This table summarizes the camera performance for a 1 hour exposure under 0.8 arcsec. seeing with 1 airmass. Those are AB instrumental magnitudes.

DIET's computations are based on actual camera performance derived from the characterization of the instrument during the semester 2003A. The observing conditions (sky brightness, camera zero points, ...) are the values given in the "General Summary" table.

DIET was calibrated and tested using raw images from the camera.

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 MegaCam 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 MegaCam 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 ~10, 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

u* filter - MagAB=25.0 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      202      378      675      299      545      959
     0.8  |      342      669     1216      517      973     1730
     1.0  |      511     1022     1872      781     1492     2667
     1.2  |      710     1438     2643     1092     2103     3769
 

g' filter - MagAB=25.6 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      197      459      843      231      533      974
     0.8  |      346      828     1530      408      962     1768
     1.0  |      528     1276     2364      623     1483     2732
     1.2  |      742     1803     3345      876     2096     3866
 

r' filter - MagAB=25.1 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      209      335      634      287      426      754
     0.8  |      370      601     1147      513      767     1367
     1.0  |      565      924     1771      787     1181     2111
     1.2  |      795     1304     2505     1109     1669     2986
 

i' filter - MagAB=24.4 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      212      212      212      331      331      331
     0.8  |      380      380      380      599      599      599
     1.0  |      584      584      584      923      923      923
     1.2  |      823      823      823     1304     1304     1304
 

z' filter - MagAB=23.5 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      223      223      223      351      351      351
     0.8  |      399      399      399      634      634      634
     1.0  |      614      614      614      978      978      978
     1.2  |      866      866      866     1383     1383     1383
 

3.3 Example of performance on field galaxies

u* filter - MagAB=24.7 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      394      780     1424      599     1137     2029
     0.8  |      671     1360     2502     1033     1990     3569
     1.0  |     1033     2118     3910     1599     3104     5580
     1.2  |     1467     3030     5604     2280     4445     7999
 

g' filter - MagAB=24.9 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      403      971     1798      475     1128     2077
     0.8  |      702     1708     3168      829     1985     3662
     1.0  |     1091     2669     4958     1291     3103     5731
     1.2  |     1560     3827     7111     1846     4449     8220
 

r' filter - MagAB=24.4 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      360      586     1121      500      749     1336
     0.8  |      627     1028     1974      874     1315     2353
     1.0  |      975     1605     3087     1363     2055     3681
     1.2  |     1394     2298     4427     1951     2945     5279
 

i' filter - MagAB=23.7 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      444      444      444      702      702      702
     0.8  |      779      779      779     1235     1235     1235
     1.0  |     1217     1217     1217     1931     1931     1931
     1.2  |     1743     1743     1743     2768     2768     2768
 

z' filter - MagAB=22.8 - SNR=5

 Seeing   |      Sky(Airmass=1.0)            Sky(Airmass=1.5)      
          |     DARK     GREY   BRIGHT     DARK     GREY   BRIGHT
      |   |------------------------------------------------------------
     0.6  |      467      467      467      744      744      744
     0.8  |      820      820      820     1309     1309     1309
     1.0  |     1280     1280     1280     2047     2047     2047
     1.2  |     1833     1833     1833     2935     2935     2935
 

3.4 Practical example: point sources

Figure 1. Examples of objects covering a range of SNRs.

Star C may actually well be a compact core galaxy as it seems to have structures further out that the other stars... Anyway, DIET results match the actual exposure time very well for the fainter objects.

Figure 2. Profile and Moffat fit (Iraf) of the star "A" from Figure 1.

3.5 Practical example: field and nearby galaxies

The following image (Figure 3) is a small fraction from the CCD13 originating from the image ID=707909o, a r' 360 seconds exposure taken at 1.27 airmass presenting an image quality of 0.71" and a sky background of 5 electron per pixel and per second. The gain of the CCD is 1.7 electron per ADU.

Figure 3. Examples of galaxies covering a range of SNRs.

DIET results match the actual exposure time fairly well but seem overall a bit short by about 5%.

Figure 2. Profile and Moffat fit (Iraf) of the nearby galaxy "A" from Figure 3.

Each exposure should however be in sky photon noise regime such that when exposures are later added together, the expected signal to noise ratio will be obtained (i.e. grows as square root of cumulated exposure time). The readout noise is low on MegaCam and is quickly dominated in the broad band filters by the sky photon noise. Taking a typical readout noise of 5 electrons, and using the darker sky brightness (dark time, 1.0 airmass), the minimum exposure time to use in order for the readout noise to be dominated by a factor of 10 by the sky background photon noise (that is: 10 * 5^2 = 250 electrons) is:

• u* band: 5 mn
• g' band: 80 sec
• r' band: 70 sec
• i' band: 35 sec
• z' band: 36 sec

The saturation level should also be a consideration: exposing too long will indeed save a couple of minutes by skipping some readouts but will result in high sky background and several objects reaching saturation. Typically, the following exposure times are a good compromise to achieve low overheads while keeping the signal in a reasonable range:

• u* band: 10 mn (to limit the impact of the atmospheric refraction)
• g' band: 12 mn
• r' band: 12 mn
• i' band: 10 mn
• z' band: 10 mn

One should consider that taking exposures as short as possible would result in a massive amount of data difficult to handle. In the end, it has to be a compromise between having at least 5 exposures all longer than the minimal time to reach sky photon noise dominated regime and equal or shorter than the recommended exposure times from this last table.