The utilization of conventional and VLBI interferometer techniques for accurate determination of UTI, polar motion, and radio source position catalog data is discussed

Johnston, K. J.

English

NASA Technical Reports Server

RADIO ASTROMETRY 
Dr. Kenneth J. Johnston 
E. 0. Hulburt Center for Space Research 
Naval Research Laboratory 
ABSTRACT 
Conventional and VLBI in te r fe rometer  techniques 
show promise for accu ra t e  determinat ion of UT1, 
po la r  motion, and r a d i o  source p o s i t i o n  catalogs.  
INTRODUCTION 
Radio in te r fe rometer  measurements of c e l e s t i a l  r a d i o  
sources  are being employed t o  determine v a r i a t i o n s  i n  t h e  
E a r t h ' s  r o t a t i o n ,  p o l a r  motion, and a catalogue of r a d i o  
source  pos i t i ons .  Both conventional i n t e r f e r o m e t r y  and t h e  
very long base l ine  in te r fe rometer  (VLBI) technique have 
shown promise i n  previous experimental  tests; t h e  VLBI 
technique has beep demonstrated t o  determine UT1 t o  an 
accuracy of 3 m s ,  p o l a r  motion t o  submeter accuracy and 
O'i l  i n  source catalogue pos i t i on  (Clark and Shapiro 1973; 
Shapiro e t  a l .  1974), and t h e  conventional technique has 
been used t o  determine UT1 t o  an accuracy of 4.3 m s  (Elsmore 
1973) and source ca ta logue  pos i t i on  accuracy t o  0':l ( R y l e  
and Elsmore 1973). Fur ther  tests a r e  being conducted t o  
eva lua te  experimental  accurac ies  and atmospheric l i m i t a t i o n s  
f o r  d i f f e r e n t  b a s e l i n e s  and measurement techniques.  
1 
I 
RADIO INTERFEROMETRY 
A s i g n a l  is simultaneously received from a c e l e s t i a l  source 
a t  two antennas which can be separa ted  by d i s t ances  of from 
hundreds of meters t o  thousands of kilometers. T h i s  s i g n a l  
is first mixed t o  an in te rmedia te  frequency. The s i g n a l  a t  
one of t h e  antennas is delayed by T t h e  geometric delay 
or t h e  d i f f e r e n c e  i n  t h e  doppler sh& t o  t h e  source a s  seen 
from t h e  t w o  sites. F i n a l l y  t h e  s i g n a l s  a r e  cross-corre- 
l a t e d .  The c ross -cor re la ted  s i g n a l  has an amplitude and 
phase. When t h e  source  size is small  compared w i t h  t h e  in- 
terf erometer f r i n g e  spacing, t h e  normalized c o r r e l a t i o n  
amplitude is uni ty .  The phase of t h e  c ross -cor re la ted  
s i g n a l  y i e l d s  information on where t h e  source is loca ted  i n  
t h e  f r i n g e  p a t t e r n  of t h e  in te r fe rometer .  One can v isua l ize  
a p a t t e r n  of  l i n e s  or f r i n g e s  pro jec ted  onto  t h e  sky. As 
t h e  e a r t h  r o t a t e s  t h e  source passes  through t h i s  pa t t e rn .  
The phase of t h e  c ros s -co r re l a t ed  s i g n a l  changes by % 
rad ians  from f r i n g e  t o  f r inge .  The sepa ra t ion  of t h e  
h 
~ W W W G  PAW BLANK Norr FILMED 373 
https://ntrs.nasa.gov/search.jsp?R=19750019124 2020-03-19T21:06:23+00:00Z
f r i n g e s  on t h e  s k y  is s i m p l y  
' r a d i a n s ,  * e  = D s i n  8 
where is t h e  wavelength of t h e  s i g n a l ,  D is the  s e p a r a t i m  
of t h e  antennas and 8 is t h e  angle  between t h e  celestial  
source and t h e  base l ine .  See f i g u r e  1, 
The phase can be determined accu ra t e ly  t o  a f r a c t i o n  of a 
f r i n g e  i n  convent ional  in te r fe rometry  and p r e c i s e  p o s i t i o n s  
can be determined w i t h  a short  basel-ine. For example a 5 
km base l ine  ope ra t ing  a t  a frequency of  5 GHz, has a f r i n g e  
spacing of 225. 
source t o  5 O  r e s u l t s  i n  a p o s i t i o n  accuracy of 0.035 a r c  
seconds or 2 mil l iseconds.  
