<p>I apologise, I'm posting an answer because I can't comment.</p>
<blockquote>
<p>What is the fastest abberation coming from atmospheric turbulence in any measurement setting (sun observation during day, night-time observations)?</p>
</blockquote>
<p>It depends on the astronomical seeing conditions at the location of the telescope, and also varies quite a lot. It could be anywhere from <span class="math-container">$1-100~ms$</span>.</p>
<blockquote>
<p>Does any astronomer need correction in the visible spectrum beyond e.g. 100 Hz?</p>
</blockquote>
<p>It depends on the what you're after. In solar physics, for example, observations are generally interested in resolving features on the Sun. You can also find polarimeters that operate beyond <span class="math-container">$100~Hz$</span>, so an Adaptive Optics system that operates in the <span class="math-container">$kHz$</span> is a fairly standard requirement for most modern Solar telescopes. However, if you're only interested in collecting unresolved spectra (say, a star), you may not really benefit from having a really fast Adaptive Optics system.</p>
<blockquote>
<p>Are fast systems practically limited by spatial resolution of the sensor?</p>
</blockquote>
<p>I'm not sure what you mean by <em>limited</em> and <em>sensor</em>. Are you talking about the sampling of the wavefront by the wavefront sensor?</p>
<blockquote>
<p>Is there any way to get a quantitative overview how widespread adaptive optics is in astronomy today and which setups are currently in use?</p>
</blockquote>
<p>I think you'd find this reference helpful: <a href="https://link.springer.com/article/10.12942/lrsp-2011-2" rel="nofollow noreferrer">https://link.springer.com/article/10.12942/lrsp-2011-2</a></p>

CC BY-SA 4.0
2021-02-17T15:35:54.653Z
Thanks for that answer. Limited was meant in the sense of the tradeoff between data bandwidth and measurement framerate/measurement resolution. Imagine a CCD camera sending its images along a USB interface. You'll get 20 2MP-images through that cable at 20 fps and therefore get into a dependency of resolution/framerate/transfer bandwidth. Do you know of any applications where they pushed that limit?
Damian
CC BY-SA 4.0
2021-04-13T10:43:15.297Z
@Damian Thanks for the clarification. I'm not sure if the tradeoff between data bandwidth and frame rate is still an issue for CCDs, but current science-grade high-resolution (~4MP) CMOS sensors allow frames to be captured at 400 fps. For freezing the atmosphere, this is quite adequate. Is this the limit you already had in mind?
Sudharshan Saranathan
CC BY-SA 4.0
2021-01-14T14:55:32.040Z
2021-01-14T14:55:32.040Z
Sudharshan Saranathan
<p>This question is massive, so I will skip the second bullet point. Coherence time (<span class="math-container">$\tau_0$</span> in AO jargon) is a few milliseconds at a favorable site, and probably even shorter in poor seeing conditions.</p>
<p><a href="https://books.google.com/books?id=UZKnDwAAQBAJ&amp;pg=PA2584&amp;lpg=PA2584" rel="nofollow noreferrer">Handbook of Laser Technology and Applications</a> defines <span class="math-container">$\tau_0 = r_0 / v$</span>, the ratio of the <a href="https://en.wikipedia.org/wiki/Astronomical_seeing" rel="nofollow noreferrer">Fried parameter</a>, a measure of the seeing, to the atmospheric velocity that is causing various parcels of air at different temperature to drift in and out of the beam. Since <span class="math-container">$r_0$</span> is a function of wavelength, <span class="math-container">$\tau_0$</span> is going to vary with wavelength. I may correct the Wiki article cited by the OP in the question comments, because the &quot;sluggishness&quot; of the atmosphere is only <span class="math-container">$v$</span>, which does not depend on wavelength. The wavelength dependence in <span class="math-container">$r_0$</span> comes from how refractive the turbulence is, which I would speculate depends on the temperature difference between the warm and cool blobs generating the turbulence.</p>
<p>An <a href="http://www.eso.org/gen-fac/pubs/astclim/paranal/seeing/adaptive-optics/" rel="nofollow noreferrer">ESO page</a> gives a nice definition of <span class="math-container">$\tau_0$</span>, and points to this table of measured values at Paranal:</p>
<p><a href="https://i.sstatic.net/y98Mq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/y98Mq.png" alt="enter image description here" /></a></p>
<p>To get a good overview of AO in use today, you could go to Montréal for <a href="https://spie.org/conferences-and-exhibitions/astronomical-telescopes-and-instrumentation" rel="nofollow noreferrer">SPIEAstro 2022</a>, or maybe view the programs of past conferences. It is a pretty big field.</p>

