Star Formation Camera Exposure Time Calculator (v.4)

Basic Exposure Time Calculator by J. Rhoads, ASU


For team use... a first draft, to be taken with a grain of salt. Results for broad-band filters will be slightly pessimistic for point sources when optimal PSF photometry techniques are used; they will be slightly optimistic when object surface brightness profiles are significantly shallower with increasing radius than a Gaussian. Applicability for narrow-band filters needs to be verified yet, but may depend on how narrow the emission line is compared to the width of a filter. If reloading this page does not reset the form below, use [SHIFT]+reload instead.
Version 3: 17 July 2008 JER; Version 4 updated by R. Jansen 13–14 Aug 2008.

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
Φte
where
(S/N) is the target signal to noise ratio;
Nexp is the number of exposures per pointing;
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;
and that's it, right? We ignore dark current for the moment.

ParameterValuePlot?Convert, etc
 S/N
Enter target S/N ratio
 Primary mirror diam (m)
 
 clear ap. fraction
 Area (cm²)
 Pixel scale (arcsec)
 
 ℜ (electrons)
 
 fap
 
 fλ (cgs/Å) @ 550nm
 AB Magnitude @ 550nm
 Slope (fλ ~ λslope)
–2 gives mAB = constant
 Nexp
 
 rh (arcsec)
half-light radius
 Δv
narrow-band filters only: emission-line velocity width in km/s
(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. The narrow-band filters in the pull-down menu that are indicated to be "(narrow)" would capture emission with −500 < cz < +500 km/s; all other narrow-band filters would capture emission with −500 < cz < +2500 km/s.

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
 
Index
 
λc
(nm)
FWHM
(nm)
EW
(nm)
Mean trans
(%)
Sky rate
(e/sec/{18mas}²)
18 mas pixels
per 4m PSF
  Emission-line flux, ∫fλdλ
(erg/s/cm²)
 

Note: the final table column above will be non-zero only for the narrow-band emission line filters. The reported value is the integral over the velocity-broadened emission line, which for reasonable velocity widths will be narrower than the filter FWHM. If an unreasonable value for Δv is specified, the integral will be over the filter FWHM.


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.





SFC ETC Revision History
15 Jul 2008 [JER] initial version of 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.