JPRS ID: 9127 USSR REPORT ELECTRONICS AND ELECTRICAL ENGINEERING

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• Content Type: REPORTS

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JPF~S L/9127 -
- 5 June 1980
USSR Re ort
_ p
- ELECTRC~i~ICS AND ELECTRICAL ENGINEERING ~
(FOUO 9/80) ~
FOREIGN BROADCAST INFORMATION SER~ICE ~
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JPRS L/9127
5 June 1980 ~
~ ~ USSR REPORT
_ ELECTRONICS AND ELECTRICAL ENGINEERING
_ (FOUO 9/80)
CONTENTS -
ANTENNAS
Statistical Characteristics of Adaptive Antenna Syetems
- ~fdximizing Signal to Noise Ratio 1
Acoustic-Optical Processing of Space-Time Signals in the
Fresnel Zcne 8
Influence That a Coherent-Optics Processo+r Has on the Diagram
Forming Properties of Radio-Optical Antenna Arrays 16
Parallel Pencil Beam Reception of Radio Radiation Using
Conformal Antenna Arrays With Coherent Optical Processing 30
_ COMMUNICATIONS; COMMUNICATIONS EQUIPMENT INCLUDING RECEIVERS AND
TRANSMITTERS; NETWORKS; RADIO PiiYSICS; DATA TRANSMISSION AND
PROCESSING; INFORMATION THEORY
The Blurring of the Mean Diffraction Pattern in the Focal Plane
of a Rec~iving Lens Due to Rain in a Turbulent Atmosphere 36
- Digital Devices Uaing Integrated Circuits in Communicationa
Engineering 47
The Us~ of Lasera for Operational Communfcations With
Industrial Units 50
The Deaign of Microwave Radio Transmitting Devices 53
A Transmitting Accessory for the R-250M2 57
Use of Computers During Dpaign of Urban Telephone Exchanges 63
ELECTROMAGNETIC WAVE PROPAGATION; ELECTRODYNAMICS
Investigation of Ionospheric Inhomogeneities 65
_ ' a' [IIS - USSR - 21E S&T FOUO]
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CONTENTS (Continued)
ELECTRON TUBES; ELECTROVACWM TECHNOLOGY
Formation of Broad Homogeneoua Electron Streams 72
OSCILLATORS, MODULATORS, GENERATORS ~
_ Radio Band Self-Excited Oecillator With Stochastic Behavior 85
QUANTUM ELECTRONICS
The Influence of the Thermophysical Properties of a Target
on Vaporization With the Action of Laser Radiation e........ 96
RADARS, RADIO NAVIGATION AIDES, DIRECTION FINDING, GYROS
On Spatial Fluctuations of Strength of Radar Signal Reflected
by Sea Surface 104
SEMICONDUCTORS AND DIELECTRICS; CRYSTALS IN GENERAL `
Film Electronics and Semiconductor Integrated Circuits 118
- b -
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~NTENNAS
- UDC 538.56:519.25
STATISTICAL CHARACTERISTICS OF ADAPTIVE ANTENNA SYSTEMS MAXIMIZING SdGNAL
TO NOISE RATIO
Gor'kiy, IZVESTIYA VYSSHIKH UCHEBNYXH ZAVEDENIY, RADIOFIZIKA in Russian
Vol 23 No 1, 1980 pp 56-60
[Article by I. Ye. Po2umentov, Gor'kiy State UniveraityJ
[Text] The basic statistical characteristics of adaptive _
antenna systems that maximiz~ the signal to noise ratio are
detexmined: the mean and correlation matrix of the vector
of~weight coefficisnts, powers of interference and of the
useful signal, output signal to noise ratio and spectral
correlation characteristics of a system. The analysis is
presented in consideration of the ~~inite correlation time
of input Gaussian interferencP.
1. Adaptive antenna systems are being used more and more widely today in _
connection with the problem of extracting a useful signal from a mixture
with noise (snterference). Systems of this kind are used for the contin- -
uous optimization of the radiatian pattern by aiming the nulls in the
directions of arrival of interference. The most widely used criteria of .
the functioning of adaptive systems are the mini.mum mean square error [1] -
~.nd the maximum output signal to noise ratio [2]. The statistical charac-
teristics of adaptive systems that maximize the signal to noise ratio, ~~sed
both in radar [3-5], and for selecting weak acoustical signals [6, 7j, are
analyzed in this article. It is important to note that the assumption that
the envelopes of the input interference are not correlated with the vector
of the weight coefficients, was used in the cited works for analyzing the
efficiency of systems. This approximation, as will be shown below, is
valid in the case of d-correlated input interference. Exact methods of
analysis, used in [8, 9], for finding the statistical characteristics of a
single-channel automatic corrector are not applicable here because of the ~
high order of the differential stochastic equation system that describes
the beh~vior of a system. Therefore an approximate method of analysis, -
which leads to correct results in the first order of smallness in terms of
the parameter a= T~/T, where T~ is the correlation.time of the interfer- -
ence em~elopes, and T is the time constant of the filters of the correlation
. 1
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feedback circuits, is used in this article for determining the statistical
characteristics of an adaptive system. We should like to mention that
some of the statistical characteristics of such systems were determined
differently in the literature [10].
2. A functional diagram of an adaptive antenna system that maximizes the
signal to noise ratio is presented in Figure 1. Here Vt =(vl, v2,
vN), where vi is the complex en�velope of the noise in the i-th ele-
rnent of the array, and the superscript "t" denotes transposition; W is the
3 vector of the weight coefficients; WtV is the output signal of the adaptive
system. Vector S is the vector of phases of the useful signal, the angle -
of incidence of which is assumed to be known:
~ ~ e~~s ~ C~pN) . ~1~ -
We will assume below that the useful signal is substantially weaker than
the interference, and its influence on th~ vector of the weight coeffi-
cients is negligible. Then the stochastic differential equation that
~ describes the behavior of W(t) acquires the form
t dt W ~t) -F 7 ~'1) ~V (t) = 7 S*, ( 2 )
_ where I is the unit matrix, M=!~*Vt, and the superscript denotes com-
plex conjugation. The envelope vector V(t) is assumed to be a complex
_ Gaussian process, which satisfies the equation .
dt ~~t) -F Y V ~t) ~ (t)~ (3~ ,
where ~(t) is a complex d-correlated random process with = 0 and
t
= Dd(~). Then V(t) is a complex Gaussian process with finite corre- _
lation time T~ = 1/v and correlation matrix _(1/2v)D. TQ determine _
. ~:he mean vector of the weight coefficients we derive from~(2)
and ~'3) -
- tha following equation for the vector of moments :
dt + 1 + 2vl < MW ) =.2v = Ys~ + 7 s~- .
~s~
-Y--7 iorl ~NA � 1U-a -I- (Nvr -f - IV+ -F NT) � 10-4J > t0= � 10=. (19 ) -
S ince t~/r2.^.: 2(NyT -f- N� Nr)/r 10 =100~ W~ have A,Q ~^104-105, which
corresponds to data of Ref. 6.
Light scattering on inhomogeneities of the optical system. High-quality
processors are characterized by inhomogeneities with dimensions that do
not exceed ra 10 um [Ref. 6]. The errors of amplitude-phase distri- _
bution caused by such inhomageneities are characterized by a correlation -
= coefficient of Ra~mXra~101�10 ~cm=1 mmC y1 the asymptote of (10) assumes the form:
V~Y)-~' 2 Q~xP f- y~ ~a � Po < R)~ (11)
Po L (2F/ka)n
~.e., the second scale, ~ust as in the case of Cn = 0, is defined as Y2 =
= 2F/ka. A comparison of the calculated curve (Figure 1b) with the asymp-
tote of (11) sflows good agreement when u= 0.62. We wi11 note that the
_ 41 .
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tyv(p) ' tyvcp) -
o . � o ~.y\ _
.
