NEW TREATMENT OF THE FOCUSING METHOD AND TOMOGRAPHY OF THE REFRACTIVE-INDEX DISTRIBUTION OF INHOMOGENEOUS OPTICAL-COMPONENTS

A new mathematical formulation of the focusing method connecting the r efractive index distribution of inhomogeneous optical components to th e transversally transmitted light distribution is presented. This form ulation has the following advantages: the characteristic singularity o ccurring in the focusing method is avoided; a single numerical integra tion is used instead of a double one, ensuring a faster data processin g; the refractionless approximation is introduced only in the final st ep of calculations, leading to smaller errors; and the avoidance of a residual logarithmic singularity. An inverse functional transform conn ecting the intensity distribution in the near field to the refractive index distribution inside the object is deduced and used to obtain ana lytical test functions. The theoretical results are supported by compu ter simulations and experiments with gradient-index rods and optical p reforms, which have shown improvements in the accuracy, stability, and speed of the method. Moreover, this mathematical formulation for the axisymmetric objects is generalized to a tomographic formulation for n onsymmetric objects using the inverse Radon transform. An efficient al gorithm and suitable computer simulations are presented for this case. (C) 1996 Society of Photo-Optical instrumentation Engineers.