JPRS ID: 10463 TRANSLATION OPTICAL METHODS FOR PROCESSING IMAGES AND SIGNALS ED. BY V.A. POTEKHIN

• Document Type: CREST
• Collection: JPRS
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00850R000500050039-9
• Release Decision: RIF
• Original Classification: U
• Document Page Count: 78
• Document Creation Date: November 1, 2016
• Sequence Number: 39
• Content Type: REPORTS

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R040540050039-9
FOR OFF[~[AL ~SE QNLY
JPRS L/ ~ 04fi3
15 Apri! 1982
Tra~ns~atic~n
OP~'ICAL ~VIETHODS FOR PROCESSING
IMA~ES AIND SIGNALS
~ Ed. by
V.A. Potekhin
_ Fgl$ FOREIGIV BROAIDCAST I~1FQ?RMATION SERVIC~
- F'OR OFFICIAY. USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R004500050039-9
1YOTE
JPRS publicatioas contain ir,~formation primarily from foreign
newspapers, periodicals and books, but also from news agency
, transmissiqns and broadcast;s. Materials from foreign-language
sources are translated; th-ose from English-language sources
a~e transcribed or reprinted, with the original phrasing and
other characteristics retained.
Headliues, editorial reports, and material ex~clnsed in brackets
are supplied by JPRS. Processing indicators suc4 as [Text)
or [Ex~:erptJ in the first line of each item, or ~a1loWing the
lest ;.ine of a brief, indicate how the original information was
processed. Where no processing itidicator is given, the infor-
- ma*ion was summarized or extracted.
UnfamiZiar names ren~ered phonetically or transliterated are
enclosed fn parentheses. Words or clames preceded by a ques-
tion mark and enclosed in parentheses were not clear in the
~ origina~. but have been supplied as appropriate in context.
Other unattribut~d par~nthetical notes with in the body of an
item originate with the so~irce. Times within ~tems are as
given by source.
~ The contents of th1.s publication in no way represent the poli-
cies, ~views or atti,`.udes of the U.S. Governcnent.
COPYRI'.~iT LAWS AND REGULATIOYS GOVERNING OWNERSHIP OF
: MATERIALS REPRODUCED HFREIN REQUIRE THAT DISSEMINATION
OF THIS PUBLICATION BE RESTR~CTED FOR OFFICIAZ USE OI~JI~Y.
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R400504050039-9
FOR dFF7CIAL USE ONLY
JPIftS L/1~1963
15 April 1982
_ OPTICAL METHCIDS FOR PROCESSTNG IMAGES AND SIGNALS
Leningrad OPT~CHE~KSYE :METODY OBRABOTI~I IZO~RAZHENZY I SIGNPrLOV in
Russian 1981 (signed to press 10 :un 81) pp 1-101
:
i
~ jCollectior_ "Optical Met:hods for Pr~ocessing Images and Signals," edited
by Doctor of Technical S~ciences Professor V. A. Potekhir~, Physico-
technical Tnst~tute imeni A. F. Ioffe, US~R Academy of Sciences, 500
copies, i01 pages]
CONTENTS
Zinov'ye~v, Yu. S., Pasmurov, A. Ya., "Using Holographic Principles
to Analyze Kadar Stations With Synthesized Aperture" 1
Mush, B. S., "Equal Observation Principle and Economic Algorithms
for Signal Processing by Quasi-Hologrsghic Pulse-Doppler Systems" 12
Mush, B. S., "Synthesizing Quasi-Holographfc Syste~.Adaptive to
Reflecting Surface" 18
Orlov, R. A., "Determining Intercoupling of Spatially Combined
~ Antennas by Radio iiolography Methods" 22
- Pasmurov, A. Ya., "Measuring Parameters of Scattering Bodies by
Radio Holography Method" 28
Astaf'yev, V. B., "Functional Capabilities of Devices With Optical
Feedback" g;
Kulgkov. S. V.. "Signal and Interference at Input uf Acousto-
. Optical Spectrum Analyzer" 40
- Molotok, V. V., '~Frequency-Re;~ponse Fun~tion of Real Acousto-
, Optical Spectrum A,-+alyzer" 47
Kuzichkin, A. V., "Statistical Characteristics of Acousto-Optic
- Receivers of Long Pseudorandom S~gnals" 53
- a- II - USSR G FOU01
FOR OFFICiAL USE ANLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/Q2/09: CIA-RDP82-00850R000500050039-9
FOR UF'F[CIAL USE ONLY
Kuzichkin, A. V., "Acousto-Optic Correlation Analysis of Complex
Signals With J~ping Ftequency" 59
Vasil'yev, Yu. "Acousto-Optical Radio Signal Demodulation" 62
Vasil'yev, Yu. G., "Peculiarities of Light Diffraction by
Complex Ultrasonic Signals" 69
i
- b -
FOR OFF'I~IAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850RQ00500050039-9
FOR OFF[CIAL USE ONLY
[Text] This collection contains individual repoxts deliver~d and discussed
at meetings of the se:tion on non-optical holography ~t the Leningrad Regional
Board of the S. I. Vavilov Scientific and Technica~ Society of the Instrianent
Ma::ing Industry. The section was arganizeci ~n 1977 at the initiative of the
directorate of the section on holography at the Central Board of the S. I.
Vavilov Scientific and Technical Society of i.he Instrument Making Industry.
This section now brings together Leningrad scientiats and engineers from in-
stitutions of higher education and research inetitutes working in the fields
- of appli~d use of inethods of radio and acoustic holography, as well a?: optical
- processing of radio and acousGic signals ?'he articles mainly give th~ .re-
sults of original research by the authors dealing with current problems of
using methods of holography and optical processing of informdtion in micro-
wave engineering.
The Science Council on the Problem of Hologra~~y Affiliated With the PrPSid{um
of the USSR Academy of Sciences was of considerable assistance in organizing
and publishi~�� this collection. The directora~te of the sec.*_ton an non-optical
holography i3 stncerely grateful to Doctor of Physical and Mat�ematical~Sci-
ences S. B. Gurevich, and Candidate of Physical and Mathematical Scien~es
G. A. Gavrilov fox expediting publication of the collection, and also to Asso-
ciate Member of the USSR Academy of Scienc ~s L. 'D. Bakhrakh for reading the
manuscript. The directorate of the secti~?~ thanks th~ authors who delivered
these papers, and who offered the;n for pub licati~n in this collection.
UDC 773.4:523.164.8
USING HO~OGRAPHIC PRINCIPLES TO ANALYZE RADAR STATIONS WITH SYNTHESIZED APER-
TURE
~ [Article by ~Yu. S. Zinov'yev and A. Ya. Pasmurov]
jTextJ An examination is made of ma~or aspecta of holographic
theory of radar with synthesized aperture [RSAj. The first
stage of holographtc procesaes in RSA (formation of radio
1
_ FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL USE ONLY
hologram) is treated as recording of the field scattered
by an ob~ect by using an artificial reference source. The
second stage (reconstructing the ob3ect) is described on
the basis of physical optics. A classification is given
of radio holograms recorded in the RSA and conditions of
subsequent processing. A physical interpretation is given
of ma~or RSA parameters. An examination is made of applica-
tion of the proposed theory to ~evaluating the influence of
trajectory instabilities of the RSA carrier, and to analyzing
images of maving observational ob~ects.
1. Introduction
Up until the present, the description ~f RSA has used mainly such methods
as the synthesized antenna technique, the method of signal selection by Dop-
pler frequencies, the method of cross co~relation, which are based on princi-
ples of the theory of electronic systems, optimum reception theory and the
like. All three approaches enable evaluation of the infl.uence that technical
parameters of the RSA have on its tactical characteristics ,[Ref. 1, 2J. Re-
sults and conclusions practically coincide.
The RSA in combination wi~h a coY~erent aptical processor [Ref. 3] is a"quasi-
holographic" system 3n wh~ch resolution with respect to one coordinate (azi-
~ muth) is attained by holographic processing of a fixed signal. In the opinion
of Leith 3nd Ir~galls [Ref. 4] such a~representation is the most flexible and
physically graphic and enables development of RSA components with working prin-
ciple that is readily explained by the theory of radio systems. This view-
point has been developed b}? Kock [Ref. 5), with proposal of same new radar
~ystems based on principles: of holograms. However, the use of th~ holographic
approach for analyzing the RSA has been limited until now to examination of
only optical proc~ssors. There is practically no mathematically valid view-
point-. enabling representation of the RSA as a whole as a holographic system.
Therefare description of th~ RSA from unified holographic principles ia of
theoretical interest. Such an analysis gives the most complets elucidation
of the essence of physical processes that take place in the RSA. In addition,
- it becoines possible to uae concepts and methods developed in the theory of
opti~al holography.
'
2. Principles of obtaining holograms in RSA �
Ja
Let us coresider an RSA (Fig. 1) mounted on ~
a vehicle moving at velocity vH along axia X ~
~ x'. The radar antenna has linear dimeneion ,po \
LR (real aperture), and width of radiation
pattern 9R along the line of the patr. The -
radar scans a strip in short pulses and
f~.xes the pattern of diffraction of the 8canning 1.~%
r,trip .
nrobing signal by the observational ob~ects
sequentially in tim~. The amplitude and
- phase of the scattered field are regiatered Fig. 1. Principal geometric re-
by interference of received and re~erence lati~ns in RSA
2
~ FOR OFF[~~AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL USE ONLY
signals in a coherent (synchronouB) detector. A8 a result, a radio hologr~u
of multiplicative tqpe is~formed [Ref. 6], the part of the reference wave
being played by a signal introdu~ed directly into the elect:onic channel ("ar-
- tificial" reference wave). The radio hologram is usually recorded by modula-
tion of ~RT luminescence intensity on a photographic film moving relative
to the CRT screen at velocity vn. To record radio holograms of ob~ects sitti-
ated at different ranges Ro from the line of the path, the pulsed mode of
operation is used with vertic~l scannir~g on tt?e CRT screen. The rFSUlt is
a set of one-dimenisonal holograms recorded in different positions with re-
spect to the width of the film, depending on the range to the corxesponding
- ob~ects.
Let us assume that all ob~ects are located at a distance Ro fram the line
of the path. In this case the radiated signal can be considered continuous
since accounting for the pulsed nature of the radiation is important only
for analyzing the resolution of ob~ects with respect ro range. Fia~ 2 shows
the equivalerit diagram of recording a o~e-
, dimensional radio hologram. Situated at point
`~~rlo~ Q with coordinates (x', 0) is an RSA (x' = vgt',
~,,,e~ where z is elapsed time) , and at point R
~q _ (xr, zr) is a hypothetical reference wave source
~ with action similar te that of a reference
Q~x~~ Jn~ signal of the synchronous detector, while point
P(xo, zo= -Ro) telongs to the observed ob~e~t
situated along axis xo. If the scattering
Fig. 2. Equivalent diagram properties of the ob~ect are describe~ by the
of recording one-dimensional function F(xo), and dimensions are sufficiently
_ hologram small compared to the quantity Ro, we get the
well known Fresnel approximation [Ref. 7] for
the diffraction field along axis x' (with conside~ation of propagation of
the probing signal from the RSA to the ob~ect and back)
- . ~�,R~ ~~~t
U~(x'1= G~ ~ F(se~e`K' K� a~. . ~1~
ra;a,...~
where xl = 2~r/7~1 is the wave number,, and C stands for some comglex constaut
both here and below.
The complex amplitude of the reference wave is Ur(x') = Arei~r. Usually this
is a plane wave, i. e. �r = xzsin Ax', where 9 is the angle of "incidence"
of the wave on the hologram. The inclination of the reference wave is equiva-
lent to a reference signal with linear phase advance, and introduces carrier
frequency K1sin 9. As a result of coherent detection, we get a radio
hologram with equation
hlx')-Re(U~(r'lUol1~~1 or hlx')=[mlU~(z')Uo(~1) . (2)
With consideration of (1), it ia clear that in the ~eneral case one-
dimensional Fresnel radio holograms are formed in the RSA. In addition, ~he
following situationa are possible, d~pending on the ratio of dimensions of
3
FOR OFFICIAY. USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850RQ00500050039-9
FOR OFFICIAL USE ONLY
~ the ob~ect, the length of the synthesized $perture LS = vHT (T is th~ time
of recording the radio hologram) and the qu~.ntity Ro. ~
1. In the case where Ro>=xlxo~/2 (xa~X is a quantity that cha~racterizes
the maximum dimensions o~ the ob~ect), instead of (1) we get the Fraunhofer
approximation
~ ' nLK~Q~ ~K~i:'L N ~LK Zr tY
~�~x~'~}~~ ~ ~ R0 ,~F(~o)~ ~ R~ dx~ ~ ~3~
. , o -,b
and as a result a Fraunhofer radio hologram is formed.
~2
2. In th~ case where Ro� xlx~aX/2 = KiLg~$~ the t~rm eiKlX ~R� in (3) can
be omitted. Then a Fourier radio hologram is formed, and the condition of
formation in the RSA can be written as
; s e V,~~ Q.o ~:r . (4>
3. I� the ob~ect is a point (F(xa~ ~ d~(x' -xo)), the Fraunk~ofer diffraction
conditions are automatically satiafied. Using tl:e filtering propertiea of
the d-function, expression (3) yields the following equation of the radio
hologram (withaut consideration of constant phase terms)
' ~x'~ , . '~~r� ( )
h(x~).- A,.Aom9~lD~x - K~ J~, Ro 5
- o
- where Ao is the amplitude of the wave scattered by the ob3ect dt the reception ~
point.
~ If in ad~ition (4) is valid, then {5) implies ~
~ ~ p .
h(ic') = A~ Apf:OS((4)~~C + 2K~ k ~6)
u
' Thus a Fraunhofer or Fourier radio hologram is formed in the RSA for z point
target. In the former case the radio hologram has the form ~f a one-dimen-
sion~il Fresnel zone plate in accordance With (5), and in the latt~er case it
takes the form of a one-dimensianal diffraction grating with c~nstant spacing
in aECOrdance with (6).
