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FM-CW LASER RADAR AT 10.6 MICRONS
Thomas Henry Chance
LiDMry
Naval Postp.raduate School
Monterey, Calitorma 93940
NAVAl POSTGRADUATE SCHOOL
Monterey, California
THE
FM-CW LASER RADAR AT 10.6 MICRONS
by
Thomas Henry Chance
December 1974
Thesis Advisor:
C. H. Rothauge
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FM-CW Laser Radar at 10,6 Microns
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Electrical Engineer;
December 1974
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19. KEY WORDS (Cpntinum on rmvmrmm oido if noemommry ond idonUfy by biock numbmr)
Optical Radar FM-CW Optical Radar
Lidar
Optical Coherent Detection
Laser Radar
20. ABSTRACT (Continum on rmvmrmm midm if nmcmmmmry mnd idmntity by bioek nutnbmr)
The feasibility of a continuous -wave frequency-modulated
radar with a CO- laser as a transmitting source was
investigated.
A developmental system was constructed and tested and
the feasibility of an optical radar utilizing coherent
detection at 10.6 microns was demonstrated. The radar had
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the capability of instantaneous range and velocity
determination.
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2
. FM-CW Laser Radar
at 10.6 Microns
by
Thomas Henry jZhance
Lieutenant, United States Navy
BSEE, Purdue University, 1969
MSEE, Naval Postgraduate School, 1974
Submitted in partial fulfillment of the
requirements for the degree of
ELECTRICAL ENGINEER
from the
NAVAL POSTGRADUATE SCHOOL
December 1974
C
C ' ^
jf
Library
Naval Postgraduate Scru. ai
Monterey, Californn 93.-0
ABSTRACT
The feasibility of a continuous -wave frequency-modulated
radar with a CO 2 laser as a transmitting source was
investigated.
A developmental system was constructed and tested and
the feasibility of an optical radar utilizing coherent de-
tection at 10.6 microns was demonstrated. The radar had the
capability of instantaneous range and velocity determination.
4
TABLE OF CONTENTS
I. INTRODUCTION--- 13
II. GENERAL SYSTEM CONSIDERATIONS 15
A. FM-CW RADAR 15
1. Analysis of a FM-CW Radar System Using
Triangular Modulation 15
2. Signal Processing in a FM-CW Radar 20
a. Receiver Bandwidth Requirements 20
b. Range Spectrum Analysis 21
(1) Spectrum of a Near Range Target-- 21
(2) Spectrum of a Far Range Target 23
c. Spectrum Spread of Acceleration 23
d. Range Resolution 26
e. Velocity Resolution 27
f. Signal to Noise Effect of Collapsing
the FM Return 2 7
g. Range and Velocity Filtering 27
B. MODULATION OF A LASER BEAM 2 8
1. Historical Basis of Acousto-Optic
Modulation 28
2. The Debye-Sears Effect 28
3. Bragg Diffraction 30
a. Modulation Frequency 34
(1) Doppler Modulation Determination- 34
(2) Particulate Analysis of
Modulation 35
4. Modulation Bandwidth 37
5. Optical Power Transfer 37
5
V
JtJt
6. Modulator Considerations 38
C. DETECTION 38
1. Photo-Voltaic Detector 38
a. Spectral Response and Quantum
Efficiency 40
b. Detector Noise 41
(1) 1/f Noise 41
(2) Generation-Recombination (g-r)
Noise 43
(3) Johnson Noise 43
c. Detector Characterization 45
(1) Responsivity 45
(2) Noise Equivalent Power 45
(3) D* --- 46
2. Coherent Detection 46
D. ATMOSPHERIC ATTENUATION 48
1. Transmissivity 48
a. Absorption
b. Scattering
c. Scintillation
d. Ray Bending
e. Turbulence
III. MAJOR SYSTEM COMPONENTS
A. LASER-- -
B. ACOUSTO-OPTIC MODULATOR-- 55
C. DETECTOR 59
D. OPTICAL ANTENNA 61
IV. SYSTEM ANALYSIS AND ALIGNMENT PROCEDURES--- 65
6
A. PRELIMINARY DEVELOPMENT 65
B. FIRST OPTICAL SYSTEM 67.
C. SECOND OPTICAL SYSTEM 71
D. THIRD OPTICAL SYSTEM 72
E. ALIGNMENT TECHNIQUES 72
1. Height Adjustments 72
2. Acousto -Optic Modulator Alignment 73
3. Collimation of the HeNe and CO 2 Transmit
Beams 74
4. Collimation of Visual Optics with the
CO 2 Transmit Beam 76
5. Alignment of the Newtonian Optics 76
6. Signal and Local Oscillator Beam
Alignment 7 8
F. ELECTRONICS AND SIGNAL PROCESSING 79
G. SYSTEM RADAR ANALYSIS 8 2
V. EXPERIMENTAL PROCEDURES AND RESULTS 84
A. DETERMINATION OF RANGE 84
B. TARGET DETERMINATION AT 305 YARDS 8 7
1. Return Signal from Retro-Reflector at
305 Yards- - 90
2. Transmit Divergence Determination 94
3. Field of View Measurement 96
4. Expected Return from a Diffuse Reflector
at 305 Yards 97
5. Calculation of Detector Quantum
Efficiency 98
6. Calculation of Noise Equivalent Power 99
C. EXTENDED RANGE CAPABILITY 101
D. VELOCITY DETERMINATION - 103
VI. CONCLUSIONS AND RECOMMENDATIONS - --109
7
A. CONCLUSIONS 109
B. RECOMMENDATIONS FOR FURTHER STUDY 109
C. POSSIBLE SYSTEM APPLICATIONS 110
APPENDIX A: EQUIPMENT LIST 112
BIBLIOGRAPHY 114
INITIAL DISTRIBUTION LIST 116
8
LIST OF TABLES
I. Laser Output Power as a Function of Driver
Setting 54
II. Acousto-Optic Modulator Characteristics 56
III. Modulator Frequency as a Function of Input
Voltage 58
IV. Detector 3 db Bandwidth and Quantum Efficiency
vs. Bias Voltage 60
V. Range Frequency Determination as a Function of
Range 85
VI. Velocity Determination Results 108
9
LIST OF FIGURES
Figure
1. Frequency vs. Time of Transmit Signal 17
2. Transmit and Return Signals vs. Time 17
3. Range Frequency vs. Time r 17
4. Return from Target with Positive Relative
Velocity 19
5. Frequency vs. Time, Near Range Target 22
6. Range Frequency vs. Time, Near Range Target 22
7. Frequency Spectrum of Range Frequency 22
8. Frequency vs. Time, Range = H Unambiguous •
Range 24
9. Range Frequency vs. Time, Range = h Unambiguous
Range 2 4
10. Frequency Spectrum of Range Frequency, Range =
H Unambiguous Range 2 5
11. Debye-Sears Effect 31
12. Debye-Sears Effect 32
13. Bragg Diffraction 33
14. Momentum Scattering for Plane Monochromatic
Optical and Acoustical Waves 38
15. Momentum Scattering for Acoustical Waves of
Finite Width and Diffraction 38
16. Acousto-Optic Modulator-- 39
17. Effective Quantum Efficiency vs. Wavelength 42
18. Equivalent Circuit of a Photodiode 42
19. Generalized Detector Noise Spectrum 44
20. Atmospheric Transmission vs. Wavelength 49
21. Acousto -Optic Modulator 57
10
Pigu re
22. Newtonian Optical Antenna 64
23. First Optical System 66
24. Second Optical System 68
25. Third Optical System 69
26. Signal Processing System 80
27. First Optical System 86
28. Third Optical System, View 1 86
29. Third Optical System, View 2 88
30. View from Spanagel Hall to Ingersoll Hall 88
31. NFS Grounds Near Range Target 89
32. Velocity Generating Model Railroad, View 1 91
33. Velocity Generating Model Railroad, View 2 91
34. Zero Range Frequencies 92
35. Unprocessed Detector Output for 305 Yard Target- 92
36. Processed Return for 305 Yard Target 93
37. Far Range Target Measurement 102
38. Processed Return for 2370 Yard Target, View 1 104
39. Processed Return for 2370 Yard Target, View 2 104
40. Processed Return for Negative Relative Velocity,
View 1 106
41. Processed Return for Negative Relative Velocity,
View 2 - 106
42. Processed Return for Positive Relative Velocity,
View 1 107
43. Processed Return for Positive Relative Velocity,
View 2 107
11
ACKNOWLEDGEMENTS
I desire to give recognition and express gratitude for
the support given by the Naval Electronic Laboratory Center
San Diego, Code 2500, particularly to Dr. Greg Mooradian
and Rudy Krautwald. Also I am grateful for the assistance
of Professors John Powers, T. F. Tao and C. H. Rothauge
and for the technical support provided by Ross Seeley and
Bob Moeller, all of the Naval Postgraduate School.
This research project was conducted with Lieutenant
Maurice F. Fraunfelder, Jr., a fellow student at the Naval
Postgraduate School.
Rockwell International Science Center provided a PbSnTe
heterojunction p-i-n diode, courtesy of Dr. J. Longo,
similar to the detector loaned by NELC (which was also
manufactured by Rockwell International Science Center) .
This detector had a slightly higher quantum efficiency than
the one provided by NELC but did not have as high a fre-
quency response even when back biased at .6 v. It was
operated at 28-35 MHz (vice 35-45 MHz) but the frequency
limitation still reduced the output to 5 db below that of
the detector utilized in the system.
Aerojet Electrosystems Co. also provided a PbSnTe
heteroj unction p-n diode, courtesy of Dr. Peter Wang, but
although it had a good quantum efficiency, its frequency
response was much too low to be utilized in the system.
12
I . INTRODUCTION
A continuous -wave frequency-modulated radar provides a
means of determining both range and relative velocity of a
target. Since the radar is continuous -wave rather than
pulsed, it enables realization of a given range capability
without requiring high peak power capability such as would
be required by a pulse radar. FM-CW radars have been de-
veloped for years but with the advent of the laser, a
transmit power source of extremely high frequency and co-
herence became available.
Initially there was not the laser stability nor the
means of frequency modulation of the beam available to make
a system such as this practical. This capability exists
now and was utilized in the developmental system.
The laser source provides a narrow beam and enables the
use of a high-gain optical antenna which is small and light
weight (since gain is proportional to X and X is 10.6 ym)
This narrow beam allows excellent bearing resolution but
requires a relatively long search time for any given volume
of interest. It would also require excellent beam steering
capability for a tracking application.
Heterodyne detection of 10.6 ym radiation at high IF
frequency has only recently become feasible with the de-
velopment of fast detectors with a cut-off wavelength
greater than 10.6 ym. Heterodyning also provides higher
sensitivity and low vulnerability to jamming.
13
Operation at 10.6 ym wavelength is outside the capability
o£ any known intercept receiver and could not be detected by
any known anti-radiation seeker.
14
II. GENERAL SYSTEM CONSIDERATIONS
A. FM-CW
FM-CW radars offer several distinct advantages over
standard pulse radars. In the CW radar the ratio of peak
power to average power is near or equal to one. Since the
maximum range of a radar is proportional to the fourth root
of the average power this allows for good range capability
without requiring components and circuitry capable of pro-
viding and switching high power and voltages as in a pulse
radar [1] . Elimination of this requirement results in large
savings in system size and expense.
R
= r
^ 1 A 'TT
P.GoA
max ^16¥^P T
( 1 )
min
where is the average transmitted power, G is the antenna
gain, 0 is the target cross section, A^ is the effective
receive aperture and is the minimum required return
signal power [2] . Normal FM-CW radars utilize two antennas
and require feed over cancellation [3] while pulse radars
require one antenna and a duplexer. Both these approaches
are improved on by an optical radar which can use one an-
tenna with no cancellation or duplexing. Additionally an
optical antenna provides extremely high gain with small size.
1 . Analysis of a FM-CW Radar System Using Triangular
Modulation
FM-CW radars determine range and velocity by ana-
lyzing the difference between the frequencies of the return
15
and transmitted signals. If the transmitted signal is as
- 1
shown in Figure 1 where ^uiodulating ~ ^ modulating
frequency and ^^j-^nsmit frequency of the transmitted
signal, the return signal reflected from a stationary tar-
get will be identical to that being transmitted only delayed
AT.
