Differential reflectivity for estimating surface properties of reflecting body - radar signal reflectio

Doran, J. A.

Erteza, A.

Lenhert, D. H.

English

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. 
The U n i v e r s i t y  of New Mexico 
Bureau of Engineer ing Research 
Albuquerque, New Mexico 
SEMI-ANNUAL STATUS REPORT 
(1 November 1964 t o  30 A p r i l  1965) 
Techn i c a 1 R e p o r t  EE - 12 4 
Ahmed Erteza 
James A. Doran 
Donald H. Lenhert  
This work performed fo r  
Nat iona l  Aeronautics and Space 
Adminis t ra t ion  under Grant 
Number NsG 129-61 
ABSTRACT 
This report p resen t s  a summary 
NASA grant  N s G  129-61 during t h e  l a s t  
of t h e  work 
s i x  months, 
performed under 
T h i s  work w a s  
aimed a t  extending 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  t o  
g ive  b e t t e r  estimates of t h e  su r face  p r o p e r t i e s  (both roughness 
and electromagnet ic)  of a r e f l e c t i n g  body. The major a reas  of 
ex tens ion  are 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 ,  b i s t a t i c  r e f l e c t i o n  from a d e t e r m i n i s t i c  s u r f a c e ,  and 
reformulat ion of  a Kirchhoff-Huygens approach i n t o  a form 
appropr i a t e  f o r  use w i t h  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 ,  
Also presented is  a s h o r t  d i scuss ion  of a r e a s  of f u t u r e  work. 
TABLE OF CONTENTS 
4 
0 2.1 Monostatic S c a t t e r i n g  from S t a t i s t i c a l  Sur faces  1 
2.2 B i s t a t i c  S c a t t e r i n g  from Determinis t ic  Sur faces  2 
2.3 A Kirchhoff-Huygens Approach-------------------- 3 
3 .1  Continuation of Monostatic S c a t t e r i n g  Study----- 4 
3.2 Continuation of  B i s t a t i c  S c a t t e r i n g  Study------- 4 
3.3  Acoustic S c a t t e r i n g  from Surfaces--------------- 5 
# 
1.0 In t roduct ion  
This r e p o r t  p resents  a summary of the t h e o r e t i c a l  work 
accomplished during t h e  period 1 November 1964 t o  30 A p r i l  1965 
toge ther  with topics for f u t u r e  study. 
of t h e  work completed and t h a t  p r e s e n t l y  cont inuing  has been t o  
devise  means of ob ta in ing  better estimates of t h e  electromagnet ic  
p r o p e r t i e s  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  
In  t h e  main, t h e  purpose 
s c a t t e r i n g  su r faces  p re sen t ly  i n a c c e s s i b l e  t o  man. An e a r l i e r  
paper' by t h e  au thors  of t h i s  r epor t  contained t h e  development 
of 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 .  
of t h e  work done during t h i s  report per iod has been toward ex- 
tending t h e  concept to: 
s t a t i s t i c a l l y  configured surface and 2 )  s c a t t e r i n g  from a deter- 
m i n i s t i c  surface i n  t h e  bis ta t ic  case. Spec ia l  emphasis i s  placed 
on t h e  p o l a r i z a t i o n  p rope r t i e s  of t h e  s c a t t e r e d  f ie lds  i n  both 
The major por t ion  
1) back-sca t te r  (monostatic) from a 
cases 
2 . 0  Theore t i ca l  S tudies  
2 * 1  
An i n v e s t i g a t i o n  i s  i n  progress  on t h e  r e f l e c t i o n  of beam- 
l imi t ed  r a d i a t i o n  from asphere w i t h  s t a t i s t i c a l  roughness ( i . e .  # 
a rough moon or p l a n e t )  using 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 -  
'Erteza, A.,  J . A .  Doran, D.H, Lenhert ,  "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  a s  Applied t o  t h e  Ref lec t ion  of Beam-  
Limited Radiat ion by a Convex Body," 
Research NBS/USNC-URSI, V o l .  690, N o .  2 ,  February,  1965. 
RADIO SCIENCE Journa l  of 
-2 - 
v i t y .  The  su r f ace  was assumed t o  have a guassian d i s t r i b u t i o n  
of he ights  about a mean sphere and an exponent ia l  c o r r e l a t i o n  
func t ion .  The p r o b a b i l i t y  d e n s i t i e s  of t h e  s i x  parameters ( h ,  
I 
' ah ah - ah and ah' w e r e  found, The i n t e g r a l  equat ions 
h f  ;SB, T ,  acp arp 
for  t h e  Her t iz ian  p o t e n t i a l  vec tor  were formulated using 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  and t h e n  converted t o  E' and ze 
r e s t r i c t i o n s  on 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  a s  o r i g i n a l l y  
