WIRCam NEW Direct Imaging Exposure Time Calculator (DIET)
NEW DIET for WIRCam is the result of unifying MegaCam and WIRCam ETC

The basics:

Table of contents:

The NEW DIET calculator

Click on this figure to launch the NEW calculator.

Quick WIRCam photometric performance table

Filter (click for details) YJHKsLow OH1Low OH2CH4 OnCH4 OffH2 v=1-0 S(1)K continuumBrackett gammaCOW
Point source - magAB - Optimal aperture 24.123.623.223.222.823.122.622.522.021.722.022.022.7
Extended object - Surface brightness in magAB/arcsec2 24.524.123.723.723.323.523.123.022.522.222.422.523.2
Conversion from AB to Vega magnitude system (mag) -0.612-0.924-1.354-1.831-0.654-0.835-1.419-1.326-1.816-1.897-1.896-1.977-1.174

This table summarizes the expected camera performance for a 5 sigma detection (SNR=5) in a 1 hour exposure under 0.7 arcsecond seeing with 1.2 airmass and GREY sky conditions, in two cases: point source with a Moffat profile (beta=3.0) and extended object (much larger than the seeing disk). For point sources, results are magnitudes in the AB system. For extended objects, results are surface brightnesses in AB magnitudes per square arcseconds and SNR is defined per square arcsecond (SNR per WIRCam pixel = 0.307 * SNR per square arcsecond). The numbers for point sources are based on standard star measurements.

Important note on sky subtraction and limiting magnitudes with WIRCam. If you need to use the nodding (sky-target-sky) observing strategy (i.e. typically when 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.

WIRCam Filter Page (click for details)

1 How NEW DIET works

NEW DIET is a calculator allowing the observer to compute the exposure time (in seconds) required to reach a given signal-to-noise ratio in various observing conditions (source type, magnitude, filter, seeing, sky background, airmass, and atmospheric transmission). The NEW DIET software results from a unification between MegaCam and WIRCam previous DIET scripts.

The interactive graphical interface allows the user to experiment with some custom parameters. Basically, one can compute exposure time (etime) corresponding to a desired signal-to-noise ratio (snr), or conversely compute an snr for a given etime. Source types are for the moment limited to point-sources or extended sources. In a near future, "galaxy" profiles will be added. Photometric modes include aperture and psf. Aperture photometry includes optimal aperture (see below), fixed aperture, or large aperture proportional to IQ (so-called 96% flux aperture).

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.

The output of DIET includes etime or snr depending on the chosen mode, plus useful informations about the calculation: radius of the aperture, fraction of flux contained into this aperture, saturation limits both for the object and the sky, corresponding to a flux of 28000 ADU, where the non-linearity of the detector becomes severe. More accurately, this limit is defined on the worst chip (chip #3), as the value where 1% of the pixels become saturated. The value varies significantly from one chip to the other: 35650 on chip #1, 30600 on chip #2 and 31250 on chip #4.

There is a log button allowing to copy and paste the adopted values to PH1.

1.1 Measured zero-points and sky brightnesses

The following table gives the recently measured zero-points for the 10 WIRCam filters (average values between 2011 and 2015) on chip 4 (detector #60) in the VEGAmag system and in ADU/sec/pix. These average values should be accurate to 0.006 mag. To convert to ZP in e/sec/pix, add 1.42, corresponding to the adopted conversion factor of 3.7 e/ADU, valid since September 2006 (it was 2.5 before the August 2006 change). To convert to ZP in ABmag, add the VEGA to AB magnitude correction. It also gives the median sky flux (ADU/sec/pixel) through each of the 13 WIRCam filters, as measured between 2009 and 2017. The corresponding sky brightness (VEGAmag/arcsec2) is obtained from the ZP, the median sky fluxes, and a correction of -2.56 corresponding to the pixel size (10.6 pixels in 1 square arcsec). The conversion from VEGA to AB magnitude system is also given (for example, J_AB = J_Vega + 0.934). Please note that prior to April 26, 2017, the sky brightness given in ABmag/arcsec2 was wrong.

