<p>The primary challenges of telescope design are keeping good focus<sup>1</sup> across a locally flat<sup>2</sup> focal plane, meeting aperture and field of view targets while using the <em>fewest optical elements.</em></p>
<p>Now most designs that do that with a few optical elements have substantial <a href="https://en.wikipedia.org/wiki/Distortion_(optics)" rel="nofollow noreferrer">field distortion</a>.</p>
<p>For small optical systems like camera lenses (see below) you add more lenses with more optical surfaces and therefore more degrees of freedom to your design.</p>
<p>We expect a camera to take an incoming light field and project it on to our CCD or film very similarly to how a <a href="https://commons.wikimedia.org/wiki/File:Pinhole-camera.svg" rel="nofollow noreferrer">pinhole camera</a> would <a href="https://en.wikipedia.org/wiki/Projective_plane" rel="nofollow noreferrer">project</a> it.</p>
<p>So these days even the tiny camera in a high-end smart phone can have as many as a half-dozen optical elements!</p>
<p>Because of gravity<sup>3</sup> reflective losses and other degradations at each surface, reflecting telescopes are preferred with as few elements as possible.</p>
<p>Since the data has to go through substantial processing and computer analysis and doesn't need to go strait to snapchat, nobody cares if there's some field distortion. It can be well characterized and corrections can be applied automatically.</p>
<ul>
<li><sup>1</sup>near-<a href="https://en.wikipedia.org/wiki/Diffraction-limited_system" rel="nofollow noreferrer">diffraction-limited</a>-<a href="https://en.wikipedia.org/wiki/Point_spread_function" rel="nofollow noreferrer">point spread function</a></li>
<li><sup>2</sup>some focal planes are tiled with CCDs tilted at slightly different angles, but each CCD is flat over at least several centimeters.</li>
<li><sup>3</sup>heavy telescope elements on Earth deform under gravity, and are expensive/difficult to put into space.</li>
</ul>
<hr />
<p><a href="https://i.sstatic.net/OCzqZ.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OCzqZ.jpg" alt="enter image description here" /></a></p>
<p><strong>above:</strong> <a href="https://en.wikipedia.org/wiki/Transiting_Exoplanet_Survey_Satellite" rel="nofollow noreferrer">Transiting Exoplanet Survey Satellite</a> (TESS) camera from Spaceflight 101's <a href="https://spaceflight101.com/tess/tess-instrument/" rel="nofollow noreferrer">TESS Instrument Overview</a></p>
<p><strong>note:</strong> Probably TESS' lens is complicated primarily to achieve diffraction-limited achromatic performance over its full field of view rather than to have zero distortion, but right now I can't say for sure.</p>
<p><strong>below:</strong>  from Vladan Blahnik &amp; Oliver Schindelbeck's <a href="https://www.degruyter.com/document/doi/10.1515/aot-2021-0023/html" rel="nofollow noreferrer">Smartphone imaging technology and its applications</a></p>
<p><a href="https://i.sstatic.net/hwDqm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hwDqm.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-05-07T11:15:05.263Z
2022-05-07T11:15:05.263Z
uhoh
<p>It's a general property of optics. In what way an image is distorted depends on the exact optical setup and will need careful calibration. Usually the best imaging quality is found in the center of an image and the edges becoming more subject to various typical imaging errors.</p>
<p>The most prominent one is <a href="https://en.wikipedia.org/wiki/Distortion_(optics)" rel="noreferrer">distortion</a>. EO sell optics but do a good job at <a href="https://www.edmundoptics.eu/knowledge-center/application-notes/imaging/distortion/" rel="noreferrer">explaining it</a>, too (no, I'm not affiliated). This effect can be approximated by a 4th order polynomial as it is symmetric to the center of the image, the coefficients are specific to your setup.</p>
<p>Besides distortion there are various types of <a href="https://en.wikipedia.org/wiki/Optical_aberration" rel="noreferrer">optical aberration</a> for various reasons.</p>

CC BY-SA 4.0
2022-05-05T17:07:00.797Z
2022-05-05T17:07:00.797Z
planetmaker
<p>You may know the issue that photos from (at least some) telescopes are stretched at the edges, so that the star locations do not fit compared to if this location would be on the center of the photo.</p>
<p>Why is this happening? I am looking for a detailed geometrical explanation</p>
<p>Is there a standard way to describe this shift? In a YouTube video about Astropy, it said that the shift is proportional to a quadratic polynomial.</p>
<p>Is there a common way to handle this issue?</p>

CC BY-SA 4.0
2022-05-05T15:41:28.407Z
Do you have an example? It sounds to me like it's simply for the same reason that a map of Earth is "stretched" toward the poles: You're trying to map a spherical coordinate system onto a flat surface, which can never be more than an approximation. The larger the field of view you have, the larger the effect you'll see.
pela
CC BY-SA 4.0
2022-05-05T15:41:34.933Z
It'd be a really good idea to provide an example of the type of distortion you're interested in.
Greg Miller
CC BY-SA 4.0
2022-05-05T20:42:45.540Z
What Pela said. See https://en.wikipedia.org/wiki/Stereographic_projection & https://en.wikipedia.org/wiki/Map_projection
PM 2Ring
CC BY-SA 4.0
2022-05-05T20:56:35.160Z
so do you mean that a telescope image is stereographic projection, it is then polynom of grade 2 not 4
user184868
CC BY-SA 4.0
2022-05-05T23:12:57.833Z
No, a photo is a perspective projection, with various optical distortions mentioned by planetmaker. But mapping the celestial sphere to a flat image requires some kind of map projection. The stereographic projection is one of the easiest projections to understand (and it preserves angles).
PM 2Ring
<telescope><image-processing>
Why are photos from telescope stretched at their edges?
user184868
# Why are photos from telescope stretched at their edges?

