MegaCam Direct Imaging Exposure Time Calculator (DIET)

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Quick MegaCam photometric performance table

Filter uSgSrSiSzS u g r i z
Modal image quality (PSF fitting) 0.83"0.75"0.69"0.63"0.63" xx xx xx xx xx
Point source in dark sky (Mag. AB) 25.3 25.7 25.1 24.6 23.6 25.6 26.1 25.6 24.9 23.5
Point source in grey sky (Mag. AB) 24.6 25.3 25.0 24.6 23.6 24.8 25.7 25.4 24.9 23.5
Transition from AB to Vega magnitude system -.346+.092-.171-.401-.554-.621+.087-.181-.392-.526

This table summarizes the camera performance at SNR=10 for a 1 hour (approximately) exposure under modal seeing conditions (2003 to 2009 statistics) with an airmass of 1.2 (this causes an important difference in sky brightness for the i' and z' filters versus zenith); 1.2 is the standard airmass data tend to be collected at CFHT. Those are AB total instrumental magnitudes (MegaCam natural magnitudes).

The ETC comes into two modes: computation of the exposure time for a fixed SNR (ETIME mode), and conversely computation of SNR for a given exposure time (SNR mode).

From 2003A to 2013B, the MegaCam ETC (DIET) was delivering an exposure time based on Kron photometry (i.e. based on the noise within a Kron aperture) for both point sources and faint extended sources (field galaxies). Starting 2014A, in order to reflect the evolution of tools available for modern photometry, the MegaCam ETC is scaled to a PSF fitting photometry for point sources (a natural choice) but also for field galaxies as MegaCam tends to be used on the fainter sources which then fall into a similar regime as point sources at low SNR. As of 2014B, the MegaCam ETC has been completely refurbished, and is now common with WirCam. It does not offer yet a mode for field galaxies, but has several modes for point sources, as well as a mode for extended sources:

  • Point Source: stars & QSOs - seeing dominated profile. The ETC has three different options here. The default option corresponds to optimal aperture photometry, i.e. for a given SNR (resp. exposure time), the exposure time (resp. SNR) is minimized (resp. maximized) with respect to the aperture radius. Note that in general the optimal radius depends on the magnitude, background and IQ, but is roughly of the order of 0.75xIQ. This corresponds to less than 70% of the source flux being kept in the aperture. This mode is particularly useful for point sources when the source profile shape, dominated by seeing, is well known. For comparison with older versions of the ETC, and/or when the source profile is less under control, a second mode in a large fixed aperture radius of 2*IQ is also offered. For a seeing-dominated profile (Moffat profile with alpha=0.5 IQ, beta=3) this aperture encompasses 96.2% of the flux. Finally, an experimental mode based on Fisher analysis is proposed for PSF photometry AstrOmatic's PSFex.Note that between the most convervative (large aperture) and most aggressive (PSF photometry) modes, the exposure times for the same SNR vary by more than a factor of 3. Be sure to know what type of SNR you are requesting.
  • Galaxy: This mode is valid for galaxies with given SÚrsic profiles (n=1,2,3,4) and half-light-radii (in arcsec), in aperture photometry mode. The choice of apertures, that was offered for point sources, is available here. This mode replaces both "field" and "nearby" galaxy modes of the old ETC.
  • Extended Source: This mode is valid for diffuse emission, or generally for object with brightness variations on scales much larger than 1". Note here that the magnitudes and SNRs are expressed per square arcsecond.

Doubling the exposure times leads to a gain of +0.4 on the limiting magnitude [+2.5log10(sqrt(2))] at the given SNR, or a factor of 1.4 on the SNR at the given magnitude [sqrt(2)]. Obtaining 0.10" better image quality over 0.85" leads to a gain of +0.13 on the limiting magnitude for point sources [+2.5log10(OldIQ/NewIQ)], or a factor of ~1.1 on the SNR at the given magnitude (0.85/0.75). The sky background and atmospheric transmission (cirrus mostly) do have dramatic impact on the SNR: the doubling of the sky background imposes the doubling of the integration time to achieve the same result, and a 15% decrease in atmospheric transmission imposes an increase of 40% of the integration time.


1. How DIET works

DIET calculates the exposure time required to reach a given signal-to-noise ratio in various observing conditions (source type, magnitude, filter, seeing, sky background, airmass). DIET is based on signal-to-noise estimations (Flux/Noise) over an optimal aperture (or a fixed aperture, or a fit to a PSF model), the delivered image quality on the image, and the sky background.

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

Note that the ETC gives the exposure time or SNR assuming a single exposure, without overheads. It is the PI's responsibility to add the corresponding overheads of multiple exposures. Note therefore, that for multiple short exposures where the readout noise may become important, the corresponding SNR may be lower than computed by the ETC. Future versions of the ETC will allow to specify the number of exposures.

DIET was calibrated and tested using single MegaCam images processed by Elixir. Be aware that it does not reflect the realities of the observing world to account for the segmentation of the global time budget within several dithered exposures as well as the inevitable fluctuations of the parameters (image quality, sky background) between exposures. MegaCam is used in the vast majority of the science programs with dithering patterns and stacking procedures implying ressampling in most cases which all work towards reducing the depth of the final integration (the commonly use median estimator will cause for example a typical lost of ~0.2 mag. over the average estimator). Also CFHT's QSO validation schemes often relax by up to 15% the requirements for the observing program (image quality, sky background, sky absorption), all working towards reducing the depth of the final integration. It is up to the user to account for this when preparing the time proposal - it is advised to add 0.2 magnitude to the desired depth when using DIET if you are planning to stack dithered exposures.

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. This "Range" mode is not available yet with the new ETC, but will come online soon.

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:

2. What DIET really computes: formulae

2.1 Formulae for point source aperture photometry and extended sources

The following document gives a description of what DIET computes for point source (optimal and fixed apertures) as well as for extended sources.

2.2 Formulae for point source PSF photometry

The following document describes the Fisher analysis approach to SNR and exposure times computations in the case of PSF photometry.

2.3 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 Em on m can be written Em = |dm/df| Ef where Ef is the error on f. Since |dm/df| = (1 / f)(2.5 / ln(10)), one gets Em = 1.09 (1 / (f / Ef)). Since SNR = f / Ef, the final relation is:

SNR = 1.09 / Em [10]

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. This SNR metric is also known as the "n-sigma" metric.

When using a source extraction software like SExtractor (the most commonly used tool 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 Elixir processed data.

2.4 Relation between SNR and photometry quality

    • SNR = 5 : Detection - Photometry error = 20%
    • 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. How to optimally fragment the total exposure time

To efficiently remove the cosmic rays and cosmetic defaults of the mosaic (gaps between the CCDs, bad columns), a minimum of 4 dithered exposures per field is required, though 5 is recommended to obtain a more uniform SNR across the gap areas.

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 fairly large amount of data 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.