WIRCam Zero-Point and Sky Brightness in AB Magnitudes
FilterYJHKsLow OH1Low OH2CH4 OnCH4 OffH2 v=1-0 S(1)K ContinuumBrackett gammaCOW
Zero Point (VEGAmag, ADU/sec/pix)23.8323.7023.8823.1221.0021.1122.7622.7120.5620.3020.4020.4822.52
Detected Sky Flux (ADU/sec/pix)391308224451.051.3931132835473548102
Sky Brightness (VEGAmag/arcsec2)17.315.914.013.918.418.214.013.914.113.614.013.714.9
VEGA to AB magnitude correction0.6120.9241.3541.8310.6540.8351.4191.3261.8161.8971.8961.9771.174

The sky variability in the near infrared is important. As a canonical rule, the level varies by 10% over a 10 minute timescale. The H band is notoriously variable by +/-0.5 mag. In J and Ks, it +/-0.3 mag.

2. Information on how DIET computes exposure times vs. magnitudes and SNRs

The following paragraphs propose a tutorial on the magnitude and signal to noise calculation schemes used in the NEW DIET.

2.1 Object types

There are now three classes of objects considered in the NEW DIET:
    • Point sources: stars, QSOs, distant compact galaxies - seeing dominated profile
    • NEW: Galaxies: extended objects, but where the seeing and the half-light radius of the galaxy are of the same order of magnitude
    • Extended source: uniform illumination over square arcseconds scales

2.2 Object profile

As provided in Iraf's Imexamine function, a Moffat function is used to fit the seeing profile:

I = Ic (1 + (r / alpha)^2)^(-beta) [1]

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 seeing for point sources, and beta defines the profile type, say how much energy is distributed in the wings of the profile (small values of beta means large wings). The median value for beta on WIRCam images, as determined at Terapix, is beta = 3.0, the same value as for MegaCam point sources.

Galaxy profile: we use the Sersic characterization of galaxy profiles, which depends on two parameters: the Sersic index n, which is 1 for exponential profiles (disk galaxies) and 4 for de Vaucouleurs' profiles (elliptical galaxies), and the half-light radius, which is a measure of the galaxy extension compared to the seeing. The goal is not to get an accurate description of the convolved profile, but it is in any case much better than fitting galaxy profiles by a small beta Moffat profile, as it was done in the previous DIET version.

2.3 Exposure time and SNR computation

The following documents written by Simon Prunet explain the details of the method and give the basic equations used by the NEW DIET:

Aperture photometry applies both to point sources and galaxy profiles, for which we provide 3 different types of apertures:

  • a radius maximizing the SNR, called optimal radius and described in the next section
  • a fixed aperture where the radius is entered in arcsec
  • a large aperture described below
  • In addition, we provide the flux fraction corresponding to the chosen aperture type, to give an idea about the compromise between maximizing the flux fraction and maximizing the SNR. In the case of point sources, the large aperture is defined as 4 times the seeing in diameter. This corresponds to a large fraction of the total flux (typically 96%) being included. In the case of a galaxy profile, we similarly define the large aperture as the one containing 96% of the flux of the resulting convolved profile. This should correspond approximately to the so-called Kron aperture, often used for instance by SExtractor to compute the MAG_AUTO parameter.

    PSF photometry applies only to point sources.

    In the case of the galaxy profile, it is VERY important to specify the aperture where the signal-to-noise is defined. We hope that our choice of 3 different aperture types will cover most of the users' needs.

    2.4 Optimal radius of flux integration

    Maximizing the SNR over R for point sources (beta = 3.0), gives approximately Ropt = 1.5 * alpha. This results in measuring about 60% of the flux within the aperture.

    For extended sources, the magnitudes have to be provided per square arcsecond.

