9.3 Calculating Sensitivities from Tabulated Data

Most observers will use the ETC or synphot to determine count rates and sensitivities for WFC3 observations. However, it is also possible to calculate count rates and S/N ratios by hand, and this exercise will give the observer better insight into the sensitivity calculations. The formulae and tabular values required to calculate sensitivities for the WFC3 imaging and spectroscopic modes are provided in this section. Using them, one can calculate the expected count rates and the S/N ratio achieved in a given exposure time, based on the spectral energy distribution of a source. The formulae are given in terms of sensitivities, but we also provide transformation equations between throughput (QT) and sensitivity (S) for imaging and spectroscopic modes.

The tabular data presented here was derived using on-orbit data that was processed with ground-based flat field reference files. (See WFC3 ISR 2009-30 and WFC3 ISR 2009-31.) These flat fields are in error by up to several percent on large spatial scales. More accurate zeropoints (see Online arrow below) have been determined by using better flat fields (see Sections 5.4.3 and 5.7.4) and by deriving filter-specific solutions instead of making a low-order fit across wavelengths. Monitoring of photometric performance over the first year of operations has shown the WFC3/UVIS detector to be stable to rms ~ 0.5% (WFC3 ISR 2010-14) and the WFC3/IR detector to be stable to rms ~ 0.5% to 1.0%, depending on filter (WFC3 ISR 2011-08).

(tick)

For more accurate photometric zeropoints, see the WFC3 Photometric Zeropoints website.

Throughputs are presented in graphical form as a function of wavelength for each of the imaging filters and grisms in Appendix A. Given the source characteristics and the sensitivity of the WFC3 configuration, calculating the expected count rate over a given number of pixels is straightforward. The additional information required is the encircled energy fraction (εf) in the peak pixel, the plate scale, and (for the spectroscopic modes) the dispersions of the grisms.

The sensitivity information is summarized in Tables 9.1 and 9.2. In these two tables, and in the following discussion, the filter transmission functions are denoted T(λ), and the overall system response function (apart from the filter transmission) is denoted Q(λ). The terms “counts” and “count rates” always refer to the number of detected electrons, which is converted to data numbers, or DNs, upon readout according to the gain factors for the detectors. The measured gain is 1.55 e/DN for the UVIS channel and ~2.4 e/DN for the IR channel (see Table 5.1).

In Tables 9.1 and 9.2, the following quantities are listed:

  1. The filter or grism designation.
  2. The “pivot wavelength” for that filter or grism, λp. Pivot wavelength is a source-independent measure of the characteristic wavelength of a bandpass, defined such that it is the same if the input spectrum is given in units of Fλ or Fν (see A. TokunagW.Vacca 2005, PASP117, 421):

    \lambda_p=\sqrt{\frac{\int Q(\lambda)T(\lambda)\lambda d\lambda} {\int Q(\lambda)T(\lambda)d\lambda /\lambda}}.
  3. The integral QλTλ dλ/λ, used to determine the count rate when given the astronomical magnitude of the source.
  4. The ABmag zero-point, defined as the AB magnitude of a source with a flat Fν that yields 1 e s1 with the specified configuration.
  5. The sensitivity integral, Sλ dλ, defined (see Section 9.4) as the count rate that would be detected from a flat Fλ source with a flux of 1 erg cm2 s−1 Å1.
  6. The ensquared energy, defined as the fraction of PSF flux enclosed in the default photometry aperture (5 × 5 pixels for the UVIS and 3 × 3 pixels for the IR).
  7. The fraction of the total PSF flux in the central pixel for a centered stellar source, useful for determining the peak count rate to check for saturation (see also Appendix D).
  8. The sky background count rate (e s−1), which is the count rate that would be measured with average zodiacal background and average earth-shine. For the IR channel, this quantity also includes the thermal background from HST and the instrument. It does not include the contribution from the detectors themselves (i.e., dark current and read noise).

The next two sections describe how to calculate two quantities:

  • The count rate in e s−1C, from your source over some selected area on the detector containing Npix ­pixels.
  • The peak count rate in e s−1 pixel −1Pcr, from your source, which is useful for avoiding saturated exposures.

