The sample used for this internal cross-calibration comparison comprised around 100 different sources with both SWS (AOT SWS01) and PHT-S (AOT PHT40 either in staring or chopped mode) spectra available in IDA, showing a reasonable signal-to-noise ratio.

The OLP data products were compared in a systematic way since the end of the Post-Operations Phase with every new release of the pipeline. This resulted in the detection of several calibration problems affecting both PHT and SWS calibration that were conveniently reported in the corresponding (Cross)-Calibration Status Report.

As an example, one of the calibration problems discovered was the effect of poorly modelled molecular features in the spectra of the calibration stars used in the dynamic calibration of PHT-S, before it was implemented in Version 9.0 of the pipeline. Based on the comparison of OLP Version 7 SWS data and staring PHT-S observations of the asteroid Hygiea with the available thermophysical model it was possible to identify the residuals left in the calibrated PHT-S spectra between 8 and 9 $\mu$ m by SiO features not considered in the original models of the late type stars taken as standards. Only excluding these stars from the generation of the calibration files (and hence accepting a larger gap in the flux range covered by the calibration standards) the spurious features were eliminated in the calibrated spectra. After the correction was introduced in OLP Version 9.0 the agreement between SWS01 and PHT-S staring observations improved significantly.

As of OLP Version 10, the level of agreement reached in terms of absolute flux between these two ISO instruments and observing modes was better than 10-15% for well-behaved data sets (bright, point-like sources not affected by any other known calibration problem). Moreover, the overall shape and even the faintest spectral features were also largely preserved from instrument to instrument (to within the few percent level in most cases) all over the spectral range covered by both instruments.

Figure 6.2 shows some examples which illustrate the good agreement found over a wide variety of sources with different spectral properties, all of them taken from this cross-calibration sample. The plotted spectra are OLP Version 10 data products directly retrieved from IDA corresponding to representative cases of sources showing a `blue' (HR 7310 and HR 6132) or `red' continuum (AFGL 4106 and OH 26.5+0.6), or sources where strong PAH emission bands and/or nebular emision lines (BD +30 $^{\circ}$ 3639 and NGC 7027) appear overimposed on the infrared continuum. A very good agreement between both instruments and the IRAS photometry at 12 $\mu$ m (indicated with a blue square in the plots) is also found.

**Figure 6.2:** SWS (black solid line) versus PHT-S (red filled triangles) OLP Version 10 spectra of a variety of sources with different spectral properties taken from the cross-calibration sample. The blue squares represent the IRAS photometry at 12 $\mu$ m when available.
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HR7310_SWS_PHT_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HR6132_SWS_PHT_OLP10.ps}}}$
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{AFGL4106_SWS_PHT_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{OH26.5_SWS_PHT_OLP10.ps}}}$
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{BD+30_SWS_PHT_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{NGC7027_SWS_PHT_OLP10.ps}}}$

The examples shown in Figure 6.2 correspond to relatively bright sources observed in all cases with PHT-S in staring mode. For the fainter sources the chopping mode of PHT-S was usually prefered and the behaviour of this mode was also investigated in terms of cross-calibration. The results obtained indicate a similar level of agreement with SWS (10-15%), in spite of the fact that the accuracy achievable with SWS at low flux levels is not expected to be as good.

Figure 6.3 shows two faint sources (flux density below 5-10 Jy) observed with SWS and PHT-S. IRAS 16342

3814 was observed with PHT-S in staring mode while IRAS 21434+4936 was observed using triangular chopping. We can see that a very nice agreement exists at absolute flux level as well as in the shape of the individual SWS and PHT-S spectra in both cases. Again, there is also a very good agreement with the IRAS photometry at 12 $\mu$ m.

Outside the overlapping spectral range, a significant jump in flux is detected at the blue edge of band 3A in the SWS spectrum of IRAS 21434+4936 at 12.0 $\mu$ m. This is indicating an inaccurate dark current subtraction by the automated pipeline (OLP Version 10). This kind of problem is sometimes observed in the SWS spectra of faint sources and needs to be manually corrected with the use of the SWS interactive software analysis (OSIA) where the right dark current level can be interactively chosen, eliminating the problem.

