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Wide Field Camera 3 Instrument Handbook for Cycle 26 > Chapter 9: WFC3 Exposure-Time Calculation > 9.9 Exposure-Time Calculation Examples

 9.9 Exposure-Time Calculation Examples
In the following sections you will find a set of examples for the two different channels and for different types of sources. The examples were chosen in order to present typical objects for the two channels and also to present interesting cases as they may arise with the use of WFC3.
What is the exposure time needed to obtain a signal-to-noise of 10 for a point source of spectral type F0 V (Castelli and Kurucz Model, T=7250 K), normalized to V = 27.5, when using the UVIS F555W filter? Assume a photometry box size of 5×5 pixels, detector chip 2 (generally the preferred chip; see Section 6.4.4), average standard zodiacal light and earth shine, and, to start with, 1 frame.
The WFC3 Exposure Time Calculator (ETC) gives an exposure time of 4579 sec = 76.3 min. A single long exposure ~48 min will fit the typical HST orbit, so this observation will require more than 1 orbit. One long exposure per orbit would be a poor choice because many pixels would have bad fluxes in both of the exposures due to cosmic rays (Section 5.4.10). For multi-orbit observations, taking two dithered exposures per orbit (to move bad pixels as well as to allow for cosmic ray removal) is generally sufficient. Recalculating the needed exposure time using 4 frames (more read noise, higher fluxes and flux-dependent noise components to preserve S/N=10) gives 5088 sec, or 1272 sec = 21.2 min per frame. In a typical HST orbit, there is time for two 23 min exposures, so a box pattern (for optimal sampling of the PSF: see Appendix C:) will nicely fit two orbits. The background level per frame far exceeds the level where CTE losses become a concern (see Section 6.9), so post-flash is not needed and the ETC does not post an advisory.
Using the pencil-and-paper method, for filter F555W Table 9.1 gives the integral QTdλ/λ as 0.0835 and indicates that the fraction of the star’s light included in the 5x5 pixel square aperture is 0.78. Table A.1 shows an ABν correction term of 0.03 for filter F555W for a star with an effective temperature of 7,500 K (the closest value to our star’s effective temperature 7250 K). The count rate for our V = 25 mag star can then be calculated from the equation
or C= 2.5×1011*0.0835*0.78*10-0.4(27.5+0.03) = 0.1584 e s−1, which agrees with the ETC-returned value of 0.158 e- s-1.
The exposure time can then be found by using the equation
to where we use
Σ = 10
Npix=25
Bsky = 0.0377 e-/s/pix from Table 9.1
Bdet = 0.0015 e-/s/pix from Table 5.1
Nbin = 1
P = 0 (no post-flash, so the post-flash noise term is not included)
which gives t = 5265 sec, compared to the ETC-derived value of 5088 sec.
Calculate the signal to noise obtained in 1200 seconds for a point source of spectral type F0 V (Kurucz & Castelli Model, T=7250 K)), normalized to Johnson V = 23.5 mag, using the UVIS F225W filter, a photometry box size of 5x5 pixels, 1 frame, detector chip 2, and with average standard zodiacal light, average standard earth shine and average Air Glow values.
Recalculate the SNR as before, but this time adding 9 post-flash electrons. Now the ETC returns SNR=4.17, and no warning messages. This SNR value is lower than the case without post flash because the postflash electrons contribute to the noise.
Σ = 10
First calculate the count rate for the object using:
and values of:
ABν=2.84
V=23.5 mag
QTdλ/λ = 0.0169
εf = 0.71
to obtain C = 0.0789 e-/second.
Now calculate the signal-to-noise ratio, using
Npix = 25
Bsky = 0.0066 e-/s/pix from Table 9.1
Bdet = 0.0015 e-/s/pix from Table 5.1