Optical remote sensing inside an inhomogeneous axisymmetric medium: the absorption field measurement

It is shown that the absorption field inside an inhomogeneous, rotationally symmetric medium with a spatially variable refractive index can be reconst ructed by means of a tomographic technique. The classic Abel transform is e xtended to non-Euclidean optical media. The optical behavior of such a medi um is described and, provided that the product of the refractive index with the radial distance is a monotonic function, an exact inverse formula is f ound. Both a numerical and an analytical test on a phantom function is carr ied out to prove the exactness of this formula. In contrast, when the assum ption of a monotonic function is not true, it is shown that the reconstruct ion problem becomes subdeterminate because of the presence of annular regio ns, known as blind areas, inside of which no curved path reaches an extremu m. The spatial localization and the size of these regions are related to th e extrema of the index of refraction times the radial distance. (C) 2000 Op tical Society of America OCIS codes: 170.6960, 120.3940, 120.4290, 000.3860 , 080.2710.