or llmit the severity of the impact.
The automatic system would also mo!litor range,
range-rate, and following vehicle ground speed.
The
automatic system would acquire any lead vehicle well ahead
of the safe separation distance.
Once the following car
closed within the safe separation distance the automatic
system would actuate accelerator and brakes to maintain
the safe separation distance.
In the semiautomatic mode the system relies mainly
on the physical and mental capabilities of the driver
which vary from person to person.
In addition, the
individual is subject to human error.
The automatic system does not depend on the human
20
except that the-driver is required to -steer the car.
Thus, the system is more reliable assuming that a highly
reliable system has been designed. and built, and for the
reasons stated above the VCAS system will be an automatic
system.
3.5 TRACKING DISTANCE CRITERIA.
The final item to be
introduced before the description of the system is
tracking distance criteria.
A survey of the literature,
(5) (6), involving radar systems, stated that a safe
separation distance was from
250 to 330 feet.
The usual
rule of thumb criteria for safe separation distance is
vehicle speed plus 30 feet.
Thus, for the VCAS system,
the following car will acquire the lead vehicle when it
is detected within
250 feet.
Now, if the following car
should catch up to the lead vehicle and the separation
distance becomes equal to following car speed plus 30 feet
the VCAS will then automatically maintain safe separation
distance.
To examine the criteria look at maximum freeway speed.
Today it is
55 MPH; it used to be 65 to 75 MPH depending
on the stretch of road\vay.
In the fog most people would
travel on the freeway between 45 and
all·lays one clri ver
~A:ho
1.s 1n a hurry.
driver is traveling 70 MPH.
55 MPH, but there is
T-+-1.Uv v 1::>
- - - ........... _
Cti::> i::> WliC
.._~-
vllC
At this speed the safe
separation distance would be 100 feet, and is less than
the target acquisition distance of
250 feet.
Therefore,
21
the criteria for separation ·di.stance is ·acceptable.
3. 6
3.6.1
\lEHICLE COLLISION AVOIDANCE SYS 1l'E~1
GENERAL OVERALL DESCRIP1'ION.
The VCAS system is
an automatic collisi.on avoidance system.
The system
determines the location of the car ahead as well as the
location of surrou..11.ding vehicles and automatically
adjusts the speecl of the car, by actuating the brakes and
accelerator, to maintain a safe following distance.
The
safe separation distance speeified in Section
3.5 does
not take into accotmt tire and road friction.
If this
factor is consid.ered 1 an additional input to the system
is required from the driver or laser tracking system.
The system is composed of two major components:
1.
Speed Cruise Control System
2.
The Laser Tracking System
The Speed Cruise Control (SCC) is similar to the one now
available as an option on most vehicles and will operate
when the driver selects the vehicle speed to be maintained.
This value is then stored in an electronic circuit.
Based on this value the vehicle acceleration is increased
or decreased depending on the difference between driver
selected speed and vehicle actual speed.
The Laser
Tracking System gathers
vehicle ground speed as sampled from the vehicle
speedometer cable.
This information is processed along
with the speed cruise setting.
Using this data the VCAS
22
sys·tem automatieally actuates .. brakes and. accelerator .to
:b,igure 3-2 sho"'-IS ·a
maintain a safe following distance.
block diagram of the system.
3.6.2
THE BASIC
------
).6.2.1
TRACKING PLAN
TRACKI1JG THE CAR AHE@.
Let's assume initially
the driver of a car on the freeway is traveling 50 IVJPH in
clear weather.
The time of day is irrelevant since the
system \'Till operate in darkness or light.
After a while
the driver decides to let the Speed Cruise Control system
maintain the vehicle speed.
This is accomplished by
making the appropriate setting.
is off.
At this time the VCAS
It is activated by pressing a pushbutton switch
on the dashboard.
Finally, the driver of the vehicle
encour1ters fog and activates the VCAS system.
If there
is no car ahead wi.thin 250 feet, the driving condition
is as previous and the dashboard display lights the
and "CLEAR" lamps.
display).
11
SCC 11
(See Figure 3-3 for dashboard
Remember, with the Speed Cruise Control on,
the driver's foot is off the accelerator.
The SCC must
be on for the system to operate and the speed cruise
setting must be made.
If the driver fails to do so, the
display will give a warning by illuminating the "VCAS
DISABLED-SCC SETTING REQUIRED"
_
l~mn
_
_ ...... .I:".
If a car is tracked
within 250 feet, the VCAS system takes over and informs
the driver by lighting the display lamps
AHEAD".
11
VCAS 11
-
"CAR
So long as the separation distance between
LASER
TRACKER
·BRAKE
COI"'I1ANIY~ BRAKE
ACTUATOR
SIGNAL
~ PROCESSOR
I
, + ,.