**Figure 6.3:** Same as Figure 6.2 for two faint sources. Note the effect of an inaccurate dark current subtraction by the pipeline at the blue edge of band 3A (12.0 $\mu$ m) in the SWS spectrum of IRAS 21434+4936. The blue squares represent again the IRAS photometry at 12 $\mu$ m.
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{IRAS16342_SWS_PHT_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{IRAS21434_SWS_PHT_OLP10.ps}}}$

6.2.1.2 SWS versus CAM-CVF

A similar exercise was performed with a sample of around 20 sources identified in IDA to have SWS (AOT SWS01) and CAM-CVF (AOT CAM04) spectra available with a signal-to-noise ratio enough to be used for cross-calibration purposes.

Again, the OLP data products were compared in a systematic way since the end of the Post-Operations Phase with every new pipeline release since OLP Version 7.

In this case, the main improvement implemented in the pipeline since the start of this cross-calibration analysis was the application of transient corrections based on the Fouks-Schubert method (Fouks & Schubert 1995, [54]) both to SWS01 (band 2) and CAM04 data, which are described in detail in the corresponding instrument specific volumes of this Handbook.

As of OLP Version 10, the level of agreement between SWS01 and CAM04 spectra was in general within 10-15% down to the limits where dark current subtraction (especially for SWS) becomes a significant contribution to the error budget. This statement is valid over the whole spectral range covered by both instruments with the exception of the edges of CAM-CVF scans, which might be affected by transient effects even after the application of the Fouks-Schubert transient correction (this is especially true in the case of bright point sources, for which this correction simply does not work).

Figure 6.4 shows two examples where comparisons are made of CAM04 and SWS01 OLP Version 10 data products directly retrieved from IDA, taken from this cross-calibration sample. They correspond to the bright star HR 7310 (left panel) and to the fainter HD 179218 (right panel), which are representative of the general behaviour observed.

**Figure 6.4:** SWS (black solid line) versus CAM-CVF (blue open triangles) OLP Version 10 spectra of two point sources taken from the cross-calibration sample. Note the strong transient observed at the blue edge of the CAM-CVF spectra of HR 7310 (left panel). The blue squares represent the IRAS photometry at 12 $\mu$ m.
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HR7310_SWS_CAM_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HD179218_SWS_CAM_OLP10.ps}}}$

As we can see, the agreement is very good with the only exception of the blue edge of the CAM-CVF spectrum of HR 7310, affected by strong transient effects at the beginning of the measurement. This is, as we have already mentioned, a common feature observed in many cases in CAM-CVF spectra of bright sources and its strength depends on the illumination history conditions. It is well known that the Fouks-Schubert correction which is applied in the pipeline only works efficiently for very weak and/or extended sources (i.e. for low flux gradients) and has a neutral effect on bright point sources like HR 7310. Unfortunately, the problem cannot be corrected with the help of CIA.

6.2.1.3 CAM-CVF versus PHT-S

Around 10 other sources were used for a similar internal cross-calibration comparison of CAM-CVF (AOT CAM04) and PHT-S (AOT PHT40 either in staring or chopping mode).

Figure 6.5 shows two examples where comparisons are made of CAM04 and PHT-S OLP Version 10 data products retrieved from IDA, taken from this small cross-calibration sample. They correspond to the bright star HR 7310 (left panel) and the faint HD 207129 (right panel), which are representative of the general behaviour observed.

**Figure 6.5:** CAM-CVF (blue open triangles) versus PHT-S (red filled triangles) OLP Version 10 spectra of two sources taken from the cross-calibration sample. As usual, the blue squares represent the IRAS photometry at 12 $\mu$ m.
$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HR7310_CAM_PHT_OLP10.ps}}}$	$\rotatebox {0}{\resizebox{!}{6.5cm}{\includegraphics{HD207129_CAM_PHT_OLP10.ps}}}$

Note that for the faint star HD 207129, the background continuum emission is not negligible. In this case, a background measurement available in IDA taken at a position 3 $^{\prime}$ away from the central source was used to subtract this contribution. The spectrum shown in Figure 6.5 is the result obtained after subtraction of this background.