CC BY-SA 4.0
2022-02-14T06:42:59.413Z
2022-02-14T07:04:15.497Z
2022-02-14T07:04:15.497Z
giardia
<p>I am interested in the astronomer's need for speed in wavefront correction, especially when measuring in NIR and visible domain.</p>
<ul>
<li>What is the fastest abberation coming from atmospheric turbulence in any measurement setting (sun observation during day, night-time observations)? Does any astronomer need correction in the visible spectrum beyond e.g. 100 Hz?</li>
<li>Are fast systems practically limited by spatial resolution of the sensor?</li>
<li>Is there any way to get a quantitative overview how widespread adaptive optics is in astronomy today and which setups are currently in use?</li>
</ul>
<p>Thank you for your thoughts!</p>

CC BY-SA 4.0
2021-01-02T02:12:41.063Z
I vaguely remember seeing 1 kHz mentioned for some wavefront correction system, but I don't know if that's a 3 dB point or not. It's not that the major frequency components are that high, but for *instantaneous tracking accuracy* (low instantaneous error) you'd like a cut-off much higher than the frequencies of what you are tracking.
uhoh
CC BY-SA 4.0
2021-01-02T05:50:51.497Z
Both wavefront sensors and deformable mirrors can work at around 1kHz. See https://en.wikipedia.org/wiki/Astronomical_seeing might help to understand the speed of refractive index fluctuations.
WDC
CC BY-SA 4.0
2021-01-02T10:04:24.977Z
Thanks for these first comments. Are these fast sensors then practically limited in their spatial resolution? And would this limit be the bottleneck in a complete sensor-actuator-system or is the actuator resolution limiting? I added this aspect to the original question.
Damian
CC BY-SA 4.0
2021-01-02T21:03:08.107Z
I found https://astronomytechnologytoday.com/2017/07/04/10372/ very insightful, where one of the main statements is that the adaptive optics has to match the framerate of the camera - which esentially means that every frame will be corrected.
B--rian
CC BY-SA 4.0
2021-01-03T21:06:37.870Z
In the wikipedia article on Speckle Imaging I found the following paragraph: "The key to the technique, found by the American astronomer David L. Fried in 1966, was to take very fast images in which case the atmosphere is effectively "frozen" in place.[1] For infrared images, exposure times are on the order of 100 ms, but for the visible region they drop to as little as 10 ms. In images at this time scale, or smaller, the movement of the atmosphere is too sluggish to have an effect; ..." The publication by Fried should then hopefully have more quantitative observations.
Damian
CC BY-SA 4.0
2021-01-04T10:49:36.943Z
A quantitative answer is given by Fried in the article "The Nature of Atmospheric Turbulence Effects on Imaging and Pseudo-Imaging Systems, and its Quantification". After some quite well understandable remarks on turbulence and optical densities within turbulence, he makes a sample calculation of the needed frequency of a wave front correcting system to be at "630 Hertz".
Damian
<adaptive-optics>
When using adaptive optics, what is the shortest timescale of atmospheric changes in refractive index that astronomers have to deal with?
Damian
# When using adaptive optics, what is the shortest timescale of atmospheric changes in refractive index that astronomers have to deal with?

(Asked by: username_0 on 2021-01-01)

I am interested in the astronomer's need for speed in wavefront correction, especially when measuring in NIR and visible domain.

* What is the fastest abberation coming from atmospheric turbulence in any measurement setting (sun observation during day, night-time observations)? Does any astronomer need correction in the visible spectrum beyond e.g. 100 Hz?
* Are fast systems practically limited by spatial resolution of the sensor?
* Is there any way to get a quantitative overview how widespread adaptive optics is in astronomy today and which setups are currently in use?

Thank you for your thoughts!