(Asked by: username_0 on 2022-05-05)

You may know the issue that photos from (at least some) telescopes are stretched at the edges, so that the star locations do not fit compared to if this location would be on the center of the photo.

Why is this happening? I am looking for a detailed geometrical explanation

Is there a standard way to describe this shift? In a YouTube video about Astropy, it said that the shift is proportional to a quadratic polynomial.

Is there a common way to handle this issue?

**Tags:** telescope, image-processing
> **Comments:**
> **username_1**: Do you have an example? It sounds to me like it's simply for the same reason that a map of Earth is "stretched" toward the poles: You're trying to map a spherical coordinate system onto a flat surface, which can never be more than an approximation. The larger the field of view you have, the larger the effect you'll see.  
> **username_2**: It'd be a really good idea to provide an example of the type of distortion you're interested in.  
> **username_3**: What Pela said. See https://en.wikipedia.org/wiki/Stereographic_projection & https://en.wikipedia.org/wiki/Map_projection  
> **username_0**: so do you mean that a telescope image is stereographic projection, it is then polynom of grade 2 not 4  
> **username_3**: No, a photo is a perspective projection, with various optical distortions mentioned by planetmaker. But mapping the celestial sphere to a flat image requires some kind of map projection. The stereographic projection is one of the easiest projections to understand (and it preserves angles).  

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## 2 answers

### Answer by username_5 on 2022-05-05. Score: 7 | Accepted answer

It's a general property of optics. In what way an image is distorted depends on the exact optical setup and will need careful calibration. Usually the best imaging quality is found in the center of an image and the edges becoming more subject to various typical imaging errors.

The most prominent one is [distortion](https://en.wikipedia.org/wiki/Distortion_(optics)). EO sell optics but do a good job at [explaining it](https://www.edmundoptics.eu/knowledge-center/application-notes/imaging/distortion/), too (no, I'm not affiliated). This effect can be approximated by a 4th order polynomial as it is symmetric to the center of the image, the coefficients are specific to your setup.

Besides distortion there are various types of [optical aberration](https://en.wikipedia.org/wiki/Optical_aberration) for various reasons.


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### Answer by username_4 on 2022-05-07. Score: 1

The primary challenges of telescope design are keeping good focus1 across a locally flat2 focal plane, meeting aperture and field of view targets while using the *fewest optical elements.*

Now most designs that do that with a few optical elements have substantial [field distortion](https://en.wikipedia.org/wiki/Distortion_(optics)).

For small optical systems like camera lenses (see below) you add more lenses with more optical surfaces and therefore more degrees of freedom to your design.

We expect a camera to take an incoming light field and project it on to our CCD or film very similarly to how a [pinhole camera](https://commons.wikimedia.org/wiki/File:Pinhole-camera.svg) would [project](https://en.wikipedia.org/wiki/Projective_plane) it.

So these days even the tiny camera in a high-end smart phone can have as many as a half-dozen optical elements!

Because of gravity3 reflective losses and other degradations at each surface, reflecting telescopes are preferred with as few elements as possible.

Since the data has to go through substantial processing and computer analysis and doesn't need to go strait to snapchat, nobody cares if there's some field distortion. It can be well characterized and corrections can be applied automatically.

* 1near-[diffraction-limited](https://en.wikipedia.org/wiki/Diffraction-limited_system)-[point spread function](https://en.wikipedia.org/wiki/Point_spread_function)
* 2some focal planes are tiled with CCDs tilted at slightly different angles, but each CCD is flat over at least several centimeters.
* 3heavy telescope elements on Earth deform under gravity, and are expensive/difficult to put into space.

---

[![enter image description here](https://i.sstatic.net/OCzqZ.jpg)](https://i.sstatic.net/OCzqZ.jpg)

**above:** [Transiting Exoplanet Survey Satellite](https://en.wikipedia.org/wiki/Transiting_Exoplanet_Survey_Satellite) (TESS) camera from Spaceflight 101's [TESS Instrument Overview](https://spaceflight101.com/tess/tess-instrument/)

**note:** Probably TESS' lens is complicated primarily to achieve diffraction-limited achromatic performance over its full field of view rather than to have zero distortion, but right now I can't say for sure.

**below:** from Vladan Blahnik & Oliver Schindelbeck's [Smartphone imaging technology and its applications](https://www.degruyter.com/document/doi/10.1515/aot-2021-0023/html)

[![enter image description here](https://i.sstatic.net/hwDqm.png)](https://i.sstatic.net/hwDqm.png)


---