1,
, ~
! s
~ "1`,`,`
-s z ~ -z z ~ �1 ~
~ ~ ~ 1
,
~ , 11
, ~ ~ r+ s ~ i
-3 -3
o ~ ~ tgp o t 2 3 typ _
Figure 1. The function V=/ as a function of the .
generalized parameter p = 2kRp/F. ~
Key: 1. -u = 0(J a 0); 2. -u = 0.62 (J_ -3 mm/hr); 3. -u =
= 2.38 (J = 10 mm/hr); 4. -u = 5(J = 50 mm/hr);
5. - = 0.27 (J = 1 mm/hr);
a) Cn = 0(the dashed curve is the asymptote of (9) when u= 0.62);�.
b) C~ = 5� 10'17 cm-2/3 (the daehed.and dotted curves) and
Cn = 5� 1016 cm-2/3 (the solid curves), the dashed curves _
are the asymptote of (11) when u= 0.62 (L ~ 1,300 m,
~=0.63 � 10-6m, R=8 � 10'2m, F~1.6m, a=5 � 10'4m).
conclusion concerning the diviaion between the turbulent and hydrosol
components was drawn for the f irst time j10] because of the considerable
difference in their characteristic scales, and thereafter in 11] using
the example of the frequency spectra of the intensity fluctuations.
Thus, for u< 1, based on the drop in the function being measured, V(y)
to the 1/e 1eve1 in the region y� y1, yt, it is possib'le to determine
the mean radius a of the droplets, and based on the quantity V(y), the
values of u and consequently the mean intensity of the rain J in the
region y1 � y� Y2. The calculated curves shown in Figure 2 for various
values of u and typical values of a i::dicate the considerable dependence
of V(y) on the parameters of the rain being sought. The practicability =
of ineasurements of the light flux, which amounts to 10'3 times its value
in the center of the diffraction pattern, was demonstrated in paper [15].
42
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t v(p)
0
~ .
_ '
-1 ~`~~,--5---1 \
\ ~
� 4 ~
-~1\ `~t
. ` ~ ;
-Z 3 ~ ~
. ~t ~~1 'i
1
1 ~ i
~ 1 ~ 1 ~ -
~ ~ ~ ~ i
1 2 3 tgP
Figure 2.
Key: Cn = 5� 10-16 cm 2~3; 1. -u = 0; 2. -u = 0.27; 3. -u = 0.62
4. -u = 2.38; 5. -u = 5;
The solid curve is for -a = 5� 10-4 m; the dashed curve is for
-a = 2.5 � 10-4 m; the dashed-and-dotted curve is for -a = 7� 10-4 m.
(L = 1,300 m; 0.63 � 10-6 m; R= 8� 10^2 m; F= 1.6 m).
2. Large Optical Thicknesses (u � 1)
Based on the decline of the function I'2(L, p) to the 1/e 1eve1, we shall
determine the coherency radius pk of a plane wave scatt~red in rain, where
U� 1. For monodiaperse particles, we find by working from (6) that p
k�
_ _(2/~rnpL)1 2< a. As follows from formulas (1) and (6) -(3), when a�
� pp (something which is practically always observed in the atmosphere),
the influence of turbulence on the function can be disregarded.
When u� 1, the determining factor in (1) ia the region n ti a/2R � 1, '
so that the asymptotic formula for is written in the form:
_ 9 ~ ~ '
0.2~r the maximum change in potential
aseociated with the in~luence of neighboring elements is not greater than
hundredths of a percent. There~ore, we wi11 make an approximate analysis
or only one element of the periodic atructure.
.
In addition, ~rom the diagram o~ the field plotted ~.ccording to (7.), fig 2,
it can be seen that a cathode grid with a spacing of a/d = U.07~r intro-
duces insignificant perturbationa into the fiald of the interelectrode gap
(perturbations of the field take place in small regions near the cathode
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in the form o~ equipotential cylindrical surfaces with a potential of
and surraunding the cathode ~1lament), wh~reby potential �n is equal
to the natural potential of the plane ~ield determined by tFie poaition of
the cathode etructure relative to the external electrodes. Therefore, in
an approximate tra~ectory analyrsis we asaume equigotential surfacea with
~ to be the aurPaces of an emitter of electrona having initial velocities
o~ v0 ~ 2
0.
, ~ .
~ p~ ~i
~5 ~
2/~
/ ~
2
' ~ ~
/ ~ -
/ ~
i ~
0,1 ~
iy i~
/ 4,5 /
/
o,~ o,os o o,os o,~ ~ o,zz
Figure 2. Distribution of Potential for a Periodic Cathode Structure
in the Field of a Plane-Parallel Capac3tor: a--spacing of
~ cathode atructure: 1--a = 0.032~r, 2--a = 0.32~r, 3--a =~r,
4--a = 3.2~r, 5--a = 32~r
T!zen for the case illuatrated in fig 1, w:~th a plane focusing electrode the
equations of motion are written in the following simple form:
d'y
_ dt, ~ ~I Ey'
d'x
- 0,
dt'
(2)
where E is the field o~ the p'lane interelectrode gap. The trajectory
equation~ have the form
y= 4 d. ~0 x=(ctg= a-t-1)+x ctg a,
~o
(3)
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- where a ie the angle o~ emiasion of electrona ,from the cathode. Elec-
trons emitted along the nornsal line to th,e_. _c.~lindrical sur~ace of the ca-
thode with an initial velocity of v~ 2~ n~~ describe parabolic tra~ec-
tories, and the ~ield deflects the eQectrons in the direction toward the
plane of symmetry, x= 0.
The distribution o~ the density o~ the electron current in the anode ie
d~termined by the equation
. 1 dt
a - '
l, ds. '
(4)
where di is the elementary current and R dx is an element of the -
anode's area. In diaregarding the space charge and with an infinitely
great number of tra~ectories leaving a uniformly heated cathode over iden-
tical angulRr intervals, each of them carries an identical elementary -
current of di . In this case the diatribution of current density in the
anode can be brought into agreement with the distribution of tra~ectories.
We get the distribution of trajectories from (3), assuming that ~fe = 0,
~aml and da=1 .
The results of calculation of the distribution of current density in the
anode plane as a function of the change in the angle of emission (a) of
an electron from the cylindrical surface of a cathode in the range of
0< a0,933. ~6~
The value of the divezgence (x /r ) o,f the electron stream accordingly
varies from 1 to approximatelya10B0, whereby the maximum width of the
line focus in the plane of the anode equals part of the distance bet.ween
the cathode a~d anode:
2x, k.,~ 30 percent is fulfilled if the collimated current equals not more !
~ t~n 30 percent of the eotal beam current. For the purpose of solving the
proble:,n of forming a homogeneous stream with minimal losses in collimation
~ it ie necessary ~o optimize the EOS. The problem of op~timizing the EOS
in terms of uniformity of the distribution of current density in the anode
- wae solved by us numerically by the method of finite differences on the
_ basis of the compiling syatem for the BESM-6 computer (the KSI BESM) [5].
The electrooptical system conaiats of a periodic structure of filamentary
cathodes, a plane anode and a focusing electrode sycnmetrically deformed ,
in relation to planes passing through the axes of the cathodes perpendicu-
lar to the plane of the anode. This system of electrodes represents a
system of cylindrical lenses with planes of sytmnetry passing through the
axis of the cathode.
The calculation of many variants made it posaible to reveal the key rulea
_ for the formation of a stream frcm a cylindrical cathode when changing the
form of the focusing electrode. On the cathode there are tw~o cc~nsiderably
different regions: the region o~ the cathode facing the anode, ~~le~trons
- from which are formed only in the accelerating field, and the reg~~.n of the
_ cathode facing the focusing electrode, electrons from whieh are firet ac-
- celerated and, passing through the potential maxir~um corresponding to po-
tential ~Q (fig 2), fall into the retarding field. Starting at the in-
stant when the longitudinal component of the velocity of the electrons
( y) becomes equal to zero, electrons ar~ accelerated toward the anode.
,
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- A Ctl&I1~P. in r:arametera o~ the retarding #ield exerts a considerable influ-
i'.ClCP. on the formation of electrons from the region of the cathode facing
the f ocusing electrode, practically not disturbing the flow o� electrons _
from Lhe region of the cathode facing the anode. This fact makes it
~~c~asible independently to control the electrons emitted from various re-
g�one of the cathode.
