Monostatic reflection from statistically rough sphere, electromagnetic properties of smooth sphere from bistatic power measurement, and acoustic differential reflectivity developmen

Doran, J. A.

Erteza, A.

Lenhert, D. H.

English

NASA Technical Reports Server

SEMI-ANNUAL STATUS REPORT 
(1 May 1965 t o  31 October 1965) 
* 
Technical R e p o r t  E E - 1 3 0  
Ahmed Erteza 
James A .  Doran 
D o n a l d  H. Lenhert 
D e c e m b e r ,  1965 
T h i s  w o r k  performed for 
N a t i o n a l  A e r o n a u t i c s  and Sp?c:e 
A d m i n i s t r a t i o n  under G r a n t  
N u m b e r  N s G  129-61 
https://ntrs.nasa.gov/search.jsp?R=19660008876 2020-03-16T23:31:33+00:00Z
-4 
c ABSTRACT 
This r epor t  preserrts a summary of the work performed under 
This work i s  NASA Grant N s G  129-61 during the last s i x  months. 
aimed a t  ' g e t e m i n i n g  the sur face  p r o p e r t i e s ,  both electromagnetic 
and roughness, of a s c a t t e r i n g  body from measurement of the 
polar ized  r e t u r n  power. 
the monostatic r e f l e c t i o n  from a s t a t i s t i c a l l y  rough sphere,  
determinat ion of electromagnetic p r o p e r t i e s  of a smooth sphere 
f rm b i s t a t i c  power measurement, and development of an acous t i c  
d i f f e r e n t i a l  r e f l e c t i v i t y .  Also presented is a sho r t  d i scuss ion  
of a reas  of f u t u r e  work, 
The major areas of i n v e s t i g a t i o n  a r e  
i 
TABLE OF CONTENTS 
Page 
1 1.0 In t roduct ion  . . . . . . . . . . . . . . . . . . . .  
. . . . . . . . . . . . . . . .  1 2.0  Theore t i ca l  S tudies .  
2 -1 Monostatic S c a t t e r i n g  from Sta t i s t ica l  
2.2 B i s t a t i c  S c a t t e r i n g  f r o m  Determinis t ic  
1 Surfaces .  . . . . . . . . . . . . . . . . . . .  
S u r f a c e s . . ~ . . e . . . e . . . . . . . . . .  2 
3 2 .3  Acoustic S c a t t e r i n g  from Surfaces  . . . . . . .  
3.0 Future  Work. . . . . . . . . . . . . . . . . . . . .  3 
3 -1 Continuation of Monostatic S c a t t e r i n g  
3 . 2  
3.3 
S t u d y . .  . . . . . . . . . . . . . . . . . . .  3 
B i s t a t i c  Sca t t e r ing  f r o m  a Stat is t ical  
Surface . . . . . . . . . . . . . . . . . . . .  
Comparison of the  Kirchhoff-Huygens and 
4 
t h e  D i f f e r e n t i a l  R e f l e c t i v i t y  Approaches. . . .  4 
4.0 Papers Submitted . . . . . . . . . . . . . . . . . .  5 
5.0 T r a v e l . .  . . . . . . . . . . . . . . . . . . . . .  
ii 
4 . 
SEMI -ANNUAL STATUS RZPORT 
(1 m y  1965 t o  31 October 1965) 
1.0 In t roduct ion  
This  report p resen t s  a summary of t h e  t h e o r e t i c a l  work ac- 
complished during t h e  period 1 May 1965 t o  31 October 1965 t o -  
ge ther  wi th  t h e  topics for  f u t u r e  s tudy ,  In  gene ra l ,  t h e  pur- 
pose of t h e  work completed and tha t  p r e s e n t l y  cont inuing has 
been t o  devise  means of obta in ing  better estimates of t h e  elec- 
tromagnetic properties and su r face  roughness of s c a t t e r i n g  su r -  
faces, and i n  p a r t i c u l a r  of those  s c a t t e r i n g  s u r f a c e s  p r e s e n t l y  
inaccess ib l e  t o  man,, T h e  genera l  approach has been t h a t  through 
t h e  use of t h e  p o l a r i z a t i o n  properties of both t h e  t r a n s m i t t e d  
and received s i g n a l s ,  t h e  su r face  p r o p e r t i e s  may be separated 
and determined ind iv idua l ly .  A major t o o l  i n  t h i s  work has been 
t h e  concept of d i f f e r e n t i a l  r e f l e c t i v i t y  which w a s  developed by 
t h e  authors. '  
report period has been on: 1) back-scatter f r o m  a s t a t i s t i c a l l y  
