<p>The problem with your approach is that the deformable mirror changes the <strong>phase</strong> of the light across the mirror, where the light is not focussed.  The light at the sensor array is focussed, and what you get is the <strong>intensity</strong> which is, roughly, the Fourier Transform of the phase front at the mirror.   By the time you have intensity, the phase information has been lost.  </p>

<h2>edit for clarity:</h2>

<p>The sensor array <em>measures</em> the intensity, at which point the phase info is irretrievable.  If you remove the sensor array and re-measure past the focal plane, yes, you can get phase info -- see <a href="https://en.wikipedia.org/wiki/Light-field_camera" rel="nofollow noreferrer">"Plenoptic cameras."</a>  </p>

<p>Now, there are other techniques -- you might be interested in searching for papers on <a href="https://en.wikipedia.org/wiki/Lucky_imaging" rel="nofollow noreferrer">"Lucky Imaging"</a> , which basically takes as many images as possible and throws away the distorted ones. </p>

CC BY-SA 4.0
2019-07-03T18:19:25.710Z
That's right. What each pixel sees is basically an integral over time (the duration of the exposure). Some information is lost. When observing in a vacuum, that would not matter. But it's precisely the information that's lost through integration that would matter if you try to reconstruct the original from a distorted image.
Florin Andrei
CC BY-SA 4.0
2019-07-04T07:58:32.820Z
This is misleading if not wrong; see [this answer](https://astronomy.stackexchange.com/a/32530/7982)
uhoh
CC BY-SA 4.0
2019-07-03T15:29:58.423Z
2019-07-04T13:01:02.333Z
2019-07-04T13:01:02.333Z
Carl Witthoft
<p>Each part of the mirror contributes to every pixel in the image, and the pockets of atmospheric distortion may be only 10-20 cm wide.
If you look at a bright planet through a 30+ cm telescope in poor seeing conditions, the image looks like a stack of several sub-images shifting in and out of alignment, each from a different part of the mirror.
To oversimplify, adaptive optics systems continually tweak the mirror segments to keep those sub-images aligned.</p>

<p>If you can accept a much higher detector cost in exchange for eliminating the actuator cost, it's possible to make an array of small telescopes, each with its own video camera, and align the shifting sub-images in software.
But then diffraction by the smaller apertures would limit the system resolution unless you built an optical interferometer, which has its own category of difficulties to overcome.</p>

CC BY-SA 4.0
2019-07-03T19:16:39.447Z
2019-07-03T19:16:39.447Z
Mike G
<p><a href="https://astronomy.stackexchange.com/a/32527/7982">@CarlWitthoft's answer</a> is misleading if not wrong.</p>

<p>The Fourier transform of a field does not lose phase information. If you let the light drift another focal length and then use an identical mirror, you completely recover the initial electric field distribution incident at the telescopes entrance aperture. Information is not lost here.</p>

<p>The problem is not related to the optics at all.</p>

<p>The problem is that the detector (silicon CCD or photographic plate or whatever) measures time-averaged intensity of the light, which is the <em>absolute value squared</em> of the field at the detector's surface. It's this <strong>squaring</strong> and <strong>averaging</strong> in conventional detection schemes that makes phase information unrecoverable.</p>

<p>There is a whole field of research into trying to make phase-sensitive pixels for cameras but it's pretty academic, and you lose significantly in resolution and other performance metrics when you try to do this.</p>

<h2>But what about longer wavelengths?</h2>

<p>Your idea <strong>can and indeed does work in radio astronomy</strong>, even for microwaves and millimeterwaves. This is because the electric field received by each pixel (which is one dish antenna of an array of them) can indeed be absolutely digitized. They down-convert frequencies as high as a THz to one or two GHz and then amplify and digitize it with extremely fast ADCs. </p>

<p>Once that is done, you can correct for distortions in the wavefront arriving at your array of antennas in software. This process is explained further in answers to <a href="https://astronomy.stackexchange.com/q/13930/7982">Would Adaptive Optics be Useful in Radio Astronomy?</a></p>

