BOSS line spread function and sinc interpolation

[andycasey]

The sinc interpolation (for resampling) needs a bandwidth: the number of pixels per resolution element. I calculated this value once, from one spectrum, averaged across all wavelengths. But it turns out that the resolution in BOSS varies significantly as a function of wavelength, and as a function of fibre.

The line spread function is stored in each specFull function at every pixel, so the number of pixels per resolution element can be used directly from this, and account for resolution differences as a function of wavelength and fibre.

The sinc interpolation function in Astra would need to be updated to allow an array of bandwidth values (instead of a single value), and some tests would need to be done to ensure this is a better thing to do.

[andycasey]

A useful test from here: https://groups.google.com/g/sci.astro.research/c/vysbZFcZs6Q

My experience with sinc interpolation concerns its use for one dimensional
spectra and that is what my comments address. I don't have the specific
reference but the discussion of the advantages of sinc interpolation for
spectra that I read was, I believe, in a PASP article by authors from
Lick Obs. For my purposes, and what I recall the paper stressed, is
that the advantage of sinc interpolation is if one shifts (interpolates
to a new origin) a spectrum by some partial pixel amount, possibly
one or more times, and then reverses the shifts then one will recover
the identical spectrum. I did find this to be true, the residuals between
the original spectrum and shifting and shifting back using sinc interpolation
were at least 10x smaller than using some other interpolation such
as a low order polynomial.

This seemed like a very good property for spectral resampling and I
intended to make it the default in the IRAF spectral software. Then
I and users tried real data. The problem with sinc intepolation is that
if the data has any sharp features, meaning cosmic rays, the sinc
interpolation rings badly and clobbers a large part of the spectrum
(since the sinc function must be carried out quite a ways to approximate
the infinite extent of the function). Polynomial interpolators, say
a cubic or quintic, will only ring within a few pixels of the cosmic
ray. This data destroying feature is the main reason I don't recommend
this type of interpolation though one has the choice of using it if
you know the data is well-behaved.