- Calculation of a great number of variant~ of an electrooptical system with
ciiLier~nt con.figurations of focusing electrodes demonstrated that from a
cylindrical cathode in the f ield between a plan~ anode and a focusing ~lec-
tr~de cannot be formed a stream with a uniform distribution of current den-
sity in the anode. At the boundariea of the stream formed there always
- exist sections with increased current density. The na~or portion of the
- ,:.urr.enr. of these sections ie made up of electrons emitted from tne portion
, of the cathode facing the focusing electrode. However, it was possible to
find a solution (fig 4 on the cor?dition that x = x ) whereby part of
the el~ctrons forming the current density maxims~'at ~'he boundaries of the
st.ream are distributed over the entire breadth of the l~.ne focus. In fig
4 is pres~nted the pR~h of the :ra~ectories of electrons emitted from -
ct~aracteristic sections of the cathode, as well as current density diagrams
{~~~1~ the purpose of clarity the ecale has not been observed). This solu-
t1or. :.s obviously optimal for the EOS aelected (*he size of the uniform
s~ccion iF~ m.:~xinal) and is implemented by means of a focusing electrode of
s.imPl~: `o:m. In plotting current density diagrams it has been assumed
~nat the el.ectrons leave the cathode over identical angular intervals and
_ ~ti1~1~ +~t~e emission is uniform over the entire surface of the cathode. For
pre'~~termined breadth of the line focus ar~ optimal solution can be ar�-
y ri~led ~1[ ~,rith different relationships between the geomatrical dimensiona
or the rOS, whereby the degree of homogeneity of the stream is also dif-
f~~rent. The necessity of optimizing the geometrical relationships of the _
EUti is cbvi.ous. The geometry of the EOS h~s been optimized over the stream
;ii.ver~ence range of 102 to 103 for varying paral~.~ters d2 , dg ~h and c.
~Jirh fixed l~alues of d and d the breadtn of the line ~ocus (x ,
� f{s~ is s function of2 c. Weearrive at an optimal solution for eac.~il
, j,_y selectitig di_mension b so that condition x = x is fulfilled.
!iE~ mini~utn value of d2 is determined by the ass~~ned v~lue of the
!.r~~adth of the line focus (2xa), eo,ual in our case to the spacing (a) of
~~,~i~di.c electrooptical system. Taking (7) into aceount, we have
, ~
- d1 r~e=a)~~7.xs. ~8`
~
- 'iht~ reriad o~ the cathode etructur~ 1.It~its dimension d~h~h , since it
c 0). A11 tra~ectories beginning and e~nding at
E can be divided into two classes: 1) lying entirely on aurface A--they
rotate around the state of equilibrium; and 2) those reaching surface B.
Theae rwo groups are separated by trajectory P, which approaches the
breakaway ltne at a tangent.
An analytical expreseion for the map of ~(y) ia possible only if f(z)
is approximated by~ ecewise linear functior. Let ue asaume, for
~
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example, that f(z) ~ z/K when z< K , f(z) - K- z) /(1 - 2K)
when K< z< 1- K and ~(z) _(z - 1+~c) when 1- K< z. Then the
equations for slow motion become linear:
x=2~x+y+tc, y=-x , (3)
where k= 0 on A(now A and B are planes) and k= b= g/(1 - K)
on plane B, and v= h- 0.5Kg . Joining solutions (3) in the standard
, zsanner on planes A and B[3J, it is not difficult to arrive at an e::-
ptession for ~(y) similarly to how this was done in [4,18J. Without
writing out cumbersome equations, we present only the diviaion of region of
parameters b, v into different typea of behavior of ~(y) (fig 4).
s~~yl ~(yJ
~ Z
j ~ j / I
~ j i i I
_ _ ~
P y P Q 9
J y
~
~
~ ~ ~
~
Z 3 ~r ~ . 04 y . P4 y
; ~ f ~
~
~s . ~ b)
I
I ~I/
~ ~ _
0 v 0~ 1 `
a) P y
- E'igure 4. a--Division of Plane of Parameters b, v into Regions
of the Different Behavior of T; b--Maps of T Arrived
at with a Piecewise Linear Approximation of f(z)
The maps in fig 4b have in addition to diacontinuity p(correeponding to
tr~jectory P) point of discontinuity The appearance of a diacontinu-
?cy at point q is associated with the fact that with thia selection of
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:(z) (f(z) = 0 with x= 1-~c) the state of equilibriu~ lies precisely
below the breakaway line. If it ~s taken fnto account that f(z) � 0
with z f 0, then tne discontinuity will disappear, as indicated in fig
4b by the broken line. On all the ausps in fig 4b there ie a reEion of
attraction which all tra~ectoriee enter. Within thie region there first
~ccur several iterations with y< p (corresponding to this is an in-
crease in oscillationa in the tr~in), and then an iteration with y> p
_ returns the mapping point to the lin?ar section (one train is replaced
- by another).
With low v within the region of attraction is fulfilled the condition
> 1, the map is one of attraction--in successive iterations
the two near points diverge. The divergence of close tra~ectories is one
of the traits of stochastic beh avior [8,10] and at once ensures the ab-
sence of etable limiting cycles. In this case the transformation has an
invariant ergodic measure in rel.ation to which it is a mixing transforma-
tian (this follows from the results of [14]).
However, the conclusions arrived at when employing a piecewise linear
approximation of f(z) can prove to be incorrect, sinc~ with this descrip- ~
tion the behavior of tra.jectories close to P is incorrectly reflected. ~
Tt~erefore, we plotted t:ans~ormation T numerically. The values of para-
meters were selected as follows: h= 0.074 , q= 2.8 and e= 0.004 ;
- characteristic f(z) was approximated by the function f(z) = z exp
exp t3.61 = 13.Sz) + exp (6.5(z - 1)) - exp (-6.5) . Integration was per-
formed on a BESM-6 compurer by the Runge-Kutta method with an interval of
2�10 Function ~(y) arrived at is presented in fig 5. Near P now
app2ared a critical point at which = 0, but it was not completely
possible to resolve the region of discontinuity. Obviously transformation
T is really continuaus, but ti exp (e 1)(!) , i.e., the assunption
that the piecewise linear approximation describes the real situation
sufficiently well has been confirmed. And nevertheless the existence withi.n
the region of attraction of critical points worsens the stochastic behav-
ior of the syst~n.
' As follows from [21,22], transformation_s with critical points with almoat
all values of parameters have a stable asyarptotic cycle. However, firstly,
the stable cycle is surrounded by a stochastic non-attracting region [23];
secondly, the period of the cycle can be very great and over long inter-
vr~1s of time the realization appears to be random; and, thirdly, the re-
gion oi the space of parameters in which this cycle is stable is as a rule
very amall. Therefore, in the numerical experimente in [24] transforma-
- tiona with critical points demonatrate stochastic behavior; however, here
poseibly more appropriate would be the term "^omplex dynamics" [18]. And
although the atochastic behavior observed here is the consequence of low
noiae (e.g., of rounding errors), the statistical properties of the aignal _
- are determined, ,judging from the whole, not by the statistica of noise,
but by the characteristic dynamica of the system. -
92
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. E~E~Tf ~t~ I~~ ~t~~ ELE~Tfi I~AL E~#G I t~EE~ i~~~
~ ~U~iE ~ F~~~ ~ _ ~ ~i~ ~

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~ !
FOR OF.~ICIAL USE ONLF
9'(y>
- r..._...._.-.~ -
_ ~ ~ ~
i ~ ~
I ~
I
I I
~
_ y -
Fj.gure 5. Tra:-~s�ormation y-~ ~(y) Plott~d for System (2) Numeri.c-
ally with h~ 0.074 , g= 2.8 and e= 0.004 . The
Artractor is Indicated by the Dot-Dash Line
~rhue, system (2) demonstrates a behavior practically indistinguishable from
- stochasCic, and the signal produced in the self-excited oscillator is ran-
dom.