    2.5 Sky background levels

    NEW: The ETC offers three pre-defined values of the sky background, namely DARK, GREY and BRIGHT. We define these levels according to the actual observed distribution of sky background at CFHT, where DARK corresponds to the median value of the darkest half, GREY to the median value between 50% and 75%, and BRIGHT to the median value of the brightest quartile. The unequal distribution mimics the 4 categories defined by Gemini, 'darkest' and 'dark' being grouped into our DARK bin.

    Previous definitions corresponded to 33%, 50% and 66% for DARK, GREY and BRIGHT. The new definitions give values which are therefore slightly darker for DARK and more significantly brighter for GREY and BRIGHT.

    The remote observer uses limits between DARK and GREY, and GREY and BRIGHT, to grade the images. These limits are now defined as the median of the observed distribution, and the third quartile, respectively. Statistics have been accumulated since 2009, so the adopted values displayed in the following table should be well determined, especially for the broad-band filters (80000 values in J and Ks). New values have been added in April 2017 for the new filters CO and W.

    Definition of WIRCam sky background levels in ADU/sec/pix
    FilterYJHKsLow OH1Low OH2CH4 OnCH4 OffH2 v=1-0 S(1)K ContinuumBrackett gammaCOW
    DARK (25%)30986313740.791.132532492841294467
    limit DARK/GREY (50%)391308224451.051.3931132835473548102
    GREY (62.5%)431489254821.261.5234835138493950124
    limit GREY/BRIGHT (75%)4817210465261.581.7638137843534354166
    BRIGHT (87.5%)5721911965933.862.5345144051584957235

    These limits correspond to observed statistics at CFHT, not to darkest or brightest sky levels that can be observed in the near-infrared. This is the reason why we added the DARK category to the previous version of DIET, which was limited to GREY and BRIGHT, on the basis that the sky is never dark in the near-infrared.

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

    Let us consider a simplified expression of the magnitude vs. flux measurement: m = -2.5 log(f). The error e(m) on m can be written e(m) = |dm/df| e(f) where e(f) is the error on f. Since |dm/df| = (1 / f)(2.5 / ln(10)), one gets e(m) = 1.086 e(f)/f. Since SNR = f / e(f), the final relation is:

    e(m) = 1.086 / SNR

    Where SNR is the signal to noise ratio on the object and e(m) the error on the magnitude on that object.

    When using a source extraction software like SExtractor (one of 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.

    2.7 Relation between SNR and photometry quality

      • SNR = 3 : Detection - Flux error = 33% - mag error = 0.31
      • SNR = 7 : Fair detection - Flux error = 15% - mag error = 0.13
      • SNR = 15 : Good detection - Flux error = 7% - mag error = 0.06
      • SNR = 25 : Quality photometry - Flux error = 4% - mag error = 0.04
      • SNR = 100 : High quality photometry - Flux error = 1% - mag error = 0.009

    2.8 Differences with the previous DIET calculator

    The previous version of DIET in use until August 2014 had a few differences with the NEW DIET:
      • beta=3.8 measured with IRAF becomes 3.0 measured at Terapix (thanks to Patrick Hudelot)
      • a missing factor in the flux fraction corresponding to a given aperture has been added
      • the ratio of optimal aperture to seeing radius varies rather than being fixed to 1.45
      • zeropoints have been remeasured using data from 2011 to 2015
      • AB to Vega mag have been adopted from magsynth (thanks to Simon Prunet)

    The optimal aperture is about the same as previously, but it was then incorrectly reported to correspond to 96% of the flux due to the missing factor in the flux fraction. It was and is still about 60% of the total flux.

    An alternative large aperture of radius 4 times the seeing radius may be used to define the SNR. It then corresponds to about 96% of the total flux.

    For extended sources, the surface brightness is given in AB mag per square arcsec. For coherence, the SNR is also defined per square arcsec. This was not the case for the previous DIET, where the SNR was defined per pixel. The ratio between the two definitions is the pixel size, 0.307 arcsec. So an SNR of 5 using the previous DIET now becomes an SNR of 16.3 with the NEW DIET.