In tt~e process of photographic recording, scaling of the radia holograms takes
place with subatitution of coordinate x for x', where x m x'/nX, and nX = vg/vn.
In this operation, a cons~ant term ho ("displacement") is added to (5) and (6)
~ for photographic rQCOrding of the.funct:~on h(x').
- 3. Image Reconstruction
We will analyze the ne~t stage of the holographic pr~cess by the method of
- physical optics. Illuminating a phetotransparency by a plane wave with wave
; number x2, :ae get a diffractidn field with distribution at distance p from
a
4 .
_ FAR OFFICIAL lJSE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R040500050039-9
FOR OFFiCIAL USE ONLY
the hologram described by the Huygens-Freanel integral
ei(K2~-Ti/~) . JGy~ ~t
V(g)' Y~1~ d h(x)e`~~' dz . (7)
- - IT~7/2
~ Substi~uting (6) in (7) we have V(~) = Vo(~) + V1(~) + V2(~), where Vo(~) is
the zero order corresponding to displacement ho, V1(~) and V2(~) are functions
that describe Che recon~~tructed images of the point ob~ect and are equal to
v C , KP ~ KenY x9 ` KJP =~~xn~ ~ i~K~ II ry~~x J~ .
uaT/Q ~
' =C~ e~~e,p " ) e'~ ~ ? Ro (8>
yt ~ - v~T/t
We find the position of the images along the z-axis from the condition of
a zero value of the exponent in~the first exponenti~l function of `8), imply-
ing
- ~ . � a~Ra/2~1Qnx , ~9~
Obviously one image is imag3nary and the other is real. Integrating (8) with
- condition (9) we get . ~
- ~ 9K~~ ~CS 11~T
~,~~~j _ C,si.n{[~Xnr ~o ~ n~~ - } (10) .
yr(a~~ ~W~~~x,f QK~.~~ xo O.T
Qo n z - ~ , 2
- Thus the image of a point ob3ect is described by a function of type sin v/v.
The position of the ima~e is detenained by the zero value of the argument
i. e. by the relation
~ _ :~�/n~ t R�/~K~~�" � (il)
Z'he first term in (11) corresponds to the cooxdinate of the ob~ect, and the
second term is due to t'`ie carrier frequency. The images of two point objects
that have identical coordinates xo but different ranges R1 and R2 will be
- characterized by different coordinates ~1 and ~2. Thus the use of a carrier
frequen~cy leads ta geometric distortions of the image of the entire scanning
strip.
According to the Rayleigh criterion, two p~ints are considered as separate
if the principal maximum of one of the functions of the type sin v/v coincides
with the first zero of the second function. From this we get an estimate
- of the resolution
~ . ex' ~ x,- y 7iR~/K,Ly . (12)
The given case (usz of Fraunhof~r radio holog~rams) has been ralled the
~ "focused aperture'� in RSA theory. Focusing is understood as compensation
af the quadratic phase advance in equation (5) on the stage of imag~ recon-
struction (compensation is accomplished by transformation (7)).
5 .
- FOR OFFICIAL U~E ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850RQ00500050039-9
~OR OFFl~'_'~~ USE ONLY
The case of the "unfo~used aperture" corresponds to the equation of the
Fourier radio hologram (6). Therefore, Faurier transformation of the function
of the radio hologram is used on the processing stage
~~r/p -iK a /
V(~)- ~ f h(x)e t~~ dx . (13)
-~.T/2
From (13) with consideration of (6) we get ~
11 "Tl
~ Vil~) t~n~[~~~ -`~l~en~ � R, nr~'o~~ ~ 1
r~ (14)
Yl~~~ �(f~~.1~.~+ R' 11,~ xp)~ PT .
0
In the given case the quantity p can be treated as the focal length of the
- Fourier lens. The position of the image of the point ob~ect is detexmined
- bq the equation
~
_ E . ~ c~.. r? + K' n.~ .L o ) . ~ 15 )
- D~ K~1 1 ~ ~p
- The image of the entire scanning strip will also be distorted a~ a con~equence
of the dependence of ~ on range Ro. Evaluation of the resolution according
to the Rayleigh criterion gives
o ~ :x, - x~ _ K~ny'~T . . ~ (16) .

~ The limiting attainable resolution in an RSA with unfocused processing with
consideration of (4) is
e x' = Y~.a
a i 4~ o,%a ti
a`
R. (
,
- It shi~uld be noted that radio holograms are recorded cont~.nuously on photo-
graph:tc film in ~he course of a prolonged flight. Therefore the focused or
unfocusec~ mode is assigned only on the stage of reconstructing the imagE by
select.ing the dimensions of the diaphragm that deteroaines th.e quantity LS/nX,
and tlzrough corresponding design of the optical processing arrangement.
Let us now consider the RSA from'the standpoint of the geometric method de-
veloped in Ref. 8, 9 and assuming a~alysis of the phase structur~e of the radio
holog�ram. For this purpose we rewrite one of the equations (2) in the form
h~y') . q~qoe~s(~r~"~o) , .
where ~o is the, phase of the wave scattered by the ob~ect.
For a point ob~ect situated at point P(Fig. 2), we can write (with consider-
ation of wave propagation from the RSA to the ob~ec~ and back) : ~o = 2x1(PQ- PO)
and ~r =?xl(RQ - RO), where RO = Rr is the distance from the hypothetical source
of the reference wave to the coordinate origin. Expanding �r and ~o in a
6
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R040504050439-9
FOR OFFICIAL US�F O'o1I.Y

J series and limiting ouraelves to firet-order te~rme, ~r~ gnt
~y _ ~ x~4 _ 9 ~ - xr _ ~0 j t1i~1
'~r ~o ~QR~ eR~ RN ~2a ~ '
In the simplest case where xo = 0, xr = 0, Rr =~(plane re~erenr.e ~,~av~ w�~~iout
linear phase advance), we get
4'r' ~o ~ 4~'2~'~/ 2,~~Ro ,
- The spatial frequency of the i.nterference pattern is
a
1111. a~' (YI`~~0~ ~ 2~~ J~ Q ~ \i91
l ~x~ ~ , o
At some value x~r= L~X/2, the frequencyv mtiy exceed the ~eaaluti~n of
the field recorder, ~?hich is determined in the given case by the aczual aper-
ture of the radar set, and is equal to v~r = 1/LR� 7.'f?:~s impliks the cQndition �
L~ma~. ~ ~~~O~~~R a ~/RQp , � ~2~~
Substituting the value ~f L~aX in (12), we get the classical relatio:~ f~~r
maximum attainable resolution in the RSA:
, ~ x~~ = i~s/2 .
Accounting for the pulsed nature of tfie signal enables u:~ *o c~et�'rmirae siae~x
an important parameter of the radar set as the ~dn~lmum va~.ue ~3' the pr.~bing
pulse recurrence rate K~in. Obvfously ~the pu? sed mode :~s az~~logn~s~ to dis-
cretization of the radio hologram. The distance b~tti~~~�i ~.:~s~i~v~.~ual readings
~x' = vg/K must satisfy the condition ~x! ~[2v(x~r) ~rEyer~ce ~aith consider-
ation .of (19) we have
~ Kmin = 2vg/Lg.
~ Following ths known procedure of Ref. 8, 9, we get relations that determine
the deviation of tha phase front of the reconstructed wave from spherical
(third-order wave aberrations)
~ 131 Ke~ D~~ _ D'~3+ DQ~~ (21)
- ~ 04
where
= x` ~ ~ F Z~ ~o x ~
_ DK ' ' n~4-~ 1 Ro R; ~ .
_ x~ and R~ are coordinates of the source of the reconstructing wave, U=~1/a2
m= nXl, and the coordinates of the image of the point ob~ect are
~ _ ~ _ � ~
~ ~ - ~ and ~I = x` � 2=~~ - x'. 1
R~ Q~ ro~ ~ Ro Rr~ RI R~ m~' Ro Rr 1.
7 '
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R400504050039-9
~s
~ FOR OFFIC[AL USE ONLY
e~
~ The value x= 0 corresponds to spherical aberration, x= 1 to cmna, and x= 2 tfl
astigmatism. These relations can be used to calculate the maximum permissible
size of the synthesized aperture LS~X on the basis of the Rayleigh condition
~ (wavE aberrations on the edges of the hologram should not exceed ~2/4). Can-
~ s3.dering that spherical aberrations are the most appreciable in order of magni-
; tude, we ge4:
~
~ 4
L s ~~u~c ' 7~ a~ R o~(1- 4~ � ~ 22 ~
F~r typical conditions of RSA operatinn, the quantity L~ calculated by
~ formula (20) is less than the value calc~alated by formula~22), 3. e. the

- influence of wave aberrations in the RSA is insigrLificant.
~ " 4. ~nfluence of RSA Trajectory Ynstabilities
~ Instability of the vehicle trajectory is ane of the ~a~or factora that distort
the images obtained by the RSA. The holographic Xreatment enables iairly
simpl.e evaluation of permissible deviations of the trajectory from li~.ear
by the method of geomet�ric opttcs. Let us E:Trite the exgres3ia~n for the phase
of the ob~ect wave ~o(x') in the form
. '~o~x')s-?r.,~~(i~o-t~)p+(x'-xp)P~'/~_~o~ ~
a where q= q(x') is dat.sglace.mera~ of the tra~ectory from the x'-axis.
: Ass�.~nin~ tlaat Ro�xo, x' and q, usir.g the binomial expansion and dropping
all t~*_~_^s of the order of q2 and highery we get the follawing approximate
. express:ion far ~ o (x' ) :
~ lx')~- 4^,~' x''~' Q~C~]C' 7~. 4~ox';+~r ~Co x'~ _~09. +~o x;F.- 2s~o xox'
� D.Ro BRo. uo 2Ro
"The equation for the phase of the wave that forms one of the reconstructed
images has the usual form
- . `~1' ~ t~o- `~r) � (23)
On the other hand, the function ~1 can be written as
~ yn ~ x2 - zx~x _ x'~_
~x I ~~c' 4xj x;4 ~ (24)
DRi g Ri �
The phases and ~r are detercriined by expressfons snalogous to (24). The
d~fferences between phases of corresponding third-order terms relative to
1./R1 in (23) and (24) are aberrations equal to
~ p~(s) + ~~*rue
~ Aberrations ~~~3~ are determined by expression (21), and
~
- 8
FOR OFFICIAL U~E ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R000500450039-9
- FOR OF'FICIAL U~E ONLY
A
; Q lSl _ ~`f~ + D x - ~ Q'X'2~ i
- ~rue 3g 6 J ' (25~
i
~ where
~ ! ~ a,?~zo~Ro , Lq=� 2Ju.;o:~o/mRo , Dsa~ fiz~/mPRo
are aberrations due to trs,i,ectory instabilities.
Relatior~ (25) that determines the distorti~ns of the ~hase s~ructure of the
' radio hologram can be used for calculatin~ the compensatin~ phase shift di-
rectlv in the process of synthesis. To da this, it is advisable to use digi-
- tal methods of signal pr~~essing in the RSA.
Applying the Rayleigh criterion to each of the tertns in (25), we get th~ fol-
+ lowing r_ondj.~ions for permis~ible deviations of the vehicle tra~ectory:
d 1~5~1~,~'+' _ /~~{~DiB~Q = l~f~gi.US~O ~ ~~Sj
- ~n jfi ~ ~ ~4 ~~cmas - Ro / 41.; ~p ~o , (27)
` ~j~/4 � { y5~. : ~1~ !a~l.,~ (28~
: ~y~ ~
~
On the other hand, knowing flight conditions and the characteristics of the
- vehicle, we ~an use (26)-(28) to detQ~cnine the ifmitations iffi~~sed on the
~ quantity cos Ao and the li.miting permi�sible dimens~.on ~f Clle synthesiz2c~ a~e.r-
ture:
! cos~io~ .~,~8~ L � ,l t2~ /4~x L~ < R Y,i .
` , timaL ~ ~ o o , ~u~u~ o !
- As a rule, the relations LS�RQ and xo�Ro are satisfied in the RSA. Therefore
the quantities D4 and DS can be disregarded, with account taken only of the
factor D3 which accordirig to (26) imposes severe conditions ori the stability
of i:he ~.ra,jectory.
5. Influence af Motion of th~ Ob~ect of Qbservation
- The effects that arise in the RSA when observing moving o~iects can be evalu-
ated from the ~tandpoint of the :~ethod of physical t~ptics~ Let a~oine ob,~,ect
~ move at law velocity vo i.n the radi~l direction (a~.ang 9:he z-axis~, so that
- �or the ~ime of 5ynthesi~ T the d~~placement of the ob~ec~ does not exceeci
v the resolution with res;~ect to r~nge. In this case, the equation of the radio
_ hologram takes the form (disrega~r~'ing constant phase terms):
: -
Vo ily'1C~ ~y;x:yx w~ fY~ 2 ~ ~
h(~:)tieo~(~xn~z c? 2rc, ~H n,~x- K, -~,p r ZK4 QU R~~ ~H, ~T x`) (29)
Substituting (29) 3n (7), w~ get the following can~.~.itian ot observation of
= a focused image:
~`�~9rc~. .n~~~~_1Y~~,~.~~ ,
x

~
9
~
FO~ ~L~~ICIAL U~~: UNLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
- FOR OFFICIAL USE ~NLY
Since the quantity vo/vg�1, the image will be obaerved practically in the
same plane as for a stationary ob~ect. Conside~ing this fact, and carrying
out the integration, we get a function that describes one of the reconstructed
- images:
- s~nl~i~?Ln~? 2K~~ nx r 2KR nY~.~o- ~1~d~~ ~2T l
N 0
_ V~~) Q~~~t.. . . , u:r
~''',~~1''r~~ n~t ~ ~y�- ni~'~~ z
N ~
- The position of the image is deltermined by the equation
~'o h W 1 Rp * Ro
nl 2K,n r nz v� �
Obviously motion of the object is equ~valent to introducing an additional
carrier frequency on the stage of recording the radio hologram, and it leads
to displacement of the image. The optical proceseor uses the real image that
~ is recorded on photographic f~lm. The f ield of view on this film is limited
by a diaphragm that cuts off background illumination. The quantity vo may
~ reach a value such that the image of the ob~ect will not be registered at
= all because of the si~ifC.
