Space Telescope Science Institute   9.6 Exposure-Time Examples  9.6.2 Example 2: SBC Objective Prism Spectrum of a UV Spectrophotometric Standard Star

9.6.1 Example 1: WFC Imaging a Faint Point Source


What is the exposure time needed to obtain a signal to noise of 10 for a point source of spectral type F2 V, normalized to V = 26.5, when using the WFC, F555W filter? Assume a GAIN of 1 and a photometry box size of 11 x 11 pixels, and average sky values.

The ACS Exposure Time Calculator (ETC) gives a total exposure time of 4410 seconds to obtain this S/N in a single exposure. Since such an exposure would be riddled with cosmic rays and essentially useless, it is necessary to specify how many exposures to split the observation into. ACS WFC observations generally should be split if the exposure time is larger than about 5 minutes, but for multi-orbit observations, splitting into 2 exposures per orbit is generally sufficient.

For a typical object visibility of 53 minutes, after applying the requisite overheads, there is time for two 1200 seconds exposures per orbit. The required exposure time can thus be reached in 4 exposures, but re-running the ETC using CR-SPLIT=4 raises the required exposure time to 5303 seconds (because of the extra noise introduced by the four extra readouts). To achieve the required exposure time would require CR-SPLIT=5, or three orbits.

Using the pencil and paper method, Table 9.1 gives the integral QTd/ as 0.0775, and the AB correction term can be retrieved from Table 10.1 as 0.040. According to Figure 5.9, a circular aperture of radius 0.3 arcseconds (which has an area of 116 pixels, close to the 121 pixel box specified) encloses about 90% of the light from a star. The count rate is then 2.5x1011*0.0775*0.9*10-0.4(26.5+0.040) = 0.423 counts/second, which agrees with the ETC-returned value of 0.42. The exposure time can then be found by using the equation

to give t = 4172 seconds, which is close to the ETC-derived value of 4410 seconds. We have inserted the background rate from Table 9.1 (Bsky =  0.055) and Table 9.5 (Bdet = 0.0032), and assumed that the noise on the background is much greater than the readout noise.

Note that this can be greatly shortened by specifying a smaller analysis box (for example, 5 x 5) and using LOW-SKY. Dropping the aperture size to 5 x 5 at average sky which still encloses 81% of the light requires 1532 seconds. Including both the smaller 5 x 5 box and LOW-SKY (Zodiacal = LOW, Earthshine = AVERAGE), using the ETC gives the required exposure time as only 1306 seconds (using CR-SPLIT=1), or 1540 seconds with CR-SPLIT=2. The LOW-SKY visibility per orbit is 47 minutes, which allows a total on-target exposure time of 2000 seconds in one orbit with CR-SPLIT=2.

Note also that the count rate from WFPC2 would be 0.167 electrons/second, a factor of 2.5 lower.


 9.6 Exposure-Time Examples  9.6.2 Example 2: SBC Objective Prism Spectrum of a UV Spectrophotometric Standard Star
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