Acousto-Optic Processors for the Detection of Spread
Spectrum Radar Signals
Andrew M. Kiruluta
A thesis submitted in conforrnity with the requirements
for the degree of Doctor of Philosopliy
Gradiiate Department of Electrical Sr. Conipiiter Engineering.
University of Toronto.
@Copyright by Andrew M. Kimhta 199%
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ACKNOWLEDGMENTS 1 woulcl like to express my heartfelt gratitude to my supervisor Dr. Y. Ristic for
his inspiring guidance arid n-hose advice that - o u cannot do engineering op tics without
knowing electronics ivell- provecl to be in~altiable. The sound advice from Dr. J . P. E-. Lee
of Defense Research Establishment Ottawa is very much appreciated. -4s well. 1 am deeply
indebtecl t O 111~- CO-super-isor Dr. -4. Iéne t sanopoulos for his encouragement ancl support.
Special thanks to my friends and colleagues ivho macle my gracluate esperience at the
L-niversity of Toronto a mernorable one. The early inspiration of m - mentors Dr. R. Don-
nelly. Dr. J . Quaicoe ancl Dr. R. Langford. al1 of Mernorial University of Xewfoundlancl.
who t aiight me. in t heir own unique way t hat the long and seeniingly chaotic pa t h to learn-
ing is through critical probing and a keen sense of obser\ation. is immenselu acknowledged.
This research effort {vas jointly sponsorcd by the Defense Research Establishment
Ottawa (DREO ). The Satural Sciences ancl Engineering Research Council of Canada
( SSERC ) . the Ontario Informat ion Technolog- Research Ceuter (ITRC ) ancl the .~coiisto-
Optic Research Laboratory (.AORL) at the University of Toronto.
Acousto-Optic Processors for the Detection of Spread Spectrum Radar Signals
Andrew M. Kiruluta, PhD 1997
Department of Electrical & Computer Engineering University of Toronto
Abstract Xewer radar systems using such techniques as direct-seqiience phase modulation. fre-
quency hopping and linear FM (chirp) require large transmission bandwidth and increas-
ingly sophis t icatecl receivers t O int ercept and classify t heir ret urns. These signals are
ctifficult to distinguish from background noise and are hence said to have low probability
of intercept (LPI). Current electronic receiver systems work ireil at cletecting and cbarac-
terizing narrowband pulse signals but are not very effective wit h spread spectrum signals.
.-\cousto-optic (.\O) processors have shon-n great potential for dealing with tvideband sig-
n a l ~ ancl offer the ability to detect and analyze \-aarioiis LPI wavefornis. In this thesis ive
present a theoretical. numerical and an esperimental stody of a t ime integrat ing acouste
op t ic processor. with an electronically inserted reference tone. to detect and characterize
linear FM and freqiiency hopped spread spectriini LPI signals corrupted hy additive noise
and narrowband interferers. Electronic and opticaI components w r e designed ancl the
processor assembled. -4nalytical espressions for chirp and freqiiency hopped signal corre-
lat ions wit h the processor were t hen derit-ed and niimerically simula ted. The processing
gain of the processor iras subseqiiently tlerived using a stochastic analysis approach for a
niirnber of SXR scenarios. It is shown that for relativelu low SSR intercept signals. the
laser noise is de-emphasized leading to a processing gain that is proportional to the square
of the detector dynamic range. .At high S'iR levels. the laser intensity noise becomes the
predominant factor. Experiment al e~daluat ion of the noise loading and effec t of the narrotv-
band interferers on the processor output w r e then carried out. -4 near real-time niethocl
based on digitally tunable not ch filters nas developed to excise the narrowbaod interferer
energy prior to correlation. The method uses a unique space-integrating electronically in-
serted reference tone arrangement. Finally. a novel way of estimating the overall optical
misalignment in the processor hardware \vas proposed and dernonstratecl. It represents a
simple and robust alternat ive t O many purely opt ical procedures. The resolution accuracy
of the rnethod is shown to be limited by the CCD pixel dimensions. .As a side result. the
scaling law that applies to the output signal when using CCD detection \ras also derived.
Contents
1 Introduction 1
1 . I Transmit tance Function of an A0 ce11 . . . . . . . . . . . . . . . . . . . . . 6
1 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Theoretical Studies 12
2.1 Frecpency Selection Constraints for the Ilultiplicative ( Iu-Line) .Architecture 13
2.2 A0 Correlator with Linear FU Inputs . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . . . . . . . . . . . . 2.3 A0 Correlator n-ith Frequency Hop Inputs 25
2.4 Xiinierical Xnalysis for the Two Tjwpes of Inputs . . . . . . . . . . . . . . . 26
2.5 Spacc-Integrarecl Output of the Correlator . . . . . . . . . . . . . . . . . . 2S
2.6 Effect of Soise on the Intensity and Correlation F~inctions . . . . . . . . . 35
2.7 Output SSR and Processing Gain in the Presence of Laser Soise . . . . . . 39
3 Experimental Investigation 50
3.1 Detection of Signals at the Spatially Integrated Output . . . . . . . . . . . 52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 CCD Scaling Law 53
3.3 Correlation of Sarrowband Signals in White Gaussian Soise . . . . . . . . 54
3.4 Optical Misalignment Estimation . . - . . . . . . . . - . . . . . . . . . . . 5s
3.5 The 50 MHz Signal Bandwidth A 0 Processor . . . . . . . . . . . . . . . . 63
3.6 Methods for SIS Detection and Remot-al . . . . . . . . . . . . . . . . . . . 64
3.7 Simulation of the LPI Signal . . . . . . . . . . . . . . . . . . . . . . . . . 6s
3.7.1 Linear F M Chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6s
3.7.2 Frequency Hop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.8 LPI Correla t ion De tect ion Circiii t Recluirenients . . . . . . . . . . . . . . . Y3
3.9 Processing Gain and Detecror Integration . . . . . . . . . . . . . . . . . . . 74
-" 3.10 Correlation of LPI S ipa l s in Soise . . . . . . . . . . . . . . . . . . . . . . J .>
3.11 SIS Escision Csing Tunable Filters . . . . . . . . . . . . . . . . . . . . . . YS
3.12 Impact of the SIS Sotching Feedback Loop . . . . . . . . . . . . . . . . . S3
4 Processor and Measurement Hardware 88
5 Conclusions 106
A Imaging Optics 109
List of Figures
1.1 Scheniatic of radar LPI correlator . . . . . . . . . . . . . . . . . . . . . . . -4
. 1.2 Bragg ce11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2.1 1-D multiplicative architecture . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Spectra grouping of the lariotis processor outputs . . . . . . . . . . . . . . . 1s
2.3 Frequency selections and spectriirn placement of LPI signals . . . . . . . . . 19
2.4 LPI signatures S ( t ) and F ( t ) are detected by two widely separatecl antennas . 21
2.5 Soise loading on the correlation for ~ar ious SSR ~al i ies . . . . . . . . . . . . 27
2.6 Effect of varying the chirp duration (Tc ) on the correlation . . . . . . . . . . 2S
2 . 7 Space integrating pin detector arrangement . . . . . . . . . . . . . . . . . . 29
2.S Simulation outputs for terms ( 1)-(4) respective15 . . . . . . . . . . . . . . 33
2.9 Overall simulation output of the space-integrating processor . . . . . . . . 34
2.10 Time integratiug A 0 intcrcept receiver . . . . . . . . . . . . . . . . . . . . . 40
2.11 For the case n-hen S-W2 + x . . . . . . . . . . . . . . . . . . . . . . . . . 4s
2.12 Output SSR for S.VR, . SXR2 >> 1 . . . . . . . . . . . . . . . . . . . . . 49
3.1 Reference tone .\O processor for radar signai processing . . . . . . . . . . . 51
3.2 A correlation peak cnvelope detected by the CCD array . . . . . . . . . . . 53
3.3 Correlatoroutpiit f o r r=1 .2p . i . P R F = O . l . V H z . . . . . . . . . . . . . . 55
3.4 Sliiltiple Correlation for P R F = 1 .\TH= . . . . . . . . . . . . . . . . . . . . 56
- - 3.5 I n a l l c a s e s t k e P R F = S O I<Hz.O.5l~ ' /DIl~and t in iebaseof20/ i s /DII ' .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Soise only figure 62
3.7 Effect of SIS on correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.S Overall optic and electronic hardware la>.oiit . . . . . . . . . . . . . . . . . . 67
3 -9 Chirp generating circuit configuration . . . . . . . . . . . . . . . . . . . . . 69
3.10 Prac tical relationship of frequencies . . . . . . . . . . . . . . . . . . . . . . . 70
3.11 Frequency Hopped LPI Generation . . . . . . . . . . . . . . . . . . . . . . 12
3.12 Processor output for a linear FM signal . . . . . . . . . . . . . . . . . . . . 76
-- 3.13 Effect of varying the chirp duration (Tc) . . . . . . . . . . . . . . . . . . . . t I
-- 3.14 Oscilloscope oittpiits shon-ing the iclentification of a chirp . . . . . . . . . . . t I
3.15 Corresponcling oscilloscope outpiits for the frccluency hopper . . . . . . . . . ï S
3.16 ( a ) in-band ancl ( b ) out-of-band SIS locations relative to the LPI banclidth . 79
3.17 Real Tinie SIS Excision Module . . . . . . . . . . . . . . . . . . . . . . . . S1
3.18 Correlation wi t h in-band interferers . . . . . . . . . . . . . . . . . . . . . . . S4
3.19 Effect of notchiog in-band interferers . . . . . . . . . . . . . . . . . . . . . . S4
3.20 Correlat ion with interferers . . . . . . . . . . . . . . . . . . . . . . . . . . . S5
3.21 Sotching of interferers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S5
3.22 Correlation with o.itt.of .band interferers . . . . . . . . . . . . . . . . . . . . . S6
3.23 'iotching of ozrt-of-band interferers . . . . . . . . . . . . . . . . . . . . . . . S6
3.24 RAIS error in approximating the peak of the correlation envelope . . . . . . S7
4.1 Laser diode source SDL-2432-Hl from Spectra Labs . . . . . . . . . . . . . . S9
. . . . . . . 4.9 Another \.iew of the laser heat sink and anarnorphic prisni pair 90
. . . . . . . . . . . . . . . . . . . . . . . 4.3 i ï e w of the fiber couplecl detector 91
. . . . . . . . . . . . . . . . . . . 4.1 Another vie\\- of the fiber coupleri detector 92
. . . . . . . . . 4 \ ïew of the spatial filter precedecl hy a Sewport Fourier lens 93
. . . . . . . . . . . 4.6 Expancled view of spatial filtering and detection sections 94
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 .-\ iisiliary elec t ronics 9.5
4.8 -4nother vietv of the tunable filter/DR controller modtile . . . . . . . . . . . 96
. . . . . . . . . . . . . . . . . . . . . . 4.9 Another vie\\* of the overall processor 97
. . . . . . . . . . . 4.10 A magnified ïiew of the single diode tap-off arrangement 98
. . . . . . . 4.11 Cornputer connection to the feedback arrangement via a GPIB 99
. . . . . . . . . . . . . . . . . . . . . 4.12 Test ancl ?ileasiirement eqiiipment rack 100
. . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Lïen* of the 50 J I H z processor 101
. . . . . . . . . . . . . . . 4.14 Another estendecl view of the 30 .\[Hz processor 102
. . . . . . . . . . . . . 4.15 Side perspective of the entire 50 .1 [ H z LPI processor 103
. . . . . . . . . . . . . . . . . 4.16 Slagnified side view of 50 .\ I H z LPI processor 104
. . . . . . . . . . . 4.1 T i ï e m of the 20 .\ I H 2 processor from the laser diode end 105
. . . . . . . 1 Colliniating and pe-detection -40 cell aperture matching optics 110
vii
ABBREVIATIONS
-40
ES11
-AR11
LPI
SIS
SSR
FM
FH
DSP
BS
SS
TDOA
CCD
RUS
AWG S
YB T
CRR
P S
s -4
GFLOPS
VCO
RIS
DR
P R F
I M P
Acoiis to-Opt ic
Electronic Siirveillance Ueasiire
Ant i-Racliat ion 'cIissiles
Lon- Probability of Intercep t
Sarrowband Interference Signals
Signal-t o-Soise Ratio
Frequency Slodulat ion
Frecluency Hopped
Digital Signal Processing
Beam Split ter
Spread Spectrum
Time Difference of Arriva1
Charge Coupled Devices
Root Mean Square
Adcli t ive llrhite Gaussian Soise
l'ariable Bias Term
Chirp Repetition Rate
Pseudo-Soise
'l'umerical Apert rire
Giga-Floating Point Operations per Second
Voltage Controlled Oscillator
Relative Intensity Soise
Dynamic Range
Pulse Repet it ion Frequency
Int ermoclulat ion Prochic t
SYMBOLS
difference freqiiency
electronic reference frecpency
static index of refraction of A0 ce11 medium
transit time of -40 ce11
ampli t ticle transmit t ance func t ion of --'O ce11
effective t ransnii t tance of A0 ce11
banclpass LPI appliecl to the laser
banclpass LPL applietl to -40 ce11
modnlat ion tlept h of laser
ratio of . s 2 ( t ) amplitude to the reference tone amplitude
Laser DC bias amplittide
reference tone amplitude
cent er frequenq- of .s2 ( t )
A0 ce11 cliffrac t ion efficiency
pliase of detectetl spatially varying correlation
iipper cittoff freciuency of -40 ceII banctwidtli
loiver ciitoff freqiiency of .\O ce11 bandwiclt h
-40 banclwiclt h
LPI bandwictth
intcnsit y of 'noiseless ' modiilated laser
intensity of noisy modulatecl laser
detected intensity at the CCD plane
time-al-eraged noise of laser source
processing gain of processor
Tt integration time of CCD array
-Y, interna1 A 0 ce11 acoustic/optic- interaction noise
1 CCD saturation voltage
- 1 (x ) -40 noise poiver contribution from mu1 tifrequenc?- diffraction
.lÉ(x) . A 0 noise poiver contribution from nonlinear acoustic interaction
(2 Bandpass filter qualit- factor CS
J u itpper cut-off frequency of the upshifted LPI applicd to -40 ceil
f; lowcr ciit-off freqiielicy of the iipshifted LPI appliecl to .-\O ce11
L' acoust ic veloci ty in -40 ce11 interaction medium
T c chirp durat ion
n chirp rate
f.v[s frequency of SIS
Chapter 1
Introduction
In the past few decacles the increased amoiint of informat ion conveyecl hj* cornmitnication
systerns has been follon-ecl iip b>- a corresponding increase in the amoiint of p r i ~ ~ t e infor-
mation [Il. [2]. In many cases. it may be usefiil to hicle the presence or the esistence of
the comniiinicator's signal. Thits. an unaut horizcd receiver cannot dis t inguis h t lie coni-
municatecl signal from the receiver noise pliis interference. Since detection is a process
of choosing between noise alone and signal plus noise. hiclclen signals chat are clifficult to
clctect hy iinatithorized receivers are said to have loiv probability of cletectiun ( L P D ) [2].
Froni an intercepter's point-of-view. LPD signals appear as backgroiincl noise.
111 ot her applications. it ma>- not be possible. using LPD techniques. to a\-oicl ha\-ing the
signals detected hy unaut horized receivers. In those circumstances. it is possible to cleny an
iiriauthorizecl intercept receiver the features of the signal that coiild be ernployecl to derive
its form. Siich signals are said to ha1.e a low probability of intercept (LPI). Therefore. the
objective of LPI signal design is to produce signal iincertainty at the iinaiithorizecl receiwr
ivhich results in a signal-to-noise ratio (SXR) much lower than coulci occiir in the absence
of LPI signal characteris tics.