- Motion af the ob3ect in the azimuthal direction (along the x'-axis) with ve-
locity-vo is equivalent to a change in the flight velocity af the vehicle.
= In this case, relation (9) that determines the position of the focused image
along the z-axis can b2 rewritter. a~s
~'_~~,Rui~,lznr s * ~~RuU'~~ /2.~;,lVN-V~)Y .

~ Thus m~tion of the ob~ect along the x'-axia leads to a change in conditions
of focusing by the quantity
_ ~
' = 2~ ,uNl 1 2~H 1 N ~ ~3~~
V
where p is defined by expression (9).
If vo ~vH, then
a
8f'a 2~?Uo/~`N � (31)
- From equation (30) we can get
a
1!~ * l`'W ( r~" S~ f(~ h 80~ ,
J
" On the oc~~r haxzd, f~.flm~t;'e ~im~lest geometric considerations we fiad the fol-
lowing expression fQx reeolutiun af tt?$ RSA along the z-axis (longitudinal
~ resolution):
~ ~~�').,Ga:~v~)`/~p~J'H m 4t(.ax')~/~2"c � (32)
~ 10
- r r
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FGR OFFICIAL USE ONLY
The depth of focusing Op is defined as displace.ment ~ram the focal plane along
the z-axis by a distance for which the azimutrsl resolution Ax' detrriorates
to half as c~mpared with the diffraction limit (12).
To observe a focused image of an ob~ect moving at velocitq vo, additional
�o~using of tne optical processor is necessary. T':~e E~elocities of the object
at which focusing is ne~essar3r we get from the conditiaa Ap < bp, where dp is
assigned by (31). Using (9) and (32), we get
tio>Q(ex'~i~N/a~R~ .
At lower velocities of mation of the ob~ect, refocusing nf the processor is
not required, and deterioration of image quality can be considered insigni~i-
cant.
- 6. Conclusion
To describe the working principles of the RSA, in addition to known ncethods
[Ref. 1, 2J that have.been extensively used heretofore, a holographic approach
can be used that represents the RSA and the optical proceasor as ~n integral
unit. The given examples confirm the phys~cal clarity and fruitfulness of
the proposed approach for analyzing the RSA.
REFE~ENCES
1. Reutov, A. P., Mikhaylov, B. A., Kondratenkov, G. S., Boyko, V.,
"Radiolokatsioninyye stantsii bokovoga obzora" [Side-Looking Radar], Moscow,
"Sov. radio", 1970.
2. R. 0. Harger, "Synthetic Aperture kadar Systems, Theory and Deaign",
Ac. Press, N. Y., 1970, pp 18-58.
- 3. Leith,TIIER, Vol 59, No 9, 1971, pp 25-44.
4. Leith, E., Ingalls, M., APPL. OPTICS, Vol 7, No 3, 1968, pp 539-544.
S. Kock, W. E., "Recent Developments ir Holography", PROGR. ELECTRO-0PT.,
- REV. RECENT DEV., 1975, pp 45-66.
6. Popov, S. A., Rozanov, B. A., Zinov'yev, Yu. S., Pasmurov, A. Ya., "Sb.
Materialy VIII Vsesoyuznoy shkoly po golografii" ~Collected Materials
_ of the Eighth All-Union School on Holography], Leningrad, 1976, pp 275-286.
7. A. Papulis, "Teoriya sistem i preobrazovaniy v optike" [Theory of Systems
_ and Transformations in Optics], Moscow, "Mir", 1971.
8. ~ieier, R. W., JOSA, Vol 55, No 7, 1965, pp 9$7-991.
9. Champagne, E. B., JOSA, Vol 57, No 1, 1967, pp 51-55.
11
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R040500050039-9
' FOR ORFICIAL USE ONLY
_ UDC 621.391.2b6
EQUAL OBSERVATION PRINCIPLE A1~D ECONOMIC ALGOYtIT@'IS FOR SIGN~lI. PROCESSING
IN QUASI-flOLOGRAPHIC PUI.SE-DOPPLER SYSTEM.S
~Article by B. S. Mush]
[TextJ p.n equation is given that relates the signal of a
qua~i-holographic puls~-Doppler sqstem to a function that
describes reflective surface properties. This is called
the principal equation. An equal observatioa p~inciple is
~ introduced that minimizes uncertainty in evaluating the
reflective surface function that arises in "solving the
principal equation. Algorithms are considered for solving
- the principal equation by a direct method and by the method
of fast Fourier transforms to calculate correlation sums,
and the effi.ciency of these algorithms is evaluated with
respect to a criterion of the minimum number of operationa
per unit area of the sur.face being evaluated with consider-
ation of the equal observation principle. Tt is shown that
there is an optimu~ ratio of sides of the correlation matrix.
i'h~ concept of the quasi-holographic pulse-Doppler sy~tem was qualitatively
introduced in Ref. 1. The signal S(t) at its input can be repreaented as
an integral equation of the first kind with a difference kernel and unknowa
~ reflective surface function:
~ ~(s(X(f~ -~:~K(yltl ~-J~ ~~~;~~nrr~~ t s,~E~.t
~A2~;~f
1.~~~ /
' ~ (~J � 5~(~ ~ � ,~~t~}, .
~c ~ i~rLhe wavelength the system,
. Kr (~r~ =~'r.t~~ylt~~ . eX~~-c~ Z~l~~ ~
X ~ ~ ~r
~'j ' ~a~i~ 2~;( tl;
, ~ .
~~~i ' ~ = yCf j Y ~t
- :~(~~'l-4~,Gj ~ ~~,~Zr
, / ~~2 2 ( ~J ) ~ ..~1 1'-~ ,
/ ?
- Q(t) is a complex function that chara~terizes the sraFs o� the ~m~.tted signal;
X(t), Y(t), Z(t) are the pro~ections of the radius-vector of the phase center
of the antenna on the x, y, z axes of the coosdinate system fixed to the sur-
face on which the region [LoX. Lay] of definition of �(x,y) is assigned, the
y-axis being collinear with the ray corresponding to the maximum of the an-
tenna radiation pattern G(x,y,z), and
_ i~) = C~ ~ X ~t` ~
~ ~ ~ ~
12
FOR AFF[CIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050Q39-9
FOR OFF7CIAL USE ONLY
.
The initial equation, ~hich will hereafter be called the principal equat~on,
can be represented ~s a system af two ha~aogeneous difference eqyations:
i K~ ( y`(tl (t/' S'(f '
~ ~ ~
~ -
K~ ( Xlf~_x~ . ~'~x,~~ ~I.~~ _ ~
Systematic solution of this equation leada to finding the reflective surface
function a procedure corresponding to the mai*~ ~ob of the radio-holographic
- system.
To an~lyze the problem of synthesizing economic algoritt~s for solving the
- principal equation, it is sufficient to consider a procedure for solving
either of th~ equations of this sqstem. To be specific, our further analqr~is
will applq to the firat eq~aation, and we will omit the subscript y in denoting
the inte~~val of evaluation af the reflective sur�ace function.
In actual systems, the si$nal is measured on the finite interval Lr over whlch
the estimate of the reflective surface function is defiaed on some interval
Lo. If the interval of surface coverage LG is commensurate with Lr, then ~
a contradictory situation muat be considered: either the reflective surface
_ function is e�~aluated from signals generated by a reflective surface function
with region af definition much greater than Lo, or the time o~ observation
of elements of the reflective surface function on interval Lp is inconstant.
Both ~actors cauae uncertainty in estimating reflective surface functions
when solving the principal equation. In connection with the given signal
formation property due to the structure, of the kernel of the principal equa-
tion, we formulate the equal observation principle: when solving the princi-
pal equat~on with respect to signals assigned on a fixed interval of observa-
tian Lr,the intervals of estiwation of the reflective surface function Lo must
be selected such that all ita infinitesimal elements are observed for an equal
time.
Calculation of the estimate f of the reflective surface function by means of
the kernel R of the inverse transform causcs considerable difficulties that
are associated with r.he necessity of carrying out a large nwnber of aritlmmetic
operations for computing correlation sums of the form
~ N-
~ s ~ R~~ . s�
/1~O
~ ' ci~
f~-.~~
where fK and Sn are discrete readings of the functions f(x) and S(X).
Inthe di-ect method of calculating fK, 2NP multiplications and additions
must be carried out. Use of the method af generalized Fourier transforms
enables us to apply effective fast Fourier transform methods [Ref. 2). Let
us consider estimates of fK obtained by the method of fast Fourier transforms.
13
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R400500050039-9
FOR 4F~[C[AL USE ONLY
Let P~ N. Then asswaing periodici~y R(n) ~?ith period N
_ ' -1I a ~N~' ~M~.
where S3(N) and R~~(N) are generalized Fourier traasiorms of Sn and 8(n) on
the interval 0, 1, N- i with peri~d N, and F- is the inverse gener-
= alized Fourier transform. In the followiag, we will limit ours~lves eo the
use of fast Four3er traasforms to the base 2. ~'hen to calculate fx it is
necessary to perform (3 log2 N+ 2)N arithmetie and logic operations (3N l0$2 N
~n calculating the fast Fourier transforms, N in ffiultiplqing spectra, and N
- in transposition of data).
Let P> N. Then the assumption of periodicity R(n) with period N is r..flt per-
- missible. Let us turn *_o a widelq used methodt we write sum (1) as ~
_ ~ ~l
f ' ~2~~-nJ St,,
-o
S� ? if o~ n, N-1
_ o , ~.f ~-aN, .
n,~ ~ o, . /7-.~.
Now the assumption of pe~iodicity R(n) witti~period P ie permissible. Then we
have � ~ ~ .
~ ~ ~
F~`l~ ~P~.~; ~~>>l, ~
~
from which it follows that to calculate aum (1) it is necessary to carry out ~
P(31o$2 P~ 2) opera~ions. ~
The given formulas for calculating the number of operations still do not de-
termine the economy of one method or another. The formal index A that charac-
- terizes the economy of a method is the number of operations per unit of area
of the surface to be evaluated.
The indices obtained above for the ninnber of operations must be normalized
to a quantity proportional to Lo. According to the equal observation princi-
- ple, the quantity Lo is related to Lr, viz.:
' b L -L c2~
Ln F .
~ Using the notation P/N ~ T, we write
40 "rLr,
x~hence
_ ~ ~ zu -t_ , ~
, , f~ c ~
14
~ FOR OFFICIAL USE ONLY ~ '
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFiCIAL USE ONLY
where L~~~ is the width of the m-th Fresael zone, equal to
!m) ~ ~1
L,,~, _ ,Zn7-.c ~.~.n,
and u is the number of the Fresnel z~on.e correspoading to the edge of the rs3i~
ation pattem.
In accordance with the condition of impermiseibility of freq.uency super-
position [Ref. 3], the number of readings N on internal Lr must satisfy the
~ inequality
~ l~r ~4~
where dK is the discretization step eque?1 to 2~- 2~) .
Based on formulas (2), (3) and (4), we 'have
1~1~-1
2(~ ~5~
? ,
f� = '
_
The resultant formula is a generalization to the case e# 0 of the well known
rule of complex signal theorq: the product of the signal band (denominator
in (5) B. M.) multiplied by its duratiQn (numerator ia (5) B. M.) ie~
equal to the number of readinga of the dis~retized signal [Ref. 2], which
- is valid only for E a 0.
It can be proved that
_ /
~
~n~ (e~r'~r-~' " r ~ u
y ~ 2cl - f -1~-
- From this, using (3) and (5), we get the asymptotic equality
'V ~i` ~
i
r ~~~~f~
j `'j�~, ~6~
or
//1 !/1
L,=~~~,~�N
Then
.l .
~~p � d~lr P'~~ for the direct method, ~
_ 15
- FOR OFF[CIAL fJSE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R400500050039-9
- FOR OFF7CIAL USE ONLY
! . ~.~(~>t Y~3t~ ~-~1 if lL.i ~
' c / f or the method of
~'1' fast Fcurier trans-
~~i ' '~~~fZ ~~~L~~rN~.x) ~ ig 1-~1 forms
L~,~ . .
~ ' Fig. 1. N~ber of operations A
t~N
per unit of aurface as a function
: af the number of readings on the
' '~i~ ~ interval Lr of signal observation
~ =1: . : / -
- i with use of the direct method (1)
y ~:j~ ~ ~ and the fast Fouries transform
~ + ~ I method (2) for values of T ~ 1 /N
/ _j- 1 ( ) and ~.0
' i _
/ ~
. ~
. .
- i~ ~
y .i a f fii0
17 ~~yy~'~
7
The resultant relations imply (Fig. 1) that when usiag systema with one or
a few readinge (Lo= 0) the direct method is preferable, the advanr_age of the
. method of fast Fourier tranaforms increasing with N. When a many-reading .
~ syst~m is used, beginning at some value T? 1/N, the fast Fourier transform �
method has the advantage o~ver the direct method at any values of N. Analysis
of the relation A ~ f(T) shows that when T~ 1, the method of fas~ Fourier trans-
forms gives the ma.~cim~um gain compared with the direct method for any N(Fig.
2). ~
. . . .
r - ~
oi .