AT = ^ (2)
where R is the target range and c is the free space velocity
of the propagation of light. The time -frequency display of
the transmit and return signals is shown in Figure 2.
If the instantaneous transmit and return signals are
mixed the difference frequency can be extracted and processed.
The time- frequency display of the difference frequency is
shown in Figure 3.
The difference frequency directly yields range in-
formation. The rate of change of transmitted frequency
(df/dt) is given by
— = = 4AF F
dt TTl ^m
(3)
where T is the modulating period, 2AF is the total range of
frequency deviation and F^^ is the modulating frequency.
Range frequency and thus range information is pro-
vided from
df
range
' ar*’'-
R
ange
p
C‘AT _ c range
“2 — 2 * “37/ at •
(4)
(5)
16
Figure 1. Frequency vs. Time of Transmit Signal.
Figure 2. Transmit and Return Signals vs. Time.
range
\/ V V
N ? I
Figure 3. Range Frequency vs. Time.
^t
17
I
Since for a given system d£/dt is constant;
R = constant • F
ange range
( 6 )
and thus range can be directly determined from the transmit
and return difference frequency.
If there is a relative velocity between the radar
and target the returned signal will have an additional shift
in frequency due to doppler shift. Doppler shift is given
by the relationship [4]
doppler
2 • V R • F
elocity elative o
(7)
where is the frequency of the transmitted optical signal.
Comparison of the transmit and return signals, when the re-
turn signal has doppler information from the positive rela-
tive velocity, yields a time -frequency display as in Figure
4.
The difference frequencies F^ and F^ can be processed
to extract both range and doppler frequency information.
F .. >
xmt
F
rev
F =
a
F
1 xmt
■=rcvl
= F - F
range doppler
(8)
F >
rev
F ^
xmt
^b =
|f -
' xmt
frcvl
= F + F
range doppler
(9)
In systems where the expected range frequency offset
is greater than the expected doppler shift, range and dop-
pler information can be extracted by processing as:
( 10 )
F
range
F + F,
a b
TF " F 'I + fF + F I
range doppler-* ^ range doppler-^
( 11 )
doppler
- Fo (F + F, 1 ) - (F
a _ range doppler-* range
dopple
r)
18
F transmit
F receive
Figure 4. Return from Target with Positive Relative Velocity.
19
If the expected doppler frequency shift is greater than the
expected range frequency of equations (10) and (11) are
reversed.
It is readily seen from equation (7) that the rela-
tive velocity is the product of a constant times the doppler
shift (any variation in due to modulation is negligible) .
2 . Signal Processing in a FM-CW Radar
There are numerous interactions between bandwidth
requirements, signal processing and expected target perform-
ance. The receiver input bandwidth must be great enough to
accommodate the return signal which is both FM and possibly
doppler shifted, IF bandwidth and processing filters must
be able to process difference frequencies, doppler broaden-
ing and range broadening. These bandwidths affect range
and velocity determination and available modulation rates,
a. Receiver Bandwidth Requirements
The receiver bandwidth must be able to pass the
FM spectrum of the transmit signal and also accommodate any
doppler shift within the range of interest.
The bandwidth requirement of an FM system is
given by
BW = 2(1+B)F^ = 2(1+AF/FJF^. (12)
For a frequency excursion of 5 MHz at a modulating rate of
1.75 kHz this yields a bandpass requirement of 10.0035 MHz
or approximately 2 AF.
As stated, additional allowance must be made
for doppler offset. The amount of the offset is given by
20
equation (7) . For a laser the optical frequency is
2.83 X 10^^ Hz. This yields
2*V . *F
5 _ relative o
'doppler ~ c
=95.8 kHz/knot.
= 52.4 kHz/km/hr
C13)
If the maximum relative velocity of interest was 1000 knots
this would require an allowable offset of ±95.8 MHz. This
requirement for a wide receiver bandwidth yields a very wide
noise bandwidth which reduces receiver sensitivity. This
can be largely offset by narrower velocity range of interest,
b. Range Spectrum Analysis
The spectrum of the range frequency requires an
IF bandwidth sufficient to pass the spectrum. Regretably
the spectrum of the range frequency varies with the range.
This spectrum will be considered at very short range and at
a range of one half the maximum unambiguous range.
Cl) Spectrum of a Near Range Target . Figures
5 and 6 show the frequency- time relationship for a near
range target. The frequency spectrum of the range frequency
can be closely approximated by assuming rectangular pulses
of duration t and period AT. This spectrum is shown in
Figure 7. It should be noted that the first sidebands exist
in the main lobe at reduced magnitudes. As the range in-
creases the ratio of the pulse width to the period decreases
and the lobe spreads until at the point where the pulse width
is less than half the period two sidebands will exist within
the main lobe of the spectrum. Before this point is reached
the approximation of a rectangular pulse is not nearly as
21
}
£4
F +AF
Figure 5. Frequency vs. Time Near Range Target.
range
\l
V
~^J
►
1 *- ^
♦ t
Figure 6. Range Frequency vs. Time Near Range Target
1.0
Sen
T
A Ni.
X X
M
.fS
Foif‘/r\ Fot
^ JL
X X
T 2
Figure 7. Frequency Spectrum of Range Frequency. t=j
22
I
exact and a better approximation is that of a trapezoidal
pulse.
(2) Spectrum of a Far Range Target . Figures 8
and 9 show the frequency- time relationships for a target
whose range is one half the maximum unambiguous range of
the radar. The frequency spectrum of the range frequency
is that of a trapezoidal pulse whose maximum frequency
exists for one half the period. The spectrum envelope is
found from the product of [5,6]
sin (irnt^/T/Z) sin [un (t /T/2]
Trnt^/T/2 * un (t j^+t^) /T/2
sin('rrnt^/T/2) sin[Tm3t j^/T/2]
Trnt^/T/2 * Trn3t^/T/2
(14)
This spectrum is shown in Figure 10. It can be seen that
the spectrum is being spread and a greater percentage of
the signal energy is in the first sidebands,
c. Spectrum Spread Acceleration
An accelerating target causes a spread in the
doppler frequency of the return signal. This is analyzed
in a straightforward manner as follows:
el o
doppler
(7)
dF
“3t = 3t /
2-A
, 2*V , -F
d ^ el o
2*F
) =
ccel
AF
ccel
At
(15)
(16)
At is determined by the filter bandwidth so in the limit of
the bandwidth
23
Figure 8. Frequency vs. Time Range = % Unambiguous Range.
range
Figure 9. Range Frequency vs. Time Range = h Unambiguous
Range .
!
24
sin(2mrt j^/T) sin (6mrt ^^/T)
2mrt 6mrt^/T
Range = h Unambiguous Range
4ti = T/2 = 1/F„
Sidelobes 18.4 db down
Figure 10. Frequency Spectrum of Range Frequency.
25
(
( 17 )
where AF is the maximum allowable spreading of the spectrum.
In practice the filter bandwidths are sufficient to accommo-
date very high accelerations.
d. Range Resolution
Range resolution is determined by the bandpass
of the resolution filter or the spectrum width of the range
frequency, whichever is greater. A well designed system
will have a filter width whose response time corresponds to
the modulating period and with the exception of targets ap-
proaching the maximum unambiguous range this will be suffi-
cient for resolution calculations. The maximum unambiguous
range can be determined by the following relationship
T
R = £ . modulation q
unambiguous 2*2' ^
This limitation is determined by the propagation time for
the target signal and the period of the modulating ramp.
If the modulation rate is matched to the range filter (it
can be slower) the range resolution is a direct function
of the modulation bandwidth [6].
Filter BW
“'d'f/dt
( 20 )
From equation (2) and matching the filter to F^ this becomes
[7]
26
AR =
( 21 )
c 1
2 * 2 ^
which indicates that improved resolution requires a larger
frequency excursion of the FM signal,
e. Velocity Resolution
Velocity resolution is similar to range resolu-
tion in that the wider the filter bandwidth the poorer the
velocity resolution. Doppler resolution is given by the
relationship
AV
el
^*^^doppler _ C'Filter BW
2F 2F
o o
( 22 )
f. Signal to Noise Effect of Collapsing the FM
Return
When the transmit and received signals are mixed
together the spectra of the two signals collapse and there
results a relatively narrow frequency signal which is a
function of target range and velocity. The resultant sig-
nals can be passed through bandpass filters and thus the
resultant noise bandwidth is drastically reduced while the
signal information is passed. The overall effect of this
processing is to reduce the noise present and greatly improve
the signal to noise ratio.
g. Range and Velocity Filtering
A means of determining the range or velocity
frequencies is necessary in order to provide the inherent
information. One method for doing this is to feed the in-
formation into a parallel bank of filters and provide a
display according to which filter passes the information.
27
An alternate and more efficient approach is to utilize a
sliding filter which sweeps the spectrum with respect to
time in a known controlled manner. This approach allows
relatively high resolution over a broad range with rela-
tively few components and thus less bulk and expense.
B. MODULATION OF A LASER BEAM
1, Historical Basis of Acousto-Optic Modulation
The diffraction of light by accoustical waves in a
medium was predicted by Brillouin in 1922 [9] . This phe-
nomenon was observed by Debye and Sears in 1932 and is now
known as the Debye-Sears effect. There was some initial
investigation of the effect but until the advent of the
laser to provide a high intensity beam which is highly co-
herent in both time and space no important application was
seen and interest waned.
The mechanism by which acousto -optic modulation is
accomplished is known as the photoelastic effect. This ef-
fect is the change in the index of refraction due to mech-
anical strain and is present in some crystals and liquids.
Ultrasonic waves propagating through a material produce
mechanical strains which in turn cause variations in the
index of refraction. In this case the variation is known
as the acousto -optic effect.
2 . The Debye-Sears Effect
When a plane wave of light of angular frequency, w,
enters a slab of material with an index of refraction, n,
the velocity of light in the material is reduced by the
28
j
factor n from its free space velocity c. The optical wave-
length A in the slab is
X =
2irc
no)
(23)
and the material acts as an optical delay line with a time
delay t for a given length 1 .
(24)
The delay, (j) , corresponds to a phase delay of
. _ An
^ ■ c *
<j) = cot =
coAn
Equation (25) can also be expressed as
2irfAn 2irAn
<t> =
o
(25)
(26)
where X^ is the free space optical wavelength. The varia-
tion of phase delay with respect to the variation of n is
If n is varied with respect to time in a controlled manner
then the phase delay is also varied directly and a means of
phase-modulating an optical beam exists.
From standard FM analysis it is known that the phase
modulated wave consists of a carrier and sidebands which are
separated by co^^ where co^^^ is the angular frequency of the
modulating mechanism, in this case the angular frequency of
the variation in the index of refraction of the slab of ma-
terial. The amplitude of the carrier and the sidebands vary
as Bessel functions where corresponds to the carrier,
to the first sideband, etc.
29
When an acoustical wave is launched in a medium and
an incident optical wavefront passes through the medium as
in Figure 11, modulation will occur. The acoustical wave
launched in the modulator with angular frequency and at
the acoustical velocity of the medium V , propagates through
a
the modulator with variations of compression and rarefactions
with an acoustical wavelength X
d.
2ttV
The rarefactions and compressions cause the corresponding
variations in the index of refraction. These "slabs" of
different indices of refraction modulate the incident opti-
cal wavefront yielding the carrier and sidebands of which
the carrier and first upper order are illustrated in Figure
11 [ 10 ].
The first upper diffracted wave is indicated in
Figure 11. Higher order upper sidebands are tilted up at a
greater angle and the lower order sidebands are tilted down.
Figure 12 shows the Debye-Sears effect and the variation in
the index of refraction in the modulator.
3. Bragg Diffraction
If the wavefront variation in the index of refraction
is characterized as a partially reflecting mirror and the
optical beam is incident upon the acoustical wavefront at
an angle 0^ as is shown in Figure 13 [9] then the diffracted
wave will be directed away with the angle of refraction 0^.
A necessary condition for diffraction in a given direction
30
Incident
Optical Wavefront
b)
Compressed
Dilating
Dilated
Compressing
Compressed
Dilating
Acoustic Wave - X , V
a * a
Figure 11. Debye-Sears Effect.
