Richard Dodson 1/28/2014 NARIT-KASI Winter School

Transcription

1 Goals: Technical introduction very short So what to cover? Things which are essential: How radio power is received - I How an interferometer works -II

2 Antenna Fundamentals Black Body Radiation Brightness Temperature Dipole Radiation Beam Patterns Visualization of Fourier Transforms Introduce Interferometers

3 Antenna Fundamentals Source Material: Essential Radio Astronomy Mike Garrett Lecture Series Wikipedia (for figures) Others

4 Garrett: Radio Astronomy is Special

5 Garrett: Radio Astronomy is Special

6 Garrett: Radio Astronomy is Special

7 Garrett: Radio Astronomy is Special

8 Garrett: Radio Astronomy is Special

9 Nature of the Signal in Radio Astronomy What is special about the Radio signal? It is electromagnetic so long range Can see infinite distances It is low frequency so low energy Little Absorption, Many photons

10 Radiation from a perfectly radiating (black) body at a temperature T described by Planck Formula Units: spectral energy density in Watts/Hz/m 2 per steradian

11 Low Frequency end is linear Gives the Rayleigh-Jean Approximation Even a low temperatures & the highest frequencies Rayleigh-Jean is valid

12 We measure a flux (Watts/Hz/m 2 /s.r.) at a frequency & convert that to Brightness Temp. T b is the temperature of the equivalent B.B. Given the measured flux at the observing freq. Often has little physical meaning, as spectrum often does not follow B.B. functional form.

13 Black Body Temperature The Cosmic Microwave Background temp. (2.7K) Molecular Clouds K Sun 50,000K Given these temperatures what is the peak brightness? Using ν=kt/h: 60GHz, 200GHz, 1PHz WMAP, ALMA, Optical

14 Reciprocity Astronomers very often swap between talking of receiving and transmitting antennas will little thought. Thus the `Gain (an out-going concept) is mixed with the Effective Area (incoming) Justification comes from consideration of antenna with load in a box. If transmitted power did not match received power the resistor would heat up

15 Antenna fundamentals: Receiving Radio Signals Signal Generator ω = 2πν Closed system so: Current at top must be zero Current driven at bottom Current: Power pattern:

16 Antenna fundamentals Charges: Current: Integrated along length Current is charge moving along wire (z-axis) With velocity v Where: Field from Lamor s Eq. Then:

17 Antenna fundamentals Current: Power is Square of E-Field Substitute In: So: To Give: Important point: Field falls as sin 2 Θ Wide Field of View`

18 Dipole Antennas in SKA Pathfinders Single dipole gives wide view of Sky Many dipoles added together For pointed sensitivity

19 Reflector Dishes To make up for the poor gain of a dipole antenna these are commonly placed inside a horn feed at the FOCUS of a parabolic dish A parabola follows the class of quadratic functions: 4fy=x 2

20 Reflector Dishes Many alternative focii can be formed and all of these have different functions and strengths: Gregorian

21 Reflector Dishes Many alternative focii can be formed and all of these have different functions and strengths: Prime Cassegrain (offset) Offset Cassegrain Images: Jodrell Bank, VLBA, SK

22 Reflector Dishes Dishes allow for a range of feed arrangements: Conventional Feed Horn Multi-beam Feed Horn Multiple Feed Horn Multi-frequency Feed Horn Phased Array Feed

23 Reflector Dishes Many alternative focii can be formed and all of these have different functions and strengths: Prime Focus: Simple No frequency or size restraints Hard to access Unbalanced Cassegrain: Easy to access Weight on axis Extra reflector Constraints on space Naysmith: Easy to access Feeds don t move No space constraints Extra reflectors Offset Gregorian: Easy to access Weight close to axis No space constraints

24 Beam Size We have ignored up till now the fact that an antenna only sees a fraction of the sky. The higher the Gain the small the fraction of the sky which can be detected. We will use discussion of Beam Size to introduce Fourier Transforms which are crucial for understanding Interferometry. Lecture 3

25 Beam Size Rayleigh relationship: Θ ~1.2 λ/d (Problem: Derive this by consideration of angle at which waves would cancel) Two beams just resolvable.

26 Beam Size A 1 Dimensional cut through the antenna: Y-axis; Reflectivity X-axis; distance

27 Beam Size Fourier Transform converts from one domain to its reciprocal: Frequency (ω) and Time (t), or Distance in wavelengths (u) and Angle in cosines (l) -1/2 1/2-1 1 Summation of Fourier Terms (sinusoids) weighed by function Fourier Transform of a box car is a Sinc function 0.5u -0.5u 1.0 exp(-i2π u.l) du = sin(π u.l)/ (π u.l) Sinc first null is when u.l=1 or D/λ. Θ =1

28 Pictorial Dictionary of Fourier Transforms

29 Pictorial Dictionary of Fourier Transforms Antenna beam shape convolves with your observations From Kraus - Antennas So you can not resolve features finer that the beamsize

30 Pictorial Dictionary of Fourier Transforms Fourier Transform of a Gaussian is a Gaussian Fourier Transforms scale reciprocally, if width in one domain doubles in the other domain it halves.

31 Pictorial Dictionary of Fourier Transforms Consider that most `things can be made of described as sums of many Gaussians. If source is very broad then it is has greater extent than the beam of the dish. In Fourier terms, the FT of the source is narrower than the FT of the beam. Only collect a fraction of the signal in one pointing

32 Pictorial Approach to Interferometry Interferometer response to signal: same approach as single antenna But with FT of Baseline+width FT of Baseline-width So resolution is fantastic: λ/b max But there is missing information on broad scale

33 Conclusions Black Body Radiation: Radio in R-J regime Dipoles: Wide Field of View Reflecting Parabolas: Narrow(er) Field of View Visualization: Fourier Transform Interferometers: Higher resolution, poor sensitivity to extended structure