We can see once more that a very good level of agreement exists (within 10-15%) in the overall shape and in the absolute flux level determined by the pipeline for CAM-CVF and PHT-S spectra, as well as between the two instrument observing modes and the IRAS photometry at 12 $\mu$ m.

Again, the main problem is the strong discrepancy observed at the short end of the CAM-CVF spectra of both HR 7310 and HD 207129 induced, as we have already mentioned, by transient effects in the ISOCAM detectors.

6.2.1.4 SWS/LWS overlap region

In order to extend our internal cross-calibration analysis to longer wavelengths we also checked the consistency of the absolute flux calibration of SWS (AOT SWS01) and LWS (AOT LWS01) in the overlapping region of these instruments. For this, a total number of 122 common pointings (separated less than 2 $^{\prime}$ $^{\prime}$ ) were selected from IDA for which both SWS and LWS measurements were available with fluxes between 43.7 and 44.4 $\mu$ m higher than 100 Jy.

Sources identified as variable in the literature in this cross-calibration sample were identified and removed from the sample except when the SWS and the LWS measurements were taken on the same revolution (usually one after the other as concatenated observations). Similarly, all sources reported to be extended were also discarded to avoid problems derived from the comparison of fluxes measured through different aperture sizes. In addition, a few other sources were excluded from the analysis because they were identified either as badly pointed (off-axis) or as sources with a possible (not previously reported) extended nature, according to the strong discontinuities observed between SWS bands (see Figure 6.1).

After this purge, the resulting sample still contains around 50 different sources suitable for cross-calibration. A reduced subsample composed of 25 sources (used as test cases) were systematically investigated every time there was a new release of the automated pipeline since OLP Version 7. For each of them the average value of the observed flux density ratio LWS/SWS at 44 $\mu$ m was determined using ISAP (assuming that the source SED shape was of the form $\nu$ $\times$ f $_{\nu}$ = constant, or equivalently $\lambda$ $\times$ f $_{\lambda}$ = constant).

As it also happened in other cross-calibration analysis performed during Post-Operations, some calibration problems were identified during the course of this exercise. The most important one in this case was the detection of an anomalous behaviour of the SW1 detector in LWS in all the spectra taken before revolution 237. The flux of this detector appeared systematically underestimated (around 20%) with respect to both the adjacent SW2 detector of LWS and band 4 of SWS. The problem was identified as related to an incorrect treatment by the pipeline of the illuminator flash sequence used by LWS before this revolution and solved in OLP Version 10.1 by applying the necessary modifications in the automated calibration software.

The results obtained as of OLP Version 10 for the 25 test cases above mentioned using ISAP Version 2.1 are listed in Table 6.1. Some examples of the corresponding composite SWS+LWS spectra are shown in Figure 6.6.

**Table 6.1:** *OLP Version 10 LWS/SWS ratios at 44 $\mu$ m of the 25 test cases used to analyse the internal consistency between SWS and LWS absolute flux calibration.*
Source	SWS TDT#	LWS TDT#	LWS/SWS	Notes
HD 161796	07100579	07100579	0.95
HD 101584	07901402	07901520	1.01
Hen 2113	07903307	07903229	0.98
HD 161796	07100579	08001732	1.03
CPD 56 8032	27301339	08401538	1.03
IRAS 163423814	45801328	08402827	0.94
Circinus	07902231	10401133	1.26	bad SWS band 4
AFGL 4106	10401225	10401227	0.95
M 178	15901853	15901854	0.90
CW Leo	19700159	19800158	1.11
$\mu$ Cep	08001274	22002005	1.07
SAO 34504	26302115	26300513	1.12	bad SWS band 4
IRAS 19114+0002	52000234	31900901	0.96
OH 26.5+0.6	33000525	33000316	1.01
VX Sgr	09900171	33100802	1.04
IRAS 154525459	45900615	48800916	1.12	bad SWS band 4
IRAS 165944656	45800441	49001642	1.02
IRAS 19114+0002	52000234	52500861	1.00
R Dor	58900918	59300644	1.03
Hen 2113	07903307	60701891	1.07
CRL 618	68800561	68800450	0.90	bad SWS band 4
IC 418	82901301	68900805	1.04
TX Cam	69501070	69501069	1.06
HD 44179	70201801	70201904	1.00
IC 418	82901301	86801205	1.03

