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The past few months I have been studying astronomy and Integral Field Spectroscopy (IFS). What I want to do is to fit a galaxy kinematic model to data (ie: estimate the model parameters that give the best fit result). At the moment I extract the velocity and velocity dispersion maps from an IFS datacube but I am not sure how to deal with the Point Spread Function (PSF).

  • What is more correct:
    • Deconvolve the data with the PSF and then fit the model to the deconvolved data?
    • Or convolve the model with the PSF and then fit the PSF-convolved model to the data?
    • The first approach sounds computationally faster to me because only one deconvolution is involved, but at the same time it won't give the best result because deconvolution is ill-posed even if the PSF is known. Is that right? The second solution sounds computationally slower because I will have to convolve the PSF with the model for every single model evaluation, but it will give better results because the convolution result/solution is well defined. Is that right?
  • The data sources I use for my experiments are products of some data reduction pipeline. Why the deconvolution of the PSF is not part of the data-reduction step? Is it because of what I mentioned above? ie: The deconvolution is an ill-posed procedure and it may affect (in a bad way) the data.
  • I am not very familiar with the deconvolution procedure but so far I have found that the Richardson-Lucy technique is a method for deconvolving with a known PSF. Are there other better techniques that are proven to give better results?
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Without having had to deal with that problem myself, I'd say that the second solution sounds better. Whenever the word "deconvolution" comes up, some warning signal in me goes off. Also, how much of a gain would it give in computational time, compared to the possible errors and uncertainties it could introduce in your work? I mean, if it was something you had to run many times over as part of some pipeline or something, speed could be essential.

Also, a PSF is not a simple function. People at our department spent a lot of dheir time doing PSF fitting. Here is, as an example, the PSF of the HST before the correctional optics was inserted:

enter image description here

(Taken from the PSF Wikpedia entry). So, a "known" PSF means a model of a certain fidelity level, not the exact function, which means I'd be extra cautious about the deconvolution part. This is probably also the reason why they don't do deconvolution as part of their pipeline: it is model dependent and would in the end degrade the data quality.

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Thank you very much for the reply my friend. I want to ask something related to your answer though. Yes, PSF is not a simple function but can't you get it by just pointing the telescope to a single light source at the sky? ie a star. This will give you a gaussian-like blob, and then you can use that as your PSF. I am totally wrong? I guess I will add a new question just for this but I would be more than grateful if you could comment on that. –  AstrOne Jun 9 '13 at 4:25
The PSF is generally much more complicated than a single Gaussian. Added an example image to my answer. As to whether you can simply model it the same way you would with the sky background, the answer is again "it's unfortunately not that simple", but let's keep the detailed discussion of this to a separate question. –  Thriveth Jun 9 '13 at 11:33
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