Optical coherence tomography using algebraic reconstruction technique with l1-optimization

• Main Author: Seck, Hon Luen
• Other Authors: Soh Yeng Chai
• Format: Theses and Dissertations
• Language: English
• Published: 2014
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Optics, optoelectronics, photonics
• Online Access: http://hdl.handle.net/10356/55760
• Institution: Nanyang Technological University

Optical coherence tomography (OCT) is an imaging modality for obtaining tomography images of subsurface structures. While primarily invented and widely used for the imaging of biological tissues, it can equally be used to perform non-destructive inspection of industrial parts. With rapid advancement of 3D manufacturing technology, non-destructive subsurface inspection has become an important issue and OCT can play important roles in these industrial applications. Hence, the development of new OCT methods for industrial inspection has attracted increasing attention in addition to the traditional applications of OCT in bio-imaging. Since its invention in 1991, the OCT technique has evolved from its early version of time domain OCT (TD-OCT) to the prevalent Fourier domain OCT (FD-OCT) implementation because of the sensitivity and speed advantages it offers. However, the advancement of the technology still faces several major challenges for both industrial inspection and bio-medical imaging applications. First, the depth resolution is limited by the coherence length of light. Second, the imaging depth of FD-OCT is limited by the resolution of the spectrometer and the autocorrelation noise (ACN). Third, the ACN in the FD-OCT reconstruction leads to errors and misinterpretation of OCT images. Fourth, there is a trade-off between the wavelength resolution and the depth resolution in spectroscopic OCT. This thesis addresses the above mentioned challenges by developing OCT technologies under a l1-optimization framework, in short l1-OCT. We shall primarily address these issues with respect to industrial applications where we can exploit the sparsity property of the samples. In this thesis, l1-OCT is first developed by using the sparsity representation of the depth profile of samples. The OCT is formulated into a sparse algebraic reconstruction problem which can be solved by l1-optimization. Since the point spread function of the depth profile has already been considered in the algebraic reconstruction, l1-OCT can reconstruct the depth profile with high resolution beyond the coherence length. In l1-OCT, the spectral measurements obtained in the wavelength domain are directly used. This means that l1-OCT does not require the spectral interferogram to be interpolated and resampled. As a kind of compressed sensing technique, l1-OCT offers longer imaging depth beyond the limit imposed by the Nyquist sampling rate. l1-OCT is then extended to remove the autocorrelation noises (ACN) in OCT by using the sparse representation of the optical field. l1-OCT is formulated into one problem of sparse filter design, and the problem is solved by a l1-optimization with quadratic constraints in l1-OCT. It is shown that l1-OCT can remove ACN effectively and thus increase the imaging depth. l1-OCT is further extended to a spectroscopic OCT, in short l1-SOCT, which is capable of reconstructing both the depth profile and the spectroscopy of features at depth locations. l1-SOCT leverages on the sparse representation of both the depth profile and the time-frequency distribution in terms of elementary Mie spectra. The time-frequency distribution reconstruction is further formulated into an algebraic sparse deconvolution problem. The Two-step algorithm is proposed to solve the deconvolution problem. This algorithm overcomes the computational difficulty of solving for the spectroscopies at all the depth locations simultaneously. To analytically assess the performance of l1-OCT, a l1-optimization algorithm by using the arctan function is proposed to approximate the l1-optimization in l1-OCT. Compared with another commonly used approximation function, the proposed approximation is shown to have a higher accuracy and comparable convergence rate. In short, by formulating the OCT reconstruction into a sparse algebraic deconvolution problem, the developed l1-OCT technologies deliver high resolution beyond the limit of the coherence length of light, attain a longer imaging depth, remove the autocorrelation noise present in the prevalent FD-OCT implementation, and overcome the time-frequency trade off in the reconstruction of time-frequency distribution. The thesis is concluded with some identified research problems for future works.