A determinat ion of t h e  phase of a c e l e s t i a l  
The d i f f e r e n c e  between VLBI and convent ional  interferometry 
is i n  t h e  phase s t a b i l i t y  of t h e  in t e r f e romete r ,  Conven- 
t i o n a l  interferometers o f f e r  phase s t a b i l i t i e s  of a f e w  
degrees for pe r iods  of  days. The p r i n c i p a l  l i m i t a t i o n s  t o  
phase s t a b i l i t y  a t  f requencies  above 5 GHz a r e  short  per iod 
v a r i a t i o n s  i n  atmospheric r e f r a c t i v i t y  and ins t rumenta l  
phase v a r i a t i o n s .  VLBI on t h e  other hand depends on inde- 
pendent l o c a l  o s c i l l a t o r s  c o n t r o l l e d  by atomic frequency 
s tandards  a t  t h e  t w o  loca t ions ,  and has  phase i n s t a b i l i t i e s  
of s e v e r a l  r ad ians  i n  a period of an hour. The p r i n c i p a l  
l i m i t a t i o n  t o  phase s t a b i l i t y  is t h e  frequency s t a b i l i t y  of 
t h e  s tandards  a t  each s i t e  used t o  genera te  t h e  l o c a l  
o s c i l l a t o r  chains .  These L.O. chains  are used t o  mix t h e  
s i g n a l  down t o  an in te rmedia te  l o w  frequency t h a t  can be 
recorded on magnetic tape. 
Since VLBI has poor phase s t a b i l i t y ,  t h e  phase of t h e  
s i g n a l  is not analyzed d i r e c t l y  but rather its de r iva t ives ,  
de l ay  which is t h e  r a t e  of change of phase w i t h  frequency, 
and f r i n g e  r a t e  which is t h e  rate of change of phase w i t h  
respect t o  t i m e ,  Thus for t h e  same base l ine ,  conventional 
in te r fe rometry  w i l l  be orders of magnitude more accu ra t e  
than VLBI. The very long base l ines  p o s s i b l e  w i t h  VLBI, how- 
ever, compensate for t h i s  d i f f e r e n c e  i n  p rec i s ion ,  
The major l i m i t a t i o n s  t o  convent ional  in te r fe rometry  a re :  
1) Short  t e r m  changes i n  atmospheric phase path,  i.e. 
t h e  s i g n a l  from t h e  celestial  source does not  pass  through 
i d e n t i c a l  atmospheric paths t o  t h e  antennas.  Small s c a l e  
v a r i a t i o n s  i n  atmospheric r e f r a c t i v i t y  due mainly t o  water 
vapor cause t h e  atmospheric phase path t o  vary i n  a random 
3 74 
manner on t h e  o rde r  of minutes. Present  da t a  on t h e  r m s  
v a r i a t i o n  i n  atmospheric pa th  length  is very incomplete, 
but t h e  t r e n d  is d isp layed  versus  base l ine  length  i n  f i g u r e  
2 ,  The s i n g l e  po in t  a t  35 k m  is preliminary information from 
Wade (1974) of the  Nat ional  Radio Astronomy Observatory where 
t h e  antennas were connected by a radio l i n k .  There is a 
marked d i f f e r e n c e  between t h e  phase pa th  dev ia t ions  on a 
summer day versus  a win ter  day. The summer n igh t s  and 
w i n t e r  n i g h t s  resemble t h e  win ter  day. Therefore  observa- 
t i o n s  obta ined  dur ing  a summer day would be expected t o  have 
one ha l f  t h e  accuracy of those  made a t  n igh t  or on a win ter  
day. 