In the self--excited noise generator described here is re~lized only one of
~ th2 posaible mechaniams for the origin of a stochastic process in self= _
oacillating e;stema. In radio engineering equipment other mechanisms can
also be realized--the decay mechaniem associated with the time lag of non- .
1lnearity, and others [10]. In connection with the investigation of self-
exc.ited noise generators per se, of obvious intere~t are questions relating
to the effect on them of an external signal, to the interaction of several
- generators of this sort and znany more. Studies along this line have etill
ju~t bPgun.
T'he authors w~ish to express thetr gratitude to A.V. Gaponov for his con-
tinued fnterest in this paper and to A.A. Andronov, Yu.B. Kobzarev and -
S.M. Rytov for their helpful diecusaions.
Bibliography
1. Go111ib, J.P., Brunner, T.O. and Danley, B.~. SCTENCE, 1978, 20~, 48. ~
93
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2. Kiyashko, S.V., Pikovskiy, A.S. and Rabinovich, M.Z. "Radio Band
Random Signal Generator," PatPnt No 69811$, OTKRXTTYA, ~ZOBRETENTXA,
PROMYSHLII3NYXE OBRAZTSY, TOVARNYYE ZNAKI, ~979, 42, 227.
3. Andronov, A.A., Vitt, A.A. and Khaykin, S.E. "Teariya kolebaniy"
[Theory of Oscillationa], ~izmatgiz, 195g. '
4. Pikovskiy, A.S. arid Rahinovich, M.I. DOKL. AN SSSR, 1978, 239, 301.
5. Smeyl, S. USPEKHZ MATEM. N., 1970, 25, 113.
6. Williama, R. TOPOLOGX, 1967, 6f 473. !
7. Ruelle, D. and Taken~, F. COMNI. MATH. PHY~., 1971, 20, 167.
- 8. Sinay, Ya.G. "Nelineynyye volny "[Nonlinear Waves], edited by A.V.
Gaponov, Izdatel'stvo Nauka, 1979.
- 9. Alekseyev, V.M. "Sy~nbolic Dynamics " in "XI letnyaya matEmatichesk~ya
shkola" [The llth ~ummer Mathematics School], Izdatel'stvo Inatituta
Matematiki AN USSR, Kiev, 1976.
_ 10. Rabinov{ch, M.I., USPEI~iI FIZ. N., 1978, 125, 123.
11. McLaughlin, J.B. and Martin, P.C. PHYS. REV. A, 1975, 12, 186.
12. Loren2, E.N. J. ATI~IOS. SCI., 1963, 20, 130.
13. Afraymovich, V.S., Bykov, V.V. and Shil'nikov, L.P. DOKL. AN SSSR,
1977, 234, 336.
14. Bunimovich, L.A. and Sinay, Ya.G. Collection "Nelineynyye volny,"
r edited by A.V. Gapo:iov, Tzdatel'stvo Nauka, 1979.
15. Ro~sler, O.E. Z. NATITRF~RSCH., 1976, 31a, 259.
- 16. Rikitake, T. PROC. CAMBR. PHIL. SOC., 1958, 54, 89.
17. Sherman, J.S. and McLaughlin, J. COMM. MATH. PHYS., 1978, 27, 1.
18. Mira, C. In "Convegno internazionale su equazioni differenziali
ordinarie ed equazioni funziona1319 [Tnternational Conference on Ordi-
nary Differential Equations and Functional Equationa], edited by R.
Conti, G. Sestini and G. Villari, 1978, Firenze [Flotence], p 25.
19. Kiyashko, S.V. and Rabinovich, M.T. ZHETF, 1974, 66, 1626. "
20. Mishchenko, Ye.F. and Rozov, N.Kh. "Differential'nyye uravneniya s
malym parametrom i relaksatsionnyye kolebaniya" [Differential
- 94
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Equations with a Minor Parameter and Relaxation Oscillations],
- IzdaL-el'stvo Nauka, I975.
21. ~akobson, M.V. DOKL. AN SS3k, 1978, 243, 866.
22. Mira, C. "VIT znt. Con,f. on Non1. Osci11.," Academic-yerlag, Berlin, -
1977, p 81. =
' 23. Li, T.Y. and Yorke, J.A. AMER. MATH. MONTHLX, 1975, 82, 985. -
- ~
24. Larenz, E.N. TELLUS, 1964, 16, 1. -
_ COPYRIGHT: Izdatel'stvo Nauka, RADTOTEICHNIKA I II,EKTRONIKA, 1980
[190-8831]
8831
- CSO: 1E60
95 _
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QUANTUM ELECTRONICS
UDC 539.04 -
THE INFLUENCE ~k' THE THER'MOPHYSICAL PROPERTTES OF A TaRGET ON VAPORIZATION
� WITH THE AGTION OF LASEP. RADIATTON
Gor'kiy IWZ RADIOFTZTKA in Ruasian Vo1 23 No 2, 19$0 pp 177-182
manuscripC received 5 Feb 79
[Article by V.I. Luchin, Tnstitute of Applied Physics of the USSR
Academy o� Sciences]
jText] The influence of the thermophysical properties of
opaque substances on the vaporization process with the action
of laser radiation at flux densities of q= 108 - 5�109 W/cm2
' is treated. Tt is determin~d that materials are broken down
according to the quan~ity and camposition of erosion products
' and the structure of the plasma flare. A br~akdown parameter
_ is the ratio of the ionization potential to the crit~cal tem-
pe~ature of the auDstance (T/kT~). Differences in tRe vapor-
ization mechanisms of the materials of the given groups are ~
discussed.
An analysis of the vaporization process of inetals wi.th the action of laser
radiation in a shielding mode, as a rule, is made without considering the
influence of the thermophysical parametere of the target material (for
example, in the self-consistent model of [1]). As experiments have shown,
this approximation is not observed, at least in the range of radiation
flux denaity of q= 10a to 5� 109 W/cm2 (the Q switched mode with a pulae
width of Ti = 30 nsec). A significant difference is observed in the nature
of the vaporization of materials with different thermophysical properties;
- in this case, it proves to be possible to split all of the absorbing con-
densed materials into two groups. The difference is manifest, in parti-
cular, in the number of vaporization products, which is determined from the
depth of the crater in the target surface and the thickness of the film on
the substrate, which is located along the scatter path of the erosion pro-
ducts in a vacuum. The crater depth for a number of materials (difficultly
fusible metals for examplel, h= 0.04 um, is approximately an order of mag-
_ nitude smaller than for the other group (for example, h m 0.2 - 0.8 um for
Cd, Sb, Pb and Bi). The thicknesses of the films condensed on the subs-
trates also differ by several times.
~ 9g
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Attention is drawn to the fact that in a large series of.investigated
mat~rials with different, but close thermophysical parameters, a sharp
d{vision of the niaterials into the indicated groups is observed. This.
m~kes it possible to preauppose a difference in the vaporization mechan-
isms, which is of a threshold nature.
The large mass removal for a number of maCerials cannot be due to surface
vaporizaticn with the action of the energy flux (reradiation, thermal flux)
from the plasma shielding the target from the laser radiation. The arrange-
~ ment of the materials studied in a series with respect to the surfa^_e
~ vaporization threshold, q* = KTi/ aTp (where Ti is the vaporization temp-
erature, K and a are the heat conductivity and temperature conductivitq
_ coefficients and the arrival time for the energy flux from the plasma Tp =
= Ti) is not in agreement with experimental data.
_ The best agreement with experiment is given by the breakdown of the mater-
' ials Lnto groups a~.cording to the specific heat of vaporization SZ. The only
possible mechanism for the vaporization of inetals, the threshold of which -
would depend on this thernophys~cal parameter is vaporization with the act-
ion of. the ultraviolet radiation of an erosion plasma, ~Only' in the ultra-
violet range in the given mode is the condition a wl � a? Tp met (where a
is tt~e absorption coefficient), for which the vaporization threshold is
q,~ = S~/aTp.
}L,MK }I~
- 0.8 ~ .
x "
x
M ~
0,4
. ~
_ 0 0,2 0,4 0,6 q~10 ,BT/cn~ wfcm2
Figure 1. The crater depth at the surface of a bismuth (1)
and titanium (2) target as a function of the radia-
tion flux density (where the diameter of the irrad-
iated area is d= 300 um).
