Intercalibration

Intercalibration is carried out in order to be able to compare measurements from different instruments. To facilitate this, three radioactive $^{14}C$ light-standards and a calibration lamp are used (Figure 4.2).

Figure 4.2: Top: The three $^{14}C$ phosphor light-standards with phosphor: Y-275, L-1614 and 920-B. Lower right: A calibration source with a tungsten lamp. (To the lower left are some parts from a calibration source based on a fluorescent light)

These light-standards are intercalibrated against other light standards during European calibration workshops held at regular intervals [for example Lauche and Widell, 2000a; Lauche and Widell, 2000b; Widell and Henricson, 2001]. As several of the light-standards used at these intercalibration sessions are traceable to National Bureau of Standards (NBS) sources, it is thus also possible to perform absolute calibration [Torr and Espy, 1981]. Results from some of the most recent calibration workshops are summarised in Table 4.3.

Table 4.3: Results from a selection of recent intercalibration workshops: The column emission rates are given in [R/Å] (Rayleighs/Ångströ). (Some sources have been omitted in order to fit the table on one page.) [after Lauche and Widell, 2000a; Lauche and Widell, 2000b; Widell and Henricson, 2001, and earlier calibration workshop reports]

Sources		Column emission rate [R/Å] at Filter [Å]
calibration	year	3914	4280	4866	5573	5882	6299	6562
Esrange, tungsten lamp
Stockholm	2000	1.3	4.1	30	212	310	532	553
Oulu	2001	0.53	1.5	11.6	82	122	233	171
IRF, UJO 920B
Lysebu	1985	5.1	126.0	61.5	18.6	10.5	6.7	8.1
Lindau	1999	4.4	102	60	22	12	7.6	2.4
Stockholm	2000	4.6	109	64	23	12.7	10	8.5
Oulu	2001	5.2	105	65	22	13	9.2	1.2
IRF, UJO L1614
Lysebu	1985	0.07	0.73	32.5	27.7	8.7	2.5	4.3
Lindau	1999	0.6	1	37	33	9.3	1	2
Stockholm	2000	0.07	1.0	40	35	9.6	0.36	0.57
Oulu	2001	0.1	1.1	38	27	7	1.2	10.2
IRF, UJO Y275
Lysebu	1985	0.03	0.3	3.8	251.0	378.0	217.0	113.0
Lindau	1999	0.01	0.2	3.8	263	383	282	165
Stockholm	2000	0.01	0.22	3.9	276	405	282	181
Oulu	2001	0.002	0.18	3.6	258	482	274	155
Mike Taylor, source
Stockholm	2000	0.03	0.98	6.8	10	1.8	0.3	2.5
<#7545#>Sodankylä,
blue lamp
Lysebu	1985	2.0	6.0	10.1	9.9	15.3	4.0	0.66
Lindau	1999	2.3	7.2	12	9.3	10	7.5	7.2
Stockholm	2000	2.5	7.3	12.5	9.3	9.5	6.3	2.8
Oulu	2001	2.6	7.6	12	8.9	13	10	12
<#7551#>Sodankylä,
tungsten lamp
Lysebu	1985	0.12	0.71	5.4	31.8	62.8	125.8	137
Lindau	1999	0.1	0.75	5.6	33.5	65	137	192
Stockholm	2000	0.10	0.65	5.2	31	61	139	285
Oulu	2001	0.01	0.6	5	30	75	133	248
IRF, tungsten lamp
Stockholm	2000	0.19	1.1	8.5	50	98	223	454
Oulu	2001	0.17	1.2	8	48	115	228	428
MPI-2 lamp
Lysebu	1985	0.02	0.16	2.43	193.7	290.7	191.8	98.2
Lindau	1999	0.03	0.12	2.2	172	258	213	235
Stockholm	2000	0.01	0.13	2.3	175	266	153	105
Oulu	2001	0.01	0.01	2.3	169	251	193	105
S.Chernouss, Glow lamp
Oulu	2001	13	143	66	84	374	392	59
S.Chernouss, Tungsten
Oulu	2001	0.01	1.6	5.5	36	293	947	679

For the $^{14}C$-sources in use for calibrating ALIS (phosphors: 920B, L1614 and Y275) the column emission rate is plotted against wavelength in Figure 4.3.