,
l
I
,
.._.~
-1
BRAKE PRESSURE
·-i
DISPLAY
VEH~~
~1
. . . . ·~
I
.t
GROUND
SPEED
r--
ACCELERATOR
r---p()siTION
DRIVER
SELECTED
SPEED
,
SPEED
CRUISE
CONTROL
SENSOR
...
I
~
v
,
ACCELERATOR
-., ACTUATOR
AMPLIFIER
AT+
I
I
I
1
VEHICLE SPEED
__j
.
BLOCK DIAGRAM OF THE VEHICLE COLLISION AVOIDANCE SYSTEM
Figure 3-2
1\)
\...)
24
vehicles is greater than driver selected speed plus
30 feet, the Speed Cruise Control set·ting is in effect 3
but car speed is in control of the VCAS.
Once the
follow·ing car speed plus 30 feet is equal to the
separation distance or less, the VCAS negates the speed
cruise setting and maintains the safe separation distance
by actuating brakes and accelerator.
"Headway Mode" of operation.
This is called the
The speed of the vehicle is
as close to the speed cruise setting as possible so long
as distance separation is maintained.
If the lead vehicle
accelerates beyond. the safe separation distance or moves
out of sensor range, the VCAS returns control of vehicle
speed to the Speed Cruise Control.
Should a car cut in
front of the following car the VCAS takes over immediately
and adjusts vehicle speed for a safe separation distance.
Finally, if the lead car should slow down, but not stop,
the VCAS will adjust separation distance to take into
account the lower speed of the lead vehicle.
However,
if the lead vehicle slows down significantly, then
following vehicle speed will be readjusted for a safe
separation distance.
If the VCAS senses a stopped
vehicle ahead, the VCAS will stop the following car.
3. 6. 2. 2
TRACKING ':PHE CAR BEHIND FOLLOWING VEHICLE.
Each
driver will have a basic understanding of system operation
from the vehicle Owners Manual.
The driver will know
what speed the car is traveling (50 MPH).
Now, each
25
vehicle is equipped l'lith a reflector at the rea.r of the
car.
When a following ca1.. starts to track the car ahead,
the signal received at the reflector
a display lamp "REAR" illuminated.
~Till
be sensed and.
The driver of the car
will then know that there is a following car within
80 feet.
3.6.2.3 TRACKING THE CARS ON THE RIGHrr AND LEFT
~IDE.
The vehicle traffic located on either side of the car
\'Till be accounted fo1• by determining closing and leaving
rates by sampling angular rate information from the system.
In other words, the system will have some form of Lateral
Control.
In addition to the Lateral Control function,
the VCAS system will need to know the direction of the
road and the orientation of the vehicles on the road to
keep track of side vehicles.
3.6.3 JNITIATING AND SHUTDOWN OF THE SYSTEM.
The VCAS
system is simply activated by pressing a pushbutton switch
on the dashboard display.
The system is deactivated by
stepping on the brakes or accelerator pedal.
This action
returns control of vehicle speed to the Speed Cruise
Control system.
In addition, an electromechanical circuit
is activated i"lhich moves the VCAS switch from the
position to
L1--
vLH~
ltA1.1T:\Ir
··vJ:'J:' ..
11
0N 11
---.:!
jJVb.Lv.LV.Ue
.&....!. - - -
accelerator or brakes once again will return complete
control of vehicle operation to the driver.
3.6.4 CONSOLE DESCRIPTION.
This section describes the
26
dashboard display of.- the Vehicle Collisj,on ,f\.voidance System.
All sections of the display are lamps:
1.- The
11
0N-OFF 11 pushbutton turns the VCAS
on and enables the display.
2.
The
11
MALF1JNCTION 11 lamp will not illuminate
unless there is a system failure or a
failtu•e during self test.
3.
The "VCAS-ENABLED 11 lamp will illuminate if
the Speea. Crui.se Control setting has been
made.
If the setting has been omitted,
then the
11
VCAS DISABLED-SCC SETTING
REQUIRED" lamp w·ill light.
4.
If there is no car within 250 feet, the
11
5.
SCC 11 and "CLEAR" lamps will illuminate.
If a car appears ahead within 250 feet,
but greater than the safe separation
distance, then the
11
VCAS 11 and "CAR AHEAD"
lamps will illuminate.
6.
If the VCAS starts to maintain the safe
separation distance, then the
11
VCAS" and
"HEADWAY HODE 11 lamps will light.
7•
The lamps
11
LEFT 11 ,
combinations.
11
REAR u , and
11
RIGHT 11 can
Their function is to inform
the driver as to the status of the
surrounding traffic.
SYSTEM
c
~:c
I
c:J
I
I
LEFT
I
~cc
I
I
--l_I
I
J
MOD~
--------~--~
j
J r REAR
VCAS DISABLED -
1--;AS ENAB.tED
CLEAR
I
CAR AHEAD
I
MONITORING
TP~FFIC
HEAmvAY
1
l
SETTING REQUIRED
MALFUNCTION
RIGHT
l
I
l
I
.. l
~
~
VEHICLE COLLISION AVOIDANCE SYSTEI1
VEHICLE COLLISION AVOIDANCE SYSTEM CONSOLE DISPLAY
Figure 3-3
M
-..:1
28
The reflector svstem
wi-ll be.
