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).
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:
- The filter or grism designation.
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, PASP, 117, 421):
\lambda_p=\sqrt{\frac{\int Q(\lambda)T(\lambda)\lambda d\lambda} {\int Q(\lambda)T(\lambda)d\lambda /\lambda}}. - The integral ∫QλTλ dλ/λ, used to determine the count rate when given the astronomical magnitude of the source.
- The ABmag zero-point, defined as the AB magnitude of a source with a flat Fν that yields 1 e− s−1 with the specified configuration.
- 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 cm−2 s−1 Å−1.
- 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).
- 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).
- 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−1, C, from your source over some selected area on the detector containing Npix pixels.
- The peak count rate in e− s−1 pixel −1, Pcr, 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 | ∫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 | ∫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 |
-
WFC3 Instrument Handbook
- • Acknowledgments
- Chapter 1: Introduction to WFC3
- Chapter 2: WFC3 Instrument Description
- Chapter 3: Choosing the Optimum HST Instrument
- Chapter 4: Designing a Phase I WFC3 Proposal
- Chapter 5: WFC3 Detector Characteristics and Performance
-
Chapter 6: UVIS Imaging with WFC3
- • 6.1 WFC3 UVIS Imaging
- • 6.2 Specifying a UVIS Observation
- • 6.3 UVIS Channel Characteristics
- • 6.4 UVIS Field Geometry
- • 6.5 UVIS Spectral Elements
- • 6.6 UVIS Optical Performance
- • 6.7 UVIS Exposure and Readout
- • 6.8 UVIS Sensitivity
- • 6.9 Charge Transfer Efficiency
- • 6.10 Photometric Calibration
- • 6.11 Other Considerations for UVIS Imaging
- • 6.12 UVIS Observing Strategies
- Chapter 7: IR Imaging with WFC3
- Chapter 8: Slitless Spectroscopy with WFC3
-
Chapter 9: WFC3 Exposure-Time Calculation
- • 9.1 Overview
- • 9.2 The WFC3 Exposure Time Calculator - ETC
- • 9.3 Calculating Sensitivities from Tabulated Data
- • 9.4 Count Rates: Imaging
- • 9.5 Count Rates: Slitless Spectroscopy
- • 9.6 Estimating Exposure Times
- • 9.7 Sky Background
- • 9.8 Interstellar Extinction
- • 9.9 Exposure-Time Calculation Examples
- Chapter 10: Overheads and Orbit Time Determinations
-
Appendix A: WFC3 Filter Throughputs
- • A.1 Introduction
-
A.2 Throughputs and Signal-to-Noise Ratio Data
- • UVIS F200LP
- • UVIS F218W
- • UVIS F225W
- • UVIS F275W
- • UVIS F280N
- • UVIS F300X
- • UVIS F336W
- • UVIS F343N
- • UVIS F350LP
- • UVIS F373N
- • UVIS F390M
- • UVIS F390W
- • UVIS F395N
- • UVIS F410M
- • UVIS F438W
- • UVIS F467M
- • UVIS F469N
- • UVIS F475W
- • UVIS F475X
- • UVIS F487N
- • UVIS F502N
- • UVIS F547M
- • UVIS F555W
- • UVIS F600LP
- • UVIS F606W
- • UVIS F621M
- • UVIS F625W
- • UVIS F631N
- • UVIS F645N
- • UVIS F656N
- • UVIS F657N
- • UVIS F658N
- • UVIS F665N
- • UVIS F673N
- • UVIS F680N
- • UVIS F689M
- • UVIS F763M
- • UVIS F775W
- • UVIS F814W
- • UVIS F845M
- • UVIS F850LP
- • UVIS F953N
- • UVIS FQ232N
- • UVIS FQ243N
- • UVIS FQ378N
- • UVIS FQ387N
- • UVIS FQ422M
- • UVIS FQ436N
- • UVIS FQ437N
- • UVIS FQ492N
- • UVIS FQ508N
- • UVIS FQ575N
- • UVIS FQ619N
- • UVIS FQ634N
- • UVIS FQ672N
- • UVIS FQ674N
- • UVIS FQ727N
- • UVIS FQ750N
- • UVIS FQ889N
- • UVIS FQ906N
- • UVIS FQ924N
- • UVIS FQ937N
- • IR F098M
- • IR F105W
- • IR F110W
- • IR F125W
- • IR F126N
- • IR F127M
- • IR F128N
- • IR F130N
- • IR F132N
- • IR F139M
- • IR F140W
- • IR F153M
- • IR F160W
- • IR F164N
- • IR F167N
- Appendix B: Geometric Distortion
- Appendix C: Dithering and Mosaicking
- Appendix D: Bright-Object Constraints and Image Persistence
-
Appendix E: Reduction and Calibration of WFC3 Data
- • E.1 The STScI Reduction and Calibration Pipeline
- • E.2 The SMOV Calibration Plan
- • E.3 The Cycle 17 Calibration Plan
- • E.4 The Cycle 18 Calibration Plan
- • E.5 The Cycle 19 Calibration Plan
- • E.6 The Cycle 20 Calibration Plan
- • E.7 The Cycle 21 Calibration Plan
- • E.8 The Cycle 22 Calibration Plan
- • E.9 The Cycle 23 Calibration Plan
- • E.10 The Cycle 24 Calibration Plan
- • E.11 The Cycle 25 Calibration Plan
- • E.12 The Cycle 26 Calibration Plan
- • E.13 The Cycle 27 Calibration Plan
- • E.14 The Cycle 28 Calibration Plan
- • Glossary