Noise

Real telescopes inevitably have some level of noise that is recorded in their measurements. This could arise from actual noise signals received by the detector (radio-frequency interference, for instance), or as instrumental noise imposed by the limitations of electronics.

Noise in MARTINI

MARTINI includes some functionality to simulate a simple form of noise: Gaussian white noise. The interface for this is provided by the GaussianNoise class.

Using MARTINI’s noise classes

The GaussianNoise class is straightforward to use. It has an rms argument that expects the desired noise level in the final mock observation (after convolution with the beam). There is also a seed argument for the random number generator seed that defaults to 0, so random results will be consistent and predictable (at least on a given system). Initializing the GaussianNoise class looks like:

import astropy.units as U
from martini.noise import GaussianNoise

GaussianNoise(rms=1.0 * U.Jy / U.beam, seed=0)

The root mean square (RMS) noise level is approximate because the noise needs to be generated before convolution with the beam, and the smoothing effect of the convolution reduces the RMS. Convolution with a Gaussian beam with axis lengths bmaj and bmin reduces the RMS by a factor of approximately \((2\pi\sqrt{\sigma_\mathrm{maj}\sigma_\mathrm{min}})^{-1}\) where \(\sigma\) are the widths of the Gaussians (recall that MARTINI defines bmaj and bmin as FWHM values) in pixels. Empirical testing reveals that this approximation is too low by about 10%, so the factor is adjusted slightly.

MARTINI then creates a Gaussian white noise array with RMS that is higher than the final desired level by the factor above such that when the convolution with the beam is done the result has (approximately) the target noise level.

Other noise models (advanced usage)

Other, perhaps more intricate models for noise can be implemented into MARTINI. A class created to do this should inherit from the martini.noise._BaseNoise class. Note that classes beginning in underscores are intentionally not documented in the online API documentation as most users are unlikely to need them. Refer to the docstrings in the source code for technical documentation. The new class needs to implement a generate() method that initializes an array of the same shape as a given datacube containing the noise. The generate() method receives the datacube and beam members of a Martini object, making their properties available within the method. Other parameters are expected to be passed to the noise class on initialization, analogous to the rms argument of the __init__() method of GaussianNoise.