<p>The precise definition of &quot;homologous&quot; seems to change based on who you talk to. A general umbrella definition is that a homologous radio telescope preserves a particular type of shape as it moves. Unless you can build an unfeasibly rigid dish, gravity will naturally shift the positions of different parts of the dish in different ways, changing the shape to one that will do a poorer job of focusing light. A homologous dish will subtly compensate for this; if it initially formed a parabola, then it will form a new parabola when you tilt it, and all you have to do is compensate for the position of the focus shifting slightly.</p>
<p>In many cases, there's the added implication that a homologous radio telescope compensates for deformations passively, like the <a href="https://en.wikipedia.org/wiki/Effelsberg_100-m_Radio_Telescope" rel="nofollow noreferrer">100-meter dish at Effelsberg</a>, which was the first homologous telescope. I've seen the Green Bank Telescope referred to emphatically as &quot;homologous&quot;, &quot;not homologous&quot;, and even <a href="https://link.springer.com/chapter/10.1007/978-3-030-32345-5_9" rel="nofollow noreferrer">&quot;partially homologous&quot;</a>. The final term is probably closest to the truth. The off-axis design makes it harder to build a passive surface that will deform properly, so a true homologous design was rejected (hence &quot;not homologous&quot;). On the other hand, there is <em>some</em> deformation to compensate for gravity (hence &quot;partially homologous&quot;) and the difference is made up by the active surface (hence &quot;homologous&quot; if you drop the passive surface requirement).</p>
<p>This active surface is also valuable because it can compensate for factors besides gravity, such as thermal gradients and effects from wind. The surface RMS can be <a href="https://www.gb.nrao.edu/scienceDocs/GBTpg.pdf" rel="nofollow noreferrer">as low as ~250-300 microns</a> under optimal conditions and several times that when conditions are worse circumstances. This is really only important once you get above a few GHz; you can probably convince yourself that small deviations are important when you get to short wavelengths/high frequencies.</p>
<p>FAST is another beastie altogether. As was true of Arecibo, it's far too large to be steered like the roughly 100-meter dishes at Green Bank or Effelsberg or Parkes. While the dish itself is 500 meters across and spherical, only a portion of it 300 meters across is used at a given time. This part of the dish <a href="https://www.sciencemag.org/news/2016/09/world-s-largest-radio-telescope-will-search-dark-matter-listen-aliens" rel="nofollow noreferrer">is deformed into a parabola by a complex system of 2,225 actuators</a>, and the parabola is moved about the dish to track sources - individual parts of the dish don't move as a normal steerable telescope would. In this sense, the deformations are shape-preserving, but they're 1) intentional, 2) achieved solely through an active surface, and 3) aren't compensating for natural deformations arising from gravity and tilting.</p>

