MOSFIRE Exposure Time Calculator - Details

Signal
For a source flux fλ in erg s-1 cm-2 Å the following equation is used used to produce a value of counts per resolution element:

fλ(λ) Astop(band) texp dλ(band) η(λ) (h c)-1 λ

where the quantities are as follows:

• fλ(λ) - Spectrum of object or sky. Sky emission is estimated with the Gemini Observatory IR Sky Background spectra assuming a 3.0 mm water vapor column. The K-band emissivity of telescope in the Gemini model is probably incorrect.
• Astop(band) - Area of the stop. In the Y, J, and H bands the area is that of Keck's: 76 m2. In K and Ks a Lyot stop is used to block stray thermal radiation and the stop area is an effective 72.2 m2 (unverified).
• texp - Exposure time specified by the user.
• dλ(band) - Size of the resolution element in Å. For a diffraction grating in order m and with a ruling pitch d using a camera with focal length f subtending Nspec pixels of pitch p the following equation holds:
dλ = d m-1 p Nspec f-1 = 6.516 [Å] m-1 Nspec.
where m is 6, 5, 4, or 3 in Y, J, H, or K respectively (see MODN06 and DDR) and Nspec is specified by the slit width. Formally the anamorphic magnificaiton changes across the spectrum and field by up to 10%, with a corresponding error in the total counts.
• η(λ) - Efficiency of MOSFIRE including atmospheric transmission, slit loss, glass (windows, collimator, filter, and camera: 70%), grating (65%), and detector quantum efficiency (85%). Typical end-to-end value is around 30%.
• h c - Planck Constant x Speed of light.
• G - Note that the gain measured at PSR is 2.21 e-/DN.

Note that slit loss is calculated assuming a Gaussian seeing profile so that for a seeing value of FWHM the loss is: 1-erf(1.665 slit width/FWHM) in appropriate units. For typical seeing of 0.75" and slit width of 0.7" (2.9 pix) the loss is about 3% (seems LOW, CHECK!).

Noise
The detected noise is estimated assuming counting statistics for the source object and sky. A square-root-of-two penalty is applied assuming that the image is subtracted from itself as is the case with A-B subtraction.

The detector noise was measured and reported in the PSR. Read noise is estimated assuming a Fowler 16 readout and is measured to be 4.9 e- per pixel. The dark current is 0.008 e-/s/pix and again counting statistics are applied to the dark current. Note that for the dark-current noise to equal the read noise an integration time of 50 minute is required.

Noise calculations often require the number of extraction pixels (Npix). The number of pixels is equal to the width of the resolution element described above (Nspec) times the number of extraction pixels (Nsptial) which we estimate as 2/3 x (seeing FWHM) where the spatial pixel scale is 0.18" per pixel. For typical seeing of 0.7" and slitwidth this amounts to: Nspec=2.9 and Nspatial=2.6. The number of extracted pixels is typically Npix=8.

Thus, after converting the signal from erg to DN, the total noise is estimated as follows:

noise = (2 source DN + 2 sky DN + (RN2 Npix) + (DC Npix texp))1/2
Systematics
Systematics will dominate the faint reach (and ultra high SNR) capabilities of MOSFIRE, because it is hard to simulate these, they are not included in this simple simulator. Depending on your application the following sources of systematic uncertainty may limit your performance:
• Detector charge persistence. See PSR.
• Flexure, which should be small with the flexure compensation system.
• Scattered light, which requires on-sky time to determine.
• Detector nonlinearity is not included; however, I do indicate when an observation is near the non-linearity limit.
• Flat fielding.
Bibliography
PSR : Pre ship review report.