Created: 2022-04-04 Mon 00:22
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)
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).
Every part of the system adds noise.
Total noise added by the system is the System Noise \(T_{s}\)
A radio telescope is a radiometer.
\(\sigma_{T} \approx \frac{T_{s}}{\sqrt{\Delta\nu t}}\)
Large bandwidths and integration time improve sensitivity
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
The low noise amplifier (LNA) and antenna contribute the most to the system noise. I work primarily on world-class room temperature LNAs.
Rayleigh Criterion \(\theta \approx 1.22 \frac{\lambda}{D}\)
van Cittert Zernike (Statistical Optics) \(V \approx \iint I_{\nu}e^{-2i\pi(ul + vm)}dldm=F(I_{\nu}(l,m))\)
Reformulate the problem as constrained, non linear optimization \(S = -\Sigma I \log{\frac{I}{P}}\)
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)