**Tags:** adaptive-optics

> **Comments:**
> **username_1**: I vaguely remember seeing 1 kHz mentioned for some wavefront correction system, but I don't know if that's a 3 dB point or not. It's not that the major frequency components are that high, but for *instantaneous tracking accuracy* (low instantaneous error) you'd like a cut-off much higher than the frequencies of what you are tracking.  
> **username_2**: Both wavefront sensors and deformable mirrors can work at around 1kHz. See https://en.wikipedia.org/wiki/Astronomical_seeing might help to understand the speed of refractive index fluctuations.  
> **username_0**: Thanks for these first comments. Are these fast sensors then practically limited in their spatial resolution? And would this limit be the bottleneck in a complete sensor-actuator-system or is the actuator resolution limiting? I added this aspect to the original question.  
> **username_3**: I found https://astronomytechnologytoday.com/2017/07/04/10372/ very insightful, where one of the main statements is that the adaptive optics has to match the framerate of the camera - which esentially means that every frame will be corrected.  
> **username_0**: In the wikipedia article on Speckle Imaging I found the following paragraph: "The key to the technique, found by the American astronomer David L. Fried in 1966, was to take very fast images in which case the atmosphere is effectively "frozen" in place.[1] For infrared images, exposure times are on the order of 100 ms, but for the visible region they drop to as little as 10 ms. In images at this time scale, or smaller, the movement of the atmosphere is too sluggish to have an effect; ..." The publication by Fried should then hopefully have more quantitative observations.  
> **username_0**: A quantitative answer is given by Fried in the article "The Nature of Atmospheric Turbulence Effects on Imaging and Pseudo-Imaging Systems, and its Quantification". After some quite well understandable remarks on turbulence and optical densities within turbulence, he makes a sample calculation of the needed frequency of a wave front correcting system to be at "630 Hertz".  

---

## 2 answers

### Answer by username_4 on 2021-01-14. Score: 4

I apologise, I'm posting an answer because I can't comment.

> What is the fastest abberation coming from atmospheric turbulence in any measurement setting (sun observation during day, night-time observations)?

It depends on the astronomical seeing conditions at the location of the telescope, and also varies quite a lot. It could be anywhere from $1-100~ms$.

> Does any astronomer need correction in the visible spectrum beyond e.g. 100 Hz?

It depends on the what you're after. In solar physics, for example, observations are generally interested in resolving features on the Sun. You can also find polarimeters that operate beyond $100~Hz$, so an Adaptive Optics system that operates in the $kHz$ is a fairly standard requirement for most modern Solar telescopes. However, if you're only interested in collecting unresolved spectra (say, a star), you may not really benefit from having a really fast Adaptive Optics system.

> Are fast systems practically limited by spatial resolution of the sensor?

I'm not sure what you mean by *limited* and *sensor*. Are you talking about the sampling of the wavefront by the wavefront sensor?

> Is there any way to get a quantitative overview how widespread adaptive optics is in astronomy today and which setups are currently in use?

I think you'd find this reference helpful: <https://link.springer.com/article/10.12942/lrsp-2011-2>

> **Comments:**
> **username_0**: Thanks for that answer. Limited was meant in the sense of the tradeoff between data bandwidth and measurement framerate/measurement resolution. Imagine a CCD camera sending its images along a USB interface. You'll get 20 2MP-images through that cable at 20 fps and therefore get into a dependency of resolution/framerate/transfer bandwidth. Do you know of any applications where they pushed that limit?  
> **username_4**: @username_0 Thanks for the clarification. I'm not sure if the tradeoff between data bandwidth and frame rate is still an issue for CCDs, but current science-grade high-resolution (~4MP) CMOS sensors allow frames to be captured at 400 fps. For freezing the atmosphere, this is quite adequate. Is this the limit you already had in mind?  

---

### Answer by username_5 on 2022-02-14. Score: 0

This question is massive, so I will skip the second bullet point. Coherence time ($\tau\_0$ in AO jargon) is a few milliseconds at a favorable site, and probably even shorter in poor seeing conditions.

[Handbook of Laser Technology and Applications](https://books.google.com/books?id=UZKnDwAAQBAJ&pg=PA2584&lpg=PA2584) defines $\tau\_0 = r\_0 / v$, the ratio of the [Fried parameter](https://en.wikipedia.org/wiki/Astronomical_seeing), a measure of the seeing, to the atmospheric velocity that is causing various parcels of air at different temperature to drift in and out of the beam. Since $r\_0$ is a function of wavelength, $\tau\_0$ is going to vary with wavelength. I may correct the Wiki article cited by the OP in the question comments, because the "sluggishness" of the atmosphere is only $v$, which does not depend on wavelength. The wavelength dependence in $r\_0$ comes from how refractive the turbulence is, which I would speculate depends on the temperature difference between the warm and cool blobs generating the turbulence.

An [ESO page](http://www.eso.org/gen-fac/pubs/astclim/paranal/seeing/adaptive-optics/) gives a nice definition of $\tau\_0$, and points to this table of measured values at Paranal:

[![enter image description here](https://i.sstatic.net/y98Mq.png)](https://i.sstatic.net/y98Mq.png)

To get a good overview of AO in use today, you could go to Montréal for [SPIEAstro 2022](https://spie.org/conferences-and-exhibitions/astronomical-telescopes-and-instrumentation), or maybe view the programs of past conferences. It is a pretty big field.


---

