How things work an overview of astronomical instrumentation
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How things work: an overview of astronomical instrumentation. John Storey. With a nod to Tove Jansson. Or, How many photons do you have in your mode?. Lost in translation. Autocorrelator. Point spread function. Beam profile. HEMT. Fabry Perot. Antenna. Closure phase. CCD. Grating.

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How things work an overview of astronomical instrumentation

How things work: an overview of astronomical instrumentation

John Storey

With a nod to Tove Jansson

Or how many photons do you have in your mode
Or, How many photons do you have in your mode?

Lost in translation
Lost in translation


Point spread function

Beam profile


Fabry Perot


Closure phase




Quantum limit

Photon noise

Local oscillator

Secondary Mirror


Single side-band

Diffraction rings



Adaptive optics

Are these fundamentally different techniques, or just different words for the same things?

Optical vs radio
Optical vs radio

In general:

  • In the optical we do most of the signal processing (imaging, spectroscopy etc) before the detector.

  • In the radio we do most of the signal processing (imaging, spectroscopy etc) after the detector.


Blackbody radiation 1
Blackbody radiation 1

This section is based closely on the NRAO Astr534 course, and uses several diagrams from that course.


First, we derive an expression for blackbody radiation in the classical limit — otherwise known as the Rayleigh-Jeans Law.

We start by calculating the number of modes of radiation at a given frequency that can exist in a cavity.

BTW, what is a blackbody?

Blackbody radiation 2
Blackbody radiation 2

Standing waves (all different wavelengths) between two boundaries.

Standing waves (all same wavelength, ie “modes”) in a two-dimensional cavity.

Here, nx = 3; ny = 2.

In three dimensions, the permitted frequencies are:

Blackbody radiation 3
Blackbody radiation 3

An x-y plane in “n” space. Permitted standing wave modes are represented by dots.

We calculate the density of modes in this “n” space.

(BTW, we can also use antenna theory to calculate the number of modes propagating through an optical system. It is simply

Number of modes ≈ A/2,

where A is beam area,  = solid angle, and  = wavelength.)

Blackbody radiation 4
Blackbody radiation 4

Blackbody radiation 5
Blackbody radiation 5

Blackbody radiation 6
Blackbody radiation 6

Planck s law 1
Planck’s Law 1

Planck s law 2
Planck’s Law 2

This is the brightness (in watts) per unit frequency interval , surface area A, and solid angle .

Planck s law 3
Planck’s Law 3

max ≈ 59 GHz . T (K)

We can also integrate B over all frequencies to obtain the Stefan-Boltzmann law:

Mode occupation number
Mode occupation number

The mode occupation number, or mean number of photons per mode, is given by:

n =

For h/kT >> 1, n is < 1. The photons behave independently and obey Poisson statistics. This is the usual situation in opticalastronomy.

For h/kT << 1, n is >> 1. The photons do not behave independently; they obey Bose-Einstein statistics. Detect one, and that’s all the information you need. If you’ve seen one, you’ve seen them all. This is the usual situation in radio astronomy.

The planck function revisited
The Planck function revisited

  • The number of modes is ≈ A/2 ≈ A2/c2

  • The mode occupation number, or mean number of photons per mode, is given by:

  • n =

  • Each photon carries energy h

  • There are 2 polarisations

  • The brightness B of a blackbody is thus 2 x (number of modes) x (number of photons per mode) x (energy per photon) =

    • per unit solid angle and surface area

Optical astronomy
Optical astronomy

At 500 nm (600 THz) and 5000 K (star):

n ≈ 0.003

In fact, if you are observing a star of angular size 1 milli-arcseconds with a detector pixel subtending 0.1 arcseconds on the sky, n is effectively 3 x 10-7.

The photons behave independently and obey Poisson statistics, producing “photon noise” (also known as “shot noise”.)

Optical astronomy1
Optical astronomy

If the only light the detector sees is coming from the star, then the signal/noise ratio for any observation is simply:

S/N = √n,

where n is the number of photons detected during the observation.

(Assuming, of course, a perfect detector that produces no excess noise. With modern CCDs, the trick is to integrate long enough that the photon shot noise swamps the detector readout noise, which is typically a few electrons rms.)