If we exclude from the analysis four objects showing calibration problems in band 4 of SWS (those presenting strong mismatches with band 3, indicated in Table 6.1), we can see that the mean LWS/SWS ratio derived from these measurements is

LWS/SWS

= 1.01, very close to unity, with a very little dispersion around this value (in most cases the agreement is at the 10% level or better). This is remarkable, if we consider that LWS and SWS were calibrated in a totally different way (LWS calibration is based on Uranus as primary calibrator while SWS band 4 calibration is mainly based on the results of ground-based ILT experiments using blackbody sources).

As a byproduct of this analysis and since some of the objects in this cross-calibration sample were repeatedly observed throughout the mission with either SWS or LWS, it was also possible to perform an independent analysis of the stability of both instruments in terms of absolute flux calibration. The results obtained indicate that both for LWS and SWS the reproducibility was better than 15% in all cases.

**Figure 6.6:** *Composite OLP Version 10 SWS+LWS spectra of some of the sources used as test cases for the consistency check between SWS and LWS. Note the excellent match at 44 $\mu$ m in most cases.*
$\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{IRAS15452-5459}}}$ $\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{IRAS16594-4656}}}$ $\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{RDOR.ps}}}$ $\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{HEN2-113.ps}}}$ $\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{TXCAM.ps}}}$ $\rotatebox {90}{\resizebox{5.5cm}{!}{\includegraphics{HD44179.ps}}}$

6.2.2 Filter measurements versus spectroscopy

6.2.2.1 ISOCAM filters versus chopped PHT-S

An excellent agreement is also found when comparing ISOCAM filter measurements with PHT-S spectroscopy. As an example of this, we present here the results obtained from a cross-calibration comparison performed at a very low flux level (a few mJy) of ISOCAM filter photometry (AOT CAM01) and PHT-S spectroscopy (AOT PHT40) of a sample of 55 Seyfert galaxies reported in Schulz et al. 2000, [147]. Seyfert galaxies in the sample were observed both with ISOCAM LW2 (6.7 $\mu$ m) and LW7 (9.6 $\mu$ m) filters and with chopped PHT-S photometry.

In this case, however, the comparison is not based on OLP Version 10 data products. Instead, calibration was performed using standard CIA and PIA routines starting from ERD. Manual recalibration of the spectra included only glitch de-tailing and transient correction of the chopped PHT-S measurements in a similar way as the Version 10 of the automated pipeline does it. Thus, the expected level of agreement reached in the final products is very similar.

In Figure 6.7 we can see two nice examples of PHT-S and ISOCAM filter measurements of the Seyfert galaxies Markarian 509 (Seyfert 1) and NGC 5953 (Seyfert 2).

**Figure 6.7:** PHT-S spectrum and ISOCAM LW2 and LW7 filter measurements of the Seyfert 1 galaxy Mrk 509 and of the Seyfert 2 galaxy NGC 5953. The position of some of the more prominant PAH bands and emission lines are indicated. The two large crosses marked LW2 and LW7 indicate the flux from ISOCAM images with its error and wavelength range. The best fit power-law continuum is shown as a continuous line (taken from Schulz et al. 2000, [147])
$\rotatebox {90}{\resizebox{6.5cm}{!}{\includegraphics{pl_mrk509.ps}}}$ $\rotatebox {90}{\resizebox{6.5cm}{!}{\includegraphics{pl_ngc5953.ps}}}$

The results obtained are very satisfactory since the global median flux ratio (ISOCAM filter/PHT-S) derived from the measurements is: 1.15 for the LW2 measurements and 0.94 for LW7, i.e. ISOCAM flux densities without colour correction are only 15% higher in LW2 and 6% lower in LW7 than the corresponding PHT-S measurements.

