**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

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 |

Filter 2 is a J band filter.

Filter 3 is an H band filter.

If the object brightness is specified as a **broad band magnitude**
(mag for point sources or mag/arcsec^{2} 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/m^{2}/micron

phot=phot*telarea*disp*thru J/s or J/s/arcsec^{2}

penergy=h*c/refwv J (penergy is the energy of a photon at the reference wavelength)

phot=phot/penergy photons/s or photons/s/arcsec^{2}

(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/m^{2}/micron

H: 1.0799E-9 W/m^{2}/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/m^{2}/A for point source and W/m^{2}/A/arcsec^{2} 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/cm^{2}/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

- exposure time - time s
- object - O photons/s/pixel
- sky - S photons/s/pixel
- background - B photons/s/pixel
- dark - D photons/s/pixel
- readnoise - rn electrons

and the S/N per resolution element is:

Last modified: Mon Jan 17 16:59:26 2000