31
Distance
Index of
Refraction
t
Acoustical
I Wave
Figure 12. Debye-Sears Effect.
32
4
V
a
Figure 13. Bragg Diffraction.
33
is for all points on the reflecting surface to contribute
in phase. To satisfy this requirement for the two points
of diffraction B and D the difference between the paths AD
and BC must be an integral multiple of the optical wave-
length This condition is satisfied when
x(cos6^ - cos0^) = mX^ (29)
where m = o, ±1, ±2,... This can be satisfied for all
points X only when m = o. This requirement indicates that
0. = 0 . Additionally for different wavefronts of the modu-
lator (separated by X ) to interfere constructively it is
ci
required that
2X sin0 = X (30)
a o
where 0. = 0 =0. This is known as Bragg diffraction since
1 r
it is the same requirement for X-ray diffraction in a lattice
Since X is much larger than the optical wavelength, X , sin0
is small and is usually approximated by 0 . It is also seen
from Figure 13 that the angular separation between the dif-
fracted and undiffracted beam is twice the Bragg angle 0.
a. Modulation Frequency
Determination of the frequency shift in the dif-
fracted beam can be determined from two approaches. The
first is a somewhat simplistic consideration of geometry
and doppler shift and the second a consideration of energy
and momentum requirements through the utilization of wave
vectors .
(1) Popper Modulation Determination . The
acoustical wavefronts which cause diffraction as shown in
34
Figure 13, are propagating through the acousto-optic modu-
lator with velocity V . This will yield a doppler shift in
3 .
the diffracted beam according to the relationship
2V sin0f
p = ^
doppler c
(31)
where f is the optical frequency. From the Bragg equation
(30) the relationship between sin0 and the two wavelengths
are shown. The doppler shift is given by
2V X^f
j _ a o _ a _ p
doppler 2X X ^m
3 3
(32)
where F^ is the frequency of the acoustical wave. If the
two wavefronts are closing as is shown in Figure 13 the
doppler shift is positive and the frequency of the diffracted
wave is F+F . If the relative velocity between the two wave
fronts is negative the frequency of the diffracted wave is
F-F
m
(2) Particulate Analysis of Modulation . Light
has a dual wave -particle nature and analysis can be done by
consideration of its particulate nature. Photons have an
energy hw and momentum hk. Similarly the acoustic phonons
have an energy ho) and momentum hk . In any interaction
between the photons and phonons both energy and momentum
must be preserved since both the incident photon and phonon
cease to exist and a new diffracted photon is created.
Figure 14 shows the wave vector relationship between the
-y -y
incident photons k^ , the diffracted photon k^ and the acous-
-y
tical phonons k^^. Conservation of momentum requires that
35
I
h(k +k.) of the colliding phonon and photon equal hk of
3. X T
the scattered photon,
k = k + k. .
r s 1
Conservation of energy requires
0) =t0. + 0) = 01 + 0)
r 1 a m
or for a negative relative velocity
a)_=03. - 0) = (i)-a)
r 1 a m
(33)
(34)
(35)
which shows that the diffracted wave is modulated by the
acoustic frequency.
Since the acoustic frequencies are less than
10^® and the optical frequencies are greater than 10^^
“r “ ■ % ■ l^rl ■ l^il
and the magnitude of the two optical wave vectors is approxi'
mately the same. From Figure 14 it is seen that
and since
l^al = 2|k^|sin0
Ikal = 2 -/\
(37)
(38)
it follows that
2X sine = X (39)
a o
which is the Bragg diffraction requirement.
Figure 14 is for perfectly monochromatic plane
waves. In actuality there is both wave divergence and some
frequency variation. Thus rather than being only one exact
angle of diffraction allowed there is a small range. This
36
m
effect is illustrated in Figure 15 where only acoustical
divergence is considered [11]-
/ 4. Modulation Bandwidth
The modulator bandwidth is inversely proportional to
the transit time of the acoustic wave across the optical
beam. A means of increasing the bandwidth is to focus the
optical beam and have its waist centered in the modulating
medium. The waist diameter can be determined from the
relationship [12]
^ llnl ^ f40")
«o “ ^ ""i" > %
where w is the focused optical waist diameter, is the
o
unfocused beam waist and F is the focal length of the
focusing lens. The expression for modulator bandwidth is
given by [13]
hf = .54
where V is the acoustical velocity.
3 .
5. Modulation Power Transfer
The amount of power transferred from the incident
beam to the modulated beam is a direct function of inter
action length I of the beam through the modulating medium
and the amount of change of the index of refraction in the
medium. The latter is a direct function of the acoustical
power up to a saturation level in the medium. This power
transfer is also inversely related to the optical wavelength
In the previous section it was noted that the modulating
bandwidth is inversely proportional to the optical waist
37
Figure 14. Momentum Scattering for Plane Monochromatic
Optical and Acoustical Waves.
Figure 15. Momentum Scattering for Acoustical Waves of
Finite Width and Diffraction.
/
38
diameter, there is a tradeoff between the waist diameter
and the length that the optical wavefront is planar so
this must be considered with respect to the diffraction ef-
ficiency. The expression for diffraction efficiency is
given in (3) . With some manipulation this reduces to
^diffracted _ ■ z r irilAn
j — sin ( ^ j , (42).
incident o
Another approach to this is given in [14] .
6 . Modulator Considerations
A diagram of an acousto-optic modulator is shown in
Figure 16. There is a transducer to couple the electrical
modulating signal into the crystal. To date the transducer
is often the limiting component with respect to the band-
width. At the opposite end of the m.odulating crystal there
is an absorbing medium to prevent reflection of the acousti-
cal waves back into the optical beam.
C. DETECTION
Detection of optical signals encompasses many aspects
however, only those pertinent to the CO 2 laser radar will
be covered.
1 . Photo-Voltaic Detector
Photo-Voltaic detectors are semiconductor diodes in
which incident photons create electron-hole pairs in or with
in one diffusion length of the depletion region of the diode
These generated carriers are accelerated in opposite direc-
tions by the intrinsic field present within the depletion
region and depending upon biasing arrangement, give a signal
38 a
I
Signal
Figure 16. Acousto-Optic Modulator.
39
either in current flow variation or output voltage varia-
tion. In properly constructed and biased diodes the genera-
ted excess carriers move at scattering limited velocity and
there is virtually no recombination within the depletion
region.
a. Spectral Response and Quantum Efficiency
The absorption of photons in the semiconductor
material is a strong function of the wavelength of the in-
cident photon. To a much lesser degree there is variation
with temperature since both the semiconductor energy gap
and surface recombination velocity are effected by tempera-
ture. The maximum wavelength that will generate an excess
carrier in the semiconductor material is given by the rela-
tionship [15]
_ he 1.24(ym)
c - Eg -
(43)
where is the cut-off wavelength and is the forbidden
energy gap. Wavelengths longer than X^ will effectively pass
through the active region of the photodiode without absorption.
Shorter wavelength photons will be more readily
absorbed until for much shorter wavelengths the photons are
essentially all absorbed very near the semiconductor surface
and the generated excess carriers are lost to the detection
process due to high surface recombination that occurs near
the boundaries of the crystal lattice. The overall effect
of the wavelength dependency of photon absorption yields a
curve as is shown in Figure 17. This shows the effective
quantum efficiency of intrinsic silicon and germanium
photodetectors.
40
The quantum efficiency is a measure of the con-
version efficiency of the photodetector in converting photons
to excess carriers. Quantum efficiency, n, is defined as
the ratio of the number of photons that generate excess
carriers to the number of photons incident upon the detector.
The current generated in a photodiode is given by
i = nqM (44)
where n is the quantum efficiency, q is the electronic
charge, $ is the incident photon flux density and A is the
active area of the detector.
The equivalent circuit of a photodetector is
given in Figure 18 [15]. The available power into a matched
load from this circuit is [15]
^avail w^c^R
(45)
gCnqM) (jj2c2R •
(46)
Due to thermally generated carriers known as
dark current all semiconductor detectors which operate at
10.6 ym must be cooled to 77°K. Due to advances in material
processing this requirement may be relaxed somewhat,
b. Detector Noise
There are three primary categories of noise in
photodetectors, all of which predominate in a general fre-
quency range.
(1) 1/f Noise . There are several types of
noise for which the power spectrum varies as the inverse of
frequency. This noise is sometimes known as modulation
41
Wavelength
(microns)
Figure 17. Effective Quantum Efficiency vs. Wavelength for
G and S. Photodetectors.
C 1
R
Figure 18. Equivalent Circuit of a Photodiode.
42
noise in semiconductors or flicker noise in vacuum tubes.
l/£ noise becomes negligible with respect to other noise
sources above a few kHz.
(2) Generation-Recombination Cg~r) Noise . In
semiconductors the major source of noise at intermediate
frequencies (above the range where 1/f noise predominates)
is g-r noise which is due to fluctuations in rate of charge
carrier generation and recombination. This variation is
due in part to the randomness of the arrival of the photons
of the incident flux. This latter effect is sometimes
categorized separately as photon noise. Generation-recom-
bination noise is relatively flat with respect to frequency
up to the value where it is approximately equal to the in-
verse of the free carrier lifetime; at this point it falls
off at about 6 db per octave.
(3) Johnson Noise . Johnson noise is thermally
generated and present in all devices in accordance with
their temperature and bandwidth. The noise is independent
of frequency up to extremely high frequencies. The expres-
sion for thermal noise power is given by [16]
4kTB
Noisej = R
(47)
where k is Boltzmans constant, T is the temperature in
degrees Kelvin, B is the device bandwidth and R is the de-
vice resistance. A profile of noise contribution as a
function of frequency from [17] is given in Figure 19.
43
Figure 19. Generalized Detector Noise Spectrum.
44
I
c. Detector Characterization
There are several figures of merit which are
useful in describing photodiode performance. Those which
are significant with respect to the laser radar are i?, NEP
*
and D .
(1) Responsivity . Responsivity , (i?) , is a
measure of a detector's output for a given input. The units
of responsivity are v/w and it is given by
where is the r.m.s. signal voltage, H is the r.m.s. value
of the irradiance on the detector and is the detector
area in cm^ .
(2) Noise Equivalent Power . A more meaningful
detector parameter is noise equivalent power, (NEP). NEP
is the radiant flux necessary to provide an output signal
such that the signal to noise ratio is equal to one. NEP
can be calculated from
HA, HA,V^2
NEP = TTlTir ' -vV- (49)
'■ s' n'' s
where is the noise voltage, is the signal voltage and
H and A^ are as in (48). A good photodiode will have a NEP
• 1 9 - 2 0
of 10 - 10 w. In shot noise limited heterodyne opera-
tion the NEP of a photodiode is [18]
NEP = — . (50)
n
45
(3) D_. Since both signal and noise are a
function of detector area and noise is a function of band-
width a measure accounting for these factors is D (dee-
star) .
*
D
(A^B)^
NEP •
(51)
B is the detector bandwidth and is the detector area.
* 1^-1
The units of D are cmHz ^w and the measurements are
usually taken at peak responsivity . The theoretical limit
*
of D for a photodiode at 10.6 pm viewing a hemispherical
surrounding at 300°K is approximately S x 10^°. A good
* 1 n
detector at 10.6 ym will have a D of about 2 or 3 x 10
cmHz'^w ^ .
2 . Coherent Detection
Optical signal processing is available in photo-
diodes by heterodyne or coherent detection. Alignment of
the phase fronts of the signal and local oscillator beams
is extremely critical and anything which causes phase front
distortions severely degrades detection.
In the detector the shot noise due to the local
oscillator power can be made to override all other noise
sources. Operation in this condition is known as shot
noise limited operation and this condition allows detection
of signals down to a theoretical minimum known as quantum
limited operation. Neglecting the noise contribution due
to dark current (at 77°K the amount of dark current is very
small) the power signal to noise ratio for heterodyne de-
tection in a photodiode is [19,20]
46
( 52 )
S
PT ■
2(nq/h£)2Pj^Pg
nrr
~TT
t ^ * t;
D
]B
where Tj^ and are the detector and amplifier temperatures
and Pj^ is the local oscillator power, Pg is the signal
power, Pg is the power due to background radiation and B is
the system bandwidth. The numerator is the power of the
difference frequency component of the detector output signal
and the denominator consists of the shot noise power and
thermal noise power.