2) Instrumental  noise--If t h e  antennas are connected by 
a r ad io  l i n k ,  noise  over t h i s  l i n k  may c o n t r i b u t e  s i g n i f i c a n t l y  
t o  t h e  data .  The re  may a l s o  be s i g n i f i c a n t  no i se  con t r ibu t ion  
by noise  generated i n  t h e  l o c a l  o s c i l l a t o r  s y s t e m .  Temperature 
effects on t h e  cab le s  connecting t h e  i nd iv idua l  antennas and 
t h e  delay l i n e s  a l s o  c o n t r i b u t e  t o  t h e  s y s t e m  phase noise .  
COMPARISON OF TECHNIQUES 
The accuracy of convent ional  in te r fe rometry  and VLBI i n  
determining UT1 has been estimated. From figure 2, an 
e s t ima te  may be made of t h e  con t r ibu t ion  of short  term 
changes in atmospheric r e f r a c t i v i t y  t o  phase noise ,  Assum- 
ing  t h i s  t o  be t h e  major c o n t r i b u t o r  t o  phase noise, t h e  
accuracy i n  t h e  determinat ion of UT1 may be predic ted ,  and 
is displayed i n  f i g u r e  3 versus e q u a t o r i a l  base l ine .  
In work done i n  co l l abora t ion  w i t h  C. M. Wade and R. M. 
Hjellming of t h e  Nat ional  Radio Astronomy Observatory (NRAO) 
prel iminary observa t ions  have been obtained over a base l ine  
of 35 kilometers .  The opera t ing  frequency was 2695 MHz 
(11.1 c m ) .  The baseline is loca ted  on an azimuth angle  of 
about - 4 5 O .  Observations were obtained of 16 r a d i o  sources  
over a f i v e  day per iod  i n  January 1974. From t h e  observed 
phases, c o r r e c t i o n s  t o  t h e  e q u a t o r i a l  and polar base l ines ,  
and source  coord ina tes  were c a l c u l a t e d  by l e a s t  squares .  
T h i s  s o l u t i o n  r e s u l t e d  i n  an r m s  phase no i se  of 16O. Th i s  
is equiva len t  t o  a p o s i t i o n  accuracy of O'iO29 or 2 m s ,  
i nd iv idua l  source coordinates ,  t h e  accuracy depends on t h e  
base l ine  geometry and source dec l ina t ion .  For a given 
basel ine,  there is a d e f i n i t e  c o r r e l a t i o n  versus  source 
dec l ina t ion .  The s o l u t i o n  for r i g h t  ascension and decli- 
na t ion  a r e  not  c o r r e l a t e d  f o r  sources  near  t h e  z e n i t h .  
Therefore, observat ions of a source  t h a t  t r a n s i t s  through 
t h e  z e n i t h  w i l l  y i e l d  t h e  m o s t  a ccu ra t e  measurement of UT1. 
For 
375 
T h i s  is a t t e s t e d  t o  by t h e  f a c t  t h a t  t h e  s o l u t i o n  of t h i s  
se t  of da t a  f o r  t h e  r i g h t  ascension of 3C84 (6 = 40°) re- 
s u l t e d  i n  an i n t e r n a l  accuracy of 2 m s .  
The accurac ies  of t h e  VLBI technique i n  f r i n g e  r a t e  and 
t i m e  delay are c a l c u l a t e d  assuming an accuracy of 1 x 
p a r t s  i n  f r i n g e  r a t e  r e s i d u a l s  (Moran et a l .  1973; Cohsn 
1971) and an accuracy of lom9 seconds i n  de lay .  The da t a  
by Shapiro (1974) agree  w e l l  w i t h  t h i s .  Therefore  a t  t h e  
present  t i m e  conventional i n t e r f e r o m e t r y  and VLBI o f f e r  
s i m i l a r  accurac ies  i n  determining UT1. 