,,,
a combination of passive and
active·co~ponents.
The
active portion encompasses the laser tracking system and
the pr·esence of the laser signal at the reflector will be
sensed.
11
The sensed signal will be used to activate the
REAR 11 lamp of the dashboard
d.ispl~y.
The passive portion of the reflector is used to bounce
back the laser signal to the following vehicle.
The
design of the reflector will encompass the optical and
reflective properties of the laser so that beam width is
maintained and a maximum amount of energy is reflected.
The reflector will be located at the rear of the
vehicle.
A suitable reflector is the license plate area.
Unsuitable areas of reflection are the rear tail gate,
tail lights, and the rear portion of the bumper.
These
locations vary too much in physical design from car to
car, but the license plates of all vehicles are usually
located in the same rear spot.
Thus, for system operation
it will be assumed that all cars will have reflectorized
license plates in the same location of the rear of the
car at a standard height above the road.
The numerals
and letters will be impregnated into the license plate
material.
The exception to this location is trucks 7
trucks with trailers, busses, and cars with trailers.
For system operation these vehicles will also have their
license plates located in the same area as the standard
· passenger vehic.l.e.
Another problem is reflector height and width.
Most
cars travel in the center of the lane, but some vehicles
travel to one side of the
l~~e.
Thus, it is anticipated
that the size of the reflector will be somewhat larger
than a standard license plate, but will not cover the
total rear bumper area.
).8
§ENSOR-REFLECTOR TRACKING
J.8.1
SYSTEM DESCRIPTION.
Since the reflector is centered
/
in the same location of the rear of the vehicle, the
sensor will be located in the corresponding position of
the grill of the car.
To achieve accurate tracking, the
optimum position for incidence on the reflector is the
center; but due to curves in the road, dips, bumps, and
grades, this might not be possible.
To overcome this
problem the sensor must track the reflector.
To obtain
optimal reflector-sensor aiming, the reflected signal will
be sampled thus allowing the VCAS to lock on to the
received signal.
If the signal strength received is within
certain specified limits, the sensor would be aimed
directly ahead.
If the reflected signal was weak, the
sensor would be slaved to a new aiming angle so that
reflected sign.al strength is maximum.
Thus, the sensor is
moveable in the horizontal and vertical directions.
3.8.2
TRACKING PROBLEI>TS.
The basic problems of
sensor-reflector tracking are:
JO
1.
Curves in the road
2.
Dips
3.
Bumps
4.
Grades
5.
Vehicles not traveling in the center of
the lane of traffic
6~
3.8.2.1
False targets
TRACKING IN CURVES.
A survey of freeway radius
of curvature determined them to have large turning radius.
Since the sensor system is gimbaled, tracking in curves
should present no problem, but there is one additional
problem associated with curves.
If no vehicle is being
tracked prior to entering a curve, the sensor is not
locked on to a target, and if a vehicle should appear
ahead, the sensor might not be aimed properly resulting
in a possible collision.
To overcome this problem, prior
to entering a curve, the sensor will be positioned by a
pickoff from the position of the steering column.
3.8.2.2
ROAD DIPS AND BUMPS.
This is not expected to be
a problem because the sensor is gimbaled.
Also a survey
of freeway surface conditions showed that road dips and
bumps were very minor.
e:ncounter>ed, it
of lock is anticipated.
If this condition were to be
..; ..,..
.J..L.L
--........
V.L.Lv
r ' l - - ,.....,....
0 <;;; v
rl
V.LJ.U.
o
l\T"'
.1lV
,..._'V'\,...,.....~
OVJ.J.OVJ..
Also, the vehicle suspension
system would tend to smooth out these types of road
disturbances.
3.8.2.3
GRADES ..
If tha VCAS is tracking a vehicle prior
to a grade, the system will maintain lock.
A problem
occurs if the grade angle exceeds sensor look angle.
It
is anticipated that momentary loss of reflected ::;ignal
'\'Till result but there '\'J'ill be no hazard in driving.
3.8.2.4 VEHICLES NOT TRAVELING IN THE
CEN~ER
OF THE
L~NE.
This problem is eliminated by optimal reflector size.
3.8.2.5
POSSIBLE FAlSE REFLECrriONS.
Since a laser will
be used this trouble is not anticipated to be a problem
because the sensor will not be able to be positioned at
extreme look angles.
3. 9
SAFET_Y REQUIRENENTS .
1.
At standstill, the laser system is inoperative.
This will prevent bodily harm should anyone look
into the sensor output.
2.
The system should be designed with the so called
"Fail Safe" feature.
Thus, a system failure
will result in system shutdown and return of
vehicle control to the driver.
The dashboard
displa.y will indicate the failure by illuminating
the ":rt'J.ALFUNCTION 11 lamp.
