Solar radio frequency reflection from lunar surface for scattering measuremen

Cooper, G. R.

Mc Gillem, C. D.

English

NASA Technical Reports Server

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khoo l  of E l e c t r i c a l  Engineering 
Electronic Systens %?search Laboratory 
Purdue Uziversity 
Lafaxette, Indiaqa 
t 
February 28, Is5 
S e n l F - i a l  S t a h u s  Zeport 
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. 
In t rn ; . J c t ion  and b k t t e m t i c s l  :.nal:;sis 
?~kthotls of messuring the  r a d i o  f reqiency s c a t t e r i n g  p rope r t i e s  of the  
-.  ~ c l n a r  sirrface are l imi ted  t o  the backscat ter ing case because of the  require-  
mnt t h a t  t he  transmi' ter and rece iver  be i n  e s s e n t i a l l y  the s- d i r e c t i o n  
r e l s t i v e  t o  the  s c a t t e r i n g  po in t  on the  luna r  surface.  As a consequence of 
t n i s  l i m i t a t i o n ,  it is  not possible  to obta in  a s a t i s f a c t o r y  estimate of 
the s c a t t e r i n g  l a w  of the  sur face  i n  which varying angles of incidence and 
s c z t t e r i n g  are taken i n t o  account. 
A s  a method o f  otercoming t h i s  l i m i t s t i o n ,  it i s  proposed t o  u t i l i z e  
solar redio frequency en i s s ion  as the energc. source and t o  meamre the  
scattering cf t h i s  raiiation by t h e  lunar suryace. 
;n the relatj-;e positlons of  the sun, noon, and e a r t h  wbich occur a s  the  
mocn goes through i t s  phases, a wide range of s c a t t e r i n g  angles can be 
obtained. Also, a wide frequency range i s  ava i l ab le  as a r e s u l t  of the  
isroai spectrum of s d n r  radiation. EQ messilrine5 the  re f lec t ic tn  c o e f f i c i e n t  
of t h e  I.in;ir surface as a function cf angle  of mcic?ence, frequency, and 
polarization, i t  m s y  be possible t o  Gbtain nuen more satisfactory es t imates  
of d i e l e c t r i c  constant ,  ccnduct ivi ty ,  and roughness of t h e  l u n a r  surface.  
Because of the  v a r i a t i o n s  
Before d iscuss ing  the d e t a i l s  of the  de t ec t ion  method we a r e  proposing, 
i t  might be kor thvhi le  t o  examine t he  magnitude of the  power involved here. 
In order  to obta in  some ins ight  i n t o  the prdblem, consider  f i r s t  a case 
where the  moon i s  represented as a c o l l e c t i o n  of s ta t i ionary s c a t t e r e r s .  If 
x ( t )  i s  the  s i g n a l  from the  sun and % i s  the  ne t  s c a t t e r i n g  c o e f f i c i e n t  of  
the s c a t t e r e r s  whose s i g n a l s  are received w i t h  de lay  'I 
s i g n a l  from the  sun, then the received s i g n a l  i s  given by 
relative t o  t h e  d i r e c t  k 
k 
t he  c ros sco r re l a t ion  of y ( t )  and x ( t )  is found t o  be: 
c -  - 2 -  
k 
The c r o s s w r r e l a t i c n  h n c t i o n  is therefore  a sum of terms, each of which i s  
a reproduction of t h e  co r re l a t ion  funct ion of x ( t )  loca ted  a t  a p a r t i c u l a r  
delay T~ and having ?a amplitude determined by a p a r t i c u l a r  s c a t t e r i n g  co- 
e ff i c  ient  , %. The c o e f f i c i e n t s  % can be related t o  the power r e f l e c t i n g  
pr -e r t ies  of t he  s c a t t e r e r  and f o r  the case of  wideband noise -- such t h a t  
i ) .X?T(~)  is zero except when T = 0 -- it i s  found that the man square 
of  t h e  received s igna l  is r e l a t ed  tc  the s c a t t e r i n g  c o e f f i c i e n t s  by: 
n -- 
value 
b 
Since R ( C )  i s  the  mean square value of the  t ransmi t ted  s igna l ,  i . c . ,  the 
bransmitted powrs, i t  fol lows thet %' i s  the  n e t  power r e f l e c t i o n  c o e f f i c i e n t  
corresponding t o  ce lay  T and can be r e l a t ed  t o  the range, antenna gain,  surface 
r e f l e c t i o n  c o e f f i c i e n t s  and o ther  parameters. 