CC BY-SA 4.0
2021-07-07T14:09:19.033Z
Clear, concise, easy to understand and definitive. *Thanks!*
uhoh
CC BY-SA 4.0
2021-07-07T13:34:12.373Z
2021-07-08T22:04:26.647Z
2021-07-08T22:04:26.647Z
HDE 226868
<p>This question is about design aspects of large radio telescope dishes which allow them to flex under the influence of gravity as they change elevation angle, and still maintain good optical performance at short wavelengths - on the order of a centimeter or less.</p>
<p><em>What is a radio &quot;homology telescope&quot; and is the 500m dish in China one?</em></p>
<p><strong>Background:</strong></p>
<p>I was reading about radio astronomy for background on <a href="https://astronomy.stackexchange.com/q/16238/7982">How did single dish (or single receiver) radio telescopes originally generate images?</a> and <a href="https://astronomy.stackexchange.com/q/16237/7982">What is the highest granularity focal-plane array on a dish radio telescope? Or is this the ONLY ONE?</a></p>
<p>In this <a href="https://www.cv.nrao.edu/%7Esransom/web/Ch3.html" rel="nofollow noreferrer">informative and entertaining</a> NRAO page I saw the term <em>homology telescope</em> for the first time, so I immediately select-right-click-serched it. At first I was confused by these Mathematics Stackexchange and Stanford Bio-X links:</p>
<ol>
<li><a href="https://math.stackexchange.com/q/1323553/284619">homology of mapping telescope of a monoid</a></li>
<li><a href="https://math.stackexchange.com/q/1341729/284619">action of a monoid on a mapping telescope</a></li>
<li><a href="https://biox.stanford.edu/research/seed-grants/genome-space-telescope-bringing-dna-sequence-homology-21st-century" rel="nofollow noreferrer">Genome Space Telescope: Bringing DNA Sequence Homology into the 21st Century</a></li>
</ol>
<p>until I realizes that these quit different <em>usages</em> of homology and/or telescope :-)</p>
<p>I found the <a href="https://books.google.com.tw/books?id=DoDBBAAAQBAJ&amp;lpg=PA191&amp;ots=vRxGPaU7AH&amp;dq=homology%20telescope&amp;pg=PA188#v=onepage&amp;q=homology&amp;f=false" rel="nofollow noreferrer">following explanation</a> in <em>Tools of Radio Astronomy</em> by  Thomas Wilson, Kristen Rohlfs and Susanne Huettemeister (Hüttemeister) particularly concise and helpful:</p>
<blockquote>
<p>7.5 The Practical Design of Parabolic Reflectors</p>
</blockquote>
<blockquote>
<p>7.5.1 General Considerations</p>
</blockquote>
<blockquote>
<p>Measurements of the mechanical properties of an antenna are of importance for its performance. This is especially true if the antenna deforms homologously. By <em>Homology</em> it is meant that, at various elevations, the main reflector deforms from one paraboloid into another. Today, homology is an intrinsic part of the design of all symmetric reflectors.</p>
</blockquote>
<p>Later in the same subsection:</p>
<blockquote>
<p>The design of an offset paraboloid has, however, complications. Since the design has less symmetry homology is more difficult to achieve and therefore active, real time adjustments of the surface are needed if the design limit of 7 mm or perhaps 3mm wavelength is to be reached. This will be accomplished by an actuator system controlled in real time by a laser measuring system. But for longer wavelengths, the GBT will not require active surface adjustment (Fig. 7.10).</p>
</blockquote>
<p>Here is a screen capture of Figure 7.10 from <a href="https://books.google.com.tw/books?id=DoDBBAAAQBAJ&amp;lpg=PA191&amp;ots=vRxGPaU7AH&amp;dq=homology%20telescope&amp;pg=PA188#v=onepage&amp;q=homology&amp;f=false" rel="nofollow noreferrer">google books</a></p>
<blockquote>
<p><a href="https://i.sstatic.net/eJSJz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/eJSJz.png" alt="screen shot of Figure 7.10 of Tools of Radio Astronomy* by  Thomas Wilson, Kristen Rohlfs and Susanne Huettemeister (Hüttemeister)" /></a></p>
</blockquote>
<p><strong>note:</strong> There are a number of nice photos and some discussion of the Green Bank Telescope and discussion of it's homology (homologusness?) on the NRAO page where I started, as well.</p>
<p><strong>So here is the question-cluster</strong> that I'm currently stuck on.</p>
<ol>
<li><p>If off-axis telescopes require active mechanical adjustments to maintain a homologous paraboloid figure, do the on-axis telescopes mentioned do it passively - <em>by mechanical design</em> alone? They naturally droop - <em>by design</em> - differently at different elevations (different angles above the horizon) in order to retain a paraboloid figure?</p>
</li>
<li><p>For the passive design, is it a) <em>the same</em> paraboloid but just a different section, b) or another paraboloid with the same focal point, or c) has a different focal point and therefore requires axial movement of the secondary mirror or feeds?</p>
</li>
<li><p>is the nearly-completed 500m dish in China (<a href="https://en.wikipedia.org/wiki/Five_hundred_meter_Aperture_Spherical_Telescope" rel="nofollow noreferrer">FAST</a>) a <em>homology telescope</em>? I know it has a lot of articulation and works off axis, but the word <em>spherical</em> is in the name and the receiver/feed translates laterally. <em>Is it still using the principle of homology</em>, but in a different way?</p>
</li>
</ol>

<radio-astronomy><terminology><radio-telescope>
What is a radio "homology telescope" and is the 500m dish in China one?
uhoh
# What is a radio "homology telescope" and is the 500m dish in China one?

(Asked by: username_0 on 2016-06-15)

This question is about design aspects of large radio telescope dishes which allow them to flex under the influence of gravity as they change elevation angle, and still maintain good optical performance at short wavelengths - on the order of a centimeter or less.

*What is a radio "homology telescope" and is the 500m dish in China one?*

**Background:**

I was reading about radio astronomy for background on [How did single dish (or single receiver) radio telescopes originally generate images?](https://astronomy.stackexchange.com/q/16238/7982) and [What is the highest granularity focal-plane array on a dish radio telescope? Or is this the ONLY ONE?](https://astronomy.stackexchange.com/q/16237/7982)

In this [informative and entertaining](https://www.cv.nrao.edu/%7Esransom/web/Ch3.html) NRAO page I saw the term *homology telescope* for the first time, so I immediately select-right-click-serched it. At first I was confused by these Mathematics Stackexchange and Stanford Bio-X links:

1. [homology of mapping telescope of a monoid](https://math.stackexchange.com/q/1323553/284619)
2. [action of a monoid on a mapping telescope](https://math.stackexchange.com/q/1341729/284619)
3. [Genome Space Telescope: Bringing DNA Sequence Homology into the 21st Century](https://biox.stanford.edu/research/seed-grants/genome-space-telescope-bringing-dna-sequence-homology-21st-century)

until I realizes that these quit different *usages* of homology and/or telescope :-)

I found the [following explanation](https://books.google.com.tw/books?id=DoDBBAAAQBAJ&lpg=PA191&ots=vRxGPaU7AH&dq=homology%20telescope&pg=PA188#v=onepage&q=homology&f=false) in *Tools of Radio Astronomy* by Thomas Wilson, Kristen Rohlfs and Susanne Huettemeister (Hüttemeister) particularly concise and helpful:

> 7.5 The Practical Design of Parabolic Reflectors

> 7.5.1 General Considerations

> Measurements of the mechanical properties of an antenna are of importance for its performance. This is especially true if the antenna deforms homologously. By *Homology* it is meant that, at various elevations, the main reflector deforms from one paraboloid into another. Today, homology is an intrinsic part of the design of all symmetric reflectors.

