This table summarizes the expected camera performance for a 10 sigma detection in a 1 hour exposure under 0.7 arcsecond seeing with 1.5 airmass. Those are AB instrumental magnitudes. These numbers are now based on standard star measurements done during the commissionning. Read the important note below if you observe an extended object or a field that requires a sky-target-sky observing strategy: these estimates then need to be offset to significantly brighter magnitudes.

Important note on sky subtraction and limiting magnitudes with WIRCam. If you need to use the nodding (sky-target-sky) observing strategy (i.e. if your target is larger than 10 arcmin) then your request should be for twice the output of the calculator, plus overheads. We urge you to read further. The quality of construction and subtraction of the sky frames strongly depends on your chosen observing strategy and target. The DIET estimates DO NOT take the sky subtraction into account. In the worst case scenario, if the constructed sky frames have the same SNR as the individual science frames, the limiting magnitude drops by a factor sqrt(2) or ~0.4 magnitudes compared to the DIET estimates. And remember that DIET's estimates is based on ON TARGET exposure times. So if you plan to use a sky-target-sky strategy, in addition to the DIET exposure time, your time proposal needs to typically double to account for the sky time. Sky-Target-Sky strategies spend typically half their time on the target such that another factor sqrt(2) is lost (for a given telescope allocation). So, if a sky-target-sky strategy has to be used and if only one image is used in the construction of the sky frame, then the limiting magnitude is ~0.8 magnitudes brighter that DIET's estimates. In a case where sky frames can be built from a larger set of science frames and the subtraction be applied to each individual science frame, then the DIET estimates do not need to be offset.

Caution! it was found by three different teams that the Vega to AB conversions were off by up to 0.2 mag in Ks. The numbers given here will need to be revised. Meanwhile, here are the numbers other teams are obtaining:

Emmanuel Bertin at Terapix:

 Y  Wircam: 0.583
 J  Wircam: 0.899
 H  Wircam: 1.335
 Ks Wircam: 1.802
 

Stephane Arnouts at CFHT:

 # FILTER	NAME    IDENT      Lbda_mean    Lbeff(Vega)       FWHM     AB-cor
 Y engineering	cfh8001.pb   1         0.9982         0.9945         0.1016   0.577
 Y		cfh8002.pb   2         1.0259         1.0221         0.1106   0.609
 J (in use)	cfh8101.pb   3         1.2545         1.2481         0.1588   0.924
 Low OH2 	cfh8102.pb   4         1.1892         1.1892         0.0113   0.836
 J (spare)	cfh8103.pb   5         1.2540         1.2478         0.1572   0.923
 Low OH1 	cfh8104.pb   6         1.0629         1.0628         0.0101   0.655
 H (in use)	cfh8201.pb   7         1.6310         1.6161         0.2910   1.352
 H (spare)	cfh8202.pb   8         1.6369         1.6222         0.2895   1.358
 CH4 On		cfh8203.pb   9         1.6919         1.6897         0.1062   1.418
 CH4 Off 	cfh8204.pb  10         1.5892         1.5875         0.0950   1.331
 Ks (spare)	cfh8301.pb  11         2.1519         2.1358         0.3280   1.826
 Ks (in use)	cfh8302.pb  12         2.1497         2.1338         0.3270   1.824
 K Cont		cfh8303.pb  13         2.2246         2.2244         0.0327   1.898
 H2		cfh8304.pb  14         2.1300         2.1298         0.0294   1.816
 Br Gamma	cfh8305.pb  15         2.1720         2.1720         0.0295   1.894
 

Mark Dickinson - COSMOS group:

 J 0.937
 H 1.365
 K 1.846
 

DIET's current computations are now based on actual on-sky measurements. The zero points have been determined and the sky median background has been measured over the full 2005B semester for all filters except LowOH2 and H continuum.

The interactive graphical interface allows the user to experiment with some custom parameters. This iterative process can be time consuming for a single set of parameters: it is recommended to use the keyword "Range" for both parameters "Seeing" and "Sky" to obtain small tables exploring the domain of input conditions.

The magnitude system in DIET for WIRCam is AB. The following link (courtesy of D. Patton) provides information on the various magnitude systems and ways to go from one to another: http://www.astro.utoronto.ca/~patton/astro/mags.html.

