Both the absolute flux calibration and the relative spectral response function (RSRF), i.e. the relationship between flux and photocurrent in grating mode, have been established using observations of Uranus and a Uranus spectral model. The semi-empirical spectral model of Uranus, used as the LWS prime flux calibrator, originates from a synthesis of results from the Voyager Infra-Red Imaging Spectrometer (IRIS)(4-50 $\mu$ m) and the JCMT near-millimetre UKT14 $^{3}$ He bolometer receiver (0.35-2.0 mm). The blue curve in Figure 5.1 represents the whole disk IRIS brightness temperatures extended to 200 $\mu$ m using a radiative transfer atmospheric model (Conrath, private communication, 1996). This model had a composition of (85 $\pm$ 3)% H $_{2}$ with the remainder being He, apart from 2.3% of CH $_{4}$ deep in the troposphere. Griffin & Orton 1993, [19] used JCMT data to extend their own atmospheric model down to far-infrared wavelengths (green curve). It can be clearly seen that in order to achieve consistency between these two results in the LWS wavelength range it is necessary to add a 0.5 K offset to the near-millimetre brightness temperatures (red curve). Since the calibration of Uranus data in the near-millimetre range is based on the Mars model of Wright 1976, [46] the introduction of a 1% offset is well within the estimated absolute calibration error.

Hence the adopted model of Uranus for calibrating LWS data, shown in Figure 5.1 as diamonds, is simply the Griffin & Orton 1993, [19] model with the 0.5 K offset. The smooth featureless continuum spectrum makes it ideal for calibrating LWS data. The error associated to the model is considered to be around 5%.

**Figure 5.1:** *Uranus model used in the LWS photometric calibration.*
$\rotatebox {270}{\resizebox{10cm}{!}{ \includegraphics{uranus_model_oct96_new.ps}}}$

The calibration spectrum is composed of scans from fifteen L01 observations of Uranus, obtained between revolutions 321 and 874.

**Table 5.2:** *Observations of Uranus used to derive the RSRF.*
TDT	Uranus	Number	Comments
	angular diameter	of scans

32103705	2.439	4	OK
32803601	2.410	4	OK
33503801	2.360	4	OK
34901201	2.310	4	OK
34901605	2.310	4	OK
35601101	2.280	4	OK
53802611	2.375	4	OK
54403301	2.399	6	OK
55205305	2.410	6	OK
69800902	2.380	12	OK
70601702	2.340	6	affected by detector warm up, only used SW1-LW1
72002004	2.290	12	affected by detector warm up, only used SW1-LW1
73401302	2.230	12	OK
73800302	2.220	12	OK
87401402	2.210	10	OK

Scans were extracted from each observation so that the number of scans in each direction was equal; i.e., for an observation with 7 scans, only the first three forward scans were extracted. A standard dark current value was then subtracted from each scan. Each scan was scaled to the first scan in the revolution 321 using the mean of all the points in the scan as a scaling factor. The scans were averaged using a median clipped mean, clipping at 3 $\sigma$ before division with the model.

5.2.1 Absolute flux calibration

The absolute flux calibration is performed by applying to all LWS observations the photocurrent to flux relationship derived from Uranus. It also involves referring the responsivity of the detectors at the time of the observation to the responsivity at the time of the calibrator (Uranus) observation. This is referred to as the absolute responsivity correction (described in detail in Section 4.4.1).
For each illuminator flash a single absolute responsivity ratio is calculated for each detector. This is done by taking the ratio between the signal measured when the illuminators were operated during an observation and the signal in the reference flash data in the LCIR calibration file. This reference flash calibration file was created as follows: previous versions of the RSRF file had relied on a special observation of Uranus taken in rev 317. Uranus was scanned many times, followed by five sequences of each of two types of illuminator flash (types 2 and 3; see Table 5.3). The two averaged sequences were then compared with the Uranus observations during those time periods to adjust them to the reference responsivity at the time of the first scan in revolution 321. These form the reference sequences in the LCIR calibration file. A further illuminator sequence (type 1) was used by LWS before the time Uranus was observed. To generate this entry in the LCIR file, sequences from observations of the HII region G298.228

0.331 during this time period were averaged together to form a reference sequence. This was then calibrated to the Uranus sequences using observations of the HII regions G298.228

0.331 and S106 and of the planetary nebula NGC 6302 taken during the three time periods denoted by different sequence types.

**Table 5.3:** *The three illuminator sequence types*
Illuminator sequence type	Revolutions used	Description

1	0-236	8 x 0.5 s ramps at levels 100 and 220
2	236-380	4 x 1 s ramps at levels 100 and 220
3	442-875	24 x 0.5 s ramps at level 180

To ensure that the power from the illuminators did not change during the course of the mission, weekly observations were made of a series of astronomical sources and the signal from these compared to that from the illuminators (Lim et al. 1998, [26]).

5.2.2 Relative spectral response function

The Uranus data described above are also used to establish the response of the instrument as a function of wavelength in grating mode - the Relative Spectral Response Function or RSRF. This is tabulated and stored in the LCGR calibration file, the content of which is shown for the 10 detectors in Figure 5.2. The basic conversion between photocurrent and flux for all LWS data is carried out using this calibration file.

**Figure 5.2:** *Relative Spectral Response Function (RSRF) shown for the 10 detectors. This data is stored in the LCGR calibration file.*
$\rotatebox {90}{\resizebox{10cm}{!}{\includegraphics{lcgr.ps}}}$

5.2 Absolute Flux Calibration and Grating Relative Response

5.2.1 Absolute flux calibration

5.2.2 Relative spectral response function