How to calculate the S/N of IFU or long-slit galaxy observations I would like to calculate the Signal-to-Noise ratio (SNR) of long-slit or integral field unit (IFU) observations of H$\alpha$ emission. I can calculate the SNR or each individual spectrum, just fine. However, how can I assign a single SNR value to an observation? Do I just quote the higher SNR or do I calculate the median/mean SNR of all spectra? Is there a convention for this? My data is low-redshift galaxy IFU observations, and thus the SNR is higher in the center of the galaxy and lower at larger radii.
Unless you in fact find a "standard" definition for the mean or collective SNR, there is no way to answer this.  As you noted, the signal strength varies with view angle (as well as wavelength), so there's really no single value.  If you have a defined algorithm which processes all your spectral data to produce a final image or analysis value, then you can use standard statistical techniques to calculate the SNR of the output as a function of the SNR of all the contributing factors. (Here "factor" means each independent input variable, i.e. spectral line).  I recommend getting a copy of Bevington to learn how to do this.   Note- that appears to be a not-necessarily-legal-copy; you can purchase the real thing anywhere, e.g. amazon