This report is a master thesis, written by an engineering physics and electrical engineering student at Luleå University of Technology.The desires of this project was to remove dislocations from wrapped phase maps using sparse reconstructive methods. Dislocations is an error that can appear in phase maps due to improper filtering or inadequate sampling. Dislocations makes it impossible to correctly unwrap the phasemap.The report contains a mathematical description of a sparse reconstructive method. The sparse reconstructive method is based on KSVDbox which was created by R. Rubinstein and is free for download and use. The KSVDbox is a MATLAB implementation of a dictionary learning algorithm called K-SVD with Orthogonal Matching Pursuit and a sparse reconstructive algorithm. A guide for adapting the toolbox for inpainting is included, with a couple of examples on natural images which supports the suggested adaptation. For experimental purposes a set of simulated wrapped phase maps with and without disloca-tions were created. These simulated phase maps are based on work by P. Picart. The MATLAB implementation that was used to generate these test images can be found in the appendix of this report such that they can easily be generated by anyone who has the interest to do so. Finally the report leads to an outline of five different experiments that was designed to test the KSVDbox for the processing of dislocations. Each one of these experiments uses a different dictionary. These experiments are due to inpainting with, 1. A dictionary based on Discrete Cosine Transform. 2. An adaptive dictionary, where the dictionary learning algorithm has been shown what thearea in the phase map that was damaged by dislocations should look like. 3. An adaptive dictionary, where the dictionary learning algorithm has been allowed to trainon the phase map that with damages. This is done such that areas with dislocations areignored. 4. An adaptive dictionary, where training is done on a separate image that has been designedto contain general phase patterns. 5. An adaptive dictionary, that results from concatenating the dictionaries used in experiment 3 and 4. The first three experiments are complimented with experiments done on a natural image for comparison purposes.The results show that sparse reconstructive methods, when using the scheme used in this work, is unsuitable for processing of dislocations in phase maps. This is most likely because the reconstructive method has difficulties in acquiring a high contrast reconstruction and there is nothing in the algorithm that causes the inpainting from any direction to match with the inpainting from other directions.

The present thesis concerns with a few investigations on sensing/measurement of small angle rotation/tilt using Pattern Imaging Method. The methodology involves looking at the tailored-objects located adjacent to the observer (CCD camera) through a mirror and extracts the angular position of the mirror from their images by processing the latter through object specific algorithm. Its principal advantage stems from the fact that small-angle measurement can be done using ambient light which is neither collimated nor filtered for single wavelength. This makes the associated optical configuration not only simple but also robust for the said application, in comparison to currently competing technologies based on Autocollimation and Interferometry. The present thesis elaborates specifically four new Pattern-Designs proposed for tailoring the spatial-brightness of the objects. Introducing for the first time, processing algorithms based on ‘Modified Fringe-Processing Strategy’ and ‘Phase-Only-Correlation’, the investigations demonstrate enhanced performance for small angle measurement with all the proposed pattern designs. The first three designs for the pattern are evaluated for 1-D measurement through fringe processing approach while the fourth pattern design is evaluated for 2-D measurement through Phase-only-Correlation. The results of the investigations are utilized to propose, design and develop a novel optical inclinometer which can work with any of the proposed pattern designs as the object. The first three pattern-designs rely upon sinusoidal modulation of the object surface and utilize three custom developed algorithms -Algorithm-A, Algorithm-B and Algorithm-C -to extract two quantities namely wrapped phase Δαw and unwrapped phase Δαuw , from the captured images. Each of these quantities will have an associated measurement range and accuracy corresponding to any of the three pattern designs. All measurements are carried out keeping the object/camera to mirror distance constant at 250 mm. From wrapped phase measurement, all the three designs, each with pitch of 2mm for sinusoidal modulation and held at a distance of 250 mm from the mirror, have been found to facilitate reliable angle measurement over a range of 850 arc seconds with accuracy better than 1 arc second after curve fitting the experimentally obtained data. From unwrapped phase measurement, the color coded as well as BCD coded composite patterns, when tested using five bands of sinusoidal modulation (with a pitch of 2mm) and held at a distance of 250 mm from the mirror, facilitated reliable angle measurement over a larger range of nearly 10 . The 2-D angle measurement using fourth pattern-design and the Algorithm-D, facilitated measurement over a range of 10 with an accuracy of 9 arc seconds when the distance between the mirror and the pattern is held at 250 mm. A comparison of the results from the present investigation with the best performance from other investigators reveals the following. The proposed modifications in the processing algorithms as well as the pattern designs help to achieve a measurement range of 750 arc seconds with accuracy better than 1 arc second from this method, with an object pattern whose lateral size is smaller by a factor of nearly 15. Such a size reduction in the object as well as the associated mirror would help to construct angle measuring instruments that work on this method more compactly. The results of the investigation have been utilized to propose and demonstrate a novel prototype optical inclinometer which has been experimentally found to work in a range of 0.40 with accuracy nearly 6 arc seconds.