W
( ? ~
3I 1
. 1 . ~
z ,
t
,
0 3 y . Lo~~ ~
Fig. 2. Number of operations A per unit of area as a func-
tion of the ratio L/Lr for N ~ 32 when uaing the direct ~
method (1) and t~a ~~st Fourier tranaform method (2)
. 16 ~
FOR OFFICIAL US~ ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R040504050439-9
_ > ~
. . +~~..a:.,~
~ FOR OFF[CIAL USE ONLY
In the case of limited procassiag intervals considerably emalZer than LG,
2X-stage signal processing can be used [Ref. 4] in which so-called preweighted
- accumulation on the first stage limits ~he baad of the signal S(t), and tl~
main processing is done on the second stage. Such a structure reduces require-
meats for speed of proceseor devices. In this case the considerations given
above concerning A are suitable for each of the processing stages individuallq.
Let us analqze the necessary productivity ~i for 2~-stage processing. On the
first stage, the parameter T= 1/Nnp (Nnp is the nunber of readinga of the
input signal) is small, and consequentlq on the first stage the dir~ect method
has an obvious advantage over the method of fast Fourier transforms. Oa the
second stage the parameter T s P/vL (vL is th~ number of signal readings at
the input of the second stage). On the whole, the productivitq A for the
= 2X-stage processing can be written as
� ~ _ + f~ iZ~
where A~1~ and A~2~ are the numbers of operations on the first and second
_ processing stages per unit of area of the reflective surface function to be
- eval.uated. Based on the above discussion, we can write for the direct method:
~ ~~~z
n i~1
Analysis of these functions ehows the presence of an optimum for the function
A= f(T) at fixed values of L and L31~. Calculations shaw that for different
values of these parameters t~e quant~ty T may differ considerably from 1,
and the gain from using the fast Fourier transform method becomes less pro-
nounced than for one-stage processing. Thus the selection of the method of �
calculating correlation sums mu~t be accompsnied by computation of x in each
specific case.
I thank L. S. A1'tman for conatructive discussion of the matters considered
in this paper.
17
F`~H~ OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFF[CiAL USE ONLY
REFERENCES
~ 1. Leith, "Quasi-Holograpnic M~ethods in Microwave Band" in: "Primeneniye ~
golografii [Osi~~ Hologr~phy], edited by J. Goodman, Moscaw, "Mir", 1973.
- 2. Rabiner, L., Gold, B., "Teoriqa i prints{pp tsifrovoy obrabotki sigaalov~~
[Theorq and Principles of Digital Signal Processing], Moacow, "Mir", 1978.
- 3. Hamneing. R. W., "Chislennyye metody" [Numerical Methods), Moscow, "Nauka",
" 196~. ~
Brown, W.~M., Aouser, G. G., Jenkfas, R. E., "S}mthetic Aperture Process-
- ing with ~i~i.ted Storage and Presumming", IEEE TRANSACTIONS ON AEROSPACE
- A~1D ELECTRONIC SYSTEMS, Vol AES-9, No 2, March, 1973.
UDC 21.391.266 ~
SYNTHESIZING QUASI-HOLOGRAPHIC SYSTEM ADAPTIVE TO REFLECTING SURFACE
[Article by B. S. Mush] .
(Text] The paper notes difficulties ia practical realiza-
tion of optimum methods of solving the principal equation ~
- of a quasi-holographic aystem that are related to a~sence
of a priori data and in large measure are eliminated when
algorithms~are used that are adaptive to a reflective sur-
face function. The principal equ$tiqn of a pulse-Doppler
quasi-holographic o,yetem is given with its.optimum solution
in the~sense of the minimum rms deviation of the estimate
of the reflective surface function from ita exact value.
. An algorithm is described that is adaptive to the operator's
, ~signal when the structure of the operator is identical to
~ that of an optimum operator and realizes an iterative pro- .
, cedure of succesaive approximations. The article presents
the proof of convergence of the iterative procedure and
gives the resulta of a numerical experiment on atudying
effectiveness of the conatructed adaptive algorithm.
Optimum methoda of solving the principal equation of ~ Quasi-holograpnic sys-
tem [Ref. 1, 2J, despite all their advantageous properties in the sense of
estimation of the reflective surface �unction f, cannot be realized in cover-
_ ing real surfaces, since in moat casea even the energy spectra of the reflec-
tive surface function are a priori unknown. However, optimum operators enable
_ us on the one hand to synthesize auboptimum and adaptive algorithms that im-
prove the estimate of the reflective aurface function by "signal tuning",
and on the other hand to evaluate the quality of these algorittm~s ~aith respect
to the degr~e that the estimate approximates the optimian. The problem of
constructing an adaptivQ algoi:ithm should be conaidered solved if "we manage
to construct algorithms... that use only realizationa accessible to measure-
ment" [Ref. 3].
18
- FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00854R000500450039-9
.
~,.,~t,.
FOR OF'Fi~i~,~. USE OI~dLY
1'aking our lead from Ref. 2, wP write the principal equation as
d .
JK~/~~t~-.~ ~iz,~~~z = .S'~E~�~x~.z~~ JCtJf/Z~EJ~ (i)
_ ~
_ where S(t) is the signal at the input of the antenna syatem,
1. ~ t
x1- /
k~ G~y~r~ ~~'X'-~~~~t~~
X(t) and Y(t) are pro3ections of the tra~ectory of the phase center of the
radiating and reception systems with polar pattern G(x/y(t)) on the x and
y axes of the coordinate system fixed to th~ reflecting surface, k= 2~/J1,
? is the wavelength of the system, n(t) are noises of the system, y= 26 + y(t),
0= t- Tn, Tn is the repetition period, and n is the probe number.
In the following we will examine equation (1) as an integral equation of the
first kind, and treat its ~aolution as a formalized target of a quasi-holo-
graphic system.
The optimum estimate f of the reflective surface function can bQ found by
using the Wiener-Kol~ogorov operator with kernel Ro~,~ [~ef. 2, 4]:
- f(a~'~= ~~o~~ f~~-X1� s(~f)� e~~,~~k JCf~~f~
~~r~
where
LJ ~L r~ ~ _
R
-
_ R` ,t - J, ~ Z P x,~ :t~ ~ ,
r _~.~/~~~IK~~)1 ~ ~
/
S(p) = N(p)/If(p)~2, N(p) :is the energy spectrum of n(t), T is the processing
period, the symbols and denote the Fourier transform and the complex
- con~ugate respectively, or in the form of the spectrum of t~e estimate
~ ~r ( ~ .r
~'s~f>> ~2>
~
where vopt is the optimum value of the Tikhonov stabilizing factor [Ref. 4]
which is equal to ti
~)c ~ ~ ~ = ( JTt
,-~v n ~ ~ ~
~ N~~l +~~j~~it I Kl )it ' ~3'
P
A special case of the optimum operator when S(p) �MaxIR(p)I is an ~perator of
the type "matched to a point obJect":
v~
~
R~x~^~ Jk ~'x~~~x'~~~ . (4)
~
19
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
I
FOR {DFFICIAL i1SE ONLY ;
!
~
~ i
Let us now consider the structure of an adaptive operator. Let us have a `
zero appr~o~simation of the estimate of the ref lective �.urface function f o(x) ~
rhat can be obtain~d by an operator thgt does not depend on the reflective ;
- surface funcrion or noise, e. g. of type (4). Let us call the function fn(x) '
the estimate of the reflective surface function in the n-th approximation. ;
The Fourier transform of this fimction takes the form '
_ ~ ~ur'S~ } l,~�-~~2�~~~ ~ ~
lP) s =N, * , . .s~P~, c5>
K C/~ ) c~~ n., lK(~)1 .
where vopt is obta:!ned from formula (3) by replacing ~f~ by its (n - 1)-th
approximation, and n~ 0, 1, 2,... This formula, combined with the formula
that assigns fo, describes the iteration procedure. Let us prove existence
of convergence of the sequence to a limit that in the senae of rms deviation
is closer to ~ than any estimate fn at least at a sufficiently low noise
level.*
- We assume that
~ _ x
. S ~
then
' ^ y'~~ .2
_ ~ _ I~CI�f~f � ~S ~ ti
�s
~ + 1 /1/+ ~y~' ~S IZ
Let us consider the positive defintte function
~ ~ ,%o'
_ ~o.~~s=~-~---~+j-.
= If 0o,1(p)> 1, the first-approximation estimate of the reflective surface func-
tion on the interval of assignment of spatial frequencies p gives a gain in the
sense of rms deviation as compared with the zero-approximation estimate.
x
We can see from the expressions f or fo and fl that
/ I - ~K ~2
_ . e~ , - '
_--~y , , ,
~
~f ~ ~ ' ~.S ~
which implies that the function 00 ~ 1(p) ~ as N-~ 0.
Analogous arguments are valid for an arbitrary function On_1, n. Consequent-
iy, at least for a aufficiently law noise level, the n-th estimate of the
reflectiv~ surface fanction gives a gain compared with the (n - 1)-th estimate.
*An operator of type (4) is optimum at high noise level.
20
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPR~VED F~R RELEASE: 20Q7/02/09: CIA-RDP82-Q0850R000500050039-9
FOR OFFICiAL USE ONLY .
To v~rify the conclusions drawn above, a computational expsriment was done.
- The conditions of the experiment consisted in asaigning tiie reflective surface
function as a data file of camplex numbers f(R,) = 0, 1, N-1 wtth Ray-
leigh distribution of the modulus and uniform distribution of the phase on
- interval [ F~~ The signal was formed in accordance with equation (1). The
estimate fn(R) of the reflective surface function was calculated from formulag
(2) and (5). Quantitatively, the quality of the eatimate was defined by the
quantity B calculated from the formula
~-~`n~ s l~ ~ 1 _ ~~n~~) ~~~~t
. .oIN,~~P ~fnp. ~
where 05B51.
The function n(t) in (1) wa3 s:~.masla~ed by an uncorrelated nianber sequence,
and the noise level was assigned ~y the quantity Y:
~ ~ l l1_ ll~` ~~`')l` ,
,1/(/~)

~ where the symbol denotes averaging of the sample.
~3 - -
_ ~
-
B~t
~r
0 1 t ~J 4 /Z ~
Normalized rm~ deviation of the estimate of the ref lective
- surface function as dependent on the number n of ttz~ step
in the iterative procedure Qf the adaptive algori~hm
The figure shows the reaults of the experiment for ~y= 100. The expPriment
demonstrated convergence of the procedure~ described above, in which there
is an appreciable gain in quality of the estimat~ c~f the retlective surface
_ function up to the fourth step of the iteratiori.
I thank Yu. V. Kuznetsova and I. V. Garina for their contributfon in doing
the experiment. .
. 21
- FOR OFFICfiAL USE 41`dLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL US~ ONT.Y
REFERENCES
~ 1. Kondratenkov, G. S., "S;~n9:hesizing an Optimian M~ethod of Processing Radio
Hologra~s", RADIOTEKHIJIKA, Vol 33, No 5, 1978.
Mush, B. S., "Synthesizin~ Artificial Aperture fo-r ?~'c~cowave Radio Holr~-
grams Reflected from the Surface of the Sea", RADIO~EKHN7KA I ELEKTRONIKA,
Vol 25, No 7, 1980.
3. Tsipkin, Ya. Z., "Osnovy teorii obuchayushchikhsya sisi:em" (Principles
~ of the Theory of Learning Systems], Moscow, "Nauka", 1970.
4. Tikhonov, A. N. , Arsenin, V. ~ A. ,"Metody . reshen~.ya nekoxr.ektny~l~h za~ac~-~"
~ [Methods of Solving Incorrect ProbleMS], Moscow, "l~aulca", 1974.
~ ~ Uri~ 621.396.67.001.24:778.38
~ DETERMINING INTERCOUPLING OF SPATIALLY CON~ INED ANTENNAS BY RADIO HOLOGRAPHY
r METHODS
~ [Article by R. A. Orlov]
(Text] A method is considpred for determin~ng the mutual
- iumnittance between two spatially comb3ned reciprocal antennas.
The ~nethod is based on using radio holograms recorded an
- a closed ~e~ere.nce surface covering the intecact3.ng atnennas.
A basis is proposed for describing the radio holograms with
arbitrary distan~e of a spheric.al refere:.ir.e surface from
the antenna ~.o be analyzed. A solution is given for the
problem c.~f f inding the imanittance of two collinear dipole
antennas.
Finding the mutu~l coupling between antennas that are spatially combine3 in
the limat~ of a singl.e radio engineering compl~x, or batween elemznts of the
same antenna system is a problem of considerabl~ current intere:,t bath for
analyzing electromagnetic compatibility and in ~he design of complex antenna
facilities. ~n exaiaination of the voluminaus researc~~ devoted to solution
- of this problem shok=~ that tb.e measure of intercou~pling in all these c~ses
- is the mutual impedance determined by various methods, inc]_ud~ng the znethod
of iiiduced emf's [Ref. 1], the method of the angular spectrum of plane caaves
[Ref. 2], etc. However, all these methcds n~~zne ~ssentlal use of thF structure
of the interactirig anten~as, which at times is a severe impedimEnt to solution
of the formulated problem, especially when it invoives antennas of different
- types. A way out of this situation might be to use a method of analyzing
= intercoupling relying only on the distribution of the electromagnetic fieid
set up by the antennas being stu.dt~d fln some surface in the vicinity of the
facility on which they are iz~st~lled, a method that utilizes radio holr~--
grams of the ~ields c~f zadiation of the antennas. The re�erence surface ma~t
$ be situated in the near zone of the antenna system to be analyzed, and the
algorith~ �ox calculating mutual impedance must enable simple and effective
use of computers.
a
~ '
~ 2~
FOR OrFICIAL Li~~: ~3I~iL.Y
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-00850R000500054439-9
FOR OFFICIAL USE ONIL`~
These requirements are mas~ simply realized if the analysis of intercoupling
uses a 1a*,~ of. cons~r~,�ation of electromagnetic energy in the space that con-
~ tains the interacting antennas [Ref. 3j. This Iaw can be w~r~~t~n as
g - - -
( a`
8 ~~~~[~K.~-1;],r~)d5 + S(~K aEr+ HK ai'`~c;tv~+ S(IK,E~)~~v ~ G,
~~K~i S v K/f
~ where Ei,k~ ~i,k are fields set up by antennas "i" a.~u "k" at an arbitrary
- point of the volume V bounded by surface S; ~ is the rsni~ ~uter normal to
surface S; ik are the currents in the antennas; N is the ~L~e~ of interactiz~g
= antennas. Zhe surf~r,e integral in the braces in (1) def~,r~es the flow of
ener-
- gy from alI sources to the surrounding space, and. ~he volume integral defir.~s
the total er.ergy of the overall electromagnetic fie~~ star~d in V. The last
_ term characterizes the balance of the powers in ear_h of the interacting an-
tennas as deterraifled by th~e power fed to the antenna from th~ oscillator,
and the sum of the partial paw~rs induced in this a.~efira by a17. other radi-
ators.