    The differences in exposure times between the previous and the NEW DIET can be estimated from examples given in Section 3. New exposure times are typically longer than previous ones for a given SNR, except in Y where they are shorter due to a better estimate of the zeropoint.

    Previous DIET calculator

    Click on this figure to launch the PREVIOUS calculator.

    3. Examples of WIRCam photometric performance and image samples

    3.1 Camera and site characteristics used in DIET

    Magnitude system AB
    Instrumental magnitude equation MagAB = Zp[e-/sec] - 2.5log(Flux[ADU])
    -2.5log(Gain[e-/ADU]) + 2.5log(ExpTime)
    - k(airmass - 1)
    Gain (e- / ADU) 3.7
    Filters Y, J, H, Ks, LowOH1, LowOH2, CH4On, CH4Off, H2, KCont, BrG
    Zero points (e-/sec) at 1 airmass (Zp) 25.87, 26.06, 26.66, 26.38, 23.08, 23.38, 25.56, 25.47, 23.80, 23.63, 23.72
    Extinction per airmass variation 0.02, 0.05, 0.03, 0.05, 0.05, 0.05, 0.03, 0.03, 0.05, 0.05, 0.05 (expected)
    Median (grey) sky brightness @ zenith (e/sec/pix) 140, 480, 2900, 1700, 3.8, 5.1, 1250, 1200, 130, 170, 125
    Sky background per airmass variation (e/s/pix/am) Estimates are: 20, 40, 180, 170, 20, 20, 42, 42, 13, 23, 23
    Pixel scale (arcsec / pixel) 0.307
    Read noise (e- / pixel) 30

    3.2 Example of performance on point sources

    Here is a comparison of the output from the previous and the NEW DIET, given the following input parameters.

    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   |        Previous    |       NEW
          |   | AM   1.0      1.5  |   1.0     1.5
          |   |------------------------------------------------------------
         0.4  |      641      692  |   895     976
         0.5  |     1065     1150  |  1396    1522
         0.6  |     1489     1608  |  2007    2189
         0.7  |     1913     2066  |  2730    2977
         0.8  |     2549     2754  |  3564    3886
         0.9  |     3185     3441  |  4509    4917
         1.0  |     3821     4128  |  5565    6069
         1.1  |     4669     5044  |  6732    7343
         1.2  |     5517     5960  |  8011    8737

    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   |         Previous   |       NEW
              | AM   1.0      1.5  |   1.0     1.5
          |   |------------------------------------------------------------
         0.4  |      205      227  |   546     600
         0.5  |      340      377  |   851     935
         0.6  |      476      527  |  1224    1345
         0.7  |      611      676  |  1665    1830
         0.8  |      813      901  |  2174    2390
         0.9  |     1016     1126  |  2750    3024
         1.0  |     1219     1350  |  3395    3732
         1.1  |     1489     1650  |  4107    4515
         1.2  |     1759     1949  |  4887    5373

    3.3 Example of performance on galaxies

    Here is a comparison of the output from the previous and the NEW DIET, given the following input parameters, in the case of optimal apertures. Note that these apertures change with the adopted galaxy profile and half-light radius, but the enclosed flux fraction in this optimal aperture does not vary much, especially in the case of an exponential disk.

    H filter - MagAB=22.5 - SNR=5 - Optimal aperture

     Filter=H               Sky=GREY               AM=1.2
     Type=galaxy            SNR=5.0                Trans=100%             
     Mag=22.5               SNR ap=Optimal         Seeing=0.7
     Half-light   |     Previous    |       NEW (n=1)           |       NEW (n=4)
     radius       | etime aper_diam | etime aper_diam flux_frac | etime aper_diam flux_frac
          |       |------------------------------------------------------------------------
     point-source |   508    1.0    |   885    1.0       0.59   |   885    1.0       0.59
     galaxy       |  1851    2.0    | 
         0.35     |                 |  1661    1.5       0.63   |  2073    1.4       0.52
         0.7      |                 |  3575    2.1       0.61   |  3856    1.6       0.43
         1.4      |                 | 10580    3.5       0.57   |  8676    1.9       0.34

