9.3 Calculating Sensitivities from Tabulated Data

Most observers will use the ETC or stsynphot to determine count rates and sensitivities for WFC3 observations. However, it is also possible to calculate count rates and S/N ratios manually, 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 acquired over ~10 years (see WFC3 ISR 2021-04 and WFC3 ISR 2020-10 for the latest UVIS and IR photometric calibration). Monitoring of the photometric performance shows that the WFC3/UVIS detector sensitivity changes by ~0.1 - 0.2 % per year, depending on the filter, so the values listed in Table 9.1 are calculated for a 'reference epoch' defined at MJD = 55008 (June 26, 2009). A new WFC3 notebook shows how to use stsynphot to compute sensitivity values for any WFC3 observing mode, 'obsmode', i.e. a combination of the desired 'instrument, detector, filter, date, and aperture'. This may be used to determine the UVIS tabular values for any observation date. The new time-dependent inverse sensitivities provide a photometric internal precision of < 0.5% for wide-, medium-, and narrow-band filters. As of late 2021, the WFC3/IR inverse sensitivities do not include any time-dependence, and the values listed in Table 9.2 are valid for all observation dates. Current estimates of the IR photometric uncertainties are ~2% for broad-band filters and 5-10% for narrow-band filters. For a more detailed discussion about WFC3 photometric calibration, see Section 9.1 of the Data Handbook.

Sensitivity data for the G280 grism listed in Table 9.1 is derived from ground-based calibration during Thermal Vacuum testing, as described in WFC3 ISR 2009-01. Sensitivity data for the G102 and G141 grisms provided in Table 9.2 were established by observing the white dwarf spectrophotometric standard stars GD153 and GD71 at several positions across the field (WFC3 ISRs 2009-17, 2009-18, and 2011-05).  For more detail on the calibration of the WFC3 grisms, see Section 9.3 of the Data Handbook.


(tick)

For the latest set of photometric inverse sensitivities (zeropoints), see the WFC3 Photometric Calibration website.


Filter throughputs are presented in graphical form as a function of wavelength for both chips, UVIS1 and UVIS2, and all 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. Here and in the following discussion, the filter transmission functions are denoted Tλ , and the overall system response function (apart from the filter transmission) is denoted Qλ. 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 Tokunaga & Vacca 2005, PASP117, 421).  For further discussion on synphot formulae, see the photometric properties webpage


    \lambda_p=\sqrt{\frac{\int Q_{\lambda}T_{\lambda} \lambda d\lambda} {\int Q_{\lambda}T_{\lambda} \lambda^{-1} d\lambda }}.
  3. The bandpass 'efficiency', defined as the integral QλTλ λ-1 dλ, is used to determine the count rate when given the astronomical magnitude of the source. In the latest python-based stsynphot software, this dimensionless quantity 'efficiency' is equivalent to the result for 'qtlam' in the older IRAF STSDAS synphot task 'bandpar'.
  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 as the count rate that would be detected from a flat Fλ source with a flux of 1 erg cm2 s−1 Å1 (see Section 9.4). The sensitivity integral is equivalent to PHOTFLAM-1, where PHOTFLAM is a header keyword defined as the 'inverse sensitivity', representing the flux density (erg cm-2 s-1 Å-1) of a source that produces a count rate of 1 e s−1.
  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 (in 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:

  • C, the count rate of the source in e s−1 over some selected area on the detector containing Npix ­pixels.
  • Pcr , the peak count rate of the source in e s−1 pixel −1, 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 the WFC3/UVIS Channel, provided for both UVIS1 and UVIS2. Values for the quad filters are listed in the UVIS1 column, but are specific to the spectral element associated with each detector amplifier. For more discussion, see Section 6.5.

Spectral Element

UVIS1

Pivot λ
(Å)

UVIS2

Pivot λ
(Å)

