On the deduction of the vertical distribution of ozone by ultraviolet spectral measurements from a satellite

In a simple scattering atmosphere, containing an absorbing constituent that absorbs differently at different wavelengths, the spectral distribution of reflected energy depends on the vertical distribution of the absorbing constituent. In fact, if the vertical distribution is represented by expressing the pressure as an explicit function of the mass of absorbent between the top of the atmosphere and that pressure level, and the spectral energy distribution as an explicit function of absorption coefficient, then, for a model with primary scattering only, the latter function is a Laplace transform of the former. This result can be utilized to obtain an approximate inversion and so to deduce the vertical distribution of the absorbing constituent. Some numerical computations are presented for the case of ozone distribution in the earth's atmosphere.