<p>Straight line, though it wont make much difference,</p>
<p>The point about the size is that it tells you about how much light the telescope can gather. This is the &quot;projected-flat&quot; area, not the curved surface area.</p>
<p>However, the difference is not much, as telescope mirrors are not highly curved. I suppose it makes more of a difference when considering radio telescope dishes.</p>

CC BY-SA 4.0
2021-07-16T19:06:49.873Z
The "projected-flat" diameter also tells you the angular resolution, if not limited by the atmosphere.
Peter Erwin
CC BY-SA 4.0
2021-07-17T05:41:45.190Z
@PeterErwin less nicely so when the mirror has a jagged edge like the telescope the OP mentions.
uhoh
CC BY-SA 4.0
2021-07-16T02:04:22.283Z
2021-07-16T02:04:22.283Z
James K
<p><a href="https://i.sstatic.net/HUDrC.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HUDrC.jpg" alt="JWST from https://www.facebook.com/NASAWebb/photos/10158883840795049/" /></a></p>
<p>Sources <strong>above:</strong> <a href="https://www.facebook.com/NASAWebb/photos/10158883840795049/" rel="nofollow noreferrer">https://www.facebook.com/NASAWebb/photos/10158883840795049/</a> <strong>below:</strong> <a href="https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope" rel="nofollow noreferrer">https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope</a></p>
<p><a href="https://i.sstatic.net/xrFLB.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xrFLB.jpg" alt="JWST from https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope" /></a></p>
<hr />
<blockquote>
<p>Do telescope measurements (in meters, usually) measure in a straight line, from edge to edge, or follow the curve of the mirror?</p>
</blockquote>
<p>The short answer is <a href="https://astronomy.stackexchange.com/a/44876/7982">@JamesK's</a>; it's the straight-line diameter of whatever defines the aperture.</p>
<h3 id="but-the-jwst-primary-mirror-has-no-diameter-jtnp">But the JWST primary mirror has no diameter!</h3>
<p>Since the OP asked about the JWST mirror which is a whole bunch of separated hexagons and <em>definitely not a circle</em>, I think this needs a more detailed answer, since as <a href="https://astronomy.stackexchange.com/questions/44875/do-telescope-measurements-in-meters-usually-measure-in-a-straight-line-from/44876#comment95588_44876">@PeterErwin points out</a> the diameter is (primarily) what gives us the angular resolution (and light collection) when not limited by the Earth's atmosphere.</p>
<p>You could come up with an effective diameter as somewhere between the maximum and minimum distance between the center and edge of the last reflecting surface, and that's likely what 6.5 meters is close to.</p>
<p>According to James Webb Space Telescope User Documentation's <a href="https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope" rel="nofollow noreferrer">JWST Observatory Hardware/JWST Telescope</a>:</p>
<blockquote>
<p>The primary mirror is comprised of 18 hexagonal segments, each ~1.4 m in diameter, which, when properly phased together, <strong>act as a single mirror ~6.5 m in diameter.</strong> The individual segments have, on average, better than 25 nm rms surface figure error. The primary mirror serves as the aperture stop for most JWST observing modes, with the exceptions of coronagraphy and aperture masking interferometry (AMI). The unobscured collecting area of the primary mirror is 25.4 m<sup>2</sup>. (The total polished area is slightly greater, 26.3 m<sup>2</sup>, but the secondary mirror support struts obscure a small portion.) An opaque border around the outer edge of the primary helps minimize stray light.</p>
</blockquote>
<p>The careful wording &quot;act as a single mirror ~6.5 m in diameter&quot; is a good way to get the basic idea across, but a jagged hexagonal outline made from hexagonal segments with gaps in between will have a very different <a href="https://en.wikipedia.org/wiki/Point_spread_function" rel="nofollow noreferrer">point spread function</a> (the shape of the spot produced by parallel light or a distant star) than that of a circular aperture with the same effective diameter.</p>
<p>Below is from <a href="https://astronomy.stackexchange.com/a/32664/7982">this answer to <em>Why not use only one support vane for the secondary mirror, to avoid multiple diffraction spikes?</em></a>.</p>
<p>The angular resolution associated with a nice circular diameter of 6.5 meters at 480 nm (the F480M filter in the first figure) is 1.22 <span class="math-container">$\lambda/D$</span> or about 0.02 arc seconds, which is that tiny central dot in the first image.</p>
<p><em>Almost everything else</em> is due to the jagged edge and the gaps between hexagons; the missing center hexagon/central obstruction of the secondary and the three vane also contribute.</p>
<blockquote>
<p>Considering that the primary mirror presents much more total &quot;diffracting edge&quot; transverse to the incoming wavefront than the secondary's three vanes, it's possible or even likely that the spider's contribution even with three vanes is small compared to that from the segmenting of the primary.</p>
<p><img src="https://i.sstatic.net/d5r5J.jpg" alt="enter image description here" /></p>
<p>From <a href="https://buildmedia.readthedocs.org/media/pdf/webbpsf/latest/webbpsf.pdf" rel="nofollow noreferrer">webbpsf Documentation Release 0.8.0</a> (click for larger size)</p>
<p><img src="https://i.sstatic.net/HXFB2.png" alt="enter image description here" /></p>
<p>Fig. 1: Sample PSFs for JWST’s instrument suite, all on the same angular scale and display stretch.</p>
</blockquote>
<hr />
<p>More optical goodies at:</p>
<ul>
<li>jwst.nasa.gov: <a href="https://www.jwst.nasa.gov/content/observatory/ote/mirrors/index.html" rel="nofollow noreferrer">Webb's Mirrors</a> (extensive resources!)</li>
<li>jwst.nasa.gov: <a href="https://www.jwst.nasa.gov/content/observatory/ote/index.html" rel="nofollow noreferrer">Optical Telescope Element (OTE)</a> (index for subsystems' resources!)</li>
<li>eoPortal: <a href="https://directory.eoportal.org/web/eoportal/satellite-missions/content/-/article/jwst-content" rel="nofollow noreferrer">JWST (James Webb Space Telescope)</a></li>
<li>eoPortal: <a href="https://earth.esa.int/web/eoportal/satellite-missions/j/jwst" rel="nofollow noreferrer">JWST</a> (different page than that above)</li>
<li>Wikipedia: <a href="https://en.wikipedia.org/wiki/Segmented_mirror" rel="nofollow noreferrer">segmented mirror</a></li>
<li>Koby Z. Smith's <a href="https://www.spacesymposium.org/wp-content/uploads/2017/10/Smith-Koby_Methodology-Results-of-JWST-Cryo-Testing.pdf" rel="nofollow noreferrer">Methodology and Results of James Webb Space Telescope Thermal Vacuum Optical System Alignment Testing and Analysis</a> 34th Space Symposium, Technical Track, Colorado Springs, Colorado, United States of America, Presented on April 16, 2018</li>
</ul>

