The absolute intensity calibration is being derived from planetary observations (most especially Mars), via the measurement of the telescope efficiencies. Once the efficiencies are known, and assuming they do not change significantly with time, internal loads can be used as the day-to-day stable reference for intensity calibration (transfer function). Differencing measurements for calibration sources are done both ON source (source-reference) and on an OFF position (off-reference). It is the double difference of these two modulated spectra that finally offers a correction of the baseline ripples (standing waves).
The error budget indicates the total error for the HIFI calibration. It is dependent on the band (maybe the frequency), on the observing mode and on the source observed. The budget includes both frequency and intensity calibration. It also takes into account the uncertainty on the telescope pointing and the effects of optical standing waves (Opt. standing waves) in each of the HIFI bands.
There are two types of error considered:
Systematic Errors: are described within the calibration framework (e.g. temperature sensor on hot and cold loads). We presume multiple measurements will not improve these errors. There are two ways to combine these error: linearly (pessimistic) or quadratically (uncorrelated errors). The error budget for systematic errors are contained in Table 5.7, “Overall error budget.”. Note that line non-linearity has been found to be a negligible error.
random errors: the normal radiometric errors which are statistical in nature. Multiple observations will reduce these errors. The cost is time.
Table 5.7. Overall error budget. The following table provides the percentage flux error associated with each component of the error budget.
Error source | Band 1/2 | Band 3/4 | Band 5 | Band 6/7 | ||
|---|---|---|---|---|---|---|
Sideband ratio | 3-4 | 4-6 | 4-6 | 5-8 | ||
Hot load coupling | <1 | <1 | <1 | <1 | ||
Cold load coupling | <1 | <1 | <1 | <1 | ||
Hot load temperature | <1 | <1 | <1 | <1 | ||
Cold load temperature | <1 | <1 | <1 | <1 | ||
Planetary model error1 | <3 | <3 | <3 | <3 | ||
Beam Efficiency | <5 | <5 | <10 | <5 | ||
Pointing | <1 | <2 | <2 | <4 | ||
Opt. standing waves | 4 | 4 | 3 | 3 | ||
1 This is our current estimate based on the standard planetary atmosphere modelling of Neptune, used as a prime calibrator across the Herschel instruments.
For astronomical observations, the statistical noise of the measurement itself must be added to obtain the error on the specific observation.
Mis-pointing is more of an issue at high frequencies where the beam is smallest for HIFI. The pointing error (Absolute Pointing Error, APE) of the telescope has been reported as 2".