Modern radars increasingly use spreacl-spectrurn techniques to arhieve the LPI contli-
t ion. Radar designers are ever considering wawfornis which are more difficult t O intercep t
to protect against anti-radiation missiles (-ARMs) and to recliice the detecrion range of other
hostile act il-i ties. Se\-eral of these radar systems are ciment 1'- operat ional tri t h man- niore
in the del-elopment stages. employiug tlirec t-sequence. frecluency-hoppect. p hase-mocliilated
or linear FM (chirp) signals. These signals have insufficient potver to be ahoïe the noise
ffoor and to be easily processecl. -4s a result. the receiver in processing these signals.
miist achieve sufficient SSR gain. From the interceptor's view point. a tliffereiit sort of
siirveillance measiire receiver is needed for these LPI radar 11-a\-efornis.
In using sitrveillance measure receivers to detect LPI radar signals. it is necessary to
estract large bandividtli signals. froni the electromagnet ic spectruni. having low SSR. One
approach to solring this problem is to use a matched filter [3]. [-LI. which produces at irs
output a signal with S S R , = ( T S B ) S T R t where TqB is the tirne-bandwidtl procliict of
the receiver input signal (of cliiration T, and bandividth B) antl. S-1-R, ancf S I R , are
the output and input SSR's of the matched filter. respectively. The procluct TsB (for
radar LPI signal. typically T, = 1 nis. B = 0.5 GHz) is often referred to as the processing
gain [5 ] of the recei\*er (in this case the filter) since its magnitiide increases S.l-Ro and tkos
facilitates signal detcction. By definition. however. the LPI radar signal form is not knoivu
a priori and. therefore. the matched filtering technique is difficult to implenient. lioreover.
the detecrion system must ha\-e flesibility to alter the matchcd filter in order to cletect a
large varicty of the LPI radar signals that are -hiclden" in the loir- SSR environment. This
rules out "ordinary- analog mat ched filters.
By using a digital signal proccssing (DSP) search technique. such as masi~iiuni-likelihood
detection [6]. it is possible. in principle. to determine the type of signal iisecl bu the LPI
raclar. In practice. the more samples of the LPI signal we collect. the larger the prohahility
of interception. Cnder tkese circunistances it niakes sense to deploy a niimber of receiving
antennas in order to capture man- signals. These antennas. a niininiiim of two. are con-
nectecl to a central processor where the LPI signals are then processecl. However. this DSP
approach is estremel- slow and for typical LPI raclar signals. inapplicable. For esample [Tl.
a 500 MHz signal. with 1s time duration. has a time-bandwidth procliict of 5 x 10" and
requires on the orcler of 3 x 10'' digital computations to produce the conipressed pulse.
If piilse compression is performed every miilisecond. 3 x 101%peertions per second are
required: well beyoncl current D SP capabili t ies.
Correlation techniques have heen clernonstrated in the past as a riahle means of cle-
tecting radar signals with LPI [SI. Csing a correlator architecture as sliown in Fiy. 1.1.
we consider t lie interceptecl wa~eforrn as i ts own reference resiilt ing iii an autocorrclator
implementation of an 'automatic' mat ched filter. The two receivers capture the wa\-efor~n
wi t h some relative time-difference-of-arri\al ( TDO A ) related to the t arget angle 8. Because
t lie two interceptecl noise signals are statis tically uncorrelatecl. only the desirecl n-iclebanci
LPI correlation is available at the output for further processing to clerire time-of-arri~al.
TD OA. cent er frequency. bandwiclt h. signal type and ampli tucle.
Complicating the detection process is the ptesence of strong narrowbancl interference
signals (SIS) mithin the LPI bandwidth [II. The SIS may be unintentional as t h e to
a nearby trammitter or intentionally inserted by a hostile jamnier. Often. the SIS has
an amplitude much greater than the wideband signal and autocorrelates to dominate the
A 1 Translater 1 1
A n t e n n a '1
Figure 1.1 : Schematic of raclar LPI correlator
A n t e n n a 1 Ampli tutle
conipressed LPI raclar signal. Thiis. one of the key technical issues is how to rernoi-e the
r Correlator
SIS hefore processing the wiclehand signal. -4fter rke SIS has heen iclentified autl ~~~~~~~~ed.
--c
a correlation rcceiver is t heu iised to characterize the u-iclebaud signals.
Correlation receivers can be classifiecl into two categories: digital and optical (91. (101.
- O Delai
4 1 )
Digit al spreacl-spec t rum correlat ioii receivers are well known as t hey are iisecl in satellite
,
communications [Il]. [12]. Hoivever. they lack the speecl and the bancl~vitlth to hanclle the
Frequency Trans la tor
demands of newer spread spectruni radar signals which are typically in the freqiiency range
\
0.5 to 26.5 GHz with a minimum bandwidth of 0.3 GHz. Recently. the most proniising
correlation receiwr architectures for carrying out detect ion and classification of LPI raclar
signals. have been t hose based on acousto-op tic (-40 ) t echnology [13]. [14]. Thcir op t ical
engines have the potential to provicle S-10 GFLOPS of processing power which is a 1000-
folcl irnprovernent over current electronic systems [9].
A 0 technology has recently played a pivotal role in no\-el c1ti.elopments applicable to
op tical comput ing and holograp hy [l5]. optical cornmitnications [l6]. (1 71. op tical sens-
ing [ l G ] . [lS]. [19] as well as to medical image processing [201. Tirne-integrating -40 based
processors have generated great interest as potential LPI receiven. These processors are
attractive for LPI receiver design from three points of v i e x ( i ) t h e - can opcrate in such
a way as to --automat ically" penerate the required mat checl filter for nitilt i tude of simult a-
neous LPI radar signals. ( i i) they can often provicie the requirecl information in real-time.
and (iii) they can provide in escess of 1 GHz real-time banclwidths and processing gain.
clefined as S.\-&/S.SRi. on the order of 10Iog(T, B) r;: 60 dB. The latter allows for the
design of LPI recei\.ers n-itk input S-YR, as low as -50 dB.
;\O based receivers for the cletection of LPI signals bal-e been investigatecl recently by
a number of researchcrs [21]. [SI. [Z]. ['BI. In the last few years. the tiw A0 processors
niost coninionly studied have been the adc1itix.e ( Slach-Zehntler ) arclii tecture [l-k] . and t lie
niiiltiplicative (in-line) architecture [l-L]. 1161. [21]. [10j. In the first approach. two A0 cells
are usecl. one for each intercept LPI signal (or one with a reference waveform). and the
signal bandwidth B is eclual to the full A0 baridwidth B.4o. Howewr. this design suffers
froni mechanical instability and requires high precision optical components ancl cletect ion
system. In the second approach [IO]. an electronic reference tone is used. The use of an
electronic reference tone offers mechanical s tabili ty and reduces clemand on t lie op t ical
and cletection cornponents. hoivever. as shown in the next chapter. the axailable signal
banclnidth is reduced hy half to B = B,lo/2. In addition. this approach reqiiires much
more ela.borate atisiliary elec tronic hardware as described in Chapter 3. Time-intcgrat ing
.-\O receit-ers based on the concept of an electronically inserted reference tone. ha\-r sho~vn
consiclerable proniise in the area of LPI cletection and are the basis of the theoretical and
esperimental investigation of t his t hesis.
In a section that folloivs. a simplifiecl analysis of the operation of an -40 (or Bragg) ceIl
is presentetl. The theory leads to the clefinition of the transmittance function of the ce11
that is esploitecl in the analysis gil-en in Chapter 2.
1.1 Transmittance Function of an A 0 ce11
An acousto-optic ce11 is a spatial and temporal ligkt niocliilating device that ericotles light
with information containeci in an electrical clri\-e signal. It consists of an interaction ma-
terial. silcli as g l a s or an esotic crystal (for esample LiTnOÎ. Li.1-bO3 J; Ti@) . to ivhich
a piezoelectric transdticer is honcled as shoisn in Fig. 1.2. The drive electrical signal f ( t )
causes the transdiicer to l-ihrate lnunching either a compression or a shear acousric wave
into the mediilni which in turn sets up strain waves in the crystal. Thesc strain waves
lead to density changes in the interaction medium and consequentl~: to incles of refractiou
changes. The net result is that light passing through the -40 ce11 in the --direction is mod-
illatecl in phase according to changes in the optical path inditcecl by message signal f ( t ) .
The diffracted light enwrging from the nieclium is t hus modulated \vit h the iuforniation
containecl in the original electrical signal.
The nature of the acousto-optic interaction is influenced by the thickness. in the di-
rection of the light wave propagation. of the interaction region. A0 clevices irith large
interaction lengt h compared to the distance between neighboring acoits tic ~va\.efronts in
incident
light
. . .
l r Acoustic Absorber
Transit time T
Figure 1.2: Bragg cell: For a given drive signal f ( t ) with center freqiienq- f. n-e see chat the acoiistic wavelength is .\ = 7. The spatial frecliiency is therefore n = +. Hence. tlie
Bragg angle of the ce11 OB = Xci = y. .An ncoustic absorber at the other end is used to prel-ent acoiistic reflections wit hin the ccll.
the cell. are said to be operating in the Bragg regime ancl are referred to as Bragg cells.
Uï th shorter interaction length. al1 cliffractiori orders are present. and the clerice is saicl
to be operating in the Raman-Sath reginie [25]. This n i ~ ~ l t i tlicle of diffracted orclers leacls
to a waste of potver. Hence. most signal processing functious are carried out in the Bragg
regime [14].
Assuming a linear isotropic interaction medium in the .-\O ceIl columri. the modulated
optical incles of refractiou is thus given bu [13]. [Xi]
1 for I z l s f r e d ( z ) =
( O otherwise
where no is the static indes of refraction of the material. L' is the acoustic velocity in the
interaction niecliiim. and ni is a constant of proportionality. nh choosc tlie niid point of
the .-\O ce11 as the origin of the CO-ordinate system so that the dri\-e signal a t the estrcme
end of the ceIl ( s = L 12) is given by f ( t - T ) 11-here T = L / L* is t ke a dela- ecliial to the
transit t ime of the cell.
At the incident plane of the ce11 (; = O ) . the optical aniplitucle of the light beam is
-4 0
11-liicli is a plane mave wit h angular frrcpenc~- dl. At the esit face of the cell. z = 2. the
aniplitucle of tlie light beam is
where the transniittance or modulation transfer function of the ce11 is clefinecl as
which is derived from a o that is a function of al1 spatial ceordinates as follows
wliere do is the iucreriiental change in the phase of the light beam as it propagates across the
acoiis to-op tic interaction mediiini wi t h \va\-elengt h A. The total phase accriiecl is oh t ainecl
hy integrating Eq. (1.5) to yielcL
- constant tcrm
By disregarding the constant phasc factor ancl keeping only the first two terms in a Taylor
series expansion of the esponential terni and with the assiiniption of a Bragg riiode of
operation. we have
where m = '":"L is defined as the rnocliilation i d e s of the cell. The transrni t t ance fwiction
consists of a constant term mhich passes the oth uncliffractecl orcler plus a linear spatially
and temporally niodulated image of the drive signal f ( t ) corresponcling to eit her a positive
or negat ive diffraction order.
Hence. the drive function f ( t ) causes the cell to behave as a phase diffraction grati~ig
in the s-direction. The light leaving the acoiisto-optic ce11 in the first positive diffraction
orcler may thiis be espressecl in phasor form hy the equivalent f~inction [14]
d w r e (s ) is the aperture function of the system xhich accoiints for nonlinear distort ions
due to the illumination function of the source. attenuation factors. laser powr le\-el. and
truncation effects from the acousto-optic ceil or ot her optical elenients in the systern. IL-hile
r i t is the mocliilation indes of the ce11 representing the power distribution in the cliffractecl
orcler relative to the uncliffractecl mode. The final term implies that f ( t ) has heen miiltiplied
by c o s ( k f , t ) to translate it to the center frecliiency f, of the acousto-optic cell. \\é are now
in a position to stuclj. the in-line optical correlator architecture based on this acousto-opt ic
interaction phenoniena.
1.2 Thesis Outline
This thesis consists of a theoretical stiicly. numerical simiilation ancl an esperimental in-
vestigation of a time-integrat ing .\O processor architecture wit h a goal of detecring and
classi-ing spreacl spectrum LPI radar signals in presence of noise and SIS.
Chapter 2 esplores the t heoret ical feat ures of the mult iplicath-e in-line architecture.
The criterion for select ing the various frecpencies and bandwidt h cons traints of the receiver
is de~doped . In addition. the overall processing gain of the receiver. assuming noisy input
signals and a noisy laser intensity. is developed using a stochastic modeling approach.
-4nalytica.l espressions for the processor output IL-hen fed wi th either chirp or frequency
hoppecl signals are also derivecl and niimericaliy ecaliiated.
Chap ter 3 iutrodtices the esperiment al setiip and equipment interconnect ion usecl in
this work. The \-arious signal and noise gcnerating siibs>-stems are first disciissed. Direct
mocliilat ion of the laser as reqiiired by the the-integrat ing archi tec t lire necessi t atecl t ke
design of aclcli t ional circuitry. The performance of a 20 JI H 2 signal banclwicl t li processor
in correlating two ptilses embedcled in noise of ~-arying SSR is presented. The influence of
additive Gaiissian noise on the correlation peak and width was nieastirecl ancl analyzed for
\arying SSR \-dues. -4 no\-el approach for estimating the overall optical misalignment in
the processor is then de\-isecl and demonstratecl. The observecl clilation in the correlation
width is esplainecl in terrns of the sampling characteristics of the CCD arra-.
-4 50 M H z signal handn-idth processor that is a scalecl i-erçion of a typical radar
receiver. ivas designed and assemblecl to correlate chirp and frequency tiopped spreacl spec-
t riini signals. An esperiment al analysis of the clet ect ion ancl categorizat ion of LPI signals
corruptecl b>. noise \vas then carried out. In a section that fol lo~s. the impact of the SIS
on the LPI is esperimentally demonstratecl. -4 novel approach for rcal-tinie detection and
removal of the XIS from the LPI signals prior to correlatioo is proposecl and denionstratecl.
C hap ter 4 illus t ra tn the hardware aspects of the various processor niocliiles. measure-
nient ancl test equipnient from a nurnber of mutage points. The O\-erall processor 1q.oiit
is also included
Finally. a summary of the results and contributions of this work is presented in Chapter
- 3.
Chapter 2
Theoretical St udies
In t his chapter. the theory of a one-dimensional .\O correlator with an electronic refereuce
tone is reviewed with the aini of deriving the frequenc?- selection constraints that niiist
be followetl in its design. The output of such a correlaror is then analyzecl for linear FI1
chirp and frecpency hop (FH) input spread spectriini signals ancl t hereafter nieasiirzcl in
esperiment al cases considered in Chapter 3. Sirnidation of t lie correlator out put II-as also
done for input signals of ~ary ing STR levels wi th the assumption of additive n-hite Gaitssian
noise (.\it'GS).
In orcler to speecl up the fectlhack loop necessary for identification and excision of the
SIS. a space-integratetl output is considered in adclition to the conventional time-integratetl
output. The idea of using a space-integrated output. witli this processor architecture. is
an original research contribution of this work.
The behavior of the correlator in the presence of noise is then analyzed ancl the detected
"noisy" intensity is espressed in tcrms of the --noiseless" intensity and an ascending order
of noise cross terms.
The correlator noise theory. first piihlished by Iiellman [26] ancl also consiclered hy other
researchers [XI. [->SI. [09] rvas generalizeti to include laser intensity noise in this work. The
correlator output SSR was then clesivecl and cliscussecl for a nurnber of scenarios. The
inclusion of the effect of the laser intensity noise to the overall processin:, gain expression.
is another original research contribution of this work.