Figure 4.3: Column emission rates [R/Å] as a function of wavelength [Å] for the three radioactive $^{14}C$ light-standards with phosphor: 920-B (blue line), L-1614 (green line) and Y-275 (red line). These plots also include intercalibration results from the Aberdeen 1980 workshop [Torr and Espy, 1981]. These values are not shown in Table 4.3. Legend: Intercalibration sessions of 1981 'x' 1985 '+', 1999 '*', 2000 'o' , and 2001 '$\Box$'. The lines connect the results from the latest calibration workshop, held in Oulu 2001. (The last points on these lines for the L1614 and 920B calibrators are probably measurement errors)

Table 4.4 presents the ratios of column emission rates

Table 4.4: Ratios of results from the latest calibration workshop [Oulu, 2002, see Widell and Henricson, 2001] to earlier calibration sessions. Bold face indicates results for wavelengths where the calibrators are most commonly used. See also Table 4.3 and Figure 4.3

Source	Year	column emission ratios (2001/year) at Filter [Å]
		3914	4280	4866	5573	5882	6299	6562
y275	1985	0.07	0.60	0.95	1.03	1.28	1.26	1.37
y275	1999	0.20	0.90	0.95	0.98	1.26	0.97	0.94
y275	2000	0.20	0.82	0.92	0.93	1.19	0.97	0.86
l1614	1985	1.43	1.51	1.17	0.97	0.80	0.48	2.37
l1614	1999	0.17	1.10	1.03	0.82	0.75	1.20	5.10
l1614	2000	1.43	1.10	0.95	0.77	0.73	3.33	17.89
920b	1985	1.02	0.83	1.06	1.18	1.24	1.37	0.15
920b	1999	1.18	1.03	1.08	1.00	1.08	1.21	0.50
920b	2000	1.13	0.96	1.02	0.96	1.02	0.92	0.14

from the latest calibration workshop (Oulu, 2001) to earlier calibration sessions. Despite the 5730 years half-life of $^{14}C$, deviations of 10-20% are present, even within a couple of years as also noted by Kaila and Holma [2000]. This is probably related to either errors in the intercalibration procedure, or to the light-emitting phosphor of the sources.

The original use of these light-standards has been to calibrate photometers. This has been done by placing the light-standard on top of the front-lens of the photometer, covering the entire field-of-view. The same procedure was followed when calibrating the ALIS imagers. As the light-emitting surface of the calibrator does not cover the entire field-of-view of the imager, this method has been questioned [Gustavsson, 1997]. Therefore, during the latest calibration workshop, the light sources were placed at a larger distance (within focus) of the imager. However due to various technical problems, the results were inconclusive. Therefore this question remains open.

Absolute calibration

The digital-output, $\mathit{DN}_{ij}$, and number of generated photo-electrons per pixel $\overline{n}_{e^{-}_{\gamma{}ij}}$ is related by:

$$\mathit{DN}_{ij}=G_{S}\ \overline{n}_{e^{-}_{\gamma{}ij}} \left[\mathrm{counts}\right]$$ (4.7)

where $G_{S}$ is the imager system gain, [Preston, 1995; Preston, 1993]:

$$G_{S}=\frac{G_{CCD}\ G_{P}\ t_{DCS}}{B_{ADC}\ \tau_{DCS}} \left[\frac{\mathrm{counts}}{e^{-}_{\gamma}}\right]$$ (4.8)

Here, $G_{CCD}$ is the CCD output sensitivity, $G_{P}$ is the programmable gain setting (5 or 10), $t_{DCS}$ is the DCS integration time, $B_{ADC}$ is the ADC bit weight ( $90.6~\mu{}V/\mathrm{counts}$), and $\tau_{DCS}$ is the DCS integrator time constant. These parameters are configured during CCU start-up (Section 3.3.3).