configured s u r f a c e  and 2 )  determination of e lectromagnet ic  prop- 
erties of a smooth sphere f r o m  two b is ta t ic  p w e s  measurements-'\ 
Addi t ional  work was accomplished on t h e  development of an a c o u s t i c  
d i f f e r e n t i a l  r e f l e c t i v i t y -  
The major por t ion  of t h e  work done during t h i s  
2 .O Theore t i ca l  S t u d i e s  
2 . 1  M o r , o s t a t i c S c a t t e r i n g r f a c e s  
The i n v e s t i g a t i o n  of r e f l e c t i o n  0f team-limited r a d i a t i o n  
from a s t a t i s t i c a l l y  rough sphere (i - e , ,  a rough moon or  p l a n e t )  
is  continuing,, T h e  su r f ace  has been assumed t o  have a gaussian 
d i s t r i b u t i o n  of he igh t s  about a mean sphere and a gaussian cor- 
r e l a t i o n  func t ion .  
I Er teza ,  A. ,  J. A. Doran, D. He Lenhert ,  siConcept of D i f -  
f e r e n t i a l  R e f l e c t i v i t y  as Applied t o  t h e  Ref l ec t ion  of Beam- 
Limited Radiat ion by a Convex Body," RADIO SCIENCE, Journa l  of 
Research NBShSNC-URSI, Vol. 69 D ,  Noo 2,  February,  1965- 
1 
Under t h e  assumption t h a t  induced cu r ren t  d e n s i t i e s  on 
the surface reach s teady  state almost ins tan taneous ly ,  m o s t  
researchers have ca l cu la t ed  the  reflected power i n  t h e  pulsed 
r a d i a t i o n  case u s i n g  t h e  steady s ta te  t i m e  averaged Poynting 
vec to r  ii.e. 8 S" = + Re{g x , Our origir-ax i n t e g r a l  formu- 
l a t i o n  of t h e  expected direct-  and cross-polar ized p o w e r s  used 
t h i s  method. However, upon in tegra t ion ,  t h e  t i m e  averaged p o w e r  
showed an  e -i2Qt term during c e r t a i n  t i m e  i n t e r v a l s ,  which i n -  
d i c a t e d  t h a t  t he  s teady  s t a t e  assurnptioc i s  ~ o t  v a l i d  dur ing  
these t i m e  i n t e r v a l s .  These w e r e  t h e  t i m e  i n t e r v a l s  i n  which 
either t h e  nose o r  the i n t e r s e c t i o n  of th.e beam-edge and the 
su r face  lies between t h e  leading and t r a i l i n g  edges of t h e  
propagat ing pulse .  N o  such term appeared f o r  t i m e s  between t h e  
above two i n t e r v a l s .  
Our problem was reformulated using the  non-time averaged 
Poynting vec to r  r e q u i r i n g  t i m e  averaging a f t e r  completion of 
the  surface i n t e g r a t i o n ,  The prel iminary r e s u l t s  i n d i c a t e  t h a t  
the  use of t h e  t i m e  averaged Poynting vec tor  a s  used by others 
i s  only  v a l i d  during a por t ion  of t h e  in te rmedia te  t i m e  i n t e r v a l .  
A d d i t i o n a l  problems have been encountered i n  t h e  i n t e g r a -  
t i o n  and eva lua t ion  of t h e  expected va lues ,  
it more d i f f i c u l t  t o  t runca te  t h e  i n f i n i t e  series of i n t e g r a l s  
t h a t  appear i n  t h e  so lu t ion .  T h i s  w o r k  i s  expected t o  be c o m -  
p l e t e d  by Spring of 1966, and a sepa ra t e  report covering t h e  
t h e o r e t i c a l  r e s u l t s  w i l l  be i s sued .  
These problems make 
2 - 2  
A n  i n v e s t i g a t i o n  of t h e  b i s t a t i c  (source and observa t ion  
p o i n t s  non-coincident ) case of r e f l e c t i o n  has been c a r r i e d  o u t .  
T h e  i n t e g r a l  equat ions  were formulated for a l l  possible loca- 
t i o n s  of t h e  source and observat ion p o i n t ,  however these w e r e  
solved for  t h e  case  i n  which t h e  e n t i r e  i l lumina ted  a r e a  w a s  
v i s i b l e  t o  t h e  observer.  T h i s  a n a l y s i s  i nd ica t ed  t h a t  f r o m  a 
determinat ion of t h e  r a t i o  of t h e  p o w e r  d e n s i t i e s  rece ived  by 
