Microtomography
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Principles of optical tomogrphy |
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.
Principles of optical tomography |
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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.
Simulation of propagation of optical wave inside a diffractive structures |
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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).
Measurement of photonic crystal fibers |
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- Two photonic crystal fibers of the same configuration but different dimensions were measured. For both fibers filterd backprojection and diffraction tomographic algoriths were applied. The reconstruction was performed using 30 angular positions over 180 deg.The results of measurment of the smaller fiber show very clear difference in in quality of reconstruction in favour of diffraction tomography method.In case of the larger fiber this difference is not so obvious any more. The wavelength used was 633nm. During the experiment the immersion technique was used, therefore the normally air-filled channels are filled with the index matching liquid.
- Fig. 5: A tomogram with a profile of refractive index
Applications |
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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.
References |
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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. Eng., 45 (12), 125002 (2006).
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).
Acknowledgements
A large part of this work was supportet by
Deutsche Forschungsgemeinschaft
© Institut für Technische Optik