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Tomography
is a process of three dimensional reconstruction of an internal
structure of an
object using its two-dimensional projections, acquired under several
angles of
incidence. Classical tomography, which is known for example from
medicine, is
based on the X-rays imaging, in contrary in optical tomography visible
range of
electromagnetic radiation is used. The consequence of using the
radiation with longer
wavelengths is that the paths of light can no longer be considered as
straight lines.
Moreover, when the dimensions of the object’s details are
close to the
wavelength the diffraction effects become significant. Even more
complex is the
measurement of diffractive structures such as photonic crystals.
The described method is based on a combination of multidirectional interferometry and tomographic reconstruction algorithm (Fig.1). The multidirectional interferometric measurement results in set of two-dimensional distributions of integrated value of refractive index. This set is then processed using a reconstruction algorithm such as filtered backprojection or more complex diffraction tomography algorithm.  Fig. 1: Principles of optical tomography There are two main groups of tomographic reconstruction algorithms (Fig.2). The most known algorithm of filtered backprojection belongs to the group based on so called "Fourier slice theorem". The algorithms of this group do not consider any diffraction or refraction of the rays. In the group of methods based on "Forier diffraction theorem" the diffraction and refraction is allowed, as long as it does not exceed the 1st. Born or Rytov approximation.  Fig. 2: Fourier
slice
theorem and Fourier diffraction theorem
Tomographic
algorithms make use of the integrated information (projection) of the
internal
structure of the thick object. The relation between the
object’s
structure and
the projection is quite obvious, as far as simple objects are
considered. However
when the object structure strongly interacts with the illumination
wave, it is
necessary to perform a simulation of this interaction. Since during the
measurement
the object is rotated, particularly interesting is the dependence of
the
amplitude – phase distribution on the incidence angle. These
exemplary
results
were obtained using RCWA method.
The simulated object
was a model of a photonic crystal fiber (3.6µm
channel
diameter, 8µm spacing).  Fig. 3: Propagation
of an optical
wave in a
photonic crystal structure
 Fig. 4: Tomograms of
two
photonic crystal fibers 
 Fig. 6: 3D
reconstruction
of
a photonic crystal fiber
The
constant
cooperation with Institut für Strahlwerkzeuge http://www.ifsw.uni-stuttgart.de/en_index.html
includes the analysis of the internal structure of photonic and special
fibers
with respect to application in fiber lasers. The further possible
application
of the method include the material analysis of any phase microelements,
with a
complex internal structure.
1. W. Gorski, W.Osten: “Tomographic imaging of photonic crystal fibers”, Opt.Let, Vol. 32, No. 14, 1977-1979 (2007). 2. W.Gorski, S.Rafler, W.Osten: ”High-resolution tomographic interferometry of optical phase elements”, Proc. SPIE 6616 (2007) 3. W.Gorski: “Tomographic microinterferometry of optical fibers”, Opt. 4. W. Górski: ”The influence of diffraction in microinterferometry and microtomography of optical fibers”, Opt. Las. Eng. vol. 41, pp. 565 – 583, (2004). 5. W.Górski, M. Kujawińska: ”Three-dimensional reconstruction of refractive index distribution in optical phase elements”, Opt. Las. Eng. vol. 38 (6), 373-385, (2002). 6. W.Górski: "Tomographic interferometry of optical phase microelements", Opto-Electronics Review, vol. 9, no. 3, pp.: 347-352, (2001). Request a copy AcknowledgementsA large part of this work was supportet by Deutsche ForschungsgemeinschaftUnser Online-Angebot
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