two q u a d r a t i c a l l y  opposed antennas,  measured a t  t w o  d i f f e r e n t  
conf igura t ions  of source,  t a r g e t ,  and observat ion p o i n t s ,  both 
B i s t a t i c  S c a t t e r i n g  from Determinis t ic  Surfaces  
2 
p and e may be determined for  a smooth homogeneous sphere of 
s u f f i c i e n t l y  l a r g e  r a d i u s .  It is f e l t  t ha t  w i t h  three observa- 
t i o n s  u, e ,  and o could be determined, 
A paper covering t h i s  work has been submitted t o  RADIO 
SCIENCE Journa l  o f  Research NBS/USNC-URSI for pub l i ca t ion .  
2.3 Acoustic Sca t t e r ing  f r o m  Surfaces  
During t h e  summer an  i n v e s t i g a t i o n  w a s  begun w i t h  t h e  ob- 
j e c t i v e  of formulat ing a d i f f e r e n t i a l  r e f l e c t i v i t y  f o r  a c o u s t i c  
waves s c a t t e r e d  f r o m  a su r face ,  This a c o u s t i c  d i f f e r e n t i a l  re- 
f l e c t i v i t y  term would then be compared t o  t h e  electromagnet ic  
d i f f e r e n t i a l  r e f l e c t i v i t y  i n  an attempt t o  o b t a i n  better j u s t i -  
f i c a t i o n  than  exists a t  present  for the  use of t h e  a c o u s t i c  
s imula tor .  
The acous t i c  wave w a s  descr ibed  i n  t e r m s  of a scalar poten- 
t i a l  and a vec tor  p o t e n t i a l .  
and observer  w e r e  immersed i n  w a t e r  t h a t  t h e  reflected f i e l d  
from a s o l i d  would be equivalent  t o  a n  electromagnet ic  reflected 
f i e l d  f r o m  an inhomogeneous body, T h i s  occurs  due t o  t h e  d i f -  
f e r e n t  t r a n s v e r s e  and longi tudina l  v e l o c i t i e s  of propagation of 
an acous t i c  wave i n  a solid. I f  t he  effects of t h e  t r a n s v e r s e  
wave could be neglec ted ,  t h e  r e s u l t i n g  a c o u s t i c  s c a t t e r e d  f i e l d  
would correspond t o  the  electromagnet ic  scattered f i e l d  f r o m  a 
homogeneous body e 
It appeared t h a t  when t h e  source 
w i l l  
3.0  
This work w a s  set aside due t o  t h e  loss of personnel and 
be r e i n s t a t e d  as  soon as  s u f f i c i e n t  personnel can be found. 
Future  Work 
3 .1 
The i n v e s t i g a t i o n  descr ibed i n  Sec t ion  201 w i l l  be continued, 
Continuation of  Monostatic S c a t t e r i n g  Study 
ob ta in ing  separate so lu t ions  f o r  both t h e  direct-  and cross- 
po la r i zed  expected power integrals  * On completion of t h e  i n t e -  
g ra t ion  and t i m e  averaging,  t h e  var iance  of s u r f a c e  he igh t s  and 
c o r r e l a t i o n  d i s t a n c e  w i l l  be eva lua ted  approximately for t h e  
case of t h e  moon by comparison wi th  lunar  r ada r  d a t a  taken by 
3 
o t h e r  researchers. 
arate  report w i l l  be s u b m i t t e d ,  
When t h i s  work has been completed, a sep- 
3 - 2  B i s t a t i c  S c a t t e r i n g  from a S t a t i s t i c a l  Surface 
B i s t a t i c  scattering f r o m  a rough spherical .  surface w i l l  be 
i n v e s t i g a t e d  w i t h  a view t o  determining var ious  parameters w h i c h  
desc r ibe  t h e  su r face  and a f f e c t  the s c a t t e r i n g  f r o m  it, 
t h e s e  parameters are those  s ta t i s t ica l  ones r e l a t i n g  t o  t h e  su r -  
face roughness such as d i s t r i b u t i o n  of he igh t s ,  c o r r e l a t i o n  dis-  
tromagnetic p r o p e r t i e s  of the  medium considered on a macroscopic 
basis such a s  permeabi l i ty ,  p e r m i t t i v i t y ,  and conduct iv i ty .  
Other characteristics of t h e  su r face  such as a layered na tu re  
