Spitzer Documentation & Tools
IRS Instrument Handbook

## 2.10            Sensitivity

The median 1-sigma continuum sensitivity for the IRS low-resolution modules is about 0.06 mJy from 6 to 15 microns and 0.4 mJy from 14 to 38 microns in 512 seconds of integration with low background.  The median 1-sigma line sensitivity estimates for the short- and long-wavelength high-resolution modules are about 2.7x10-19 W/m2 and 8.5x10-19 W/m2, respectively, for 512 seconds of integration with low background (see Figure 2.14 through Figure 2.18).

### 2.10.1         Equations for Calculating Sensitivity and Signal-To-Noise for Point Sources

This section illustrates the procedure by which the expected instrumental sensitivity and signal-to-noise ratios were calculated.

The background photocurrent from sky and telescope is given by Equation 2.1

where h is the Planck constant and Equation 2.2

where 2hc2 = 1.19x10-4  W micron2, all lengths are in microns, fstray is the ratio of total sky throughput to that of an ideal f/12 telescope, and are sky emissivities at temperatures Ti.  We also define the following: = the telescope throughput in cm2 sr. =the spectral bandpass falling on one pixel (= /R) in cm.  Note: while there are 2 pixels per resolution element, the slit width is also two pixels.  Hence, is proportional to the slit width if the spectral plate scale is unchanged.

Ti = effective blackbody temperature of sky + telescope. = the cold optical throughput for extended sources (i.e., omitting slit losses). = the detector responsivity (electrons/photon) [= ]. =quantum efficiency of the detector at the desired wavelength.

βG = the dispersion-gain product.

In the faint source limit, the total noise in electrons/pixel is the sum of the photocurrent shot noise (isky), read noise, and dark current shot noise.  It is given by: Equation 2.3

where id is the dark current contribution, RN is the read noise in electrons, tint is the integration time in seconds, and is the dispersion-gain product for the dark observations.

The relationship between photocurrent/pixel and the incident flux density of a source in mJy is given by: [electrons/pixel/mJy] Equation 2.4

where 1 mJy = 10-26 erg s-1 cm-2 Hz-1, D is the telescope aperture (in cm2), is?the slit throughput of a point source with angular diameter (without considering losses), and are throughputs accounting for losses in the telescope, alignment effects, and slit, respectively.  The second factor of 4 in Equation 2.4 comes from dividing the point source flux over 2 pixels per spectral resolution element and 2 pixels spatial extent. Again assuming the faint source limit, the 1 staring point source continuum sensitivity (PSSC) in mJy at the full resolution of the spectrograph is: [mJy] Equation 2.5

where the factor accounts for the variation in PSF with wavelength and details of the point source extraction.  Its value lies between 0.8 and 1.2.  The 1 staring point source continuum sensitivity (in mJy) smoothed at the required resolution of the spectrograph (Rreq = 50) is referred to as the PSSCS, and is given by Equation 2.6

The spectra are smoothed from R to Rreq and the S/N is assumed to increase as the square root of the number of pixels averaged.  Suitable sub-pixel smoothing is assumed.

The 1 staring point source sensitivity (in W m-2) for unresolved lines is then Equation 2.7

where the factor 3x10-15 = c (micron/s) (10-29 W m-2 Hz-1/mJy), PSSC is in units of mJy, and is in microns.