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

Data

• 5 drift scans were made – 10:40 am MST– 11:07 am MST– 1:09 pm MST– 3:16 pm MST– 3:31 pm MST

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.

Extensions

VIBA

Very Itty Bitty Array

VIBAVIBA

The Very The Very Itty Bitty Itty Bitty ArrayArray

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>.

Acknowledgements

• Dr. Mark Clausen • Dr. Robyn Harrison

• Dr. Lisa Young