Exposure Time Calculator - Details
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:
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
Sky Background spectra assuming a 3.0 mm water vapor column.
The K-band emissivity of telescope in the Gemini model is probably
- 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
- 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
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!).
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
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 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
- 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.
PSR : Pre ship review report.