CC BY-SA 4.0
2021-07-17T15:36:01.420Z
This also applies, of course, to ground-based [segmented-mirror telescopes](https://en.wikipedia.org/wiki/Segmented_mirror), of which there are quite a few.
Peter Erwin
CC BY-SA 4.0
2021-07-17T07:18:15.723Z
2021-07-17T07:37:53.223Z
2021-07-17T07:37:53.223Z
uhoh
<p>Let's pretend we have a mirror in the shape of a spherical cap, with dimensions the same as JWST: diameter d=6.5m and radius of curvature r=15.88m. Then the distance along the surface of the mirror between two opposite points on its rim is given by 2r arcsin (d/2r), which comes to about 6.546m. This is only about 0.7% longer than the straight-line distance d.</p>
<p>The mirror is not perfectly spherical, and its circumference is definitely not a circle, but you can see that the choice of measurement makes little difference.</p>

CC BY-SA 4.0
2021-07-18T10:41:44.547Z
2021-07-18T11:12:54.357Z
2021-07-18T11:12:54.357Z
TonyK
<p>Somehow, no site or book or magazine has clarified this question for me....</p>
<p>Perhaps I am an idiot, but,</p>
<p>Is the parabolic primary mirror on the new James Webb Space Telescope (JWST) 6.5 meters from edge-to-edge in a straight line?  Or do they use an imaginary tape measure to follow the parabolic curve (or hyperbolic, for most modern telescopes) of the primary mirror?</p>

<observational-astronomy><telescope><space-telescope><hubble-telescope>
Do telescope measurements (in meters, usually) measure in a straight line, from edge to edge, or follow the curve of the mirror?
Kurt Hikes
# Do telescope measurements (in meters, usually) measure in a straight line, from edge to edge, or follow the curve of the mirror?

(Asked by: username_0 on 2021-07-16)

Somehow, no site or book or magazine has clarified this question for me....

Perhaps I am an idiot, but,

Is the parabolic primary mirror on the new James Webb Space Telescope (JWST) 6.5 meters from edge-to-edge in a straight line? Or do they use an imaginary tape measure to follow the parabolic curve (or hyperbolic, for most modern telescopes) of the primary mirror?

**Tags:** observational-astronomy, telescope, space-telescope, hubble-telescope

---

## 3 answers

### Answer by username_1 on 2021-07-16. Score: 6

Straight line, though it wont make much difference,

The point about the size is that it tells you about how much light the telescope can gather. This is the "projected-flat" area, not the curved surface area.

However, the difference is not much, as telescope mirrors are not highly curved. I suppose it makes more of a difference when considering radio telescope dishes.

> **Comments:**
> **username_2**: The "projected-flat" diameter also tells you the angular resolution, if not limited by the atmosphere.  
> **username_3**: @PeterErwin less nicely so when the mirror has a jagged edge like the telescope the OP mentions.  

---

### Answer by username_3 on 2021-07-17. Score: 4

[![JWST from https://www.facebook.com/NASAWebb/photos/10158883840795049/](https://i.sstatic.net/HUDrC.jpg)](https://i.sstatic.net/HUDrC.jpg)

Sources **above:** <https://www.facebook.com/NASAWebb/photos/10158883840795049/> **below:** <https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope>

[![JWST from https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope](https://i.sstatic.net/xrFLB.jpg)](https://i.sstatic.net/xrFLB.jpg)

---

> Do telescope measurements (in meters, usually) measure in a straight line, from edge to edge, or follow the curve of the mirror?

