National Radio Astronomy Observatory Sept – Indiana University How do Radio Telescopes work? K. Y. Lo

National Radio Astronomy Observatory September 2005 – Indiana Universe Electromagnetic Radiation Wavelength Radio Detection techniques developed from meter-wave to submillimeter-wave: = 1 meter  = 300 MHz = 1 mm  = 300 GHz

General Antenna Types Wavelength > 1 m (approx)Wire Antennas Dipole Yagi Helix or arrays of these Wavelength < 1 m (approx)Reflector antennas Wavelength = 1 m (approx) Hybrid antennas (wire reflectors or feeds) Feed

National Radio Astronomy Observatory Sept 2005: Indiana University REFLECTOR TYPES Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam Waveguide Dual Offset (NRO) (ATA)

National Radio Astronomy Observatory Sept 2005: Indiana University REFLECTOR TYPES Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam WaveguideDual Offset (NRO) (ATA)

National Radio Astronomy Observatory Sept 2005: Indiana University What do Radio Astronomers measure? Luminosity of a source: L = dE/dt erg/s Flux of a source at distance R: S = L/4  R 2 erg/s/cm 2 Flux measures how bright a star is. In optical astronomy, this is measured in magnitudes, a logarithmic measure of flux. Intensity: If a source is extended, its surface brightness varies across its extent. The surface brightness is the intensity, the amount of flux that originates from unit solid angle of the source: I = dS/d  erg/s/cm 2 /steradian

Measures of Radiation The following should be clear: L =  S d  = 4  R 2  S for isotropic source 4  S =  I d  source Since astronomical sources emit a wide spectrum of radiation, L, S and I are all functions of or, and we need to be more precise and define: Luminosity density: L( ) = dL/d W/Hz Flux density: S( ) = dS/d W/m 2 /Hz Specific intensity: I( ) = dI/d W/m 2 /str/Hz The specific intensity is the fundamental quantity characterizing radiation. It is a function of frequency, direction, s, and time. In general, the energy crossing a unit area oriented at an angle to s, specified by the vector da, is given by dE = I(, s, t) s  da d d  dt = I ( ,  ) s  da d d  dt

National Radio Astronomy Observatory Sept 2005: Indiana University Analogs in optical astronomy Luminosity is given by absolute magnitude Flux, or brightness, is given by magnitudes within defined bands: U, B, V Intensity, or surface brightness, is given by magnitude per square arc-second Optical measures are logarithmic because the eye is roughly logarithmic in its perception of brightness Quantitatively, a picture is really an intensity distribution map

National Radio Astronomy Observatory Sept 2005: Indiana University Rayleigh-Jeans Law and Brightness Temperature The Specific Intensity of thermal radiation from a black- body at temperature T is given by the Planck Distribution: I = (2h 3 /c 2 )/[exp(h /kT)  1] = (2hc 3 / 2 )/[exp(hc/ kT)  1] = 2kT/ 2 if >> hc/kT or h << kT, R-J Law Brightness Temperature T b  ( 2 /2k)  I = T for thermal radiation Brightness temperature of the Earth at 100 MHz ~ 10 8 K (due to TV stations)

National Radio Astronomy Observatory Sept 2005: Indiana University Antenna = Radio Telescope The function of the antenna is to collect radio waves, and each antenna presents a cross section, or Effective Area, A e ( ,  ), which depends on direction ( ,  ) The power collected per unit frequency by the antenna from within a solid angle d  about the direction ( ,  ) is given by dP = ½ I ( ,  ) A e ( ,  ) d  W/Hz The ½ is because the typical radio receiver detects only one polarization of the radiation which we assume to be unpolarized.

National Radio Astronomy Observatory Sept 2005: Indiana University The power density collected by the antenna from all directions is P = ½  I ( ,  ) A e ( ,  ) d  W/Hz Antenna Temperature T A is defined by T A = P /k in K (Nyquist Theorem) Therefore T A = (1/2k)  I ( ,  ) A e ( ,  ) d  K For a point source, I = S  ( ,  ) kT A = ½ A e,max S W/Hz if A e ( ,  ) has a maximum value A e,max at ( ,  ) = (0, 0) (Maximum) Effective Area of an antenna: A e,max =  ap A g m 2 where A g is the geometric area and  ap is the aperture efficiency. But, for a dipole antenna, A g is zero but A e is not.

