Exposure Time and S/N calculated by the ETC for the G130M/1055 and
G130M/1096 Settings are not correct
The focus of the G130M/1055 and G130M/1096 settings were recently adjusted to increase their resolution. As a consequence, the spectral height and size of the resolution
element (resel) have changed. Because of these two changes, exposure times may be underestimated by as much as a factor of 4, and S/N may be overestimated by as much as
a factor of 2. The ETC assumes a resel of 30 pixels and an extraction height of 47 pixels,
but the true resels are smaller and depend on wavelength; the true extraction heights are
larger. The ETC will be updated for phase II of Cycle 21, in the meantime the correction
factors given in the Known Issues page of the ETC should be used. Conversely, users
can refer to the formulas below to determine their own correction based on more detailed
information.
ETC Corrections for resel size and extraction height The correction factors
were calculated in the following manner by utilizing the standard exposure time and S/N
calculations as detailed in the ETC Users guide. The ETC assumes that all flux from
the source is captured within the default extraction height multiplied by the spectral resel
width to determine the total count rate per resel. The corrections can be determined by
ratioing the equation for exposure time or S/N with the correct resel size and extraction
height and with what the ETC calculates.
If one defines the ratio of source count rate per pixel to dark count rate per pixel as:
α=
C
Bdark
(1)
The correction for exposure time is given by:
t=
30 α + EH
tET C
R α + 47
(2)
where EH refers to the extraction height (listed in Table 1) for a given central wavelength,
R is the resel size in pixels (which can vary with wavelength and is listed in Table 2) and
tET C is the ETC calculated exposure time. As an example, consider a faint source where
α ∼ 0 at λ=950Å in the G130M/1096 central wavelength. The extraction height for this
setting is 59 pixels and the resel is roughly expected to be 12 pixels. The full correction
factor would be 3.1×tET C . If α ≫ 59 as would be the case for a very bright source, then
the full correction factor would be 2.5×tET C . Similarly, one can calculate a new S/N:
S/N =
R α+1
30 α + EH
47
!1
2
SN RET C .
(3)
Tables 3 and 4 give corrections to the ETC derived S/N and exposure time for given
values of α as a function of wavelength.
1
G130M/1055
G130M/1096
63
59
Table 1: Extraction Heights for the 1055 and 1096 central wavelengths
Caveats Since these central wavelengths have not been fully characterized, the quoted
resel sizes may change at a later date. The resel sizes quoted here are estimated from raytrace models of the settings at the current focii that include the mid-frequency wavelength
errors which broaden the COS FUV line spread function. If the wavelength of interest is
near a bright geocoronal line such as Lyman α, the sky will need to be taken into account.
In those cases, one must return to the original S/N and exposure time equations and
determine the correction for the specific situation while taking the sky contribution into
account. Similarly, the equations above are most appropriate for point sources. Observers
doing calculations for extended objects should contact the STScI helpdesk for further
information.
Setting
Segment
B
1055
A
B
1096
A
Wavelength
900
950
1040
1050
1120
1190
940
1000
1050
1080
1100
1170
1230
Resel Size
10.6
8.3
19.0
21.5
32.1
42.6
11.9
8.4
8.6
11.9
15.3
23.9
31.6
Table 2: Predicted Resel Sizes
2
Setting
Extraction Height
(pixels)
Segment
B
1055
63
A
B
1096
59
A
λ
(Å)
900
950
1040
1050
1120
1190
940
1000
1050
1080
1100
1170
1230
Resel
(pixels)
10.6
8.3
19.0
21.5
32.1
42.6
11.9
8.4
8.6
11.9
15.3
23.9
31.6
α=0
α=1
α=10
α=100
α=∞
3.79
4.85
2.12
1.87
1.25
0.94
3.16
4.47
4.36
3.16
2.46
1.57
1.19
3.77
4.83
2.11
1.86
1.25
0.94
3.14
4.45
4.34
3.15
2.45
1.57
1.19
3.62
4.64
2.03
1.79
1.20
0.90
3.04
4.31
4.21
3.05
2.37
1.52
1.15
3.13
4.01
1.75
1.55
1.04
0.78
2.72
3.85
3.76
2.73
2.12
1.35
1.03
2.82
3.62
1.58
1.40
0.93
0.70
2.51
3.56
3.48
2.52
1.96
1.25
0.95
α=0
α=1
α=10
α=100
α=∞
0.51
0.45
0.69
0.73
0.89
1.03
0.56
0.47
0.48
0.56
0.64
0.80
0.92
0.52
0.46
0.69
0.73
0.90
1.03
0.56
0.47
0.48
0.56
0.64
0.80
0.92
0.53
0.46
0.70
0.75
0.91
1.05
0.57
0.48
0.49
0.57
0.65
0.81
0.93
0.57
0.50
0.76
0.80
0.98
1.13
0.61
0.51
0.52
0.61
0.69
0.86
0.99
0.59
0.53
0.80
0.85
1.03
1.19
0.63
0.53
0.54
0.63
0.71
0.89
1.03
Table 3: Exposure Time correction factors
Setting
Extraction Height
(pixels)
Segment
B
1055
63
A
B
1096
59
A
λ
(Å)
900
950
1040
1050
1120
1190
940
1000
1050
1080
1100
1170
1230
Resel
(pixels)
10.6
8.3
19.0
21.5
32.1
42.6
11.9
8.4
8.6
11.9
15.3
23.9
31.6
Table 4: S/N correction factors
3