La Silla - Science Operation Department

Correcting the chromatic and airmass dependent extinction for TIMMI2 spectra 

1. The influence of atmospheric extinction in the mid-IR

For spectroscopy a target star and its corresponding calibrator should be observed at a comparable airmass to avoid a varying extinction between the two objects. Different to near-IR observations, in the mid-IR a good calibrator at the same airmass is often difficult to find and the theoretical behaviour of the extinction with airmass and wavelength is not really known up to now. Some authors claim there would be no clear dependence and thus for photometry no airmass correction needs to be applied. However these authors used dozens of standard star observations, while we apply several hundred measurements. 

In mid-IR spectroscopy the influence of extinction is more evident than for photometry. No good spectral flux calibrations are possible unless the target and calibrator star are observed close in time and very close in airmass (within 0.1 airmass distance). Therefore, some observers often use additional photometric measurements to correct the spectral fluxes. Since the extinction as a function of wavelength varies significantly within the N-band, also the spectral slope needs to be corrected, if the target and calibrator had been taken at different airmass. 

Our goal is to explain the extinction in the mid-IR as a function of airmass. We further demonstrate that the extinction has a non-linear wavelength dependence in the N-band. 

2. Data analysis

All observations of standard stars obtained with TIMMI2 are archived from the beginning of operations in 2001 until present. The conversion factors between measured counts and known fluxes depend on the filter and lens scale used as well as the airmass (all systematically), but also vary with the sky conditions (statistically). A decreasing count rate as a function of rising airmass corresponds to an increasing conversion factor towards larger airmass.

We first separate all standard star measurements according to the filter and lens scale used. Data obtained before the TIMMI2 upgrade in October 2002 are treated separately because of different electronical gains in the previous readout system, but after a normalisation with the conversion factor for airmass AM = 1.0 both results are comparable.

In Fig. 1 we show for several N-band filters the conversion factors (hereafter called Conv) as a function of airmass. Note that in all plots a clear trend for Conv increasing with airmass can be seen, especially if you look towards the lower margin of the distribution.

Why can we constrain our analyse to the lower margin? For a given detector and instrument configuration there exists a well defined optimal sensitivity for a star, i.e. the least extincted count rate achieved for best weather conditions. This corresponds to a minimum conversion factor. On the other side, the sensitivity deteriorates arbitrarily with worse sky conditions, there is no clear maximum for the conversion factor. This is the reason why the distribution of points in Fig. 1 seems to be confined in lower y-direction but spreads towards higher y.

Since we need measurements obtained under identical weather conditions, it is sufficient to make a fit only with the lower-value points. We normalise for each filter the conversion factors by the value for AM = 1.0, in order to make comparable the measurements obtained before and after the TIMMI2 upgrade as well as to make these results comparable to other instruments.

3. Results

3.1. Differential extinction as function of airmass

We present relations, deduced as explained in Sect. 2, which describe the dependence of the atmospheric extinction with airmass (AM). Equation (1a), for example, signifies that at this wavelength the (spectral) flux must be corrected by 22% to account for the extinction between AM = 1.0 and AM = 2.0. For mid-IR filters not given below the number of standard star measurements was not sufficient to calculate a firm result. Since the TIMMI2 archival of standard stars is an ongoing effort, we can add results for these passbands at a later stage.

In Eq. (1a-1d) AM represents the airmass of observation and Corr is the factor to correct the targets' flux into measurements at airmass 1.0. Note that the TIMMI2 filters are not always named according to their central wavelength lambda_0.

For spectroscopy, both the target and calibrator must be flux corrected before their division. The wavelength dependence of Corr has to be taken into account. In a first approach, we use a linear interpolation between Corr for N1 and N11.9, since most observations and therefore the best fits are achieved in these passbands. Due to their lower statistical weight, Corr for N8.9 and N10.4 will be considered in a near future when the TIMMI2 database contains more observations for these filters. The good results shown in Table 2, Table 3 and Fig. 2 justify this first approach a posteriori.

The factor '3' in Eq. (2) expresses the difference in wavelength between N1 and N11.9. Errors for the coefficients are within 0.003. Finally, Corr(lambda, AM) is multiplied with the uncorrected spectral flux F(lambda, AM):

In any data reduction script which also extracts the airmass from the file headers, Eq. (2) and (3) can be conveniently included. With this approximation already a significant improvement of the spectral fluxes is seen in Fig. 2, especially for large distances in airmass. At a later stage, when we can include further correction factors for other N-band filters, the flux correction can be improved to an even higher perfection.

3.2. N-band extinction coefficients

From the relative increase of atmospheric extinction between AM = 1.0 and AM = 2.0 we can, in principle, calculate the extinction coefficients K for La Silla (usually given in mag/AM). These values depend on the observatory site, especially on the altitude and climatic conditions.

Table 1 summarises the median N-band extinction coefficients. Thereof an unextincted photometry with magnitudes m_real can be obtained via the relation:

The wavelength dependence of our extinction coefficients is similar to data for Mauna Kea, while the absolute values differ because of the other altitude.

4. Application to spectroscopic data

Formula (2) and (3) were tested with a cross-calibration of different standard stars taken from the same night. We used test data obtained both in December 2002 and September 2003. A calibrator at low airmass is taken while the objects were observed at higher airmass (see the headers of Fig. 2 for the actual airmass value).

Illustrations for the airmass correction are shown on this page.

Spectra shown in Fig. 2 were obtained in December 2002 when the detector had a dead column between approximately 9.0 micron and 9.8 micron. By intention we did not correct spectral line features in order to show how these may develop with increasing airmass between target and calibrator. Look especially to the CO_2 absorption features at 11.73 micron and 12.55 micron.

Further we derive spectrophotometric fluxes for the N11.9 filter and compare these with literature values. As shown in Table 2 and 3 our airmass correction improves the flux calibration both for targets observed at low and high airmass and reaches an accuracy up to 2% within the literature flux.


Last revision:   2004-Feb-09 by Oliver Schütz
Contact:   schuetz @  and  ls-infrared @
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