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5. Uncertainties from background subtraction

There are several ways to subtract the background emission from the (source+background) emission obtained by pointing on target.

by chopping. The chopper offset/vignetting (section 3.12) and signal losses due to the chopper modulation are introduced during the background subtraction. In OLP7 the default responsivity instead of the FCS measurement is used for the signal conversion to power on the detector. This adds a systematic error.
by nodding. Assuming that the individual nodding plateaux have sufficiently long integration time (t_int > 64 sec) such that responsivity transient uncertainties are minimized, no extra photometric errors are introduced from the background subtraction.
by separate on-source and off-source observations. The uncertainty depends on whether the same or different instrument settings were used for both observations. In the latter case the statistical and full systematic errors of both AOTs should be added, in the former case only the statistical uncertainties should be added.
by ``minimapping''. Many C100/C200 point-source observations were performed by observing a ``minimap'' in which the source is centred in the map and in which raster parameters are such that all pixels of the C100/C200 array have been centred on target. No extra photometric uncertainties are introduced.
by general raster mapping. In case the target is randomly positioned in the map one can extract the fluxdensity of sources in several ways: (1) by applying a point source fitting procedure. If the units in the map are in Jy/pixel the peak flux divided by the f_psf yields the point source flux. The fitting procedure require assumptions on the shape of a point source, therefore errors are introduced due to uncertainties in the assumed footprint profile. The error is smaller for oversampled maps. (2) by integrating the surface brightness contribution from the source by means of e.g. aperture photometry. The uncertainties are caused by uncertainties in the conversion from point source flux (Jy/pixel) to surface brightness (MJy/ster) which depends on the accuracy of ${\Omega}_{eff}$ the effective footprint solid angle.
by PHT-32 mapping. This oversampled mapping mode is frequently used to minimize the cirrus confusion. Since a high frequency modulation of the sky brightness by the chopper is involved, signal losses are expected causing an underestimate of the source-background contrast. The error due to signal losses should be added to the flux extraction methods described in the previous point.

**Table 5:** Summary of point source photometry methods
Method	statistical	systematic	photometric
	error	error	bias
chopping	${\sqrt 2}{\Delta}a$	${\Delta}R_{def}$	${\Delta}C, {\Delta}V, {\Delta}f_{psf,array}$
nodding	${\sqrt 2}{\Delta}a$	${\Delta}S_{on}$	${\Delta}f_{psf,array}$
minimaps	${\sqrt 2}{\Delta}a/{\sqrt N}$	${\Delta}S_{on}$
mapping	${\Delta}a/{\sqrt N}$	${\Delta}S_{on}$	${\Delta}{\Omega}_{eff}$
P32 maps	${\Delta}a/{\sqrt N}$	${\Delta}S_{on}$	${\Delta}C$ , ${\Delta}{\Omega}_{eff}$
on/off pointing	${\sqrt 2}{\Delta}a$	${\Delta}S_{on}$ , ${\Delta}S_{off}$	${\Delta}f_{psf,array}$

**Table 6:** explanation symbols:
Symbol	description
${\Delta}a$	statistical error for one pixel assuming about
	the same error at different pixels and pointings
N	number of pixels that covered the source
${\Delta}C$	uncertainty the signal loss correction for chopped measurements
${\Delta}V$	chopper offset or vignetting uncertainty
${\Delta}R$	uncertainty in responsivity due to statistical uncertainty
	in FCS signal
${\Delta}R_{aper}$	uncertainty in responsivity due to non-standard
	aperture for FCS measurement
${\Delta}R_{def}$	uncertainty in the default responsivity
${\Delta}R_{lin}$	uncertainty in responsivity due to responsivity non-linearities
${\Delta}S_n$	systematic error of AOTn propagating from SPD
${\Delta}R_{trans}$	uncertainty due to responsivity transients
${\Delta}{\Omega}_{eff}$	error in the effective solid angle
${\Delta}f_{psf,array}$	error in the point spread function factor for the whole array
${\Delta}f_{psf}$	error in f_psf for non-standard apertures

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ISOPHOT Error Budgets: Derive_SPD Processing Steps, Version 1.0, SAI/98-091/Dc