<p>After digging a little, I found the key sentence at the start of section 2.1.4 of <a href="http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002A%26A...395.1061G&amp;link_type=ARTICLE&amp;db_key=AST" rel="nofollow noreferrer">Greisen et al (2002)</a>, which reads:</p>
<blockquote>
<p>&quot;Note that integer pixel numbers refer to the center of the pixel in
each axis, so that, for example, the first pixel runs from pixel
number 0.5 to pixel number 1.5 on every axis.&quot;</p>
</blockquote>
<p>As an example, a coordinate system is defined in the .fits header to have a pixel size (CDELT1, CDELT2) of 1deg by 1deg, with a reference pixel coordinate (CRPIX1, CRPIX2) of (1, 1), whose coordinate value (CRVAL1, CRVAL2) is 30.0deg, +45.0deg. Consequently, the bottom left pixel (pixel coordinate of (1, 1) at its centre) will have a bottom left coordinate of 0.5pix, 0.5pix and 29.5deg, 44.5deg in real world coordinates and a top right coordinate of 1.5pix, 1.5pix and 30.5deg, 45.5deg.</p>
<p><em>Thus, if the third, spectral axis is defined with a reference pixel (CRPIX3) of 1., reference value (CRVAL3) of 1E8Hz, and a pixel size (CDELT3) of 0.5E8, then that first spectral channel of the cube will cover 0.75E8 Hz to 1.25E8 Hz with an 'average' frequency value of 1E8 Hz.</em></p>

CC BY-SA 4.0
2022-11-28T16:37:31.213Z
2022-11-28T16:37:31.213Z
simonp2207
<p>A .fits cube has 3 dimensions, where the 1st axis is RA, 2nd axis is Declination and 3rd axis is frequency.</p>
<p>My question is rather simple, but causing pain none-the-less. Given a .fits cube, what is the frequency range (in Hz) of the first channel?</p>
<p>For example, if CRPIX3=1, CRVAL3=1E8 and CDELT3=0.5E8, does the first frequency channel cover 1E8 Hz to 1.5E8 Hz or 0.75E8 to 1.25E8 Hz?</p>

CC BY-SA 4.0
2022-11-25T17:24:10.463Z
No clue, but I will be surprised if that is universally the same. It should be documention which ships with your specific data
planetmaker
<fits><fits-header>
Frequency coverage for first spectral channel of .fits cube?
simonp2207
# Frequency coverage for first spectral channel of .fits cube?

(Asked by: username_0 on 2022-11-25)

A .fits cube has 3 dimensions, where the 1st axis is RA, 2nd axis is Declination and 3rd axis is frequency.

My question is rather simple, but causing pain none-the-less. Given a .fits cube, what is the frequency range (in Hz) of the first channel?

For example, if CRPIX3=1, CRVAL3=1E8 and CDELT3=0.5E8, does the first frequency channel cover 1E8 Hz to 1.5E8 Hz or 0.75E8 to 1.25E8 Hz?

**Tags:** fits, fits-header

> **Comments:**
> **username_1**: No clue, but I will be surprised if that is universally the same. It should be documention which ships with your specific data  

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## 1 answers

### Answer by username_0 on 2022-11-28. Score: 2

After digging a little, I found the key sentence at the start of section 2.1.4 of [Greisen et al (2002)](http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002A%26A...395.1061G&link_type=ARTICLE&db_key=AST), which reads:

> "Note that integer pixel numbers refer to the center of the pixel in
> each axis, so that, for example, the first pixel runs from pixel
> number 0.5 to pixel number 1.5 on every axis."

As an example, a coordinate system is defined in the .fits header to have a pixel size (CDELT1, CDELT2) of 1deg by 1deg, with a reference pixel coordinate (CRPIX1, CRPIX2) of (1, 1), whose coordinate value (CRVAL1, CRVAL2) is 30.0deg, +45.0deg. Consequently, the bottom left pixel (pixel coordinate of (1, 1) at its centre) will have a bottom left coordinate of 0.5pix, 0.5pix and 29.5deg, 44.5deg in real world coordinates and a top right coordinate of 1.5pix, 1.5pix and 30.5deg, 45.5deg.

*Thus, if the third, spectral axis is defined with a reference pixel (CRPIX3) of 1., reference value (CRVAL3) of 1E8Hz, and a pixel size (CDELT3) of 0.5E8, then that first spectral channel of the cube will cover 0.75E8 Hz to 1.25E8 Hz with an 'average' frequency value of 1E8 Hz.*


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