Combining Equation 4.6 with Equations 3.20 and 3.22 yields for uniformly illuminated central pixels of the CCD, $\mathit{DN}_{Cij}$:

$$\frac{I_{cal}}{\mathit{DN}_{Cij}}= \frac{1}{t_{\mathit{int}}}\, \... ...0^{10}\, G_{s}\, {Q_{E}}\, T\, A_{pix}}\ \left[\frac{R}{\mathrm{counts}}\right]$$ (4.9)

The ``known'' column emission rate, $I_{cal}$, which is obtained from a light-standard by integrating over the filter passband, $\lambda_{1}\cdots\lambda_{2}$ is given by:

$$I_{cal}=\int_{\lambda_{1}}^{\lambda_{2}} I_{ls}(\lambda)\, d\lambda \approx I_{ls}(\lambda_{2}-\lambda_{1})=I_{ls}\, \Delta\lambda \left[R\right]$$ (4.10)

Here, the column emission rate of the light standard, $I_{ls}(\lambda)$, is a function of wavelength $\lambda$, that must be integrated over the filter passband, $\Delta\lambda$. However during the intercalibration workshops, $I_{ls}(\lambda)$ is measured only for one wavelength in the filter passband, hence the approximation in Equation 4.10 (see Table 4.3 and Figure 4.3).

Now, consider the right-hand part of Equation 4.9. The quantum-efficiency, transmittance and system gain is a function of wavelength and pixel-coordinates among other things, such as for example filter-temperature (i.e. ${Q_{E}}={Q_{E}}(\lambda,i,j,\ldots)$, $T=T(\lambda,i,j,\ldots)$ and $G_{S}=G_{S}(i,j,\ldots)$). Due to the difficulties of determining these functions as well as the approximations and uncertainties related to the $f_{\char93 }$ Equation 4.9 is rewritten as follows:

$$\frac{I_{cal}}{\mathit{DN}_{Cij}}= \frac{1}{t_{\mathit{int}}}\, C_{abs\lambda{c}}\, \mathit{F}_{ij\lambda} \ \left[\frac{R}{\mathrm{counts}}\right]$$ (4.11)

Here $\mathit{F}_{ij\lambda}$ (Equation 4.4) corrects for both the dependence on pixel-coordinates as well as on wavelength for a particular filter. (The index $\lambda{c}$ in the absolute calibration constant, $C_{abs\lambda{c}}$, indicates that the constant is unique for each filter of each imager $c$). Hence, the importance of a proper flat-field calibration cannot be underestimated (Section 4.1.3). Unfortunately, a proper flat-field calibration is not yet available for ALIS, and some approximations are required:

$$\frac{I_{cal}}{\mathit{DN}_{Cij}}\approx \frac{1}{t_{\mathit{int}... ...{abs\lambda{c}} \mathit{F}_{Mij\lambda}\ \left[\frac{R}{\mathrm{counts}}\right]$$ (4.12)

In this case the modelled flat-field correction $\mathit{F}_{Mij\lambda}$ of Equation 4.6 is used together with a normalised filter transmittance function, $T'(\lambda)$, by integrating over the vendor-provided filter transmittance curve and normalising (i.e. set $T'(\lambda)=1$) at peak filter transmittance (Figure 4.4).

Figure 4.4: Example filter transmittance curve $T_f(\lambda)$ as measured by the filter manufacturer for a 40 Å wide 5590 Å filter (Lot. No. 3697). The measured peak transmittance of the filter is 0.6 and the centre wavelength at normal incidence ( $\lambda_{cw}$) and filter bandwidth is measured to 5587.2 Å and 38.4 Å respectively. This filter is intended for the $O(^1S)$ 5577 Å auroral emission line. The deviation from normal incidence shifts the centre wavelength, which explains why a centre wavelength of 5590 Å was selected, (see Equation 3.45 in Section 3.5). As can be seen, this filter has a rather uniform transmittance in the passband.