UVIS1

Efficiency
QλTλ λ-1dλ

UVIS2

Efficiency
QλTλ λ-1dλ

UVIS1

AB zeropoint

UVIS2

AB zeropoint

UVIS1

Sensitivity
Sλ dλ

UVIS2

Sensitivity
Sλ

Ensquared energy

Energy in central pixel

Background (sky) rate

F200LP

4971.9

4875.1

0.3614

0.3770

27.336

27.380

1.9518E+19

1.9556E+19

0.75

0.17

0.1277

F218W

2228.0

2223.7

0.0061

0.0078

22.937

23.212

6.8194E+16

8.7489E+16

0.70

0.13

0.0005

F225W

2372.1

2358.4

0.0171

0.0209

24.063

24.279

2.1811E+17

2.6305E+17

0.71

0.14

0.0066

F275W

2709.7

2703.3

0.0186

0.0197

24.157

24.222

3.1030E+17

3.2800E+17

0.74

0.15

0.0037

F280N

2832.9

2830.0

0.0010

0.0010

20.918

20.930

1.7173E+16

1.7333E+16

0.74

0.16

0.0000

F300X

2820.5

2805.8

0.0392

0.0425

24.964

25.051

7.0686E+17

7.5838E+17

0.74

0.16

0.0133

F336W

3354.5

3354.7

0.0304

0.0313

24.691

24.719

7.7760E+17

7.9777E+17

0.77

0.17

0.0018

F343N

3435.2

3435.2

0.0145

0.0150

23.887

23.924

3.8886E+17

4.0228E+17

0.77

0.17

0.0011

F350LP

5873.9

5851.2

0.2465

0.2399

26.965

26.936

1.9360E+19

1.8702E+19

0.76

0.17

0.1077

F373N

3730.2

3730.2

0.0023

0.0024

21.908

21.935

7.4080E+16

7.5971E+16

0.78

0.18

0.0003

F390M

3897.2

3897.0

0.0113

0.0115

23.622

23.638

3.9206E+17

3.9780E+17

0.78

0.18

0.0017

F390W

3923.7

3920.7

0.0569

0.0575

25.372

25.381

1.9932E+18

2.0061E+18

0.78

0.18

0.0098

F395N

3955.2

3955.2

0.0047

0.0047

22.668

22.670

1.6774E+17

1.6808E+17

0.78

0.18

0.0008

F410M

4109.0

4108.9

0.0111

0.0111

23.596

23.594

4.2562E+17

4.2499E+17

0.78

0.18

0.0028

F438W

4326.2

4325.1

0.0348

0.0347

24.837

24.834

1.4794E+18

1.4754E+18

0.78

0.19

0.0099

F467M

4682.6

4682.6

0.0121

0.0122

23.694

23.698

6.0474E+17

6.0750E+17

0.78

0.19

0.0046

F469N

4688.1

4688.1

0.0021

0.0022

21.816

21.820

1.0754E+17

1.0793E+17

0.78

0.19

0.0008

F475W

4773.1

4772.2

0.0772

0.0767

25.704

25.696

4.0026E+18

3.9727E+18

0.78

0.19

0.0278

F475X

4940.7

4937.4

0.1172

0.1166

26.156

26.152

6.5024E+18

6.4704E+18

0.78

0.18

0.0444

F487N

4871.4

4871.4

0.0031

0.0032

22.227

22.241

1.6953E+17

1.7182E+17

0.78

0.19

0.0012

F502N

5009.6

5009.6

0.0034

0.0034

22.326

22.322

1.9647E+17

1.9562E+17

0.78

0.19

0.0014

F547M

5447.5

5447.2

0.0323

0.0324

24.755

24.759

2.1759E+18

2.1838E+18

0.78

0.18

0.0148

F555W

5308.4

5307.9

0.0853

0.0843

25.810

25.796

5.4573E+18

5.3891E+18

0.78

0.18

0.0377

F600LP

7468.1

7453.7

0.0913

0.0894

25.882

25.857

1.1546E+19

1.1242E+19

0.72

0.16

0.0575

F606W

5889.2

5887.7

0.1100

0.1093

26.087

26.079

8.6738E+18

8.5992E+18

0.77

0.18

0.0569

F621M

6218.9

6219.2

0.0283

0.0281

24.612

24.607

2.4865E+18

2.4732E+18

0.76

0.18

0.0163

F625W

6242.6

6242.0

0.0657

0.0656

25.525

25.525

5.8055E+18

5.8035E+18

0.76

0.18

0.0374

F631N

6304.3

6304.3

0.0023

0.0023

21.885

21.890

2.0722E+17

2.0819E+17

0.76

0.18

0.0014

F645N

6453.6

6453.6

0.0032

0.0032

22.243

22.238

3.0211E+17

3.0063E+17

0.75

0.17

0.0019

F656N

6561.4

6561.4

0.0006

0.0006

20.422

20.457

5.8353E+16

6.0241E+16

0.75

0.17

0.0004

F657N

6566.6

6566.6

0.0047

0.0047

22.659

22.658

4.5840E+17

4.5821E+17

0.75

0.17

0.0029

F658N

6584.0

6583.9

0.0010

0.0010

21.027

21.038

1.0260E+17

1.0356E+17

0.75

0.17

0.0006

F665N

6655.9

6655.8

0.0050

0.0050

22.734

22.721

5.0485E+17

4.9898E+17

0.75

0.17

0.0031

F673N

6765.9

6765.9

0.0044

0.0043

22.588

22.562

4.5598E+17

