<p>Yes, <a href="https://www.dlr.de/content/en/downloads/news-archive/2013/20131219_gaia-reaches-for-the-stars_9053.pdf?__blob=publicationFile" rel="nofollow noreferrer">Gaia</a> makes extensive use of this technique.</p>
<blockquote>
<p>The measurement accuracy of star positions for the brightest stars is 10 to 20 micro- arcseconds – up to 100 times better than that the precursor mission, Hipparcos; this angular resolution corresponds to the observed diameter of a Euro coin on the Moon, viewed from Earth.</p>
</blockquote>
<p>The underlying principle is the <a href="https://en.wikipedia.org/wiki/Standard_error#Standard_error_of_the_mean" rel="nofollow noreferrer">standard deviation of the mean</a>. It depends on the sample size, more precisely on the square root of the sample size. In this case the sample size is the number of the measured photons. Therefore it works better for bright stars.</p>

CC BY-SA 4.0
2016-01-22T00:44:49.130Z
2021-02-22T18:48:43.433Z
2021-02-22T18:48:43.433Z
Gerald
<p>The diffraction limit deals with the ability to determine if two things are separate.  I am interested in the ability to find the the centroid of a single object.  </p>

<p>Imagine a star with no near neighbors would it be possible to determine the centroid of that star at a resolution higher than the diffraction limit?</p>

<p>The star is essentially a point source and I wonder if looking at the edges of the airy disk would allow a centroid to be determined if I had a magical camera with infinite pixels.</p>

<p>It seems to me that I should be able to see the disk and then calculate a centroid that is smaller than the airy disk.</p>

<p>Thanks for any help you can provide =)</p>

CC BY-SA 3.0
2016-01-04T14:05:46.607Z
Not sure, but it sounds like speckle interferometry might interest you: https://en.wikipedia.org/wiki/Speckle_imaging  (look for the example images)
Andy
<telescope><optics><astrometry>
Can angular information be known more precisely than the diffraction limit?
Darrin Taylor
# Can angular information be known more precisely than the diffraction limit?

(Asked by: username_0 on 2016-01-04)

The diffraction limit deals with the ability to determine if two things are separate. I am interested in the ability to find the the centroid of a single object.

Imagine a star with no near neighbors would it be possible to determine the centroid of that star at a resolution higher than the diffraction limit?

The star is essentially a point source and I wonder if looking at the edges of the airy disk would allow a centroid to be determined if I had a magical camera with infinite pixels.

It seems to me that I should be able to see the disk and then calculate a centroid that is smaller than the airy disk.

Thanks for any help you can provide =)

**Tags:** telescope, optics, astrometry

> **Comments:**
> **username_1**: Not sure, but it sounds like speckle interferometry might interest you: https://en.wikipedia.org/wiki/Speckle_imaging  (look for the example images)  

---

## 1 answers

### Answer by username_2 on 2016-01-22. Score: 2

Yes, [Gaia](https://www.dlr.de/content/en/downloads/news-archive/2013/20131219_gaia-reaches-for-the-stars_9053.pdf?__blob=publicationFile) makes extensive use of this technique.

> The measurement accuracy of star positions for the brightest stars is 10 to 20 micro- arcseconds – up to 100 times better than that the precursor mission, Hipparcos; this angular resolution corresponds to the observed diameter of a Euro coin on the Moon, viewed from Earth.

The underlying principle is the [standard deviation of the mean](https://en.wikipedia.org/wiki/Standard_error#Standard_error_of_the_mean). It depends on the sample size, more precisely on the square root of the sample size. In this case the sample size is the number of the measured photons. Therefore it works better for bright stars.


---