A number of facts contradict the mechanism of vaporization wita the action .
of energy flux from the plasma.
1) The e:cperimental division of materials {nto the indicated groups does ~
not depend on the laser radiation fltix density q.
2) The depth of a crater at the surface of a target depends slighCly on
q for all materials (the curves shown in Figure 1 for bismuth and titanium
are characteristic representatives of the groups), It ie clear that the
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energy flux from the plasma should depend greatly on q, since the bulk of
- the radiation energy in the shielding mode goes to heating the plasma.
3) The shielding influence decreases in the case of small dimensions of the
irradiated area (Figure 2), because of the non-one-dimenaional acattering
of the plasma. We shall turn our attention to the similarity of the curves
for both groups of materials; the difference in the depth of the craters
does not depend on the d~ameter. Thia means that the characteristic dimen-
sion for the process which assures the large mass removal during evapora-
" tion of materials of the second group is much less thar~ the characteristic
ahielding dimensions 100 um).
_ A dependence of the laser flare structure on the propertiea of the target
material is likewise established in this paper. A complex structure with
an opaque nucleus at the surface of the target [2] is not observed for all -
materials in the range considerdd here. The opaque region is absent in
ehadow photographs of the flares of a series of materials. Tn this case,
the diviaion of materials into two groups precisely corresponds to position
in the series arr2nged according to the depth of the craters.
_ h.
~
. Z
,
. ~ _
_ ~
.
� ~ ~ r
�
~ Z
0 50 100 iS0 d,nK N~
Figure 2. The crater depth at the surface of a bismuth (1)
and titanium (2) target as a function of the
light spot diameter (where the radiation flux density
is q = 109 W/cm2).
The flare structure and the crater depth were recorded in the same experi-
. menE. The projection configuration with a phase corrector of [3] made it
possible to produce a uniform a uniform light spot on the target (nonuni-
_ formity of no more than 20%), as well as change the diameter of the apot
given a specified radiation flux density. The structure of an erosion flare
_ was studied by the shadow method with various delays relative to the irrad-
_ iating pulse. The second harmonic of the radiation comprising the plasma
was utilized for the photography; the exposure time 30 nsec) was deterrt~,
mined by the pulse width. The delay line was composed of a resonator with -
- coaxial spherical reflectors and provided for delay of the trsnsilluminating
pulse of up to 120 nsec.
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A shock wave is observed in the shadow photographs (the experiment was ~er-
formed dt at,nospheri~ pressure), the front of which propagates with a velo-
city which is the same for a11 materials: v= 106 cm~sec. Under the condi-
tions of the experiment, a point explosion approximdtion [4] can be used
to estimate the shock wave parameters, where the position of the fror.t is u5
determined by the energy liberated (E) during the explosion: Rg = F,p(E/pp) ~
�t2~3, where ~p = 1 and pp is the denaity of the undisturbed medium. The
~.ndependence of the shock wave velocity from the target material means that
energy li.h~ration in vapors as a result of shield~tng is the same for the
variuus materials. This is a natural result, since in the shielding mode,
the bulk of the radiation energy goes to heating the plasma.
It is important to note that not only the overall liberated energy ie the
same for the various materials, but also the heating of that portion of the
plasma from which the fast electrostatically accelerated ions are emitted.
This conc:lusion is drawn on the basis *_hat in this mode, the quantity,
energ}~ and amounc of charge of the fast ions registered in a laser mass -
spectrometer depends only slightly on the target material [5). It follows
from the energy balance that the portion of the plasma emitting fast ions
carries a greater share of th~ energy, though thP bulk of the vaporization
products are of 'low energy.
Thus, the precess of the vaporization of inetals with a complex flare struc-
Cure sh~u7.~1 occur in two stages. In the stage common to all material3,
there is ti~e onset of shielding, fast ions are formed and a shock wave is
excited (for the case of vaporization in a gas atmosphere); duxing the
second ~tage, a considerable mass of vapor and liquid phase droplets are
removzd fr~r a number of materials, where these form an opaque nucleus, the
- front of which propagates at a velocity of (1 - 3) � 105 cm/sec.
F'e will note that the presence of liquid phase droplets in tbe composition
of the vaporization products registered on the substrate during vaporiza-
ci.on in a vacuum precisely correlates with the presence of an opaque zone
in ;.iie rlare and deep craters in tne surface of the target. The absorptior.
. and scattering of the radiation at droplets is inherently due to the opa-
queness oF the nucleus. The plasma opaqueness is possible only at densi-
~ ties much greater than those attainable in an experiment (less than 1020
cm�3); the electron concentration, which corresponds to the plasma fre-
c{uency, is equal eo the frequency of the transilluminating radiation, n=
= 4~ 10~1 cm'3 � 1020 cm 3. There remains the absorption and scattering
. at the droplets; in this case, to explain the aharp boundary of the region
c~f opaqt~eness, it is necessary to meet the condition a'1 � R(a is the ab-
sorpti.on coefficient, R is the dimension of the opaque nucleus). This con-
dition, as estimates show [6], is not met when the size of the droplets is
. r� a= 0.53 um, or vice versa, when r� a. The requisite size of the
dt�oplets, r=~, corresponds to that observed experimentally (r = 0.1.-
- 1 um).
_ As was 3hown above, the second vaporization stage cannot be due to energy
flux from the plasma. The energy needed for the vaporization of the bulk
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of the material is appsrentl~ atored in the target prior to the shie:l_ding
of the surface. Photographing a f1Are at sma11 de7.ays has shown that the
opaque nucleus appeare a~`. the onaet of the pulse. The ma~oz masa removal
cannot be due to this load relief of the material following the completion
of the pressure pulae, something which is presuppoaed in the caee of aev-
eral Zarge fluxes j2]. Th.e energy which is stored in the shock wave over
a amall portion of the pulse is ineufficient for intense vaporization. The
second stage likewise Gannot be related to surface vaporization of the la-
yer heated up prior to the onset of shielding in view of the rapid cooling
of the surface during vaporization.
- The experimentally observable removal of mass can be due only to the bulk
explosion of the heated layer. The most acceptable model is that of ex-
plosive decay of a metastable state of a superheated liquid phase [7].
We have to expand the model by explaining why the explosion of the super-
heated liqu~d does not occur for a number of mater3als.
The assumption of liquid metal dielectrification effects and the explosion
of the superheated melt is made in paper [7] to explain the special features
of the behavior of the recoil presaure pulse during the vaporization of
lead [8]. Lead belongs to materials having a complex flare structure.
We shall turn our attention to a qualitatively dif.ferent kind of pressure
pulse in the case of the vaporization of aluminum j8] - a material which
belongs to the other group. We explain the absence of explosive decay of
a metastable state during the vaporization of materials of this group by
the fact that the shielding begins earlier than the heating of the super-
heated alloy up to the temperature of absolute instability. Since the
. radiation heating of the liquid is terminated due to shielding, while the
temperature and pressure of the vapors rise, the degree of superheating of
the melt decreases and explosive decay of the metastable state does not
occur.
We divide the mater3als into groups based on a parameter which defines the
development of shielding at a vapor temperature corresponding to the tem- ~
perature of absolute instability of the melt (T = 0..9 T~)o We sha11 as-
sume that prior to shielding, the vapor temperature is proportional to the
surface temperature of the target [6J. Then the condition for explosive ~
boiling of the melt will be absence of shieldin~ at a certain vapor tem- ~
perature T* _~T~ (g ~ 1). The proportionality factor s does not depend
on the target material, and for this reason, varioua materiala at the point
in time of the explosion arz in correaponding statea with the cited temper-
ature T~ = T*/T~ = s. The exponential factor e-e/kT* (e is the vaporiza-
tion energy per atom) which enters into the shielding criteria [9] is the
same for different materials. The single strong parameter which defines
the ahielding process will be the ratio.T/kT*, which enters into the ab-
sorption factor of a weakly ionized gas K= e'r~ZkT [4] (T is the ioniza-
tion potential).
l0a
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_ ~ v~� v~ ~ tVt~u.1 ~vL VL\L~
_ Thus, the ratio y= I/kT~ wi11 determine whether the explosion of a super-
heated liquid has time to occur (Y > Y*) or the ~hielding wi11 set in ear-
' lier and prevent explosive boiling ( Y< Y*). The materials inveatigated
here are arranged in order in the Tab1e according to the paramete~ y. Tin
can be considered a threshold material (y = y* = 10.3) under the ,:onditions
of the experiment: an opaque nucleus was not always observed in the flare.
