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TIMMI2 Filters

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1 Filter characteristics

1.1 General

There are two groups of filters. A first group of comes from the Reading University (UK), and their transmission curve tables at T=40K were provided by the maker. A second group of filters comes form the Optical Coating Laboratory, Inc. (OCLI; California), and hardcopy plots of the transmission curves at T=77K were scanned and converted into data tables by us. Unfortunately, only room temperature (RT) scans are available for filters N1 and N2. Using these tables, the wavelengths of $50\%$ transmission were computed ( $\lambda_{50,1}$ and $\lambda_{50,2}$), plus the central wavelength ( $\lambda_{{\rm eff}}=(\lambda_{50,1}+\lambda_{50,2})/2$), the FWHM ( ${\rm FWHM=\lambda_{50,2}-\lambda_{50,1}}$), and the equivalent width ( ${\rm {EW}=T_{{\rm max}}^{-1}\times\int T\, d\lambda}$ where $T_{{\rm max}}=100$). These parameters are listed in Table 1 for the main filter set, and Fig. 1 show the transmission curves in graphical form (clicking on the figures opens the PostScript version).

This tar file contains all transmission tables. Unfortunately, no information is available for the L and M filters, but their transmissions are similar to the corresponding ISAAC filters. 

1.2 Choosing filters in the N band

In the N region there are several spectral ranges that are covered by more than one filter, so we propose in Fig. 2 a scheme to concisely summarize the filter characteristics. The filters are represented in the EW vs. wavelength plane, and the arrows span indicates the FWHM of each filter. Using the plot the user should be able to easily choose his/her filters, by privileging sensitivity (higher EW) or spectral information (smaller FWHM). Fig. 3 shows that there is a linear relation between the filter EW and FWHM (residual dispersion less than $10\%$). Neglecting the very small constant term, the relationship can be expressed as the EW being roughly $90\%$ of the FHWM. This means that the shape of the transmission curves is very similar one to the other.

We also tried to simulate the effect of the transmission of the atmosphere on the shape of the filters' curves. To model this, we took the atmospheric transmission from Allen's Astrophysical Quantities (4th edition, 1999)¹. The result is shown in Fig. 4, where it is clear that most of the filters are almost unaffected by the atmosphere. However, two dips in the atmospheric transmission curve affect filters N7.9-OCLI and N8.9-OCLI, and the forest of absorption bands affects both filters Q1 and Q2. This is made clear by comparing Fig. 5 with Fig. 2: the two aforementioned N-band filters are indeed the ones that show the largest drop in EW. In Fig. 7 we show the percent difference between a filter quantity after and before the introduction of the atmosphere. The top plot shows that the central wavelength is very little affected (the median difference is $0.1\%$), and the central plot shows that this is true also for the FWHM. However the dispersion is $\sim5\%$, two filters have a FWHM which is smaller by more than $10\%$ (it's $14.7\%$, and $20.1\%$ smaller for the Q1 and Q2 filters, respectively). The biggest effect of the atmosphere is on the equivalent width, which is shown in the bottom plot. The EW is more than $5\%$ smaller in median, with a large dispersion of almost $13\%$. The most affected filters are N7.9-OCLI ($-52\%$), N9.8-OCLI ($-45\%$), Q1 ($-42\%$), and Q2 ($-36\%$).

The analogous to Fig.  3 is Fig. 6, which shows that the good linear relation is mantained (correlation coefficient almost equal to $1$), but now with a significant zero-point offset.

 

Table 1:  List of TIMMI2 filters. The effective wavelength is computed as the average of the red and blue points defining the FWHM of the filter.

Filter	$\lambda_{{\rm cen}}$	FWHM	EW
L	3.92	-1.00	-1.00
M	4.64	-1.00	-1.00
N7.9-OCLI	7.79	0.71	0.66
N1	8.70	1.23	1.10
N8.9-OCLI	8.73	0.78	0.73
N9.8-OCLI	9.68	0.93	0.85
N10.4-OCLI	10.38	1.02	0.99
$[$SIV$]$	10.45	0.16	0.11
N2	10.68	1.45	1.25
--	10.71	2.55	2.27
N11.9-OCLI	11.66	1.16	1.00
SiC	11.78	2.26	1.85
N12.9-OCLI	12.35	1.18	1.01
$[$NeIINeII	12.79	0.22	0.13
Q1	17.72	0.82	0.59
Q2	18.74	0.86	0.53
--	23.01	8.40	5.03

 

Figure 1: TIMMI2 filters. Blue-shaded histograms are filters from OCLI, while red-shaded filters come from the IR lab of the Reading University. The very broad filter in the bottom panel is not offered. The dashed curve represents the atmospheric transmission.

 

Figure 2: EW vs. wavelength for TIMMI2 filters in the N region. The arrows delimit the FWHM of the filter, and the effective wavelength is reported underneath each data point. In case of more than one filter centered the same wavelength, this scheme should allow users to make their choice, balancing throughput over FWHM.

 

Figure 3: A linear relationship is clearly existing between the filter EW and the FWHM. The equation is printed at the top of the graph, where the rms around the fit and the correlations coefficient are also given. Filter Q (with a FWHM greater than $8$) has been excluded from this fit.

 

Figure 4: Same as Fig. 1, but with the transmission curves after modification by the atmospheric transmission

 

Figure 5: Like Fig. 2 after including the effect of the atmosphere on the filter transmission curves.

 

Figure 6: Like Fig. 3 after introduction of the atmosphere.

 

Figure 7: From top to bottom, the effect of the atmosphere on the filter effective wavelength, FWHM, and EW.

...¹

Although the water content of the atmosphere changes a lot with time, we assume that the wavelength dependence of the absorption is conserved. So relative equivalent widths of the filters (and their sensitivities) should be maintained. This is consistent with our separate study of the relative intensities of TIMMI2 filters (http://www.ls.eso.org/lasilla/Telescopes/360cat/timmi/Reports/limfluxes/).