3.
Should the system malfunction in a lock-up mode
the brakes will be applied.
3.10
~ELF TES~ RE2UIREMENT~.
test the- VCAS system.
Starting the car will self
The console display will indicate
a pass condition by not illuminating the
lamp.
11
MALFUNCTION 11
CHAPTER 4·
Laser Propagation Study
4. 0
IN1'RODUCTION.
Based on· the initial survey conducted
in Chapter 1, the effect of scattering on the
propagat:i.on of laser light through dense fog is
examined.
4.1
BASIC ASSUMPTIONS OF THE S'rUD~.
See (13), (15),
( 18) , ( 21 ) , and ( 26) :
1.
The scattered light has the same frequency
as the incident light.
2.
Scattering by well defined particles will
only be considered.
Such scattering is
called independent scattering.
3.
The assurnption of independent scattering
implies there is no systematic relationship
between scattering phase angles.
4.
The effects of multiple scattering will not
be considered.
5.
The scattering angle is for forward
scattering.
6.
Thus -e- = 0.
The medium is uniform.
Such a medium is
called monodispersed.
7.
Particles are spherical.
8.
The medium consists of homogenous spherical
particles.
9.
The index of refraction is equal to 1.33.
32
33
4.2
DESGRIPT.;rON OF rrHE
rviEDTU~1.
Dense fog consists· of
ma.l'l.y tiny spherical Nater droplets.
The physical
properties of each droplet are:
1.
Spherical. in nature with radius a
2.
Homogenous
).
Clear
The radius of the droplets range (18) (19) (20) from
5 microns to 80 microns with the predominant droplet
size being from 25 microns to 50 microns.
4.3 SCATTERING CONDITIONS.
The determination of the
·'
scattering conditions is based on a comparison of particle
radius versus laser wavelength.
There are obviously
several conditions:
1.
2.
a ( {
a
>>
~
(4-1)
~
where
a == droplet radius
)\ = laser wavelength in microns
Condition 1 is described by Rayleigh Scattering Theory (21),
condition 2 is described by
~lie
Scattering Theory (26),
and both conditions 1 and 2 can be described by Angstrom's
Scattering Equation (26).
4~4
RAYJ.ETn-H SCATTERING.
restricted to the case \'lhere a((A.
theory for the scattering
i~tensity
made the following assumptions:
In deriving the
of light, Rayleigh
J4
1.
The scattered intensity·is proportional to
the intensity of the incident radiation.
2.
The volume, V, of the spherical particle,
the ~rave length,
A ,
the indicies of
n~,
refraction of the particle,
J.
and the
medium, n , and the distance,·r, to the
2
point of observation are tL"'lkno\'.rn.
3.
The ind.icies n 1 and n 2 are not complex.
Based on the above assumptions, Rayleigh hypothesized that
I = f
( Vi r , )... , n , n
1
2
) I
0
(4-2)
where
I
0
=
intensity of the incident wave of light
I = scattered intensity of the \'lave of light
Now, the function
f
( V, r,
A,
n , n
1
is a dimensionless parameter.
2
)
In determining the value of
V, r,)\J n , and n , Rayleigh deduced the following points
1
2
based on a diagram of an incident beam of light on a
sphere (See Figure 4-1):
1.
The dipole radiates energy in all directions
and the intensity of radiation decreases as
l/r2 •
to the dipole moment, which for a given
uniform exciting field is proportional to
the volume of the particle.
J5
z
H
---~·~
X
GEOMETRY OF RAYLEIGH SCATTERING
Figure 4-1
y
· · J;
scattering intensity is proportional to
~rhe
the square of the. field so it \'.rill vary· as
v&." .
Thus, the scattering intensity becomes
I = f
[ (n
1
n
2
) (V2/r 2
)..L~ )]
I
0
(4-3)
In deriving the equation for the scattering intensity, the
scattering is in the direction from the origin through the
point defined by the polar coordinates r, ~~ and ~ where
x = r sin
-e- cos
~
y = r s in -9- s in !\)
(4-4)
z = r cos -eand
1.
lf
is the angle from the scattering
direction to the dipole.
2.
~
is the angle of observation.
So the intensity of the scattered wave at a distance r was
surmised by Rayleigh to be
(4-5)
All the quantities in the above equation are constant
except the wavelength.
Thus, it can be seen from
or
(4-6)
Equation 4-6 is the well knoNn Rayleigh equation for
37
scattering ..
4.5
4. 5.1
:NIE SCATTERING THEORY
IN'rRODUC'J.1ION.
l!!ie theory ( 13) ( 15) ( 18) ( 21} ( 26) ·
is used to study scattering of light by a sphere irridated
by a plane wave emanating from a single direction.
Figure 4-2 depicts the geometry of the situationo
4. 5. 2
PARTICLE CBOSSECTIONS ..EOR EXTINCTION, SCATTERING,
AND ABSORPTION.