J Let us assume for ttie sake of simplicity that the interacting antenn~s are
= located in fr~e space, and that the radiate~i fields ar2 ~onochr~matic and
~ are lir~ear functions of th~ir generatea ci;rrent distributions. Then, repre--
- senting the values of the powers in eact: radiator as the product of currents
Ik multipZied by th.e equiva~er.t applied vo~tages Uk (comprised of the excita-
i tion voltages and the sum of the induced emf's), writin~ the system of equa-
ti~ns for the currents in r.,ie antennas with consideratio~~ af their mutual
impedances, where thQ eorre;~ponding Uk are :tn th~ ~econd m?~b~r~ af these
= equations, and solving this system with re.sp~:ct to impedances, we get the
following expression for the mutual impedance of an arbitrary pair of radia-
~ tors:
Md ~ '~t~) Z ci1 ~
. +
~K ~K ~K
4 ~
~ ~j ~ - z ~ ~ ~ ~~~,H~ ~ ~ ~EK,H; ];,h ) d$ % ~2>
c~~ ~w ' ~ ` ~ ' 1
~~K = ~ S 3 ~E~,~K (~�LK} i (F~;,HK ) - (H,,~~~ d~;
~
i where the pr:~mes denot~ fields set up by antennas in which the currenC dis-
tributior. is normalized to unity.
~ An examination of expressions shows that radio hologranhic information
can be used only to find the ca*nponent z~~~ detPx~mined by distributions of
" the fields of radiation of t?~.e antennas over the su:~�a~e S that encompasses
these antennas. Moreover, ~e can readily see that to get this comnonPnt it
is sufficient to integrate the radio ho1.GgI'ont obta:~ned hy using the fi~ld
� distribution of the otlier interacting antenna as a reference s~gnal. How~ver,
there are considerable difficulties involved in ~irectly prc~duci:ng such radie
~ holograms, and it is preferable in this problem to use holographic infonaation

~ in the form of distributions of the amplitude and phase of the field of radi-
ation of each of the antennas individually. Such information also enables us
23
~
FOR OFFIC[AL USE ONLY
~
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR Q~FfiICt~?1L ~JSE ONLY
to find the parameters of the azite~nas with consideratic~n of their interaction
and conforms to present-day methods of r~r.or~iing holograms ~n ~the radio wave
band.
y
Seque~~ial registration of radio halograms assiunes storage of data files on
amplitude, phase and polaxizati~a of the field over the entire ~~irface S,
i. e. a large volnme of operating computer memory, a requirement that in-
. creases with increasing ~al�.ia betwee~ the li.near. dimensions of the investi-
gated antenna system and the wavelengt~: af the radiated field, and involves
a cumbersome procedure o� successive ca~putations with the use of these data
files. Th.erefore when finding z~k~ it is desirable to use a method of field
p representation that sharply r~duces th~ ~a~ume of stored information while
retaining data about the radio ~ialogran on the entire surface S and to de-
~ scribe the fi.el.d distrit~ution at an arb~tra~y distance from the antennas (~.n-
cluding ir_ the near zone), which carresponda to conditions of radio hologram
registratio~z on measurement stands.
0
The simplest closed surface is that of a sphere; when such a surface is used
- as S, we can represent the a~agliphase distribution of the field on S as an
_ expansion with respect to spherical vector wave functions [Ref. 4]:
~K ~ ~ L, ~ ~e~.,~'`~xt~.,~e,V'~ � k rn{ L ~e~.,~~~xtM~8~~~1~~ %
- ~ed (3)
EK = ~ ~ k [ ~er.,~"~ x~� (B,~)~+ 9e~.~~")Xe,�(o,~;~;
~ e�o M��c
where
- X~~ � ~~e ~ ~ ~~jf~. ;8,~) ? 1.~ - - ; [r. Q:1
is a vector differential operator; Y~m(0;~) are scalar sp~.erieaZ harmonics
~ that take the form
~/e
M (P
~~'m~~'~~ L G,flA'~ tC~ ~in~~ ] ~e ~C.OS~J,~'~P~l
Outside of the sources, the radial functions can be written in the form
` (4~
(r) ? (a~(Q,?~,~ht~(kr~ ; ~1~.~~~ ~ Q?~~P.~n) ~i~~(k~~~
~M
where h~l~(kr) are spheri~a~ Hankel functions, and the coef.ficients ag(k,m)
and aM(k,m) in the generai ::ase are defined by the following formulas:
~ : �
~ p~~Q~~�~.. 4Tk ~ ryt?~(0,~4){P dr~",~c~h~~~+
~ i �(C� J
.f
i j'~ jt (kr~ - i.~' o~iv ~ t~~l"~l~ J~~kr/ ~ O~V~:
� ~ J (5)
4pkt ~ '
Aa(P,?�) = r--=~ S "~eM~~+~~f~{div(c rr".I])~~(kr)F
. ;ye~e,~)
t divM dr ~'`,Je ~ kr)~ _ kt (N1"l~~elk~) ~ dv'
24
FOR OFFICIAL USE ONLY

~
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R400504050039-9
FOR OFF[C[AL USE ONLY
ia which ~~(kr) are spherical Bessel functions of the firet kind, integration
is casried out only over the regioa that cont~ins the sources, aad M denotes
magneti.c current ~ensity. In practice, these eupreesions are considerably
simplified since M- 0, and the charges aad currents are related bq the equa-
tion of continuity.
The given expansions are valid at an arbitrarq distance from sources of radia-
tian with the excepti~n of a sphere of miaimum radius that contains the system
of interacting antennas and is determined by the maximYm4 overall ditn~naions
of this system. Thus, assinning that the surface S has the form of a sphere
of radius R, substituting (3) in (2) and considering the absolute convergence
of thp series with respect to vector spherical harmonics, as well as the con-
~ ditions of orthogonality for these series and the fact that the normal ~ coin-
cides wi~th the radial unit vector ~o of tYie spherical coordinate ~ystem, we
_ find
`Q: o. t ~ * ~ ~ i �
' 2k Q~ ~ a r9rr~. 9u~, - 9~eM 5i~~, +
~ i~ ~ + i oi9 eM
~
t ~KHw ~l~n~ ~i~w~, ~kf~n ~k~ dF IrsQ ~6~
- ~ t d9itMl ,t' df ~e~,~ d~e~.I
~ n. R Jit�. 01 r r� a tcw ~ r.p
Now Iet us consider the contribution made by the real and imaginarq,components
to the quantity z~k~. To do thie, we will assume that the surface S is situ-
= ated rather far away (radius R is large) and we will use an asymptotic repre-
- sentation for the spherical Hankel function at large values of the argument.
Then we get the expression
lt)~ T~~r i 1~. r~ ~ ~
~1M @
fk L~ ~QKN QIN ~ AKti Q~M ~ Qi~ AR~ ~ Q~
~ q~~ t
e'�'"'' (7)
i kR LQ~'QIM - Q?1~QfM f Qt~ ~f� Q1~ Qk~ ~ i.
from which we can see that the component of mutual impedance z~~ in the gen-
eral case has a reactive comp~nent th~t approaches zera as radius R~ncreases.
Carrying out an analoguus study o~; the other part of the mutual impedance
that differs only in the fact that integration in this case is carried out
over the spa~e external to a sphere of large radius, we can establish the
purely reactive nature of component z~k~.
Thue, radio holographic information enables direct determination only of the
resistive component of mutual impedance between spatially combined gntennas.
Let us deal briefly with finding the reactive component of mu~ual impedance
Im zik. Here as a rule we use indirect methods based on utilizing additional
informati.on concerninR the resistive camponent of mutual i~tittance, and name-
Iy the way that Re zik depends on electrj.cal distance between antennas or on
frequency.
- 25
- FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R400504050039-9
FOR OF'F[CIAL USE ONLY ~
The firat such method makea use of the fact that the dependen~e ,f R~e Z~ on
spatial separation of the antennas is oscillatorq and vanishes at val~es of
the phase of zi~ equal to _-n /2 - a(k - 1) [Ref . 5]. Taking these points
as nodes of interpolation, we can find the phase functioa of mutual iwpedance,
the modulus of ziy~ and then Im z~. At small distaaces between antennas, the
phasc fuac~ion is determined by extrapolation only to the middle of the '~ain
lobe" of the fun~zion Re zi~, since in a close approach the inductive and atat-
- ic fields of the anteanas begin to make the major contribution to the reactive
camponen~ of zik�
The second method use~ the frequency dependence of the resistive component
of mutual impedaace Re z~(w) . While a aimilar approach was suggeat~d in Ref.
3, the method considered there for determining the frequency dependence of
the Green's function and subaequent sw~ation with consideratioa of the dis-
tribu~ions of currents and charges as well as the configuration of ~he an-
tennas to get the complete reactive component of z~ ia rather awkward and
complicated. Besides, it is completely unsuitabl.e if we are ueing onlq radio
holographic in~ormation. Therefore when finding Im zi it is advisable to
use direct reconstruction of this component from the ~ependence Re zi~(~) based
on algorithms available in the literature [Ref. 6]. The resultant error due
to the fact that in the general case the systean of interacting antennas is
not a minimal-phase sqstem in view of tr.~ presence of multiple scattering
is a small error, and the accuracy obtained iaa any event is no poorer than
in ~he method of induced emf's that accounts for only one-time interactions.
In conclusion, we give a solution for the problem of determining mutual im-
, pedances of two thin dipoles of arbitrary length. Let the antennas be situ-
ated on segments z 6[a, b], z E[-a, bJ of the z-axis, and let them have
- small gaps in the center.for excitation. We take the current dietribution
to be the same in the antenna systems, and we assume that this diatribution
is described by an even functi.on of z and vanishes on the ends of the antenna.
Since the currents are radi~l, 0, and all co~.ponents of magnetic multi-
poles are equal to zero. The current densi~y appearing in expression (5)
is determined in sphericgl coordinates for r E[a, ~bJ, and in the case of haY-
monic time dependence, it can be.written as
_ to ~
I~~~ ~r~ * ZTrs I+.~ ~`~CO~6 i d, t~P iw~;, ~8)
where d is the Dirac delta function. Determining the char,ge distirbution
on the basis af the equation of continuity, and calculating t~e integrals
appearing in (5) over 6 and we find as already noted in Ref. 4 that for
such antennas only multipolea with indices m ~ 0 are excited. To calculate
the radial integral we muat know the current distribution along the antenna
nor~nalized to the maximum. Considering that thia distribution can be
repreaented ae a Fourier expanaion, and for the sake af aimplicity taking
I1,2(r) as coincident with only one apatial harmonic of the expansion, the
_ remaining integral can be computed fairly easily, yielding
(9)
--Q, `e,o, e ck r 4~Pti; ~'~'~k~Q.b~~c ~~(c1�b)~- ~Q~~(ka)- kb~~(~b)},
~
26
FOR OF'FICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R000500450039-9
FOR OFF[CIAL USE ONLY
- The general expression for the activs component of mutual impedance in +the
given case takes the form:
I/t ~i 7
R,~ = k~ ~ ~ Q~. * Q,~ Q~. ~ �
_ .
Substituting expression (9) in this expression, we get the following relatiort
for calculating the resistive camponent of immfttance of the two antennas:
. ~b-+ at..~ ~ i k
Rn t~ C(l~l~ k~A*~i~.~t~~~A~b~~.~ k=Q~~~kA~?
. w k'b`~~(kb)-~ku(a~b)~~(ka)~~~~`(arb)~-~k`6(4�b). (1~)
� ~~(kb)~~(~(~*b)~ * Ek'ab~~(k~)Ja~kb){.
In accordance with expression (10), calculations of R12 were done for di.poles
of length a/4 as a function of the electrical distance 2a/~ between antennas.
_ Camparison of the results of the calculation with a curve for the mutua]. re-
sistance under the same conditions calculated by the method of induced emf's
[Ref, 1] showed that both solutions give similar relations for R12. Maximum
discrepancy is no mare than 5X with 10 terma retained in the series. It should
be noted that when the distance between dipolea is increased a greater number �
of ternns must be considered, involving an increase in the radius Ro of the
sphere that contains these antennas, which agreea completely with results
obtained previously on the necessity of accounting for terms with indices
1C> kRo in calculations [Ref. 7J.
, REFERENCES
_ 1. Lavrov, G. A., "Vzaimnoye vliyaaiye lineynykh vibratornykh antenn" [Mutual
Influence of Linear Bipole Antennas], Moscow, "Svyaz 1975. .
2. Deshpande, M. D., Das, B. N., "A New Appro~~h to the Mutual Immitance
Between T~o Radiators", J. INT. EI,ECTRON. AND TLLECOi~A1IJN. EATG. , Vol 23,
- No 6, 1977, pp 359-364.