Some of t h e  advantages of t h e  conventional interferometry '  
technique over VLBI a r e :  
1) Var ia t ions  i n  atmospheric r e f r a c t i v i t y - - t h e  con- 
vent ional  technique is less inf luenced by v a r i a t i o n s  i n  
atmospheric r e f r a c t i v i t y  s i n c e  t h e  antennas a r e  located 
c l o s e r  together and see more near ly  t h e  same atmospheric 
pa th  condi t ions.  
2) Solid Body Earth Tides--the r e l a t i v e  effect of 
s o l i d  body Ear th  tides between t h e  antennas of a convention- 
a l  in te r fe rometer  is n e g l i g i b l e  whereas for VLBI it is not .  
3) Frequency Standards--there is no need for highly 
s t a b l e  and precise frequency s tandards  i n  a convent ional  
in te r fe rometer ,  whereas VLBI r e q u i r e s  hydrogen maser fre- 
quency s tandards  and clock synchronizat ion t o  a microsecond. 
4) Data Reduction--the da t a  may be r e d u c e d i n  r e a l  t i m e .  
A f t e r  a day's observat ion,  UT and po la r  motion may be c a l -  
cu la t ed  immediately. There is no need t o  correlate magnetic 
t apes  from w i d e l y  s epa ra t ed  l o c a t i o n s  t o  o b t a i n  c o r r e l a t i o n  
funct ions.  
5) S t a t i o n  Management--it is much easier t o  manage 
s t a t i o n s  t h a t  a r e  10-100 k m  a p a r t  than  thousands of km 
apa r t  . 
PLANS 
Conventional in te r fe rometry  w i l l  be i n v e s t i g a t e d  i n i t i a l l y  
through eva lua t ion  of observa t ions  obtained w i t h  t h e  NRAO 
in te r fe rometer  and VLBI techniques w i l l  be f u r t h e r  evalu- 
ated. These data w i l l  d e f i n e  basic accuracy l i m i t a t i o n s  and 
guide t h e  design of optimum techniques for radio a s t r o m e t r y .  
The author  thanks C .  H. Mayer for h e l p f u l  d i scuss ions .  
376 
e H I M E R I I 9 7 0 1  SUYYER M Y  + HINDeR(IS101 WINTER M Y  
0 E4ASART et al(1970) JANUARY 
0 W R T  et a1 119701 APRIL 
A EASARTrtol (1910) JULY + WADE 0974) 
w 
BASELINE IKN1 
Fig. 1-Celestial Source and 
Antenna Configuration 
Fig; 2-Variation of RblS Path- 
length With Baseline 
Fig. 3-Accuracy in UT1 Determination Versus 
Equatorial Baseline 
377 
REFERENCES 
1. Clark, T. A. and Shapiro, I. I. 1973, "Time, Geodesy and Astrometry: 
Results from Radio hter€erometryt' in Proceedings of the Fifth Precise 
Time and Time Interval Planning Meeting, Goddard Space Flight Center, 
Greenbelt Md. , p. 33. 
2. Cohen, M. H. 1972, Astrophys. Letters, - 12, 81. 
3. Elsmore, C. 1973, Nature, 14, 423. 
_I_- 
4. Moran, J. M., Papadopoulos, G. D., Burke, B. F. , Lo, K. Y. $ Schwartz, 
P. .R. , Thcker,  D. L., Johnston, K. J . ,  Knowles, S. H., Reisz, A. C., 
andshapiro, I. I. 1973, Ap. J., 185, 535. - -
5. Ryle, M. and Elsmore, B. 1973, M.N.R.A.S., - 164, 223. 
6. Shapiro, I. I., Robertson, D. S., Knight, C. A., Counselman, C. C., 
Rogers, A. E. E., Hinteregger, H. F., Lippincott, S., Whitney, A. R., 
Clark, T. A. , Niell, A. E., and Spitzmesser, D. J. 1974, Science, - 186,
920. 
7. Shapiro, I. I. 1974, private communication. 
8. Wade, C. M. 1974, privatecommunication. 
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