5.6 Photometric Accuracy

The accuracy of the photometric calibration is determined by a number of factors:

The measurements of Uranus that were used for the calibration result in a high S/N spectrum. However for sources brighter than Uranus that are observed long enough, the S/N of the resulting spectrum is limited by the S/N of the Uranus spectrum. The uncertainty in the RSRF is written in the calibration file containing it (see Section 7.3.2.4).
Transients or memory effects may have an influence on the photometric accuracy of the data. The extent of their influence is not clear at this time.
Ramp (non-)linearity will also influence the accuracy. It is believed that Derive-SPD is handling this reasonably well, except for really bright sources for which a correction is needed (see Section 5.7). However, comparison of planet and asteroids spectra with their models have suggested that some detectors (LW1, LW2 and LW3) could have a non-linearity behaviour resulting in a few % photometric errors in their ranges. This effect is still under investigation.
The dark background removal will, especially for faint sources, be an important factor in the photometric accuracy. The effect depends on the source strength and the spectral shape (see Section 6.4). For very faint sources the drift correction applied in AAL may result in negative fluxes (see Section 4.4.1.3).
Glitches also influence the photometric accuracy, since they have an effect on the responsivity of the detectors.

All these factors together lead to a photometric repeatability for LWS grating mode spectra of 10% between scans on the same detector (this is mainly due to the effect of responsivity changes), and 30% between adjacent detectors (mainly due to dark background removal problems for faint point sources and to the source extent for extended sources).

5.6.1 Calibration sources used for photometric purposes

To check the photometric calibration and the relative response calibration several sources were used during PV phase and during the routine calibration observations. Table 5.6 gives the sources used for different calibration purposes.

**Table 5.6:** Sources used for checking the photometric calibration and the relative response calibration of the LWS grating and Fabry-Pérot subsystems. The primary source for the grating flux calibration is Uranus, the other sources have been observed regularly for monitoring purposes. FG: Fixed Grating; FP: Fabry-Pérot.
Source	Type	Observation
Absolute Flux Calibration and Relative Response Function
Uranus	planet	End to end grating scans (extended range)
Absolute Flux Calibration: checking and monitoring
Uranus	planet	FG position On and Off source and full scan
Neptune	planet	FG position On and Off source and full scan
Ceres	asteroid	FG position On and Off source
Pallas	asteroid	FG position On and Off source
Vesta	asteroid	FG position On and Off source
Arcturus	star	FG position On and Off source and full scan
Aldebaran	star	FG position On and Off source and full scan
$\gamma$ Dra	star	FG position On and Off source
S106	HII region	FG and full scan
G298.2880.331	HII region	FG and full scan
NGC 6543	PN	full grating scan
NGC 7027	PN	full grating scan
Fabry-Pérot `throughput correction' (transmission $\times$ resolution element)
Mars	planet	Fabry-Pérot scans with fixed grating (mixed mode)

5.6.2 LWS photometric stability checked with observations of Mars

Sidher et al. 2000, [39] used ten LWS full grating scan observations (L01) of Mars to demonstrate that the observed $\sim$ 3% rotational modulation of the FIR disk-averaged brightness temperature can be detected with the LWS and that it compares very favourably with the predictions of the thermophysical model developed by Rudy et al. 1987, [37]. Figure 5.5 shows the observed and predicted modulation in each detector (except SW1 which is excluded because it suffers from memory effects) as well as a detector-averaged modulation. All these observations were processed as 1/4 s integration ramps by discarding the second-half of each 1/2 s ramp (see Section 5.8) in order to eliminate the non-linear behaviour seen in some LWS detectors for high fluxes. The absolute photometric accuracy evidenced by this figure is better than 10% for most detectors (observations and model differ by up to $\sim$ 15% in LW1 probably due to some residual non-linear effects). But what this figure shows primarily is that the LWS photometry is very stable, to a few % level, and that LWS can be used to detect variations as low as 3%. Mars is a very bright source (25000 Jy at 100 $\mu$ m) so the uncertainties due to dark current or background subtraction are minimal. For faint sources, such a high level of stability might be hidden due to dark current uncertainties.