In shot noise limited operation the power of the
local oscillator is increased until its power is greater
than the signal and background power and the shot noise due
to the local oscillator dominates all other noise contribu-
tions. At this level the signal to noise ratio becomes
S _
N hfB •
(53)
This is twice the SNR of a shot noise limited photoconductor
[ 21 ].
For homodyne operation the signal to noise ratio is
doubled and is [14]
2nPc
S
N
hfB
(54)
The value of heterodyne SNR given in (53) is for
optimal phase front alignment. If misalignment is due to
angle of incidence in only one coordinate the amount of
misalignment which will degrade the heterodyning efficiency
by 10% or less is [14]
47
( 55 )
where is the amount of angular misalignment, X is the
optical wavelength and d is the detector size. For a 10
mil detector at 10.6 ym
\p < 10.4 mrad.
D. ATMOSPHERIC PROPAGATION
The propagation medium for an optical radar is the
atmosphere which affects the transmitted and return beam in
several
ways .
1.
Transmissivity
Energy attenuation in the atmosphere is a strong
function of wavelength. There are several atmospheric
windows
which are located in the following approximate
ranges :
(Figure 20)
of both
.2 - 1.3
1.5 - 1.8
1.9 - 2.6
3 - 4.2
4.5 - 5
8 -13.5.
The attenuation in the atmosphere is a consequence
absorption and scattering. The transmittance of a
path can be expressed as [17]
t = e'^^ (56)
where a
is the extinction coefficient and x is the path
length.
The extinction coefficient is the sum of the absorp-
tion coefficient a which accounts for molecular absorption
and the scattering coefficient y which accounts for scattering
48
(luaDJsd) SDUBUtmsuBJx
49
Figure 20. Atmospheric Transmittance as a Function of Wavelength.
I I
by molecules, haze and fog. Both a and y vary as a function
of wavelength, climate conditions, temperature, humidity
and altitude.
a. Absorption
In the region of interest (10.6 pm) there are
two absorbing molecules which are of significant importance.
These molecular absorbers are CO 2 and H 2 O. Water content
may vary from as much as 21 of a very humid atmosphere at
sea level to a very minor amount in extremely arid regions.
The water vapor content of the atmosphere decreases rapidly
with altitude until at 40,000 ft it is considered negligible.
Water vapor content is also inversely proportional to tem-
perature, thus cold climates or weather minimize the
absorption due to H 2 O.
Carbon dioxide constitutes approximately .0321
of the atmosphere by volume. This percentage is relatively
constant up to an altitude of about 30 miles, then decreases
by a factor of ten for every 10 miles increase in altitude.
CO 2 content varies little with temperature or weather and
thus is a much less variable component than water vapor.
There are several other absorbers such as
ammonia, carbon monoxide, sulfur dioxide, methane or ni-
trous oxides which are normally present in negligible
amounts. In industrial or polluted regions these gases may
be present in sufficient quantities to produce significant
attenuation .
50
b. Scattering
The relationship between the scattering coef-
ficient and wavelength which is often used in predicting
transmissivity is [17]
where is a function of the ratio of the particle size to
the wavelength. If the particles are small with respect to
the wavelength \p is equal to 4 and the scattering process
is known as Rayleigh scattering and is strongly dependent
upon wavelength. It is this wavelength dependent scattering
which causes the sky to appear blue. For larger particles
the value of \p approaches zero, this process is called Mie
scattering and is independent of wavelength. For most fogs
is zero for the visible spectrum and thus the fog appears
white .
In general the atmospheric categorization of
haze consists of particles whose radii range up to .5 ym
and that of fog consists of particles which range from .5 -
80 ym with a distribution peak which usually ranges from
5-15 ym. These numbers indicate that at 10.6 ym haze
will have minimal effect but fog will greatly reduce trans-
missivity. Actual experience obtained by the Naval Elec-
tronics Laboratory Center at San Diego seems to indicate
that fog may not scatter as much as was expected.
Rain reduces the transmissivity in direct pro-
portion to its intensity. Raindrops range in size up to
approximately 3 mm and thus \p has a value of zero and Mie
51
scattering with wavelength independence is the scattering
phonomonon. All experience to date indicates that rainfall
is the predominate attenuating factor at 10.6 um.
c. Scintillation
Scintillation is the phenomenon which causes
uncorrelated variation of intensity and apparent directional
changes in a radiant source. This phenomenon is caused by
relatively rapid discontinuous variations in the index of
refraction in the propagation path. Scintillation is the
primary effect which renders amplitude modulation of an op-
tical beam for atmospheric propagation a poor second choice
when compared to frequency modulation.
d. Ray Bending
Variations in the index of refraction of a more
continuous nature can cause beam bending. This can cause
errors in angular location of targets and other abberations
due to ducting as is experienced in more conventional radars.
e. Turbulence
Atmospheric turbulence causes pheonomona such
as scintillation and phase front distortion. Turbulence
causes variations of intensity and phase across the beam
surface. Direct detection [14] allows integration of the
intensity variation as the receive aperture increases, but
for coherent detection there can be a decrease in signal to
noise ratio as aperture size is increased since the varia-
tions in phase front degrade the signal rather than inte-
grate out.
52
I
4
III. MAJOR SYSTEM COMPONENTS
A. LASER
The laser utilized in the radar system is a 3 w, ver-
tically polarized CO 2 laser (10.6 ym wavelength) built by
Honeywell Corporation. The laser is a closed system laser
and is water cooled. It has an internal piezzo-electric
transducer (PZT) which allows some modulation and control
for line shifting. The PZT was not utilized in the system.
The laser power output as a function of driver setting
is given in Table I. The divergence of the laser was com-
puted as 1.71 mrad. This value is somewhat lower than the
value estimated by NELC but NELC did not measure the
divergence .
A cooling water hose connection inside the laser head
came unconnected during operation of the laser. The water
caused a short from the high voltage leads (±10 KV) to
ground which resulted in the destruction of an inductor in
the laser power supply filter. This required operation of
the laser with an unfiltered power supply and as a result
the output power dropped from 3.05 w to 2.3 w and contained
a 120 Hz ripple. The result of this was a drop in peak
transmitted power from 1.2 w to .65 w and a drop in un-
focused local oscillator power from .93 w to .51 w.
The laser was microphonic (amplified low frequency
mechanical vibrations) but this was filtered out in the
signal processing and presented no problem.
53
Driver Supply Setting
Power Output (Watts)
72
.25
76
.64
80
1.1
82
1.25
84
1.5
86
1.7
88
1.95
90
2.15
92
2.3
94
2.45
96
2.54
98
2.68
100
2.76
102
2.89
104
2.95
110 (Max)
3.05
Table I. Laser Output Power as a Function of Driver Setting.
(Data taken 18 July 1974)
54
B. ACOUSTO-OPTIC MODULATOR
The acousto-optic modulator utilized in the system is
made by Isomet. Its specifications are listed in Table II
[22]. The crystal is germanium and both the modulator and
driver are RFI hardened. A sketch of the modulator is shown
in Figure 21. Table III shows the modulation frequency as
a function of input voltage. While the laser power supply
was filtered the modulator was frequency modulated from
35 - 45 MHz and the modulated output power was 1.2 w while
the unmodulated beam power was .93 w for a modulating ef-
ficiency of 56%. During unfiltered operation the efficiency
was unchanged. This performance was completely satisfactory
considering that the Bragg angle varies with frequency and
the modulator angle was held constant at approximately 2.2°
(the Bragg angle for 40 MHz operation) .
The modulator crystal is germanium which has an acousti-
cal velocity of 5.4 x 10® cm/sec [23]. This yields an
acoustical wavelength at 40 MHz of 135 ym.
There are two 5 inch focal length focusing lenses with
the modulator. The first is to focus the incoming beam to
a minimum waist size to increase the modulator bandwidth
and the second lens is to recollimate the output beams.
There is a time delay between the driver output and
the interaction of the acoustical and optical beams. This
propagation delay in the crystal is due to the time delay
required to propagate from the transducer to the optical
beam and gives an additional frequency offset to the range
frequency. In earlier system alignments this time delay
55
o
Tl
Modulator
Operating wavelength 10.6 ym
Rise time 70 nsec
Deflection efficiency
> 60% with DC input
Contrast ratio
1000:1
Static transmission efficiency
88%
Coatings
AR at 10.6 ym
Optical aperture
1 mm
Acoustic center frequency
40 MHz
Nominal impedance
50 Q
Cooling
water cooled
Driver
Bandwidth
35 - 45 MHz
Input impedance
50 ohms
Linearity
> 5% deviation
Input voltage
- 6.27V (35 MHz) to
- 9.27V (45 MHz)
Output amplitude variation
± 1 db
Table II. Acousto-Optic Modulator Characteristics.
56
BNC Connector
Impedance Matching Coil
Aluminum Case
Electrode and Heat Sink
Transducer
Germanium Crystal
Copper
Acoustic Absorber
Figure 21. Acousto -Optic Modulator.
57
Input
Voltage
(V)
Output
Frequency
(MHz)
6.0
35.2
6.1
35.6
6.2
35.9
6.3
36.2
6.4
36.6
6.5
37.0
6.6
37.3
6.7
37.6
6.8
37.9
6.9
38.3
7.0
38.6
7.1
38.9
7.2
39.2
7.3
39.6
7.4
39.9
7.5
40.2
7.6
40.5
7.7
40.8
7.8
41.2
7.9
41.5
8.0
41.8
Input
Voltage
(V)
Output
Frequency
(MHz)
8.1
42.1
8.2
42.4
8.3
42.8
8.4
43.1
8.5
43.4
8.6
43.7
8.7
44.0
8.8
44.3
8.9
44.6
9.0
44.9
9.1
45.2
9.2
45.5
9.3
45.8
9.4
46.0
9.5
46.3
9.6
46.6
9.7
46.9
9.8
47.1
9:9
47.4
10.0
47.7
Table III. Modulator Frequency as a Function of Input
Voltage .
58
nr
was approximately 1.6 ys which translates to a frequency
offset of 56 kHz. After realignment and repositioning of
the height of the modulator the delay was approximately
1 ys which corresponds to 35 kHz. A 1 ys delay corresponds
to 5.4 mm travel through the crystal.
C. DETECTOR
The detector used in the system was a PbSnTe heterojunc-
tion p-i-n photodiode made by Rockwell International Science
Center [19] . The detector area was 4 x 10 cm^ and opera-
tion at liquid nitrogen temperatures (77°K) is required.
The zero bias quantum efficiency was listed as .14 with
a peak quantum efficiency of .32 with .2 v bias (Table IV).
The measured zero bias quantum efficiency was .034. No rea-
son is known for this change except apparent detector degra-
dation. Some of the personnel at NELC expressed the opinion
that the detector had degraded. Determination of quantum
efficiency in heterodyne operation indicates a biased
quantum efficiency of approximately .12.
Shot noise limited operation was not achieved with the
detector. An estimated local oscillator power incident upon
the detector was .1 mw. The detector dynamic impedance
varies with biasing but with zero bias the resistance is ap-
proximately 50 SI. Using a quantum efficiency of .14 either
signal or local oscillator power greater than .9 mw would
be required. For a quantum efficiency of .034 greater than
3.7 mw would be required. This exceeds the incident power
capability of the detector (3 mw) .
59
►
♦
-m-'
I
m
4
Bias Voltage 3 db Bandwidth Quantum Efficiency
(Volts) (MHz) (%)
0 200 14
.02 20
.05 27
.1 30
.15 200
.2 32
.3 200
1.0 32
Table IV. Detector 3 db Bandwidth and Quantum Efficiency vs.
Bias Voltage [19]
60
The 3 db bandwidth is listed as 200 MHz. The maximum
frequency at which the detector was operated was 55 MHz. No
roll-off due to frequency response was noted.
The detector was mounted in a stainless steel SAT dewar
with a side looking window. The window transmissivity is
unknown but a transmissivity of .8 was estimated for calcu-
lation purposes.
