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Space Telescope Imaging Spectrograph Instrument Handbook for Cycle 25 > Chapter 6: Exposure Time Calculations > 6.2 Determining Count Rates from Sensitivities

In the simplest terms, the instrumental sensitivity (S) times the flux from your object of interest gives the counts/s (C) expected from your source times the gain (G) (i.e., it gives counts for the MAMA and electrons for the CCD):Later in this chapter we provide specific formulae appropriate for imaging and spectroscopic modes, which can be used to calculate the expected count rates from your source and the signal-to-noise ratio. The formulae are given in terms of sensitivities, but we also provide transformation equations between the throughput (T) and sensitivity (S) for imaging and spectroscopic modes.Sensitivities and throughputs are presented in graphical and tabular form as a function of wavelength for the spectroscopic modes in Chapter 13, and for the imaging modes in Chapter 14. Given the source characteristics and the sensitivity of the STIS configuration, calculating the expected count rate over a given number of pixels is straightforward. The additional information you will need for spectroscopic observations is the aperture transmission (TA), the encircled energy fraction (εf) in the direction perpendicular to the dispersion, the number of pixels per spectral resolution element (or line spread function FWHM) and the plate scale, which are provided in Chapter 13. For imaging observations you need only the encircled energies and plate scales. Below, we describe how to determine two quantities:

1:

2: The peak per-pixel count rate (Pcr) from your source—useful for avoiding saturated exposures and for assuring that MAMA observations do not exceed the bright object limits.6.2.1 SpectroscopyThe spectroscopic point source sensitivity, , has the following units, depending on the detector:

CCD: (e- / s / pixλ) / (incident erg / cm2 / s / Å)

MAMA: (counts / s / pixλ) / (incident erg / cm2 / s / Å)

where:

• pixλ = a pixel in the dispersion direction;

• The spectroscopic diffuse source sensitivity, , has the following units, depending on the detector:

CCD: (electrons / s / pixλ / pixs) / (incident erg / s / cm2 / Å / arcsec2)

MAMA: (counts / s / pixλ / pixs)/ (incident erg / s / cm2 / Å / arcsec2)

where:

• pixλ= a pixel in the dispersion direction;

• pixs= a pixel in the spatial direction.

• ms is the plate scale in arcsec /pix in the spatial direction (i.e. in the direction perpendicular to the dispersion);

• W is the slit width in arcseconds;For a point source, the count rate, C, from the source integrated over an area of Npix = Nλpix × Nspix pixels can be expressed as:

• G is the gain (always 1 for the MAMA, and 1 or 4 depending on the choice of CCDGAIN for the CCD);

•

•

• εf = the fraction of the point source energy contained within Nspix pixels in the spatial direction;

• Nλpix = the number of wavelength pixels integrated over. For an unresolved emission line, Nλpix is just the number of pixels per spectral resolution element and Fλ is simply the total flux in the line in erg/s/cm2 divided by the product of the dispersion in Å/pix and Nλpix (i.e., divided by the FWHM of a resolution element in Å);

• Nspix = the number of pixels integrated over in the spatial direction.The peak counts/s/pix from the point source is given by:

• εf(1) is the fraction of energy contained within the peak pixel;

•

•

• Nλpix = the number of wavelength pixels integrated over in the dispersion direction. For an unresolved emission line, Nλpix is just the number of pixels per spectral resolution element, and Iλ is simply the total flux in the line in ergs/s/cm2/arcsec2 divided by the product of the dispersion in Å/pix and Nλpix, (i.e., divided by the FWHM of the resolution element in Å);

• Nspix = the number of pixels integrated over in the spatial direction.For a diffuse, spectrally unresolved emission line source the peak counts/s/pix, Pcr, is essentially independent of slit size and is given by:

•

• FWHM is the full width half max of the instrumental profile in Å, which for STIS is nearly always 2 pixels × d, where d is the dispersion in Å/pix;

• w is the slit width in arcseconds which projects to n pixels in the detector plane, where n is the width of the resolution element in pixels. Note that w is numerically equal or close to twice the plate scale in the dispersion direction for all modes;

• W is the actual slit width in arcseconds.

• d is the dispersion in Å/pix;

• mλ is the plate scale in the dispersion direction;The counts from the emission line will be spread over Nλpix pixels where Nλpix is the slit width per plate scale in the dispersion direction (Nλpix = W / mλ).6.2.2 ImagingThe imaging point source sensitivity, , has the following units, depending on the detector:

CCD: (e-/s/Å) / (incident erg/s/cm2/Å)

MAMA: (counts/s/Å) / (incident erg /s/cm2/Å).The imaging diffuse-source sensitivity, , has the following units, depending on detector:

CCD: (e-/s/Å/pix) / (incident erg/s/cm2/Å/arcsec2).

MAMA: (counts/s/Å/pix) / (incident erg/s/cm2/Å/arcsec2).

• ms is the plate scale in arcsec/pix.

•

• The peak counts/s/pix from the point source are given by:

• εf(1) is the fraction of energy encircled within the peak pixel;

•

• Bλ is the effective bandpass of the filter.For a diffuse source, the count rate, C, can be expressed as:

•

• Npix = the number of pixels integrated over;

Space Telescope Imaging Spectrograph Instrument Handbook for Cycle 25 > Chapter 6: Exposure Time Calculations > 6.2 Determining Count Rates from Sensitivities