2.1 Object types

• Point sources: stars & QSOs
• Galaxies: distant compact to sub-compact sources - seeing dominated profile
• Nearby galaxy: profile dominated by the object itself
• Extended source: uniform illumination over square arcsecond scales

2.2 Objects profiles

where Ic is the peak value, r is the radius, and the parameters are alpha, and beta. The alpha value is equal to half the FWHM of the object (FWHM = seeing for seeing dominated profiles, and FWHM = object width at half maximum for large nearby galaxies), and beta defines the profile type, say how much energy is distributed in the wings of the profile. Based on a large sample, the median value for beta on WIRCam images, using Iraf's Imexamine, is:

• Point sources: beta = 3.8
• Galaxies: beta = 2.5
• Nearby galaxies: beta = 1.8
• Extended source: non applicable

2.3 Exposure time and SNR computation

If R is infinite, the flux represents the total flux received from the object:

Equation [2] becomes:

And F(total) can be computed simply from the magnitude equation, considering flux in electrons per second (Fe):

With Zero the zero photometric point in electron per second, k the airmass term, a the airmass and Fe the total flux in electrons generated per second by the object of magnitude MagAB.

Integrated over the exposure time Texp, we have:

Now let us compute the signal to noise ratio over the aperture of radius R (flux considered in electrons):

Where Se is the flux in electrons per second and per pixel coming from the sky background and noiseccd is the CCD readout noise. Pi R^2 represents the circular area of integration of the profile. Since the sky background to be subtracted from underneath the object is more often than not totally noise-free due to some modelling problem or crowding, the factor n is introduced. n can range from 1 for a perfect sky subtraction to 2 for a 1-1 pixel type subtraction. n could be higher than 2 actually in some crowded fields when some earby object flux is subtracted to the object itself. In DIET, a value of n=1.5 is used. Now solving the quadratic equation from [8] for Texp, one gets:

2.4 Optimal radius of flux integration

By picking a radius for all three cases that lead to the integration of 96% of the light, the difference in magnitude between the total magnitude and the magnitude within the aperture is 0.044 mag. This will be of importance when comparing DIET results to real measurement by SExtractor which will have to be corrected for the 0.044 mag (subtraction).

For extended sources, the SNR is computed over a single pixel though the magnitudes have to be provided per square arcsecond.

2.5 Direct relation between the SNR and the error on the magnitude

Where SNR is the signal to noise ratio on the object and Em the error on the magnitude on that object. For example, a error in magnitude of 0.1 mag gives a SNR of ~9, say a ~10% error.

When using a source extraction software like SExtractor (the most commonly used software today for large images) the error on the magnitude is estimated within the defined aperture. SExtractor derives the variance of the background (should it be sky background and/or detector read noise) regardless of its level. Hence it assumes the image is not affected by a convolution and/or resampling. In that regard, all the testing of DIET was done directly on raw data, knowing that further pre-processing and processing should increase the detection performance and the quality of the photometry.

2.6 Relation between SNR and photometry quality

• SNR = 3 : Detection - Photometry error = 33%
• SNR = 7 : Fair detection - Photometry error = 15%
• SNR = 15 : Good detection - Photometry error = 7%
• SNR = 25 : Quality photometry - Photometry error = 4%
• SNR = 100 : High quality photometry - Photometry error = 1%

3.1 Camera and site characteristics used in DIET

3.2 Example of performance on point sources

J filter - MagAB=23.5 - SNR=5

 Filter=J               Sky=GREY               Bin=1pix               
 Type=point source      SNR=5.0                Trans=100%             
 Mag=23.5               SNR ap=Optimal         
 ______________________________________________________________________
 Seeing   |           Airmass           
          |      1.0      1.5
      |   |------------------------------------------------------------
     0.4  |      761      823
     0.5  |     1265     1367
     0.6  |     1769     1912
     0.7  |     2273     2457
     0.8  |     3028     3274
     0.9  |     3784     4092
     1.0  |     4540     4909
     1.1  |     5548     5999
     1.2  |     6556     7088
 

Ks filter - MagAB=22.5 - SNR=7

 Filter=KS              Sky=GREY               Bin=1pix               
 Type=point source      SNR=7.0                Trans=100%             
 Mag=22.5               SNR ap=Optimal         
 ______________________________________________________________________
 Seeing   |           Airmass           
          |      1.0      1.5
      |   |------------------------------------------------------------
     0.4  |      505      544
     0.5  |      839      905
     0.6  |     1174     1267
     0.7  |     1509     1628
     0.8  |     2011     2170
     0.9  |     2513     2711
     1.0  |     3015     3253
     1.1  |     3684     3975
     1.2  |     4354     4698
 

