• The "limiting magnitude" of an IR instrument can be easily predicted when the observations are taken in the background-limited case (i.e. the readout noise is negligible compared to the background shot noise).

  From the zeropoints and the background brightnesses in J, H, K and Ks, as measured during the INGRID's new foreoptics commissionig (1 April 2001), we have calculated the expected limiting magnitude as a function of: the required signal to noise ratio, the exposure time and the seeing (the latter for point sources only). Keep in mind that the background brightness is highly variable, so that the calculated limiting magnitude can vary from night to night. See the notes below.

  • Point sources
  • Extended sources
  
  
• You can also use SIGNAL to calculate the number photons (from the object and from the sky) which will be detected during an INGRID exposure of a point or extended source.

• The limiting magnitude has been calculated using the equation (McLean 1997)

  

  which assumes that observations are taken in the background limited case and where
  

  	is the predicted limiting magnitude
  	is the zeropoint of the instrumental scale (i.e. magnitude of a source which gives a flux of 1 ADU/s).
  	is the signal to noise ratio for the detection of the limiting magnitude.
  	is the gain (in e-/ADU) of the detector.
  	is the background signal per pixel(in e-/s/pix).
  	is the number of pixels covered by a point source (n=pi*(seeing/0.238)2). Assuming that the source radius is equal to the seeing (fwhm) is probably pesimistic. For extended objects, the limiting magnitude per arcsec2 has been given instead (i.e. n=1/0.2382).
  	is the total on-object integration time (=number of object frames*exposure time of each individual frame).

• From the formula above, if the background increases by a factor of (say) 2, the total on-object exposure time should be increased by the same factor in order to reach the same limiting magnitude. The same increase in exposure time would be necessary if the seeing gets worse by a factor 2.

• If the background levels were (say) twice the values measured during the 1/4/2001, the limiting magnitude represented in the plots would decrease by ~0.4 mag (or ~0.4 mag/arcsec² for extended objects).

• If a S/N equal to 5 were necessary (instead of 3), then the exposure time should be increased by a factor ~2.8 to reach the same limiting magnitude.

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Last Updated: 25 September 2002 Almudena Zurita azurita@ing.iac.es