Alignment of SA grating

George,

This could quickly devolve into an argument about the meaning of words.  So off the bat I want to be clear that depending on how you define "best" can be literally correct that the "best" results are obtained by aligning your CCD and your grating.  If "best" is defined as closest to ideally perfect in a simply stated way, that statement is factual.

However in this case the difference between ideally perfect and any other random orientation is not "significant."  Where "significant" is defined as anything that will have a noticeable effect on your results.

For some people the calculation in deciding what is "best" might also include amount of frustrating effort to obtain a legitimate result.  In this case the definition of "best" that relies on perfection directly conflicts with the definition of "best" that considers effort vs return on investment.

My bona fides for answering this question are three years as a post-doc for a project involving the HST/STIS spectrograph.  The spectrum for that instrument has far more spatial resolution on the cross-dispersion axis than any ground-based instrument.  But it had not been used to its full potential when we started the Treasury project I worked on.  The spectrum for the STIS does not align with the columns or rows on the CCD.  It turns out that as long as you are not completely boneheaded about the way you extract a one dimensional spectrum in that situation, that you do not loose that much information by putting the spectrum at an angle with respect to the CCD axes.  

So you can extract information from a spectrum in a simple straight forward way without loosing a significant amount of information without regard for if it is aligned with the CCD axes or not.  I have done the experiments to prove it.  If you knew everything to an infinite precision there would be a detectable difference between a spectrum aligned with the axes and misalignment.  However the noise in the CCD and other factors mean that you will never know your system to enough precision for that to make an appreciable difference.

The one exception to this is if your CCD axes is almost aligned with the spectrum, but not quite.  In this case you can be screwed.  Because of the way the cross-dispersion PSF is pixilated by the size of the pixels you a spectrum that has a very slight mis-orientation will be harder to extract via a simple method than one where the misalignment is more than a few degrees.  The lesson in that is you probably will end up screwing yourself if you attempt to align your CCD axes with your grating and not quite succeeding.  It is far better just to "drop it in" because the chance that you randomly align your grating in a way that screws you is much lower than if you are attempting to align it to start with and you end up just a little off.  The technical memos I give the link to below adress this in a robust way, especially this one:  http://etacar.umn.edu/treasury/techmemos/pdf/tmemo001.pdf

This doesn't really apply to what most of us will do, but the project I worked on went well beyond the simple approach for extraction we are talking about.  You actually gain more information when the spectrum and CCD axes are misaligned if you have an algorithm that takes advantage of the misalignment.  The reason for that is the same reason that we can get increased resolution in a digital image by dithering it over the pixels.  The human eye does this automatically to achieve better resolution than it could from a non-dithered image.  Misaligning the spectrum and the CCD axes dithers the cross-dispersion PSF over the pixels and can be used to increase the information you get out of the spectrum.

But I digress.  To get more information out you need immaculate focus and detailed knowledge of your setup.  Most of us are never going to break out that sledge hammer to extract our spectrum when a simpler approach will work perfectly fine.  If you want more information about it the documents Kris Davidson and I produced with respect to this are available online:

http://etacar.umn.edu/treasury/techmemos/

So to sum it up.  You can drop the grating in at any angle.  In fact I recommend it.  You might end up inadvertently creating a worse situation by attempting to align it and just missing.  Also most of us rather spend time observing than endlessly fiddling with the alignment of our grating in a system that is not completely fixed and stable to change.

If you do decide to run your spectrum diagonally check if you derotate that the software algorithms you use does not produce artifacts (some image processing programs are not good at this) You will soon know though when you take your first spectrum of a hot star  eg Vega if you have a problem you need to address as there will be artifacts, typically ripples in what should be a   smooth continuum. 

Good  programs make such geometric corrections as part of the data reduction with minimal risk of artifacts. For example I do not have any problems even with small angles when using IRIS or ISIS with monochrome cameras, though I know of undersampled systems (eg small aperture fast refractors) which have had problems where the star image is smaller than the pixel size. (problems of this sort with such systems are not unique to spectroscopy though)

Colour camera are a different matter though. Artifacts due to uneven sampling of pixels can be severe with colour cameras where only 25% of the area (1 in 4 pixels) is sensitive in the red and blue regions. These are therefore best avoided but if you want to use them the solution is to align and stack multiple images allowing tracking errors or deliberate dithering to smooth out the pixel coverage. An example of this sort of problem is covered on my webpage on using DSLR here.

http://www.threehillsobservatory.co.uk/astro/spectroscopy_11a.htm

Robin

I should preface everything I said with one more detail.

A lot of this depends on how well your CCD samples the point-spread-function for your optical system.   Most of you are optimized for good photometry.  This is good because if you are optimized to spread your point-spread-function over at least 3 to 5 pixels then everything I said applies.

If you are over-sampled for your point-spread function, even better for a spectrum not aligned with the CCD axes. It is easier and closer to "perfect" to extract a misaligned spectrum if you are over-sampled.

The caveat comes in if your point-spread-function is under-sampled.  This is where pixelation and being close but not quite on your alignment can really hurt you.  When you are under-sampled and the CCD axes are not aligned with the spectrum you are more likely to end up with a nasty "saw tooth" shape in your extraction.  Everything I said assumed that because most of you are optimized for photometry, that this will not be the case for your system.  But beware if it is, because in that case you may be better off trying to align the spectrum with the CCD axes... and it will be easier to do it because the pixels are huge relative to your PSF.

Here are two documents with examples of the  data quality using standard stars that I generate from my Star Analyser and ALPY 600 systems and reduced using ISIS software  The spectra here were approximately but not exactly horizontal (actually taken to demonstrate correcting for instrument response, the effect of atmospheric extinction and a typical problem encountered when using  achromatic telescope optics for slit spectroscopy)

http://www.threehillsobservatory.co.uk/astro/spectroscopy_21.htm

I have also in the past made similar comparisons against standard spectra for my high resolution LHIRES spectrograph

I can recommend this exercise to anyone wanting to  test their setup as it gives confidence that the data being produced is of good quality or flags up any potential issues. 

Robin