We consider the cases of point sources and diffuse sources separately in each of the following imaging and spectroscopy sections.

Table 9.1: Sensitivity Data for WFC3/UVIS Channel.  

Spectral Element

Pivot λ
(Å)

QλTλ dλ/λ

ABMAG zero-point

Sλ dλ

Ensquared energy

Energy in central pixel

Background (sky) rate

F200LP

4970.9

0.3543

27.36

1.99E+19

0.75

0.17

0.1277

F218W

2230.6

0.0060

22.93

6.77E+16

0.70

0.13

0.0005

F225W

2373.6

0.0169

24.06

2.17E+17

0.71

0.14

0.0066

F275W

2710.1

0.0183

24.14

3.06E+17

0.74

0.15

0.0037

F280N

2833.5

0.0010

20.93

1.74E+16

0.74

0.16

0.0000

F300X

2822.1

0.0378

24.93

6.86E+17

0.74

0.16

0.0133

F336W

3354.8

0.0292

24.65

7.49E+17

0.77

0.17

0.0018

F343N

3435.2

0.0146

23.90

3.93E+17

0.77

0.17

0.0011

F350LP

5858.4

0.2425

26.95

1.90E+19

0.76

0.17

0.1077

F373N

3730.2

0.0024

21.94

7.63E+16

0.78

0.18

0.0003

F390M

3897.3

0.0115

23.63

3.97E+17

0.78

0.18

0.0017

F390W

3924.5

0.0567

25.37

1.99E+18

0.78

0.18

0.0098

F395N

3955.2

0.0047

22.67

1.68E+17

0.78

0.18

0.0008

F410M

4109.0

0.0112

23.61

4.31E+17

0.78

0.18

0.0028

F438W

4326.5

0.0345

24.83

1.47E+18

0.78

0.19

0.0099

F467M

4682.6

0.0122

23.70

6.10E+17

0.78

0.19

0.0046

F469N

4688.1

0.0021

21.81

1.07E+17

0.78

0.19

0.0008

F475W

4773.6

0.0763

25.69

3.96E+18

0.78

0.19

0.0278

F475X

4941.4

0.1173

26.16

6.52E+18

0.78

0.18

0.0444

F487N

4871.4

0.0031

22.22

1.68E+17

0.78

0.19

0.0012

F502N

5009.6

0.0034

22.31

1.93E+17

0.78

0.19

0.0014

F547M

5447.4

0.0312

24.72

2.11E+18

0.78

0.18

0.0148

F555W

5308.1

0.0835

25.79

5.36E+18

0.78

0.18

0.0377

F600LP

7451.3

0.0892

25.86

1.13E+19

0.72

0.16

0.0575

F606W

5887.5

0.1090

26.08

8.60E+18

0.77

0.18

0.0569

F621M

6218.6

0.0280

24.60

2.47E+18

0.76

0.18

0.0163

F625W

6241.4

0.0651

25.52

5.78E+18

0.76

0.18

0.0374

F631N

6304.3

0.0023

21.90

2.09E+17

0.76

0.18

0.0014

F645N

6453.6

0.0032

22.26

3.07E+17

0.75

0.17

0.0019

F656N

6561.4

0.0007

20.54

6.48E+16

0.75

0.17

0.0004

F657N

6566.6

0.0048

22.68

4.70E+17

0.75

0.17

0.0029

F658N

6584.0

0.0011

21.09

1.08E+17

0.75

0.17

0.0006

F665N

6655.9

0.0051

22.74

5.10E+17

0.75

0.17

0.0031

F673N

6765.9

0.0044

22.58

4.54E+17

0.74

0.17

0.0027

F680N

6877.4

0.0137

23.83

1.47E+18

0.74

0.17

0.0086

F689M

6876.4

0.0249

24.48

2.68E+18

0.74

0.17

0.0156

F763M

7613.6

0.0196

24.21

2.58E+18

0.71

0.16

0.0130

F775W

7648.3

0.0354

24.86

4.72E+18

0.71

0.16

0.0236

F814W

8029.9

0.0443

25.10

6.51E+18

0.70

0.15

0.0299

F845M

8437.6

