vis_DFT

erwans3.Visibility_Computor_class.vis_DFT(baseline: Quantity, pixmap: PixMap, freq: Quantity, phased_dir: Optional[ndarray] = None, v_relat: Optional[Quantity] = None, tau: Optional[Union[Quantity, TimeDelta]] = None, df: Optional[Quantity] = None) → Quantity

Compute visibilities using Discrete Fourier Transform

Simulate the visibilities using the Discrete Fourier Transform. Not FFT, a phasing per direction ie. per pixel

The visibilities can be simulate as phased in a given direction. For that, use the parameter phased_dir.

The decoherence due to the bandwidth and the integration time can be accounted by specifying the parameters df, tau, v_relat The relative velocity of the baselines can be significant for an orbiting interferomter.

\[\mathcal{V}_{ij} = \sum_{\vec{s}} B( \vec{s}) e^{-i k \vec{b_{ij}}\cdot \vec{s}}\]

\[\text{sinc}(k \vec{b_{ij}}\cdot \vec{s} \frac{\Delta\nu}{2\nu}) * \text{sinc}(k \vec{v_{ij}}\cdot \vec{s} \frac{\tau}{2})\]

Parameters:

baseline (Quantity [m]) – Baselines of the interferometer with the shape \((N_{baseline},3)\)
pixmap (PixMap) – Map class that holds brightness of the skymap
freq (Quantity [Hz]) – Frequency of the observation (a scalar)
phased_dir (ndarray or None, optional) – Direction of the phase center as a unitary vector \((3,)\), by default None
v_relat (Quantity [m/s] or None, optional) – Relative velocity of the baselines shape \((N_{baseline},3)\), by default None
tau (Quantity [s] or TimeDelta or None, optional) – Integration time, by default None
df (Quantity [Hz] or None, optional) – Bandwidth of the observation, by default None

Returns:

Set of Visibilities with shape \((N_{baseline},)\) in Jansky

Return type:

Quantity [Jy]

Notes

This function computes visibility using Discrete Fourier Transform (DFT) based on the provided parameters. It includes considerations for phased direction, relative velocity, time delay, and frequency resolution.

Examples

>>> import astropy.units as u
>>> from your_module import vis_DFT, astro  # Assuming relevant imports
>>> b = 100 * u.m
>>> freq = 1000 * u.MHz
>>> pixmap = astro.PixMap()  # Instantiate pixmap
>>> vis = vis_DFT(b, pixmap, freq)
>>> print(vis)
50.0 Jy  # Example result in Jansky units