Calculating Optimal SNR (PSF-Fitting)
The Optimal SNR is an estimate of the SNR when photometric information is extracted using a PSF fitting algorithm. Another use of the Optimal SNR is to allow direct quantitative comparison between instruments with different scales (i.e. arc seconds per pixel). The formulas used in this calculation are based upon Heyer, Biretta, 2005, WFPC2 Instrument Handbook, Version 9.1, see also Keith Horne, PASP, 1986, 98, 609. This formula uses the PSF sharpness, which is effectively the reciprocal of the number of pixels contributing background noise. For calculating the sharpness, we have considered the conservative case in which the point source is centered in the corner of a pixel. Note that this may be the cause of some apparent discrepancies when comparing with standard SNR-t calculations for the brightest pixel (which assume the conservative case of the object being centered on the pixel).
Where:
OSNR = Optimal Signal To Nosie Ratio
Sc = Total Source counts
RN = Read Noise
BGc = Background counts
Sharpness = sum of i,j (PSF(i,j)^2)
where:
Sr = Source count rate
T = Exposure Time
where:
BGc = Total Background counts/pixel
Skyc = Sky counts (Earth Shine + Zodiacal Light + Geocornal Emission Lines)
DCc = Dark Current counts
(Thermalc) = (Optional) Thermal Background counts
(CSc) = (Optional) Coronagraphic Source