Affiliation
American Association of Variable Star Observers (AAVSO)
Thu, 03/28/2024 - 05:41
I am trying to setup equipment so that I can submit my first spectrum. I am a little confused about resolving power. I know the formula is R=λ/Δλ. I need help in calculating this for my setup. I am using an SA100 and the dispersion for my setup is 13.91 ang/pix. How do I calculate Δλ? And what λ do I use?
Barbars
R is a dimensionless whole number that represents the ability of the spectrometer to resolve spectral features, which can vary somewhat from the blue to red end of the visible spectrum, so that's where the numerator of the equation comes into play.
To determine R, pick a spectral line somewhere near the center and in a featureless part of your spectrum, say 550 nm for your slitless set-up. Next, measure the full width at half maximum (FWHM) of a spectral line in the vicinity (if you can, do this for three or so lines in the vicinity and average them). If you're using RSpec, you will find a calculation of FWHM is provided, otherwise you can estimate it visually and get reasonably close. Divide the center wavelength by the FWHM, dropping the fractional part, and you now have R. For your set up, this should be around 100.
Scott
Note additionally that for this method to work, the line you measure the FWHM on must be intrinsically significantly narrower than the resolution of your spectrograph. This may not be the case for example for Balmer lines in main sequence stars which are very wide. For very low resolution setups like the Star Analyser I use P Cygni as a test target as that has narrow emission lines (relative to the typical Star Analyser resolution) see here for example when I was developing the SA200
http://www.threehillsobservatory.co.uk/astro/spectroscopy_16.htm
In general, measuring the resolving power of slitless systems like the Star Analyser reliably is particularly difficult, (unlike slit spectrographs where you can use the very narrow lines from the calibration lamp or in the sky spectrum) and it also depends on the seeing so varies between observations. An estimate can be made by measuring the FWHM of the zero order, (when brought to focus not with the focus adjusted for sharpest spectrum) The resolution in angstrom is then the zero order fwhm in pixels x the dispersion in Angstrom/pixel. This an upper estimate though and the true resolution, for example as measured on narrow lined stars, will be lower due to other aberrations in the simple star analyser setup.
Robin