Title: New treatment of the focusing method and tomography of the refractive index distribution of inhomogeneous optical components
Abstract: A new mathematical formulation of the focusing method connecting
the refractive index distribution of inhomogeneous optical components
to the transversally transmitted light distribution is presented.
This formulation has the following advantages: the characteristic singularity
occurring in the focusing method is avoided; a single numerical
integration is used instead of a double one, ensuring a faster data processing;
the refractionless approximation is introduced only in the final
step of calculations, leading to smaller errors; and the avoidance of a
residual logarithmic singularity. An inverse functional transform connecting
the intensity distribution in the near field to the refractive index distribution
inside the object is deduced and used to obtain analytical test
functions. The theoretical results are supported by computer simulations
and experiments with gradient-index rods and optical preforms, 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 nonsymmetric
objects using the inverse Radon transform. An efficient algorithm and
suitable computer simulations are presented for this case.
Publication Year: 1996
Publication Date: 1996-05-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 7
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