2.1 F'requency Selection Constraints for the Multi-
plicat ive (In-Line) Architecture
In a t inie-integrating -40 correlation receiver. shown in Fig. 2.1. the laser is directly niocl-
ulated with one of the intercepted LPI dong with an appropriate DC bias l e d The laser
iight is then matched to the active aperture of the -40 cell by colliniation ancl ananiorpliic
optics.
-4t the other encl. another interceptecl LPI (or reference wal-eforni) is iisecl to phase
nioclulate the .-\O ce11 transmit tance fiinction t h e r e - converting the LPI inforniatiou to
optical form. The optical intensity incident on the detectors is the procliict of the laser
intensi t ~ - ancl the intensi ty diffraction pattern from the illiiminat ed A0 cell. Detector
integration then yields the reqiiired time averaged correlation of ttvo LPI signals. The
position ( h g ) of the correlation peak on the charge couplcd detectors ( CCD ) is proportional
to the tinie-differencc-of-arriva1 (TD0.A) between the two interceptecl waveforms.
In what follo~vs. al1 the terms in the output expression for the processor as they relate
to frecpency and LPI handwidth selection requirenients. are consiclered. Tliese selection
constraints are derived t hroiigh the following analysis. IVit h refereiice ro Fig. 2.1. the
intensity of the niodulated laser diode is giveii by
where .-li is the DC hias aniplitiide. ni1 is the niotliilation depth. s l ( t ) is the banclpass LPI
signal of intercst and do is the modulation carrier frequenc.
For the correlat ion. ire i d 1 use the negat il-e diffraction order as it natiirally ?-ieltls
the cornples conjugate in the correlation integral. The -40 cellas amplitiide t ransniit tance
function for this negative diffraction orcler (when the oth order is ornittecl). as given
in (1-11 and modifiecl to apply to the architecture in Fig. 2.1. is
where r = T/2 + .r/c*. rl is the A0 ce11 diffraction efficiencj-. A; is the electronic reference
frequency. d l ~ = dc + J, is the crnter frecluenc~. of the spread spectrurn LPI signal s 2 ( t )
niodulating the acousto-optic cell: and rnz is tlie ratio of tlie signal amplitude to the
reference frequency oscillator arnplitiicle.
The correspondiiig effective transrnittance that applies to the intensities is giwn by the
product of the mot mean square (RLIS) \allie' of t.40
'LC'ith a small modulation depth (m2 << 1 ) needcd to mairitain linearity iri intensity. Eq. (2.2) is approsimately equal to a constant amplitude pliasor.
Figure 2.1: l-D nlultiplicative architecture: do = . i . l ~ - dc: do = difference (offset) fre- qwncy: xc = refereuce freqiiency: the center frequency of the s 2 ( t ) signal.
The intensity iniaged onto the CCD a r r q is
Espanding Eq. (2.4) r-e have
ivhere we have used the itlentity
The first terni contains the DC hias q.4i-42/2 and a signal depenclent bias terni rlr ic: . -L1 .A2/' 1
s 2 ( t - r ) I q h a t integrates to a constant for sufficiently large integration tinie T,. Terms
( 2 ) . ( 3 ) and (4 ) are bandpass terms that integrate to zero for T, >> k. Of interest is the
last terni in Ecl. (2.5) which can be sliomn to eclual
ivhere the tinie integration of (Sb) term leads to the desired correlation.
In Eq. (2.7). (5,) is a bandpass terni at frequency L,. outside the acoiisto-optic band-
width. that also integrates to zero for T, >> 112 f,. Terms (1) and ( a b ) after integration.
becorne
- \ciriahle bias term (L-BT)
Hence. the amplitude rather than intensity modulation of the A0 cell. bas producecl R ( r )
where t lie elcctronic refereuce frecluency f, allows one to separate the correlation terni from
the \-BT. This correlation oiitpiit can be written as
where o12(r) is the phase of the tirne averaged terni JO s l ( t ) . s i ( t - r)dt such that
Therefore. we can find R ( i ) by recovering the envelope .412(r) and the phase 0 1 2 ( r )
of the spatial carrier by coherent detection. Xote that since T = T / 2 + .c/c. the peak of
- the correlation i d 1 occur at s = -2 2 - -L 2 ' which corresponds to the bottom edge of the
out put plane. leading to a one-sided correlat ion func tion. This correiat ion funct ion can
thiis be centered in the output plane by introducing a relative ciel- eciiial to T l 2 in either
Tetriporal Freqtrency Spectruni
-B O B 10 2 J O
Figure 2.2: Spectra grouping of the varioiis processor outptits from Eq. (2.5)
r - - - - - - I I I I I I t
s ( t ) or s 2 ( t ). né choose to dela? si ( t ). the LPI signal mocliilating the laser source.
Finally. it is instructive to consider the \arious terms given in Eq. ( 2 . 5 ) in the temporal
freclueuc~ do~iiain as shon-n in Fig. 2.2. In order for the VBT not to overlap with the
correlation signal at fo. we require that f, - 8 1 2 3 B or f, 2 3B/2 . Similarl~: to avoicl
overlap with the signal at 2 f o carrier (terni ( j a in Eq. (2.7)). ive must have f, + BI2 5
2fo - BI'. or f, 2 B. Both these constraints are siniiiltaneously saiisfiecl if 1 f, 12 3 BI?.
where B is the handwidtk of spread spectriim LPI signals s l ( t ) and s 2 ( t ) . Biit the center
frequeuc- of the signal s z ( t ) niodulating the cd1 is f iF = f a + f,. Hence. two solutions are
possible with the constraint 1 f r F - f, 12 3Bl': fi = f f r F - l.5B or f:' = f I F f l.5B. In
I I * frequency
- . . - . . . . . . - . . . - . . - . . . -- : - - - . . . - . . - . . . - * - . . . . .- *- : . . . - . - . : : : . - - . . .. . . - S . . - . -
the first soiution. the electronic rcference f, is placed nt the lower cutoff frecluenc- of the
.-\O passbancl while the upper cutoff frequency of the radar LPI signal s 2 ( t ) is p ~ t at the
upper cutoff frequency of the -40 passbancl. This solution is shown in Fig. 2.3.
Alternat ively. the frecpency selection const raints can also be sat isfiecl by placing the
elcctronic reference f, at the upper cutoff frecpency of the A0 passband. The lower cutoff
frequency of the radar LPI signal is then placecl at the lower cutoff frequency of the -40
(2).(3).(4) and (.5b) . . . . - . . . .
0 . . . . . .+ ..- :- B.-- - . . . . . . . - . * . . - .
terni (.?a) . . . . . .
+.a
10 (a) laser diode input
(b) :\O ceIl input
Figure 2.3: Frequency selections and spectriini placement of LPI signals modiilating (a ) the laser and ( b ) the acoiisteoptic cell. The electronic reference f: is at the lon-er ciitoff ( flo) of .-\O passband. The upper cutoff freqiiency ( f r F + B / 9 ) of the LPI is at the iipper ciitoff ( fko ) of the cell. Alternative solution with f: at fito and LPI downshiftcd to f iF - B/3 = f)' is also possible. Sote that in the figure shown. the modulation carrier frequency of s z ( t ) is f r F = f, + fo. and = f i o - ftO.
passhand. Froni a theoretical point of view. both solutions are iclcntical. In this thesis. the
first sol~ition iras useci througlioiit .
Before we leave this section. let lis cliscuss one last constraint iniposecl by the -40 ce11
bandwidth ( B.4o ). In the soliition aclopted in this thesis. n-e have that fi;'' = f r F + BJZ.
where f:' is the iipper cutoff frequency of the -10 ce11 handi\-idth and B is the LPI
handwiclth. Ré also reqiiire that the lower cutoff frequency of the A 0 ce11 bancl~viclth
fiLo = f:. But Iiellrnan's frequency constraints require t hat
f l F - f: = l 3 B . hence
Thus. the A0 ce11 bandwidth m u t therefore be twice the LPI banclwiclth. -4lthough the
insertion of an electronic reference tone tielps to make the design practical stahilizing
the output ancl provitling a means for controlling the bias ternis. the pena1t)- ire pay is a
net reduction in the overall availahle -40 bandn-iclt h.
These constraints were theu iised to select the various frecpeucies necdecl to setup the
processor. The recpired spectrurn placenient for the signals motlulating the laser diode
and driving r he -10 ce11 are as shown in Fig. -2.3 respectively.
2.2 A 0 Correlator with Linear FM Inputs
Consicler the -40 processor nioclel for LPI detection shomn in Fig. 2.4. LI-e shou-ed in the
last section how the various freqiiencies and banclmiclth. shown in insets. are clerivecl in
terms of placement and specifications. Let us assume that linear FM chirp signals S ( t )
Seu t ral Density Filter
1 L-- - R B P F
Figure 2.4: LPI signatures S(t ) and F ( t ) are detected by tmo widely separated antennas: boosted bp an LX -4 t hen subsec~uently clown comrerted to the frecpency band specifications of the optical processor. The spectrum at each critical stage of the processor are shoim in the insets. The ciel- line in the circuit for input S(t ) is not shown. Further details can be found in the text.
and F ( t ) are received frorn tivo wiclely separated antennas. This is characteristic of a real
situation in which correlation of these two signals provicles a good indication of n-hethcr
or uot a transniitting source esists in the vicinit- This is the classical detection problenl.
.-\ltcrnati~ely. the second signal F(t ) is used as a reference signal ishich is comparecl with
the interceptecl signal S ( t ) . The problem then is one of identification by correlatirig S ( t )
isith a series of sample reference signals until a strong correlation is cletectecl signifying
that a niatch has been founcl.
\Ié i d 1 restrict oiirselves to the matchcd filtering of the former case. Il-e ivill motlel
the LPI chirp signals detectecl by the processor after passing through a loi\- noise amplifier
( LX;\). clown-con\-ersion and bandpass filtering as
and
F ( t ) = cos(i?af,t + ant' + < P t ) + I I > ( f )
where the phase terms <DI. are uriiformly distributecl ranclom Lariables over the intcrval
O to 'a and a is the chirp rate in Hzlscc . The addition of tkis rancloni phase recoguizes
the fact that the timc origin is arhitrarily chosen for the case when the signals corne froni
tn-O widely separated antennas. Since the correlator shifts one of the inputs h - a tinie slot.
before each integration until a correlation peak occurs. this phase dela. is thits inherent in
the design and will be ignored in the subsequent analysis. \iè mil1 also represent the noise
corruption in the signal paths by the additive white Gaussian noise processes Ilel ( t ) and
I4>(t) with spectral densitp .\o/2.
The classical time-integrating correlator with an electronically inserted reference tone
leacis to an iutegrating action by the photocletector given 11'- Eq. ( 2 . 5 ) and repeated Lere
for convenience. ;'
where I,(t) ancl 12(x. t ) are the modulatecl intensities of the laser source and light esiting
the -40 ce11 respectively. Rt( T,. r ) = J: S( t ) F ( t + r )dt is the desired correlation. T = + f is the displacement kariable and Ti is the integration time of the detectors. \Ié non- proceed
to calculate this correlation iising tlie mode1 of LPI i~aveforms that are pickecl up by the
ant ennas.
In man? practical situations. the only thing ive usiiallj- have a\ailable is the recorcling
of one or a sniall nuniber of saniple fiinctions of the randorn process. né then consider
the time averages of indi\-iclual sarnple functious of the processes. Let us clenote tlie
saniple functions of each of the processes hy f ( t ) = ci cos(?;; fol + a n t L + BI ) + c r i ( t ) and
~ ( t ) = (i2 c o s ( 2 ~ f ~ t + ;id2 + 0 2 ) + ~ ( t ) . In anticipation of the limitation of having a single
noise source for the esperirnental setiip in Fig. 3.8. ive will cousider the specific case i h e n
0 , = Br ancl tri ( t ) = w2(t ). The output of the noise generator is ecluallj- clividetl iising a
power splitter and added to each LPI signal path.
Of interest here is the last term in Eq. (2.14) representing the spatially varying cor-
relation function. Let c i l = ci2 = rect{$) for brevity and the instantaneous frcquency of
the chirp f; = fo + a t . The linear FM correlation term V(T,. r ). assuniing a single chirp
'.-Ifter integration when al1 bandpasa terrns with carrier frequcncies at JO and ?Io have vanished.
wi thin the integration n-inrlow Tl . ma- thtis be expressecl as
For an integration tinie Tl which is much greater than tlie ;\O ce11 dela- T . Eq. (2.15) can
be approsiniatecl as
This resiilt shows t h the correlator oiitpiit is thiis a spatial carrier niocliilating a sinc
fiinrtion 11-ith a niain lobe of diiration -& meastirecl froni a zero to zero crossing. But the
R CI' 2 Te chirp rate is given hy o = 7. hencc & = m. This expression re\-eals t hat the wiclth of
the niain lobe of the correlation is inversel- proportional to the protliict of the integration
tinie ( Tl ) and the chirp hanclwidt h ( BI.1.-): and direct ly proportional to the chirp durat ion
Tc.
Son+ the acltlit ive white Gaiissian noise component is ergoclic in tlie autocorrelation and
equals to ) 6 ( ~ ) . Hence. the total espression for the correlator otitpiit can be su~nrnarizecl
.-&-A2n2 1m2T( -Yo a ( - 4 [ r l => cos(2n for)s inc(aTir) +,d(r) + VBT]
L'(Ti *T)
where <i ( r ) is the aperture function of the processor as derived I>y \7anderliigt [l-l] and
repeated herc for convenience
and .r, = -&Y s .4 is the shifted central \ d u e of the Ciaussian illumination profile of the
laser. c is the atteniiation constant of the A 0 niaterial. L is tlie lengtk of the ce11 and -4
defines the light amplitude at the edges of the cell. The Gaussian ilhimination is modifiecl
hy a frequency dependent (f k i n g the center freqiiency of the -40 cell). esponentially
at teniiating factor of the for* (1, = E - ( ' ~ ! ~ / . ' ) ( L-cLf2/8-4).
2.3 A 0 Correlator with Frequency Hop Inputs
-4nother popular spread spectriini signal commonly iised in radar applications tocla>- is the
frequency hopper schenie. Consider the same setup as sholvn in Fig. 2.4 trith signals
n B 1.1,-t F ( t ) = (1.~ COS(^ fOf + - + (a2) + lV2(t)
&V + 1
d e r e again ive set (11 = « 2 = 1. Bit' is the total hop hanclivitlth. -1- + 1 is tlie to-
tal numher of discrete frequeiicies hoppecl ciiiring integration periods such that If,) =
nB\\' - +
= f l . . . . fn . - - . f-y. does not imply a monotonie secpience of freqiiencies and
3 ~ s e d to describe the amplitude aeigliting function of the laser illiiniination and truncation effects due to lenses or other elements in an optical systern.
(ri } = --\'/2. -( .Y/2) + 1. . . : SI2 in rancloni order. The rvicleband LPI correlation yielcls
Hence. for Ti >> T . where T is the A0 ce11 clelaj- aperture. Eq. (2.21) can be approsi-
niated as TB\\' --11=12m1rn2T; stn(-)
\-(Tl . Î ) z q c o s ( 2 ~ f o r ) L 9 - B C I ' - (3- + l).sirz(-)
rB \ lW r B LI' Sote that in the limiting casc. for S > > B1.l'. sin(-) z - ancl the freqiiency
hopper approaclies the linear FI1 ckirp case as Eq. (2.22) ceduces to
The nest section investigates the under1:-ing features of Ecp. (2.17) and (2.22) iising a
numerical simiilat ion approach.