A spherical particle contains a certain
crossectional area.
When a beam of light passes through
this crossection, energy is abstracted from the
transversing light beam.
The energy is removed through the
process of scattering and absorption.
This loss of energy
is called extinction and is defined as
Extinction = Scattering + Absorption
(4-7)
The crossections of a particle with radius a for
extinction, scattering, and absorption are designated
cext = Extinction Crossectlon
0 sca = Scattering Crossection
c
From Equation
4.5.3
Absorption Crossection
abs -
Lr,-7
c
(4-8)
ext
then
= c
sea
'RFFTC!TF.NC!Y FACrrQRS.
+ c
(4-9)
abs
In the stud.y of light,
particle orientation and the state of polarization of the
light are important parameters.
These parameters are
described by a dimensionless constant called "Efficiency
X
E
p
Direction of Propagation
"-
z
MIE SCATTERING DIAGRAM
Figure 4-2
w
co
39
Factors 11
•
They are designated for extinction, scattering,
and absorption as
Qext
= Extinction
Efficiency Factor
(4-10)
Qsca = Scattering Efficiency Factor
Qabs = Absorption Efficiency Factor
The efficiency factor is defined as
(4-11)
Q = C/G
Thus
Qext = Cext/G
(4-12)
Qsca = csca/G
Qabs = Ca b s /G
where
G
= the
area of a sphere with radius a
and
(4-13)
From Equation 4-7 then
(4-14)
4.5.4 SCATTERING AMPLITUDE FUNCTION.
Light penetrating
a sphere of radius a causes a disturbance in the medium at
a distance P from the particle.
This disturbance is
characterized by an amplitude functionS(~, \P).
In
reality, the disturbance is the forward scattering of the
incident light by the sphere.
The scattering angle,
-e-,
40
is for for;-iard scattering and is· defined as ..g.. = 0.
The
amplitwie function is defined to be
s (-&, lf)
=k
(4-15)
)\
where
k
=
G ==
21f/>-.
= wave
1T a 2
= area of the sphere
number
D(-e-, 4-') = a complex function
Since the scattering angle -9- = 0, D(-e-, tp) is defined to be
equal to 1.
Thus
S(O) =_k_
G (1)
)\
or
(4-16)
G
4.5.5
THE MIE SOLUTION.
The solution to the problem is
based on two dimensionless quantities
x = 2 IT
a/~
k=2lT/>-.
(4-17)
where
x
= the
size parameter
a = radius of the sphere
k = free space propagation constant
A= wavelength
Assumptions made in clerivingthe solut.ion are
1.
m
=1
{index of refraction)
2. -& = 0 (for\'mrd scattering)
3.
The incident plane wave of ligbt is
vnpolarized so that the electric and
magnetic fields are perpendicular to each
other.
4.
When the field interacts with an inactive
homogenous sphere, the result is a scattered
field of radiation in the direction other
than the incident field direction.
4.5.5.1
1.
THE RESULTS OF THE MIE SpLUTION.
The amplitude function in terms of Mie expressions
are
s 1 (m,
,.0
X'
-B-) =
2n
+ 1
1
~
n~n
+
1)
(
\
aulT + ~>
(4-18)
f't'\,.
"'""' ::.. l
s 2 (m,
X'
-6-) =
cO
2
-?'\,:Z
Since -e- = 0,
s1
=
s2
o
2n + 1
n(n + 1l
l
(bnTII'?V +an1::)
:.y.,
(4-19)
Integrating Equations 4-18 and
4-19 from zero to infinity reduces the expressions to
G
or
Re
{
s(o)}
=
G
(4-20)
42
2.
The efficiency. factors in terms of Hie ·
expressions are
1
( 2n + 1 ) Re (.~ + b)- ( 4-21 )
2
L
rr_)
Upon integrating Equation 4-21 from zero to infinity the
efficiency factor becomes
4
3.
(4-22)
The solution of the extinction crossection is as
follows; from Equation 4-12
cext
=Tia2 Qext
=n a2
4
v2
Re
[s(o)}
Re
[sea>}
A.
=
a2
4lT
41f~2
>!so
cext
4.6
=
47T
k2
EXTINCTION COEFFICIENT.
Re[s(o)}
(4-23)
The extinction coefficient
is an expression of the amount of attenuation of the
medium.
The attenuation is a function of scattering and
absorption and the fact that the intensity of the laser
beam decreases as the square of the distance.
The medium is considered to have a real index of
.
refraction composed of N particles with ra.clii from a to
a + da per unit volume.
'11he particles are assumed to be
spherical and of the same composition.
The extinction
coefficient per em is defined to be
~=
e<:l
£Qext
N(aJ'TI a
2
da
(4-24)
whez~e
y~ = extinction coefficient
Qext == extinction efficiency
a
N(a)
= radius
= number
of spherical particle
of particles per unit volume
Since Equation 4-24 assumes m is real the result is a
non-absorbing sphere.