**Figure 5.5:** The modulation of the brightness temperature as a function of sub-Earth longitude for detectors SW2 to LW5. The last panel shows the brightness temperature averaged over all nine detectors. The observations are shown as squares and the model as diamonds. The absolute photometric accuracy evidenced by this figure is better than 10% for most detectors but the LWS photometric stability is much better since it allows to detect the predicted variations of $\sim$ 3%.
$\resizebox {14cm}{!}{\includegraphics{sidher1_2.eps}}$

5.6.3 Comparison with IRAS fluxes

An extensive study comparing LWS and IRAS fluxes over a wide range of flux values has been performed by Chan et al. 2001, [6]. A summary of the study is given here highlighting the results concerning the photometric comparison between IRAS and LWS.

5.6.3.1 Sample selection

The objects used for the comparison were selected among all LWS observations on the basis of the following criteria:

Objects included in the IRAS Point Source Catalogue (PSC) and observed with LWS with AOT L01
Non far-infrared variables
Non-fringed LWS data
IRAS flux density qualities $\geq$ 2 in the 60 $\mu$ m and 100 $\mu$ m bands
$F_\mathrm{\nu}$ (100 $\mu$ m) 1000 Jy - to avoid detector non-linearity
$F_\mathrm{c}/F_\mathrm{s} < 0.5$ where $F_\mathrm{c}/F_\mathrm{s}$ is the flux ratio of cirrus and source
IRAS `Point source correlation coefficents' A (100%) or B (99%) in the 60 $\mu$ m and 100 $\mu$ m bands
Only source within 2 $^{\prime}$ search radius
IRAS CIRR3 $\le$ 254 MJy/sr, with no strong cirrus background at 100 $\mu$ m on the IRAS Sky Atlas Map or on the LWS Parallel Map in the LW1 detector

The sample selected following the above criteria contains around 120 objects.
To check if the comparison of the IRAS and LWS fluxes is source-dependent (via the spectral shape for example), the sample was divided into six groups of different object types: group 1: dust stars; group 2: planetary nebulae; group 3: galaxies; group 4: interstellar medium; group 5: young stellar objects; and group 6: Vega-like stars.

5.6.3.2 Corrections applied

The LWS spectra were first corrected for the presence of near-infrared leak features when needed (see Section 6.7 for the description of the feature and the correction).
A `cirrus correction' was applied to take out the contribution of the background flux due to the interstellar medium emission at the source position. Two different corrections were applied: either the IRAS flux was corrected using the CIRR2 value given in the IRAS PSC, or the LWS flux was corrected based on the IRAS CIRR3 value.

**Figure 5.6:** Comparison of IRAS and ISO LWS fluxes at 100 $\mu$ m for a wide range of fluxes. The different symbols indicate the different groups (object types) listed in the text. No trend is seen with object type.
$\rotatebox {90}{\resizebox{9cm}{12cm}{\includegraphics{iras_fig2.ps}}}$

**Figure 5.7:** *Ratio of the IRAS flux to ISO LWS flux at 100 $\mu$ m for various source types.*
$\rotatebox {90}{\resizebox{9cm}{12cm}{\includegraphics{iras_fig3.ps}}}$

5.6.3.3 Results

Figure 5.6 shows the distribution of IRAS fluxes versus LWS fluxes at 100 $\mu$ m. Each type group is plotted with a different symbol, and one can check that there is no noticeable difference between the groups.
Figure 5.7 shows the same results, but this time the ratios of LWS to IRAS flux densities are presented.

First one should note that there is a reasonably good agreement between IRAS and ISO flux values (within 30%), in spite of the relatively large uncertainties associated with the needed correction factors.

However, the plots do evidence systematic effects that deserves more attention: in average ISO fluxes are 12.5% higher than IRAS fluxes and the differences seem to increase with increasing flux.