2.4 Numerical Analysis for the Two Types of Inputs
The niodels of tlie LPI correlations rvi th the -40 processor tleveloped in the previous section
w r e implemented in the MAT LAB numerical simulation pachge and the resul t s coniparecl
to the approximations in Eqs. ( 2 . ) a n ( 2 . 2 ) Figure 2.5 shows the processor oiitput
simulations for \-arying S N 3 levels mith Gaussian noise. The most noticeable effect is the
scnsitivity of the processor in detccting a correlation ewn under severe noise conditions
( < -20 dB). -4s ivell. as predicted. the base of the correlation is broadened 1>y tlic additive
noise. Similar resiilts werc obtainecl with the freqiiency hopper case iising 300 hopper
frequencies in the signal ba~iclividt h. 2 : 2 :
Cc) Cd >
Figure 2.5: Soise loaciing on the correlation for i+arioiis S S R tdties: (a ) O dB (b ) -20 dB ( c ) -40 dB and (cl) -50 dB. Horizontal scale: lag position in riuniber of points: Xértical scale: arbitraq- units.
Consistent !vit h the t keoret ical predict ions. the envelope of t lie correlation was found to
be a jinc function tri th a duration of the niain lobe giwn by &. -4s well. the predicted
frecliiency of the spatially iar3-ing carrier on which the correlatiou is riding was in direct
agreement with the theory. Figure 2.6 shows the hehavior of the correlation as a fiinction
of the ratio of the chirp rate to the signal bandwiclth ( &= ).
Figure 2.6: Effect of Larying the chirp cliiration (Tc) on tlie correlation. ( a ) 10 paec. ( 1 1 ) 5 pscc. ( c ) 2.5 pet. ( d ) 1.5 psec. Horizontal scale: tirne ( p s e c ) : kértical scale: arbitrary
2.5 Space-Integrated Output of the Correlator
In this section. Ive consider the case where a beani splitter (BS) is inserted as as shoivn in
Fig. 2.7 follon-cd by a Fourier trausforni lens that integrates the spatial light clistribiition
and focuses it on a single PIS photodetector element. The goal of siicli a design is to pick
out tlie freqiiencies of the SIS signals with high speed. as selecting of the SIS signals froni
the CCD detectors is de1-d by the integration tirne Ti. This information is then used to
identify and excise tlie interferer energy from the LPI signal spectriini with near real-tinie
speed.
Our starting point. in applying this metlod. is the temporal aiid spatial light interisity
distribution at the photocletector plane giren by Eq. ( 2 . 5 ) Let us cousider. term by term.
the effect of the wide angle Fourier transform leas followed by spatial f rcc~uenc~ integration
Digital Sarnplirig Osci Ilosco pe
k Spectruni Analyzer
modules
Figure 2.7: S p c e integrating pin detector arrangement. -4 beam split ter (BS) is iised to channel part of the optical beam into a Fourier lem ( L 3 ) which focuses it ont0 a photodc- tector (PD) connected to a sampling oscilloscope for analysis.
the pin cletector.
The action of the Fourier lens is to integrate the temporal and spatiall- \ar>-iug intensity
profile I& ( t . r j gii-en in Eq. (2.5) leading to
n-here T = T/2 + x/c and with the asstimption that the lem dianieter is sufficiently large
relative to the optical heam widt h and hence the choice of limits. The transforni idet ( t . ci )
is centerecl at no. the spatial carrier frequency at the photodetector plane and spans an
fo+Bl'L interval 2ûd. where ad = - corresponds to the spatial cut-off frequency of LPI signals
a , ( t ) and . s 2 ( t ) n-ith bandwidth B. The Fourier transform of the aperture function of a
single element p hotodetec t or is modeled as [l-t]
and clo = l / h m is the Syquist sanipling interval. The photocurrent obtainccl bj- integrat-
ing the iutensity over the photodetector surface is proportional to
In this analusis. \se are going to assunie P(a) is uniform oïer the surface of the cletector
and with iinity magnitiicle so that
This then is oiir kernel function operating on al1 the terms in Eq. ( 2 . 5 ) . Siibstituring in
Eq. (2.26). ive get
with r = Tl2 + s / ~ * : hence for the 13' terni of Eq. (2 .5) . LI-e have"
where i t is assiimecl that the system's aperture function n ( r ) = 1. Invoking the sifting
theorem of delta fiinctions, we have
ive apply the same analysis to the remaining ternis to yield
n-here to th .s 1 ( t ) and s z ( t ) were assurned real.
" Where we have ignored the multiplicative constant 7.4 i.-lz/2.
-- 7-
out-of-band
I lé make the argiinient that the last terxn in Eq. (2.33) ~mishes . Since the detector is
centered nt n o = fo / r spanning an in t end of spatial freqiiencies 2nd. this last terni ivill
1~ out of band.
The overall temporal signal output from the detector is thus sunimarizrd as
1
58 iee ISE!
c2 >
I I 8.82 ' sa iee ise se iee 158
(3 1 (4) Figure 2.S: Simulation oiitput s for ternis ( 1 ) - ( A ) respect ively. Sote t hat because both the modulation clepth ( n z ) of the laser ancl that of the -40 cell ( r n z } are sniall ( n2 1. rnz < 1) for improved processor gain. both terms ( 2 ) and (4) ivill be negligible in the overall output.
lié can t hiis directly recover ail LPI frequencies incliiding t hose of the nt tendant SIS hy
connecting the output to a spectriirii analyzer. Eqrtation (2.36) was siniulatcd in 1I.XTL.AB
for each of the component terms as sho~n i in Fig. S.S.
Ternis ( 1) and (3 ) are sirnply double sidehancl .AM with one being a delayecl hy T/i?
relative to the other. The second term is nonlinear -411 while the last terni is analogous
to envelope detection of the prodiict sl ( t ) s 2 ( t - T / 2 ) . Because in general the modulation
tlept hs rn 1 . m < < 1. terms cont aining produc ts of t hese dept hs are thiis negligible relative
to term ( 3 ) . As a result. the overall output is a linearly chirped AS1 ivave riding on a
Figure '7.9: Overall sinidated oiitput of the Eq. (2.36 ) showing the li~iearly chirpetl signal.
hias as shown in Fig. 2.9. Heuce. ive can recover the freqitency content of the ititercepted
signals si ( t ) ancl sz(t). bj- Fourier transforrning Ecl (2.36). This result is esplorecl furrher
in the nest chapter.
2.6 Effect of Noise on the Intensity and Correlation
Funct ions
Consider the schematic shoim in Fig. 2.1. the iritensity of a noiseless laser diode is
where .Ai is the DC bias amplitude. m l is the modulation depth. .sl ( t ) is the bandpass
signal of interest. and do is the modulation carrier frequency. \Ve can espancl this eqiiation
as
and ru-Al = .4,, is the magnitude of .si ( t ) . In the presence of laser intensity noise n r D ( t ) .
insteacl of the Eq. (2.3s). ive haïe tkat for the intensity Id( t ) of the nais>- laser diode.
In the presence of both laser intensity noise and the signal .-voltage-- noise .\;, n 1 ( t ).
where .Ys, is the magnitude (assuinecl real) and where the noise signal has been representecl
as a bandpass signal n L D ( t ) : is the tinie-averaged quantum AM noise intensity for a directly
modulated semiconductor laser. LVe will rcstrict ourselves to ALI noise as it directly affects
the shape of the correlation envelope. However. any directty modtilatecl laser cliode will
exkibit both AM and FhI noise characteristics [30]. [31]. The FM noise will impact the
sampling requirements of the CCD array and the stabiliry of the correlation in the detection
plane as it affects the spatial carrier frecpency on which the correlation is riding. LI-e will
assume that this effect is negligible since the spatially \ar>-ing carrier does not pl- a
role in the analysis that folloi~s. Denoting by S L D ( t ) = ~ ~ ~ ( t ) / - 4 ~ . -Y3, /-A,, = .\Tl and
m l = .4,,/--Li. ive can then w i t e as
Ecliiation (2.11 ) is the expression to be iised for a noisy laser cliode intensity. Coinparing
E c p (2.373 ancl (2.41) we have
where I d ( t . -ho. n ) is the noisy part of IA(t) dependent on the laser intensity uoise .j-LD ( t ).
ancl the signal noise n l ( t ) . né aclopt the same approach to cleriïe the noisy ecl~iivalcnt of
the -40 ce11 transmit t ance funct ion.
The noiseless -40 ce11 transmit tance. tmlo of the -ve diffraction order . IL-hen the O l h
order diffraction light is ornitted is gii-en bj-
where r = T/9 + s/r. A; is the electronic reference frequency. is the center frecpency
of . s 2 ( t ) such that do = - 4; and rn2 is the ratio of the signal magnitude .A,, to the
reference freqiiency oscillator magnit iicle fi. Eqoation (2.43) can be writ ten as
-\oltage" noise .\;, n 2 ( t ) is real. ive can mite the noisy -40 transmit tance
that the signal
t;,(t - r ) as
n-here ive have neglectecl the reference oscillator noise. Equation (2.45 ) can be re-wri t t en
as
-4:- .-L" .y:., ',Y2-, and where nt- = = x. -11, = - = - .a:* .4a2
The effective noisy transniitrance of the A0 ce11 can be m i t ten as
The noisy intensity IA,(t. r ) . iniagecl onto the CCD is thns given by
Combiriing Ecls. (3.41). (2.48) and ('7.49). ive Lave
1" order noise temi
+ &(t )TEj f (n2) + Id(t.-l'~~.rri)Rf{t.40(f - ~ ) f ; ~ ( f - T - h ) } }
v
3rd order noise term
therefore. Eq. (2.50) can be espressed as
a n )
For our purposes. we are going to assume that the noisy intensity is sufficiently accuratel-
descril~ed 11y the first order approximation. narnely that
Cpon detector integration. we haw
where R( r ) is the correlation function of the noiseless signals.
2.7 Output SNR and Processing Gain in the Presence
of Laser Noise
-4s pointeci out earlier in this chapter. the first noise analysis of the time-integrating A 0
correlator was clone by Iïellman [XI. In this thesis. ive generalize these results to accourit
for contributions froni the laser intensitl- niodtilation noise.
For two comples signals s , ( t ) and .s?(f). the cross-correlation function is defined as
where E { - } represents an ensemble average. The tirne-integrating est iniate ( clenotetl liere
by R ) of the function is
ivhere Ti is tlie integration tirne. Uiith reference to Fig. 2.10. the output STR for tlie
correlator is then definecl as
Again. with reference to Fig. 2.10. the input S'YR's. S.VRI and S.VRr corresponding
39
Figure 2.10: Tinie int egrat ing .-\O intercep t receiver. -4tlapted from [5] .
ro signals si ( t ) and s r ( t ) respect il-ely. are defined at the peak of the correlation as
where RI (0 ) and Rz(0) are input noise powers [A] and R,(O) is the input power of the
signals
s i ( t ) = s ( t - ta) + r l ~ ( t - ta)
40
and
wherc for ivhi te Gaiissian noise R 1 ( t - f ) = n 1 ( f ) .
If B is the signal bandxidths ancl S.VRi < < 1. S-YRz < < 1. with the assuniption of
zero mean .\\I'GS in Eq. (2.56). it can be shoim that [-61. [29] if the peak of t ke correlation
occurs a t t = tu. we have
This allows us to define the processing gain Gp as
Thus for B = 50 l IHz and T, = 0.2 nis. the processing gain can be at niost 40 dB. If the
objective. for esaniple. is to actiicl-e S.\-Rn = 1 ( O dB) . i r e rnay choose to process to signals
each ivith S.YR = S S R i = S.\;R2 = -20 dB. or tivo signals. one with S'.\-RI = -30 dB
and the otker n-ith S.l-RZ = - 10 dB. This is an important conclusion tkat is of reh-ancc
to the practical use of the receiwr. Rewriting Eqs. (2.59) and (2.60) with ta = T/2 . ive
i~liere s{ ( f ) is the noisy signal modiilating the laser. clelayecl by half the active A0 ce11
aperture T to ensure that the correlation is centered in the niiddle of the outpiit plane.
i d d e s!,( t ) clrives the A0 ce11 transclucer. The t ~ o sigrials cliffer only in their respective
adcli tive noise components.
The action of the CCD tletectors is to integrate the intemit' in Eq. (2.52) leacling to
Terms containing factors of cos(2;; fot J and cos(4;; for) are bantlpass ternis that intrgrate
to zero for integration tinie T, > > l/fu ancl have thiis heen neglectecl in Eq. (2.66). Soi\-.
terrn ( 1) contains a DC hias proportional to Ti. ancl a baselxmcl terni r u : 1 s;(t - r ) 1'. thnt
iutegrate to a VBT for large T,. while term ('7) contains the required correlation fuiiction.
Terxns ( 3 ) ancl (1) are the laser noise component and intermodulation proclucts respcctively.
The last term is noise power interna1 to the .-\O ce11 arising froni thc interaction of the
acoustic heam ivith the optical intensity [SI.
Applying Eq. (2.56) to the RHS of Eq. (4.66). it follows that
.1 .4?nii ni-, 3 ' 1 ' 2 S-YR3 = , Y 1 ~ { k , & } l 2 (2.61)
=Iqîn1 n l - y { ~ 1 R,,., ( T ) l 2 - 1 E{R, , y , ( . i ) } 12) + O; + O: + U; + O;-@ - 2
where the \-ariance of the correlation estimate r n r { ~ , , , , ( r ) } = E 1 R , , , , ( T ) 1" 1 -41 A2n1: E { R ~ , , ~ ( T ) } 1'. 0; =</ r l y E { - i i D ( f ) } j Z > and a: =<I r l ~ E{- l -LD( t ) 1 . s i ( t - Ï ) l2
} 1 2 > : R,, ,? ( 7 ) is the tirne average of the product . s ; ( t ) . s l , ( t - 7)' with < - > clenoting
time-averaging by the cletector array. Fiirtliermore. 02 is the niean of 1 I 1'. the electrical
noise voltage. times the number of cletector elements per correlation wiclt h wi-hile o& is cliie
to the niiiltifreqtiency diffraction component noise pan-er and the nonlinear acoiistic
component noise power .\É(s) as disc~ssed in (51.
Son-. with the assumption that n , ( t ) and n z ( t ) are zero niean independent 115th white
Ganssian statistics. Ise have that at the peak of the correlation function
Similarl~: the variance of the correlation peak estirnate is
n-here it is assumed that the integrartion time T, > > 1/ B and u-here the effective noise
N o ) banclwiclt h is definecl as B = = JXX S ( j ) d f '>s'(O) : S( f ) is the noise pon-cr spectnirn [32].
- -G
Iiellman [36] o b s e r t d that the first term in Eq. (2.69) refers to the error in the correlation
esti~riation clue to finite integratiou while the last term is the error due to the additive
Gaussian noise terms n ( t ) and n 2 ( f ). For the correlator sholvn in Fig. 2.10. B a 12
where Blo is the acousto-optic 1)andwidth clefined in Fig. 2.3.
To include the laser iritensity noise. consider first t he noise cross term with mriance 4 in Eq. (2.6;). If -Y and 1- are an- ranclom variables. real or comples. n-e have the follov-ing
ineqiiali ty [33]
1 E { - Y I - } 1'4 E 1 -Y l 2 E 1 1- 1' (2.70)
Hence. rve set the iipper liniit on the fourth term as
since E { s 4 ( t ) } = 30.' = 3E2{ .5 ' ( t ) } = 3Ri(O) O for S-YRL << 1 and S.YR2 << 1. the
latter being a typical case in an intercept receit-er requiring an increase in the processing
gain of the signais.' i i . \ é can thus neglect the cross noise power contribution of terni ( 4 ) in
Eq. (2.67) for low SSR cases.
