An algorithm for carrying out the deprojection process to derive emiss
ivity distributions from sky maps is developed which incorporates the
Lucy method (Lucy 1974). Model images with and without noise are used
to test the algorithm. It is then applied to the Einstein X-ray image
of the Cygnus Loop supernova remnant. The emissivity distribution is d
erived for a full set of radial slices of the image. Most image slices
of the Cygnus Loop are consistent with spherical symmetry or with wea
k angular dependence. The presence of clumps in other regions requires
an emissivity which has a stronger angular dependence.