Reference: Gaussian Modeling with MIRIAD maths

2012 April 17

A note to self. Sometimes I want to use `maths`

to generate an image with a
large Gaussian component. Let’s say that the total flux I want to capture is F
(in Janskys). Using what we know about normalized Gaussians the expression I
want is something of the form

. Assuming circularity and simplifying, we get

, where

and

.

For now I’ve thought through the implementation using arcsecond units. Say we
have a 2047×2047 image with a pixel scale of 10 arcsec that’s uniform across
the image. If I want σ to measure the ATA primary beam, with a FWHM of
3.5°/GHz, I get σ = 5350.7 arcsec/GHz. *To generate a model-type image, we
need to work in Jy/pixel*, so A must be scaled by the arcsec²/pixel conversion
ratio, 100 in this case.

Implementing this in `maths`

is straightforward. You use the `xrange`

and
`yrange`

keywords to implement the Gaussian expression, ranging them from
-10230 to +10230 in the example here.