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Here,

• oi (A) is the absorption cross-section of constituent i at wavelength A,

Note that, in Eq. (2), only absorption takes part in the extinction process. The contribution of molecular scattering has been neglected so far. The impact of such an approximation is still under investigation. It is foreseen to introduce it later in the model for the channels for which it is relevant.

LYRA is a full-Sun radiometer. Due to the wide angular size of the Sun (30 arcmin), the optical path is highly dependent on the emitting zone of its surface. At the nearest point to the Earth's surface (the so-called tangential point), rays emitted by the different zones of the Sun's surface span over approximately 25 km (Fussen et al. 1997, 2001), which would drastically limit the vertical resolution of our retrieval, if not taken into account in the modeling. The measured atmospheric transmittance, defined as the ratio of the irradiance after absorption to the unattenu-ated irradiance, observed in the LYRA channel c, may be modeled by

OO 0max 2n

/ dAFc(X) f d9 sin(0)cos(0 + f)/ dp exp(-r(A,0,p))k(A,0,p) T ( ) _ a_o_0_

where

• 0, p, and f are illustrated in Fig. 1. Parameters 0 and p identify the emitting zone of Sun surface,

• Fc is the instrumental response in channel c.

Since the Sun radius (rSun) is tiny compared to the Sun - detector distance dSD, we can neglect f and replace 0max by |. As a startpoint, let us also consider a revolution symmetry on I with respect to <, which is a rather crude approximation in which the major emission spatial variability would come from the limb darkening or limb brightening, depending on the considered wavelength. This approximation will be given up later without too many difficulties.

Then, following Lumpe et al. (1991), we will apply the variables substitution:

We obtain

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