der ived by t h e  au thors  t h a t  t he  angle  between t h e  su r face  normal 
and t h e  vec tor  t o  t h e  observer could not be zero ,  and t h a t  t h e  
Fresne l  r e f l e c t i o n  c o e f f i c i e n t s  could not be complex w e r e  removed, 
The 
The expected p o w e r  was obtained i n  i n t e g r a l  form by t h e  
expansion of t h e  random heights  i n t o  orthogonal random v a r i a b l e s  
using t h e  Karhunen-Lo&e theorem. Mow i n  progress  i s  t h e  i n -  
t e g r a t i o n  of  t h e  equat ions obta ined  and t h e  o rde r ing  of t h e  
terms so t h a t  approximations can be made. S ince  t h e  vec to r  na tu re  
of t h e  s o l u t i o n  i s  m a i n t a i n e d ,  t h e  expected d i r ec t -po la r i zed  acd 
cross-polar ized  power expressions a r e  kept s epa ra t e ,  
A r e p o r t  covering t h i s  work and the matching to da ta  pre- 
v ious ly  taken by o t h e r  researchers  w i l l  be issued dur ing  the 
summer 
2,2 B i s t a t i c S c a t t e r i n g f r o m i s t i c  Surfaces  
With 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  considered 
as b a s i c ,  an 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 o b s x v a -  
t i o n  p o i n t s  non-coincident) case of r e f l e c t i o n  from a smooth sphere 
has  been c a r r i e d  ou t .  P a r t i c u l a r  emphasis has been placed on 
t h e  p o l a r i z a t i o n  of t h e  
information r e l a t i n g  t o  
of a r e f l e c t i n g  su r face  
-3 - 
s c a t t e r e d  f i e l d s  a s  it i s  expected t h a t  
the  electromagnet ic  parameters o and F 
may be r e a d i l y  ob ta inab le  from a s tudy  
of t h e  p o l a r i z a t i o n  p rope r t i e s  of t h e  scattered f ie lds  due t o  
a known o r b i t i n g  source.  
obtained f o r  t h e  2 and 5 f i e l d s .  
u s e f u l  form of these i n t e g r a l  expressions has been nea r ly  com- 
p l e t ed .  
s epa ra t e  r epor t  i n  t h e  near f u t u r e .  
2 .3 
Vector i n t e g r a l  expressions have been 
Approximate eva lua t ion  an 
The r e s u l t s  of t h i s  s tudy  w i l l  be released i n  a 
A Kirchhoff -Huygens Approach 
From a cons idera t ion  of tk form of t h e  equat ion 
+ + 
Il = S i o I l i d s  
S r 
an attempt was made t o  re-formulate t h e  problem of r e f l e c t i o n  of 
a Il f i e l d  from an a r b i t r a r y  su r face  as a Kirchhoff-Huygens type 
problem. The 
volume i n t e g z a l  over t he  cur ren t  d e n s i t y  3, where ? was rep laced  
b y v ~ z - ~ .  aD 
g r a l  over t h e  su r face  enclosing t h e  volume and a volume i n t e g r a l  
which vanished under t h e  assumption t h a t  3 was i d e n t i c a l l y  zero 
i n  t he  i n t e r i o r  of t h e  volume. 
n f i e l d  could be constructed from a knowledge of an inc iden t  Il 
f i e l d  g iv ing  r ise a t  t he  sur face  t o  a system of f i e l d s  e q u i v a k r a - ,  
t o  a d i s t r i b u t i o n  of  cur ren ts  there. However, in a d d i t i m ,  a 
knowledge of t h e  r e f l e c t i o n  c o e f f i c i e n t s  for the 2 and 
a t  t h e  su r face  was necessary i n  o rde r  t o  express  t h e  reflected 
f ie lds  i n  terms of t hose  inc iden t ,  These could be a r r i v e d  at 
+ 
-B 
f i e l d  a t  an a r b i t r a r y  poin t  was expressed a s  a 
T h i s volume i n t e g r a l  reduced tc a su r face  inte- 
It was a s s e r t e d  t h a t  a reflected 
-9 4 
f i e l d s  
-4- 
on ly  through a s o l u t i o n  of t h e  exact  boundary va lue  problem 
4 
and so, r a t h e r  than  t a k i n g  recourse t o  approximations,  t h e  problem 
w a s  temporar i ly  l a i d  a s ide .  Since it appears t h a t  u se fu l  r e s u l t s  
might be forthcoming from an exhaust ive i n v e s t i g a t i o n  of t h i s  type 
of s o l u t i o n  of t h e  s c a t t e r i n g  problem, a resumption of work on 
it i s  planned a t  some f u t u r e  da te .  
3.0 Future Research 
3o 1 Continuation of Monostatic Scat ter inq Study 
The i n v e s t i g a t i o n  described i n  Sec t ion  2 . 1  w i l l  be con- 
t i nued  ob ta in ing  s e p a r a t e  i n t e g r a l  s o l u t i o n s  f o r  both t h e  