However for most filters it is acceptable to take $T'(\lambda)\approx 1$ over the entire filter-passband. Equations 4.5 and 4.11 yield the following equation (substituting Equation 4.10) to be used when a proper flat-field calibration is available:

$$C_{abs\lambda{c}}=\frac{1}{\overline{\mathit{DN}}'_{C}} \int_{\la... ...\lambda_{2}} I_{ls}(\lambda)\, d\lambda\ \left[\frac{R}{\mathrm{counts}}\right]$$ (4.13)

where $\overline{\mathit{DN}}'_{C}$ is obtained by averaging together a number of uniformly illuminated pixels in the central part of the image.

The present more approximative calibration is described by Equations 4.6 and 4.12:

$$C_{abs\lambda{c}}\approx \frac{1}{\overline{\mathit{DN}}'_{C}} \i... ...ta\lambda}{\overline{\mathit{DN}}'_{C}}\ \left[\frac{R}{\mathrm{counts}}\right]$$ (4.14)

Hence, an absolute-calibration must be carried out for each filter of each imager.

The results from the two most recent absolute calibrations of the ALIS imagers are found in Table 4.5.

Table 4.5: Calibration results from ALIS obtained in 1996 and 1997. The large difference for ccdcam1 occurs because it was equipped with filter-wheel and new optics between these calibrations. Some filters (see Tables 3.4 and 3.5), as well as ccdcam6 were not yet available during these calibrations. Both calibrations used the Lysebu, 1985 intercalibration. The last column gives values of the calibration of 21 May 1997, adjusted by the 2001 intercalibration result (Table 4.3). Finally it should be noted that no suitable light-standard for calibration of the 8455 Å filters is available.

					96-07-10	97-05-21	2001 adj.
ccd	$\lambda_{cw}$	$\Delta\lambda$	$\overline{\mathit{DN}}_{C}'$	$\langle \mathit{DN}_{C}' \rangle$	$C_{abs\lambda{c}}$	$C_{abs\lambda{c}}$	$C_{abs\lambda{c}}$
cam	[Å]	[Å]	$[\mathrm{counts}]$	$[\mathrm{counts}]$	$[\mathrm{R}/\mathrm{counts}]$	$[\mathrm{R}/\mathrm{counts}]$	$[\mathrm{R}/\mathrm{counts}]$
1	5590	40	217.5	2.6	32.4	46.2	47.4
1	6310	40	173.4	2.6		50.1	63.2
1	6230	40	254.2	2.9		34.1	43.1
1	4285	50	116.8	3.4		53.9	44.9
2	5590	40	300.6	3.6	28.2	33.4	34.3
2	6310	40	339.3	3.5	25.6	25.6	32.3
3	5590	40	484.2	4.1	21.9	20.7	21.3
3	6310	40	427.3	2.8	22.2	20.3	25.6
4	5590	40	468.0	5.3	23.7	21.5	22.1
4	6310	40	402.2	4.1	23.7	21.6	27.3
5	5590	40	333.8	4.0		30.1	30.9
5	6310	40	390.5	4.2		22.2	28.1

As can be seen, the last absolute calibration of the ALIS imagers was carried out in 1997. At that time ccdcam6 was not yet delivered; neither were all filters available. Also no suitable light-standard is available for the near-infrared 8446 Å emission line. An attempt was made to perform a re-calibration of all imagers and filters in 2001. However this effort failed due to technical problems and limited time. Hence a new calibration must be performed as soon as possible.

A comparison of auroral measurements from ccdcam6 and a Russian photometer (calibrated in Russia) both co-located in Kiruna indicates a disagreement in absolute intensities of $\approx 20\%$ between the two instruments [Sergienko, 2003]. This comparison as well as extrapolated values have been in use for the filter/imager combinations not appearing in Table 4.5 (i.e. ccdcam6. See also Tables 3.4 and 3.5).

There is furthermore an interesting possibility of performing absolute calibration by using known spectra of stars, which has been done for the 8446 Å emission-line [Gustavsson, 2003]. This method would simplify the calibration procedures considerably. However this is a new method and these results have yet to be intercalibrated with the present calibration method. Regardless of whether the new method will be a verification procedure, or replace the present calibration procedure, it will no doubt represent a major improvement of the absolute calibration for ALIS.