Therefore, to further investigate this behaviour, the flux comparison has been extended to the 60 $\mu$ m band and has been broadened by including other sources: on one hand, 23 sources used for cross-calibration between SWS and LWS in the context of the ISO cross-calibration (García-Lario 2001, [18]) and on the other hand, 155 galaxies observed with LWS, the fluxes of which were measured and compared to IRAS fluxes by Brauher & Lord 2001, [3]. At 60 $\mu$ m, the LWS observations do not cover the whole IRAS band. In the cross-calibration sample only sources that were observed also with SWS were used in order to reconstruct the ISO flux at 60 $\mu$ m; for the extragalactic sample a small correction was applied in order to compensate for the fraction of the spectral energy distribution not covered by LWS. Complete details are given in García-Lario 2001, [18] and Brauher & Lord 2001, [3].

**Figure 5.8:** *Comparison of IRAS and ISO LWS fluxes in Jy at 100 $\mu$ m for the three samples described in the text. The first plot is a close-up of the second one at low fluxes.*
$\resizebox {8cm}{8cm}{\includegraphics{lws_iras100a.ps}}$ $\resizebox {8cm}{8cm}{\includegraphics{lws_iras100b.ps}}$

**Figure 5.9:** *Comparison of IRAS and ISO LWS fluxes in Jy at 60 $\mu$ m. The first plot is a close-up of the second one at low fluxes.*
$\resizebox {8.2cm}{8.2cm}{\includegraphics{lws_iras60a.ps}}$ $\resizebox {8.2cm}{8.2cm}{\includegraphics{lws_iras60b.ps}}$

Figure 5.8 and 5.9 show the ISO versus IRAS fluxes for the three samples.
It is clear on these plots that there is a systematic difference between ISO and IRAS fluxes for bright sources. For faint sources, IRAS and ISO fluxes agree within a few % in average, with a high dispersion due to uncertainties in the dark current. However for brighter sources, ISO fluxes are systematically higher than IRAS fluxes, and the difference increases with flux level, from about 15% difference around 100 Jy, to a level of about 20% for sources up to 400 Jy, and 30-50% for sources brighter than 400 Jy.

The reason for this behaviour is not understood. It is not due to inaccurate dark current subtraction since this would affect the faintest sources unlike what we observe here. On the other hand it does not seem to be due to cirrus background contamination, since no trend is observed with the IRAS CIRR2 parameter value.
A possible cause could be some non-linear effects in the IR detectors. However, the problem could be associated with IRAS and not with ISO.

Indeed, Figure IV.A.4.2 of the IRAS Explanatory Supplement, ([20]) does evidence detector non-linearity behaviour and Section VI.B.4.d quotes errors of respectively 30% and 70% at 60 and 100 $\mu$ m for sources above 100 Jy.

Further investigation is needed to decide if the systematic difference is imputable to IRAS or LWS calibration inaccuracies.

5.6.4 Checking the Fabry-Pérot photometric accuracy

For the Fabry-Pérot mode, the photometric accuracy was determined by comparing the integrated line fluxes observed with the FP with the fluxes observed with the grating or line fluxes published in the literature. The sources and lines are given in Table 5.7. It was found that for strong lines accuracy is typically better than 30%. For faint lines however, the FP fluxes can be off by almost a factor two. This is mainly due to the removal of the dark current which is known to be problematic for low signal levels (see also Section 4.4.1.3 and 5.4).

**Table 5.7:** *Sources and lines used for the determination of the photometric accuracy of the Fabry-Pérot data.*
Source	Type	Lines
NGC 6543	PN	57.3, 88.4 $\mu$ m
NGC 7027	PN	51.8, 63.2, 145.5, 157.7 $\mu$ m
NGC 6357I	HII region	51.8, 57.3, 63.2, 88.4, 145.5, 157.7 $\mu$ m
M 82	Galaxy	63.2, 88.4, 121.9, 157.7 $\mu$ m

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ISO Handbook Volume III (LWS), Version 2.1, SAI/1999-057/Dc