M 
k 
When motion of the s c a t t e r e r s  is taken into account, tfie probiem 'uecmes 
cc , r re l s t ion  of L i t e  trensmitted ( i . e . ,  so l a r )  s igna l  and r e f l e c t e d  ( i .e. ,  l una r )  
signa2 leads t o  the following expression. 
= b 3 [ S o  - T l  + (S l -1) t j  + b R - T + (g2-1) t J  + .. 1 x x  2 xx fTo 2 
w h e r e  : 
v 
v; : -"-elacity of l.th sca t te re r  
c = veiocit;: ot l i g h t  
.- 
' .  
- 3 -  .= 
In 3 practicsl c o r r e l a t o r  the t k e  co r re l a t ion  function will be 
nleasured 2nd t h i s  is re la?ed  to the tine average of the  ensemble cor re l a t ion  
f l inc t inn .  It, i s  seen tt'.at t h e  en.xmble c o r r e l a t i o n  funct ion given abow i s  
B :'ixxtion of' t i r e  and so its average w i l l  4epend on the  form of 
? [T). If R ( T )  Ls osc ; l la tor&,  as i n  the  case of bandlimited noise, then 
xx xx 
%::e :hi everase w i l l  be zero and tile c o r r e l a t o r  output would be zero. By 
cor re l a t l rg  wit?! a ma?i?ied f inc t ion ,  z = x(3 t - T), a more u s e m  result 
Is  c5taine-i. -;'hat ';:?is mounts  to is us in2  3 c o r r e l a t o r  w i t h  a con t inwus lg  
111 
k 
Viis cor re l a t ion  fhnct ion will have a time average of zero for a l l  Ei + 3 - 
& -  x m 
c 
1 si!c)ws a gic',c.-i?l reprcse-itst icn of +Ire s p e c t r a l  densit:,  and the  
- .  
- 4  - 
n 
I 
c 
b’ 
> 
to 
I 
I= 
OJ 
<n 
0 
0 
Y 
a 
n - 
Y 
X x a 
I- 
I 
 
3 
d m 
Ir. 
0 
- 5 -  
N 
r u b s t i t u t i n g  t h e  e -p res s ion  f o r  E ( 5 )  i n t o  t h e  equat ion  for  I! ( T  ) gives: 
xx y z  0 
If ( 5  
i f  t h e  c o r r e l a t o r  delay  i s  set t o  correspond c lose ly  t o  some p a r t i c u l a r  locus 
- T ) i s  small c q n r e d  to the r ec ip roca l  of t b e  bendwidth -- i - e . ,  m 0 
of cons5-t tine de lay  on 
the above equat ion can be 
func t ion  Secames: 
t he  lunar  sur face  -- then t h e  (sin x);x factor i n  
approximated as un i ty ,  and the c rossco r re l a t ion  
4 s i m i l a r  approxination cannot be made f o r  t h e  cosine funct ion,  s ince  i n  a 
p r s c t i c a l  case f migh t  be 10 cps and, accardingly,  
be much smaller then ll;-lC i n  order fo r  the  f’unction cos 2nf (7  
near uni ty .  If t h e r e  w e r e  an uncertaini5y i n  ( T  - T ) i n  the order  of one 
pa.rt i n  10 , then the cos 2nf (7 - T ) might have any value fran +1 t o  -1, 
m d  no cor rec t ion  would be possibze. 
