<p>Given your reply it seems your definition of diffusion is slightly different from my sense. But the phenomenon is true that at segmentation locations wavefronts are being deflected not in a uniform manner, causing the diffusion issue posted in this question.</p>
<p>Before addressing this issue, let me briefly describe how adaptive optics works in practice. In a typical AO system, a wavefront sensor measures the incoming wavefront distortion (usually it's slopes), given which a deformable mirror corrects for. The deformable mirrors consist of multiple actuators, which enable the mirror deformation. These actuators are controlled by commands.</p>
<p>The input/output are:</p>
<ul>
<li>Input: wavefront slopes <span class="math-container">$\mathbf{y}$</span></li>
<li>Output: actuator control commands <span class="math-container">$\mathbf{x}$</span></li>
</ul>
<p>These two are usually related through a so-called interaction matrix <span class="math-container">$\mathbf{A}$</span>:
<span class="math-container">$$
\mathbf{y} = \mathbf{Ax}
$$</span>
This matrix models all system artifacts, including the diffusion issue in this question. Since we would like to solve <span class="math-container">$\mathbf{x}$</span> from <span class="math-container">$\mathbf{y}$</span>, we would also like the pesudo-inverse of <span class="math-container">$\mathbf{A}$</span>, denoted as <span class="math-container">$\mathbf{A}^{-1}$</span>, so in real-time the AO system can solve the actual commands as:
<span class="math-container">$$
\mathbf{x} = \mathbf{A}^{-1} \mathbf{y}
$$</span>
<span class="math-container">$\mathbf{A}$</span> and <span class="math-container">$\mathbf{A}^{-1}$</span> are usually calibrated before running the AO system.</p>
<p>Now consider this question:</p>
<ul>
<li><p>Yes, there are diffusion reflection from the mirror. But this issue contributes in part to the interaction matrix <span class="math-container">$\mathbf{A}$</span>. As long as people calibrate it carefully it does not really affect AO performance.</p>
</li>
<li><p>For normal AO systems both measurement and correction wavefront lateral resolutions are low: typically at thousands of measurements, i.e. <span class="math-container">$\mathbf{x}\in\mathbb{R}^{1000}$</span> or so. In such a situation, I would conjure that the diffusion reflection at segmentation locations is not significant enough compared to the overall sub-mirror reflection, i.e. the fill factor of the sub-mirror is high enough to ignore this effect.</p>
</li>
</ul>

CC BY-SA 4.0
2020-11-26T18:19:09.563Z
2020-11-26T18:30:59.947Z
2020-11-26T18:30:59.947Z
WDC
<p>We have all seen images like this of deformable mirrors:</p>
<p><a href="https://i.sstatic.net/xdAH1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xdAH1.png" alt="enter image description here" /></a></p>
<p>Continuous deformable mirrors are known to have a higher <a href="https://www.rp-photonics.com/deformable_mirrors.html" rel="nofollow noreferrer">quality</a> over segmented mirrors, but it seems to me that a continuous mirror (or even a segmented tip tilt mirror) would cause diffuse reflection.  Here is a figure showing a segmented and a continuous mirror</p>
<p><a href="https://i.sstatic.net/qQN0V.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qQN0V.png" alt="enter image description here" /></a></p>
<p>Since the light is coming in normal to the telescope (let's just say space telescope so we can avoid all possible atmospheric non-normal light), the purpose of the deformable mirror is to adjust the <strong>phase</strong> of the light.  It would appear to me that a continuous deformable mirror would also diffuse the light as seen from my rough drawing (I know that most mirrors are placed at a 45 degree angle, but you get my point).  Here is a figure showing the diffuse reflection at a 45 degree angle.</p>
<p><a href="https://i.sstatic.net/7CBbF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7CBbF.png" alt="enter image description here" /></a></p>
<p>It is well known that a segmented mirror causes light scatter (at each segmentation location), but I have not been able to find any literature on light diffusion on a continuous deformable mirror.  This must be true, but how is it not a problem and how do they address it? (pointing towards scholarly resources would be appreciated)</p>
<p><strong>UPDATE</strong></p>
<p>I will accept the answer posted below, but I think it is missing something important.  In the fourth bullet it is stated,</p>
<blockquote>
<p>I would conjure that the diffusion reflection at segmentation locations is not significant enough compared to the overall sub-mirror reflection</p>
</blockquote>
<p>This is still an opinion (though it could be correct), which is why I specifically asked for scholarly resources.</p>
<p>I reached out to Professor Thomas Bifano from Boston University who specializes in deformable mirrors and his answer made sense and was readily verified in scholarly <a href="http://www.graphics.cornell.edu/%7Ewestin/pubs/TorranceSparrowJOSA1967.pdf" rel="nofollow noreferrer">papers</a></p>
<blockquote>
<p>Diffuse reflection occurs when the reflective surface is rough: scale of surface asperities is large in comparison to the wavelength of light reflecting from it. In diffuse reflection, incident light at a fixed angle of incidence reflects (actually, scatters) at many different angles. If the local roughness of the surface is &lt;&lt;wavelength, there no diffuse reflection.</p>
</blockquote>

