Astrophysical Techniques VII Radio Astronomybn204/lecture/2012/aptech-bn-l7.pdf · 2018. 12....
Transcript of Astrophysical Techniques VII Radio Astronomybn204/lecture/2012/aptech-bn-l7.pdf · 2018. 12....
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Astrophysical Techniques VII –Radio Astronomy
B. Nikolichttp://www.mrao.cam.ac.uk/˜bn204/mailto:[email protected]
Astrophysics Group, Cavendish Laboratory, University of Cambridge
March 2012
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Outline
Basics
Noise and sensitivity
Implementation
Back matter
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Power radiating from a black body& Rayleigh-Jeans limit
Planck law:Bν =
2hcλ3
1exp hν
kBT − 1(1)
When hν << kBT can use the Rayleigh-Jeans limitapproximation:
Bν ∼2kBTλ2 (2)
For T ∼ 20 K→ kBT/h ∼ 410 GHz
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Power from a resistor & relation totemperature
Johnson Noise equivalent circuitPhysical temperature T
V∼ =√
4kBT R∆ν
RΩ
RΩ Pnoise = kT ∆ν
Power of a random white-noise signal←→ temperature ofa resistor that would produce the same power:
Pnoise = kBT ∆ν (3)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Antenna temperature
Physical temperature TA
Antenna
RΩ Pnoise = kBTA∆ν
1. Imagine isolated passive system as above2. In equilibrium, the resistor must be at same
temperature as the black body3. When a source completely fills beam, antenna
temperature = brightness temperature of source
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Gain measurement example
From: Srikanth et al, www.aoc.nrao.edu/evla/geninfo/memoseries/evlamemo95.pdf Actually gain of a corrugated horn designed as
a feed!
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Antenna gain
Physical temperature TB
Antenna
RΩ Pnoise = kBTA∆νsolid angle Ω
Power arriving
(single polarisation)
Pin =Bν(TBw)
2ΩAe∆ν
(4)
Pin ∼kBTBΩAe
λ2 ∆ν (5)
Power radiated byantennaInto solid angle Ω
Pant = kBTA∆νΩ
4πg (6)
Equilibrium⇒
g =4πAe
λ2 ; gmax ∼4πΩB
(7)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Antenna gain II
Very useful for analysis of antennas using transmittingconfiguration (e.g., when geometric optics a very poorapproximation)Gain normally quoted in dB
I dB = 10 log10 gI Pulsar array at Lords Bridge: ν = 81.5 MHz,λ = 3.7 m, g = 46 dB
I 25 m dish at ν = 10 GHz, λ = 3 cm, g = 68 dB (e.g.,one VLA dish)
I 15 m dish at ν = 850 GHz, λ = 350µm, g = 103 dB(e.g., the JCTM)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Signal from point source
S
Point source, flux density Sν
Antenna
RΩ Pnoise = kBTA∆νsolid angle Ω
Single polarisation:
Pin =12
SνAe∆ν = kBTA∆ν (8)
TA =Ae
2kBSν (9)
ALMA, VLA, GBT all have Ae2kB∼ 1− 2 K Jy−1 depending
on frequency
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Finite source not filling the beam
S
Source brightness TB
Antenna
RΩ Pnoise = kBTA∆ν
beam ΩB
source ΩS
TA ∼ΩS
ΩBTB (10)
Source is ‘diluted’ by the beam
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Outline
Basics
Noise and sensitivity
Implementation
Back matter
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Sources of noise in radio telescopes
1. Fundamental noise in amplifiers/mixers/detectorsUncorrelated, white noise→ ‘Thermal’ noise
2. Backgrounds:2.1 Losses in telescope, spillover to ground2.2 Atmosphere2.3 Astronomical – at low frequencies dominated by
galactic synchrotron emission
3. ‘Self-noise’: uncertainty due to quantum fluctuationsof incoming signal
4. Gain fluctuations: limit sensitivity of total-power broadband measurements
5. Standing waves (dominated by radiation fromthe receiver)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Quantum Limit for Amplifier Noise
Uncertainty principle:
∆E∆t ≥ ~/2 (11)
Put E = n~ω and φ = ωt , where φ is the phase:
∆n∆φ ≥ 1/2 (12)
⇒ coherent amplifiers must add noise:
TN ≥~ω2kB
(13)
(Zero-input signal output is:
T0 =~ωkB
(14)
)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Multiple uncertainty sources
Usually one can add multiple uncertainty components:
TSys = Trec + Tspill + Tbackground + Tsrc (15)