CC BY-SA 4.0
2019-07-04T12:58:30.797Z
The **image** loses phase info.  I'm aware of plenoptic cameras.
Carl Witthoft
CC BY-SA 4.0
2019-07-10T13:28:25.970Z
So, if you had a detector with an extremely high frame rate, this approach would be possible for visible light too, right?
speedplane
CC BY-SA 4.0
2019-07-10T13:43:34.377Z
@speedplane If "detector" means a photodetector, then no. Those always **square** and **average** the electric field. However, if "detector" means that you have an optical wavelength antenna that could receive the AC signal of the light and an optical-speed amplifier and ADC, or if you used a nonlinear crystal to downconvert to GHz, then you could digitize the AC signal and recover the phase.
uhoh
CC BY-SA 4.0
2019-07-04T07:57:56.907Z
2019-07-04T07:57:56.907Z
uhoh
<p>With enough computational power every pixel of a camera sensor could be processed individually. Outputs amplified or reduced to compensate for variations of light levels across the sensor. Stacking algorithms can discard those pixels that do not receive a constant input. </p>

<p>Photo shopping to the max. Make the Astro Photographers life easier. The problem for everyone else would be in deciding where science becomes art.</p>

CC BY-SA 4.0
2019-07-03T20:13:11.593Z
You're talking about generic image processing in astrophotography. The question was asked specifically about adaptive optics, which compensate for atmospheric turbulence - that is not a problem that can be solved in the digital domain. The amount of compute power is irrelevant, the phase information is simply missing at that level. See the other answers on this page.
Florin Andrei
CC BY-SA 4.0
2019-07-03T18:45:28.570Z
2019-07-03T18:45:28.570Z
L d Bonnie
<p>Adaptive optics generally apply slight changes to mirrors to account for atmospheric turbulence. These generally require either a mirror to be broken up into smaller mirrors, each with their own actuator, or for a single large mirror to be slightly deformed by many different actuators.</p>

<p>Is it possible to do much of this digitally? </p>

<p>Couldn't software slightly attenuate or amplify each pixel at each time-slice collected from a passive mirror? These changes would depend on the distortions measured by a guide star or laser (this digital system would still require a guiding light)? I suspect this would probably be less accurate than true adaptive optics, but it would also be far less expensive (as you wouldn't need so many actuators).</p>

<p>Has this approach been studied and dropped? Is it ridiculous and not even theoretically possible? I'm curious if anything has researched this idea.</p>

CC BY-SA 4.0
2019-07-03T12:56:21.427Z
Amplifying or attenuating the signal detected at a pixel does not reduce wavefront distortions induced by atmospheric turbulence.
amateurAstro
CC BY-SA 4.0
2019-07-04T17:41:49.307Z
Maybe most important is the calibration , because the noise of system(mirror quality, atmospheric conditions, latitud, longitud .altitud, diameter , etc )  in a long array system (multiples mirrors)  to adaptive system in each actuator with a mirror this is contrasted or compared with most optimal mirror is current time to adaptive every others mirrors, so when you use only one , you need a past or early most optimal image to contrasted to apply adaptive system, to work it you need apply a right train calibration.
Adrian R
<adaptive-optics>
Are digital adaptive optics possible?
speedplane
# Are digital adaptive optics possible?

(Asked by: username_0 on 2019-07-03)

Adaptive optics generally apply slight changes to mirrors to account for atmospheric turbulence. These generally require either a mirror to be broken up into smaller mirrors, each with their own actuator, or for a single large mirror to be slightly deformed by many different actuators.

Is it possible to do much of this digitally?

Couldn't software slightly attenuate or amplify each pixel at each time-slice collected from a passive mirror? These changes would depend on the distortions measured by a guide star or laser (this digital system would still require a guiding light)? I suspect this would probably be less accurate than true adaptive optics, but it would also be far less expensive (as you wouldn't need so many actuators).

Has this approach been studied and dropped? Is it ridiculous and not even theoretically possible? I'm curious if anything has researched this idea.

**Tags:** adaptive-optics
> **Comments:**
> **username_1**: Amplifying or attenuating the signal detected at a pixel does not reduce wavefront distortions induced by atmospheric turbulence.  
> **username_2**: Maybe most important is the calibration , because the noise of system(mirror quality, atmospheric conditions, latitud, longitud .altitud, diameter , etc )  in a long array system (multiples mirrors)  to adaptive system in each actuator with a mirror this is contrasted or compared with most optimal mirror is current time to adaptive every others mirrors, so when you use only one , you need a past or early most optimal image to contrasted to apply adaptive system, to work it you need apply a right train calibration.  

---

## 4 answers

### Answer by username_3 on 2019-07-03. Score: 6

The problem with your approach is that the deformable mirror changes the **phase** of the light across the mirror, where the light is not focussed. The light at the sensor array is focussed, and what you get is the **intensity** which is, roughly, the Fourier Transform of the phase front at the mirror. By the time you have intensity, the phase information has been lost.