Infrared astronomy
Infrared astronomy

Much the same, except now almost all of the photons are coming from the background (sky, telescope, instrument). The noise is given by the square root of the number of all of these photons detected per measurement interval.

The sensitivity is usually described by the NEP (Noise-Equivalent Power); ie, that signal power required to give a S/N of 1 in one second.

Let , the quantum efficiency of the detector, be the fraction of incident photons it actually detects ( < 1).

Infrared astronomy1
Infrared astronomy

  • If the detector generates no noise of its own, it is said to be background limited (ie, all the noise comes from the shot noise of the background, not from the detector). In this case,

  • NEPBLIP = (2hBPb/)1/2 watts per √Hz,

  • Where

    •  is the observing frequency

    • B is the post-detection bandwidth

    • Pb is the background power

    • is the detector quantum efficiency

      “BLIP” stands for “Background-Limited Infrared Performance”

      all assuming that Pb >> Ps and h >> kT.

Infrared astronomy2
Infrared astronomy

The signal/noise ratio of an observation is just:

S/N = (Psignal/NEPBLIP). t1/2

Where t is the integration time.

If the detector does generate noise of its own, it can be ascribed a value for its NEP, say NEPDetector


S/N = (Psignal/NEPDetector). t1/2

although to complicate things, the NEP of the detector probably varies with the background anyway.

Radio astronomy
Radio astronomy

For h/kT << 1, n is >> 1. This is the usual situation in radio astronomy.

Eg, at 5 cm (6 GHz) and 10,000 K (HII region);

n ≈ 3 x 104

The photons do not behave independently; they obey Bose-Einstein statistics.

At 6 GHz, even for cool sources (2.7 K), n ≈ 9.

(At mm and sub-mm wavelengths, however, h can start to approach kT, where T is the temperature of the background. )

Radio astronomy1
Radio astronomy

Because we are in the Rayleigh-Jeans regime, power is proportional to temperature:

Radio astronomers thus speak of the brightness temperature of a source, or the antenna temperature or the receiver temperature.

The detection process
The detection process

  • Optical astronomy:

    • Collect photons at a CCD pixel until you have enough, like catching rain drops in a bucket.

    • The detection process destroys all the phase information (eg, photograph)

    • On one pixel you can detect as many modes as you like — just increase the field of view

  • Radio astronomy:

    • Measure the amplitude and phase of the radiation field.

    • With one receiver you can only detect one mode; ie, you are always diffraction limited. (Or more accurately, only receiving an amount of signal equivalent to a diffraction-limited beam).

    • Alternatively you can use direct detection; eg, a bolometer, and have an arbitrary field of view.

Radio sensitivity limits
Radio sensitivity limits

We describe the sensitivity in terms of a system temperature, Tsys, made up of:

  • Receiver “temperature”

  • “Sky” “temperature”

  • Various losses

  • Spillover

    The fundamental limit is quantum noise, ie, n = 1, or

    Tquantum = h/k = 48K/THz. However, real instruments never approach this in the cm bands.

    (For example, at 10 GHz, Tquantum ≈ 0.5 K, and Tsys is typically 50 K.)

Image: James Di Francesco

National Research Council of Canada

  • IF and “Back end”

  • Autocorrelator

  • Digital Filter Bank

  • Power detector/integrator

Heterodyne receivers

Feed Horn

In a radio telescope, it is usual to shove the waves down a feed horn, then convert them into an electrical current on a wire. This process is sensitive to only one mode and one polarisation of radiation.

Now we have an electrical signal, it is “mixed” with a local oscillator signal. The resulting IF (Intermediate Frequency) is given by

fsignal = fLO ± fIF

Heterodyne receivers

For example, we might mix a 115 GHz signal with a 110 GHz local oscillator to create a 5 GHz IF signal. This IF signal retains all the amplitude and phase information of the original signal, but is now at a much easier frequency to process.

There is no noise penalty in doing this, as long as we are dealing with system temperatures, Tsys, of

Tsys > h/k (≈ 0.5 K at 10 GHz)

The process of amplifying the signal is equivalent (in terms of noise penalty) to heterodyning.

In both cases, we are increasing the mode occupation number by 1.

