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