15.11.99 Completed version 1 of exposure time calculator. Calculates S/N at a given wavelength for point source or extended objects. Input object brightness can either be broad band (J or H) or flux at given wavelength value. If input is broad band magnitude the source spectral energy distribution is assumed to be flat.
Updates required:
Ability to input spectral energy distribution, and flux at any wavelength
or magnitude in any filter. Program will then calculate object flux at
required wavelength.
Extinction corrections
The area of a lenslet is given by
(3*sqrt(3)/2)*(fd/2)2/2 where fd is
the fibre diameter.
This is because the lenslet is hexagonal. Each
of the 6 equilateral triangles making up the hexagon has an area of
(fd/2)2*sqrt(3)/4.
Suppressor and/or window temperature (C) |
Emissivity | Filter near detector | Filter in wheel | Accessible wv range (microns) |
Detected thermal background (e/s/pix) |
4 | 1 | Filter 1 | none | 0.85-1.80 | 142.8 |
-37.7 | 1 | Filter 1 | none | 0.85-1.80 | 0.82 |
-45.5 | 0.2 | Filter 1 | none | 0.85-1.80 | 0.05 |
4 | 1 | Filter 1 | Filter 3 | 0.85-1.65 | 10.1 |
-37.7 | 1 | Filter 1 | Filter 3 | 0.85-1.65 | 0.05 |
4 | 1 | Filter 1 | Filter 2 | 0.85-1.35 | 0.11 |
-4.4 | 1 | Filter 1 | Filter 2 | 0.85-1.35 | 0.05 |
If the object brightness is specified as a broad band magnitude
(mag for point sources or mag/arcsec2 for extended sources),
then the following calculations are carried out to give object photons/s/pixel
(total number for a point source and per fibre for an extended source).
phot=fzero*10(mag/-2.5) J/s/m2/micron
phot=phot*telarea*disp*thru J/s or J/s/arcsec2
penergy=h*c/refwv J (penergy is the energy of a photon at the reference wavelength)
phot=phot/penergy photons/s or photons/s/arcsec2
(if extended source phot=phot*fibarea photons/s)
phot=phot/2 photons/s/pixel
The values of fzero used are:
J: 3.2064E-9 W/m2/micron
H: 1.0799E-9 W/m2/micron
Note that at the moment the SED is assumed to be flat. Also the wavelength at which the S/N is calculated does not have to be in the filter bandpass used to specify the object magnitude.
If the object brightness is specified as a flux at the reference wavelength
(W/m2/A for point source and W/m2/A/arcsec2 for an extended source)
then the following calculations are carried out to give object photons/s
(total number for a point source and per lens for an extended source).
phot=phot*1E4 W/cm2/cm
phot=phot*telarea*disp*thru W
penergy=h*c/refwv J (penergy is the energy of a photon at the reference wavelength)
phot=phot/penergy photons/s
phot=phot/2 photons/s/pixel
The final /2 in each of these cases is because the light from each lens is assumed to fall on two pixels in the spatial direction.
For the S/N calculation the flux per lens is required. The above gives the flux per lens for extended objects, but the total flux for point sources.
To calculate the flux per lens for point sources, it is assumed that the object brightness profile is Gaussian with a FWHM given by the specified seeing. The ETC assumes that the point source is centred at the middle of a lenslet, so that the amount of light in each of the lenslets surrounding the central lens is radially symmetric. The fraction of light from the source going down each lens (assuming the source has a Gaussian profile and approximating the lenses by circles) is calculated. The ETC calculates the S/N both in the central lenslet and then from summing all the lenses within each ring, out to the ring at which the distance from the central lenslet is > 5sigma.
For each type of object the inputs to the S/N calculation are