3.3 Example of performance on field galaxies

Ks filter - MagAB=22.0 - SNR=5

 Filter=KS              Sky=GREY               Bin=1pix               
 Type=galaxy            SNR=5.0                Trans=100%             
 Mag=22.0               SNR ap=Optimal         
 ______________________________________________________________________
 Seeing   |           Airmass           
          |      1.0      1.5
      |   |------------------------------------------------------------
     0.4  |      374      404
     0.5  |      578      623
     0.6  |      815      879
     0.7  |     1120     1208
     0.8  |     1459     1574
     0.9  |     1831     1976
     1.0  |     2238     2415
     1.1  |     2712     2927
     1.2  |     3221     3475
 

H filter - MagAB=20.0 - SNR=20

 Filter=H               Sky=GREY               Bin=1pix               
 Type=galaxy            SNR=20.0               Trans=100%             
 Mag=20.0               SNR ap=Optimal         
 ______________________________________________________________________
 Seeing   |           Airmass           
          |      1.0      1.5
      |   |------------------------------------------------------------
     0.4  |      138      146
     0.5  |      212      225
     0.6  |      299      316
     0.7  |      410      434
     0.8  |      534      565
     0.9  |      670      709
     1.0  |      818      866
     1.1  |      991     1050
     1.2  |     1177     1246
 

3.4 Example for units conversion from Jansky to AB mag for time proposal purposes

By definition, the zero point is the magnitude of a source which yields 1 e-/sec (detected). The AB system uses for mag=0 the constant flux of 3720 Jansky (i.e. 1 Jansky = 10^-26 J/s/m2/Hz). So, if you know your source flux in Jansky, you can compare it to the zero point magnitude and deduce the flux of detected photons that you should expect for your source. For example:

In H2, a zero point of 23.75 means that a flux of 3720 Jy / 2.512^(23.75) = 1.2x10-6 Jy produces a flux of 1 detected electron/sec. Say your source flux at the wavelength of H2 is 10^-3 Jy, then your source has a magnitude of magAB = 2.5*log10(3720/10^-3) = 16.43. And a magAB=16.43 in H2 produces a flux of 2.512^(23.75-16.43) = 847 detected photons/sec.

If you integrate for 100 sec, you should expect 85000 photons on your source.

To efficiently remove the cosmic rays and cosmetic defaults of the mosaic (gaps between the detectors, bad columns), a minimum of 4 dithered exposures per field is required. To obtain a reasonably uniform SNR across the gap areas, we recommand using at least 5 positions whenever a contiguous coverage is desired. The number of positions and their placement, however, will often be driven higher by sky-subtraction considerations: the sky background in the IR is both much higher and more variable (specially in the first few hours after sunset) than in the optical. The sky signal is usually estimated from the neigbouring positions in the dither pattern, which then need to be spaced by more than the size of the largest structure of interest in the image.

Each exposure needs to be in the sky photon noise regime, so that their coaddition will produces the expected signal to noise ratio for the total exposure time. WIRCam has a low readout noise (by IR camera standards), which in the broad band filters is very quickly dominated by the sky photon noise: except (marginally) at Y, the minimum exposure time of 5s actually prevents obtaining a sky exposure that has significant readout noise. This is, on the other hand, a significant consideration for the narrow band filters, and in particular for the low OH filters in the J band.

The saturation level is usually a more important consideration: exposing too long will indeed save a couple of minutes by skipping some readouts, but will result in high sky background and too many objects (and even possibly the sky) reaching saturation. For the broad band filters, the longest reasonable exposure time (e.g. 20s at Ks) would often result in very large overheads if the telescope would move between every exposures (we estimate that each offset will initially take 60s, to be later optimised down to ~20s). Multiple exposures are then taken at a given telescope position, before moving to the next position in the pattern. The maximum number of exposures at each position, which must be a multiple of 4 if microstepping is used, is then set by the timescale of the background fluctuations.

We estimate that the following exposure times and times per position will be good compromises to achieve low overheads while keeping the signal in a reasonable range:

• Y band: 2 mn and 8 mn
• J band: 45s and 3 mn
• H band: 10s and 1.5 mn
• Ks band: 20s and 1.5 mn
• CH4on band: 30s and 2 mn
• CH4off band: 30s and 2 mn
• LowOH1 band: 10 mn and 10 mn
• H2 band: 3 mn and 12 mn

The following table gives the maximum exposure times allowed for WIRCam designed so that the sky background uses no more than half the detector potential well. The threshold adopted is based on the 75% percentile of the first year of WIRCam observations.

The following table gives the expected overheads for WIRCam.