National Radio Astronomy Observatory Sept 2005: Indiana University Antenna pattern: P n ( ,  ) = A e ( ,  )/A e,max P n (0,0) = 1 if the pattern is maximum in the forward direction If the antenna is pointed at direction (  o,  o ) T A (  o,  o ) = (1/2k)  I ( ,  ) A e (  o,  o ) d  In terms of T b and P n, T A (  o,  o ) = (A e,max / 2 )  T b ( ,  ) P n (  o,  o ) d  = (1/  A )  T b ( ,  ) P n (  o,  o ) d  where 2 /A e,max =  A. Note the antenna temperature, which measures the power density P (W/Hz) collected by the antenna is the convolution of the antenna pattern P n with the source brightness distribution T b

Antenna Properties Effective area: A e ( , ,  ) m 2 On-axis response A e,max =  A g  = aperture efficiency Normalized power pattern (primary beam) P n ( , ,  ) = A e ( , ,  )/A e,max Beam solid angle  A =  P n ( , ,  ) d   4 ,  = frequency all sky  = wavelength A e,max  A =  2

National Radio Astronomy Observatory Sept 2005: Indiana University Mapping by an Antenna

Milky Way

National Radio Astronomy Observatory Sept 2005: Indiana University Maxwell Equations? Radio telescopes operate in the physical optics regime, ~ D, instead of the geometric optics regime, << D, of optical telescope  diffraction of radiation important Easier to think of a radio telescope in terms of transmitting radiation A point source of radiation (transmitter) at the focus of a paraboloid is designed to illuminate the aperture with a uniform electric field The diffraction of the electric field across the aperture according to Huygens’ Principle determines the propagation of the electric field outward from the aperture or primary telescope surface The transmitted electric field at a distant (far-field) point P in the direction ( ,  ) is given by the Fourier Transform of the electric field distribution across the aperture u( ,  ): u( ,  )   u( ,  ) exp[  2  (   +   )/ ] d  d 

National Radio Astronomy Observatory Sept 2005: Indiana University Antenna Pattern: Directional Response Field Pattern of an antenna is defined by the Fourier Transform of the illumination of the aperture: u( ,  )  u( ,  ) Antenna Pattern is defined in terms of power or the square of the E field,|u| 2.  P n ( ,  ) = |u( ,  )| 2 /|u(0,0)| 2 Alternately, the antenna pattern is proportional to the Fourier Transform of the auto-correlation function of the aperture illumination, u( ,  )

Aperture-Beam Fourier Transform Relationship u ( ,  ) = aperture illumination = Electric field distribution across the aperture ( ,  ) = aperture coordinates ; u( ,  ) = far-field electric field ( ,  ) = direction relative to “optical axis” of telescope : : |u (  )| 2 |u (  )| 2

National Radio Astronomy Observatory Sept 2005: Indiana University Antenna Key Features

Types of Antenna Mount + Beam does not rotate + Lower cost + Better tracking accuracy + Better gravity performance - Higher cost- Beam rotates on the sky - Poorer gravity performance - Non-intersecting axis

National Radio Astronomy Observatory Sept 2005: Indiana University Antenna pointing design Subreflector mount Quadrupod El encoder Reflector structure Alidade structure Rail flatness Az encoder Foundation

What happens to the signal collected by the antenna? At the focus, the radiation is collected by the receiver through a “feed” into a receiver that “pre-amplifies” the signal. Then, the signal is mixed with a local oscillator signal close in frequency to the observing frequency in a nonlinear device (mixer). The beat signal (IF or intermediate frequency signal) is usually amplified again before going through a bandwidth defining filter. (Frequency translation) Then the IF signal is detected by a square-law detector. Pre-amplifier LO at f LO Amplification and filtering Voltage  |E| 2 RF at f sky IF at f sky  f LO Heterodyne Detection

VLA and EVLA Feed System Design VLA EVLA

National Radio Astronomy Observatory Sept 2005: Indiana University Wideband LBand OMT and Feed Horn

Receivers in the telescope Gregorian Receiver Room PF 1-1: GHz PF 1-2: PF 1-3: PF 1-4: PF 2 : L : GHz S : C : X : Ku : K1 : K2 : Q :

National Radio Astronomy Observatory Sept 2005: Indiana University Radiometer Equation For an unresolved source, the detection sensitivity of a radio telescope is determined by the effective area of the telescope and the “noisiness” of the receiver For an unresolved source of a given flux, S, the expected antenna temperature is given by kT A = ½ A e,max S The minimum detectable  T A is given by  T A =  T s /  (B  ) where T s is the system temperature of the receiver, B is the bandwidth and  is the integration time, and  is of order unity depending on the details of the system. The system temperature measures the noise power of the receiver (P s = BkT s ). In Radio Astronomy, detection is typically receiver noise dominated.

National Radio Astronomy Observatory Sept 2005: Indiana University High Resolution: Interferometry Resolution  /D –5 cm/100m = 2 arc-minute Uses smaller telescopes to make much larger 'virtual' telescope Maximum distance between antennas determines resolution VLA = 22-mile diameter radio telescope –5 cm/22 miles = 0.3 arc-second Aperture Synthesis: Nobel Prize 1974 (Ryle) D

National Radio Astronomy Observatory Sept 2005: Indiana University VLA = Very Large Array (1980) Plain of San Augustine, New Mexico 27-antenna array: Extremely versatile Most productive telescope on ground

Interacting Galaxies Optical image (left) shows nothing of the Hydrogen gas revealed by radio image by VLA (right).

National Radio Astronomy Observatory Sept 2005: Indiana University Very Long Baseline Array 10  25m antennas Continent-wide: 5400-mile diameter radio telescope 6 cm/5400 miles = arc-second Highest resolution imaging telescope in astronomy: 1 milli-arc-second = reading a news-paper at a distance of 2000 km