Tabl.e
(1~Marep~an xxutettel Ti I A1 I Sn Pb B! Cd Sb
I~I
!/kT~ 6,7 8,6 ]0,3 17,3 22,5 37,1 38,9
~ 2 ~IertpospayNOe
AAPO D ~8KC11G~ , - - f -I' "I"
rJIY6HH8~~
(3~panpa, .NK~NYQ. 0,04 0,04 G,3 0,4 0,8 0,2 0,4
Key: 1. Target material;
2. Opaque nucleua in the flare*
3. Depth of the crater**, m�icrometers/pulsa;
* The sign corresponds to the presence of a nucleus in the :
flare and the sign corresponds to the absence of a nucleus.
The crater depth at the surface of the target was measured
following irradiation with a eeries of 100 - 200 pulses.
The thickness of the superheated liquid layer is h= 1/a (a is the radia-
tion absorption factor in the condensed medium), since thermal conductivity
is not significant at the point in time of tha explosion. The absorption
factor of inetals, a= 105 - 106 cm-1 cannot assure fihe deep heati,ng cor-
responding to the crater depth of h= 10'4 cm. Drawi,ng on the effect of
liquid metal transmis~ion augmentation for the mode7. [10] provides agree-
ment saithin an order of m~gnitude of the thickness of the superheated _
_ layer j7] with the E~xn~rimental values of the deptR of the crater at the
target aur~ace.
The model treated here is in agreement with a number of experimental facta.
The depth of the crater depends slightly on the radiation flux density
(Figure 1) just as the thickneas of the superheated melt layer [7]. -
With a reduction in the eize of the ~rradiated area, an increase is obser-
ved in the depth of the crater for all of the materials studied (Figure 2).
For materials with an opaque nucleus in the flare, the curve is elevated
by the amount of the depressio~ corresponding to the explosive stage of
vaporization (for all sizes). Nonuniformity should be manifest for the
other p:resupposed mPChanisms, something wnich wculd lead to the absence
of a similarity in the curves of the two groups of materials. Tn the
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proposed model, the characteristic dimension - the size of the nuc?.eation
of the gas phase in the melt - is much less than the diameter of the ir-
radiated area and does not manifest itself.
- The influence of uniformi~y in the diatributi~n of the flux density over ~
Che croae-section of the light beam on the aubdivision of the materials
into two groupe argues in favor of the meehaniRm coneidered here. In the
caae of poor ~~niform~Lty, the lifetime of Ctie metastable etate of the melt
decreases, since bu~.k boiling in the pure ~iquid begins at the thermal in-
homogenei,ty. As a reault, the boundary ~etween the groups should shift in
the d.:::; *.ion of~'the materials with a lower Y, something which is also ob-
served exp;~rimentally. With the vaporization of aluminum by focused radia-
tion, droplets of the liquid phase are observed in the e.~osion products,
while the depth of the crater is increased by an order of magnitude as com- -
pared to the case where a spatial corrector is utilizedo
The author would like to express his gratitude to Yu.I. Nikitin for assis-
ting in the performance of the experiments and S.V. Gapoa,ov and N.N.
Salashchenko for their usefuJ, discusaions of the work.
BIBLIOGRAPHy '
1. Yu.V. Afanas'yev, O.N. Krokhin, TRUDY FTAN jPROCEEDINGS OF THE INSTITUTE
OF PHYSICS OF THE USSR ACADEMY OF SCTEIdCES T'MENT ~R.N. LEBEDEV], ~2,
118, ~1970).
2. N.G. Basov, O.N. Krokhin, G.V. Sklizkov, TRUDY FTAN, 52, 171, (1970).
3. S.V. Gaponov, N.N. Salashchenko, Ya.I. Khanin, KVANTOVAYA ELEKTRONIKA ~
[QUANTUM ELECTRONTCS), No 7, 48, (1972),
4. Ya.B. Zel'dovich, Yu.P. Ray2er, "Fizika udarnykh voln i vysokotempera-
turnykh gidrodinamicheskikh yavleniy" ["The Physics of Shock Waves and
High Temperature ~iydrodynamic Pher.~mena"], Nauka Publishers, Moscow,
1966. -
5. G.G. Devyatykh, N.V. Larin, G.A. Maksimov, ZH. ANALIT~ KHIM~ (,TpURNAI,
- OF ANALYTICAL CHEMISTRY), 29, 1516, (1974).
_ 6. S.I. Anisimov, Ya.A. Imas, G.S. Romanov, Yu.V. Khodyko, "Deyatviye
lazernogo izlucheniya bol'shoy moshchnosti na metally" j"Z'he Action
of High Power Laser Radiation on Metals"], Nauka Publishers, Moecow,
1970.
7o B.M. Kozlov, A.A. ~amolchin, A.B. Uspenskiy, KVANTOVAYA ELEKTRONIKA,
4, 524, (1971).
8. Ya.T. Gnoyevoy, A.T. Petrukhin, Yu..Ye. Pleshanov, V.A. Sulyayev,
PIS ~MA. V ZhETF [LETTERS TO THE JOURNAL OF F~XPERtMENTAZ .s,ND THEORETICAL
PHYSICS), 11, 440, (1970).
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9. G.G. Vilenskaya, I.V~ Nemchinov, ZhPM i TF [JOURNAL OF APPLTED
MATHEMATICS AND ENGrNEERTNG ~HYSICS], No 6, 3, (1969)
10. V.A. Batanov, F.V. Bunkin, A.M. Prokhorov, V.B. Fedorov, ZHETF,
63, 58~, (1972).
COPYRIGHT: "Izvestiya vysshikh uchebnykh zavedeniy," "Radiofizika," 1980.
[192-8225]
8225
CSO: 1860 -
~
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- RADARS, RADIO NAVIGATION AIDES, DIRECTION FINDING, GYROS
UDC 621.37Z2:551.46
ON SPATIAL FLUCTUATIONS OF STRENGTH OF RADAR SIGNAL REFLECTED BY
SEA SURFACE
Gor'kiy, IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENIY, RADIOFIZIiCA in Russian
Vol 23 No 1, 1980 pp 79-89 manuscript received 11 Jan 79
[Article by L. S. Dolin and V. V. RodinJ
[Text] Expressions for the spatial spectra of fluctuations
of the strength of a radar sigrzal refiected by a sea surface
are derived within the framework of "resonance" theory of
the scattering of a microwave field on the sea surface. It
is shown, in particular, that large-scale formations in a
radar image of a water surface may occur as a result of non-
linearity of the relation between radar signal strength and
the slopes of surface waves (the "detection" effect). The
possible influence of irregularities of the wind field above
the sea surface on the formarion of its image is discussed.
Radar systems have been attracting increasing attention in recent years for
studying the wavy sea surface and, in particular, for recording different
kinds of surface formations, for example ocean swells, pollution (oil
_ slicks), currents, etc. They provide quality images of a surface and of
large-scale disturbances on it (see, for example, [1-3]), but the latter
have to be identified against a background of spatial noises of different
origins. A statistical analysis of some of these noises is the subject of
this article.
1. Strength Structure of Echo from Wavy Sea Surface
We assume that the radar observation system uniformly irradiates the sea
surface within the scanning sector (Figure 1) and performs reception-
transmission of quasimonochromatic pulses of identical polarization p
(which in the numer-ical calculations is assumed to be vertical). A radar
(RL) image of the surface is defined as the intensity of the backscatter
field (Ep) as a function of the coordinates of the center of the resolution
_ area (pulse area). We will find the characteristics of the reflected
signal from the formulas of the "resonance" theory of the scattering of
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_ ultrashort radio waves [4], developed for a two-scale model of the surface.
