Below are curves showing SNR vs. wavelength for WFOS configurations, R=1500 and R=3500, for m(AB)=16, m(AB)=21, and m(AB)=24 for 3600 second integrations. To scale the tabulated SNR to other apparent mag levels and integration times:
1) m<20 : objects significantly brighter than the sky background for a typical slit width
- SNR(m,t) = SNR(16,3600) * 10^[(16-m)/5] * [t/3600]^0.5 (i.e., SNR scales as the square root of both object brightness and integration time)
2) m~21 (objects and background comparable)
- SNR(t) ~ SNR(3600) * [t/3600]^0.5
3) m>22 (background-limited)
- SNR(m,t) = SNR(24,3600) * 10^[(24-m)/2.5] * [t/3600]^0.5 (i.e., SNR scales directly with object brightness, since noise is dominated by backgroung contribution.
For the red channel, there are two different curves, one showing a spline fit to the SNR curves that excludes the night sky emission lines, tracing the sensitivity between the OH lines, the other curve is the full resolution SNR spectrum showing the impacts of the strongest OH lines. For the blue channel, only the spline fit is shown as the night sky emission lines have a very small impact.
Curves are generated with the following assumptions:
1) R1500 assumes the B1210 and R680 VPH gratings on blue and red channel, respectively, with fixed camera angles that place the maximum diffraction efficiency at the center of the spectral range.
2) R3500 assumes the B2479 VPH grating (blue) and R1520 VPH grating (red), which have similar peak efficiency as the currently planned VBG gratings, but fall off more rapidly away from the peak. The throughput curves were generated by combining 4 different angle of incidence for each channel, and using the maximum diffraction efficiency achieved at each wavelength.
3) The reflectivity of the telescope optics assumes a UV enhanced coating and makes reasonable assumptions about performance shortward of 3400 A. The currently baselined Gemini-type coating would significantly degrade the performance below 4000 A compared to the assumed coating, and would be close to zero by 3400 A. However, telescope optics coatings with enhanced UV performance are being explored, it is quite probable that an enhanced coating could be available for the time of TMT First Light and WFOS is designed to operate up to the UV atmospheric cutoff at ~3100 A.
4) Slits are assumed to be 0.75". Seeing 0.65". Targets are point sources with extraction aperture of 1" along the slit; these assumptions lead
to a 23% slit loss that is included in all of the SNR calculations.
5) The sky spectrum assumes no significant moonlight.
