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Updated Extraction Heights in the COS ETC

For the COS spectroscopic ETC, the S/N of a given observation depends on the extraction height. The extraction height, or the size in the cross-dispersion direction on the detector over which a spectrum is constructed, determines how many pixels are sampled, and determines what fraction of the source's flux is included. Previously, the ETC had assumed a singular extraction height for G130M, G160M, and G140L modes, with separate extraction heights for the 1055 and 1096 central wavelengths of the G130M grating. However, CalCOS actually extracts spectra with heights that differ as a function of central wavelength in the G130M grating, and uses different extraction heights for the G160M and G140L gratings. In the ETC, it is assumed that the extraction height contains 100% of the source's flux, so an incorrect extraction height does not impact the source counts in an ETC calculation. It does impact the number of pixels sampled on the detector, which for COS means an over- or under- estimation of the noise associated with the dark rate. For most observations, the dark is a small fraction of the counts within a resolution element, but faint sources can be impacted beyond the 10% quoted accuracy of the ETC.

Currently, the ETC has the correct extraction heights for the G130M/1055 and G130M/1096 modes. The extraction height for all other modes has been updated from the previous value of 47 pixels. The extraction height of G130M/1222 Segment B has been updated to 45 pixels. The extraction heights of the other G130M modes as well as of all G160M modes have been updated to of 35 pixels. The extraction heights of all G140L modes have been updated to 57 pixels.

Users can calculate the impact for a given mode by comparing the expected source count rates (C) to those reported by the ETC for the dark rate (B_dark), A=C/B_dark. The impact on exposure time is then dependent on the extraction height (EH) and A as follows:


For sources where the dark rate dominates (A~0), the ETC will now return an exposure time 11% higher for the G140L grating, and 25% lower for the G160M grating. Observations of bright sources, where A >> 47, will be largely unaffected by these changes. Signal-to-noise calculations will be affected by a factor of SQRT[(A+EH)/(A+47)].

We also remind users that the ETC explicitly assumes Poissonian statistics in the limit of high numbers of counts, which over-estimates the uncertainties for very low count observations. Therefore, users wishing to better understand the expected noise at low count rates should consult references such as Gehrels 1986, ApJ, 303, 336 ( to modify their ETC calculation results.