In Preparing input and generating exposure map we generated a pointing pattern with very small steps, showing how this can cause calibration problems. Later (in Larger steps sizes for better calibration) using larger steps is discussed. In this section, let’s see how we can get an accurate measure of the area that is covered in a certain depth.

A first thought would be to simply multiply the widths along RA and Dec reported before: \(1.8808\times1.3924=2.6189\) degrees squared. But there are several problems with this:

- It ignores the fact that RA only has units of degrees on the equator: at different declinations, differences in RA should be converted to degrees. This is discussed further in this tutorial: Pointings that account for sky curvature.
- It doesn’t take into account the thin rows/columns of blank pixels (NaN) that are on the four edges of the
`deep.fits`image. - The differing area of the pixels on the spherical sky in relation to those blank values can result in wrong estimations of the area.

Let’s get a very accurate estimation of the area that will not be affected by the issues above.
With the first command below, we’ll use the `--pixelareaonwcs` option of the Fits program that will return the area of each pixel (in pixel units of degrees squared).
After running the second command, please have a look at the produced image.

$ astfits deep.fits --pixelareaonwcs --output=deep-pix-area.fits $ astfits deep.fits --pixelscale Basic info. for --pixelscale (remove extra info with '--quiet' or '-q') Input: deep.fits (hdu 1) has 2 dimensions. Pixel scale in each FITS dimension: 1: 0.00154403 (deg/pixel) = 5.5585 (arcsec/pixel) 2: 0.00154403 (deg/pixel) = 5.5585 (arcsec/pixel) Pixel area: 2.38402e-06 (deg^2) = 30.8969 (arcsec^2) $ astscript-fits-view deep-pix-area.fits

You see a donut-like shape in DS9.
Move your mouse over the central (white) region of the region and look at the values.
You will see that the pixel area (in degrees squared) is exactly the same as we saw in the output of `--pixelscale`.
As you move your mouse away to other colors, you will notice that the area covered by each pixel (its value in this image) deceases very slightly (in the 5th decimal!).
This is the effect of the Gnomonic projection; summarized as `TAN`

(for “tangential”) in the FITS WCS standard, the most commonly used in optical astronomical surveys and the default in this script.

Having `deep-pix-area.fits`, we can now use Arithmetic to set the areas of all the pixels that were NaN in `deep.fits` and sum all the values to get an accurate estimate of the area we get from this pointing pattern:

$ astarithmetic deep-pix-area.fits deep.fits isblank nan where -g1 \ sumvalue --quiet 1.93836806631634e+00

Therefore, the actual area that is covered is less than the simple multiplication above. At these declinations, the dominant cause of this difference is the first point above (that RA needs correction), this will be discussed in more detail later in this tutorial (see Pointings that account for sky curvature). Generally, using this method to measure the area of your non-NAN pixels in an image is very easy and robust (automatically takes into account the curvature, coordinate system, projection and blank pixels of the image).

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GNU Astronomy Utilities 0.22 manual, February 2024.