4.4549E+17

0.74

0.17

0.0027

F680N

6877.6

6877.4

0.0136

0.0133

23.818

23.797

1.4634E+18

1.4355E+18

0.74

0.17

0.0086

F689M

6876.8

6876.5

0.0250

0.0248

24.478

24.468

2.6854E+18

2.6620E+18

0.74

0.17

0.0156

F763M

7614.4

7612.7

0.0198

0.0194

24.226

24.205

2.6112E+18

2.5606E+18

0.71

0.16

0.0130

F775W

7651.4

7648.3

0.0359

0.0355

24.871

24.861

4.7778E+18

4.7284E+18

0.71

0.16

0.0236

F814W

8039.1

8029.3

0.0453

0.0446

25.127

25.112

6.6756E+18

6.5651E+18

0.70

0.15

0.0299

F845M

8439.1

8437.3

0.0136

0.0135

23.822

23.812

2.2101E+18

2.1910E+18

0.68

0.14

0.0092

F850LP

9176.1

9169.9

0.0141

0.0135

23.856

23.810

2.6964E+18

2.5816E+18

0.66

0.13

0.0086

F953N

9530.6

9530.5

0.0006

0.0006

20.425

20.383

1.2343E+17

1.1878E+17

0.65

0.12

0.0004

FQ232N

2432.2

-

0.0006

-

20.412

-

7.9447E+15

-

0.71

0.14

0.0000

FQ243N

2476.3

-

0.0008

-

20.738

-

1.1074E+16

-

0.72

0.14

0.0000

FQ378N

3792.4

-

0.0049

-

22.751

-

1.6584E+17

-

0.78

0.18

0.0006

FQ387N

3873.7

-

0.0014

-

21.340

-

4.7783E+16

-

0.78

0.18

0.0002

FQ422M

4219.2

-

0.0047

-

22.673

-

1.9275E+17

-

0.78

0.18

0.0013

FQ436N

4367.2

-

0.0018

-

21.630

-

7.8839E+16

-

0.78

0.19

0.0005

FQ437N

4371.0

-

0.0013

-

21.268

-

5.7864E+16

-

0.78

0.19

0.0004

FQ492N

4933.4

-

0.0056

-

22.868

-

3.1361E+17

-

0.78

0.19

0.0023

FQ508N

5091.1

-

0.0058

-

22.881

-

3.3360E+17

-

0.78

0.19

0.0028

FQ575N

5757.7

-

0.0007

-

20.530

-

4.9392E+16

-

0.77

0.18

0.0004

FQ619N

6198.5

-

0.0024

-

21.940

-

2.1192E+17

-

0.76

0.18

0.0015

FQ634N

6349.2

-

0.0024

-

21.958

-

2.2567E+17

-

0.76

0.18

0.0015

FQ672N

6716.4

-

0.0006

-

20.395

-

6.5820E+16

-

0.75

0.17

0.0004

FQ674N

6730.7

-

0.0006

-

20.692

-

6.0035E+16

-

0.75

0.17

0.0003

FQ727N

7275.2

-

0.0017

-

21.581

-

2.1112E+17

-

0.73

0.16

0.0012

FQ750N

7502.5

-

0.0017

-

21.502

-

2.1647E+17

-

0.72

0.16

0.0011

FQ889N

8892.2

-

0.0011

-

21.057

-

1.9722E+17

-

0.67

0.13

0.0007

FQ906N

9057.8

-

0.0010

-

20.951

-

1.8748E+17

-

0.66

0.13

0.0007

FQ924N

9247.6

-

0.0008

-

20.753

-

1.5735E+17

-

0.66

0.13

0.0005

FQ937N

9372.4

-

0.0007

-

20.648

-

1.3818E+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 the WFC3/IR Channel.

Spectral Element

Pivot λ
(Å)

Efficiency
∫QλTλ λ-1

AB zeropoint

Sensitivity
∫Sλ dλ

Ensquared energy

Energy in central pixel

Background (sky + thermal) rate

F098M

9864.7

0.0745

25.666

1.6487E+19

0.79

0.38

0.6106

F105W

10551.1

0.1293

26.264

3.2779E+19

0.78

0.37

1.0150

F110W

11534.5

0.2149

26.819

6.5283E+19

0.76

0.36

1.6611

F125W

12486.1

0.1257

26.232

4.4551E+19

0.74

0.34

0.9986

F126N

12584.9

0.0056

22.849

2.0132E+18

0.74

0.34

0.0957

F127M

12740.3

0.0287

24.625

1.0579E+19

0.74

0.34

0.2697

F128N

12831.8

0.0062

22.956

2.2999E+18

0.74

0.33

0.0984

F130N

13005.7

0.0063

22.981

2.4145E+18

0.73

0.33

0.0993

F132N

13187.7

0.0060

22.933

2.3755E+18

0.73

0.33

0.0976

F139M

13837.6

0.0247

24.466

1.0737E+19

0.71

0.32

0.2391

F140W

13922.9

0.1536

26.450

6.7755E+19

0.71

0.32

1.1694

F153M

15322.1

0.0244

24.447

1.2960E+19

0.67

0.29

0.2361

F160W

15369.2

0.0963

25.936

5.1469E+19

0.67

0.29

0.8002

F164N

16403.5

0.0058

22.892

3.5389E+18

0.65

0.28

0.1050

F167N

16641.6

0.0061

22.937

3.8146E+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