The short answer is [@JamesK's](https://astronomy.stackexchange.com/a/44876/7982); it's the straight-line diameter of whatever defines the aperture.

### But the JWST primary mirror has no diameter!

Since the OP asked about the JWST mirror which is a whole bunch of separated hexagons and *definitely not a circle*, I think this needs a more detailed answer, since as [@PeterErwin points out](https://astronomy.stackexchange.com/questions/44875/do-telescope-measurements-in-meters-usually-measure-in-a-straight-line-from/44876#comment95588_44876) the diameter is (primarily) what gives us the angular resolution (and light collection) when not limited by the Earth's atmosphere.

You could come up with an effective diameter as somewhere between the maximum and minimum distance between the center and edge of the last reflecting surface, and that's likely what 6.5 meters is close to.

According to James Webb Space Telescope User Documentation's [JWST Observatory Hardware/JWST Telescope](https://jwst-docs.stsci.edu/jwst-observatory-hardware/jwst-telescope):

> The primary mirror is comprised of 18 hexagonal segments, each ~1.4 m in diameter, which, when properly phased together, **act as a single mirror ~6.5 m in diameter.** The individual segments have, on average, better than 25 nm rms surface figure error. The primary mirror serves as the aperture stop for most JWST observing modes, with the exceptions of coronagraphy and aperture masking interferometry (AMI). The unobscured collecting area of the primary mirror is 25.4 m2. (The total polished area is slightly greater, 26.3 m2, but the secondary mirror support struts obscure a small portion.) An opaque border around the outer edge of the primary helps minimize stray light.

The careful wording "act as a single mirror ~6.5 m in diameter" is a good way to get the basic idea across, but a jagged hexagonal outline made from hexagonal segments with gaps in between will have a very different [point spread function](https://en.wikipedia.org/wiki/Point_spread_function) (the shape of the spot produced by parallel light or a distant star) than that of a circular aperture with the same effective diameter.

Below is from [this answer to *Why not use only one support vane for the secondary mirror, to avoid multiple diffraction spikes?*](https://astronomy.stackexchange.com/a/32664/7982).

The angular resolution associated with a nice circular diameter of 6.5 meters at 480 nm (the F480M filter in the first figure) is 1.22 $\lambda/D$ or about 0.02 arc seconds, which is that tiny central dot in the first image.

*Almost everything else* is due to the jagged edge and the gaps between hexagons; the missing center hexagon/central obstruction of the secondary and the three vane also contribute.

> Considering that the primary mirror presents much more total "diffracting edge" transverse to the incoming wavefront than the secondary's three vanes, it's possible or even likely that the spider's contribution even with three vanes is small compared to that from the segmenting of the primary.
>
> ![enter image description here](https://i.sstatic.net/d5r5J.jpg)
>
> From [webbpsf Documentation Release 0.8.0](https://buildmedia.readthedocs.org/media/pdf/webbpsf/latest/webbpsf.pdf) (click for larger size)
>
> ![enter image description here](https://i.sstatic.net/HXFB2.png)
>
> Fig. 1: Sample PSFs for JWST’s instrument suite, all on the same angular scale and display stretch.

---

More optical goodies at:

* jwst.nasa.gov: [Webb's Mirrors](https://www.jwst.nasa.gov/content/observatory/ote/mirrors/index.html) (extensive resources!)
* jwst.nasa.gov: [Optical Telescope Element (OTE)](https://www.jwst.nasa.gov/content/observatory/ote/index.html) (index for subsystems' resources!)
* eoPortal: [JWST (James Webb Space Telescope)](https://directory.eoportal.org/web/eoportal/satellite-missions/content/-/article/jwst-content)
* eoPortal: [JWST](https://earth.esa.int/web/eoportal/satellite-missions/j/jwst) (different page than that above)
* Wikipedia: [segmented mirror](https://en.wikipedia.org/wiki/Segmented_mirror)
* Koby Z. Smith's [Methodology and Results of James Webb Space Telescope Thermal Vacuum Optical System Alignment Testing and Analysis](https://www.spacesymposium.org/wp-content/uploads/2017/10/Smith-Koby_Methodology-Results-of-JWST-Cryo-Testing.pdf) 34th Space Symposium, Technical Track, Colorado Springs, Colorado, United States of America, Presented on April 16, 2018

> **Comments:**
> **username_2**: This also applies, of course, to ground-based [segmented-mirror telescopes](https://en.wikipedia.org/wiki/Segmented_mirror), of which there are quite a few.  

---

### Answer by username_4 on 2021-07-18. Score: 1

Let's pretend we have a mirror in the shape of a spherical cap, with dimensions the same as JWST: diameter d=6.5m and radius of curvature r=15.88m. Then the distance along the surface of the mirror between two opposite points on its rim is given by 2r arcsin (d/2r), which comes to about 6.546m. This is only about 0.7% longer than the straight-line distance d.

The mirror is not perfectly spherical, and its circumference is definitely not a circle, but you can see that the choice of measurement makes little difference.


---