The colour correction for the large bandpass-filter could explain the difference for LW2 up to 10%, as the spectral energy distribution of the Seyfert galaxies observed are red, and with the PAHs contribution in the reddest part of the filter wavelength range. On the other hand, the higher fluxes detected in the LW2 5-8.5 $\mu$ m filter might also be contaminated by the contribution from the stellar content of the underlying extended galaxy which may still be detectable even for the almost point-like Seyferts, the ISOCAM aperture being wider than the PHT-S one.

6.2.2.2 ISOCAM filters versus SWS

Observations of the Orion bar complex made with CAM-CVF and SWS by Cesarsky et al. 2000, [19] are shown here as an example of this cross-calibration analysis. The spectrum of this region of the sky shows a combination of strong emission features corresponding to PAHs and amorphous silicate grains together with narrow emission lines coming from an ionised region around the isolated O9.5 V star $\Theta^2$ Ori A, as we can see in Figure 6.8.

The simultaneous presence of broad and narrow emission features makes this comparison quite interesting for cross-calibration purposes since it constitutes an excellent laboratory to test the internal consistency of ISO calibration in the presence of emission lines.

**Figure 6.8:** SWS spectrum (full line) compared to the CAM-CVF spectrum (dotted line) of the region around $\Theta$ Ori A. All the ISOCAM pixels falling in the SWS aperture have been co-added (from Cesarsky et al. 2000, [19]).
$\resizebox {9cm}{!}{\includegraphics{img22.ps}}$

The CAM-CVF observations employed the 6" per pixel field of view of ISOCAM. Full scans of the two CVFs in the LW channel of the camera were performed with both increasing and decreasing wavelength. The results of these two scans are almost identical, showing that the transient response of the detector was only a minor problem for these observations. The raw data were processed using CIA in a standard way and the Fouks-Schubert transient correction was applied to the data resulting in only minor corrections. The CAM-CVF spectrum of $\Theta^2$ Ori shown in Figure 6.8 was obtained co-adding all the pixels falling within the SWS aperture.

The full range (2.4 to 46 $\mu$ m) SWS spectrum of the HII region surrounding the star $\Theta^2$ Ori A was reduced with SIA using version 30 of the Cal-G files.

Since the interactive data reduction performed was done in a similar way as Version 10 of the pipeline does it both for ISOCAM and SWS data, the level of agreement reached is expected to be comparable to that obtained using OLP data products. And this was actually found to be excellent, within 20% both for the continuum and for the emission lines.

6.2.2.3 ISOPHOT filters versus ISO spectroscopy

Observations of comet Hale-Bopp taken in October 1996 with ISOPHOT using 4 different detectors (P1, P2, C100 and C200) and 10 filters covering the range between 3.6 and 170 $\mu$ m by Grün et al. 2001, [66] have been compared with quasi-simultaneous observations taken with PHT-S (Crovisier et al. 1997, [37]), SWS (Crovisier et al. 2000, [38]) and LWS (Lellouch et al. 1998, [109]).

Figure 6.9, taken from Grün et al. 2001, [66] shows the ISOPHOT photometric fluxes together with the PHT-S, SWS and LWS spectra taken on 6-7 October 1996, scaled to a 19 $^{\prime}$ $^{\prime}$ aperture. This required the application of aperture correction factors which assumed a 1/ $\rho$ brightness distribution, where $\rho$ is defined as the projected distance from the nucleus. Details on the data reduction of each dataset used in this cross-calibration comparison can be found in the above referenced paper.

