Directional properties of ultrasonic waves scattered from rough surfaces with applications to electromagnetic scatterin

Moore, R. K.

Parkins, B. E.

English

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IVERSITY OF KAISAS 
,a-298 
ABSTRAkCT 
The resulzs of an investigation of the directional properties 
of waves scattered from rough surfaces are presented. The bi-static 
scarering of ultrasonic waves has been measured for planar surfaces 
o: czerent known roughness, and the average differential scattering 
cross section computed. The value of the acoustic measurements is 
considered from the viewpoint of validation of electromagnetic 
theories of scattering. 
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OMNIDIRECTIONAL SCATTERING OF ULTRASONIC WAVES
 
FROM ROUGH SURFACES OF KNOWN STATISTICS
 
'WVTH APPLCATION TO ELECTROMAGNETiO SCATTERING
 
R. K. Moore and B. E. Parkins * 
Introduction 
In the investigazion of electromagnetic radiation phenomena,
 
t has ofzen proven useful to conduct acoustic model experiments in
 
cases where the analogous electromagnetic problem presents difficulties 
This has been done successfullynot easilV or conveniently solved. 
in the study of antennas [ and-in the areas of scattering in 
areas ofturbulent media[ 2 and from rough surfaces L 3 j . The 
investigation are restricted, however, by the scalar nature of the 
acoustic waves, and the study of polarization effects is necessarily 
An important application of model experimentazion is thenexcluded. 
phenomena for which polarization is notthe study of electromagnetic 
more important, application, and the oneimportant. Another, perhaps 
considered here, is the verification of theories for which the acoustic 
and electromagnetic forms have common foundations.. 
The model experiments described here were performed to 
scatter from roughinvestigate the characteristics of omnidirectional 
surfaces. The scattering surfaces were constructed to be smooth 
Kansas
• Center for Research, Inc., University of Kansas, Lawrence, 
ptA N Aeu1sT 4IOa 
2 
enough 	to sar_,sfy the conditions of the Kirchhoff theory of scatteringr 
and the experiments, therefore, provide information useful for
 
z,e verification of this theory.
 
,3chnieue of Exoerimenz 
The charac'teriszics, of omnidirectional scatter were investigated 
by measuring bi-statically the average differential scattering cross 
section QSI o, as a function of the set of angles (@e ' "2 ) 
(see figure :K) ax~d the parameters describing the rough surfaces. At 
the frequency used, the surfaces were sufficiently rough to achieve 
a A.ear-complete conversion to scatter power. vthis case, the 
average power received is 
T 2 o r-2 dA (1) 
s 4 rr 	 4 vr 
where: 	 <P> is the configuration average of the received power 
Gr!) and t(,It) are the gain functions of the acoustic 
transducers
 
X is the wavelength
 
S is the illuminated area
 
P is the transmitted power
 
The transducers used were of high direczivOify (0 0 between half power 
--. perrmitting the arroximaztion. to be made that a0 is constant 
over the illuminated area; using this in eq. (1) gives 
. ££ P )G_ !t 2 ( r 
<P>p G 2 ) 2 dA (2). 
s 40rr 4 ir 
The measurement of a 0 was done by measuring <P> over an ensemble 
of rough surfaces and evaluating the integral over the illuminated area 
(thereby accounting for "aperture effect") as a function of the angles 
0a ' 01 ' 02 
The experiments were performed in a water rank of dimensions 
6'x 8' x 11' ) (see figure 2). Because of the proximity of the tank 
wallsand the surface of the water, it was necessary to use a pulse 
modulated oscillator, which operated at a frequency of one megacycle 
was( = 1.5 millimeters in water). The pulse width of the modulation 
sufficlently long to establish a beam width limited condition ro3 and the 
transmnzzed power in eq. s (1) and (2) is a constant in time. The ensemble 
of rough surfaces was obtained by.rotating the rough surface targets 
(shown in figure 2) through the transducer beam thereby generating the 
fading signal from which the average power was calculated. 
Two planar rough surfaces with different reflectivizies and 
surface roughnesses were constructed. One of these was made by 
striking mild steel sheet randomly with a ball peen hammer. The 
other surface was made by flowing grout over a sand surface thereby 
producing a smooth surface with reflectivizy different from steel. The 
surface roughnesses were determined by making' sampled height 
measurements using a depth gauge .mounted on a machined surface. 
From these measurements the sample distribution of heights and 
sample autocorrelation function of both' surfaces were calculated. 
These are shown in figures 3 and 4. The waves of.the sample auto­
correlation funcions are fit, approximately, by the Gaussian function 
2 
r = e 
nowever, near the origin a three halves power function gives better 
agreement. The sample di-stribution functions are seen'to be approximately 
Gaussian. 
Results 
Measurements of a 0 were made as a function of the azimuthal 
angle, 0 , for a range of values of the depression angles 1 and 
ao against 0. for variation of 
€2 " Figures 5 and 6 show curves of 
the depression angles when they are both equal. Figures 7 and 8 show 
the variation of 0 against 0 when the depression angle @ is fixed 
at.400 and 2 is allowed to vary. The curves. for both surfaces are 
similar in shape and-the difference in the surfaces is shown, largely, 
by the relative amplitudes of the curves. An important feature which 
is common to the curves of figures 5 and 6 is the near-constancy of 
( 2' o=0).a0 in the specular direction 1 =  
Summarwand Conclu-sions 
The measurement of the scatter of acoustic waves provides a 
basis for determining the validity of theories for the prediction of the 
analogous electromagnetic scatter as all- electromagnetic scatter theories 
also take an acoustic form. The omnidirectional measurement of 07o 
gives a complete description of the scattering (no restriction on angles 
of incidence or observation) and therefore affords the opportunity to 
make a nore rigorous test of theory validity. The experiments 
described here are especially useful for this purpose as the scattering 
surfaces are of known roughness. A prediction of the experimental 
resulzs based on the Kirchhoff approximation has been made and will 
be reported on at a later time. 
.cknowledgements 
The support of the National Science Foundation under grant 
NSF GP 2259 and the National Aeronautics and Space 4dministraz±on 
under grant NSG 298 is- gratefully acknowledged. 
_ 
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61 
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References
 
Jordan, E. C. 
-Acoust 
 c Models of Radio Antennas, " Ohio 
State Universitv Engineering Experiment Station Bulletin 
.108, May, 1941.
 
Edisofn, 
 A. , D. Bliss, and G. Fol<icky. "Acoustic WavePropagation in a Random Medium, " presented at theTall, 1963 tYRS! meetxng.
 
Moore, R. K. 
 "Acoustic Simulation of Radar Returns,Microwaves, vol. 1, no. 7, Dec. 1962, pp. 20-25. 
FL1 
_zc.mann, P. and A. Soizzichino. The Scatering ofEleciromaanetic Waves from Rough Surfaces,Macmillan Comany, 29. 
TheNew Yorkp. 
Morse, P. M. and H. Feshbach.Phvsics Mezhods of TheoreticalMcGraw-Fill Book Company, Inc., New
York, p. 1O6. 
Moore, R. K. and C. f. Williams, Jr. "Radar Terrain Returnat.Near-Vertical Incidence, " Proc. IRE, vol. 45, Feb.1957, pp. 228-238. 
rtort Yt	 r 
r 
r 
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GEOMETRY 	 OF BI-STATIC SCATTER)NG 
FIGURE 1 
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Omnidirectional scattering of ultrasonic waves from rough surfaces of known statistics with application to electromagnetic scattering

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