D. OPTICAL ANTENNA
The special antenna utilized in the radar system is a
dual transmit/receive Newtonian lens system [24] . Figure
21 is a diagram of the lens system. The antenna has the
following parameters:
Dual antenna - transmits and receives
Transmit/receive folding mirror - double flat parallel
surfaces elliptical Ih” x 2^"
Receive aperture mirror - 6" diameter parabolic, 60"
focal length
System ‘ 10
Effective ^/no (due to blockage) [17] - 10.45
The system yields the following system performance cap-
abilities for diffraction limited optics:
Airy disc diameter [25] d = 2.44X(f/o) = 259 ym (58)
Due to blockage of transmit ellipse [17] d = 270 ym
Depth of focus x = 4X(f/no)^ = 4.24 mm (59)
Near limit of field to achieve airy disc
X£ = DV2X = 1096 m 1199 yd (60)
Field of view for detector diameter equal to airy disc
[17]
61
3 = d/£ = 170 prad x .01®
(61)
Field of view for 8 mil detector [14]
3=0
127 yrad
(62)
r
T^. d^.
airy mirror
Angular target resolution
a
= 85 urad == .005®.
(63)
Maximum allowable incident angular wavefront misalignment
between signal and local oscillator beam for 101 heterodyning
degradation using an 8 mil diameter detector: [26]
Receive aperture = ir(6/2)^ = 28.3 in^
Folding mirror surface = tt( 3/4)^ = 1.77 in^
(blockage area somewhat larger)
Percent blockage - - 7 %
In the above relationships X is the optical wavelength
of 10.6 ym, f is the focal length (60") and D is the receive
mirror diameter.
To transmit directly ahead of the optical antenna the
elliptical flat is turned 45° with respect to the antenna
axis and the transmit beam comes in at 90° with respect to
the antenna axis (Figure 22) .
To provide a visible indication of the CO 2 beam location
a HeNe laser beam at 632.8 nm is being transmitted aligned
with the 10.6 ym beam. As can be seen in photographs (Figures
T]/ = ;^ = .013 rad
(64)
62
27, 28 and 29), there is a rifle scope trained on the mirror
through which the HeNe beam enters the transmit system. The
scope view follows the transmit beams and allows specific
location of the output beams. When the system is aligned
beam steering by moving the optical table will not require
any additional alignment.
Receive alignment can be accomplished by looking into
the receive folding surface of the elliptical mirror. Re-
ceive view can be determined by moving horizontally and
vertically and insuring the target is in the center of the
elliptical mirror blockage.
63
Detector |^— “ Z.
Return
Beam
Parabolic
Receive Mirror
F = 60"
I
Ti^
ansmit Beam
Transmit/Rece ive
Elliptical Flat
Transmit Beam
Rpturn Beam
47h”
■4- 6 ' OJ
Figure 22. Newtonian Optical Antenna.
64
IV. SYSTEM ANALYSIS AND ALIGNMENT PROCEDURES
A. PRELIMINARY DEVELOPMENT
The radar system development proceeded through several
stages. The initial step was the assembly and alignment o£
a system which would modulate the laser beam, transmit the
beam, receive the return and utilizing heterodyne detection
extract the modulated signal. Figure 23 shows the initial
system utilized to accomplish this.
Alignment of the system is very crucial and is somewhat
complicated by the fact that the CO 2 beam at 10.6 ym is
invisible. The presence of the CO 2 beam can be determined
by using heat sensitive graph paper or heat sensitive plastic
encapsulated liquid crystals. The graph paper is used when
the power is relatively high and the liquid crystal paper is
utilized for powers down to a few milliwatts.
The beam splitters utilized are germanium with one side
anti-reflection coated for 10.6 ym wavelength. The germanium
lens and splitters are opaque to visible light. The values
listed for the beam splitters first show the reflectance
then transmittance. A 90/10 splitter means that 90% of the
CO 2 beam is reflected and 10% is transmitted through the
splitter. Unless indicated otherwise the lenses, splitters
and mirrors are 2 inches in diameter. All mirrors are front
surfaced.
Beam splitters provide a means of separating portions of
a beam into known components or combining two beams together
65
Unmodulated
Beam Blocking Mirror
Aperture . „ . . Mirror
O
^ LO
•H LO
rH Cn
+-» o
^ u
bOC/D
•H
CO
66
Figure 23. First Optical System.
for collimated joint transmission. One effect of using beam
splitters is that to split and combine beams the reflecting
surfaces must be at an angle to the beam paths, for a right
angle deflection the surfaces must be oriented at a 45°
angle with respect to the transmission path. The angular
presentation of the surfaces reduces the amount of surface
area available for transmission or reflection and at 45°
the circle presents an apparent ellipse with a horizontal
minor axis of 1.4 inches. The transmittance or reflective
area is reduced by the angular presentation to .707 of the
original, or in other words, a 1.5 db reduction. This re-
duction in size presents no problem for the transmit path
but for the return path it can reduce the collected energy
by 1.5 db.
The holders for the splitters and mirrors have uncoupled
horizontal and vertical rotational mobility which allows
exact direction of reflected beams. Additionally the A-0
modulator and detector holders have 3 degree uncoupled axis
mobility with micrometer adjustment for up to one inch
travel in each direction. The A-0 modulator focusing lenses,
blocking aperture, and in systems two and three (Figures 24
and 25) the transmit beam elevator and receive/LO splitter
are mounted on holders with motion in one direction up to h
inch with micrometer adjustment.
B. FIRST OPTICAL SYSTEM
The configuration of the first system developed to be
utilized as a laser radar is shown in Figure 23. The trans-
mit path was from the CO 2 laser reflected from the 95/5 beam
67
m
iM
I
o o
IH
^ *H O
O rH
P. Qi
•H
CO
68
Figure 24. Second Optical System.
4
-I
69
Figure 25. Third Optical System.
splitter (5% power losses) to the input focusing lens of
the acousto-optic modulator, through the modulator to the
output focusing/collimation lens, through the modulation
pass aperture where the unmodulated portion of the beam is
blocked, through the 50/50 splitter where half the power
is reflected out of the system, through the 5/95 splitter
(5% power loss) where the HeNe beam is collimated with the
CO 2 transmit beam and off of the transmit/receive mirror to
the target.
The return signal after being reflected from the target,
enters the system at the transmit/receive mirror, through
the 5/95 splitter (5% power loss), reflected off of the
50/50 splitter (50% power loss) , through the 5/95 splitter
(5% power loss) where the local oscillator beam is brought
in, through the focusing lens to the detector.
The local oscillator path is from the laser through the
95/5 splitter (95% power loss), off three folding mirrors,
reflected off of the 5/95 splitter (95% power loss) where
it is combined with the return signal, through the focusing
lens to the detector.
In the transmit path approximately 50% of the power into
the A-0 modulator is absorbed by the modulator and approxi-
mately 45% of the output is unmodulated and blocked. Of the
remaining transmit power 50% is lost in the 50/50 splitter
and another 5% is lost in the 5/95 splitter. Using these
numbers, if 1 watt is transmitted from the laser approximately
124 mw is transmitted. In the LO path of 50 mw through the
95/5 splitter approximately 2.5 mw is focused on the detector.
70
The return signal is reduced to 45% o£ the original power by
the splitters and to .707 of that by the aperture blockage
mentioned in the previous section, for a net return on the
detector of approximately 32% of the incoming power. In
this manner the signal power out of the A-0 modulator is
reduced by 3.2 db in the transmit path and by 4.9 db in the
return path for a net ideal optics loss of 8.1 db.
C. SECOND OPTICAL SYSTEM
The optical configuration of the second system utilized
is shown in Figure 24. The important difference is the
utilization of a Newtonian lens system as a transmit/receive
antenna and using an unfocused local oscillator beam. The
transmission, receive and local oscillator paths are shown
in Figure 24. For the same 1 watt output from the laser
approximately 235 mw is transmitted for a transmit gain of
2.8 db over system one.
The receive aperture of the second system is the 6 inch
parabolic mirror of the Newtonian optics. The aperture
area of the 6 inch mirror is nine times that of the 2 inch
mirror less the elliptical mirror blockage of approximately
7% for a net 8.37 fold increase which is a 9.2 db gain due
to aperture size alone. The loss due to one 5/95 splitter,
the 50/50 splitter and due to the elliptical presentation
of the angled splitters is eliminated for another 4.7 db
gain. This nets a total gain in signal power of 16.7 db.
The utilization of an unfocused local oscillator beam
instead of a focused beam greatly reduces the difficulty in
71
1
aligning the return signal and LO beam. It also provides a
safety factor in the event the LO power should increase
without operator knowledge because only a small portion of
the increased power would fall on the detector. The adverse
effect of using an unfocused LO beam is that it becomes much
more difficult to provide enough local oscillator power in-
cident upon the detector to achieve shot noise limited
operation. Shot noise limited operation was not achieved in
any of the three configurations.
D. THIRD OPTICAL SYSTEM
The third and final configuration is shown in Figure 25.
The differences between system two and three are the replace-
ment of the 90/10 splitter at the output of the laser by a
mirror and the unmodulated output of the modulator is utilized
as the LO beam. This provides a 10% increase in output power
(.46 db) and a total LO power available of 510 mw as compared
to approximately 230 mw.
E. ALIGNMENT TECHNIQUES
The alignment of the optical system is extremely critical.
Because of the strict requirements a detailed description of
the alignment procedure is presented.
1 . Height Adjustments
All beams must move in a path parallel to the plane
of the optical table to provide optimum alignment. To
achieve this beam, height is measured at the output of an
optical device and measured again at a distance as far away
on the table as possible. If the heights are not the same
72
shims are introduced to adjust height or axis adjustments
are made. As an example, the height o£ the laser beam at
the laser output was measured. The first beam splitter was
then adjusted so the beam was the same height at the oppo-
site end of the table. The horizontal axis was adjusted so
the beam was changed in direction by 90°.
2 . Acousto-Optic Modulator Alignment
The CO 2 beam is focused into the germanium crystal
in the modulator through a germanium focusing lens with a
five inch focal length. The height of the lens was adjusted
by shims until the CO 2 beam passed through the lens center.
The modulator was mounted on a holder which would be adjusted
with a micrometer setting so the angle of modulator axis
could be adjusted with respect to the plane of the optical
table. The modulator and holder were both mounted to one
of the holders which are adjustable in three axes. The
modulator was then positioned so the input beam passed
through the center of the input aperture at a distance of
five inches from the modulator center to the focusing lens
so the beam waist would be in the center of the crystal.
By using a level, the modulator was rotated until its axis
was approximately two degrees from the vertical and then
slowly adjusted until the output beam split into two beams.
The positioning of the modulator was adjusted for maximum
power in the modulated beam.
The recollimation lens was positioned in the two
output beams five inches from the modulator center at a
height where the two beams passed through near the lens
73
center. The recollimation lens serves a dual purpose in
that it prevents a further divergence of the beams after
their focal point and it collimates the beams so the modu-
lated beam (which was deflected down at twice the Bragg
angle) travels parallel to the plane of the table.
3. Collimation of the HeNe and CO 2 Transmit Beams
A visible beam from a HeNe laser was transmitted
with the CO 2 beam to provide a visual indication of the lo-
cation of the CO 2 beam. The HeNe beam entered the transmit
path by reflecting off of the 5/95 beam splitter just prior
to transmission from the system. Since the germanium splitter
is opaque to visible light virtually all of the HeNe beam is
transmitted .
For the HeNe beam to be collimated exactly with the
CO 2 beam it must be positioned on the face of the 5/95
splitter at the exact position that the CO 2 beam passes
through the splitter. The superpositioning can be deter-
mined by pressing a piece of liquid crystal paper on the
face of the splitter. The intensity of the CO 2 beam is re-
duced by passing it through an aperture prior to the modu-
lator. Care must be taken to position the aperture so the
beam goes through the exact center so that the HeNe is
positioned on the high intensity center of the beam. The
HeNe beam can be adjusted in height by placing shims under
the laser and horizontal adjustment is accomplished by ro-
tating the laser slightly in the holder.