3. Vendik, 0. G., "Determining Mutual Impec~ance Betw~en Aatennas From Known
Radiation Patterns in the Far Zone", RADIOTEKffidIKA, Vol 17, No 10, 1962,
pp 11-20.
4. Jackson, J., "Klassicheskaya elektrodinamika" [Clasaical Electrodynamics],
Moscow, "Mir", 1965.
5. Sazonov, D. M., "Raschet vzaimnykh impedaneov proizvol'nykh antenn po
ikh d~agraaunam napravlennoati" [Calculating Mutual Impedances of Arbitrary
Antennas From Their Radiation Pai?~arns;, RADIOT~IRA I ELEKTRONIKA,
- Vol ~5, No 2, 1970, pp 37b-37$.
6. Gadel'shin, R. M., Golubkov, A. G., Gonoatarev, V. A., "M~thod of Deter-
mining the Phase-Frequency Response of a Minimum-Phase Target From the
27
FOR OFFICIf,L USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2447/02/09: CIA-RDP82-44850R444544454439-9
FOR OFFlCIAL USE ONLY
Amplitude-Frequ~ncq Response Asaigaed in a Limited FreQuencq Band",
IZVESTIYA VYSSH~H UCI~BNYKH ZAVEDENIY: RADIOELE&T80NIRA, Vc~l 22, No 3,
1979, pp 89-92.
7. Ludwig, A. C., "Near-Field Far-Field Transformations IIsing Spherir_al Wave
Expansions", IEBE TRANSACTIONS ON ANTENNAS Ad~D PROPAGATION, AP-19~, No 2~
1971, pp 214-220.
UD~~ 535.317.1
1~PASURING PARAMETERS OF SCATTERING BODIES BY RADIO HOLOGRAPHY 1~TB;OD
[Article hy A. Ya. Pasmurov]
[Text] An edge wave method [Ref'. I] is used ta get ana-
lqtical r~lations for calculating the scattering char~ic-
_ teristics of individual "shining" points of an ideallq con-
- ductive cqliader of finite dimensions. On this basi~a an
equation ia derived for a a standard camplex Pourier.~ radio
hologram, and a test algorithm is developed for mod.eling
_ the radio holographic process. It is sriown that tc~e poten-
tial accuracy of ineasuring the effective acatteriiig ~surface
- of "shining" points of an ob~ect b~ the method of�' Fourier
radio holography can be brought to 0.5 dB.
The ~esults of theory, modeling and experiment are compared,
and recommendations are made on etandardizing measurements
of local ecatterin� chara~teristics of rodie4.
To solve various applied problems in diffraction of electromagnetic waves
in Lhe high-fxequency approximation requires diagrams of the effective scat-
tering surface of individual "shining" goints of an ob~ect. Such scatter~ng
characteristics, termed "local" CRef. 2], can be obtained analytically or
experimentally. It is advisable to use theoretical metY~ods for calculatinR
local scattering characteristics of ideally conductive bodies of simple geo-
metric ~hape (cqlinder, cone and the like). The local scattering character-
i.stica of a complicated ahape can be determined'only experimentally as a rule.
Methods of radio holographq are used to do this, in particular the ffiethod
of invert~~~d syntTnesie of one-dimensional Fourier radio holograMS by rotating
the ob~~ct ~round its cent~r of masa [Ref. 3, 4J.
A fundamental condition of cioing experimente of this kind is the availability
of a reference scatterer for which analytical expressions can be found that
describe its local acatteria~ characteristica. The reference is necessary
for getting a quantitative measuret~ent standard, for checking operation of ~
the experimental �acility by comparing theoretical and experimental data,
a~~d for evaluating the experimental error. In addition, the reference can
be used to model the radio holographic proceas. The latter circumstance is
the most important since the methud of Fourier radio holography has a funda-
mentally inherent error of ineasurement of local scattering characteristics
whose cauaes will be elucidated below. Comparison of rpsults of theory and
28
~'OR OFF'ICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R040500050039-9
FOR OFF7CIAL USE ONLY ~
- modeling based on general analytical rel,ations eaab~es evaluation of the mag-
nitude of this error, i. e. determination of the potential accuracy of the
method. Comparison of the given resulte trith experimental data eaables de-
termination of the instrumeatal error of a specific measurement facilit}r.
Up until naw, aaalqsis of the method of radia holographq has relied on use
of a hypothetical body made up of a set of point scatterera [Ref. 3j. Ob-
viously such an object cannot serve as a standard. In our paper, an ideally
conductive cylinder of finite dimensions is taken as the reference scatterer.
The edge wave method is used to get analqtical expresaions for calculating
the local scattering characteristics of this reference. On the basis of these
expressions, an equation ie derived for a camplex oae-dimensional Fourier
radio hologram, and a test algoritlmm is developed for modeling the radio holo-
gxaphic process.
~
Upon diffraction uf a plane wave bq an ideallq conductive cylinder of length
Z and rad3us a(Fig. 1), a scattered field is formed ia +the far zoae whose
compoinents for E- and H-polarization are respectivelq equal to [Ref. lJ:
- s ~a el%R
Fd 4 Cox R ~~~,t~i) , (1)
Hoar ~ R~(tl,~1,) ~ (Z)
_ where k is the wave number (k = ~ ki ~ a ~ k,~
. _
- ~ .
~
s ~
_
~ ,
~ p
Tran~nitter
~ Receiver
Fig. 1
� In contrast to Ref. 1, the angle functions E(e,eo> and E(9,Ao) are represented
in th�~ form of three terms, each characterized bq a corresponding scaCtering
~ center of the cylinder (Fig. 1),
~(~,do)i~~t'~,u~)*~l(~,~~)*Ea(~. (3)
~(~,d�~'~~L;~�)+~p(d,~o) *E~(U~b�)� (4)
_ 29
FUR OFFICtAL USE ONLY
~
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
F'OR OFF[CIAL USE ONLY ~ ~
d = I ) ~ i~~ ( g~ ~~aos~~eas~~y
~ , ~i ~ ~ : ~ Ke ' (5)
~~(~.~.1~fQ~'~~C~)+i,~p(~)]e~ e
(ros0+eaiJ,) ~6~ .
~3t~~~.) `~s[-~~(~ ) * t~~(~),j e ` s ~eoso-'eosd~~~ t7)
w~here J1 and J2 are Bessel funczions of the firet kind of first and second
. order respectivelq.
Ka ( S~n + c~n d~ j.
For the functions En(e,eo) (n = 1, 2, 3) we can get expressions analogous to
(5)-(7) by replacing the functions fn with gn defined by relations
ti s sin ~ ~~do8 ~ - ~e F ~COS m = FOS ~
~ ~ ~ ~ ( 8)
9~ m ~
~
+
9 ~ ~`ry1 [(cos m - ~b ~m ) m - ms ] ' ~9~
c
f3 ,�m~ _~sti-v~~+~~~r_~:7-~ ~�j'J~ cio)
9, m F ~n n
ZQ � .7/2 e
Expressions (3) and (4) are valid under condition that S
where w3B is the frequency of the harmonic input eignal; T= L/v is the dura-
tion of the sa~ple being analy~ed; L is the dimension of the aperture of the
acoustic light modulator in the direction of elastic wave propagation; v is
the velocity of the elastic wav~~s in the medium of acousto-optical interactfon.
It can be easily demonstrated that when the passband of ~he acoustic light
modulator is limited and the elastic waves are damped in the modulator mediimn,
the frequency-response function is defined by the relation
, ~ . e ~�~),c e i~~-~.3r).~ sh ~~,.)Y-s ~,~1) ,i P-;~~- ~2~
Gr~,, ~ � x~ r~~
- r~ ~w,.~~ .
where I~n(~il38) is the complex transfer constant of the p~ezoelectric transducer
of the acoustic light modulator a(w30) is the frequency-dependent damping
- factor of elastic waves in the medium of acousto-optical interactioa.
The fre~uency-response function of the anglyzer enables us to find the output
spectral distribution in accordance w~th the expresaion [Ref. 1, 2):
S6a%~ ~li; = !~e. r ~~w~~) ~ ~~'e ~,d, ~~it , ( 3)
_ J
41
FOR OFFICIAL USE O1VLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-04850R000500054439-9
FOR QFF7CIAL USE ONLY
where $(w) is ti~e spectrum of aa arbitrarq iaput signal; S~(~,t) ia the
instantaneous output spectr~; A~ is the modulation index corz~spoading to
a harmonic input signal of unit am~litude. We will use this defining charae-
teristic of the device to analyze tsansmission of raadom signals through it.
- For linear sqstems, including the Lambert analyzer at low iaput signal level
[Ref. 2J, the energq spectr~ and autocorrelation ~unction of a random input
signal are most simplq found [Ref. 3, 4].
Let a continuous random steady-state (in the broad sense) ergodic pro~ess
.%(t) with normal distribution law be sent to the input of tti~ device. Its
energy spectrum is W(w), autocorrelation function ~,(T), and variance
a2. Let us find analogous characteristics of a random signal in the output
- pl~n~ of the analqzer, i. e. in the spatial frequency plane.
Let us isolate one realization of.the randam signal ICi(t). Its spectral den-
sity is
� ~
Ji h, where k X h is the area of the transduce~. In this caae the e~astic
wave can be considered divergent only with respect to ~he dimension h of the
piezoelectric trans ducer. Then a wave
: s;
E,x, y~= A~x~y~~~~~ -kx ~~r~zy~l
propagates in the material of interaction of light and sound (Fig. 4j, wher~
A(x, y), ~(x, y) are the amplitude and phase of the wave excited in the
: interaction ~edium when a harmonic wavefarm
of unit amplitude with frequ~acy w` is ap-
- osh y y/ plied.
- ~ .z'
_Qsti ` To determine the amplitude and phase of the
wave, we consider oscillations (pressure
~ Fig. 4 change in the interaction medium). ~erturba-
tions of the interaction mediuac caused by the
- transducer can be ci~fined as [Ref. 5]:
M a
_ ,~(xiy')= ~ z f .~~y)~~ "`~~x ] dy,
~
, where a is the wave length of the elastic wave, f(y) is the pressure dj.stribu-
tion over the trans ducer. We assume that pressure distribution over the
- transducer is unif orm, i. e.
_ ,~~j~/~ � ~ ~ lyl ~ ~ '
o, l yl ~ ~ .
- then
_ + ~ ~ ;
~ a ~ ' d
- ) ~ x . ~x ) _
- f ~c(rK) -~~~el~*%~S(t~)-S~ri))}=~A~x,f/~~~�~,Jy~~~~~
1
where .
, ~
Z ~ ;t ~ ~i hl~ ca. ~z (y-
- N ~ y
= ~ ~
_ ~~g,, ~~j ~~)q~.x is the Fresnel cosine integral;
! 1 '
~ ~ ~'x ~.x is the F~esnel sin~ ~nie~;r~l;
J~ t S~r
~ -n/ tS~ .
- ' l.~E ' .
D S . su, a . .~.zj
_ ~ , IX~ ~ ~~fS~~feY'e~
- C~x) _ ~x~2
6 (Sn~ co~-2) ~s~ < l,,ts,
~Al 1 ~~C - ~ ! ~ . .
C~~--- - 5~~~
~ ~
~ ~ ,e ~ /
~ Q6 a6
_ ~ ~ -
RV ~4
o,~ qt
x .r
s~ ~ ,~,r ~1~ ~~c e,v ~,s
Fig. S
For negative values of x: c(-x)=-c(x); s(-x) _-s(x). Fig. 5 sh~ws the re-
sults of calculation of Fresnel integrals by the exact formula (curve 1) and
by the approximat.e formula (curve 2).
52
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFIC[AL U~E ONLY ~
REFERENCES
1. Khurgin, Ya. I., Yakovlev, V. P., "Finituyye funktsii v fizilce i tekhnike"
[Finite Functions in Physics and Engineering], Moscow, "Naulca", 1971.
2. Rulakov, S. V., "Akustoopticheskiye ustroystva spektral'nogo i
korrelyatsionnogo analiza signalov" [Acouato-Optic Devices for Spectral
and Correlation Analysis of Signals], Leningrad, "Nauka", 1978.
3. Cohen, M. G., Gordon, E. J., "Acoustic Beam Probing Using Optical Tech-
niques", THE BELL SYSTEt4 T1:CHIdICAL .10URNAL, April 1965, pp 693-721.
4. Molotok, V. V., Razzhivin, V. P., "Influence of Acoustic Wave Damping
- on the Characteristics of Acousto-Optical Spectrum Analyzers" in:
"Akustoopticheskiye metody i tekhnika obrabotki informatsii" [Acousto-
Optic Methods and Aata Piocessing Techniques], Leningrad, 1980.
5. Papulis, A., "Teori~a sistem i preobrazovaniy v optike" [Theory of Systems
and Transformations in Uptics], Mascow, "Mir", 1971.
6. Abramovits, M., Stigan, I. M., editors, "Spravochnik po spetsial'nym
funktsiyam" [Handbook on Special Functions], "Nauka", 1979.
- UDC 621.396:535.8
STATISTICAL CHARACTERISTICS OF ACOUSTO-OPTIC RECEIVERS OF LONG PSEUDORANDOM
- SIGNALS
[Article by A. V. Kuzichkin]
[Text] An examination is made of the problem of finding
pseudo-random signals from code aequence delay by using
- a system comprising an acousto-optic convolver and recircu-
lation delay line. Expressions are obtained for the proba-
bility of correct determination of the time position of
a pseudo-random signal and the average duration of the sig-
na1 detection procedure for the case of recepticn against
a background of white gaussian noise. It is assumed that
- tha duration of the received signal considerably exceeds
- the ~ime of signal delay in the region of acousto-optical
_ interaction ~f the acousto-optic convolver.