Later in the same subsection:

> The design of an offset paraboloid has, however, complications. Since the design has less symmetry homology is more difficult to achieve and therefore active, real time adjustments of the surface are needed if the design limit of 7 mm or perhaps 3mm wavelength is to be reached. This will be accomplished by an actuator system controlled in real time by a laser measuring system. But for longer wavelengths, the GBT will not require active surface adjustment (Fig. 7.10).

Here is a screen capture of Figure 7.10 from [google books](https://books.google.com.tw/books?id=DoDBBAAAQBAJ&lpg=PA191&ots=vRxGPaU7AH&dq=homology%20telescope&pg=PA188#v=onepage&q=homology&f=false)

> [![screen shot of Figure 7.10 of Tools of Radio Astronomy* by  Thomas Wilson, Kristen Rohlfs and Susanne Huettemeister (Hüttemeister)](https://i.sstatic.net/eJSJz.png)](https://i.sstatic.net/eJSJz.png)

**note:** There are a number of nice photos and some discussion of the Green Bank Telescope and discussion of it's homology (homologusness?) on the NRAO page where I started, as well.

**So here is the question-cluster** that I'm currently stuck on.

1. If off-axis telescopes require active mechanical adjustments to maintain a homologous paraboloid figure, do the on-axis telescopes mentioned do it passively - *by mechanical design* alone? They naturally droop - *by design* - differently at different elevations (different angles above the horizon) in order to retain a paraboloid figure?
2. For the passive design, is it a) *the same* paraboloid but just a different section, b) or another paraboloid with the same focal point, or c) has a different focal point and therefore requires axial movement of the secondary mirror or feeds?
3. is the nearly-completed 500m dish in China ([FAST](https://en.wikipedia.org/wiki/Five_hundred_meter_Aperture_Spherical_Telescope)) a *homology telescope*? I know it has a lot of articulation and works off axis, but the word *spherical* is in the name and the receiver/feed translates laterally. *Is it still using the principle of homology*, but in a different way?

**Tags:** radio-astronomy, terminology, radio-telescope


---

## 1 answers

### Answer by username_1 on 2021-07-07. Score: 5 | Accepted answer

The precise definition of "homologous" seems to change based on who you talk to. A general umbrella definition is that a homologous radio telescope preserves a particular type of shape as it moves. Unless you can build an unfeasibly rigid dish, gravity will naturally shift the positions of different parts of the dish in different ways, changing the shape to one that will do a poorer job of focusing light. A homologous dish will subtly compensate for this; if it initially formed a parabola, then it will form a new parabola when you tilt it, and all you have to do is compensate for the position of the focus shifting slightly.

In many cases, there's the added implication that a homologous radio telescope compensates for deformations passively, like the [100-meter dish at Effelsberg](https://en.wikipedia.org/wiki/Effelsberg_100-m_Radio_Telescope), which was the first homologous telescope. I've seen the Green Bank Telescope referred to emphatically as "homologous", "not homologous", and even ["partially homologous"](https://link.springer.com/chapter/10.1007/978-3-030-32345-5_9). The final term is probably closest to the truth. The off-axis design makes it harder to build a passive surface that will deform properly, so a true homologous design was rejected (hence "not homologous"). On the other hand, there is *some* deformation to compensate for gravity (hence "partially homologous") and the difference is made up by the active surface (hence "homologous" if you drop the passive surface requirement).

This active surface is also valuable because it can compensate for factors besides gravity, such as thermal gradients and effects from wind. The surface RMS can be [as low as ~250-300 microns](https://www.gb.nrao.edu/scienceDocs/GBTpg.pdf) under optimal conditions and several times that when conditions are worse circumstances. This is really only important once you get above a few GHz; you can probably convince yourself that small deviations are important when you get to short wavelengths/high frequencies.

FAST is another beastie altogether. As was true of Arecibo, it's far too large to be steered like the roughly 100-meter dishes at Green Bank or Effelsberg or Parkes. While the dish itself is 500 meters across and spherical, only a portion of it 300 meters across is used at a given time. This part of the dish [is deformed into a parabola by a complex system of 2,225 actuators](https://www.sciencemag.org/news/2016/09/world-s-largest-radio-telescope-will-search-dark-matter-listen-aliens), and the parabola is moved about the dish to track sources - individual parts of the dish don't move as a normal steerable telescope would. In this sense, the deformations are shape-preserving, but they're 1) intentional, 2) achieved solely through an active surface, and 3) aren't compensating for natural deformations arising from gravity and tilting.

> **Comments:**
> **username_0**: Clear, concise, easy to understand and definitive. *Thanks!*  

---