The HeNe transmit beam can be adjusted with the
axis adjustments on the. holder in which the splitter is
74
mounted. This adjustment does not effect the direction of
the CO2 beam transmission. A piece of heat sensitive graph
paper was placed in the CO2 beam approximately ten feet
from the output, as soon as the graph paper began to darken
the CO2 beam was blocked and the HeNe beam was positioned
on the small darkened spot. In this manner the HeNe beam
can be positioned in the highest intensity portion of the
CO2 beam. The alignment was checked by passing both beams
through an aperture onto a piece of liquid crystal paper
located about forty feet from the output and about thirty
feet from the aperture. If the beams are not collimated
they will not be coincident at both the aperture and liquid
crystal paper. Again care must be taken to position the
aperture so the beams pass through its exact center or the
beams on the liquid crystal paper may appear to be slightly
misaligned when they are not. This appearance can be
caused by passing parts of the CO2 beam with a significant
difference in power density. The difference in intensity
will show on the liquid crystal and may give an appearance
of misalignment.
A final alignment check was made approximately 305
yards from the output, on the roof of Ingersoll Hall. The
dimension and location of the CO2 beam was determined by
chopping the transmit beam and reading the chopped output
with a PbSnTe detector whose output was amplified 40 db and
displayed on an oscilloscope. In the final alignment ad-
justment at this range the HeNe beam was lowered two inches
75
and moved horizontally one half inch. This movement was
less than the divergence of either beam. - .
4 . Collimation of Visual Optics with the CO ^ Transmit
Beam
A visual sighting capability was incorporated into
the system to enable placement of the transmit beam on a
desired position. This is accomplished by utilizing a
rifle sighting scope and a mirror with a hole in its center.
The visual system is shown in Figures 23, 24 and 25.
The sighting mirror is positioned so the beam from
the HeNe laser passes through the hole in its center. The
rifle scope is then positioned so it looks onto the surface
of the sighting mirror. The mirror is rotated until the
rifle scope is sighting along the HeNe path. Initial align-
ment is facilitated by placing a mirror in the HeNe trans-
mission path and adjusting it so the HeNe beam is folded
back onto itself. The sighting mirror is adjusted properly
when the HeNe beam reflects back through the rifle scope.
Visual alignment is completed by adjusting the scope cross
hairs on the bright return from a retro-reflector placed in
the HeNe beam on the roof of Ingersoll Hall. Once alignment
is completed the transmit beam can be positioned by sighting
through the rifle scope and adjusting the optical table
until the cross-hairs are positioned on the desired location.
5 . Alignment of the Newtonian Optics
Alignment of the Newtonian transmit/receive optics
is very critical since the theoretical field of view is only
127 yrad for an eight mil diameter detector (measured field
of view was 180 yrad) . Once the receive optics are aligned
76
with the transmit beam the detector is positioned at the
focal point of the lens system. If the target is then moved
out of the field of view but is still in the beam (which is
much larger than the receive field of view) the focused
energy moves off of the detector. At this point if the de-
tector is repositioned in the received focused beam the
signal can be processed as before. This demonstrates that
there is a direct interaction between receive alignment and
detector size and positioning.
By removing the 5/95 beam splitter which is positioned
between the folding elliptical mirror and the detector (Figure
25) and placing a folding mirror in front of the detector the
view of the receive optics can be determined. Looking back
into the receive optics the blockage of the elliptical flat
can be seen. When the HeNe beam is positioned on a retro-
reflector located on the roof of Ingersoll Hall the red re-
flection can be faintly seen through the blockage image.
This reflection is positioned in the center of the blockage
by adjusting positioning screws on the back of the six inch
parabolic' mirror . The positioning can also be checked by
moving horizontally and vertically and adjusting the para-
bolic mirror until the reflection bisects the blockage both
vertically and horizontally.
Once the receive and transmit optics are aligned
the return visible energy from the HeNe laser can be located
by placing a white paper at the focal length of the optics
(60 inches from the parabolic mirror). If the paper is
moved slightly forward of the focal point the pattern of
77
the returned HeNe beam with its dark spot in the center
(caused by the elliptical mirror blockage) can be seen.
If the receive optics are properly aligned at this point
the received pattern will be distorted by moving a paper
in from the sides and top and bottom in front of the para-
bolic mirror. If the received pattern distorts as soon as
the paper moves in front of the mirror from all sides then
the Newtonian optics are aligned properly.
6 . Signal and Local Oscillator Beam Alignment
The signal beam and local oscillator beam phase
fronts must be aligned upon the detector surface nearly
exactly. The local oscillator beam is unfocused to facili-
tate this alignment. While one beam was being aligned the
other beam was blocked and vice versa.
With the 5/95 beam splitter removed as in the pre-
vious section, the HeNe return can be seen and the detector
dewar can be positioned so the detector is very near the re-
turn signal. The CO 2 beam was then chopped by a fan and
the detector position was varied in a raster type scan until
the chopped output, amplified by 40 db, was seen on the
oscilloscope. The 5/95 beam splitter was then repositioned
in the signal and local oscillator path (oriented at approxi
mately 45° with respect to each path). The beam splitter
shifts the signal beam slightly and the detector was repo-
sitioned in the beam. After the detector was again posi-
tioned in the signal beam for maximum chopped signal
amplitude the local oscillator beam ivas unblocked and the
transmit beam was blocked. The local oscillator beam was
78
swept across the dewar aperture face in a raster pattern
until the chopped output of the detector was maximized.
After the detector was properly positioned and the rest of
the system was aligned, the alignment is maintained and is ^
correct as the table is repositioned to illuminate different
targets .
F. ELECTRONICS AND SIGNAL PROCESSING
The block diagram of the signal processing system is
shown in Figure 26. The system will be first analyzed con-
sidering a constant frequency IF of 30 MHz.
The driver for the acousto-optic modulator consists of
a voltage controlled oscillator and a power amplifier. The
output is coupled to the modulator with a tri-axial lead
which minimizes RFI . Some of the output power was reflected
back to the input terminal at a greatly reduced level. This
reflected power provided a convenient means of obtaining the
instantaneous transmitted frequency for comparison with the
instantaneous received frequency for determination of the
range and velocity frequency. The reflected reference sig-
nal is amplitude modulated by the input modulating signal
which is a DC bias with a superimposed triangular modulating
voltage. The reflected reference signal is passed through
a high pass filter which eliminated the 1.75 kHz modulating
wave form.
The transmit signal was connected to the R terminal of
a balanced mixer. A 30 MHz reference signal of 1 volt am-
plitude (this amplitude was very critical for proper
79
4
4
1
Oscilloscope
Figure 26. Signal Processing Systera.
80
operation of the balanced mixer) was connected to the L
terminal. Both the sum and difference frequencies are pre-
sent at the output of the mixer. This output was passed
through a third order Butterworth filter with a bandpass
of 60 - 80 MHz.
The 65 - 75 MHz signal was amplified 60 db and then at-
tenuated 8 db (to obtain the one volt necessary for the
balanced mixer) and connected to the L input of the second
balanced mixer.
The output of the PbSnTe Detector is a 35 - 45 MHz signal
offset by any doppler shift which may be present. This sig-
nal is amplified by a 23 db bias amplifier with a 3 db noise
figure and then by a 30 db amplifier. This signal is then
connected to the R input of the second balanced mixer where
it is mixed with the 65 - 75 MHz reference signal. The out-
put of the second mixer is 30 MHz + F + F, and
^ range doppler
a 100 - 120 MHz spread. The range information is present
at the output as a signal at 30 MHz + F and 30 MHz -
Frange* double frequency spikes are present because of
the triangular frequency modulation.
The output frequencies were observed in a spectrum
analyzer. If the 30 MHz output of the signal generator into
the first balanced mixer is varied the output range frequencies
are varied in the same way. In this way the range frequencies
were swept across a 3.5 kHz crystal filter centered at 30
MHz. As the range frequencies were swept across the filter
bandwidth the signals were connected to the vertical input
of an oscilloscope. The input to the horizontal grids of
81
the oscilloscope was the sweep output from the sweeping
signal generator and in this way the horizontal sweep was
calibrated to the frequency sweeping of the return signal.
The resultant output of this processing was an A scope
range presentation on the oscilloscope. The A scope pre-
sentation was not very satisfactory because of the frequency
output of the signal generator drifted making a range dis-
placement calibration impossible. Other than a demonstra-
tion of its feasibility the A scope presentation was not
utilized. The range and velocity information was determined
directly from the spectrum analyzer.
G, SYSTEM RADAR ANALYSIS
The theoretical development for a FM-CW radar is pre-
sented in Chapter II section A. The specific system parame-
ters are as follows:
Carrier frequency
Wavelength
Resolution filter bandwidth
f = 2.83 X 10*^
o
X = 10.6 ym
Hz
Triangular wave modulation
frequency
Total frequency deviation
BW = 3.5 kHz centered at
30 MHz
FM = 1.75 Hz
2AF = 10 MHz centered at
40 MHz
\,
These parameters yield the following system performance
capabilities
3.5 X 10^° Hz/sec
df/dt
(equation 3)
Unambiguous range
(equation 19)
Range frequency
(equation 5)
42.9 km
233.3 kHz/km
213.3 kHz/100 yds
82
J
Velocity frequency
(equation 13)
Range resolution
(equation 21)
Velocity resolution
(equation 22)
Acceleration spectrum spread
tolerance
(equation 17)
52.4 k.Hz/km/hr
97 kHz/knot
15 m
.036 knots
6.6 g
83
V. EXPERIMENTAL PROCEDURES AND RESULTS
A. DETERMINATION OF RANGE
For an initial determination of the practicability of
determining range by the expected range frequency signals
the first system (Figure 23) was used. The output power
was reduced and attenuated until only a few milliwatts were
transmitted. The output beam was folded around the room
and out along the top of the sixth floor of Spannagel Hall.
A front-surfaced mirror was placed at several known dis-
tances and the range frequency was determined and compared
with the expected frequency shift. It was during this op-
eration that the offset from zero range was first noticed
(explained in Chapter III, Section B) . Table V contains
the results of this series of experiments. It should be
noted that the results agree well within the accuracy of
the frequency readings. Figure 27 is a photograph of the
first system configuration.
An unexpected phenomenon was the appearance of a zero
range beat frequency. This is believed to be caused by
a reflection of some of the modulated beam from the output
face of the modulator crystal back into the laser. Once
in the laser, the modulated frequency is amplified and
transmitted along with the normal unmodulated frequency and
in this manner it is introduced into the local oscillator
beam. It was determined to be in the local oscillator path
because it remained even when the output beam was blocked.
84
Table V. Range Frequency Determination as a Function of
Range .
Triangular Modulation F
2AF = 10 MHz df/dt
Range Frequency Shift
Spectrum Analyzer Dispersion
10 kHz
2 X 10*^ Hz/sec
1.22 kHz/rd
50 kHz/cm
Range
43
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
17.5 kHz
345 kHz
327.5 kHz
1.64 ysec
Range
67
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
27.2 kHz
360 kHz
332.8 kHz
1.66 ysec
Range
91
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
37 kHz
367 kHz
330 kHz
1.65 usee
Range
115
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
46.8 kHz
375 kHz
328.2 kHz
1.64 usee
Range
139
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
46.3 kHz
387.5 kHz
341.2 kHz
1.7 usee
Range
163
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
66.3 kHz
395 kHz
328.7 kHz
1.64 usee
Range
187
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
76 kHz
405 kHz
329 kHz
1.64 usee
Range
211
ft
Expected Range Frequency
Actual Range Frequency
Frequency Offset
Corresponding Offset Time
Delay
85.8 kHz
415 kHz
329.2 kHz
1.64 usee
85
Figure 27. First Optical System.
Figure 28. Third Optical System, View 1.
86
The zero range frequency is believed to be due to internal
laser amplification rather than a reflection from the output
mirror because of the marked variation of the amplitude of
the signal at different times. The signal on the LO path
was first noticed at NELC during the experience tour in San
Diego. Prior to bringing the laser to NPS it was recharged
and for the first couple of weeks of operation at NPS the
signal was not present on the LO beam. At other times the
signal was not present when the laser was first turned on
but became present after the laser had warmed up. The sig-
nal strength fluctuated from week to week and for the last
several weeks was significantly lower than at other times.
All of these variations can logically be reasoned to be due
to the effects of pressure and temperature line broadening
and due to the variations in line width of various laser
transmission lines.
