Studies on wavefront estimation and refraction corrected image reconstruction in optical tomography

Abstract

In this thesis we report the development of two experimental phase measurement techniques for application in optical tomography and the modifications of the existing inversion algorithms for reconstructing the refractive index distributions of strongly refracting objects. Since the input in optical tomography is the optical path delay (opd) data, direct measurement of this phase change is not possible through intensity detectors. We have developed a method based on optical differentiation of the input light and another method in which the phase is retrieved using the intensities measured in the object and spectral planes respectively. These methods have been experimentally applied to collect opd data from two test objects: a capillary glass tube immersed in an index?matching liquid and three glass rods arranged in a triangular array in a background?matching liquid. The reconstruction of the differentiated data from the three glass rods and the integration of the same are presented. The contribution of this thesis in the reconstruction part is the development of iterative schemes for inverting the optical tomographic data. Since light travels through a refractive medium along Fermat’s path, the application of straight?path algorithm for inversion results in degraded reconstructions. The optical tomography is thus a generalisation of the X?ray tomography and algorithms incorporating correction for refraction have to be developed. We have modified the FBP (Filtered Back Projection) algorithm and with an iterative loop in which the forward projection and the backprojection are done through ray?tracing, the error is shown to decrease. A correction for the error introduced due to diffraction is applied on the last iterate with the reconstruction of the difference term done using diffraction tomography. The improved results of the reconstructions of the capillary tube cross?section are presented. We have also reconstructed the capillary tube cross?section with a modified SART (Simultaneous Algebraic Reconstruction Technique) wherein an error?reduction loop similar to the one applied to the FBP algorithm is used. In addition we have incorporated an additional heuristic gradient term in the update step which resulted in faster convergence and improved reconstructions. The results from these are presented and compared. Thus it is shown in this work that iterative algorithms incorporating refraction & diffraction correction give superior results compared to straight?path inversion algorithms when applied to opd data from highly varying refractive index distributions.