Atmospheric refraction

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Toni Šarić

Jul 10, 2022, 5:08:48 AMJul 10
to astrometry
How does astrometry handle atmospheric refraction?
In the text and code below, refraction is calculated using the formulas of Bennet and Sæmundsson:

Let's assume the 7.5deg height of the image, and that camera is pointing at the 45deg altitude.
At the top of the image, the altitude is 48.75deg, but when corrected for atmospheric refraction it is 48.7386 which is a difference of ~41 arcseconds.
At the bottom of the image, the altitude is 41.25deg but when corrected for refraction it is actually 41.235 with a difference of ~53.2 arcseconds.

If all stars are at the same altitude(or distributed on a small altitude difference - narrow FoV), then refraction would not matter much, since astrometry for plate solving is only interested in the relative position of stars.
And the solution, the center of the image, can be corrected for refraction afterward.
But, with relatively wide FoV, like in this example 7.5deg, if astrometry does not handle refraction, there is an error of ~12 arcseconds in star positions between the top and the bottom of the image.
Example code calculation is in the attachment.
The refraction effect is more pronounced when solving with a larger index file, where one star in the quadrangle could be located at the top of the image, and one at the bottom.
The effect matter less when solving with a smaller index file., but the error is still there.
To recap, in this example, with 7.5deg FoV an error is ~12arcsec, and with 18 arcsecperpix camera resolution, gives an error of almost 1 pixel.


Dustin Lang

Jul 10, 2022, 11:02:38 AMJul 10
to Toni Šarić, astrometry
Hi, doesn't deal with this during the solving stage.  It can be fit out as a distortion (SIP solution).

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David W Hogg

Jul 10, 2022, 11:17:56 AMJul 10
to Dustin Lang, Toni Šarić, astrometry
The fundamental assumption of the zero-distortion is that the image is conformal (or a pure tangent-plane projection or something like that). So atmospheric refraction is naturally captured inasmuch as the refraction only moves the effective telescope boresight. But atmospheric refraction is not captured at all inasmuch as it breaks conformality. I agree with Dustin that this latter effect (distorting the field) should be captured completely by a distortion solution, provided that there are enough good stars to measure it well. But we don’t currently have any way to directly input the atmospheric term, which depends on zenith angle, photometric bandpass, stellar color, and atmospheric conditions (weakly).

David W. Hogg —
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