- T ) would have t o  10 (‘In 0 0 
- ) to be 
00). 0 
m 0 
10 
o m  0 
This d i f f i c u l t y  can be overcome by 
- ‘i ), of t’he Ro(Tm 0 e~plc:;in,r a correla‘,or Vkiich reasures the  en-.-e:ope, 
c c r r e l a t i o n  f’unction r a t h e r  t h a n  the t o t a l  c o r r e l a t i o n  m c t i o n .  In t h i s  
wa:: t h e  n e z e s s i t y  for t k  prec i se  at?,.:ustment of T = T w i l l  be avoided and 
ti.e c o r r e l a t o r  output  w i l l  be: 
m 0 
2 
m bm R o ( G )  = bm fi ( 0 )  = b xx 
Cor re l a to r  Design 
The c o r r e l a t o r  design t h a t  has evolved i s  an ex tens ion  of t h e  p o l a r i t y  
coincidence type which has been used successfu l ly  by o the r  experimenters. The 
extension i s  i n  several di rec t ions :  a narrow sampling gate  permits c o r r e l a t i o n  
of wideband s igna l s  using a low sampling frequency; an add i t iona l  channel i s  
incluiied in the c o r r e l a t o r  t o  permit measurement of the  envelope of the  
c o r r e i z t i o n  f m c t f o n ;  a vern ier  d i f f e r e n t i a l  delay between samplers i s  provided 
i c j  z,llow t he  rielaj; tlrrte t o  be ccintrviied t o  a f r a c t i o n  of tile r e p e t i t i o n  period 
and t o  be varied a s  a funct ion of t h e .  
.- - 6 -  
. The basic c o r r e l a t o r  block dicgvx. i s  sh0.h.n i n  Fig. 2. The operat ion 
is as follows. The input  rignzds f r o m  t h e  s-m and moon are received i n  
separate recei;ers w i t h  sepzrate  azennas .  Each s i g n a l  is heterodyned from 
a Smdpass s i g n a l  at t he  receiver  ?enter frequency down t o  a low pass video 
signel. Feparate l o c a l  o s c i l l a t o r s  are used with a frequency displacement 
corresponding t o  t h e  des i r ed  delay rate; and i n  the  case of the  s i g n a l  from 
t he  moon, a dual  mixer is used which provides t w o  signal channels i n  
quadrature w i t h  each other.  The s i g n d s  are then passed through a wideband 
c l i p p e r  t h a t  preserves  t h e  ze ro  crossing information, and are p e r i o d i c a l l y  
smFled  w i t h  a very narro6 pu l se  t o  determine whether the s i g n a l s  a r e  positive 
or negat ive a t  t h e  sampling in s t an t .  Clock frequencies f o r  the  two s.mplers 
a r e  d i f f e r e n t  5 y  an mount corresponding t o  the  desired delay rate. The 
r e s u l t  of eech s m p l i n g  operation i s  coded as a binary d i e i t  by t he  pulse 
generator  which produces a pos i t i ve  pulse f o r  a p o s i t i v e  sample and no pulse 
for  a negative sample. 'R& pulse t r a i n  from the  sun channel i s  then delayed 
3: r,omC, ?; ar.d zorrela+&d kith esch the txo lunar chamleis i n  the 
p o l a r i t y  ccincidence c i  rcuitr;: md c o m t e r s .  The normalized c r o s s c o r r e l a t i o n  
c.oefficLenf, sf t h e  c l i r p d  signa;s 12 each cfiknne: L s  the n e t  change i n  the 
c o m t e r  for  that chaxiel  divided by the t o t a l  nurqber of counts. Combining the 
two c o r r e l a t i o n  coef:'icients i n  t h i s  fashion gives the amplitude of the 
envelope of t h e  c o r r e l a t i o n  f'unction. A d e t a i l e d  d e r i v a t i o n  of t h e  mathematical 
r e l a t i o n s h i p s  f o r  t h e  correiator +as been c a r r i e d  out. 