CC BY-SA 4.0
2020-11-24T04:22:56.500Z
I'm not sure that you have the same understanding of "scatter" as how it's used in optics. Scattering is when there are rays going different directions from the same point, but I get the impression that you are using it to mean different directions from different points.
Acccumulation
CC BY-SA 4.0
2020-11-24T17:19:50.707Z
@Acccumulation Yes you are correct if you are discussing a single photon. If you are describing a wavefront, then scattering is still appropriate.  Since I mixed the two together without a clear distinction, I updated my question.
Josh
CC BY-SA 4.0
2020-11-25T05:37:08.760Z
(1) If you look at any mirrors at home, you may find litter diffuse reflections -- that said, mirrors are highly specular, not to mention crafted high-performance deformable mirrors for adaptive optics. (2) The AO diagram shown at 45 deg is for visualization purposes -- in reality the incoming beam is impinging almost perpendicular to the deformable mirror, and this makes the mirror more specular. Given (1)(2), I do not think your statements hold.
WDC
CC BY-SA 4.0
2020-11-26T15:51:16.367Z
@WDC To address both of your points, 1) yes it is a mirror so it is specular (it will reflect at the same angle from the normal); however, since it is deformable, the normal changes meaning that the wavefront will diffuse.  2) it doesn't matter if it is at a 45 degree or normal to the mirror, if the localized normal is not consistent, then it will cause diffuse reflection.  Also, you said it is "more specular", yes I agree that the majority of the wavefront will have the same refection, but diffuse reflection will occur because of the deformable mirror, so how do they minimize it?
Josh
CC BY-SA 4.0
2020-11-26T18:31:25.770Z
@Josh Okay I understand the issue here. Please see my answer.
WDC
<exoplanet><mirror><adaptive-optics>
Does a continuous deformable mirror cause diffuse reflection?
Josh
# Does a continuous deformable mirror cause diffuse reflection?

(Asked by: username_0 on 2020-11-23)

We have all seen images like this of deformable mirrors:

[![enter image description here](https://i.sstatic.net/xdAH1.png)](https://i.sstatic.net/xdAH1.png)

Continuous deformable mirrors are known to have a higher [quality](https://www.rp-photonics.com/deformable_mirrors.html) over segmented mirrors, but it seems to me that a continuous mirror (or even a segmented tip tilt mirror) would cause diffuse reflection. Here is a figure showing a segmented and a continuous mirror

[![enter image description here](https://i.sstatic.net/qQN0V.png)](https://i.sstatic.net/qQN0V.png)

Since the light is coming in normal to the telescope (let's just say space telescope so we can avoid all possible atmospheric non-normal light), the purpose of the deformable mirror is to adjust the **phase** of the light. It would appear to me that a continuous deformable mirror would also diffuse the light as seen from my rough drawing (I know that most mirrors are placed at a 45 degree angle, but you get my point). Here is a figure showing the diffuse reflection at a 45 degree angle.

[![enter image description here](https://i.sstatic.net/7CBbF.png)](https://i.sstatic.net/7CBbF.png)

It is well known that a segmented mirror causes light scatter (at each segmentation location), but I have not been able to find any literature on light diffusion on a continuous deformable mirror. This must be true, but how is it not a problem and how do they address it? (pointing towards scholarly resources would be appreciated)

**UPDATE**

I will accept the answer posted below, but I think it is missing something important. In the fourth bullet it is stated,

> I would conjure that the diffusion reflection at segmentation locations is not significant enough compared to the overall sub-mirror reflection

This is still an opinion (though it could be correct), which is why I specifically asked for scholarly resources.