## edit for clarity:

The sensor array *measures* the intensity, at which point the phase info is irretrievable. If you remove the sensor array and re-measure past the focal plane, yes, you can get phase info -- see ["Plenoptic cameras."](https://en.wikipedia.org/wiki/Light-field_camera)

Now, there are other techniques -- you might be interested in searching for papers on ["Lucky Imaging"](https://en.wikipedia.org/wiki/Lucky_imaging) , which basically takes as many images as possible and throws away the distorted ones.

> **Comments:**
> **username_4**: That's right. What each pixel sees is basically an integral over time (the duration of the exposure). Some information is lost. When observing in a vacuum, that would not matter. But it's precisely the information that's lost through integration that would matter if you try to reconstruct the original from a distorted image.  
> **username_5**: This is misleading if not wrong; see [this answer](https://astronomy.stackexchange.com/a/32530/7982)  

---

### Answer by username_6 on 2019-07-03. Score: 3

Each part of the mirror contributes to every pixel in the image, and the pockets of atmospheric distortion may be only 10-20 cm wide.
If you look at a bright planet through a 30+ cm telescope in poor seeing conditions, the image looks like a stack of several sub-images shifting in and out of alignment, each from a different part of the mirror.
To oversimplify, adaptive optics systems continually tweak the mirror segments to keep those sub-images aligned.

If you can accept a much higher detector cost in exchange for eliminating the actuator cost, it's possible to make an array of small telescopes, each with its own video camera, and align the shifting sub-images in software.
But then diffraction by the smaller apertures would limit the system resolution unless you built an optical interferometer, which has its own category of difficulties to overcome.


---

### Answer by username_5 on 2019-07-04. Score: 2

[@CarlWitthoft's answer](https://astronomy.stackexchange.com/a/32527/7982) is misleading if not wrong.

The Fourier transform of a field does not lose phase information. If you let the light drift another focal length and then use an identical mirror, you completely recover the initial electric field distribution incident at the telescopes entrance aperture. Information is not lost here.

The problem is not related to the optics at all.

The problem is that the detector (silicon CCD or photographic plate or whatever) measures time-averaged intensity of the light, which is the *absolute value squared* of the field at the detector's surface. It's this **squaring** and **averaging** in conventional detection schemes that makes phase information unrecoverable.

There is a whole field of research into trying to make phase-sensitive pixels for cameras but it's pretty academic, and you lose significantly in resolution and other performance metrics when you try to do this.

## But what about longer wavelengths?

Your idea **can and indeed does work in radio astronomy**, even for microwaves and millimeterwaves. This is because the electric field received by each pixel (which is one dish antenna of an array of them) can indeed be absolutely digitized. They down-convert frequencies as high as a THz to one or two GHz and then amplify and digitize it with extremely fast ADCs.

Once that is done, you can correct for distortions in the wavefront arriving at your array of antennas in software. This process is explained further in answers to [Would Adaptive Optics be Useful in Radio Astronomy?](https://astronomy.stackexchange.com/q/13930/7982)

> **Comments:**
> **username_3**: The **image** loses phase info.  I'm aware of plenoptic cameras.  
> **username_0**: So, if you had a detector with an extremely high frame rate, this approach would be possible for visible light too, right?  
> **username_5**: @speedplane If "detector" means a photodetector, then no. Those always **square** and **average** the electric field. However, if "detector" means that you have an optical wavelength antenna that could receive the AC signal of the light and an optical-speed amplifier and ADC, or if you used a nonlinear crystal to downconvert to GHz, then you could digitize the AC signal and recover the phase.  

---

### Answer by username_7 on 2019-07-03. Score: -2

With enough computational power every pixel of a camera sensor could be processed individually. Outputs amplified or reduced to compensate for variations of light levels across the sensor. Stacking algorithms can discard those pixels that do not receive a constant input.

Photo shopping to the max. Make the Astro Photographers life easier. The problem for everyone else would be in deciding where science becomes art.

> **Comments:**
> **username_4**: You're talking about generic image processing in astrophotography. The question was asked specifically about adaptive optics, which compensate for atmospheric turbulence - that is not a problem that can be solved in the digital domain. The amount of compute power is irrelevant, the phase information is simply missing at that level. See the other answers on this page.  

---