Furtherniore. for term (3 ) . a3 = < 1 qy E {-Go ( t ) } 1 2 > can be nornializecl with respect
to the correlation signal power of term ( 2 ) resulting in
?.-\ssurning Ciaussian noise statistics.
wliich ive recognize bu definition. as the relative irrtemitp noise ( R I S ) for a laser cliocle [30].
11-e assume that riiode partition noise is negligil~le and that al1 lasirig modes are eqiially
tletcctable ivitk none of the emitted light reflected back into the laser. n l e n niode partition
noise is prescrit. each lasing mode generates a photon nuniber S, witk its respective R I S
refereucecl to the control mode So as
ivliicli is siniply an additive component to ECL (2.72). llethocls for rneasuring the R I S for
clirectl?- rnodiilated laser diodes have been dernonstratecl by a nitniber of researchers [3l]. [34].
R I 5 values are often providecl by laser diode manufacttirers and are generally specifiecl as
a fiinction of system bandt~-idth. ivhich in oitr case is B.
Conihining al1 the results. the output SSR. after integration. is thiis gi\-en hy
where 3 = 20 BT* wit h ci the nuniber of detector elements per correlation ivitlt h and where
parameter X represents the nornialized error due to finite integration and is giwn by [26]
witL typical values in the range O 5 X < 1. In deriving Eq. (2.75). it is iinderstood that
the signal bandwidth B is eclual to the noise banclmidth throughout the system.
i\é identifj- three specific cases for analysis here: ( a ) With our original assuniption of
moderately low STR intercep t signals (S.VRi. ST Rr < < 1 ) . ive have the further approsi-
mat ion that
The dynamic range (DR) of the processor. definecl as the ratio of the peak correlation
output to RAIS noise. is given bl-
trkere 1.; = r , ~ . - I ~ . - L ~ r n m.,/?. is the peak voltage of the correlation signal. The processing
gain of the processor. for these sniall input SSR's. can thils be summarized as
wliich is ec~iiivaleut to the simple case of a noiseless laser source with the adclitional as-
sumption of a noiseless acoiistic and optical \va\-e interaction in the A0 cell. Hence. the
1011- SSR condit iou tends to de-ernphasize t ke effect of laser intensi ty niotlulation noise
leacling to the faniiliar forni @\-en I>y B a d a et al. [PJ]. This ecluatioli sets the uppcr botincl
on the processing gain of the recei\-er as dictatecl by r he finite lalue of the DR. Horvel-er.
the overall DR and processing gain of the receiver are further restricted bu the saturation
voltage of the detectors. A high attendant L-BT tends to saturate the detectors resirlting in
a reduced gain. For esample. we sliowed in Eq. (2.63 ) t hat for B = 50 MHz. Tt = 205 p rris.
and DR = 500 and with the assumption of 10 detectors per the length of the correlation.
the resultant processing gain has a limiting value of about 40 dB. This limit is a ftmction
of the hanclwidth of the signals (B ) and the integration time (Ti). hoth of which can be
mrietl. In practice. the CCD array imposes the ultimate ceiling on the processing gain of
the receiver due its own DR limitations. clefined as the ratio of the saturation 1-oltage of
the array to the detector peak-to-peak noise (b>;LT/\'b-P ). The CCD array usecl in this
work had a liniiting DR = 2600. ancl theoreticallu. GS dB of processing gain \vas achielxble
n-i t h t his receit-er.
This gain ma!- not be sufficient for \+ery low signals in a high noise environnient and is
further reduced by other interfering signal contributions in the bandn-iclth that tend to acld
to the bias of the output. These aclclitional contribiitions inclticle .\O ce11 intermoclulation
prodiicts as well as laser niodulation artifacts as in the general case 11-ith R I .Y # 0.
( b ) For a noiseless refercnce case (S-V R2 + x ). as in in a search ancl itlentify receircr.
In such a scenario. the intensity mocliilation noise of the laser conies into play. Both the
interisi ty niodiila tion noise and the fini te integration paraniet er X iriversely affect the 01-erall
processing gain. -4 plot of the output S.1-R3 versiis the intercepted signal poiwr is given
in Fig. 2.11.
-4s the input S.VRl increases. the output SSR.3 increases asyniptotically to its linii t ing
value approximated by 1 / ( A + R1.Y). Howewr. for very large input SSR \dhliies. the effect
of the laser intensity noise becomes niore dominant as terni (4) in Eq. (2.66) is no longer
negligible. This gives rise to the nest case.
( c ) For S S R i . S:VR2 >> 1. Ecb (2.71) no longer ~xnishes and so we may espress the
1.99 la al 3a 40 !5a M m
S ( R 1
Figure 2.11: For the case when S-\-R2 -+ x. The output SXR is asymptotically I~ounclecl by 1 / ( A + RI.)-) n-here tj-pical values usecl in the siniiilation were DR=5OO. n = 10 tletec- tors/correlation width. T, = 205ps. B=5O MHz. R I T = je-"/B and X is e\-alii.îtecl from Eq. ('2.75).
output SSR as
for sufficient ly large signal- to-noise ratios. i t is reasonable to approsiniate t ka t % ( O ) 5
SSR: where S-YR: = R:(O)/S:(O) and from Eq. ('2.2). ive set the upper boiind on
acliie~-ahle output SSR in this case as
where we have incorporateci the additional assurnption t bat the two autennas are located
in a statistically similar noise environment such that S-\'Ri % S S R 2 . The laser iritensity
niodulation noise becomes a significant limitation on the processing gain of the system.
From Eq. ( 2-81 ). we see t hat t Le laser intensity noise is aniplified by a factor corrcsponding
to the SSR. The higher the SXR, the more the influence of the intensity nioclulation noise
Figure 2.12: Output S3'R for S.l'Ri. S S R 2 >> 1
is reflected in the output throiigli a rechction in the processing gain. Figure 2.12 shows
the degradation in the processing gain as the input SXR is increased.
Returning to the low input signal-to-noise ratio case in ( a ) given in Ecl. ('2.7s). we can
proceed to iclentif>- three suh-cases similar ro Ristic and Lee's analysis in [j]. For very
videb band and short A0 t ime aperture. the noise power cout ribut ion froni t lie nonliuear
acoustic cornponent .VE(r) is negligihle resultirig in a larger processing gain.
Similarlc for long time apertures and wide bandwiclt h. the niultifrequency diffraction
component is sniall relative to .\É(.r ) and can tlitis be ueglected in Eq. (2.73) leading
to irnproved processing gain performance due to a reduction in the overall hias. Since
.YD is approsimately equal to the poiver of the cliffracted beam (-1'~ zz I';l. wtiere Id is
the intensity of the diffracted light beam with cross-section area -4). it is evident that a
strong .\O ce11 modulating signal will inadvertently reduce the overall processing gain of
the receiver. Tlius. the dynamic range limitation is aggra\-ated bu the presence of these
noise terms which add to the signal dependent bias term of the correlation output. Hence.
the overall processing gain can be increased significantly by ~ising cletectors with higher
saturation values and relatively loir SSR intercept signals.
Chapter 3
Experimental Investigation
In general. a correlator serves two piirposes: ( a ) ctetection of the presence of a signal ancl ( b )
spectrtim analysis of the cletected signal. Each of these tivo applications usually reqiiires
a difÏerent architecture [l-l]. [?Il. [Z!. [?-LI. The objective of this thesis. as esplained in
Chapter 1. \vas the detection of the presence of a signal.
In carrying out the esperimental investigation. two -40 deflectors were tisecl. The first .
nianufact iireti b!- SEOS. was used because i t was iriimediately aiailable in the laboratory.
It had a handu-idth = 40 M H z centerert at feqo = SO .\IH- n-ith a delay tinie
of T = 10 pa. The resiilting in-line A0 design. clisctissed in Cliapter 2. and shorr-n in
Fig. 3.1. protluced a correlator witli signal bandrvidth B = 20 .\IH= and integration tinie
of Ti 0.2 ms.
ii.\'ith reference to Fig. 2.3. the system freqitencies were: fu = 30 -11 H z . f = 90 JIHi
and f, = 60 J I H - . This correlator mil1 be referreci to as the 20 JIHi signal baridwiclth
processor. -4s shoivn in Insets A. B and E. the tivo input signals s, (t)cos(2a fot) and
s2(t)cos(2~ fot ) mere used to simulate pulsed C W radar signals in the subsequent esperi-
DC Bias CoILiniat
Seri t ral Densitv Filter
k
CSSB 4) Slodulator
cos(2r foi) cos (2 nfct )
Figure 3.1: Reference tone .IO processor for radar signal processing. Simiilated radar signals si ( t ) cos(2;i f,t ) and sz ( t ) cos (2r f0 t ) are introditced to the processor as shown. CSSB is an upper single sideband modulator that is used to translate the input signal to f, + fo. and to remove signal bandividth redundancy by passing only the iipper band as shown in Inset C. B = 20 M H z is the signal bandividth. and = 40 M H z is the bandwiclrli of the - A 0 cell.
mental work carriecl out in t bis section.
In the arcliitectiire shown in Fig. 3.1. the focal length of hoth lenses L 1 and L2 !vas
3s. 10 nini providing for an overall magnification of F2/ Fi = 1. The effective Lmgt h of the
A0 ce11 was 6 nim. hence the niinimum reclitirccl CCD array length to niatch this aperture
Iras F2 x 6 rnm/FI. The CCD arr- used in this esperinient hacl 20-1s pixels each of
dinielision 13 ltnl x 13 /<ni a d a reatlout rate of 10 .\IHz. This translates into a total
length of 13pni x 20% 2 26.6 niiii IL-hich is weil above the niinimum reqiiired to meet the
SJ-quist smpling constraint .
3.1 Detection of Signals at the Spatially Integrated
Output
At this point it ivas instructif-e ro look at another wa?. of detecting the signals that cloes
not in\-olve CCD arrays. In this approach. a beani splitter \vas placecl nt plane P? as shoivu
in Fig. 2.7. The beam propagating downwarcls was focussed on a large arca photocietector
by a ivide angle Fourier transforni lem. Tlie oiitput of the detector !vas fecl into a digital
sampling oscilloscope for analysis. -4 mathemat ical de r in t ion of t ke out put of the p h -
todetector in siich an arrangement was given Section 2.5 . Here 11-e \vil1 coucentrate on the
esperirriental mlidation of this resiilt. Figures 3.2 (a) and (b ) illustrate the same signal
detected by (a ) a CCD arra!.. after tinie-integrat ion. and follo~vecl bu coherent detection
which results in the envelope of the correlation and ( b ) a single photodetector. after spatial
integration. that is connected to digital sampling oscilloscope.
This technique niakes fast identification of high power interferers possible by removing
the waiting period associated with the CCD integration time T, zz 0.2 nis. Tkese narroiv
Figure 3.2: ( a ) .A correlation peak envelope clctected by the CCD array. ( b ) tlie sanie signal with a tinie varj.ing carrier detected at the spatially integrated outpiit .
band interference signais. taken from the spat ially integratetl out put. are Fourier t ranc
fornied. tlieir frequencies identified. and a cornniancl issiied to a bank of cligirally tiinable
notch filters to escise tkeir respective enegies. Details of this SIS notctiing tecli~iic~iie are
given in Sections 3.11 and 3.12 of this thesis.
3.2 CCD Scaling Law
Consider a sample output of a typical correlation of tivo pulses each of cliiration t'. The
total time duration of the correlation triangle iri the tletector plane is W . Howewr. if we
plot the correlation as a function of r. its cliiration .cf ~vill be clilated by a factor of r : tlie
velocity of the acoustic wave in the A 0 cell. As well. other factors can contribute to the
change in spatial dimension of the correlation: na~riely the niagnification of the irnaging
optics. eqiial to one in oiir case. and proper alignment of the ce11 aperture to the CCD
cletector array. This spatial correlation is sampled by the CCD pisels at a rend-out rate
of 10 -11 H z . LVith the correlation width of x'. the number of pixels to (.ol-er this ividth is
2' - 4 - where O is the length of each pixel in the a r r . The resiilting ividth of the correlation
z' in the time domain (as viewed on the oscilloscope) d l thiis he given hj- t" = l , o I H z 1 6 .
Since the CCD pixel dimension \vas 13 prn x 13 prn it follows thar t" = &. The original
tinie correlation rvas rnapped into the spatial domain t hrough 2t' = 5. hence. the observer1
correlation 11-iclt h tu is related to the original tirne correlation hy
Therefore. the ohserved correlat ion d l have i ts base dilat ed by a factor of = 5 relative
to the original [%]. [36].
3.3 Correlation of Narrowband Signals in White Gaus-
sian Noise
The output of the processor for the simulated narrom band pulse radar signals is sholvn
in Fig. 3.3. The farniliar triangular shape of the waveform is consistent with the elcpected
shape of correlating tivo square pulses. The base of the maleform should be twice the size
of the pulse duration. However. due to imaging considerations and rhe nature of the spatial
correlation when CCD detection is used. it appears dilared as explained in the previous
section.
The simulaied radar pulse used had a pulse duration r = 1.2 ps and a pulse repetition
Figure 3.3: Correlator output for r = 1.2 ps. PRF = 0.1 -1lHz. The optical center rvas establishect ancl maintainecl at the 22 11s time location for al1 siibsecluent esperinients in tbis section.
frequency (PRF = 0.1 -11 H z ) . Since the A0 ce11 transit tirne T eqiials the pulse repetition
periocl. only one correlation can fit into the active ce11 aperture during each PRF cycle as
shown in Fig. 3.3.
In Fig. 3.4. the PRF iras increased to 1 M H z while keeping the pulse duration at
1.2 p s . In this case. ive have a number of correlation peaks fit ting witliin the 10 p s -40 ce11
apertiire rvinclow since the period of the sirnuiated radar signal is now 1 p. Theoretically.
tve should be abie to fit about ,.,s+ , z 4 correlation peaks. Sote the roll off in the P H F
peak amplitude away from the center of the .\O cell. This ma!. be attributcd to a drop
in the cell' s diffraction efficiency close to its eclges reducing the power of the correlation
peaks at t hese locations.
To e d u a t e the processor' s performance in presence of noise. r~liite Gaussian noise ivas
added to both signals being correlated. Fig. 3.5 shows the processor output for varying
SSR values.
Figure 3.4: hliiltiple Correlation for PRF = 1 -1IHz.
The first noticeable effect. as the noise was introduced. was the hroatlening of the corre-
lat ion base. This broadening was inversely proportional to the SSR. This effec t iras due to
the fact that the noise was not time-limitecl to the pulse duration Ï of either sl ( t ) or h ( t )
and hence the correlation of the composite signal vanished outside of tirne period 27. In
addition. the noise acted as a DC bias on the output. progressively pushing the correlation
peak into the saturation region of the CCD array as shown in Fig. 3.5(tl) [35].[36].
Cc)
Figure 3.5: In al1 cases the PRF = SO I iHz . 0.5V/DIV and tirne base of 20 p s / D I I - (a)
S-VR = 20 (b ) S-YR = 6.4 ( c ) S.\-R = 0.7 (d ) S-VR = 0.4 The pectiliar shapes are due the noise component as i t drives the correlation envelope into the saturation regions of the CCD array.
3.4 Opt ical Misalignment Estimation
Csing the resiilts of the previous sections ancl a white Gatissian noise source. a procediire
was devisecl to estimate the overall optical misalignment in the processor. Because white
noise contaius all freqiiencies in eqiial proportion. it is a convenient signal for systern
rneasiirement s since i t covers any chosen signal bandwiclt h full>-.