Why? Ask Heisenberg.

Heterodyne receivers
Heterodyne receivers

  • With our signal now in electrical form, and converted down to a user-friendly frequency, we can do amazing things with it. For example:

    • We can have almost unlimited spectral resolution,

    • We can simultaneously have as many spectral channels as we want,

    • We can correlate the signal from one antenna with the signals from as many other antennas as we like,

    • We can build the SKA!

  • There is no reason not to add a second receiver to the antenna, to detect the other polarisation.

  • While we’re at it, we may as well add additional receivers, each seeing its own single spatial mode on the sky (ie, a multibeam receiver).

  • Actually, we can do even better with a Phased Array Feed (PAF).

So back to the optical

So, back to the optical…

We always use direct detection (for example, a CCD).

Why can’t we use amplifiers and heterodyne techniques on an optical (or infrared) telescope?

Well we could, but…

We’d incur a noise penalty of one photon per mode. At 500 nm, this would be equivalent to increasing the sky temperature to:

Tsky = 42,000 K

Hardly what you’d call dark time…

And so
And so,

  • Optical astronomers must ignore the phase of their photons, and process the light before it is detected.

  • Referring back to the Planck function, the energy in the signal is proportional to the area-solid angle product (A) of the beam.

  • In fact, A/2 ≈ Nmodes, the number of modes.

  • A must be conserved throughout the instrument, so instruments that accept a lot of modes (large primary mirror, poor spatial resolution) become enormous.

  • However, an instrument that operates with a single mode (ie, a diffraction-limited beam) is the same size regardless of the size of the telescope (8-inch Celestron to ELT). Hence the importance of adaptive optics on ELTs.

  • Because the light must be processed optically (no digital filter banks!), achieving high spectral resolution also involves building large pieces of hardware.

Thz astronomy
THz astronomy

  • h/kT ≈ 1

  • Is it better to use radio techniques or optical?

  • That depends in exquisite detail on the observation to be conducted, and the technology available.

  • For example, CCAT (Can’t Compete with an Antarctic Telescope) will have several spectrometers:

    • - Long slit echelle grating, R~1000 at 350 m

    • - Parallel plate grating cavity, R~300 at 850 m

    • - Heterodyne focal plane arrays, R~100,000

The perfect telescope
The perfect telescope

  • Wavelength coverage: 300 nm - 30 metres

  • Field of View: 2 steradians

  • Integration time: days to months

The instrument as a filter
The instrument as a filter

  • Spatial filtering

  • Spectral filtering

  • Temporal filtering

  • Polarisation?

  • Multiplex advantage(s)

  • Sensitivity is (preferably) set by fundamental limits

    • Photon statistics s/n = √(no. of photons) or

    • Quantum limit Tsys = h/k

  • May need to trade off resolution against sensitivity

  • May need to compromise anyway (eg, seeing)

How do we achieve spatial resolution
How do we achieve spatial resolution?

  • Optical/infrared

    • Rarely at the diffraction limit

    • More usually seeing limited (lots of modes)

    • Adaptive optics

    • Aperture masking

    • Interferometry is hard (-ish)

  • Radio

    • Always at the diffraction limit (single mode!)

    • Interferometry is easy (-ish)

How do we achieve spectral resolution
How do we achieve spectral resolution?

  • Optical/infrared:

    • Diffraction grating

    • Fabry Perot

    • Fourier Transform Spectrometer (FTS)

    • Big instruments

  • Radio

    • Digital autocorrelator

    • Digital filter bank

    • Nifty electronics


  • Rarely do we approach the truly fundamental limits of sensitivity.

  • Most often, we are limited by systematics, such as

    • Fluctuating sky noise

    • Seeing

    • 1/f noise ( a subject in itself…)

    • Interference

    • Drifts

  • We deal with these by chopping, beam switching, dark frames, calibration lamps and noise diodes, etc.

Image: KPNO

In general, a dish will work at any frequency lower than its design frequency.

115 GHz

Image: AAT Board

Gillespie, White & Watt, 1979

Maybe the two tribes aren t so different after all

Maybe the two tribes aren design frequency.’t so different after all.

With more than a nod to Tove Jansson