can be pos tu la ted  and the  components of t h e  s c a t t e r e d  f i e l d  
s t u d i e d  t o  determine i n  what manner t he  layer ing  can be detected 
from a f a r .  
Among 
I etc, I n  a d d i t i o n ,  t h e r e  are those  r e l a t i n g  t o  t h e  elec- 
3.3 Comparison of t h e  Kirchhoff-Huygens and t h e  D i f f e r -  
The Kirchhoff-Huygens approach assumes t h a t  t h e  t o t a l  f i e l d  
a t  t he  su r face  of t h e  s c a t t e r i n g  body is krrown and then  o b t a i n s  
t h e  s c a t t e r e d  f i e l d  a t  an o b s e r v a t i m  point  by i n t e g r a t i n g  over 
t h e  surface cu r ren t  and charge d e n s i t i e s  e q u i v a l e ~ t .  t o  t h e  t o t a l  
f i e l d s .  In order t o  o b t a i n  t h e  t o t a l  f i e l d  a t  t h e  surfac? it is  
necessary t o  o b t a i n  the  reflected f ie lds  by either an exact or 
approximate s o l u t i o n  t o  boundary v a l c e  problem. One method of 
approximating the  boundary va lue  problem i s  t h e  assimption t h a t  
t h e  inc iden t  e lectromagnet ic  wave is  r e f l e c t e d  a t  every po in t  
of t h e  s u r f a c e  as though a n  i n f i n i t e  p lane  wave w e r e  i nc iden t  
upon an i n f i n i t e  tangent  plane a t  the poin t  . 
The d i f f e r e n t i a l  r e f l e c t i v i t y  approach a s s e r t s  t h a t  t h e  
reflected Hertzian p o t e n t i a l  f i e l d  is  desc r ibab le  by a su r face  
i n t e g r a l  of a dyadic d i f f e r e n t i a l  r e f l e c t i v i t y  ope ra t ing  on t h e  
inc iden t  f i e l d .  The dyadic d i f f e r e n t i a l  r e f l e c t i v i t y  u t i l i z e s  
t h e  r e f l e c t i o n  of a weighted plane wave family corresponding t o  
t h e  inc iden t  f i e l d  a t  a point on the  body., 
made t h a t  any m e m b e r  of t h e  plane wave family i s  reflected by 
an i n f i n i t e  tangent  plane a t  t h e  p o i n t .  
An ass-mption i s  
4 
Both methods r e q u i r e  su r face  i n t e g r a t i o n  and t h a t  t h e  re- 
flected f i e l d  a t  a p o i n t  is obtained through t h e  u s e  of t h e  
"tangent plane approximation. 'I A point  of d i s s i m i l a r i t y  i s  
t h a t  t h e  Kirchhoff-Huygens approach approximates t h e  inc iden t  
f i e l d  a t  a poin t  by an i n f i n i t e  plane wave and the  d i f f e r e n t i a l  
r e f l e c t i v i t y  approach does not make t h i s  assumption. Conse- 
quen t ly ,  an i n v e s t i g a t i o n  w i l l  be made of t h e  comparison of t h e  
t w o  methods w i t h  t h e  ob jec t ive  of determining t h e  r e l a t i o n s h i p  
of t h e  two methods. 
4.0 Papers Submitted 
"A B i s t a t i c  Radar Method f o r  t h e  Determination of e and 
for a Smooth Sphe r i ca l  Target ,"  by A,  Er teza and J. A. Doran. 
(Submitted t o  RADIO SCIENCE, Journa l  of Research of NBS/USNC- 
URSI, Sect ion  0.) 
5.0 Travel  
The  fol lowing t r i p  w a s  made by r e sea rch  personnel  for t h e  
purpose of d i scuss ing  research  work, a t t end ing  t e c h n i c a l  con- 
f e rences ,  and exchanging research notes  w i t h  o t h e r  people i n  
t h i s  and a l l i e d  f ie lds .  
Mr. J.  A. Doran at tended t h e  f a l l  URSI meeting a t  Dartmouth 
College,  Hanover, N .  He, i n  October, 1965. 
I 5 


Investigation of radar echoes from the moon and planets, using methods and data from earth radar-return studies  Semiannual status report, 1 May - 31 Oct. 1965

Investigation of radar echoes from the moon and planets, using methods and data from earth radar-return studies Semiannual status report, 1 May - 31 Oct. 1965

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