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Background- and Source-brightness Limited Exposures: Choosing optimal exposure times

This page gives information on the limitations to spectroscopic exposure times due to sky and telescope background and due to source signal. (Acquisition exposure times are given here.) The information can be used to determine optimal exposure times for science observations. Examples are given below the two tables.

Limitations due to Sky and Telescope Background

When observing very faint targets at 1.0 - 2.3 µm, OH emission lines dominate the flux on the detector and for sufficiently long exposures will saturate the array at many wavelengths. In the X and J bands with the short blue camera and in X, J, H, and K with the long blue camera the exposure times for this to happen are far longer than should be used. In the thermal infrared (3 - 5 µm), except for the very brightest objects the maximum exposure time is determined by the background.

The table below gives, for 2-pixel wide slits, the exposure times that would fill at least some of the array detectors to half of their full well capacities. Saturation / non-linearity effects are noticeable beyond that level. The values for the L and M bands assume the deep well is used. Note that exposure times are generally inversely proportional to slit width. For example, for the 31.7 l/mm grating, short blue camera, and 0.45 arcsec wide slit, the the value for 3.2 - 3.5 µm in the table implies that the maximum recommended exposure time for that slit is 8 seconds in that wavelength region.

As shown in the table below the background depends strongly and not necessarily monotonically on wavelength. The table gives approximate maximum exposure times for different portions of the L and M bands. For details of the dependency on wavelength the Integration Time Calculator should be used. Note that when short exposures are required one normally should "co-add" many such exposures to build up signal in their target without saturating on the background. Very short (< 0.5 sec) exposures are not recommended, as the shortest read time possible is 0.2 seconds and thus overheads are large.

EXPOSURE TIMES (sec) FOR WHICH BACKGROUND FROM SKY + TELESCOPE
HALF-FILLS DETECTOR WELLS
Grating
l/mm
X J H K L (deep well) M (deep well)
1.0-1.2µm 1.2-1.4µm 1.4-1.9µm 1.9-2.5µm 2-8-3.2µm 3.2-3.5µm 3.5-3.8µm 3.8-4.2µm 4.5-4.8µm 4.8-5.4µm
SHORT CAMERAS, 0.3" SLIT(a), NO AO
31.7 1500(b) 1800(b) 300 900(b) 30 12 12 3 0.8 0.25(c)
110.5 1500(b) 1800(b) 300 900(b) 60 30 25 10 2.5 0.8
LONG CAMERAS, 0.1" SLIT(a), NO AO
110.5(d) 13000(b) 16000(b) 5000(b) 8000(b) 700(b) 240 450 180 30 10
LONG CAMERAS, 0.1" SLIT(a), ALTAIR
10.44 13000(b) 16000(b) 5000(b) 5000(b) 5.0 2.0 1.0 0.5 - -
31.7 13000(b) 16000(b) 5000(b) 8000(b) 15 6 3 1.5 - -
110.5 13000(b) 16000(b) 5000(b) 8000(b) 45 18 9 5 - -

(a) Exposure times generally scale inversely with slit width.
(b) Actual individual exposure times should not exceed 600 sec.
(c) This configuration and exposure time not recommended because of large overheads.
(d) This configuration (without ALTAIR) often used for high spectral resolution (R up to 18,000), especially at L and M.




Limitations due to Source Brightness

The following table gives approximate brightnesses of stars for which the signal in a 1 second exposure fills the detector's well to the 50% level in the peak spectral row. The table assumes "good" (IQ70) image quality and narrow slits (0.3" for the short cameras and 0.1" for the long cameras). Note that:

  • (1) because the minimum exposure time is 0.2 sec, the absolute magnitude limits are 1.7 mag brighter than in the table for these narrow slits;
  • (2) limiting brightnesses are similar for low and medium resolution in the X, J, H, and K bands with and without AO (when using AO the smaller pixel size is approximately balanced by the more concentrated image).
  • For estimates of limiting brightness (or maximum exposure time) with other slit widths and sky conditions use the GNIRS ITC with "Analysis Method: software aperture of diameter" set to either 0.15" or 0.05" depending on the camera you are using. The ITC will then generate a spectrum of the peak row.

    MAGNITUDE OF STAR FOR WHICH A 1-SECOND EXPOSURE
    HALF-FILLS DETECTOR WELLS IN PEAK ROWa
    Grating
    l/mm
    Camera AO? X
    shallow well
    J
    shallow well
    H
    shallow well
    K
    shallow well
    L
    deep well
    M
    deep well
    31.7 Short No 4.6 5.0 4.7 4.6 2.9 2.3
    110.5 Short No 3.4 3.8 3.5 3.4 1.7 1.1
    110.5 Long No(b) 0.9 1.0 0.6 0.3 -1.4 -1.9
    10.44 Long Yes 5.5 5.8 5.8 5.7 -0.6(c) n/a
    31.7 Long Yes 4.3 4.6 4.6 4.5 -2.3(c) n/a
    110.5 Long Yes 3.1 3.4 3.4 3.3 -3.4(c) n/a

    (a) Assumes IQ70, CC50, WV80, airmass 1.5, 0.30 arcsec slit with short camera, 0.10 arc sec slit with long camera. Wider slits increase signal in peak row.
    (b) Large light loss without AO. However, better sensitivity than with AO at L and M.
    (c) Transmission of ALTAIR is ~0.05 in the L band.



    Choosing an appropriate exposure time

    In general, optimal exposure times can be determined using the integration time calculator, with the constraints that individual exposures cannot be shorter than 0.2 sec and (at present) should not be longer than 600 sec. The tables on this page also can be used for such a determination. Two examples are given below.

    Example 1: The goal is to obtain the highest S/N on a K=10.0 mag point source in 30 minutes of actual exposure time, using the 32 l/mm grating, the short blue camera, and the 0.45 arcsec wide slit. From the upper table one can determine that the background through the 0.45" slit limits the exposure to 900 x (0.30/0.45) = 600 seconds. From the lower table, a 600 second exposure will fill the well to the 50% level for a K=4.6 +2.512 log(600) =11.6 mag source in a 0.3" slit and with the 1.5 times wider 0.45" slit a somewhat fainter star (K~12) would do this. Thus, a shorter exposure is required to avoid saturation on the continuum of the K=10 point source. One probably should reduce the individual exposure at least by a factor of 6 (~2 mag), to ~ 100 sec, and then choose to obtain 30 such exposures (or somewhat fewer as there will be overheads associated with multiple exposures). If the source is suspected of having bright line emission, one would choose larger numbers of shorter exposures (say 60 seconds, or less) to avoid saturation on the emission lines.

    Example 2: The goal is to get a spectrum of an L=10 star in the 3.8-4.2 micron interval using the 110.5 l/mm grating and the short camera with the 0.45 arcsec wide slit. From the upper table, one can see that individual exposures must be limited to about (0.30/0.45) x 20 ~ 13 seconds to avoid the onset of saturation on the background. The lower table indicates that in a 13 second exposure only stars brighter than L=4.7 mag (i.e., 1.9 + 2.5 log(13)) will be a problem. Because the star is much fainter than this, exposures of 13 seconds are OK. Because these are rather short exposures, individual frames should probably consist of several exposures in order to improve efficiency.