L~-14
Now, recalling Equations 4-9 and
the following similar relationship results
{4-25)
and from Equation 4-9
but since m is real
Qabs = 0
so
Qext = Qsca
{4-26)
Extending Equation 4-26 results
cext = csca
(4-27)
Thus; from Equations 4-25 to 4--27
( 4--28)
or
.,.()
~=
[Qext N(a)Tf a 2 da
(4-29)
Equation 4-29 is important because its solution will
indicate the amount of scattering for a particular radius
of fog droplets as a
f~~ction
of laser wavelength.
4.7 SOLUTION OF THE SCATTERING
EQUATIO~
...0
Y~ --
N(a)7f a 2
[Qext
Qext =
4
x2
S(O) =
k2
2Tf
k =
21T
Re[s<o>}
G
;>-.
=
Qext =
=
2TTa
A
2
k2 -·
4Tr
x2 -
41T a2
G = 1T a 2
X
da
>!
e
~'2..
4
-47t'1a2
)...2.
Re [s<o>}
4 ~2.
41T2a2
Re[s(o)}
Re
S(O) =
[s(o)1
(1T a2 )
=
=
so
at?
\(.6ecft,
=
£
21T a 2 N(a) da
-o
=
217 a21 N(a)
da
and the integral
1
et£J
-
N(a) da = N
......
so
(4-30)
or
46
(4-31)
Equations 4-30 and 4-31 state that the scattering is
independent of the wavelength and is a constant value
over a great portion of the spectrum.
The maximum value
for the constant value of sea tterj.ng ( 26) usually occurs
at ~n....,..... ~= a if the index of refraction of the medium has
been assumed to be equal to 1.33.
After ~the
wavelength increases until ~ = lOa where the amount of
scatter·ing is considered negligible.
4.8 b_@STROM 1 S SCATTERING EQUATION.
Angstrom's Equation
is used to describe scattering as a function of
wavelength per the following relationship
(4-32)
where
V
A
o<.
= scattering coefficient
= wavelength
= an integer whose value depends on
particle size
Since A is known the value of"" must be determinedo
First,
it is assumed that the distribution of particles takes
the form of a power law;
dN = C a-v-l da
where there are dN drops per cm3 in a size range da.
i.p
'
Recalling Eqnation 4-29
.0
y
.ua,;
=£ra2 Q(a)
=TT c
dN
~
~· a-Y+l
'>rr )
2
=lfC (
Q
-v- 2
The above integral converges for 2
(-·2~a)
1
da
x-v+l Q(x) dX
< v ~ 6.
Also, from
the above equationo< and v are related by a size
distribution equation
o(_
(4-33)
= v - 2
Thus ...( = 1 to 2 and v = 3 to 4.
large spheres (a >~A).
In reality
c<--~PO
for
This means that the value for
scattering is constant and independent of wavelength.
This is in agreement with the results of Equations 4-30
and 4-31.
If~
if a<. }. then
co(.
and a are relatively close,.:<.= 1; while
= 2.
4.9 OPTICAL PROPAGATION OF LASER LIGHT IN THE MEDIUM.
This section constructs three graphs and a composite
graph depicting the amount of scattering as a function of
wavelength and fog droplet radius.
These graphs will
show the total range of laser light that will be
scattered by the fog medium.
fog droplet radius of
~'
fog droplet radius of
2~,
Figure 4-3 is a graph for a
Figure 4-4 is a graph for a
and Figure 4-5 is a graph for
a fog droplet radius of
5~.
Finally, Figure 4-6 is a
composite of all three graphs.
It shows that as the fog
droplet radius increases the amount of scattering
increases.
Using equations 4-6 and 4-31, Figure 4-3 was
constructed.
The results of the Figure 4-3 graph were
~~=a and that the scattering becomes negligible at
~= lOa.
These two critical points plus Equations 4-6,
lt.-30, 4-31, and 4-32 were used in the construction of
Figures 4-4 and 4-5.
As the wavelength for particle
radius increases as well as the wavelength for light,
Rayleigh's ·law does not exactly apply.
Thus, when
Rayleigh's law breaks down Angstrom's Scattering
Equation was used to·continue the plot of the graph.
4.10
LASER SURVEY.
There are six different types of
lasers that are available:
1.
Solid State Lasers - Pulsed Operation
2.
Solid State Lasers
3.
Semiconductor Lasers
4.
Tunable Lasers
5·
Gas Lasers - Pulsed Operation
6.
Gas Lasers - CW Operation
- CW
Operation
Table 4-1 to Table 4-6 summarize these various
according to type and wavelength (28) (29).
4.11
DISCUSSION OF THE RESULTS.
In Section 4.7 the
solution of the scattering equation, Equation 4--30, shows
~
-~
-.....::
I;
~
('\
I
..::7
Q)
~
rr
~
II
II
~
'
8
l{)
t'
T
'
~{
1
c.::l
.........