According to this model the profile of the sea surface is approximated by
the sum z(r, t) _~(r, t) +~(r~, t}, in which the first term describes
large flat surfaces with a radius of curvature much larger than working ~
wavelength ~ of the radar, and the second describes level irregularities
of relief with a small, in the scale of a, c}iaracteristic height ("rip-
ples"). Through r~ we denote the radius-vector on the profile of a large
wave: r~ = r+~(r, t)z~, where r is the radius-vector of a point on -
median plane z= 0. The spectrum of the spatial correlation function of
the large-scale component of wind wave action -
- W:~x) = t ~ f e-r%Q dp ~1~ -
~2r~1 ~ ~
is assumed to be [5]
. W: (Y~ _ ~ exp 2 ~ ~
x~ ~ - 0,74 u4 x~ 1 ~ CO5 - 'Yn) ~ ~2~
L ~
. where x- ~ x -(x,
x�), u- ~ u u is the wind velocity 19. 5 m above sea
~
level, and ~o =(u, x�), g= g,g Mfc~, ~3� 8� 10-3 (the Pearson-Moskowitz
spectrum).
a
~ p' -
i
i
~ Ro ~ ,
i
i ,
i
i
~ -
_ i
i
- ~ i ~
- ~ ~o -
i - -
~ ~
I r0 ~
- I
, , qe i
i
f ~o ~ o
~ az
Figure 1. Geometry of problem: x~ direction of prc~pa-
gation of probing pulse, ~x, ~y dimensions of resolu-
tion area (rectangular), r~(x~, y~) radius-vector of -
its center, RD distance between radax and point (x ,
0
y0)' ~p grazing angle of incident wave, p-- polariza-
tion vector of receiving-transmitting antenna.
lOS
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_ The ripple spectrum
-
WE ~x) _(2~)~ f c(r; -i- P? t) ; lr~, t) e-t"P d P~
~ (3)
in accordance with Phillips [5], is written as
WE (x) ~ Cx-+, ~4)
and we will assume that the parameter C that characterizes the mean square
height of a ripple may depend on r and t: C=~~[1 + u(r, t)J. This -
assumption does not contradict spectral representation (3), if the charac- -
teristic scales of an irregularity u(�) spatial (~ru) and time (~t~)
are large in comparison with the radius and correlation time of the
ripples. The symbols - and denote statistical averaging of sets of
sampYes of ripples and large ~vave.
Intensity I of the echo from the described type of surface, based on
results published in the literature [4], is expressed as
~~ro~ t) EP ~ro~ t~ Ep ~~o, t) = K~~o, t)N(ro~ t)~ ~S~ -
K(~o~ t) = k~4 ~ BP ~Y (To, t)1 1-F- �~ro~ t) . ,
2n o 1- v'(ro? t) ' (6)
_ N ~ J J', ~
~
fJ `~(r~)~"(ro+ r,, e)exp[--iq~ro~ t)r~l ~r,,
_ro
9(ro. t) 2k cos z� - 2k s i n~~o p C(r,,, t); ~
~~r~ 1 for ~ z Ox/2 and ~ y Dy/2 =
1 O for ~z~ > ~x/2 or I y I > ~ y/2 ~ ~8)
where v(�) is the projection of vector ~(�1 of the unit external normal to
the surface onto plane z= 0, the expr~ssi~n for Bp[v(�)] is presented in
the literature [6] [see formula ~4)], ~St(�) is a statistically homo-
geneous field with space spectrum C~x-4, k= 2~r/a.
Formulas (5)-(7) are based on the following assumptions: 1) the resolution
area (~x, ~y) is small in comparison with ~ru and characteristic wavelength
of a large wave A; 2) ~(r, t), ~(r, t), u(r, t) changes slowly in scale
2R~/c (c is the speed of light); 31 the self-shading ~ffect of the surface -
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is insigriificant (~V~ ' ~~~max~' 4~ the pulse area is located in the
Fraunhofer zone of the radar antenna.
A radar image of a sea surface is made by real systems by means of repoatod
irr~di~tion of each element of the surface (with dimensions (~x, ~y)) and -
accumulation (in time ~t~) of the energy of a sufficiently large number n
of samples of the reflected signal. An image made in this way can be -
described as
' [H=1rii t ] f~m ~~o) = K (ro, f�) ~t N (rn, tN -f- m/F~) ~ ~9~
- where tinit is the initial time of observation of a given element of the
surface ~tir~it - y0~~init if the discussion refers to~a side-looking radar,
installed on an airplane flyi:zg at velocity V. along y~); we assume that
init
~ ~~fiinit +~tE~ ~~~tinit~' Fn is the probing pulse repetition frequency
(~n~t~ � 1); n ~ Fn~t~.
Iim may be expressed as
l~m = ~tm -f- ~1~~m = lt~ ~ 1-{- o I~m) (10)
(I~m is the result of averaging of Iim from samples of ripples on the
f-rozen relief of large waves);
S I~m ~~m _ ON(r~, t F~ rr~~Fn )~Ntc,
~~m +n-?
~N(�) ` N(�) -N; (11)
- ~im = ~tK(�)!V. ~12)
Imag~ (10), generally speaking, is random in nature in view of the
- irregularir.y of wind wave action. It represents an additive mixture of
two noise components, one of which Iim depicts the structure of a specific -
sample of the large-scale component of wave action and spatial irregular-
ities of the ripple distribution [see (12), (6)], and the other ~I. is
im
noise with zero mean [see (11)], modulated by the function Iim. The -
analogous representation can also be found for Iim in Zagorodnikov's
work [7].
Spatial noise DIim occurs because the field scattered on the resolution
area has a random, very "choppy" angular distribution, since it is the
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result of the interference of many uncorrelated w..~ves, coming from
different "elementary scatterers.~' We will call this noise interference
noise to distinguish it from noise Iim, which, in turn, is called modula-
_ tion noise. We will examine two varieties of the latter below. In part 3
we will talk about modulation noise (linear and nonlinear), which occurs
during the observation of spatially homogeneous wind wave action (u = 0),
whiZe the noise exaT=ned in part 4(u ~ 0), modulation wind noise, owes its
origin entirely to turbulent pulsations of the wind velocity in the near- =
surfaco layer of the atmosphere. _
2. Interference Noise
An echo from a fixed resolution area, as is known, fluctuates in time and
has a finite correlation time ~t~. In the time it takes to accumulate sig-
nal ~t~ from the element ninit -~t~/~t~ uncorrelated parcels of pulses
will be received, each of which will contain n/ninit correlated pulses.
- Converting in (11) from the adding up of pulses to the adding up of
uncorrelated parcels, we write the expression for a sample of interference
noise in the form
~ ~
[k=c] Sl,m = n~;�~~~N~~'o~ tE~ m ~tH)lNn. (13)
R~ m,e~
In accordance with (7) the real and imaginary parts of the scattered field
may be viewed as being the sum of a large number of independent random
variables with zero mean. Therefore Re J and Im J can be expected to have
normal distribution, the modulus of the complex amplitude of the radar sig-
nal can be expected to have a Rayleigh* distribution, and N=(Re J)2 +
+(Im J)2 has an exponential probability distribution:
P(N) _ ~ exp.(- ~ 1 , _(oN)= _ (NY, ~14~
\ /
_ Then it follows from (13) and (14) that (dI~ = 1/ninit'
Assuming random field ~St(�) to be normal w~th a radius of correlation much
smaller than Ox, ~y, we obtain from (5) and (13) for the sp3tial correla-
tion function of interference noise the expressions
*This assumption does not conflict with existing experimental data on ~
deviations of the statistics of a radar signal, scattered by a sea sur-
face, from Rayleigh (see, for example, On the contrary, as was
shown in [9], such deviations (for ~x, ~y � A) may be viewed as being the
result of chaotic modulation of the amplitude of the echo signal ~y large
waves and the signal has Rayleigh statistics during the time the large- -
~ scale relief is "frozen." _
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8~~,,, ~P) = S I~m (P ro) s f~m (ro) _ ~bm ~P))`/ ~bm nx ;
~ (15)
bs ~P) = 1 J J`~ ~r -I- P) ~(r) d r,
(~z~y)
~
JJ bafP)dPa 1. (16)
_ The correlation function of relative fluctuations, as we see, does not
depend on the parameters of ripples and is determined entirely by the I.ind
nf "system" �unction ~(r), i.e., by the size and shape of the pulse area.