B. TARGET DETERMINATION AT 305 YARDS
/
The next step in system development was to determine the
system capability at a greater distance. For this work, the
system configuration of the second system (Figure 24) was
initially used and finally that of the third system (Figure
25). Figures 28 and 29 are photographs of the third system.
Figure 30 shows the view from Spannagel 704 to the top of
Ingersoll Hall and Figure 31 shows the NPS grounds.
During this and subsequent experimental stages the target
was a two-inch diameter, gold surfaced retro-reflector.
The retro-reflector is shown mounted on a model railroad car
87
■ii
f
Figure 29. Third Optical System.
Figure 30. View from Spanagall Hall
to Ingersoll Hall.
88
Figure 31. Naval Postgraduate Grounds, Near Range Target.
89
in the photographs of Figures 32 and 33. The retro-reflec-
tor is diffraction limited at 10.6 ym and the reflected
energy from it has the same divergence as the incident
beam.
The modulator was readjusted between the experiments of
Section A and determining the target on Ingersoll. At the
new height position, the time delay was approximately 1 ysec
which for the 1.75 kHz modulation rate corresponds at a
35 kHz frequency offset. Figure 34 shows the zero range
frequency signal. The small spikes offset about 35 kHz
from the center in Figure 36 and are the zero range fre-
quencies along with the signal from the retro-reflector.
In both photographs the spectrum analyzer dispersion was
50 kHz/cm.
1 . Return Signal from Retro-Reflector at 305 Yards
Ingersoll Hall and optimized for maximum signal. Figure 35
shows the unprocessed return out of the detector and Figures
36 and 37 show the processed return. The following condi-
tions existed:
The system was aimed at the retro-reflector on
Transmit Frequency
Modulating Rate
Target Range
35 - 45 MHz
1.75 kHz
305 yards
Analyzer Dispersion and Noise Bandwidth
For Range Frequency
For Total Spectrum
2 MHz/cm
50 kHz/cm
3.5 X 10‘° Hz/sec
df/dt
90
,
Velocity Generating Model
Railroad, View 1.
32.
Figure 33. Velocity Generating Model
Railroad, View 2.
91
Dispersion 2 MHz/cm
S/N 50 db
Total
Spectrum 10 MHz
Figure 35. Unprocessed Detector
Output for 305 Yard
Target .
I
92
Dispersion
Total Separation
Zero Range Frequencies
305 Yard Range Frequencies
Range Frequencies
Expected Frequencies
50 kHz/cm
200 kHz/cm
± 35 kHz
± 100 kHz
± 65 kHz
± 65.1 kHz
Figure 36.
Processed Return
for 305 Yard Target.
93
I
I
The following are the resultant data:
Total Spectrum S/N
55
db
Range Frequency S/N
60
db
Zero Range Frequency
±35
kHz
Time Offset
1
ysec
Range Frequency (including zero range)
±100
kHz
Actual Range Frequency
65
kHz
Expected Range Frequency
65.1
kHz
Transmitted Power
.65
w
LO Unfocused Power
.51
w
Chopped Signal Output
5.5
mv
Chopped LO Output
1.4
mv
Returned Signal Power
.75
mw
(Prior to the 5/95 splitter)
The range frequency results agreed almost exactly with those
expected. The noise bandwidth of the processed signal was
16 db narrower than the total spectrum bandwidth. There
was a 5 db S/N gain and there was a 6 db insertion loss at
the input of the balanced mixer. The other 5 db could be
accounted for by noise addition of the mixer.
2 . Transmit Divergence Determination
With both the transmitted and returned power known
and the target range known, the beam divergence can be
calculated. The returned power was readily measured because
the HeNe focused return was easily seen. The returned power
was measured with the low-range (<200 mw) digital power
meter while the transmit power was measured with the high-
range meter. This is a possible source of error but all
94
calculations are based upon these readings being correct.
The divergence calculations are made considering the reflect-
ing and receive aperture areas as compared to the total
area of an arc subtended by a beam of a known divergence
at the known range. Since everything is known but the di-
vergence, it can readily be determined.
The arc length of a beam of a given divergence at
a given range is given by
d = R6 (65)
and its area is
( 66 )
The area o£ the retro-reflector compared to this area is
7T
7T
( ^)
C^)
2
2
(67)
The divergence from the return from the retro-re-
flector is the same as the incident beam. This results in
an illuminated area at the receive aperture the same size
as that at the target. The ratio of the received power to
returned power is thus
TT
TT
D
( f )
( !^)
2
2
The net return power is thus given by
( 68 )
95
f ;
(69)
P =
P^TT'
D.
D
(
M
2
P^
t t r
"(R0) “»
In this situation the return power is known and thus the
divergence can be determined from
e
0
\ .65 w
1.75 mw
2 2
2in* 6in
(305 yd* 36 in/yd) **
(70)
1.71 mradian
3. Field of View Measurement
The field of view of the receive optics was measured
by placing the retro-reflector in the beam in a position
where the return signal was maximum. The reflector was then
moved a known amount and the signal strength was noted.
The beam width was defined as the 3 db points of the signal
decrease. The field of view was determined using equation
(65).
The 3 db beam width was determined to be nearly
symmetrical at 5 cm. At a range of 305 yards this gives
a field of view of 179 pradian. This compares reasonably
well to the theoretical far-field field of view of 127
yradian .
There are two effects not considered in this compu-
tation. The first is that the target range is not in the
far field of the optics (305 yards vice 1199 yards). The
effect of this is an enlargement of the Airy disc diameter
96
which reduces the theoretical field of view. Offsetting
this is the effect of the finite reflector size (2 inches
vice a point) . The separation was measured from the reflec-
tor center so the reflector extended on both sides of this
point. Since the beam intensity distribution should be
nearly Gaussian this would tend to increase the apparent
beam width.
4 . Expected Return from a Diffuse Reflector at 505 Yards
The return from a diffuse target would greatly de-
crease the return signal received at the receive aperture.
If one assumes an ideal Lambertian return [14] from a dif-
fuse reflector, the area illuminated is that subtended by a
solid angle of tt radians. The resultant reflected energy
would then be reflected over an area of
The difference in area and thus power density is the square
of the beam divergence. For a divergence of 1.71 mrad,
this is a 61.3 db reduction of signal power. With a pro-
cessed S/N of 60 db , it might be possible to see the return
for an ideal diffuse reflector larger than the retro-reflector.
The target that was utilized for the diffuse target
consisted of two 1-1/2” x 6” pieces of sandblasted aluminum
placed side by side. The target had been exposed to air for
several months so there was undoubetdly some surface
A = ttR^
(71)
instead of
(72)
97
oxidation. Additionally, the assumption of a perfectly
diffuse reflector was an approximation. The larger area of
the diffuse reflector provided a gain in reflecting area at
the target of approximately 7.6 db. The surface of the tar-
get caused attenuation of the incident power and a 6 db
reflection loss as compared to an ideal Lambertian is not
unreasonable. Using these numbers, the expected return of
the diffuse reflector would be .3 db. No return signal was
detected from the diffuse reflector even though the target
was varied widely in angular presentation.
5 . Calculation of Detector Quantum Efficiency
The quantum efficiency of a detector is that propor-
tion of incident photons which are converted to a utilizable
signal as compared to the total incident flux. The quantum
efficiency of a photodiode can be calculated from the
relationship [15]
hf V
where n is the quantum efficiency, f^ is the frequency of
the incident photon, v is the detector output voltage, q is
the electronic charge, P is the incident power and R is the
zero bias detector resistance. The incident power is the
power incident upon the detector. The Airy disc for a far
field target is not in the far-field, the actual Airy disc
is somewhat larger. The detector size is 200 pm so it is
smaller than the Airy disc. The energy density profile of
the Airy disc is shown in Figure 5.5 of [17]. Since the
detector size is less than 74% of the Airy disc diameter,
98
(
I
f
i
it is estimated that approximately 80% of the power in the
Airy disc is incident upon the detector. The power contained
in the Airy disc is approximately 84% of the total focused
power [17] . The dewar window transmittance is estimated at
.8 which is reasonable for a good window. The total power
incident at the dewar (after passing through the 5/95 beam
splitter) was .7 mw. When all of the aforementioned effects
are considered, the estimated power incident on the detector
is .38 mw. Thus the quantum efficiency is given by
(6.63 X 10'^‘*)(2.83 x 10^^)(5.5 x lO'^) _
7] ___ _ .Uo4.
(1.6 X 10 ) (3.8 X 10 )
As mentioned in Chapter III, Section C, this value is sur-
prisingly low and tends to indicate that the detector has
degraded. There are several possible sources of error in
this calculation but the result is still nearly one order
of magnitude below the expected value of .14.
6 . Calculation of Noise Equivalent Power
Noise equivalent power id defined as the amount of
power necessary for a signal-to-noise ratio of one with a
unity noise bandwidth. This can be computed if the signal
power, noise bandwidth and S/N are known. Using measured
values and the same estimations utilized in the previous
section, the computation is as follows:
Signal Power .38 mw
S/N = 60 db
Noise bandwidth = 50 kHz
99
NEP =
(S/N)B
- 4
3.8x10
= 7.6 X 10
106*5 X lO**
w/Hz
From equation (52) , it can be seen that for shot noise limited
operation
hf B
NEP =
(74)
For unity bandwidth and quantum efficiency
NEPideai = hf^ = (6 . 63xl0’ ^ “) (2 . 83x10 ^ ^) = 1.88xl0'^°w
For a noise bandwidth of 50 kHz, this becomes 9.4 x lO"^^
and for n = .034.
NEP = 2.76 X 10 w.
This value is larger than the computed value which indicates
that either the noise bandwidth is incorrect, S/N is incor-
rect or the computed value of n is incorrect. The noise
bandwidth is determined by the dispersion of the spectrum
analyzer and the S/N ratio 60 db has been repeated several
times. These factors indicate that the computed value of
conversion efficiency is incorrect. For shot limited opera-
tion, this would correspond to a value for n of .12 which
is near the tabulated value of approximately .32 (for a
reverse bias of .17 v) . Since shot noise limited operation
was not obtained, this value is reasonable. The readings
utilized for the computation of n in Section IV were repro-
duced several times also.
100
C. EXTENDED RANGE CAPABILITY
After successfully detecting the retro-reflector at
305 yards, an extension of target range was completed.
There was a clear area at the edge of El Estero Lake at
an unknown range. The retro-reflector was taken to this
area and illuminated. The resultant signal had a S/N ratio
of 35 db and a frequency shift of 260 kHz including the
zero range shift of 35 kHz. The net frequency shift of
225 kHz corresponds to a range of 1055 yards. The range
of 1055 yards iS' approximately 3-1/2 times as far as 305
. 4
yards. Since the signal strength decreases as R , this
should give a corresponding reduction in the S/N ratio of
21.5 db. The total range (both directions) is approximately
2 km so this would provide an additional attenuation of
approximately 2 db. Thus the expected S/N ratio was 36.5
db which agrees very closely to the experimental value of
35 db.
The next step in range was to illuminate the retro-
reflector while it was on the Coast Guard pier at a range
of approximately 2400 yards (Figure 37). This is approxi-
mately eight times the range of Ingersoll Hall and again
considering the R signal relationship, this should cause
a reduction of the S/N ratio of 36.1 db. The total range
is slightly more than 4 km which would give an expected
reduction in signal strength of 4 db due to attenuation.
These considerations indicate an expected signal - to-noise
ratio of 20 db and a frequency shift (including the zero
101
Figure 37. Far Range Target Measurement.
102
range shift) of 547 kHz. The experimentally determined
values were :
S/N 20 db
Frequency Shift 540 kHz
This frequency shift indicates an actual range of 2370
yards. Figures 38 and 39 show the signal from the Coast
Guard pier.
