Approximate WFIRST/WFI Exposure Time Calculator (v.1)

Basic Exposure Time Calculator by J. Rhoads and R. Jansen, ASU

This is an approximate exposure time calculator for the Roman Space Telescope (formerly WFIRST) Wide Field Instrument (WFI) imaging modes. The software engine and interface was developed originally by James Rhoads and Rolf Jansen for another project (the Star Formation Camera instrument concept for the Theia observatory concept). We have modified it in a basic way for WFI parameters, but have not yet modified the underlying calculations to fully model read noise in an IR detector sampled up the ramp. It is offered without warranty.

The calculations assume aperture photometry, with the fraction of light enclosed in the aperture being a user-selectable parameter.

We base the background count rates and the PSF sizes on a draft document Jeff Kruk has written on WFIRST S/N calculations. We have compared the results from this calculator with tabulated results in that document. The results of this calculator are generally optimistic by about 30% for exposure times of order 100 sec; and within 10% for significantly deeper exposures.

If reloading this page does not reset the form below, use [SHIFT]+reload instead.

Version 1β: 11 December 2018 RAJ+JER. Version 1α: 17 October 2018 JER. Original software: late summer 2008, J. Rhoads and R. Jansen.


Illustration showing the location of the Wide Field Instrument in the WFIRST observatory structure.
Credit: NASA's Goddard Space Flight Center

This JavaScript calculator solves a basic exposure time calculation for the SFC. Starting from:

  (S/N)2   =   Nexp ( fap Φte )2
Npix (2   +   Ste )   +   fap
(S/N) is the target signal to noise ratio;
Nexp is the number of exposures per pointing (assumed to be dithered);
fap is the fraction of the total object flux falling in the photometry aperture;
Φ is the object flux in units of counts/second;
te is the exposure time (for each individual exposure);
is the read noise per pixel in electrons;
S is the sky count rate in electrons per pixel per second;
We ignore dark current for the moment, and have not taken a sophisticated approach to up-the-ramp fitting.

To use the form: Select the target S/N ratio. Change either the source flux density f_lambda or the AB magnitude. If you choose AB magnitude, it's important to click the "Calculate f_lamdba" button, becuase the calculation is actually done on f_lambda. Change the N_exp line to the number of exposures you plan to co-add: the reported integration time is per-exposure. For galaxies, put in a nonzero r_h value. To tabulate needed exposure times, click the "tabulate exposure time" button. After tabulating results, return to the form by hitting the "reload" button on your browser. Unfortunately, in the present version of the form, this resets the form inputs.

There is also a plotting capability that we will document better in the next update.


ParameterValuePlot?Convert, etc
Enter target S/N ratio
 Primary mirror diam (m)
 clear ap. fraction
 Area (cm²)
 Pixel scale (arcsec)
 ℜ (electrons)
 fλ (cgs/Å) @ 550nm
 AB Magnitude @ 550nm
 Slope (fλ ~ λslope)
–2 gives mAB = constant
 rh (arcsec)
half-light radius
(no plot)

Plotting parameters:

We can only plot one filter at a time. The plots should show the exposure time required to achieve some S/N ratio, for the input parameters tabulated above, and for one selected filter. One selected parameter is varied by a factor from (value/plotrange) to (value*plotrange), where "plotrange" is selected below, and the parameter is selected by the check buttons above. To start, change the filter from its selected default to another filter (and back if you wanted that default). The parameters for the selected filter should then be displayed in the information fields below.

Filter to PlotDynamic range Plot param

Parameters of the selected filter. Information only; make changes only via the filter pulldown menu above. (To tinker with filter properties, you need to get into the source code, and be sure to change the filter arrays in three places, consistently.)

Filter name
Mean trans
Sky rate
110 mas pixels
per 2.37m PSF

Output: x-axis: log(independent variable) in default units (i.e. the same units as input on the form).
y-axis: Log of exposure time (per individual exposure) required to reach the requested s/n ratio.

WFIRST ETC Revision History
15 Jul 2008 [JER] initial version of Theia/SFC ETC; hacked incredibly much from the MMTF Fabry Perot calculator by Weiner and Rupke; filter parameters taken from Jansen's FOV trade study [Jul 15]
17 Jul 2008 [JER] implemented plotting; first version with all bells and whistles.
06 Aug 2008 [RAJ] updated effective filter parameters after change in camera design with additional optical elements (folds) and more realistic dichroic curves; re-optimized filters (narrow-filters, except F656N and F658N are now all 1% wide; got rid of narrow narrow-band [OII] and H-beta, but added two medium-band Ly-alpha filters; changed output format a bit (formatted HTML output table)
13 Aug 2008 [RAJ] changed HTML format of main ETC page a bit; added back in the narrow narrow-band [OII] and H-beta filters – design change [three wheels] appears to accomodate up to either 16 or 18 science filters again in each channel; we may still have to get rid of 2 filters in the Red Channel – Beware
14 Aug 2008 [RAJ] implemented field reporting flux integrated over velocity broadened emission line (narrow-band filters); implemented check for Δv > FWHM. If so, the integral will be over the filter FWHM.
17 Oct 2018 [JER] Adapted SFC ETC for WFIRST/WFI.
28 Nov 2018 [RAJ] Restored plotting functionality, fixed a few typos.
11 Dec 2018 [RAJ] Removed some vestigial narrow-band and Lyα-related SFC stuff from the WFIRST/WFI ETC, increased equivalent read-noise floor from 3 to 5 e, improved some of the formatting, and added an illustration.