Suppose that the signals s l ( t ) and sG(t - T ) are replaced by a white Gaiissian noise
sarnple function n ( t ) and its delayed version n R ( t - r ). The tirneaverage correlation integral
in Eq. (9.10) can be ivritten as
1 " n ( t ) n œ ( t - r ) d t = - Ti 1% 1 -Y( f. T,) l 2 &TfTi ( I f
where a truncatecl sample segment of the noise process n ( t ) . clefined over the integration
range O 5 t 5 Ti with short-time Fourier transform .Y( f. Ti ) given by
If this white noise process is then passed though a band-pass filter of center frecioency k
ancl qualit- factor Q. the spectral density Ss. for Q > > 1. is given by [32]
*Y, / 2 l + _ i Q 2 ( f - I C ) ~ / / ?
for f > O S d f ) = .y, / 2
~ + ~ Q 2 ( f + f c ) ' / f ~ ot herwise
and .\o/2 is the peak power spectral clensity.
The time averaged correlation is thus given by
where 3-' {. } clenotes the inverse Fourier transform operator. Subst ituting the correlation
function given by Eq. (3.5) in Eq. (2.9) yields
n-here it is understood that the CCD discards the carrier information and hence R , ( Ï )
represents the envelope of the oittput plus bias.
A ivicleband white Gaussian noise generator was used to protide the input signals.
.A pair of banclpass filters ivith center freqiienc- equal to the clifference frequency fo =
30 M H z and bandwidth B = 50 I ï H z for a Q = fo /B = 600. provided inputs shown
in Inset .A and B of Fig. 3.1. Such a high Q-factor was chosen in order to 'sharpen' the
correlation response peak and provide a niore accurate measurement of the misalignnient
.Yo / 2 error. Furt hermore. for an arbitrary Q-factor. Say( f ) = [ f c l l 1 2 and its inverse
Fourier transform ( R';(r) = F1 {Sn( f ) } ) cannot be solved in closed form ivit hout a large
Q assumption as in Eq. (3.5). This is an important consideration because the methoci
proposed here requires the existence of a closed form espression for R X ( r ) which is then
used to fit the experimental data and subsequently estimate the alignment error.
The resul ting noise- only correlation data. after bias r e m o d , ivas then fit ted niimer-
ically with the correlation mode1 given in Eq. (3.6) iising a least squares fit ivitli Gauss-
Sewton optimization of the cost function. The residtials of the fit ting function w r e then
used to calculate the \ariance and confidence in tends of the fit. This error ivas partly
at tributecl to the optical misalignrnent in the system which introciuced clistortions in the
correlation envelope and was estimated by ~napping it to the spatial domain using the CCD
scaling latv given in Eq. (3 .1) .
Howeïer. additional factors. predominantly CCD t rapezoicial spatial responsc effects.
system aperture function and detector nonlinearities. ais0 play a part in the size of this
error. The apertiire funcrion component is intrinsically tied to the overall processor mis-
alignment problem and hence is assumed to be accounterl for in the estimated displacement.
CCD trapezoidal spatial response effects d l introduce errors in estimating the location
of the correlation peak. This error mas Iumpecl together with other anomalies by fitting
the data of a 'perfectly' aligned system. The resulting fitting error was then assurnecl to
inclilde the spatial response effects and becornes the limiting kalue of the accurac- of this
approach. More on this later.
For situations where the operating range of the processor includes the non-linear regions
of the CCD response cun-e. the output data m u t first be compensated prior to the fit ting.
If R ( r ) represents the correlation of signals sl ( t ) and s2(t). the CCD detector response
is then giveu by g [ R ( r ) ] . where g[ - ] is the detector nonlinearity [37]. This amounts to a
dynamic range compression of R ( r ) . In theory. if the nonlinearity is known and nionotonic
then we ma' find its inverse g-l [el' and the inverse can then be used to recover R( r ). CCD
dynamic transfer plots are usually provided by the manufacturers and the inverse g-l[-]
can readily be obtained from them to linearize the output.' Once the non-liuearity has
'Sote that in niost cases. this step is unnecessary as the CCD array is normally operated in its linear range thus avoiding over-drive and sat utation.
been removecl. the correlation data is then fitted with the second term of Eq. (3.6) as
shown in Fig. 3.6.
The error in estiniating the displacement between the data and the fit dong the r -
asis was used to calculate the overall misalignment by mapping. using Eq. (3 .1) . its tinie
domain represent ation. as sampled by the oscilloscope. to i ts corresponding spatial clornain
image while also compensating for the overall dimensional dilation relative to the original.
In the esperinient. the laser-beani optical asis n-as ixried with respect to the .r'-asis
of the CCD plane Pl shown in Fig. 3.1. The amount of misalignment so introduced n-as
foiind to be approsimately equai to that from the fit estimates. This then beconies an
independent check on the accuracy of the method. The correlation data dong with the
corresponding fits for mrying degrees of misalignments relative to the optical asis is shown
in Fig. 3.6. The various estimates of the misalignment errors. for ~xrying laser-beam offsets
from an established optical center. ranged from 0.05 nim to 1.2 min.
In theorc the accuracy of this method is boundetl b). tLc degree of confidence in the
fit ting algorithm usecl and bl- the size of the pixels in the CCD array which determines the
spatial resoliition. The array used in this work consisted of 13 /lm length pisels. Hence.
we cannot resolve a rnisalignment less than this magnitude. The trapezoiclal aperture
response of the array sets this limitation. Figure 3.6(a) was usecl to estimate the acciiracy
of this method. In this case. the residual error was obtainecl by fitting the data for the hest
possible alignment of the laser beam. Hence. 50 prn is the best accuracy of the alignment
error that can be obtained mit h this particular esperi~nental setup. -4s such. this beconies
the uncertainty associated will al1 subsequent rneasurernents.
Figure 3.6: Fit of the noise only correlation data (represented b?- t x x x 1 . ) the secoud term of Eq. (3.6). The estimatecl alignmerit error \\-as: ( a ) 0.05 mm ( h ) 0.3 k 0.05 mm ( c )
1.0 f 0.05 mni (d ) 1.2 k 0.05 mm. Horizonral asis: lag position in seconds. ièrtical scale: arbitrary.
3.5 The 50 MHz Signal Bandwidth A 0 Processor
In practice. the minimuni instantaneous buidwiclth that is acceptable in radar signal pro-
cessing is B = 0.5 GHz. Radar signals of interest are usually in the frecluency range
from 0.5 to 26.5 GHz. Tuners that c m translate any banchidth B 5 0.5 G H z in this
frequency range to an IF output of 0.75 to 1-25 GHz have recently become amilable.'
In terms of the ;\O ce11 of the in-line architecture. the reciuired ;\O bandwidth m u t be
3 2B = 1 GHz as discussed in Chapter 2. Furthermore. in order to al-oid two-tone
interniodulat ion prodiicts ( IMPs) . the center frecpency fOo of the ;\O ce11 must sat isfy
fOo 2 l.jB,io = 1.5 G H z .
The design of the multiplicative radar signal optical processor also requires. in orcler to
al-oid spectral overlapping in the detector plane. that the clifference frequency f, 2 1.5 B =
0.75 GHz. If me choose to place the reference tone frequency at j:*. as sho~vu in Fig. 2.3.
then we have that f, = Po = 1 GHz. Before being applied to the A0 cell. the signal
bandwidtli B is upshifted to the center frecluelicy f r F = f, + fo = 1.7s GHz in orcler for the
signal spectrum to be situated between f; = 1.5 GHz anci f: = fto = 2 GHz. Thus the
upper cut-off frecpency of the upshifted signal fi coincides. nsing the solution in Fig. 2.3.
n-ith the upper cut-off frequency of the .-\O cell. To sumrnarize. the characteristics of the
A0 ce11 that are required for the prototype construction of this processor. are:
-10 bandwidth: 1 GHz
A 0 center frequency: 1.5 GHz
Present A0 technology allows dwdl time for suck an XO ce11 of about T = 0.4 p. This
results in time-bandnidth product of TB-4o = 400 that is sufficiently high for envelope
' For instance, LVatkins-Johnson 1V.J-TX-170 tuner, or Condor T3-6 18.
signal processing in the detector plane.3
The real life mode1 just described in the prececling paragraphs. iras freqiiency scaled
clown 10 times in order ro arrive at design characteristics of a custom tlesigned A 0 deflector.
nanielu
-10 bandwidt h: 0.1 GHz
A0 center frequency: 0.15 GHz
The Brimrose Company was cont acted to procluce t his cus tom -40 deflector designatecl
as TED- 150-100. wit h drive RF power amplifier designatecl as Pal- 150-100-2-2211- O t hcr
relelant design parameters of the deflector were the transit time T = 5 { r s . optical aperture
0.75 ni m x 21 n2 rn ancl an acoustic \.elocity of I* = 4200 m/s . The system freqitencies were
fo = 75 M H z . f, = 100 .\IHz ancl f r F = 175 M H z . This 30 J I H z signal bancln-idth
processor was then used in the LPI esperiments that follow.
3.6 Methods for NIS Detection and Removal
.in important consideration in the LPI signal cletection problem is the rejection of high
power SIS. The 371s autocorrelates and dominates the compressed LPI radar pulse wave-
form at the detector plane. This is illustratecl in Fig. 3.7. shotving the effect of an attendant
SIS on the correlation. In (a ) . the SIS is locatecl outside the LPI banclrvidth leatling to a
correlation peak that dominates the clesired signal. The case of an in-band SIS is shown ii i
Fig. 3.7(b). In this case. the desirecl correlation envelope is distortecl by the autocorrelation
of the XIS energy. In a typical intercept radar receiver situation. the high TIS p o w r can
Tp to 1 p s is available using acoustic longitudinal niodc. Ho~vever. severe attcniiatian at CiHz fre- quencies lirnits the usable tinie delay t o about 0.5 p.
lead to fdse cletection by owrpotvering the desired correlation signal. Shus. the r e m o ~ d of
the SIS before processing the wicleband LPI radar signal is of critical importance [37]. (381.
- . .. #
. . l . , , . , , . - . . . . , . . . . . ; - . j.. ..; . ; . . . j . . . ' . . . . a . .
.: . .,-. * : r
't
...
Figure 3.7: Oscilloscope pictures of (a) XIS outside and abo1.e the LPI correlation ivaveforrn and ( b ) inside the LPI corrclation envelope. Oscilloscope set tings: SOOmVJDIV. 5Olis/DI\-.
Two methods were used for detection of the SIS in this thesis. One methocl used
a feedback loop originating. after integration. at the post-detector circuit. as shotvn in
Fig. 3.S. This methocl is slow and t ~ a s first described in [39].
More recently. a real-tirne feedback scheme was proposed and demonstrated by Ward
and Vanderlugt [3S]. In this methocl. an optical Fourier transformer is iised to detect the
frequencies of the narrowhand interferers. The energy of the interferer is then no tchecl in a
feedback arrangement using a spatial light modulator (SLII). The methocl has a relatively
slow response time of about 5 m s due to the CCD readout rate and the speed of the
post -processing elec troriics.
In this thesis. ive use a feeclhack loop frorn the spatially integrated output of the pro-
cessors described in Section 2.5. followed by an electronic Fourier transformer to itlentify
XIS frequencies. The resulting feedback notcking scheme promises to be fast ( << 100 p.<
response tirne)" and robiist. This method is one of the original contributions of this thesis.
A schematic block diagram of the processor in ternis of its op t ical anci electronic modules
is shon-n in Fig. 3.S. The major suhcomponents of the layout in Fie. 3.8. designecl and
assembled. in t his work were: ( a ) spread spect riim LPI generat ion circiii t ry ( b) correlat ion
cletec-tion and cligitizing mocliile (c) XIS cletection ancl excision subsysteni (c i ) laser and
colliniation optics and (e ) imaging optics. Item (cl) is cliscussecl in -4ppendis A. while the
ïes t are presented in the sections that follow. These modules are further ill~istrated in the
photographs given Chapter 4.
Furthermore. two types of signals were used to siniulate the LPI signal: ( a ) the lintar
FlI chirp and ( b ) the freqiiency hop signal.
" W t h a custom designed chip for FFT operations and SIS identification.
RS-232 CO JI Jl Cornputer GPIB interface (IE'EE -188) c Control
t rigger
TEK.506
VCO
SIS escision filter barik
sptitter l I\
pu Ise generator
DC bias .\O ceIl L 1
Laser
Seutral Density Filter
i(
dela? line
diode
Collimat optics T
C'CD array
band pass cont rol Bri tnrose
P.\- 1.50- 100-22 IO
generator splittcr filter spli tter \C'JH'>
l A to oscilloscope
digi tizer
TIi:I!lO.-\ D t
Figure 3.8: Ovcrall optic and electronic hardware layoiit of an acous to-optic processor tor LPI detection ancl classification. L1 and L2 are part of the iniaging optics discussed in -4ppendix A.
3.7 Simulation of the LPI Signal
3.7.1 Linear FM Chirp
In general. a linear FM chirp signal can be characterizecL by
wkere a is the chirp rate in H z / s e c and Tc is the ckirp ditration. The instantaneoiis
frequency f, within the chirp hancln-idth is given hy
B This instautaiiecus freqiiency stveeps over the signal banclwitlth B at rate n =
The chirp signals tvere generatecl froni a fast IIini-Circuit POS-100 voltage cont rollecl
oscillator (l'CO 1. The \-CO sweep cliiration and estent were deterniinecl hy a ranip signal
suppliecl 1,~- an esternally triggerecl Il%\-etek 1% generator as shown in Fig. 3.9. The time
duration of the ramp determines the chirp cluration Tc while its voltage dynamic range
(escursion) sets the lowest and highest freqiiencies of the chirp banclwidtli. The \-CO hacl
a timing voltage of 1 to 16 C.* requirecl to cover the 50 JI Hz LPI bandwidtli ( a frequeucy
sweep of JO - 100 3 1 H z ) . a tuning sensitivity of abolit 9.4 .IIHz/L.- ancl a 3 dB mocliilation
bancln-idth of 100 IiHz. The chirp repetition rate (CRR) \vas determinecl by the oiitpiit
freqiiency of a Tektronir FG5Ol fiinction generator that provided an esternal trigger to the
HP pulse generator (HPSOlPB). Operated in this mode. the pulse generator output coiilcl
he varied independent of the pulse train frecluency. leacling to long dwell tirries betwen
t rigger pulses. Instrumentation linii t ations led to the relocat ion of the difference frequency
FG.50 1
TEK Gerierator
TRG W R R Ranip HP Pulse ni C;eiierator
HP 1053A double balanced miser
HP Function Cienerator ZHL-3. l l$!JS* 'O ' O ceil
h
Generator
llirii-circuit Z >[SC-2- 1 B Conibi ner
A ZHL-3:l fVV\ = I I P w
Figure 3.9: Chirp generating circuit configuration.
SIini-Circuit POS- 100
\-CO HP80 1% iiavetrk 185
f o fc f.40 = IF Figure 3.10: (a) The proper rclationsliip of processor frequencies and ( b ) the processor frequencies used due to instrumental limitations.
fo to the loivest freqiiency (50 11 HI ) of the LPI 11-weforni which led to an frF = 150 JI H z .
as shorm in Fig. 3.10. This re-arrangement of frequencies allorvs for a uat ural sweep of the
spread spectrum bancl from loiv to high rvith the VCO.
3.7.2 Frequency Hop
-4nother popiilar LPI spread spectrum signal is obtained by randomly kopping a chta mod-
ulated carrier froni one frequency to the nest. In effect. the spectrum of t ke transmit ted
signal is spreacl sequent ially rat her t han instant aneouslÿ. This leacls t O a pse~itlo-randoni
ortlerecl sequcnce of frecluency hop .
