Exposure time calculator manual

Notes and Updates

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

Instructions

Reference wavelength

The S/N calculation is carried out at this wavelength. Currently this only changes the conversion from W -> photons/s. In the future it may effect the throughput, and the calculation of object flux from the SED.

Exposure time

This is the total exposure time. The HAWAII near-infrared arrays allow for non-destructive reads (NDRs) and the counts in each pixel of the array can be sampled several times during the total exposure time without resetting the array. This `sampling-up-the-ramp' technique enables cosmic-ray hits to be easily identified. However, the optimum S/N on background limited observations is achieved using double correlated sampling (DCS). This is where the initial read is subtracted from the final read to remove the background counts from each pixel. As the majority of CIRPASS observations will be background limited, the ETC assumes that DCS is used to calculate the final counts in each pixel and therefore only the total exposure time is required.

Telescope and Instrument parameters

Lenslet diameter

The CIRPASS IFU has 499 lenslets each of which is a hexagon. The scale of the lenslets can take several values - 0.36, 0.25, 0.12 and 0.05 arcsec/lenslet.

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.

Background parameters

Seeing

The seeing is assumed to be a Gaussian with the input FWHM.

Interline sky background

The default value of 590 photons/s/m2/micron/arcsec2 is that measured between the lines by Maihara et al 1993, PASP, 105, 940.

Thermal background

The thermal background depends upon the temperature of the instrument, the emissivity of the assumed black-body and which filters are in place. The calculated instrumental background for various scenarios is given in the table below.

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 1 is a blocking filter located close to the detector which cuts out radiation longer than 1.9 microns.
Filter 2 is a J band filter.
Filter 3 is an H band filter.

S/N calculations

Object brightness

The object can either be a point source or an extended source. The object brightness can be specified as either a magnitude in J or H or as a flux at the reference wavelength.

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.

Calculation

For each type of object the inputs to the S/N calculation are

It is assumed that the sampling technique used is double correlated sampling (DCS), that is, that the initial read is subtracted from the final read to produce the object counts and remove the background counts. The signal-to-noise per pixel after this subtraction is:
sn = sqrt[(O+B+S+D)*time + rn2] photons
and the S/N per resolution element is:
sqrt(nres)*sn
Last modified: Mon Jan 17 16:59:26 2000