Due to the inherent difficulties of absolute intensity calibration, an error of the order of $50~\%$ is often regarded as acceptable. The largest errors appear to be related to the intercalibration of the light-standards (about 10-20 %, refer to Table 4.4). Furthermore, the calibration results appear to be fairly stable over one year (Table 4.5). On the other hand there are still many uncertain factors in the calibration procedure, most notably the absence of a uniform source needed for the flat-field calibration (Section 4.1.3). Therefore, to be on the safe side, it might be stated that the absolute calibration error lies in the range of 25-50 %. The intercalibration error of the ALIS imagers is probably much lower, at least for pixels in the central region of the image. For an imaging instrument, these errors are probably to be considered as acceptable. However improvements are still required.

Finally, the absolute calibration is applied to the object-images ( $\mathit{DN}_{ij}'$, see Equations 4.5 and 4.6):

$$I_{ij}=C_{abs\lambda{c}}\mathit{DN}_{ij}'-I_{bg,ij}\ \left[R\right]$$ (4.15)

In this equation, $I_{ij}$ is the calibrated pixel-value, and $I_{bg,ij}$ is the sky background correction.

Removing the background

Different schemes are employed to remove the sky background in Equation 4.15, depending on available data and the measurement situation. Therefore background removal is only outlined here.

In the case of HF pump-enhanced aurora, linear interpolation with time is sometimes used. Also a polynomial could be fitted line by line on each side of the emission region. In the most recent papers (Section 6.4) weighted sums of keograms through the emission region and on the side of it are used. This is done under the assumption that there is no aurora.

Regarding PSC studies (Section 6.6.1), brute-force median/min. filtering was applied [Enell, 2002].

For general auroral studies, background determinations are extremely difficult, as there is always some diffuse aurora present. In this case background images must be obtained by using a filter for a wavelength region with no auroral emissions. For the ALIS imagers, background filters are available: 5100 Å and 6230 Å. However these filters have seldom been used as they are only present at some stations (Section 3.5). For the future, permanent background photometers might be a solution of the problem.

Related issues

On-chip binning

The absolute calibration has been found to scale accurately with the binning factors, thus:

$$C_{abs\lambda{c,binxy}}=\frac{C_{abs\lambda{c}}}{x_{bin}\times y_{bin}}$$ (4.16)

Where $C_{abs\lambda{c,binxy}}$ is the absolute calibration constant with binned pixels, $x_{bin}$ is the binning-factor in the x-direction, $y_{bin}$ is the binning factor in the y-direction.

Linearity

As no variable light-standard is available, the linearity has been checked by varying the integration time ( $t_{\mathit{int}}$). As expected, the CCD detector appears to be completely linear until it reaches the saturation-equivalent exposure (Section 3.1.10).

Interference filters

Both the transmission characteristics and passband of a narrow-band interference filter are subject to aging effects. The filter-wheels of the ALIS imagers are also sometimes subject to high temperatures due to day-time sunlight. This is known to have a permanent degenerative effect on the filters. Questions have therefore been raised regarding the long-term stability of the filters. To clarify these issues, it would be desirable to re-measure filter characteristics for the filters. This was planned for the autumn of 2001, but had to be postponed for a number of reasons.

Another concern is to measure the transmittance of the filter, $T_{f}(i,j,\lambda)$, as a function of pixel indices, $(i,j)$, (columns, lines). A monochromator system for filter transmission measurements was developed for ALIS [Vaattovaara and Enback, 1993]. Provided that an ALIS imager has a valid flat-field calibration, it should in principle be possible to check the transmittance of the optical system (including the filter) as a function of wavelength and pixel coordinates. Such a study would be beneficial for all optical instruments, using interference filters, and could provide answers to questions posed by Kaila and Holma [2000] regarding absolute calibration of wide field-of-view photometers and camera systems.