0 
One of t h e  Icajor problems i n  the c o r r e l a t o r  i s  t h a t  of obtaining t h e  
larze ; n i t i d  d e l a y  require6 to  bring t h e  d i r e c t  solar s i g n a l  i n t o  time 
s;-nct,rnnization wi th  the luna r  ref lected s igna l .  The ma.gnitude of t h i s  delay 
i s  shown i n  Fir?. 3. It was p r m z r i i j  f o r  the  ourpose o f  solving t h i s  problem 
that a sampled. system w i t h  d i g i t a l  processing w a s  s e l ec t ed .  After tY.e 
InciminF; am104 sisnals are d i p p e d ,  sampled, and converted t o  binary digits, 
~ 
4 .  
c- 
- .  
* I  
a 
a 0  
30 
1 I+ !i 4 ii
I 
w 
a 
0 
J 
w 
!z 
a 
m 
t 
*O ... Cb 
- t. - 
P 
s -
8 
8 
8 
0 
Q 
W 
k 
0 
W 
J 
lL 
W 
K 
LL 
0 
A 
W 
Q 
* - 3 -  
the  s i g n a l s  i n  tile sui1 charme2 T.List 3e dela:,ed before the c o r r e l a t i o n  function 
cqn  be compute?. T h i s  d e l a b  ?an be acccqlis!ied by delay lines, s h i f t  r e g i s t e r s ,  i 
c3Zr:etic c-re bcf'ers, CP o the r  s++rrai;i.tfor*;zrd oet?.@ds f o r  the d i S i t a l  s i g n a l s .  
t t  i s  virtilail;: impossible t o  delq; tile or ig in$  zxidog s i g n a l s  due t o  the 
i o n q  dela,r tines (13. :) to 2 sec.  ) avl t!-e l a r g e  bandwidths (120 nc). In practice, 
it  i s  planne3 t o  rccorci t'ne s i sna i s  at the  output  of the  pulse generators  on 
r;z,peti.r tape and c a r r ;  nut the reminder  of tke processing subsequent t o  t he  
+ 
sn b_ -I ~ . z t ; n a t e  of I. 
- TT?S vz:i e of nc i se  in l u m r  ckannel 
= r s  va;*Ae of s o l a r  s ;gnd  
'JX 
pyx, 
* 
=I est im3te of nonilalized c ros sco r re l a t ion  function. 
%? variance of tkjs e s t h a t e  i s  found to be 
7:i.ere 7: is the nujber of sar,p?es xe - i  i n  nz~ing the es t ima te .  Fig. 4 shows a 
p i o t  0:- s iqd- :o-na ise  ratio il;.;pro-.enPn: --ersus number of s m l e s .  For 
+; p 'c=d s i j n a l  l e v e l s  a n d  receiver  f i c i se  f l e r e s ,  i t  i s  expected t h a t  F? will be 
:ri t h e  order  02 1~~ 50 give good est i rnnfes  of' tine s c a t t e r i n g  p a r m e t e r s .  
n 
0 - w P 
I 
0 
0 
8 
!3 
8 
0 
<y 
Q 
0 
t z 
W x 
W 
a 
2 
B 
Q 
0 
5 a 
W 
v) 
8 1 
v) 
W 
J e 
Tnterpretstion CZ Yessureirents 
c o r r e l a t o r  output ,  w!ien mliltipiieci b;; the rns v a h e s  of  t h e  lunar  
;.:?sfinel signal and :Fie sun channel signal, gives a 4 i r e c t  m e s s u r e  of t he  s igna l  
r e f l e c t e d  w i t h  the  delay and dela;: r a t e  set i n  the  c o r r e l a t o r .  The expression 
fo r  the  s i g n a l  i s  bk qX 
of the pcwer i n  the  s o l a r  s i g n a l  reflected with a delay T~ a d  d e l s y  rate (1 - 3k). 
"his value of bk 
d e f i n i n g  a r ada r  s c a t t e r i n g  cross-sect ion,  m--, and equating the  received power 
a s  expresse3 i n  terms of F L ~  If w e  l e t  w be %ke power per u n i t  area 
c?f +,:?e solar sigazl a s  receive6 on ea r th ,  t l p r i  t h e  power per u n i t  a rea  a t  the 
2 1 CI %here bk is, f o r  all practical purposes, the  f r a c t i o n  
2 can be r e l a t ed  t o  more faxi l iar  measures of s c a t t e r i n g  by 
:. 