    H filter - MagAB=22.5 - SNR=5 - Fixed aperture

     Filter=H               Sky=GREY               AM=1.2
     Type=galaxy            SNR=5.0                Trans=100%             
     Mag=22.5               SNR ap=Fixed           Seeing=0.7
     Half-light   |     Previous    |       NEW (n=1)           |       NEW (n=4)
     radius       | etime aper_diam | etime aper_diam flux_frac | etime aper_diam flux_frac
          |       |------------------------------------------------------------------------
     point-source |                 |  1444    2.0       0.90   |  1444    2.0       0.90
     galaxy       |                 | 
         0.35     |                 |  1843    2.0       0.79   |  2376    2.0       0.70
         0.7      |                 |  3590    2.0       0.57   |  4048    2.0       0.54
         1.4      |                 | 13744    2.0       0.29   |  8701    2.0       0.37
    In that case, the aperture is fixed and then, obviously, the enclosed flux fraction decreases when the half-light radius of the galaxy increases. These examples show the importance of a well-defined choice of the aperture where the signal-to-noise ratio will be measured.

    3.4 Example of performance on extended objects

    Here is the output from the previous and NEW DIET, given the following input parameters. For meaningful comparison, SNR in NEW DIET have been adjusted to the OLD definition, so that in the first example we used 5.0 for the previous DIET and 16.3 for the NEW DIET, and in the second example, we used respectively 20 and 65.

    Ks filter - 22.0magAB/acrsec2 - SNR=5

     Filter=KS              Sky=GREY               Bin=1pix               
     Type=galaxy            SNR=5.0 / 16.3         Trans=100%             
     Mag=22.0               SNR ap=1 pixel         
     Seeing   |         Previous   |       NEW        
              | AM   1.0      1.5  |   1.0     1.5
          |   |------------------------------------------------------------
          -   |      853      945  |  1507    1656

    H filter - MagAB=20.0 - SNR=20

     Filter=H               Sky=GREY               Bin=1pix               
     Type=galaxy            SNR=20 / 65            Trans=100%             
     Mag=20.0               SNR ap=Optimal         
     Seeing   |          Previous  |       NEW
              |      1.0      1.5  |   1.0     1.5
          |   |------------------------------------------------------------
          -   |      555      586  |   620     657

    3.5 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 3630 Jy (where 1 Jansky = 10^-26 W/m2/Hz). So, if you know your source flux in Jy, 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 3630 Jy / 2.512^(23.75) = 1.1x10-6 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(3630/10^-3) = 16.40. And a magAB=16.40 in H2 produces a flux of 2.512^(23.75-16.40) = 870 detected photons/sec.

    If you integrate for 100 sec, you should expect 87000 photons on your source.

    4 How to optimally fragment the total exposure time

    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

    4.1 Maximum Exposure Times

    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.

    Maximum WIRCam Exposure Times (per single slice)
    FilterMax. etime
    Y 150s
    J 60s
    H 15s
    Ks 25s
    Low OH1 3000s
    Low OH2 3000s
    CH4 On 50s
    CH4 Off 50s
    H2 200s
    K Cont. 200s
    Br. Gamma 200s

    4.2 Overheads

    The following table gives the expected overheads for WIRCam.

    Expected WIRCam Overheads
    ActionOverheadCharged to CFHT or PI?Comment
    Readout Overhead10 secPIWith final 32-amp controller
    Small Telescope Offsets10sCFHT
    Large Sky Offset60 secPICharged twice: going to Sky and returning from Sky
    Filter Wheel Change20 secCFHTRecommend completing one filter before going to next
    FocusingminutesCFHTAs part of QSO
    Standard starsminutesCFHTAs part of QSO unless needed photometry is better than 3-5%