_ Correlation reception of pseudo-random signals is one of the most promising
areas for using acousto-optical processors. The interest that has arisen
' in the design of pseudo-random signal receivers based on acousto-optical pro-
cessing systems can be attributed primarily to the comparati~~e simplicity
- of rea~izatir~n by using algorithms of matched filtration of pseudo-random
signals undar conditions of considerable uncertainty in the time position
of signals to be received. From the standpoint of maximizing flexibility
xn adaptation of receivers to changing conditions of pseudo-random signal
" reception, it is advisable to make the processing system in an acousto-optic
53
FOR OF'FICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2407142/09: CIA-RDP82-00854R000540050039-9
FOR OFF7C[AL USE ONLY
convolver arrangementi [Ref. 1] in whic~ the procesaing algorithm is restruc-
tured by changing the law of formation of the reference signal.
~ In the general case, ths acousto-optic con~olwer is not a processor tbs~: is
i~ivariant to the time position of the sigaal to be processed. Ho~erer, if
the duration of the received signal does ndt exc~ed the time of delay (T3)
of the signal in the region of acousto-optical interaction of the acousto-
optic convolver, then determination of the time of pseudo-rand~m signal ar-
= rival can be ensured for practical purposes within a single recepti.nn cycle
at the expense of slightly increased complexity of the receiver and the use .
_ of continuous-wave transmission of the reference signal. t3nfortunatelq in
most actual cases the pseudo-random signal duration is considerablq greater
than time T3. To eliminate the energy loeaes that arise when proceasiag such
signals in an acousto-optic c~nvolver, the output responses of the co~~olver
are accumulated by using recirculation delay lines [Ref. 2] or photo-CCD's
[Ref. 3J. As a result, the acousto-optic receiver loses the capacity for
searchless determination of pset~do-random signal arrival time, and requires
~ the use of spec~.al synchronization procedures [Ref. 4].
Ttiis paper evaluates.the statiatical characterist{cs of procedures of pseudo-
- random signasl search and processing by i~sing an acousto-optical receiver con-
sisting of an acousto-optic convolver and recirculation delay line. A block
output
input - - ` ~ ~
AOC ADD DL
I AMP ~
- RSG ~ CC (
L- - - - - -
- . eaet
- F~g. 1
diagram of the device to be analyzed is shown in Fig. 1, where RSG is the
_ reference signal generator, AnD is an adder, DL is a delay line, At~ is an
amplifier, GC is a gating circuit that cuts off accumulation of the output
signal of the acousto-optic convolver [AOC, and RDL is the recirculation delay
line]. The choicQ of the recirculation delay line as a cumuletive element
is dictated by the fact that in many casea the use c~f a recirculation delay
line gives the required accumulation interval (up to a few milliseconds),
and realization of an acousto-optic receiv~r with recirculation storage is
far simpler than for a xeceiver with photo-CCD storage.
In the most general case, the procedure o� searching for gseudo--randos signals
by using an gcoueto-optic convolver with recirculation delay line consists
in sequential atep-by-step correlation analyais of the aign~l being received
at different delays of the reference s3gnal. The decision on detection of a
54
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-40850R040500050039-9
FOR OFF7CiAL USE ONLY '
acousto-ogti.c convolver is made with respect to the ma~l'im~ uutput sigaal
of the recirculation delay line after analyzing the ~atc~ire~region of temporal
uncertainty of the signal being received.
~Valuation of the statistical characteristics of pseudo-random sigaal detec~
_ tion by an acousto-optic receiver of the given tqpe will be based on the
following quite general assem~ptions.
1. The size of the region of acousto-~ptical iateractioa of the convolver
is selected in such a way that a whole number of recirculation cycles R= T~/T9
is required for processing a pseudo-random signal of durat~on T~.
2. The signal arriving at the receiver input is formed bq pseudo-random sigaal
repetition formed in accordance with a law of the same pseudo-random sequence.
3. The reference signal sent to the acousto-optic convolver is formed by
breaking down the initial pseudo-random signal into [missing letter] aegments
of duration T3 each,~and by time inversion of the re~ultant s~gments.
4. The beginning of the recirculation period coincides with the be.ginning
of the first segment of the reference pseudo-random signal.
Let us use the symbol ~T to denote the timie mismatch between the beginning
of the received pseudo-random signal and the b~ginning of the reference pseudo-
random signal. In doing this, we will asswne that if the input signal leads
- the reference signal, ~T < 0, while if the input signat lags, ~T~O (I~T~~T~/2)~
We can readily see that the ou~put correlation peak of the recirculation delay
line and the time of its appearance are linearly dependent on the insta~ntane-
' ous value of ~T, and are determined by expressions of the form
~ - e, (~i - IsTI/Y1'i) : (1)
~t - - ~T/2 , ~ (2)
where co is a proportionality constant snd Ot is the interval between the
beginning of the reference signal and the occurrence of the correlation peak.
The principal characteristics of a correlation receiver nperating in tihe mode
- of pseudo-random si$nal search are mean duration of the signal detectifln pro-
cedure (To) and prebab~lity of correct determination of i;:s time position
(Pnp). We will find these characteristics for the most typical case of inco-
herent reception of pseudo-random signals against a background of gaussian
- white noise wi~h zero average and correlation function of the form '~1od(t2-tl).
_ The average time of pseudo-random signal detection by the algorithm considered
in this paper will be found as
~ - T~PM +zT,(4- P,,)P,~ * +KT~(!-P,~)~~t ' ~/~P.~ K ~ (3)
55
FOR OF?^ICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL USE ONLY
_ Here Ta is the duration of t1n~ pr~acedure of analqzing the output sigaal of
the recirculation delay ?ine ~.n. investigation of 4:he entire regioa of temporal
- uncertainty of th~ pseudo-rarsdam signal being received. The quantitp Ta
is determineci bq ttre duration rf the recei~~~d signal, the time of delay of
the signal in the acousto-optic c~nvolver., the number of recirculation cycles
required and the search step ATm (i. e. the time shift of tbe reference sigaal
of the acousto-optic convolver in step-bq-step examination of the zone of
~ possible ~ime position of the pseudo-random eigaal):
1; ~ T Ts II~~Tr .
~ In this paper the statistical values are analyzed for two values of the search
step: AT~i= T9 and AT~2= 2T3. The selection of just these values of ~Tm is
dictated bq the follawing factors.
1. To get correlatio.n peaks at the output of the recirculation delay line
with amplitud~ at any initial temporal mismatch AT ~hat would be sufficient
for comparatively successful detection of pseudo-random signals against a
background of intenae noises, relation (1) tells us that the condition
~T~ ~ ZT~
mtist be met.
2. Displacement of the reference signal by an amount that is a multiple~of
Tg considerably aimplifies realization of a tunable reference pseudo-random
signal generator and a generator control system.
In the case of search for signals with step ~Tml= T3,the procedure for anal-
ysis af the output signal of the recirculation delay line takes up time inter-
val Tal=~~T~R, and in searching for the time position of the pseudo-random
signal with step ~Tm2 = 2T3, th~ duration of the analysis procedure is equal
to Ta2= T~R/2. In the case of search with step T~ for analysiEa time Tai+ ~
four signal correlation peaks will be observed at the output of the recircu-
lation delay line, whereas there will be ~~ily two correlation peaks in the
case of search with step 2T9 for analysis time r82. The occurrence of such
a number of correlatic. peaks is due to the fact that for the given search
a ste~s the temporal mismatch between the received ~nd referenc^ signals falls
within the principal correlation region given by (1) (~AT~~ 2Tg) several
times (four ti~a~s for ATml ~ T3 and Cwice for AT~2 = 2T3) . Then sin~e the time
position of the sicnal being received can be determined from the
~tlme of occurrence of any signal correlation peak, probability PnP is found
- as the probability of detecting at leas~ o~e correiation peak:
p~~ ' ~ " i~ P~) ~ (4>
:
p�~t � i - (~-P~) , (s)
?�i
~ where Pi is the probability that the amplitude J of the signal corr~lation peak
is greater than rimplitude Z of all noise spikea at the output of the recircu-
= lation delay line.
56
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R040500050039-9
ROR OFF'[CIAL USE OM.Y
In the case of incohere~t reception of a pseudo-raadom signal
~ ~ M
P - f ~,c~?~ [ l~,cz~ ~z] . {6>
0
where
s ~
r~,(~) � ~ cxP ~ i.(~) %
~
(z) - ~ ~xP ~ ~ :
M is the total number of noise spikes (M= S- 4 for aT~l and M= B- 2 for Arm2);
S is the base of the pseudo-rsadom signal; ho= 2En/No; En is the energy of
the signal that yields a correlation peak of magaitude J at the output of
the recirculation delay line; Io(�) is a modified Bessel functic~n of the first
kind of zero order.
Transforming expression (6) by a technique such as that described in F_f. 5,
we finally get
- . y
P~ - j w eup~ (u
*}~.)/Z~ I.(~.t~)~i- e~ du , t>>
_ ,
where u = J/ho .
T~/RTe ~~~/RT~
1. 6~ 16384 ~ ~ 1 6~ 1638~
2~ ~ 4. 6- 10~ 2 6~ 4046
~ 3, � b � 512 ~ ~ ' ~ 6 - S~?
~ ~ ~ ~
. ' : ' ~ ~ �
. o ' o ~
~0 ?0. ~0 i0 20 30
Fig. 2 Fig. 3
Fig. 2 and 3 show the average time of pseudo-random signal detection as a
function of the signal-to-noise ratio ho for different values of the base
of the pseudo-random sigmal with maximum mismatch between the received and
reference signals. The curvea on Fig. 2 are plotted for a search ateP T9,
and on Fig. 3 for a aearch atep 2T9. Fig. 4 and 5 show ~l:e way that To de-
pends on hb at large excesaea of the signal over noise (1. S~ 4096~ AT~1� 2Ts~
2. B= 4096, ATml = T3i 3. B~ 512, AT~1 = 2T9i 4. B s 512, ~T~1= Ts; 5. B= 16384,
~TW1= T3; 6. B~ 16384, ~Tm2~ 2T9). All calculations were done by formula
(3) with consideration of relations (4), and (6). Analysis of the re-
sultant curves shows that at comparatively low values ~f h~ (~10-15} the
57
_ FOR OFFICIAL USE ONLV
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR (DFF7CIAL USE ONLY
Ti~~e ~e
~ : ! 5
J ~ ~
_ 6 ~
1
~ .
4 .
� ~ � ~
�
IS 20 ?S ~0 20 ?5 30 35
Fig. 4 Fig. 5
greatest rate of search of pseudo-random signals is reached at a search step .
equal to T3. In the case of signal reception at weak noise levels (ho3 20)
it is advisable to use search with a step 2T9 for rapid determination of the
time position of pseudo-random s~gnals. The mean duration of the pzocedurQ
for pseudo-raadom sigaal detection is close to RT~/2 in this case, which fs
B/R times faster then for the case of search using cox~ventional correlation
receivPrs [Ref. 6].
REFERENCES
1. Ru2akov, S. "Akustoopticheskiye ustroystva spektral'nogo i
korrelyatsionnogo analiza signalov" [Acousto-Optic Device for Spectral
and Correlation Analysia of Signals], Leningrad, "Nauka", 1978.
2. Morgan, D. P., Hannah, J. M., "Surface Wave Recirculation Loops for Signal
Proceasing", IEEE TRANS. SONICS AND ULTRASONICS, Vol 25, No 1, 1978, p 30.
3. Sprague, R. A., Koliopoulos, R. L., "Time Integrating Acousta-Optic Cor-
relator", APPL. OPTICS, Vol 15, 1976, p 80. ~
4. Kuzichkin, A. V., "Optical Processing of Camplex Signals With Unknown
Time Position" in: "Tezisy dokladov III Vseaoyuznoy shkoly po opticheakoy
- obrabotke informatsii" [Abstracts of Reports to the Third All-Union School
on Optical Data Pro%;essing], Riga, Part 1, 1980, p 135.
5. Viterbi, E. D., "Printeipy kogerentnoy avyazi" [Principles of Coherent
Communicatione], "Sov. radio". 1970.
6. Tuzov. G. I., "Statiaticheskaya teoriya priyema sloahnykh sig~nalov" [Sta-
tisti~al Theory of Complex Signal Reception], Mos~ow, "Sov. radio", 1977.
58
FOR OFFICI,~L USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL USE ONLY
UDC 621.396:535.8
ACOUSTO-OPTIC CORRELATION ANALYSIS OF COI~LER SIGNALS WITH JUMPING FREQUIIdCY
[Article by A. V. Ruzichkinj
[Text] A method is proposed and analyzed fflr constructing
acousto-optic correlation analyzers that enable determination
of the arrival time and carrier frequency of complex sigaals
- with ~umping frequency practically within the limits of
a single reception cycle.
The solution of many problems in present-day electronics involves correlation
analysis of signals of complex shape. The use of conveational methods of
acousto-optic data processing [Ref. 1, 2] enables correlation aaalysis oaly
- when the carrier frequencies of received and reference signals coiacide, which
considerably complicates processing of s{gnals produced by combining pseudo-
random modulation and stepwise change nf carrier frequency [Ref. 3]. The
case of frequency uncertainty of the received signal necessitates either con-
siderable complication of the acousto-optic analysis system, using a large
number of processing channels with different reference signal carrier fre-
quencies, or else considerable time expendiLUL~~ ~n determfning the program
for tuning the received signal.