d i r e c t -  and cross -polar ized  expected power. On completion of 
t he  i n t e g r a t i o n ,  t h e  t w o  unknowns (i .e. ,  va r i ance  of su r face  
he igh t s  and c o r r e l a t i o n  d i s t ance )  w i l l  be eva lua ted  f o r  t h e  
case of t he  moon by comparison w i t h  lunar  r ada r  d a t a  taken by 
o t h e r  researchers .  A r epor t  covering t h i s  work w i l l  be sub- 
m i t t e d  dur ing  t h e  summer. 
3 . 2  Continuation of B i s t a t i c  S c a t t e r i n g  Study 
Following t h e  completion of t h e  s tudy  of s c a t t e r i n g  from 
a smooth sphere as discussed i n  Sec t ion  2 . 2 ,  it i s  intended t o  
a.pply similar techniques t o  t a r g e t s  of o t h e r  than  s p h e r i c a l  
shape. Study w i l l  be made of t h e  t r a n s i e n t  case a s  w e l l  a s  of 
t h e  s t eady  s t a t e  one. I n  a d d i t i o n ,  a s t u d y ' w i l l  be made of t h e  
doppler effects on t h e  s c a t t e r e d  r a d i a t i o n  as a r e s u l t  of motion 
of t h e  source r e l a t i v e  t o  t h e  t a r g e t .  The s i t u a t i o n  here i s  
t h a t  of a t r a n s m i t t e r  of known c h a r a c t e r i s t i c s  o r b i t i n g  a body 
such as t h e  moon w i t h  t h e  observat ion p o i n t  being s i t u a t e d  on 
t h e  earth. Should promising r e s u l t s  ensue from t h i s  i nves t iga -  
-5- 
t i o n  it i s  planned t o  submit a proposal t o  NASA f o r  an exper i -  
ment a long these l i n e s .  
3 . 3  Acoustic S c a t t e r i n g  from Surfaces 
This t o p i c  i s  c a r r i e d  over from t h e  last report. No 
w o r k  w a s  accomplished i n  t h e  area during t h i s  report per iod due 
t o  concentrat ion i n  o t h e r  a reas .  However, a d d i t i o n a l  personnel 
w i l l  be added during t h e  summer months t o  work on t h e  problem. 
Using 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  an i n v e s t i g a t i o n  
w i l l  be made of t h e  acous t i c  s c a t t e r i n g  of a s p h e r i c a l  wave from 
a su r face .  T h e  purpose i s  t o  o b t a i n  b e t t e r  j u s t i f i c a t i o n  than  
e x i s t s  a t  present  f o r  t he  u s e  of t h e  acous t i c  s imulator  t o  
determine electromagnet ic  s c a t t e r i n g  from a su r face .  Present ly ,  
t h e  use of t h e  acous t i c  s imulator  i s  j u s t i f i a b l e  only  on t a r g e t s  
for which electromagnet ic  s ca tke r ing  has been experimenfally 
measured. I f  t h e  long i tud ina l  pressure  waves r e f l e c t e d  from a 
p a r t i c u l a r  su r f ace  can be r e l a t e d  t o  t h e  d i r e c t  po la r i zed  com- 
ponent of e lectromagnet ic  r e f l e c t i o n s ,  then t h e o r e t i c a l  methods 
of determining electromagnet ic  r e f l e c t i o n  can be v e r i f i e d  by 
t h e  use of t h e  acous t i c  s imulator  and possibly extended t o  cases  
which would otherwise r equ i r e  t h e  u s e  of l a r g e  d i g i t a l  computers 
f o r  numer ica l  eva lua t ion  of c e r t a i n  i n t e g r a l s .  Any r e s u l t s  ob- 
t a i n . e d  which t a k e  i n t o  account body effects (i.e.,  due t o  s e t t i n g  
up of t r ansve r se  and long i tud ina l  waves i n s i d e  t h e  t a r g e t )  w i l l  
be of considerable  importance i n  t h e  s tudy of t h e  corresponding 
electromagnet ic  cases .  
-6- 
4.0 Travel  
The fol lowing t r i p  w a s  made by research  personnel for  
the  purpose of d i scuss ing  research  work, a t t e n d i n g  t e c h n i c a l  con- 
fe rences  and exchanging research  no te s  w i t h  o t h e r  people i n  
t h i s  and a l l ied  f i e l d s .  
Mr. D.H. Lenhert a t tended the  sp r ing  URSI-AGU meetings 
a t  t h e  Nat ional  Academy of Sc iences ,  Washington, D.C., i n  
A p r i l ,  1965. 


<investigation of radar echoes from the moon planets, using methods and data from earth radar-return studies<  semiannual status report, 1 nov. 1964 - 30 apr. 1965

<investigation of radar echoes from the moon planets, using methods and data from earth radar-return studies< semiannual status report, 1 nov. 1964 - 30 apr. 1965

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