Radio Astronomy

Kiran Shila

Created: 2022-04-04 Mon 00:22

1. Introduction

1.1. Me

EE PhD student @ Caltech
Background in wireless engineering

2. How does a radio telescope work?

2.1. Noise

Astronomical objects are blackbody sources

For low frequency, Raleigh-Jeans (\(h\nu \ll kT\)), spectral brightness is \(B_{\nu}(T) \approx \frac{2kT}{\lambda^{2}}\) (linear with temp)

2.2. Space Noise

The radio emission from (most) astronomical sources is a stationary random process. (long timescales == steady mean power)

This noise is indistinguishable from thermal noise (like that of the system).

2.3. Noise Confusion

Every part of the system adds noise.

Cosmic microwave background
Galactic emission
Thermal behavior of the ground
Oxygen absorption
Physical antenna temperature
Receiver electronics

Total noise added by the system is the System Noise \(T_{s}\)

2.4. Radiometer

A radio telescope is a radiometer.

\(\sigma_{T} \approx \frac{T_{s}}{\sqrt{\Delta\nu t}}\)

Large bandwidths and integration time improve sensitivity

2.4.1. Example

If \(T_{s} \approx 30K\), and we observe for 5 seconds at 1 kHz of bandwidth: \(\sigma_{T} = 2*10^{-4}*T_{s}\)

If we want \(5\sigma\), that’s \(0.03K\) of sensitivity.

Consider Johnson-Nyquist noise power \(P = kT_{source}\delta \nu \approx 10^{-14}\) W

2.5. Receiver Design (my work)

The low noise amplifier (LNA) and antenna contribute the most to the system noise. I work primarily on world-class room temperature LNAs.

3. Radio Interferometry and Aperture Synthesis

3.1. Big Telescope Hard

Rayleigh Criterion \(\theta \approx 1.22 \frac{\lambda}{D}\)

3.2. Arrays to the rescue

van Cittert Zernike (Statistical Optics) \(V \approx \iint I_{\nu}e^{-2i\pi(ul + vm)}dldm=F(I_{\nu}(l,m))\)

3.2.1. Long Wavelength Array

3.2.2. UV Coverage

3.2.3. Synthesized Beam

3.3. Compressed Sensing

3.4. Maximum Entropy

Reformulate the problem as constrained, non linear optimization \(S = -\Sigma I \log{\frac{I}{P}}\)

3.5. Solve in Julia

function regularize(model, prior, total_flux)
    entropy_loss = βent * entropy(model,prior)
    flux_loss = βflux * flux(model,total_flux)
    total_variance_loss = βtv * total_variance(model)
    return entropy_loss + flux_loss + total_variance_loss
end

Zygote.gradient(x -> regularize(x, prior, total_flux), model)