**Figure 6.9:** Comparison of ISOPHOT photometry (open squares) and the PHT-S, SWS and LWS spectra of Comet Hale-Bopp on 6-7 October 1996. All fluxes have been scaled to a 19 $^{\prime}$ $^{\prime}$ diameter aperture.
$\resizebox {10.5cm}{!}{\includegraphics{gruen_fig4.eps}}$

In the case of the ISOPHOT filter measurements, background observations were performed with identical instrument settings at the same positions on the sky several days after the comet observations to subtract the contribution from the sky emission to the on-source photometric measurements. All observations were done in single pointing, single filter absolute photometric mode (PHT05 and PHT25).

A reasonable agreement was found between the independently calibrated photometry and spectroscopy in most cases in spite of the many different correction factors applied to the data. These correction factors are needed in the case of ISOPHOT to cope with the different apertures used per filter, positional offsets (observations where the source was not perfectly centred in the aperture), PSF effects on coma measurements, and the usual colour corrections. For SWS, additional scaling factors were applied to the different bands to make the spectrum continuous; these scaling factors were always close to one.

6.2.2.4 ISOPHOT filters versus LWS

We present here the results obtained from the cross-calibration analysis performed at the long wavelength spectral range covered by ISO between 60 and 200 $\mu$ m using a combination of PHT-C measurements and LWS01 observations.

As it has already been mentioned before, this comparison is difficult because of the limited common dynamic range and the lack of astronomical sources observed both with PHT-C and LWS suitable for cross-calibration.

Searching the ISO Data Archive it is possible to select around 200 different positions in the sky where ISO observations were performed both with PHT-C filters (photometry beyond 60 $\mu$ m) and LWS01, corresponding to about 100 different astronomical sources. However, there are very few of them with both PHT and LWS observations of enough quality to derive reliable numbers. In addition, the strong infrared background sometimes completely dominates the measurements especially at the longest wavelengths making cross-comparisons more difficult.

Moreover, we need to purge as usual this cross-calibration sample for bad-pointed observations, variable and extended sources, which at the end limits the number of suitable sources to just 9 common observations which are presented in Tables 6.2 and 6.3. These were the observations selected as test cases for this cross-calibration analysis.

For the derivation of the fluxes quoted in Tables 6.2 and 6.3 we retrieved from the ISO Data Archive the OLP Version 10 PHT-C photometric data together with the corresponding OLP Version 10 LWS spectra. In the case of the PHT-C photometry we just took directly the values provided by the automated pipeline while the LWS spectra were further processed with ISAP Version 2.1 in order to derive the equivalent `synthetic photometry' at 60, 100, 120, 150 and 200 $\mu$ m.

For this we used the syn_phot application in ISAP, which allows the convolution of the ISO LWS spectrum with the transmission profile of the different IRAS PHT-C filters used in the comparison. The programme assigns a monochromatic flux at each of these wavelengths as output under the assumption that the source SED shape is of the form $\nu$ $\times$ f $_{\nu}$ = constant, or equivalently $\lambda$ $\times$ f $_{\lambda}$ = constant, in the same way as PHT-C calibration did.

**Table 6.2:** *List of cross-calibration sources used in the comparison between PHT-C100 and LWS*
	C100	C100	C100	LWS	LWS	LWS	IRAS
Source	60 $\mu$ m	100 $\mu$ m	120 $\mu$ m	60 $\mu$ m	100 $\mu$ m	120 $\mu$ m
CRL 3068	-	-	70.0	-	-	67.0	1
Y CVn	21.0	10.5	-	14.6	8.3	-	1
HD 161796	-	-	54.8	-	-	54.1	1
R Cas	102	38.5	-	85.5	32.9	-	2
IRAS 163423814	-	-	269	-	-	146	4
OH104.9+2.4	84.5	63.0	-	89.2	44.6	-	5
$\chi$ Cyg	92.8	50.5	-	82.3	36.6	-	5
$\mu$ Cep	112.5	64.0	177.5	108.5	52.9	39.0	5
VX Sgr	-	-	1240	-	-	205	6

