In this dissertation, the reconstruction algorithm based upon a projection function, which renders the conventional computerized tomography (CT) scheme applicable to microwave imaging directly and moreover without interpolation processing, is suggested to reconstruct the permittivity profiles of inhomogeneous dielectric object under the Born and far-field approximation. A way to improve the degraded imagery resulting from the violation of the Born condition is also suggested here. The proposed method by using the projection function can explicitly explain the limiting factors in the degrading reconstructed image due to the Born approximation. The validity of the proposed method is assured by showing the results obtained by numerical simulation and laboratory experiment from the X-Band scattered data for the various dielectric cylinders. The results of simulation are well consistent with the images of experimental results.
In spite of several potential advantages over other imaging schemes, microwave imaging of inhomogeneous dielectric object in practical situation has been hampered by lack of an adequate reconstruction algorithm accounting for the effects of refraction and diffraction accurately. This limitation has been overcome by development of the Fourier diffraction projection theorem under such a basic assumption as the first-order Born approximation to the equivalent source induced on dielectric objects, which is valid only for weak scatterer. Then the scattered fields, measured in far-field region by using frequency and angular diversity, take the form of spatial-frequency data in a polar format. In particular, it is well recognized that these data after the range correction are directly equal to the Fourier transform of the permittivity profile of the dielectric scatterer. In consequency the reconstruction process on the Fourier diffraction projection theorem consists of interpolation and the inverse FFT. The interpolation, however, becomes a key factor of the degradation in the retrieved image.
A new algorithm for microwave imaging is presented here. It consists of two steps. At first, the projection data for all aspect angles are collected. And next, the X-ray CT algorithm to all projection data is employed to retrieve the image and then the Shepp and Logan filter was adopted in our CT algorithm. Then, one of the interesting features in the proposed method is a possibility to improve image quality by modification through each step. These advantages led to the better image quality in comparison with the result obtained by the other algorithms such as direct Fourier inversion and circular convolution integral.
To explore why the retrieved image of object is degraded under the Born approximation, the various projection functions and reconstructed images for 2-dimensional dielectric cylinder as a function of relative dielectric constant and object size are examined by computer simulations and laboratory experiment in the frequency range from 0.1 to 12.0 GHz. The simulated and experimental results were shown that the object images can be successfully reconstructed under the Born Condition, which restricts the difference between optical path length in dielectric object and that in free space to keep much smaller than the half of the wavelength. When the condition of the Born approximation is violated, the reconstructed images are affected from the severe degradation. The reason of such degraded images was interpreted by the difference between the actual diameter of object and the reconstructed diameter of projection function which is extended in proportion to the product of refractive index and object size.
In order to improve the image quality for the degraded image, the projection functions should be modified to restore those real sizes. If the size of object is known, the procedure for modified projection function can be directly accomplished. Applying the above procedure to each projection function obtained by all aspect angles, the improved image is routinely reconstructed by applying the X-ray CT algorithm to the modified projection functions.
Finally, to find the limitation of the presented method for image improvement, the numerical simulation for the projection function was accomplished for the homogeneous and inhomogeneous dielectric cylinder. From the simulation results, the criterion for the presented method may be extracted as the product of the change in refractive index and diameter of object is approximately 1.2$\lambda$ In comparison with the conventional limitation of the Born approximation which provides 0.5$\lambda$, the applicable limitation increases 2.4 times in the presented scheme. Therefore the presented method will be expected to play an important role in overcoming the canonical limitation inherent to the first-order Born approximation in the area of diffraction tomography imaging.
