The problem of interpreting polarimetric maps of nebulae is discussed in terms of deconvolving the nebular structure from the observed distribution of Stokes' parameters on the sky. It is shown that for an optically thin self-luminous nebula in which light from a single star is scattered from spherical particles, the problem can be expressed by a pair of integral equations of Volterra type, to be solved for the effective (two-dimensional equivalent) spatial distribution of scattering particles n0 (cm–3) and of nebular emission l0 (erg cm–3 s–1) from the observed distribution of total and polarized intensities I, Ip. In these equations the kernels depend on the nature of the spherical scatterers. However, an analytic solution is obtained, for any such scatterer, in terms of an integral moment representation of the desired functions n0, l0 , which can be used to obtain quantities of physical interest. In the case of Rayleigh or Thomson scattering, it is shown that the equations can be reduced to Abel's equation and hence explicit inversion formulae are obtained for n0, l0 in terms of I, Ip. The importance of this deconvolution approach, in contrast to model fitting, in terms of error analysis and model uniqueness is discussed and emphasized.