**Table 6.3:** *List of cross-calibration sources used in the comparison between PHT-C200 and LWS*
	C200	C200	LWS	LWS	IRAS
Source	150 $\mu$ m	200 $\mu$ m	150 $\mu$ m	200 $\mu$ m
CRL 3068	43.0	23.0	36.5	24.4	1
Y CVn	11.7	7.3	3.0	5.0	1
HD 161796	31.2	17.2	17.4	19.1	1
R Cas	52.7	37.9	13.3	4.7	2
IRAS 163423814	221	171	97.0	70.5	4
OH104.9+2.4	246	270	33.2	35.3	5
$\chi$ Cyg	161	136	33.3	46.8	5
$\mu$ Cep	179.5	147.5	25.8	18.3	5
VX Sgr	1640	1210	216	229	6

In Tables 6.2 and 6.3 the sources have been sorted according to the increasing value of the parameter CIRR2 as quoted in the IRAS Point Source Catalogue Version 2.1. This is a logarithmic function which describes the contamination expected from background cirrus emission at 100 $\mu$ m and responds to the equation:

where

is the cirrus flux and F

is the source flux (see the IRAS Explanatory Supplement, [84]). A value of CIRR2=1 corresponds to the cirrus flux being less than 1% of the source flux while CIRR2 larger than 5-6 indicates that the flux measurement is probably dominated by the cirrus contribution.

The cirrus contamination effect has clearly been detected in the cross-calibration measurements shown in Tables 6.2 and 6.3, especially beyond 100 $\mu$ m.

While the consistency between PHT-C and LWS is better than 20-30% in most cases at 60 and 100 $\mu$ m (detector C-100), we can see that at longer wavelengths (detector C-200) the situation becomes worse and this good level of agreement is only reached by the sources showing a very low value of the CIRR2 parameter (and not always). For the rest of the sources in the short list under analysis the cirrus contamination completely dominates the flux detected at 120, 150 and 200 $\mu$ m. This is clearly reflected by the fact that the flux ratios PHT-C/LWS at these wavelengths closely approach a constant value (between 6 and 8) which is a pure consequence of the difference in size of effective apertures between both instruments.

A similar analysis was carried out by Müller & Lagerros 2002, [127] using a combination of LWS01 grating scans and LWS02 fixed grating observations on a number of asteroids. For this cross-calibration comparison further processing of OLP Version 10 data products was performed using ISAP Version 2.0.

In the case of LWS01 grating scans the detector signals were deglitched, $\sigma$ -clipped (2.5 $\times$ r.m.s.) and averaged. Detectors SW1 to SW5 were then smoothed with the nominal resolution element of 0.29 $\mathrm{\mu m}$ , LW1 to LW5 with a resolution element of 0.6 $\mathrm{\mu m}$ and both scan directions averaged. Observations on a large number of standard sources (planets, asteroids, stars) have shown that the responsivities of the detectors LW1, LW2 and LW3 might be flux dependent. In order to correct for these suspected non-linearities empirical correction values were derived and applied to the asteroid scans (Müller 2001, [124]). The background values were taken from COBE/DIRBE (Hauser et al. 1998a, [75]) weekly maps (25-100 $\mathrm{\mu m}$ ) and yearly maps (140-240 $\mathrm{\mu m}$ ). LWS solid angles and correction factors for extended sources were taken from the ISO Handbook Volume III on LWS, [68]. Maximal background contributions were 4% for Ceres and up to 50% for Hygiea with the largest influence at long wavelengths.

For the fixed grating LWS02 observations the data reduction was also performed manually taking only the last 100s of the measurements where the signals were usually stabilised. Dark current subtraction and flux calibration was done in the ISAP command mode. The detector non-linearities and the backgrounds were corrected in the same way as for the LWS01 mode. Maximal background contributions were up to 16% for Ceres, up to about 10% for Pallas and Vesta and up to 40% for Hygiea. The dark current signals in LW4 (160.6 $\mathrm{\mu m}$ ) and LW5 (178.0 $\mathrm{\mu m}$ ) were in many cases unstable during the integration times and the corresponding fluxes could therefore not be used.

