In a previous blog I have described the use of instrument response for the flux calibration of meteor spectra. One would like to have a plot of energy against wavelength. Unfortunately the measured intensity is influenced by detector sensitivity, grating efficiency, transmission of optics (window, lens, filters) and atmospheric transmittance (all wavelength dependent). The basics is repeated here, for the reader who does not work with these problems on a daily basis.

As long as we are interested in only the relative intensities (in order to determine chemical composition ratios e.g.), the different contributions for the detector signal can be combined with
I(λ) = IR(λ) * Tatm(λ) * S(λ)
This equation is used to calculate the instrument response from the intensity I(λ) of a measured star with known flux S(λ) and for the calculation of meteor flux from the measured intensity I(λ) of the meteor spectrum.

In the last blogpost the instrument response and atmospheric transmission were combined into an overall response
R(λ)  = IR(λ) * Tatm(λ)
From this equation the instrument response corrected spectrum is calculated as
S(λ) = I(λ) /R(λ)
This is perfectly valid as long as the the atmospheric transmission is identical for the reference star which was used to calculate R(λ) and the meteor to which the response is applied. However the atmospheric transmission varies with the sky conditions and the elevation of the observed object above the horizon.
It is therefore advisable to measure the reference star for the flux calibration under the same sky condition (clear, no haze) and at the same elevation as the meteor.

If this is not possible, the script gives the possibility to correct for changes in atmospheric transmittance. It is based on a model of atmospheric transmission by Hayes and Latham and described by Christian Buil in http://www.astrosurf.com/aras/extinction/calcul.htm. The model contains Rayleigh scattering, ozone absorption and aerosol optical density. The atmospheric transmittance is written as
T(λ) = exp[-tauz0(λ)/cos(z)],
where tauz0(λ) is the optical density of the atmosphere at the zenith and z the zenith distance (90° – elevation).

atmospheric transmission for AOD = 0.1, for different elevations, black: zenith … blue: 20° elevation

As mentioned before, the atmospheric transmission depends on air quality. This is described by the aerosol optical density, a value of 0.1 was selected, typical for a clear night in winter. In summer, typical values are higher and the change of transmission with elevation more severe.
The value of AOD can be determined with measuring the response R(λ)  = IR(λ) * Tatm(λ) at different elevations (details not described here).

In the script the correction of the atmospheric transmittance can be applied to the response function as well as the meteor spectrum. In both cases the original spectrum (or reponse function) is divided by the atmospheric transmittance for given AOD and elevation and the resulting spectrum (response function) saved with an appendix “_AM0” (corresponding to air mass 0 or atmosperic extinction removed).

window for calculating atmospheric extinction correction
original response and corrected for atmospheric extinction with AOD = 0.1 and elevation 30°

Further details on the theory and how to apply it in practice can be found in the manual for the script: meteor spectroscopy instrument response.pdf. You can download the newest version of the script from Github: meteor-spectrum-calibration, together with example files. This contains all the changes. The response branch is no longer active.

As always, comments and questions are welcome.

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