.Analytically. the transmitted signal is giveu by [Z]
w herc
t - a 1 for « - 612 5 t 5 a + b / 9
O otherwise
rvhich describes a srclilence of .\I frequencies {f,} = f i . . . . . f,, . f-\[ each of chirp cltiratiou
t u correspontling to mto 5 t 5 ( m + l ) to . centerecl at t = ( m + f )t,. This sunimation
describes a secluence of frequencies used in the clifferent tu time dots.
-4 cornputer interface to a freqiiency synthesizer shown in Fig. 3.11 was osecl to randomly
generate freqitencies nithin a pre-determinecl banclwidth of 50 .\IHi resol\-ecl iuto 300
frequency bins. The LPI signal \ras then itseci to characterize the processor' s cletection
performance as cLscussed in a subsecliient section.
data Signetics
t I
I
I I
F S 1' / r wave I
I I
FSIi Barid p a s I 2-
Filter t
t I C'-50- I --I B B I
I I
Freqiiency r-- 1 Signet ics
HEF-li.50\'
Corn pu ter generat cd random P S code
Figure 3.11: llodificatious of Fig. 3.8 to acconimodate freqiiency hop generation. The frecluency synthesizer is clriyen by a pseudo-noise (PT) code generatecl from a cornputer. The oiitput frecpenc- is hopped within the sigrial banclwidth which is then niised with tlie baseband data
3.8 LPI Correlat ion Detection Circuit Requirements
The correlation signal was detected iising a CCD array. Each eiement of the detertor array
beliaves as a photocapaci tor on ivhich an electric charge accuniiilates proport ioual to the
square of the incident light and to the integration time. The array is reacl out seriall- by
transferring the charge frotn a CCD structure. Invoking Sycpist sampling tkeorern. the
ininimum number of detectors needed to adequately sample the correlation signal is ttvo
for each period of the highest spatial fretluenc-
The correlation signal at the detection plane P3 ivas shown in Eq. (2.10). to he given
by :
n-here ive have neglected the bias terni. ancl f ' = fo + BI2 is the highest frequency in
the correlated LPI signal. One cycle of tLis freqiienc- lias cluration T' = +. To record
this signal. according to the sampling tlieorem. Ive neecl pisel spacing eqiial to or less than
O.5T'. Thus. for an -40 ce11 tr-ith total aperture T = 5p.q. the number of pixels iri the
. ~ p y e c -- cletector plane must be at least m. For fo = ta J IH2 . the spatially ~arying carrier at
f f = 100 -1IHz recpires a minimum niimber of pisels eclual to 1000 which is i\-el1 rvithin
the arrq- capability used in this work.
As shotm earlier. to separate the bias rerms from the rcqtrired correlation. the integra-
tion time must be much larger than the difference period i. The integration time ( T t ) of
the CCD array used in this mork mas 2048 + & 0.2 rnsec. Hence. al1 ternis containing
-- co.i;(%r fot) or C O S ( ~ ; ; fat). fo = , a M H z . integrated to zero since Ti is substantially larger
s T than - = 13.3 nsec. The peak of the correlation occurs when r = O = + 7 or at
.r = - 7. To mow the correlation peak to the center of the c d . a delay of approsimately
= 2.5 ps was requirecl between the tira signals being correlatecl. This dela>- i.as realizecl
electronically iising the piilse generators ' biiilt-in delay network.
3.9 Processing Gain and Detector Integration
In Section 2.7. we bat-e defined the processing gain in Eq. (2.62) without coherent i n t c
gration of niiiltiple radar returns within time span Ti. In the prcsence of coherent detector
integration [SI. the processing gain can be written as
ivhere Tp = 1IPRF is the interval between the radar pulses and KIT, = .\- is the nimber
of radar pidses integratecl. In terms of clecibels. this can be writ tcn as
Since Ive are stuclying autocorrelation. S S R i z S.\-R2 and ive choose to define the inpiit
SSR in dB as
For the 20 .II Hz signal handmidth processor with B = 20 -\{Hz. T, = 0.2 rns and
Tp = 10 11s. the maxinium processing gain. as giwn in Eq. (3.1 1) is 49 dB. \l'hile for
the 50 WH: signal bandwidth processor witù Ti = 0.2 rns and Tp = 10 p s . the masinium
processing gain is 53 dB.
3.10 Correlation of LPI Signals in Noise
The numerical results of Sections 2.2 and 2.3 were further validatecl esperimenrallc -4
50 M H z bandwidth optical LPI correlator 11-as assemblecl and usecl to verify the princi-
ple of operation as cliscussed in Section 3.5. .A widebancl white Gaiissian noise generator
was also used to corrupt the system commensitrate with the loacling anticipated in wire-
less communication channel. The bandwidth of the noise \vas bandlirni ted to the same
bandwidth as that of the LPI.
As predicted and esperimentally verified. the correlation was a sinc envelope riding on
a spatially ~xry ing carrier for both chirp and frecliiency hoppetl LPI signals. -A niimber of
factors were foiind to pl- a role in distorting the shape of this en\-elope. These incltided sta-
bilit y of the frequency sweep hetween chirps. detector non-lineari t ics. phase nou-linearit ics
of correlating signals. and stahilitj- of the optical setiip. Detcctor non-linearities were coni-
pensated for by post-processing the correlat ion clat a. while optical art ifacts were foiincl to
he minirnized by proper alignnicut procedures using the approacli developecl in this work
and discussed in Section 3.4. The setup yielclecl reasonable processing sain and scrisiti\-ity
to low STR signals with goocl noise immiinity characteristics commemurate with practical
radar operating environments. Even for a very low input S S R of -50 dB. the correla-
tion peak was still detectable for the case of a reference signal correlation as shown in
Fig. 3.13(a) with a processor gain of about 50 dB. This result clearly denionstratecl tlie
capahility of the processor in tletecting very weak sig~ials.
Similady. the theoretically predicted relationship between the main lobe of t Le corre-
lation envelope and the chirp duration \vas es~er iment ally demonst rated by the results
shown in Fig. 3.13. Compared to Fig. 3.12(b). it is clear that tlie correlation wiclth is cli-
Figure 3.12: (a ) Processor output for a linear FI1 signal (SSR of -30 dB) and ( h ) the reference cliirp: vertical scale. 0.5 V/DIJW. horizontal scale. 5Op.s/DI\'.
rectly proportional to the chirp diiration as pre~ioiisly establishecl bu nunierical sinidation
and siimrnarizecl in Fig. 2.6 In this case. the chirp diiration \vas 1.5 tinies the cluration
usecl in Fig. 3.li?(h). The sinc envelope in Fig. 3.13 shoivs a proportional incrcase in the
width of the correlation. [ X higher chirp dtiration results in a wide correlation i d t h : cf
Figs. 3.12 and 3-13.]
Figures 3-14 and 3.13 show the progressi\-e effect of ~xry ing S S R levels on the cor-
relation for chirp and frequency hopped signals respectivel- It is clear from the results
that the processor is capable of operating in relatively noisy environment and still pick
out hidden radiating LPI sources with iip to -50 dB of input STR. f i r y often hoivever.
tliese LPI signals are not only masked by noise but are also overwhelmecl by s trong nearby
interferers. This additional energy greatly climinishes the capacity of the processor to ideri-
Figure 3.13: Effect of \ar!-ing the chirp duration (Tc) on the correlation. -4 siniilar resiilt ivas obtained with a frequency hopper signal rvith 300 hopper freqiiencies: x-ertical scale. 0.5 L-/DI\-: horizontal scale. 5O/ts/DIV.
Figure 3.14: Oscilloscope outputs shoiving the identification of a chirp gelierating source for \-arying SXR levels: vertical scale. 0.5 V/DI17: horizontal scale 5Ops/DIV. ( a ) correlat ion of chirp signals with a ratio of peak to the sidelobes 20 d B . (b ) SSR=lO dB (c) SSR=5 dB (d ) SSR=-5 dB
Figure 3.15: Corresponding oscilloscope oiitputs for the freqtlency hopper LPI case under varying SSR levels: vertical scale. 0.5 i-IDIL': horizontal scale 5Op/DIL'. ( a ) correlation of chirp signals n-ith a ratio of peak to the sidelobes is % 20 dB. ( b ) SSR=10 dB ( c )
S S R S dB (cl) SSR=-5 dB
tif? weak radiating sources due to the CCD dynamic range limitation. Hence. the renionl
of these interferers becomes a key design issue. The nes t section esanlines the impact of
these interferers on the correlatiori and ivays to O\-erconie them.
3.11 NIS Excision Using Tunable Filters
Two scenarios of corriiptive SIS on the correlation are investignted: in-band and o-ut-
of-bartd. For the in-band case. the SIS lies within the signal ba~icltriclth (B) siich thnt
T IF - BIS 5 ffvlS 5 f i F + BI2 while in the O-ut-of-band case. the SIS lies outside the
signal bandividth but s tays within the -40 ce11 bandu.iclth (B.40). jc <_ f.vtr < IF - B/?.
as shown in Fig. 3.16.
4 4 4 I I I I I I
' l ... l 1 I I I I I I I I 1 I I
lc 11 F Figure 3.16: (a) in-band and (b) out-of-band SIS locations relative to the LPI haridwidtk.
Consider an LPI chirp signal corritptecl hl? 'i interferers sitch that
with amplirucles -4,. frecliiencies fj and random phases O,. for j = 1. - - . . -\-. which is
re-IL-ri t ten as
Because -4, >> -4 V j . the SIS autocorrelates and dominates the conipresseci LPI
n-a~eform. Hence. a niethocl is recliiired to notch the XIS energy prior to the correlatiou
operation.
In this section. n-e descrihe an aclaptive system in rvhick the responsc time of tlie
feedback loop is fast enough to track changes in the LPI bandwiclth for niost applications.
Figure 3.17 shows the sub-modiile of a time-intgrating recei\*er usecl to escise the SIS
energ? from the spatially integrated outpiit signal. -4 heam splitter was used to tap off
some of the optical energy incident on the CCD arrac This tappetl off light beam \vas then
focussecl ont O a single photodiode t O recover the correlat ing signals dong wi t h the attendant
tcniporally \ q - i n g carrier and any present interferers. -4 cletailecl mathe~iiatical treatnient
of the signal plus SIS detected bj- this arrangement was del-eloped in Section 2.5. The
resulting analog signal \vas then sampled bj* a 10-bit digitizer and the output digital streani
fcd into a cotnputer for analysis via a General Piirpose Interface bus (GPIB) connectiou.
The computer performed a Fourier transform on the stream wkich decomposecl the
signal into the center frequency of the LPI. fo. SIS frecpncies f,. j = 1. . . . . .Y aucl
Filter Bank
ptiotodetector 7;)
C'CD
Con1 piiter PC-S-lSfi/(ifj 11 Hz
10-bit TEK digitizer
GPIB
RS-232 Iriterface
Figure 3.17: Real time detection and escision of NIS using digitally titnable filters and a single photodetect or arrangement.
their respectil-e higher order terms fu k 2 f j . fo f 3f, ancl so on. Al1 higher orclcr terms
are oiitside the A0 ce11 banclwiclth and hence do not iuterfere with the correlation otitpiit.
Ouly the frequencies at f, were deerned as NIS and hence the computcr comparecl their
respective energies to a threshold that can he fised or aclaptix-el- set in the prograni. If
a givcu energy esceecled this threshold. a cornmancl \vas issiiecl to the SIS suppressiou
niodule. via an RS-232 serial interface". to a tunable notch filter" to escise the SIS cnergy
at that offencling frequency. The freqiiency to notch was translatecl linearly into a coclccl
digital word corresponding to the center freqiiency of the notch.
For multiple NIS notching. the tunable filters were setup in a parallel hank arrangement.
The first tirne the specrriini !vas compiitecl. the system aiitornatically set the threshold to
i ts largest value. The nuniber of interferers esceecling t his t hreshold w r e t hen comparecl
to the preset nuniber of interferers. In subsecLiient processing. the nimber of interferers
esceeding this threshold were again counted and conipared to the preset nurnber so that
the appropriate filters can he tiined to reniol-e the SIS that esceedecl the threshold. The
thresholcl remainecl fisecl until sonie SIS disappearecl or appearctl in the spectrum. or a new
preset nuniber $sas then chosen. The electronics design inclucled operator control circiiitr?-
to d u c e or increase the threshold depending on hors man- SIS n-ere to be escisecl.
\Vithout taking into account the speed of the electronic Fourier transformer ancl the
PC notch decision circuit. the folloiving can he statecl: when the notching feedback loop
was connectecl to the post-detection electronics. as shown in Fig. 3.8. the speed of notching
"or faster throiighput, digitally turiabie filters with a parallel interface are also available. 'POLE/ZERO Corporation's tunable notch filtcrs are liigh Q. narrowband filters whose center frequency
is controlkd digitally. Ttiey have a tuning range from 1.5 . l lHz to 1 G H z . Filter tune tinies are typically I O ps to any freqiiency within the barid after receipt of tunc command. 3 dB bandwidth of about 1.0 .\IN: and an insertion loss of 20 dB at the center frequency.
n-as about 0.2 rns. Hotvever. when the notching feedback was connectecl to the spatially
integratecl output. as shomn in F i 0 3.17. the speetl of the notching was abolit 10 p s
The electronic P C basecl Fourier t ransform operation slows dorrn the feedbark loop
to about 1 nis thiis partially masking the benefits of the spatially integratecl oiitpiit.
.A specially designeci controller with a declicated DSP chip coulcl perform the reqiiirecl
elec tronic Fourier t ransform and not ch select ion decision in consitlerabl- fast er t ime t hus
benefiting of the novel architecture.
3.12 Impact of the NIS Notching Feedback Loop
To illustrate the SIS escision techniqtie developed in this thesis. wc corriipted the LPI
wa\-eforms n-i t h in-batid and out-O f-band interferers respectil-ely Figure 3.1 S shows corre-
lations with a number of in-bancl interferers located as shown in (a)-(cl). The interferers
were added to rhe LPI to produce a composite signal. The LPI signal \vas thiis cornplere1~-
ol~scured in the composite signal. Clearly in al1 tlicse cases the desirecl correlation signal
is dominated 11'- the autocorrelation of the in-band 31s. In case of an intercept rcceiwr. a
false alarm can be raised when the SIS is confused with the desired nideband LPI activitj:
After notching out the interferers. the output of the correlator is s h o ~ n in Fig. 3.19
for the same varying number of in-band interferers. This esample illustrates that the
notching technique is capable of recovering the LPI correlation even in multiple in-band
SIS en\-ironments. Siniilar results were obtained for the freqiiency hopped case. Hoivever.
it was founcl that the uotching technique excises a portion of the desired correlation energ-
leading to a dis tort ion in the correla t ion envelope.
Figure 3.1s: Correlation with in-band interferers at ( a ) 55 LIHz ( b ) 55 MHz and 7.5 1IHz -- (c) 55 UHz. 75 MHz and S5 AlHz (cl) 55 > ~ H Z . ~ C I MHz. S5 MHz ancl 100 MHz on the correlat ion en\-elope. Oscilloscope set tings: 1 .O i-/DI\.'. 50 ps/DI\-.
Figure 3.19: Effect of notching in-band interferers at (a) 55 MHz ( b ) 55 MHz and 75 MHz (c ) 55 MHz. 75 SIHz and S5 MHz (cl) 55 UHz. 75 11Hz. S5 MHz and 100 MHz on the correlation envelope. Oscilloscope settings: S00 niV/DIV. 50 ps/DIV.
-- Figure 3.20: Correlation with interferers nt ( a ) 55 SIHz and (b) a I I Hz in the in-band case wit h SIS to LPI S S R ratio of 5 dB. Oscilloscope set tings: 1 .O \-/DI\' and 50 ps/DI\-.