The ISOPHOT observations were calibrated against standard stars and planets only with the help of PIA, using `ad-hoc' Cal-G files excluding intentionally all the asteroids from them (they are also considered calibration standards for ISOPHOT), and treating the asteroid measurements this way as independent scientific observations.

All these observations were compared with thermophysical models of the asteroids (Müller & Lagerros 2002, [127] and references therein), which consider aspects like size, albedo and shape together with the spin vector, a beaming model, thermal inertia and a wavelength-dependent emissivity.

The observations/model ratios are shown in Figures 6.10 to 6.13. It may be interesting to remark here that this cross-calibration comparison comprises a large variety of observing geometries, aspect and phase angles, typically 2-3 orders of magnitude in flux and different background conditions for each asteroid. The observation from the 2 instruments (LWS, ISOPHOT) were taken in different observing modes (LWS01, LWS02, PHT22, PHT25, PHT99) and quite different integration times. They underwent completely different data processing and calibration schemes. Nevertheless, the observations/model representation gives a consistent picture, expressed in ratios close to one. In general no systematic offsets on absolute terms between the instruments or observing modes can be seen with the exception of the well known flux underestimation of the SW1 detector of LWS for observations taken before revolution 237 (some of which are represented in the plots as outliers), corrected in the final Version 10.1 of the LWS pipeline, and a few residual jumps betwen detector bands which are not yet fully understood.

**Figure 6.10:** LWS (fixed grating: squares; grating scans: dots) and ISOPHOT (triangles) observations of Ceres divided by its thermophysical model. A few LWS-SW1 fixed grating observations taken before revolution 237 are visible in the plot as outliers as well as a few measurements taken with the LWS-LW4 and LWS-LW5 detectors. No other systematic differences between LWS and ISOPHOT can be seen (from Müller & Lagerros 2002, [127]).
$\rotatebox {90}{\resizebox{7.9cm}{!}{\includegraphics{ceres_all_rat.ps}}}$

**Figure 6.11:** LWS (fixed grating: squares) and ISOPHOT (triangles) observations of Pallas divided by its thermophysical model. Only one LWS-SW1 fixed grating measurement taken before revolution 237 and a couple of individual LW5 measurements show strong discrepancies with respect to the ISOPHOT data and/or the thermophysical model (from Müller & Lagerros 2002, [127]).
$\rotatebox {90}{\resizebox{7.9cm}{!}{\includegraphics{pallas_all_rat.ps}}}$

**Figure 6.12:** LWS (fixed grating: squares) and ISOPHOT (triangles) observations of Vesta divided by its thermophysical model. Again, with the exception of a few measurements at the longest wavelength range, no strong systematic differences between LWS and ISOPHOT can be seen (from Müller & Lagerros 2002, [127]).
$\rotatebox {90}{\resizebox{7.9cm}{!}{\includegraphics{vesta_all_rat.ps}}}$

**Figure 6.13:** LWS (fixed grating: squares; grating scans: dots) and ISOPHOT (triangles) observations of Hygiea divided by its thermophysical model. Note the $\sim$ 20% discrepancy of the LWS-SW1 measurements, both taken before revolution 237. Other jumps between LWS bands are calibration artifacts. Especially the high quality ISOPHOT C200 measurements are consistent with the model predictions. Note that the flux level in this case is of only a few Jy at the longest wavelength range, close to the detection limit for LWS (from Müller & Lagerros 2002, [127]).
$\rotatebox {90}{\resizebox{7.9cm}{!}{\includegraphics{hygiea_all_rat.ps}}}$

6.2 Internal Cross-Calibration

6.2.1 Between the ISO spectrometers

6.2.1.1 SWS versus PHT-S