(Sometimes effects of atmospheric absorption are takeninto account by scaling up the uncertainties – confusing!)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Sensitivity of radio receivers
‘Radiometer’ equation:
δTSys =TSys√t∆ν
(16)
where∆ν Bandwidth
t Integration timeNot Poisson statistics due to correlation between photonswhen occupancy levels > 1
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Practical measurement
I Must take a difference:
Tsrc = TSys,on − TSys,off (17)
I Tsrc usually << TSys
δTsrc =√
2δTSys (18)
I Need to integrate for about same duration ‘on’ and‘off’ source
I ThereforeS/N =
Tsrc
TSys√
2
√∆νt (19)
where t is ‘on’-source integration time
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Outline
Basics
Noise and sensitivity
Implementation
Back matter
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Antennas
I At metre-wave wavelengths, dipoles can be used,usually in combination with passive elements to givesome forward gain
I Dipole + parabolic/cylindrical dishes can also beefficient
I At higher frequencies use feeds + parabolic dishes
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Dipole antenna
PAPER telescope element:
http://eor.berkeley.edu/
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Large parabolic/Gregorian reflector
The Green Bank 100 m telescope
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Dipole feed example
GBT PF1 feed ∼ 300 MHz
Photo by Steve White/NRAO, www.naic.edu/˜astro/sdss5/talks/ReceiverSystemPR.ppt
AstrophysicalTechniques VII
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Noise andsensitivity
Implementation
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Horn feeds
Focal plane array for the GBT at 20 GHz
https://safe.nrao.edu/wiki/bin/view/Kbandfpa/WebHome
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Horn feeds
Focal plane array for the GBT at 20 GHz
https://safe.nrao.edu/wiki/bin/view/Kbandfpa/WebHome
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Cross section of a corrugated horn
190 GHz corrugated horn
From: http://www.millimeterwave.com/corr.html
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Horn feed gain
Gain of horn feeds for the (J)VLA at ∼5 GHz
From: Srikanth et al, www.aoc.nrao.edu/evla/geninfo/memoseries/evlamemo95.pdf
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Free-space bolometer array
MUSTANG 90 GHz array
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Simplified heterodyne receiver
Typical arrangement for a mm/sub-mm telescope:
×4 for each BB
S
Source
horn
Mixer
1st LO
IF Filter Mixer
2nd LO
Baseband filter Digitiser
Square Law detector
Correlator
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Mixers – principle of operation
Multiplying a signal with a pure harmonic locally generatedsignal (“LO”) shifts down the signal frequency:
cosω0t × cosωt =cos [(ω − ω0)t ]
2+
cos [(ω + ω0)t ]2
(20)
Multiplication implemented using a non-linear device (atmm/sub-mm: Superconductor-Insulator-Superconductor“junction”)
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
White noise signal
seq_along(s[0:200])
Re(
s[0:
200]
)
−1.0
−0.5
0.0
0.5
1.0
1.5
50 100 150 200Frequency
Pow
er
0.0
0.1
0.2
0.3
0.4
0.5
0.1 0.2 0.3 0.4 0.5
Simulation!
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Band limited signal
(spectral line, or e.g., RF filter)
seq_along(s[0:200])
Re(
s[0:
200]
)
−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
50 100 150 200Frequency
Pow
er
0.0
0.1
0.2
0.3
0.4
0.5
0.1 0.2 0.3 0.4 0.5
Simulation!
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Mixing signal
seq_along(s[0:200])
Re(
s[0:
200]
)
−1.0
−0.5
0.0
0.5
1.0
50 100 150 200Frequency
Pow
er
0.0
0.1
0.2
0.3
0.4
0.5
0.1 0.2 0.3 0.4 0.5
Simulation!
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Mixed signal
The up-shifted signal is easily filtered out
seq_along(s[0:200])
Re(
s[0:
200]
)
−0.2
−0.1
0.0
0.1
50 100 150 200Frequency
Pow
er
0.0
0.1
0.2
0.3
0.4
0.5
0.1 0.2 0.3 0.4 0.5
Simulation!
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
Outline
Basics
Noise and sensitivity
Implementation
Back matter
AstrophysicalTechniques VII
B. Nikolic
Basics
Noise andsensitivity
Implementation
Back matter
References I