AstrophysicalTechniques VII

B. Nikolic

Basics

Noise andsensitivity

Implementation

Back matter

Astrophysical Techniques VII –Radio Astronomy

B. Nikolichttp://www.mrao.cam.ac.uk/˜bn204/mailto:b.nikolic@mrao.cam.ac.uk

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

B. Nikolic

Basics

Noise andsensitivity

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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