2 and q,. 
IC S 
m o n  would be e s s e n t i a l l y  the same. The signrll scRttered from the  moon and 
received a t  e a r t h  with a n  anterm& ol gain C would be 
w h e r e :  ?, = wavelength 
= d i s t ance  from moon t o  
e a r t h  De 
n 
The me3\nrred v a r i a t i o n  of with angle of incidence and angle of s c a t t e r i n g  
will allow prec i se  determinat ion of the scattering l a w  of the lunar surface.  
k 
Xeasurements a t  var ious po la r i za t ions  and f requencies  w i l l  provide f u r t h e r  data 
upon which t o  compute the  d i e l e c t r i c  cons tan t  and o the r  parameters of the  luna r  
sur face .  
Measurenent of the s c a t t e r i n g  c o e f f i c i e n t  f o r  regions away from the  
specular  r e f l ec t in@ po in t  will provide d a t a  on the  roughness of the  surface 
&pd should permit more d e f i n i t e  conclusions t o  be drawn than are possible with 
the backsca t te r  da t a  of ac t ive  radars. 
- 12 - 
The re so lu t ion  of d e t a i l s  on the lilnar surface i s  direct ly  r e l a t e d  t o  
the capab i l i t y  of the c o r r e l a t o r  t o  separate various delays and delay r a t e s .  
The  reso lu t ion  of delays is inversely proport ional  to the handwidth of the  
c o r r e l a t o r  and, f o r  a bandwidth of 30 me, permits a t h e o r e t i c a l  r e so lu t ion  
away from the l una r  equator of less  than 10 meters. 
reso lu t ion  i s  s u b s t a n t i a l l y  less. 
War the equator the  
Tfie resolut ion of delay rates is propor- 
t i o n i l  t o  t he  in t eg ra t ion  time and can be increased by increasing t h i s  time. 
-4s the in t eg ra t ion  time is increased, however, the stability requirements on 
the  local oscillator and clock frequencies a l s o  increase.  
rl. r t g .  5 shows the g r i d  praiuced by i n t e r sec t ion  of l o c i  of constant  delay 
and loci of constant delay r a t e .  The va r i a t ion  i n  delay rate over the lunar 
surface is  due primarily to ro t a t ion  of tke moon and i s  superimposed on the 
large delay rate cornon to d l .  poin ts  on the surface r e s u l t i n g  frm o r b i t a l  
motion and r o t a t i o n  of the earth. The delay ro t e  r e so lu t ion  and antenna beam- 
widtn w i l l  determine how much of a p a r t i c u l a r  locus will cont r ibu te  t o  the  net 
s i  ?:nd obtained after i n t ea -a t ion .  
the rnin;imun: delay md accordiW,ly corresponds t o  811 e s s e n t i a l l y  constant delay 
The specufarly r e f l ec t ed  signal occurs a t  
locus. Therefore t h i s  s i g n a l  c m  be resolvei? independently of the delay rate 
resolut ion.  It i s  thls component tha t  i s  expected to give t.he largest  signal 
and which w i l l  provide the most accurate da t a  on t'ne e f f e c t s  of angle of  
incidence,  po lar iza t ion ,  e t c .  
Present S ta tus  and Future Vork 
The various components of the c o r r e l a t o r  have been assenbled and tested 
with the exception 02' l o c d  oncillators and t a p  recorder. 
L%+,ure work w i l l  Inc lude prcyramc7in-J the  13E 703 coquLer  t o  handle the d a t a  
d e l a y  and cmputs t ion  of  the corr.e;r,ticm f i i n c t i o n s  f o r  t he  ear ly  experiments. 
It i s  planned t h a t  
. report will be i s s2ed  to C C - T F  t f  e ?echnic?l aspects 0.f this ;;roKrarr, in 
ncre “,tail. 


Study of lunar reflective components of solar radio emission semiannual status report

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