Upload
chloe-jennings
View
216
Download
2
Embed Size (px)
Citation preview
The Effect of the Apparent Baseline on Fringe Amplitude
and Period
By
Dana Dawson
Rhonda Tully
July 2004
MST 562
PurposeUse an interferometer to compare the effect that the apparent baseline length has on the fringe amplitude and period pattern of radio waves emitted by the sun at different positions in the sky.
This is not an interferometer but we liked this picture…
Hypothesis
• The fringe amplitude will increase when the sun is directly overhead
• The fringe period will decrease as the amplitude increases.
Background Research
• Sensitivity- increases as the diameter of the dish increases
• Resolution- increases as the diameter of the dish increases
• There are physical limits to dish size
D
What is interferometry?
• A simple interferometer involves the combining of signals from two telescopes.
• The distance between the telescopes, combined in this fashion, effectively becomes the diameter of the collection instrument.
What is interference?
• Interference is a phenomenon that occurs when multiple waves come together at the same time and at the same place.
• The amount of interference depends on how out of phase the waves are with respect to each other and their amplitudes.
What is the geometry of the interferometer?
• Radio waves reach the elements at different times due to the rotation of the earth
• Radio waves will reach the right element first• Radio waves that reach the left element will travel farther
θ
D (Distance between elements)
D*sin(θ)
D*cos(θ)(Apparent baseline)
Baseline
N
What is a fringe?
• The addition of radio waves produces interference fringes.
• The amount of interference depends on how out of phase the waves are with respect to each other and their amplitudes.
Formulas – Fringe Amplitude• Relative Fringe Amplitude=
• Visibility Fringe Amplitude =
• b=apparent baseline
• λ=observing wavelength
• ά=source size
minmax
minmax
PowerPower
PowerPower
b
b)sin(
Global maxima
Local minima2Local minima1
Formulas – Fringe Period
• Fringe Period =
t = time
b=separation of the dishes
=angle of declination of the Sun
E=how fast the Earth turns
H0=hour angle
oE Hb coscos
Why do we use interferometry?
• The distance between the telescopes, combined in this fashion, effectively becomes the diameter of the collection instrument.
• Increase angular resolution and sensitivity.
Equipment/Materials
• Interferometer• (Etscorn)• Computer
system to point telescopes and collect data
24 m baseline 2.1m dishes
Procedure
Observe Sun
• local noon (1:00 pm)
• 2 hours before local noon (11:00)
• 2 hours after local noon (3:00)
Procedure
• Set-up the interferometer
• Initiate data collection
• Run drift scan– Point the interferometer
5° ahead of Sun– Take readings every 3
sec
Observations• 10:30 MST
• Antenna Coordinate:
azel 103.8 56 deg
• Sun: radec
7.8 hrs 20.7 deg Fringes
Drift Scan Target: Sun07-19-2004 16 40 (UTC)
0
2
4
6
8
10
0 200 400 600 800 1000 1200 1400 1600
Time (sec)
Po
we
r (v
olt
s)
Observations• 11:07 MST
• Antenna Coordinate:
azel 110.2 61.2 deg
• Sun: radec
7.8 hrs 20.7 deg Fringes
Drift Scan Target: Sun07-19-2004 17 07 (UTC)
0
2
4
6
8
0 200 400 600 800 1000 1200 1400
Time (sec)
Po
we
r (v
olt
s)
Observations• 1:09 MST
• Antenna Coordinate:
azel 187.1 76.5
• Sun: radec
7.8 hrs 20.7 deg Fringes
Drift Scan Target Sun07-19-2004 19 09 (UTC)
0
1
2
3
4
0 200 400 600 800 1000 1200
time (sec)
Po
we
r (v
olt
s)
Observations• 3:16 MST
• Antenna Coordinate:
azel 253.6 58.2
• Sun: radec
7.8 hrs 20.6 deg Fringes
Drift Scan Target: Sun07-19-2004 21 16 8 (UTC)
0
0.5
1
1.5
2
0 100 200 300 400 500 600 700
Time (sec)
Po
we
r (v
olt
s)
Observations• 3:16 MST
• Antenna Coordinate:
azel 257.4 54.8
• Sun: radec
8.0 hrs 20.6 deg Fringes
Drift Scan Target: Sun07-19-2004 21 31 10 (UTC)
00.5
11.5
22.5
3
0 100 200 300 400 500 600 700
Time (sec)
Po
we
r (v
olt
s)
Results – Apparent Baseline
• Apparent baseline did vary
• Maximum apparent baseline approached the actual baseline at noon standard time or 1:09 pm daylight savings time.
Apparent Baseline LengthBased on Observaton 07-19-2004
0
5
10
15
20
25
30
1 2 3 4 5
Observatons (order by time)L
en
gth
(m
)
Results – Extra Length Traveled
• Extra length traveled by the radio waves to reach the second element of the interferometer
Extra Length Traveled by Radio Waves Based on Observations 07-19-2004
0
5
10
15
20
1 2 3 4 5
Observations (ordered by time)
Le
ng
th (
m)
θ
D (Distance between elements)
D*sin(θ)
D*cos(θ)(Apparent baseline)
Baseline
N
Results – Fringe Amplitude
• The primary fringe amplitude varied with the apparent baseline length.
• The maximum fringe amplitude occurred when the apparent baseline was the longest.
Average Amplitude at Peak Fringe
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6
Observations (ordered by time of observation)A
mp
litu
de
(vo
lts
)
Average
Results - Theoretical
• Observed amplitudes follow the same trend as the theoretical for the first two and last two observations, but is significantly different for the third observation.
Comparison of Experimental and Theoretical Fringe Amplitudes
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5
Observations (ordered in time)A
mp
litu
de
(vo
lts)
Average Amplitude(Observed)
Visible Fringe(Theoretical)
Results – Amplitude Relative Size
• Comparison of the ratio of amplitudet/amplitudet+1 for both
the observed and theoretical amplitudes
• Compare relative sizes of the
amplitudes. • Trends are comparable for the
first two observations and the last two observations and significantly different for the third observation.
Comparison of Ratios of Observed Amplitudes versus Theoretical Amplitudes
02468
10121416
1 2 3 4
Observations (ordered by time)A
(t)/
A(t
+1) relative amplitude
observed
relative amplitudetheoretical
Results - Period
• The average period of the fringe decreased during the observation day
Average Period of Peak Fringe
020406080
100120140160
0 1 2 3 4 5 6
Observation (ordered by time of observation)
Pe
rio
d (
sec)
average
P1 P2
P3
Results - Theoretical
• The experimentally observed fringe periods agree with the theoretical values somewhat for the first three observations but is significantly different for the last two observations.
Comparison of Experimental and Theoretical Fringe Periods
0
50
100
150
200
1 2 3 4 5
Observations (ordered by time)P
eri
od
(se
c) Average Period(Observed)
Fringe Period(Theoretical)
Conclusions
• The amplitude of the fringe pattern collected with the interferometer did increase during the observation where the apparent baseline was close to the actual baseline,
• The fringe period did decrease as the amplitude increased as expected.
• Further investigation is necessary to resolve discrepancy between observed and theoretical results.
References
• Moran, James M., George W. Swenson,Jr., and A. Richard Thompson. Interferometry and Synthesis in Radio Astronomy. New York: John Wiley and Sons, Inc., 2001.
• Westpfal, David. The Adding Radio Interferometer. National Radio Astronomy Observatory. NRAO, Socorro, NM.
• What is Radio Astronomy? 11 Mar. 2003. National Radio Astronomy Observatory. 7 July 2004 <http://www.nrao.edu/whatisra/radiotel.shtml>.