Deconvolution of Spectra for Near-Infrared Astronomical Instruments

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Long slit spectroscopy in the near-infrared range (0.950 to 2.2 microns) faces challenges due to the convolution of steep spectral features with the line spread function (LSF), which varies with wavelength. The LSF, represented by a sinc function, causes rapid flux variations to appear less steep in the observed spectrum. Deconvolution methods may help to partially correct these effects, but the specifics of effective techniques are not detailed. The discussion seeks recommendations for deconvolution approaches suitable for this context. Additional visual aids may be provided for clarity if needed.
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Hi,

I am working on long slit spectroscopy for an astronomical instrument, and I think I need deconvolution, but I am not sure, so maybe you will be able to answer me :) Currently those are only simulations. I work in near-infrared (0.950 -> 2.2 micron) with a low resolution (R=30).

My problem is that the spectrum I am supposed to observe can be very steep (ie I can have a quick flux variation between \lambda and \lambda+\delta\lambda), but when I watch them through my instrument, this spectrum is convolved with the slit LSF (line spread function), which is a sinc function (sinc(x)=sin(\pi x)/\pi x). Of course the width of the LSF varies acording to wavelength, and then is much larger at 0.95 micron than at 2.2 micron. And when I observe a steep change in the spectrum through the spectrograph, the change is much less steeper because it has been convolved with the LSF which is less steeper.

Are there some deconvolution methods that can correct, at least partialy what I describe?

I hpe what I say is making sense. If it's not I can post some picture to illustrate this. Thanks a lot in advance.

-- Arthur;
 
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Deconvolution. With applications in spectroscopy, PA Jansson - New York: Academic Press, 1984, edited by Jansson, Peter A., 1984

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