I reached out to Professor Thomas Bifano from Boston University who specializes in deformable mirrors and his answer made sense and was readily verified in scholarly [papers](http://www.graphics.cornell.edu/%7Ewestin/pubs/TorranceSparrowJOSA1967.pdf)

> Diffuse reflection occurs when the reflective surface is rough: scale of surface asperities is large in comparison to the wavelength of light reflecting from it. In diffuse reflection, incident light at a fixed angle of incidence reflects (actually, scatters) at many different angles. If the local roughness of the surface is <

**Tags:** exoplanet, mirror, adaptive-optics
> **Comments:**
> **username_1**: I'm not sure that you have the same understanding of "scatter" as how it's used in optics. Scattering is when there are rays going different directions from the same point, but I get the impression that you are using it to mean different directions from different points.  
> **username_0**: @Acccumulation Yes you are correct if you are discussing a single photon. If you are describing a wavefront, then scattering is still appropriate.  Since I mixed the two together without a clear distinction, I updated my question.  
> **username_2**: (1) If you look at any mirrors at home, you may find litter diffuse reflections -- that said, mirrors are highly specular, not to mention crafted high-performance deformable mirrors for adaptive optics. (2) The AO diagram shown at 45 deg is for visualization purposes -- in reality the incoming beam is impinging almost perpendicular to the deformable mirror, and this makes the mirror more specular. Given (1)(2), I do not think your statements hold.  
> **username_0**: @WDC To address both of your points, 1) yes it is a mirror so it is specular (it will reflect at the same angle from the normal); however, since it is deformable, the normal changes meaning that the wavefront will diffuse.  2) it doesn't matter if it is at a 45 degree or normal to the mirror, if the localized normal is not consistent, then it will cause diffuse reflection.  Also, you said it is "more specular", yes I agree that the majority of the wavefront will have the same refection, but diffuse reflection will occur because of the deformable mirror, so how do they minimize it?  
> **username_2**: @Josh Okay I understand the issue here. Please see my answer.  

---

## 1 answers

### Answer by username_2 on 2020-11-26. Score: 1 | Accepted answer

Given your reply it seems your definition of diffusion is slightly different from my sense. But the phenomenon is true that at segmentation locations wavefronts are being deflected not in a uniform manner, causing the diffusion issue posted in this question.

Before addressing this issue, let me briefly describe how adaptive optics works in practice. In a typical AO system, a wavefront sensor measures the incoming wavefront distortion (usually it's slopes), given which a deformable mirror corrects for. The deformable mirrors consist of multiple actuators, which enable the mirror deformation. These actuators are controlled by commands.

The input/output are:

* Input: wavefront slopes $\mathbf{y}$
* Output: actuator control commands $\mathbf{x}$

These two are usually related through a so-called interaction matrix $\mathbf{A}$:
$$
\mathbf{y} = \mathbf{Ax}
$$
This matrix models all system artifacts, including the diffusion issue in this question. Since we would like to solve $\mathbf{x}$ from $\mathbf{y}$, we would also like the pesudo-inverse of $\mathbf{A}$, denoted as $\mathbf{A}^{-1}$, so in real-time the AO system can solve the actual commands as:
$$
\mathbf{x} = \mathbf{A}^{-1} \mathbf{y}
$$
$\mathbf{A}$ and $\mathbf{A}^{-1}$ are usually calibrated before running the AO system.

Now consider this question:

* Yes, there are diffusion reflection from the mirror. But this issue contributes in part to the interaction matrix $\mathbf{A}$. As long as people calibrate it carefully it does not really affect AO performance.
* For normal AO systems both measurement and correction wavefront lateral resolutions are low: typically at thousands of measurements, i.e. $\mathbf{x}\in\mathbb{R}^{1000}$ or so. In such a situation, I would conjure that the diffusion reflection at segmentation locations is not significant enough compared to the overall sub-mirror reflection, i.e. the fill factor of the sub-mirror is high enough to ignore this effect.


---