In the simplest case, rapid correlation analysis of signals with ~~unping fre-
quency can be realized by repeatedly shifting the spatial carrier frequency
of the reference signal fed to the input of an acousto-optic convolver, which
in virtue of its advantages [Ref. 1J is the main element for acousto-optical
processing of complex~signals. The necessary displacement of the carrier
frequency of the ref~rence signal is most ~imply accomplished by an optical
deflector placed _s_n front of an acousto-optic modulator with reference signal
to change the angle of incidence of light on the modulator. A considerable dis-
_ advantage of such a processing algorithm is the difficulty of realization when
searching for signals with a larg~ number of possible values of the carrier
frequency. Since the spatial frequency cf the reference signal must vary
over the entire range of frequency uncertainty of the received signal within
a time interval equal to the duration of a single symbol of a pseudo-random
- sequency of the complex signal*, pr~sently unattainable requirements are im-
posed on the number of positions of th~ optical deflector and on the switching
speed: in the case of discrete tuning of the carrier frequency of the refer-
ence signal, the required spfed Wl for switching the opt~cal deflector, and
its capacity E1 (the ntnnber of deflection positions that are resolvable for
~ the Rayleigh criterion) are defined by expressions of the form
U/~ ' ~ E, ' ~r . (1>
*Only in this case can we get simultaneous coincidence af received and
reference signals with respect to frequency and delay of the pseudo-random
sEquence, and consequently only in this case will a correlation peak of maxi-
- mum possible amplitude be obtained at the output of tt.e acousto-optic process-
inR system for any values of the time and frequency mismatch between the re-
ceived and reference signals.
_ 59
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R004540050039-9
FOR O~IC[AL USE ONLY
where Nf is the total number of possible frequeney positioas of the received
signal, and to is the duration of one symbol of the pseudo-randam sequeace.
The requirements for E1 caa be considerably relaxed for exaaple by ensuring
rppeated coincidence of the received and reference sigaals with respect t~
delaq of the pseudo-random sequence duriag propagation of one perio~ of the
received signal in the region of acousto-optic interaction of the conv6lver
(T3). In this case th~ initial region of frequency search is broicen daan
into m se@neats (m is the necessary n~nber of coincidences of the received
and reference sign~ls with respect to delay of the pseudo-raadam sequence
for time T9), each of which is analqzed in different time iatervals of dura-
tion T3/m. The requiremeats for parameters of an optical deflector that rea-
lizes such seriea-~paralle3. search for tfie carrier frequency of receivad si~g-
nals are define3 by the following relgtions:
Wj ' X~~~� : Ea ' ~I ~M , ~2)
showing a reduction in the necess~ry capacity of the deflector by a factor m.
The capabilitq of getting repeated coincidence of one period of the received
and reference signals with respect to delay of the pseudo-random sequence
is implipd by the theorem on displcement from the theory of Fourier trans-
formE [Ref. 4]:
_ 3'{f~~-t~)} - Ftw)aP(-i~t.) ~ cs)
wh~re F is the operator of Fourier transformation.
The outp~xt electric signal formed at the output of the photodetector of the
acousto-optic analysis system in an acousto-optic convolver arrangement [Ref.
1] is obtained by inverse Fourier transformation of the praduct of the spatial
spect~a of the received signal Fn(w -~n) and reference signal Fa(w - wo):
I~,,,, ' ~ ~l{ f.~~'~~~ F.(~'+~�~} ~ ~4~
wh~ere wo are the angular carrier frequencies of the received signal and
the reference signal respectively, and relation (4) is one of the possible
forms of writing the field of uncertainty of the complex signal [Ref. 5]:
I,M,(t) X(.r, em) - ~~{F.(a+-eer)F,jw)t'wr~~ . cs)
If the epatial apectrum of the received signal is phase~modulated in accor-
dance with (3)
j~(!)w (b)
F~(w-ar.)~ .
and the apatial apectrwn of the referer.ce signal is diacretely shifted in
frequency
" F,[t~-~.~ - ~cE~] .
60
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
F~UR (3~FICIAL USE ONLY
then the output signal of the processing system will be defined hy an ex-
pr~esaion of the following form:
- I,~ ~t~ - x [.r-a~t~ ~Mct~] .
where a(t) is the law of phase modulation of the received signal spectrum;
~~M(t) is the law of frequencq moduZation of the reference signal.
By appropriate selection of the modulation lawa AwM(t) and a(t), we can make
the output signal of the acoustoroptic convolver proportional to the sought
correlation function
' I~ (t) - R [ sT - d(t) ] when eW = e�� .
Consequently, at the time when a(t) _ ~T, a correlation peak of maximum ampli-
tude will be formed at the output of the acauato-optic analysis system. One
of the poss~ble versions of variation of ~~M(t) and a(t) is shown in the dia-
gra~, where ~r~, ~m are respectively the greatest time and frequency mismatch
- ~ 4~Y ~ _ .
t
o ~
- ' ~ ~ corre ation
~ peak
d(U
~~'y,, - ~ _ correlat ion
~ ~ ~ ~
~ ~
_ ~
~
~ . m
~
between the received and reference signals, and the broken line shows the cur-
rent value of time mi~match that varies due to the movement of acoustic wave~
_ in the acoustic liRht modulator, the dot denoting the instant of formation
of the maximum correlation peak.
The phase modulation (6) that is necessary for implementing the given algo-
rithm can be rea~lized by using an opticnl deflector placel in the region of
the spatial spectrum of the received si~nal. In the case of discrete phase
modulation of the received signal spectrtan, the speed and capacity of this
optical deflector are def ined by a relation of the form
~y~ . ~ E~ . b .
where B is the base of the cmaplex sign~~l.
Thus, if B~Nf (a condition that is met as a rule when signals with stepwise
variation of the carrier frequency are ~~sed). with proper choice of the param-
- eter m
61
FOR OFFICIAI. USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
F'OR OF~'iC[AL USE ONLY
i1L,,~ s .Kf/6
- we can considerably relax the requirements for capacity of optical defZectors
that are used witho~t increasing requirements for maxjmu~ speed:
Wt .rc - Y; / r, ; N?~ ~ Jf; / 6t, : E~ ,~t . E~ ' 6 .
REFERENCES
_ 1. Kulakov, S. V. "Akustoopticheskiye ustroystva spektral'nugo ~
korrelyatsionnogo analiza signalov" [Acousto-Optic Devices for Spectral
and Correlation Analysis of Signals], Leningrad, "Nauka", 1978.
2. Krupitskiy, E. I., Yakavlev, V. I., "Akustoopticheskiqe grotsessory radio-
signalov" [Acousto-Optic Radio Signal ProceasorsJ, in: "Akustoopticheskiye
metodq obrabotki infurmatsii" [Acousto-Optic Data Processing Methods],
Leningrad, "Nauka", 1978, pp 30-45.
3. Dikson, R. K., "Shirokopolyusnyye sistemy" [Wide-Bxnd SystemsJ, Moscow,
"Svyaz"', 1979.
- 4. Coodman, J., "Vvedeniye v Fur'ye-optiku" [Introduction to Fourier Optics],
r(oscos~, "Mir", 1970.
5. ;:loka, V. K., "Voprosy obrabotki radiolokatsionnykh signalov" (Problems
of Radar Signal ProcessingJ, Moscow, "Sov. radio", 1970.
UDC 621.376.2.:535.42
ACOUSTO-OPTZCAL RADIO SIGNAL DEMODULATION
[Article by Yu. G. Vasil'yev]
- [TextJ The paper describes an acousto-optic method of de-
modulating amplitude~nadulated (AM) signals. A method of
perturbation theory ia used to solve the prablem of light
diffraction by a complex AM signal when light is obliquely
incident on an ultrasonic col~nn. Expressic~ns are derived
for distributiQn of the light f~eld in the region of acousto-
optic interaction, and for the intensity of the diffracted
ligh*_ it? the spa~ial frequency plane. Crnnputer-calculated
curves are given for the amplitude distortions of the light
field as a function of the radio aignal frequency bandwidth,
ae well as the results of an experimental study of an acousto-
optical AM signal demodulator working in th~ Bragg diffrac-
tion mode.
~ AcouF:to-optical methods are currently being used extensively for radio signal
processing. They are used for apectral and correlation analysis [Ref. lJ,
filtration [Ref. 2] and time acale variation [Ref. 3, 4]. Acousto-optical
devices are also known for demodulating frequency~nodulated (FM) signa3~s [Ref.
S, 6] that demodulate signals of unit amplitude. However, the need arises in
' 62
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
FOR OFFICIAL USE ONLY
Homc� processing probleme for isolating laws of amplitsde asodulation (AM) of
- wlde-band radio signals. Besides, when a collimated l~inous flux is dif-
fracted by a complex signal, amplitude distortions of the space-time spectrum
arise that are due to frequency selectivity of. Bragg diffraction. ~t ~.s neces-
sary to account for such distortions for selecting the frequency band of the
linear mode of demodulation.
Let us consider diffraction of a plane light wave
E(x,~.t) = C,vrp{~~~(zsi.w`P+rcat`P)-',~t]~
by a phase diffraction gra~ing excited by an AM-FM radio signal in the acousto-
= optical demodulation system depicted in Fig. 1
S~t~' ~~t~~ ~2t~~~{ +t~t~~~, ~l)
Here Co is the amplitude of the light; k= w~/c is the wave number of the light;
c is the speed of light in vacuum; w~ is the cyclic frequenc:y af the light;
fo is the carrier frequency of the radio signal; 2~r~,(~) is the sZowly varying
part of the signal phase.
t
3
~
S
_ ~ ;
.
~ ~ a~j
_ - - i~~ ~ �
_ ' ~ ~
1 Y~
: ~
t
slt) j~
Fig. 1. Acousto-optical demodulation sy~rem: 1--luminous
flux; 2--aperture diaphragm; 3--ultrasonic light modulator;
4--Fourier lens; 5--photocell
- The distr~bution of light along the cross section of the ultrasonic column
in direction Oy is taken as constant and equal to unity in the interval
0~ y~ h, where h is the dimension of thE~ u? trasonic columi. in direction Oy.
Since the frequency of light (w~/2n) considerably exceeds the frequency ~
f(t) =fo+ ~,(t) of the radio si,gnal, we can limit ourselves to the quasi-steady
case in solving the diffraction problem [Ref. 7].
Distribution of the indPx of ref ractio~~ of the acaustic line of the ultrasonic
light modulator is described by the relation
?t(x,t) _ ?~,[9+ ~S(~~t)~ .
63
FOR OF}~ICIAL USE JNLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R004540050039-9
FOR OFFit'~aL USE ONLY
_ where no is the index of refraction of the unperturhed medi~mm? Y= (~n/na)
- is the relat~ve char.g~ it~ arnplitude ~n of the index o� refract;.~n of the dis-
_ ~turbed mdeium;
= a(~.~)_~(~'~t;cos~2~t~f,(t-~- +'~t~,t))} ,
T= Z f v is a tin~e sa~ple corresponding to the working aperture of the acoustic
line of the ultrasonic lieh~ modulator; v i.s the velocity of propagation ~f
ultra-sound.
_ When the quasi-harmonic condition
_ ~~.~~.~~I~~~= ~ ~~s ~2)
and the inequality
i ~A'ct-~)~ �~~ct-~~~ ~3~
are satisf ied, the amplitude A(x, t) and phas~:i~(x, t) of the ultrasonic wave
can be respectively representPd in the form
~(=,t! A(t'~) ,
t(~,tJ ~ - t~l~-~)�
Conditions (2, 3) mean that within the l~.mits of the aperture
. : ,
~ ~ I t'tt'$
a quasi-harmonic ultrasonic wave progagates with frequency tha*_ varies with
el~psed time t according to the law
~(t) �f.+f(tl. .
The amplitude A(x, t) of the wave is a slowly ~hanging fw:~ction within the
limits of the working aperture of the uZtrasonic light modulator.
- Taking our lead from Ref. 7, let us :~cermi.nA the spectx~l component E(u~ n)
- of the light field iu the r~gfan of acousto-optical interaction that is de-
scribed by the equation
~ ~ ~ ~ (4)
- a~CE(~,~) + pa
~Eiu,P1; ~ ~rA(t-~~~K~~~ ~
and boundary conditions of continuity on the n~e~~.a interfaces:

~
E (u,-ol = E lu,�o) , (5)
~ ~ (u,4e-o) = ~ (u,~t+o) ~
64
~ FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500050039-9
- FOR OFFICIAL USE O~fLY
~ where p=kz; u=K(t)x; S= ti;~t)/k]2; K(t)= ~-~[fo+!~'~t-2~] is thQ w~�,~e numbex
of the ultrasonic wave.
~ It is convenient to seek the solution ~f eq~~tion (4) in the form of a seires
with respect to powers of y:
E ~u~?~ _ [~.+~~~~u?P)''~:1~~'~~j b . . t�cP~~~Pco~~+ u~~~~. (61
A
= Let us limit ourselves to the function C1(u, n) that describes the first dif-
fraction orders. ~re seek the solution in the form
N ~'~~u~P) _ ~~~~u~P)~P~iu)~~y~u~P)~P~tu) ~ (7)
where the B�1(u, p) are components of the amplitude of the light wave that
forms the first diffracti~n flrders.
_ Substituting expression (7) in (6) and then in equation (4) with boundary
= conditions (5), we Qet the following expression for the coefflcients:
Ktt)
_ ~}~(x,~,t1= je,~it-~)z~os~r S~~.c ~~K~t = 2sin~,K(f)x'os~P } a�`p -r ; 2siK~P~ ~~~~zcos~P ~ .
where sinc u= sin ~ru/nu.
~
- Then light field E+1(x, 2, t) that arises in the plus of ttie {{.rst ~iff*:,~ction
- order is described in th~ region of acousto-optic intera~~~ion a~ z=~, by ~t~~e
expressian
~�(x,t,ti`~e.~tx~~~t)~P~-r~~t)] ~P~t~~x~s:k~P-~)~} ,
= where ~(t~=(J~t-2x~f,~t-2~ }~~~-~}~-~COS'~ .
- Considering that ligh;. 3istribution along the y-coordinate is constant, ~~e
can represent field E+1(x, R,, y, t) in the form
= E., (~~d~~.t1 � ~(~l E,,tx,e,t) ,
where
}~'t1= ~ , O~~S~
- o , ~