<p>The method of doing this is called <a href="https://en.wikipedia.org/wiki/Deconvolution" rel="nofollow">Deconvolution</a>. <strong>In theory</strong>, yes, it's possible if you know the exact distortion function, and an exact result image - but, <strong>in reality</strong>, the image you have is not exact, so the result of deconvolution may not be very useful.</p>

CC BY-SA 3.0
2014-08-02T10:33:56.380Z
2014-09-02T01:47:51.857Z
2014-09-02T01:47:51.857Z
Volker Siegel
<p>That would be possible theoretically. However, in practice, the lensed images are highly non-linearly distorted and due to the limits in resolution, they are often limited to a thickness of a few pixels at best. Due to the non-linear transformations, this would cause the reconstructed original image to be even blurrier.</p>

<p>Having said that, I don't see any real need of reconstructing the original image. You can get most parameters (like a rough estimate of the size and type of the background galaxy) from the distorted image anyway.</p>

CC BY-SA 3.0
2014-08-19T16:04:54.793Z
"That would be possible theoretically." - can you prove it/give a reference? Or in other words, given a well resolved image of gravitationally lensed object, how would one go about reconstructing the original?
Alexey Bobrick
CC BY-SA 3.0
2014-08-22T09:30:15.577Z
Knowing mass and position of the lensing galaxy, you can map (numerically, at least, if not analytically) each point in the distorted image back to a point on the 'true' background image (using the GR formalism of lensing; for example - https://en.wikipedia.org/wiki/Gravitational_lensing_formalism). I don't get why doing that would be very difficult at all, in theory. In practice, it will be difficult, yes.
Takku
CC BY-SA 3.0
2014-08-22T13:06:56.897Z
1) You might not know the lens mass distribution (would it all still be possible?), 2) Even on the famous Hubble photo you see that one same object may give two images.
Alexey Bobrick
CC BY-SA 3.0
2014-08-22T19:37:23.917Z
The question states 'using known parameters of mass and position of the lensing galaxy', so I would assume the mass distribution is also known. And one object giving two/multiple images is fine, because there won't be another point on the source which will generate the image(s) at the same location(s).
Takku
CC BY-SA 3.0
2014-08-24T12:49:11.177Z
Agreed with 1), but not yet with 2). Consider a continuous background image like CMB. How would that be not a problem?
Alexey Bobrick
CC BY-SA 3.0
2014-08-02T07:18:02.100Z
2014-08-02T07:18:02.100Z
Takku
<p>There's been another report of <a href="http://hubblesite.org/newscenter/archive/releases/2014/33/full/">gravitational lensing</a> in the news.  <a href="http://en.wikipedia.org/wiki/Gravitational_lens#mediaviewer/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG">Wikipedia</a> has a good image of an example of gravitational lensing taken by the Hubble Space Telescope.  This brings me to wonder that, since they understand the math behind the lensing, shouldn't they be able to reconstitute the original image of the galaxy <em>behind</em> the galaxy that is acting as a lens?  That is, take the image and run it through a computer program that reconstructs the image using known parameters of the mass and the position of the lensing galaxy?</p>

<gravitational-lensing>
With gravitational lensing, is it possible to mathematically compute the correct image of the galaxy that is being distorted?
Kevin Holmes
# With gravitational lensing, is it possible to mathematically compute the correct image of the galaxy that is being distorted?

(Asked by: username_0 on 2014-08-02)

There's been another report of [gravitational lensing](http://hubblesite.org/newscenter/archive/releases/2014/33/full/) in the news. [Wikipedia](http://en.wikipedia.org/wiki/Gravitational_lens#mediaviewer/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG) has a good image of an example of gravitational lensing taken by the Hubble Space Telescope. This brings me to wonder that, since they understand the math behind the lensing, shouldn't they be able to reconstitute the original image of the galaxy *behind* the galaxy that is acting as a lens? That is, take the image and run it through a computer program that reconstructs the image using known parameters of the mass and the position of the lensing galaxy?

**Tags:** gravitational-lensing

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## 2 answers

### Answer by username_2 on 2014-08-02. Score: 6 | Accepted answer

That would be possible theoretically. However, in practice, the lensed images are highly non-linearly distorted and due to the limits in resolution, they are often limited to a thickness of a few pixels at best. Due to the non-linear transformations, this would cause the reconstructed original image to be even blurrier.

Having said that, I don't see any real need of reconstructing the original image. You can get most parameters (like a rough estimate of the size and type of the background galaxy) from the distorted image anyway.

> **Comments:**
> **username_3**: "That would be possible theoretically." - can you prove it/give a reference? Or in other words, given a well resolved image of gravitationally lensed object, how would one go about reconstructing the original?  
> **username_2**: Knowing mass and position of the lensing galaxy, you can map (numerically, at least, if not analytically) each point in the distorted image back to a point on the 'true' background image (using the GR formalism of lensing; for example - https://en.wikipedia.org/wiki/Gravitational_lensing_formalism). I don't get why doing that would be very difficult at all, in theory. In practice, it will be difficult, yes.  
> **username_3**: 1) You might not know the lens mass distribution (would it all still be possible?), 2) Even on the famous Hubble photo you see that one same object may give two images.  
> **username_2**: The question states 'using known parameters of mass and position of the lensing galaxy', so I would assume the mass distribution is also known. And one object giving two/multiple images is fine, because there won't be another point on the source which will generate the image(s) at the same location(s).  
> **username_3**: Agreed with 1), but not yet with 2). Consider a continuous background image like CMB. How would that be not a problem?  

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### Answer by username_1 on 2014-08-02. Score: 4

The method of doing this is called [Deconvolution](https://en.wikipedia.org/wiki/Deconvolution). **In theory**, yes, it's possible if you know the exact distortion function, and an exact result image - but, **in reality**, the image you have is not exact, so the result of deconvolution may not be very useful.


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