D. VELOCITY DETERMINATION
If a target with relative velocity is illuminated by
the radar, the return should be shifted in frequency by
the amount of 188.7 kHz/msec ^ relative velocity with the
sign being the same as that of the relative velocity. To
facilitate velocity measurements, a model train was set-
up on the roof of Ingersoll so that the beam only illum-
inated one side of the oval track. A meter stick was po-
sitioned along a straight portion of the track and an
electric timer was used to measure the amount of time the
reflector was alongside the meter stick. Figures 32 and
33 show the experimental set-up for this measurement. Some
problems were experienced with the electric timer switch
and the train was not stable enough to obtain the desired
velocity range. Additionally there are inherent errors
I
which are unavoidable when manually timing. Doppler shifts
of both senses were obtained by reversing the direction of
the model train. Due to a difference in elevation there
was a 5.5° angle between the velocity motion and the radar
beam; because of this, the measured velocity must be
103
Dispers ion
Range
S/N
Zero Range
Range
Frequencies
Range Return
38.
Figure
Processed Return for
Yard Target, View 1
2379
200 kHz/cm
2370 yard
20 db
± 35 kHz
±505 kHz
±540 kHz
Dispersion
Range
S/N
Zero Range
Range
Frequencies
Range
Return
200 kHz/cm
2370 yard
20 db
± 35 kHz
±505 kHz
±540 kHz
Figure 39. Processed Return for
2370 Yard Target,
View 2 .
1
104
multiplied by cos 5.5° to obtain the velocity component
relative to the radar. Four photographs are included of
the doppler shift measurements; these are Figures 40, 41,
42 and 43. Table VI lists the results of the velocity
measurements. The measured values were well within the
tolerances of measurement error.
A totally unexpected phenomenon was noted during the
velocity measurements. In addition to the expected doppler
frequency shift, the range frequencies with no doppler
shift were present at a much reduced signal strength. There
was no return from the tracks until the train with the re-
flector moved into the beam. All parts of the train were,
of course, moving at the same speed. Later the reflector
was hand held and moved and again this phenomenon was ob-
served. This zero velocity component should not have been
present since any return reflection should have been doppler
shifted.
105
Dispersion
'iguie 4U. Processed Return for Negative
Relative Velocity, View 1.
50 kHz/cm
Dispersion
50 kHz/cm
Figure 41. Processed Return for Negativ
Relative Velocity, View 2.
106
50 kHz/cm
Dispers ion
Figure 42. Processed Return for Positive
Relative Velocity, View 1.
Dispersion 50 kHz/cm
Figure 43. Processed Return for Positive
Relative Velocity, View 2.
107
Figure 40
Dovm Doppler Shift
1/v
V
Expected Frequency Shift
Actual Frequency Shift
2.7 sec/m
.37 m/sec
69.5 kHz
80 kHz
Figure 41
Down Doppler Shift
1/v
V
Expected Frequency Shift
Actual Frequency Shift
1.8 sec/m
. 56 m/sec
104 kHz
110 kHz
Figure 42
Up Doppler Shift
1/v
= 1.6
sec/m
V
= .63
m/sec
Expected Frequency Shift
117
kHz
Actual Frequency Shift
= 120
kHz
Figure 43
Up Doppler Shift
1/v
= 1.7
sec/m
V
= .59
m/sec
Expected Frequency Shift
110
kHz
Actual Frequency Shift
= 115
kHz
Table VI. Velocity Determination Results.
108
f
VI. CONCLUSIONS AND RECOMMENDATIONS
A. CONCLUSIONS
The experimental results obtained closely agreed with
the theoretically expected results and prove the basic
feasibility of constructing a FM-CW optical radar and
frequency modulation and coherent detection of a laser beam.
The capabilities of the developmental system were somewhat
disappointing but drastic improvements could be obtained in
signal processing (reduce the noise bandwidth), increased
transmission power, shot noise limited detector operation
and the reduction of noise inserted in the filtering and
luixing processing.
The alignment requirements of this type of system are
extreme and would present problems in both fabrication and
maintenance. Additionally, actual systems would have to
be rigidly constructed and either environmentally controlled
or fabricated with materials having nearly the same coeffi-
cient of thermal expansion.
B. RECOMMENDATIONS FOR FURTHER STUDY
There are several areas which warrant further study.
One area would be to determine the exact mechanism causing
the zero range frequency being imposed upon the local
oscillator beam and determine the variation of this with
different laser variables such as temperature and pressure
broadening and different line operation.
109
V
Another and more intriguing question is that of the
occurrence of the zero velocity frequency components in
the velocity measurement part of the system investigation.
Since all of the returned energy should have been doppler
shifted in frequency, this presents a perplexing question.
It would also be worthwhile to extend the system
development to determine the true limit of its capabilities.
Initially this would require improvements in signal process-
ing and perhaps eventually in the area of controls to
develop steering and tracking capability.
Since a system operating at optical frequencies has
such large doppler shifts for relatively low relative
velocities, it may be feasible to determine the vibrational
signatures of many objects (such as a jet engine of an air-
craft) and utilize this in a target recognition scheme.
C. POSSIBLE SYSTEM APPLICATIONS
There are several possible applications for an optical
radar. At the start of this project, it was hoped that
clear air turbulence could be determined and that a light-
weight low-power system could be developed for utilization
in aircraft. There is still a possibility of this applica-
tion being realized if system development is continued.
Another possible application is signature recognition
as mentioned in the previous section. It is quite conceivable
that a radar which could detect, provide range and velocity
information and target identification could be developed
along similar lines as this developmental system.
110
Another application which is both very desirable and
conceivable would be in low flying, high closing speed
target detection. The small beam size would allow detection
of near the horizon targets with extremely fine bearing
resolution capability. If a dual mode transmission capa-
bility were incorporated, a constant frequency beam could
be transmitted and instant velocity determination of any
return could be accomplished. If a doppler shift threshold
were set (say for 400 knots relative speed) a threat
warning system would be inherent. Upon recognition of a
threat (and simultaneous velocity determination) the FM
mode could be activated and range information provided.
The same characteristic which allows near the horizon
search and high bearing resolution (small beam size) pre-
vents the rapid scanning of a large volume of space. Thus
any system for this threat recognition application would
require numerous radars with each scanning a relatively
small sector. With the advent of signal storage capability
and digital processing and computer control, a system such
as this may become feasible in the relatively near future.
Ill
APPENDIX A: EQUIPMENT LIST
Crystal Filter
Mfg. Damon Model 6647A
£ = 30 MHz BW = 3.5 kHz
o
Optical Table
Mfg. UNIDEK
Stainless steel - honeycomb
CO 2 Laser
Mfg. Honeywell
Power 3 watt - vertically polarized
Amplifier (2)
Mfg. Hewlett Packard
Gain 20/40 db
Oscilloscope
Mfg. Tektronix
Signal Generator
Mfg. Wavetek
Variable Frequency
Signal Generator
Mfg. Hewlett Packard
Signal Generator
Mfg. Wavetek
Frequency sweeping
Amplifier
Mfg. NELC
Gain 23 db
Amplifier
Mfg. Miteo
Gain 30 db
Model 461A
Wideband
Model 546
Model 134
Variable waveform
Model 606A
Model 1001
Bias -amp
NF - 3 db Wideband
Model Au-IA
NF - 5 db 2-100 MHz
112
Power Meter
Mfg. Coherent Radiation
Power Meter
Mfg. Jodon
< 200 mw
Spectrum Analyzer
Mfg. Tektronix
Power Supply (3)
Mfg. Hewlett Packard
DC
Frequency Counter
Mfg . CMC
Balanced Mixers (2)
Mfg. Relcom
.2 - 500 MHz
Acousto-Optic Modulator
Mfg. Isomet
f - 40 MHz
o
Modulator Driver
Mfg. Isomet
f - 40 MHz
o
Power 0 - 5 w
Model 201
Model PM-550
Model 491
Model 6216A
Model 904
6 db insertion loss
Model DE-IR-20
BW - 10 MHz
Model DE-IR-10/5
BW - 10 MHz
113
LIST OF REFERENCES
1 .
2 .
3.
4.
5.
6 .
7.
8 .
9.
10 .
11 .
12 .
13.
Skolnik, M. I., Radar Handbook , McGraw Hill, 1970.
Skolnik, M. I., Introduction to
Hill, 1962.
Bonnelle, G. J. , ”FM-CW Radar,"
p. 143-148, August 1960.
Radar Systems , McGraw
I f\ eiAi n
~ Ac r o 5 pat* q — E lo c t roJiic^
Hoisington ,
presente
Systems ,
1972.
D. B., Multiple-Target CW FM Radar , paper
d at Asilomar Conference on Circuits and
Sixth, Pacific Grove, California, November
Reference Data for Radio Engineers , 5th ed. , P. Howard
W. Sams ^ Co., New York, 1973.
Hymans, A. J., and Lait, J. ,
Modulated Continuous -Wave
ings I .E.E. fBritish) , p.
"Analysis of a Frequency -
Ranging System," Proceed -
365-372, July 1960.
Richter, J. H., "High Resolution Tropospheric Rada
Sounding," Radio Science , v. 4, no. 12, p. iZbi
1268, December 1969.
Kay L., "A Comparison Between Pulse and Frequency-
Modulation Echo-Ranging Systems," Journal British
I .R.E . , p. 105-113, February 1959.
Yariv, A., Introduction to Optical El ectronics , p.
30 5-333 , Holt, Rinehart and Winston, 19 71 .
Adler, Robert, "Interaction Between Light and Sound,"
IEEE Spectrum , p. 42-54, May 1967.
Gordon, E. I., "A Review of Acousto-Optical Deflection
and Modulation Devices," Proceedi ngs IEEE, v. 54,
no. 10, p. 1391-1401, October 1966.
Dixon, R. W. and Gordon, E. I., "Acoustic
lators Using Optical Heterodyne Mixing
System Technical Journal , p. 367-389,
Light Modu-
The Bell
February 1967.
Fang-Shang Chen, "Modulators
tions," Proceedings IEEE ,
1465, October 1970.
for Optical Communica-
V. 58, no. 10, p. 1440-
14.
Pratt, W. K. , Laser Communication Systems , Wiley, 1969
)
15. Sze, S. M. , Physics and Semiconductor Devices , p. 655-
683, Wiley, 1969.
16. Oliver, B. M. , "Thermal and Quantum Noise," Proceedings
IEEE , p. 436-454, May 1965.
17. Hudson, R. D. , Jr., Infrared System Engineering, Wiley,
1969.
18. Peyton, B. , DiNarda, A., Chiou, W. , Lange, R. , Arams,
^ F. , Aita, M. and Pace, F. , Coherent Infrared Re -
ceivers for Laser Communications and Radar , Inter-
nal paper of AIL, a division of Cutler-Hammer,
Melville, Long Island, New York, 1973.
19. Rockwell International Science Center, 10 . 6 Micron
Photodiodes, Miscellaneous Report, September 27,
1973.
20. Delange, 0. E., "Optical Heterodyne Detection," IEEE
Spectrum , p. 77-85, October 1968.
21. Mocker, H. W. , "A 10.6 pm Optical Heterodyne Communi-
cation System," Applied Optics, v. 8, no. 3, p.
677-684, March 1969.
22. Isomet Corporation, Instruction Manual for 10.6 Micron
Acousto -Optic Modulation System , December 1973 .
23. Hogarth, C. A., Materials Used in Semiconductor De -
vices , Interscience Publishers.
^ 24. Ross, M. , Laser Receivers , Wiley, 1967.
25. Haliday, D. and Resnick, R. , Physics Parts I 8 II,
p. 1112, Wiley, 1966.
26. Read, W. S. and Fried, D. L., "Optical Heterodyning
with Noncritical Angular Alignment ," Proceedings
IEEE , p. 1787, December 1963.
27. Fraunfelder, M. F., Jr., A Heterodyne Detection FM-CW
Laser Radar Using a 10.6 pm Source , Engineers
Thesis, Naval Postgraduate School, Monterey,
California, December 1974.
115
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4. Professor C. H. Rothauge, Code 52Rt
Department of Electrical Engineering
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5. Assoc Professor T. F. Tao, Code 52 Tv
Department of Electrical Engineering
Naval Postgraduate School
Monterey, California 93940
6. Asst Professor J. P. Powers, Code 52Po
Department of Electrical Engineering
Naval Postgraduate School
Monterey, California 93940
7. Dr. C. C. Wang (53/6241)
Aeroject Electrosystems Co.
1100 W. Hollyvale Street
Azusa, California 91702
8. Dr. Greg Mooradian
Code 2500
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