_\:)
::sQ()
..........
·r-1
--
I
I
\()
(
~
..
lit
L' (I
.)..-
-~
~
~
<\.!
II
~
(J
-~
.........
...::}-
I
...::}Q)
H
_\:)
...._
::sb.O
·rl
IIi
I
~
~
il
<:::l
...........
~
~
J~
. '.J
I
~
--
II
I
l()
I
(:)
...........
51
c}
Cl
-~
..._
to
n
\.(\
~
I
..::t
(])
-~
..........
- ..._
.
I
~
..._
~)
II
~
\::)
........
1
!:1~
t~
~'-J
I
I
-
\:::)
I
LC)I
I
C)
-.
-
H
;j
bO
•M
rT.j
52
~
-~
-am
"
H
0
..::t
Q)
Q)
.p
~
·r-l
tf.l
_C)
0
p.
E
0
0
'-0
I
\
CJ
lr)
II
~
'
~
(\J
J
11
~
-
II
~
........
_______1__~_1------~~~------~,.~ .
.........
I<;:::)
...._,
-
::s
b.O
·r-l
~
Table 4-1 Solid State Laser•s - Pulsed Operation
Type
·Wavelength
(microns)
·Ruby
Nd-yag
I
.6943
1.06, 1.034, 1.064
Nd-glass
1.06
Ruby/Nd-glass
Yag, Ruby & Glass
.694, 1.06
.26.5, .35, .53, .69,
1.06
Ruby/Glass
.6943, 1.06
Nd-yag & glass
1.06
Dbld Nd-glass
.530
Dbld Nd-yag
•.530
Table 4-2 Solid State Lasers - CW Operation
Type
Nd-yag
Wavelength
(microns)
1 • 06' 1. 064' 1. 34'
.53, .6?, .26
Nd-glass
1.065
Ruby
.6943
Table 4-3 Semiconductor Lasers
Type
\
Wavelength
(microns)
GaAlAs
.90, .850
GaAs
.90, .904
55
Table 4-4 Tunable Lasers
Pumping Method
Active Material
N2 laser
Flashlamp
Organic dyes
3,600 to 6,700
Dye
3,400 to 6,300
Nd-yag laser
Dyes
2,650 to 4,150
Wavelength
(Angstroms)
5,300 to 6,700
Nd-yag laser
Optical Parametric
3,400 to 6,500
Oscillator
Ar laser
Organic dyes
5,250 to 7,000
Flash lamp
Organic dyes
4,350 to 7,000
Ion Laser
Organic dyes
5,800 to 6,300
Ruby laser
Li03
4,150 to 21,000
C02
9,219 to 10,836
TEA
C02
9.1 to 11 microns
TE
HF
2.8 to 3 microns
Electrical
DF
3.5 to 4 microns
TE
co
5 to 6 microns
Electrical
N20
10.5 to 11 microns
N2
Flowing dye
3,500 to 74,000
Coax Flash lamp
Organic dyes
2,200 to 96,000
Discharge
N2 laser
Linear Flashlamr
I
Organic dye
3,600 to 7,000
4,400 to 6,500
Table 4-5 Gas Lasers - Pulsed Operation
Type
Wavelength
(microns)
HCN
311' 337
H2 0
28, 78, 118
C02
9.1 to 11
N2
-3371, 1 to 3-5
Ne
.5401
Ar
.479 to .514,
.)51, .364,
1.2 to 7-3
Hli'
l
& CO
2.8, 5
Copper vapor
• 5106' -5782
He-Cd
.4420, .6328
HF
2.8 to 3
DF
co
3-5 to 4
5 to 6
N20
10.5 to
Xe
.)645,
Kr
•.l.J.?h?
'I_,_
11
2
h"\
v~
to )v6
{..ry{..lr.
• ....., I \..rT
57
Table 4-6 Gas Lasers
- cw
Operation
-
'l
Type
Wavelength
(microns)
HCN
311, 337
H2 0
C02
28
9.2 to 11
Ar
.3511 to .5287
He-Ne
.6328, 1.152,
'
78' 118
3.391
Kr
.3507 to .7993
Ar/Kr
.4579 to .6764
He-Cd
• 4416' .3250,
.4420
He-Se
.46 to .56
co
5.2 to 5.7
N20
10.5
58
that light scatters at a constant value until
A
~
= a~
Also, the scattering is independent of the l'.ravelength
until this point is reached.
In Section 4.9 graphs were plotted for scattering vs
wavelength as a function of fog droplet radius for .5, 2.5:
and .50 microns.
The results were:
1. )\ =.a
~
2.
The amount of scattering becomes negligible
when the value
)\. == lOa is reached.
Also, as particle radius increases the amount of
scattering increases-See graphs in Section 4.9.
Figure 4-7 is a graph for the amount of scattering
vs wavelength as a function of fog droplet radius (20),
and was obtained by quantitative measurement of a typical
fog medium.