0.0133

23.79

2.15E+18

0.68

0.14

0.0092

F850LP

9168.4

0.0123

23.71

2.35E+18

0.66

0.13

0.0086

F953N

9530.6

0.0005

20.34

1.14E+17

0.65

0.12

0.0004

FQ232N

2431.1

0.0005

20.13

6.12E+15

0.71

0.14

0.0000

FQ243N

2476.4

0.0007

20.52

9.10E+15

0.72

0.14

0.0000

FQ378N

3792.4

0.0052

22.78

1.70E+17

0.78

0.18

0.0006

FQ387N

3873.7

0.0015

21.44

5.21E+16

0.78

0.18

0.0002

FQ422M

4219.2

0.0050

22.73

2.02E+17

0.78

0.18

0.0013

FQ436N

4367.2

0.0019

21.67

8.16E+16

0.78

0.19

0.0005

FQ437N

4371.0

0.0014

21.32

5.92E+16

0.78

0.19

0.0004

FQ492N

4933.4

0.0058

22.90

3.23E+17

0.78

0.19

0.0023

FQ508N

5091.0

0.0066

23.03

3.89E+17

0.78

0.19

0.0028

FQ575N

5757.7

0.0007

20.64

5.51E+16

0.77

0.18

0.0004

FQ619N

6198.5

0.0025

21.99

2.20E+17

0.76

0.18

0.0015

FQ634N

6349.2

0.0026

22.02

2.38E+17

0.76

0.18

0.0015

FQ672N

6716.4

0.0007

20.61

7.30E+16

0.75

0.17

0.0004

FQ674N

6730.7

0.0005

20.22

5.09E+16

0.75

0.17

0.0003

FQ727N

7275.2

0.0018

21.65

2.21E+17

0.73

0.16

0.0012

FQ750N

7502.5

0.0017

21.57

2.19E+17

0.72

0.16

0.0011

FQ889N

8892.2

0.0011

21.05

1.91E+17

0.67

0.13

0.0007

FQ906N

9057.8

0.0010

20.94

1.79E+17

0.66

0.13

0.0007

FQ924N

9247.6

0.0008

20.70

1.50E+17

0.66

0.13

0.0005

FQ937N

9372.3

0.0007

20.53

1.31E+17

0.65

0.13

0.0005

G280

5047.0

0.3172

25.87

2.89E+18

0.81

0.27

0.1136


Table 9.2: Sensitivity Data for WFC3/IR Channel.

Spectral Element

Pivot λ
(Å)

QλTλ dλ/λ

ABMAG zero-point

Sλ dλ

Ensquared energy

Energy in central pixel

Background (sky + thermal) rate

F098M

9864.7

0.0753

25.68

1.67E+19

0.79

0.38

0.6106

F105W

10551.0

0.1297

26.27

3.29E+19

0.78

0.37

1.0150

F110W

11534.4

0.2161

26.82

6.55E+19

0.76

0.36

1.6611

F125W

12486.1

0.1269

26.24

4.51E+19

0.74

0.34

0.9986

F126N

12584.6

0.0060

22.93

2.16E+18

0.74

0.34

0.0957

F127M

12740.2

0.0293

24.65

1.08E+19

0.74

0.34

0.2697

F128N

12831.5

0.0065

23.01

2.43E+18

0.74

0.33

0.0984

F130N

13005.4

0.0065

23.02

2.50E+18

0.73

0.33

0.0993

F132N

13187.5

0.0063

22.98

2.49E+18

0.73

0.33

0.0976

F139M

13837.5

0.0252

24.49

1.10E+19

0.71

0.32

0.2391

F140W

13922.8

0.1550

26.46

6.84E+19

0.71

0.32

1.1694

F153M

15321.9

0.0245

24.46

1.31E+19

0.67

0.29

0.2361

F160W

15369.1

0.0970

25.95

5.22E+19

0.67

0.29

0.8002

F164N

16403.1

0.0060

22.93

3.67E+18

0.65

0.28

0.1050

F167N

16641.1

0.0058

22.89

3.65E+18

0.64

0.27

0.1092

G102

9970.4

0.1110

26.10

2.51E+19

0.79

0.42

1.2040

G141

13860.0

0.1796

26.62

7.86E+19

0.73

0.34

1.8619