Figure 3.21: Sotching of interferers at (a) 55 MHz and ( b ) 75 SIHz in the ai-band case
with SIS to LPI SSR ratio of 5 dB
Figure 3.2'2: Correlatiou with out-of-band interferers at (a) 30 MHz and ( b ) 100 MHz for a SIS to LPI SXR ratio of 5 dB. Oscilloscope settings: 500 mi-/DI\.-. JO ps/DIV.
. ... A.. ............. ........................................................ ......................-.r...........................-............... 4
i tr r
Figure 3.23: Xotching of out-of-band interferers at (a) 30 MHz and (b ) 100 MHz for a SIS to LPI SXR ratio of 5 dB.
Figure 3.24: RSIS error in approsimating the peak of the correlation ewdope as a function of the location of the peak of the narrowband interferer.
This penalty [cf Fig. 3.20 and Fig. 3.21)] is more severe when comparecl to the out-of-
band SIS case shown in Fig. 3.22 and after notching in Fig. 3.23. These Figures show the
effect of notching SIS energies for the same NIS power-to-SSR of the LPI. Clearlc the
envelope and niagni t i d e of the correla t ion are niore aclversely affect ecl in t lie i7t- band case.
Since niost of the LPI signal energy is in the banclwiclth B = 50 M H z . Ive espect the
greatest distortion of the correlat ion to occur when notching in-band XIS. Figure 3.24 shows
the root-mean-square (R l IS ) error as a fiinction of the location of the interferer. II'here
the RAIS error is defined as the root mean square of the clifference between the location of
the peak of the correlation output in absence of interferers and its corrrsponding location
after the escision (381.
The RAIS error is small whcn the interferer frecliiency is locaterl far awa- froni the
center of the LPI bandwidth: as in the out-of-band case. The RUS progressi~ely increases
until it peaks at the point whcre the interfcrer is at the center of the LPI banclwidth.
This can be attribiited to the fact that in notching a centrally locatetl SIS. a considerable
amount of signal energ'. in addition to escising the interferer. is removecl. The results are
again shomn to h e consistent for the frequency lioppecl case.
Chapter 4
Processor and Measurement
Hardware
The \arious processor moclules. nieasiirement and sigiial condi tioning elec troniçs disciissecl
in the previoiis chapters. are s h o ~ m in the photographs that folloiv ivi th the riames of the
manufac t iirers and coniponent specificat ions
ji-itli referruce to Fig. 3 3 . n-e consider the following stzbs~-steriis:
a (a ) laser n-ith DC bias. direct mocliilation network and colliniating optics.
O ( b ) .\O deflector with RF driver aniplifier.
a ( c ) pre-detection optics.
(d ) CCD array and post-detection electronics.
O (e) beam-split ter for spatially integrated output and the feedback loop ivith SIS
excision notch filters.
a ( f ) input radar LPI signal generation and XIS sources.
SS
Figure 4.1: Laser diode source SDL-2432-Hl from Spectra Labs operating at X = '791 nm with Pm,, = 500 mW and a horizontally polarized beam. It is mounted in an SDL-SOOH heat sink. The output laser bearn is expanding at half angles OL = 40' and = 10'. A collimating lens, LiCONiX L80, with numerical aperture (NA=0.65) collects this light and outputs a parallel beam. This parallel beam has an elliptical cross section. In order to evenly illuminate the A 0 cell, the beam was expanded into a circular cross section using a llelles Griot anamorphic prism pair (06-GPA-003).
Figure 4.2: Another view of the laser heat sink and anamorphic prism pair. In an anamor- phic prism pair' two identical prisms are mounted at an incident angle which is the Brew- ster's angle. The prism pair introduces an anarmophic expansion of the beam while shifting the beam a small amount literally. The particular pair used had a magnification factor of 6x. wavelength range 780 nm-1550 nm and a clear aperture=& 0.5 mm.
Figure 4.3: View of the fiber coupled detector connected to an oscilloscope via a Tektronix optical-toelectrical converter. This module was used to characterize the modulation depth and sensitivity of the laser diode to direct high frequency modulation. The OR503 opti- cal/electrical (OIE) converter is connected to a Tektronix TM500 power module mainframe for its power supply. It has a wavelength sensitivity of 700 - 1500 nm delivered through a 12.5 prn multi-mode fiber, maximum optical tolerance of +20 dBm and a modulation response of 10 K H z - 1 G H z .
Figure 4.4: r\nother view of the fiber coupled detector along with the laser diode assembly, collimating optics and an anamorphic prism pair. The laser diode's bias current is provided by an SDL-800 Spectra diodes labs driver. The bias range was 10 to 1000 mA which translated into O to 0.5W CW optical output from the laser. A current limit control network provided overdrive protection for the diode. The driver allowed a modulation bandwidth of 100 KHz. This bandwidth Ras too low for LPI requirements hence a custom modulating network was designed and interfaced to the driver. The purpose of the driver was thu î reduced to simply providing a DC bias to the laser
Figure 4.5: View of the spatial filter preceded by a Newport Fourier transform lens of focal length f = 38.1 mm and an equivalent lens at the other side of the filter for the inverse operation. Detection is achieved with a CCD EG & G Reticon RL2048D.4G-011 linear array with pixel dimension of 13 pm x 13 p m and 2048 pixels. The arraj* was pre-mounted on the RCOï30LNN evaluation board that supplied the bias and sampling requirements of the device. Maximum throughput from the array is 10 M H z with a typical peak-to-peak pixel noise of 3 mV and a saturation voltage of 2.4 V. The data rate can be increased t o 20 :\IV: hy ronfiguring the board to read "odd" or "p-2'' ~ I x ? ! s only.
Figure 4.6: Expanded view of spatial filtering and detection sections of the processor. The A0 ce11 is attached to a rotating platform with 4 degrees of freedom (x, y, z and rotation about the z-axis). The cell, a Brimrose TED5-150-100 deflector, had center frequency f.40 = 150 M H z , bandwidth = 100 M H z I acoustic velocity v = 4200 m/s. active aperture 0.75 mm x 21 mm, efficiency = 5576, a Bragg angle es = 14 mrad and time aperture T = 5 ps. The ce11 had a TeOz crystal and could accommodate a maximum RF drive power of 2 W terminated into a 50 R irnpedance. The driver that provided power to the ce11 was a n RF amplifier with a frequency range 40 - 250 M H z . gain="- dB (at j-40 = i50 J l f i z ) and a noise figure=9.5 dl3 maximum.
4.7: Auxiliary elect ronics showing ampli fiers, mixers, phase shifters, power combin- Figure ersfsplitters used for LPI signal generation and conditioning. On top of the power supply are the POLE/ZERO digitally tunable notch filters (Maxi-Notch 90-200-20) with accom- panying controller. The filters have a tuning range of 1.5 MHz to 1 GHz, a notch depth of 20 dB at t he center frequency, 3 dB bandwidth=3.5% of selected band, and tune times of about 10 ps to any frequency within the band after receipt of tune command from the D i l controller. The filter can handle up to 10 W input power and has a maximum passband insertion loss of 1 dB. The controller in turn is connected to a cornputer via an RS-232 int enace for programmed operation.
Figure 4.8: Xnother view of the tunable filter/DR controller module sitting on top of a white DC power supply, linear chirpfhop LPI generating circuitry and measurement equipment in the foreground. The fiber coupled detector module is located next to the laser diode assembly.
Figure 4.9: Another view of the overall processor from the A 0 ce11 plane to the CCD detection board. At the detection plane is a Melles Griot beam splitter (03BSC027 with near-infrared spectral response 700- 1100 nrn that channels some of the intensity downward to a single photodetector arrangement. This ilelles Griot 13DAH001 photodiode had a spectral response of 350-1100 nm, a response at 830 nm of 0.35 A/W, active area of 0.04 mm2, and a typical rise time of 0.35 nsat -9 VDC.
Figure 4.10: A magnified view of the single diode tap-off arrangement used to detect and excise XIS energies in a feedback loop. The long black rod holds the beam splitter that directs part of the intensity downwards to the diode. The black coax cable is connected to the diode. then to a Mini-Circuit ZHL-SA amplifier. The output of the amplifier is connected to channel A of a Tektronix TK39OAD digitizer which directs the bitstream to a computer via a GPIB (IEEE-488) interface.
Figure 4.11: Computer connection to the feedback arrangement via a GPIB interface. Beloiv the monitor is the Tektronix TK39OAD 10-bit digitizer that samples the processor output. This digitizer has the full functionality of an oscilloscope with the added benefit of remote or programmed control via a computer interface. The computer performs Fourier analysis and peak detection on the input and sends control signals to excise the NIS energies through an RS-232 connection to the DR notch filter controller. This overall real-time operation is controlled by a C program.
Figure 4.12: Equipment rack with oscilloscope, HP 8590 spectrum analyzer, HP 8012 pulse generators, Noise/Com NC6107 generator, HP8690B sweep oscillator, power supply, optical power meters, HP 5301A 10 AlHz counter and SDL-800 laser diode driver.
Figure 4.13: View of the 50 M H z processor along with the test and measurement equip- ment with specifications: difference frequency fo = 73 M H i , LPI bandwidth B = 50 M H z , -40 bandwidth BAO = 100 AlHz and reference tone frequency f, = 100 M H z .
Figure 4.14: Another evtended view of the 50 !CI H z processor.
Figure 4.15: Side perspective of the entire 50 M H z LPI processor.
Figure 4.16: Magnified side view of 50 M H z LPI processor. Note the infrared viewer (FJW) used for alignment and beam find purposes. The viewer has a focusing range of 15 cm to infini ty allowing for close monitoring support.
Figure 4.17: View of the 20 M H z processor from the laser diode end with system specifi- cations: ciifference frequency fo = 30 M H z , LPI bandwidth B = 20 M H z , A 0 bandwidth B.4o = 40 M H z and reference tone frequency f, = 60 M H z .
Chapter 5
Conclusions
The objective of t his work iras to design and irnplemenr tinie integrating optical processors
for the purpose of detecting and iclentifying spread spectriini LPI radar signals in Ion- SSR
ancl SIS corrupted environnients. To this end. the folloiving original research contribiitious
have been macle:
1. A stochastic clerilation of the processing gain of a tirne-inregrathg -40 processor
2. .A novel nier Lod for real- t inie escision of corritp th-e IiIS energ:. iising digit ally t iiuat~le
notch filters in a ttniciiie space integrating refereiice tone detection and feedback
arrangement has been devised and integrated in the processor.
The professional coutriliitions of this work can be suniniarized as:
1. -4 novel optical alignment niethod that is a cheap ancl rohitst alternative to niauy
piirely optical procediircs. has been devised and denioustratcd in this work.
2 .Anal-t ical espressions for the noisy inteusi ty A 0 transmit tance ancl correlation func-
t ions w r e clerivcd.
3. .A CCD scaling law \vas postulatecl and demonstrateci.
The designed processor consisted of an intensity modulatecl laser diode followed by col-
liniating optics to produce the reciuired beam cross sectional match for optimum escitation
of the A 0 cell. The necessarl- design constraints in meeting this niatching were presentetl
dong n-it h the lem rnagnification factor. eqiial to F2/ Fi for sniall angles.
B y an appropriate choice of op t ical. high-freqiiency elec tronic component s. precision
alignment and detection circuit ry. the processor vas broiight close to an op tirnuni operat ing
point. This operating point mis shown to be very sensitive to the correlation signal-to-bias
ratio as the overall d!*naniic range of the processor is cleterminecl 11)- the dj-naniic range
of the CCD array. Hoivever. operating a laser nt a high average potver leads to a high
nioclulation deptli at the espense of an increased signal-to-bins ratio. To o\*ercome these
conflicting requirements hetween the CCD ancl the laser' s opti~iiiini operation. a neiitral
density filter ivas used to liriearl?- a t teniiate the overall optical poil-er prior to detectiori.
The sigrial-to-bias problem was also shown ro he controllable 1ij. an appropriate choice of
reference tone poiwr. The scaling laws that apply when CCD detection is used were also
de\doped and esperimentally \aliclated.
The optimum operating point of the processor was also fount1 to he liighly dependent
on the overall optical alignment of the \arious components. -4 niechoc! was thus requirecl
to acciirately quanti- the overall optical niisalignnient relative to the oprical center ancl be
able to iteratively correct it throiigh a feedback approach. -4 totally new and robiist schenie
for rneasuring the overall optical misalignment error mas developecl and denions trated.
.-\nalyt ical expressions for the correlat ion of eit her linearly chirped or frecpency hoppetl
signals with the processor were also derivecl. It was shon-n that in both cases. the correlation
is a sinc function envelope moddating a spatially var>-ing carrier. In the special case of the
frecpency hupper scheme. for a sufficientl~r large nuilmer of hopper frequencies S. it 1r.a~
shown that the output is siniilar to the chirp case with the signal hop handwidth ( BIfI.')
replacing the product of the chirp rate (a) and the integration time (T,,). The effect on
the correlation output. of SIS energy in the bandwitlth of the LPI. was also cliscussed.
-4 novel approach for notching this XIS energ'- usin:, digitally tunable filters and a
space integrat ing reference tone arrangement was shown to be very effec t i\.e part iciilariy
for out-of-band cases. The processor's performance in the presence of both in-band ancl
out-of-band narrowband interferers. in adcli t ion to broadband noise. mas studied and the
esperiment al results were found to be consistent n-i t h t heoretical predictions. -4 technique
for aclaptil-el? identifying the SIS based on an alarrn nwchanism and notching it 11-as
proposed ancl denionstrated. It rvas shown that the error in notching SIS energy peaks at
the center of the LPI frequency span and falls off siil~stantially for SIS freclucncies locatecl
away from the center. This discrepancy was attributcd to the practical limitation of the
filters to restrict the notch only to the SIS energy.
Finall!: the processing gain of the processor was derivecl using a stochastic analysis
approach for a number of input SSR scenarios. This deri~xtion represents a unique new
approach to evaluating a tirne-integrat ing receivcr sensitivity.
Appendix A
Imaging Optics
The light soiirce was a GaA1.k semiconductor Laser operating at a wavelength of 791 nrn
and a niasirnurn lasing potver of 500 rnIV at a 1 -4 drive curent . The laser is modulatecl by
a reference spread spectrum signal si ( t ). In addition to the laser mocltdating signal. a bias
is added to prevent the laser frorn being pushed belom its t hresholcl and allow operat ion
iri the linear region of its power transfer curve.
The light. as i t leaves the laser diode. is espanding at lialf angles = -10' and = 10'.
This leads to a requirenient for a narnerical aperture (T..i.) of 0.65 to coilimate the beam.
-4 colliniating lem with a S..\. of 0.65 was then mecl to collect this light and output a
paraIlel heam. This output parallel beam. hoirever. has an elliptical cross section. In orcler
to evenh illuminate the .A0 cell. the elliptical cross-section is espanded into a circular
one using an anamorphic prism pair. To efficiently focus the beam energy to the A0 ce11
aperture. a cylindrical lens was then used to provide the line illumination that fits the ce11
aperture windom.
LVith an ohject ?;.-A. of 0.65 and an object distance of 10 mm. the recpired dianieter
collimating optics Cl
Figure -4. 1: Collimat ing and pre-detect ion .-\O ce11 aperture mat ching op t ics.
(O) of the lens to collect al1 the Laser light \vas giren bu:
O 0.65 = O = 13rnrn
2 * 10 mnz
- 1.6. Thus. the The requirecl magnification ( rn ) to match the -40 aperture i ras - - focal length of the reqiiired cylindrical lens was determinecl to be:
Accomplishing t his imaging t ask wi t h a single cylindrical lens would t herefore reqiiire
an optic with a 5.92 mm focal length. ancl a 13 mm diameter. the optimum clear aperture
of the lem.
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