Comparison of Figures 4-3 to 4-6 and
Figure 4-7 indicates that the measured curves are in close
agreement with the plotted curves; the only significant
difference being the location of )\
~
This difference
is due to:
1.
The medium composition changes.
2.
As the wavelength approaches the infrared,
the index of refraction contains an
l.JJ.
Then
A-..ry. is greater than the value
of particle radius; the net result is that
the value for constant scattering covers
59
a large part of .the spectrum.
Tables 4-1 to 4-6 show
aYailable today.
th~
.commercial lasers that are
The wav·elength range of these are less
than .6 microns to 337 microns while the scattering curves
extend from .1 microns to 500 microns.
Comparison of the
curves of Figures 4-3 to 4-7 and Tables 4-1 to 4-6
indicate that if a laser is to be of a.'1y practical use
it must have a wavelength of 500 microns or greater.
region is the submillimeter wavelength region.
This
To date,
no practj.cal laser has been developed in this area;
research is being performed in this section of the
spectrum.
The only successful attempt in this region has
been accomplished in the laboratory (30) by mixing two
co 2 lasers and bombar-ding a crystal of GaAs or CdTe.
This
unit is still in the laboratory in an early experimental
stage and consists of a physically large and cumbersome
setup.
Therefore, at this time the laser tracking device is
not practical enough to be used in this particular
application.
60
_cs~ a
~
Ll.J
~
:::::1
(.{')
G:
ltJ
\J ~
-~
~
.........
A:
V:l
>
_\:)
tl
.........
\:S
~
,
..........
~~
_...._
II
I
~
...........
(])
H
::3
Q()
Iii
~
I
I
...::::r
·r-1
Lq
t}l
I
['-
~
~
...........
I
I
~
tn'I
I
J~
~
I
~
............
C)
..........
~J
Conclusions
In Chapter 2 a mathematical model--for traffic flm-i
on a typical freeway was developed; this resulted in the
car-following law.
Based on the above, in Chapter. 3, a mathematical model
of the proposed system
·~ms
car-following law derived.
constructed and the system
Next, a general discussion of
the system and the basic tracking plan were presented along
with a study of sensor-reflector tracking and associated
problems.
In Chapter 4 a study on the propagation of laser light
through fog was conducted.
The above research shows:
1.
The system is not feasible with present
technology.
2.
Fog consists of large spherical droplets
which results in scattering of light that is
essentially independent of wavelength.
Conclusion number 2 is the reason for the white _appearance
of fog; i. e. wavelengths are essentially scattered
equally.
-~~~~1~
o~·ct!Jll
~.r:-
Vl.
See Figures 4-3 to 4-6 versus Tables 4-1 to 4-6,
u.:~
.. ~~
J.'..LoU..!.'C
),
..,
"t"-{•
A,~-
.tl...Li:>V'
1-tl"'\
\.1..//J
,....,,.,,
\t:..VJ,
---"'In!'\
O.l.lLl \t:..U/o
.... __
J.ll
addition, any design would have to be operational over the
entire range of fog droplet radii encountered.
Fog
droplets with a radius of 80 microns would continuously
61
62
scatter light to 200 mtcrons a:nd \-;ould effectively
scatter all light until 800 microns (See Figure .5-1).
Thus
for a laser to be effective, its wavelength vmuld have to
be in the upper submillimeter region (At this time there is
no operational laser in this region).
Finally, required
laser power output and absorption, ·Which is a significant
problem in the far infrared, will have to be investigated
to determine if this system is at all practical.
CJ
-a
....._
..-1
I
\ll
Q)
H
-~
...._
-I
-'
I
~
..........
I
I
I
~I
~
I
-
C)
~'f\
~!
)
CJ
..........
I
- ..._.
Ln'
I
-
()
~
bD
·r-1
IIi
-•-
·•
--
••-
o•-
••·•~
.-ow·-•
·•
••
-
•·•o
••
'
BIBLIOGRAPHY
1.
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2.
Haight, F. A.; l'la~_matica1 Theories of Traffic Flow;
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3.
Pipes, L.A.; A Proposed Dynamic Analogy of Traffic;
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4.
Pipes, L.A.; Wave Theories of Traffic Flow; Journal
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Bender, J. G., Fenton, R. E.; A Study of Autom~tic
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~r
6.
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?.
Flagie, C. D., Huggin, H. J., Roy, R. H.; OJ2eratim}.§.
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64
14.
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Kerker, M.; The Scattering of Light and o~her
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V..a...'-"-'- ...... . _ . ,
... ~.&.
27.
.TA"hv>
V'-".L.I.~.L.
\,T;1ou
UJ...~'-'J
9,
\..XI
C::Av>CO
....,'-'oi..l."'-''
&
Sons;
Engine9~ing;
Wiley
TV\n
•
...L.J..i..V•J
l\To1•T
.1.'11¥V1
VAY>lr•
-L.V..L.n.. ,
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