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

There's been another report of gravitational lensing in the news. Wikipedia 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?

-

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.

-
"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 Aug 19 '14 at 16:04
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 - 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 Aug 22 '14 at 9:30
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 Aug 22 '14 at 13:06
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 Aug 22 '14 at 19:37
Agreed with 1), but not yet with 2). Consider a continuous background image like CMB. How would that be not a problem? – Alexey Bobrick Aug 24 '14 at 12:49

The method of doing this is called 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.

-