In the case when ~(r) is given by formula (8), we obtain from (15) and (16)
Ba~ / 1 ~ P.~ ~ s-- ~ Pr ~ Z l fos~ ~ px~ < t1x and ~ py~~~y
Im \P~ - (1 - (1 l j
- nx \ ~ ~Y 1 l 0 for ~ Px~ > ~x or ~ py~ ~ Dy~ (17)
_ Here the energy spectrum of spatial noise is
_ Wa~,~, (x) (2r)~ J J Ba~~,~ ~P) e-txpd p_ -
~ 4~z~y Il1- sin ax \11 1- sin ~18~
R�~az ay ` ax / ~ Qy ~ '
~vhere ax = ~xKX, ay = ~yKY. In the range of low space freqUencies (KX �
� 1/~x, KY � 1/py) expression (18) yields a spectral density that does
n~t depend on K:
ax~y
~d/~m .
2'~'n~ (19 ) -
~iodulation Noise in Homogeneous 3Vind ~Vave.,Action
4ve now will calculate the spatial fluctuations of Iim. According to the
formulas in section 1
,~~~ro) = 2~ k~ f J f~Y~r)~ Il F~~r)~ ~'(r - io)dr,
Ro
f~Y) = 1~ I Ba~y) ~Z W: - 2k cos ~,ox� 2k sin ~2 y (20)
1 y- L .YI y J
(We note that when writing (20) we are not required to satisfy the condition
~x, ~y � fl, ~r
u
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Table 1
I 2 I 5 S 10 20 30 50 70
de I ( I I
j(0) 10-~ 0,13 0,34 d,5 1,2 1,5 l,4 1~1
ax 90 27 14 9~9 3,9 2~9 4,2 10~4
o.TX 2,5~I0~ I60 ?1 5,5 0,8 3~0 12 � 70
ayy -2,5 -2,2 -2,0 -1,8 -1,7 -2~0 -4,0 -16 , .
~omment: aY = 0. The data in the table pertain to the case when
- a= 3 cm, e= 60.5 - i30 (e is the dielectric constant
of water), p=-sin ~,~x~ + cos ~,Oz~ (radiated and
received signals vertically polarized).
We expand f(v) into a series by powers of v(vX, vy) (see Table 1):
f(y) = f(~)~1 -f a: "X -F d.~.~ vx arrvy -f- . . (21)
and, after substituting (21) into (20), ~e obtain the function
T~rn) = I~~(roU~~~~]�:o = 1 (~'r [1 -f- a,~vx(r)
(~x~y) J~, (22)
aXrvz(r) arv~y(r) . . [1 + ~l(r)]m~(r - ro)dr,
which yields the amount of contrast at an arbitrary point on the radar
image in relation to the horizontally oriented (v = 0) elements of the pro-
file of a large wave with an undisturbed spectrum of small-scale irregu-
larities (u = 0).
Equation (22) shows that in the absence of a la7ge wave (v - 0) the radar
will give a linear image of spatial variations of the mean square height
of a"resonance" ripple (the latter has the wave vector K x 2k cos ~,Ox~,
see (7)). When v~ 0, but u- 0, and the terms of series (21) with powers
vX, vY higher than the first are ignored, the radar image may be viewed as
being the result of linear filtration of the spatial distribution of the
slopes of the profile of the surface in the plane of sight [lOJ. Now,
however, when the quadratic terms (which we shall stipulate below) in (21)
are taken into consideration a unique kind of space noise, produced by
"detection" of a"linear" image on a quadratic nonlinearity (v2, v v,
x x y
etc.), will appear in the image of the surface. The strength of this noise
_ is determined by the mean square fluctuations of the normalized intensity
of the echo signal T(r~))'- >(~1 T(ra) = T(rol T~), assuming that wind _
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- wave action produces a homogeneous rar,dom field of irregularities ~(r)
(with spatial spectrum (1), (2)), and assuming u(r) = 0(the case u(r) ~
- ~ 0 will be examined ir *he next part). We find the desired estimate by
finding the space spectrum W~T(k) of fluctuations ~T(r~). The correspond-
ing calculation (it is not presented here because it is unwieldy), carried
out on the assumption that v(r) has a normal distribution [11]*, using
formula (22)**, yields _
lY/, T(x) - 4a'w'(x) ~ ai W ~x (x)'
(23)
_ 2aXr lY/~x (x - x, ) ll%~x (x,) d x, l ~ ,
where
m
W'r ~x~ (2,~), s~ T~~� -f- p) ~ T~ro) ) e-t xP d P,
I~y (x) _ 1 ~ f C v~r P) � r> e !xa d _
x (2~)2 ~ x o x~ o) p, ~~4)
1 r sln (x.r ~x/2) sin (xv 0 v/2)
w (x) _ ~
(2~)~ L x,~ o x/2 . ~x
y ~ y~2 ,
_ _
w(K) is the spectrum of the function By (P) = 1 f~ Q~'(r-{-p) 4~~(r) d r,
(Ox ~y)~ ,
,vith the condition that ~(r) is of the form (8).
'Co simplify the ensuing calculations we will replace spectrum (24) with the
"equivalent step spectrum," which satisfies the conditions
~ � -
~'3 _ .~f w. ( I x I ) d x � .~f w (x) d x
~
an:.i is written in the form
~s ~x~ _ J~/4'~' for I x I G xo 4r. ~ t~
l 4 for I~ I~ x o ~ ( Ox~ Y /
_ *This assumption enables us to express the fourth-order moments of field
v through the second-order rr~ments,
**We keep the first two terms in the integrand in (22), since (see Table 1)
ayY � aXX everywhere, where aXX z aX (i.e., the term that is quadratic
in terms of vX may make an appreciable contribution to aT).
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In (23) we replace w(K) with we(K), integrate the resulting expression for
WaT(K) (considering the fact that when ~v~ � 1 W~ (K) _(Kx~)2W~(K)) and
- x
find thP desired value . It is the sum of the linear (MA ~ 3 sin' po ~ for m ~ 1 +
(26)
2a~X vX ))Z for m~> 1
~ 4- u' 4r= u~
m 0~74 g~ (Oz ay) ~ < Yz 8 r In U~74 gz - 0,581c1-}-2 cosz~oo).
L J
The form of is found, as in [11], by integrating WJ (K) in the inter-
_ va 1 0 G ~ x 2~~~. x
Table 2
0 5 ~ 0 ~ r~= 3.u~c 1
~ ' ~ Oz, Dy-+0 1
'~a Nn I < (c1%' )A ((~1 7' )~)aa I < >n T )~)un I < r >n
deg
2 9,3 8.3 � 10-~' 37 i,3 ~ 10-~ 7,8 � t03 200
5 4� 10-~ 7,5 �]0-~~ 0,16 6,G �!0-' 32 l8
8 7� 10-~ 2� 10-'~ 2,i � 10-3 I,8 � 10-3 0,55 4,9 .
- 10 4,5 � 10-5 ~ 10-'a I,g . iQ-' 8,8 � 10-+ 3,8 � l0-~ 2,4
~ 9,6 � 10--' ; 1,6 � 10-13 3,9 � t0-6 1,4 � 10-' 8� 10-' 0,38
30 1,3 � 10-s . g 5, ~p_~+ 5,4 � 10-5 7,5 �!0-s l,l � 10-~ 0,21
50 2, I� 10-~ ~,g � 10-~' 8,4 � 10-' I,G � 10-~ 0,18 0,44
70 7� 10-~ ~ ~p-~a 2,g. I(3-~ 10--3 6.1 2,7
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, The values of > ~y~). = l