Alfredo Dubra's PhD thesis - Imperial College London

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3. Data processing y y y x x s x -s (a) (b) (c) Figure 3.3: Geometry of autocorrelation of an image consisting of two sheared copies of an object with finite dimensions: a) the image to autocorrelate, b) and c) the situations in which the autocorrelation has local maxima other than at the origin. the peaks are visible, they are not strong compared with the background, and in order to improve this and therefore the sensitivity of the algorithm, we also remove the very low spatial frequencies of the object. We therefore virtually retain only the edges of the figure as illustrated in figure 3.4 (e). This stage requires the non-overlapping AC and DC spectra. 3.2.3 Implementation details The interferogram band-pass filtering and the autocorrelation calculation were performed using the DFT and the autocorrelation theorem. There are two advantages of using the DFT rather than the straightforward calculation of the autocorrelation here: firstly a significant speed increase by making use of the fast implementations of the DFT and secondly, the bandpass filtering in the Fourier domain becomes simply a multiplication by a binary mask. Before using the DFT we pad the data with zeros so that the area of the padded data is no less than twice the size of the interferogram plus the shear to avoid overlapping of the periodized autocorrelation (resulting from using the DFT). The mask that performs the band-pass filtering is simply a binary annular mask. The inner radius was chosen so that the spatial frequencies within the shear search range [s min , s max ] would be preserved and all the lower frequencies removed. The outer radius was chosen to keep all the frequencies within the carrier frequency search range and remove those above it. Finally, once the correlation of the filtered interferograms has been evaluated, the 47
3. Data processing mk1/46 (a) (b) (c) (d) (e) (f) Figure 3.4: Improvement on shear estimation algorithm by filtering in Fourier domain: (a) raw shearing interferogram, (c) and (e) the same interferogram after low- and bandpass filtering respectively, (b), (d) and (f) show frontal views of the corresponding autocorrelation plots. The position of the two side peaks with respect to the central peak in the autocorrelation plot in (d) is the shear. 48
Page 1 and 2: A Shearing Interferometer for the E
Page 3 and 4: Acknowledgements Pursuing the PhD d
Page 5 and 6: Contents Contents 4 List of Figures
Page 7 and 8: CONTENTS 5.1 Prydal type experiment
Page 9 and 10: List of Figures 1.1 Young’s exper
Page 11 and 12: LIST OF FIGURES 5.2 Sequence of ref
Page 13 and 14: Chapter 1 Introduction Assessing an
Page 15 and 16: 1. Introduction (a) (b) Figure 1.3:
Page 17 and 18: 1. Introduction was then modified a
Page 19 and 20: 1. Introduction been achieved by us
Page 21 and 22: 1. Introduction A less significant
Page 23 and 24: 1. Introduction It should also be m
Page 25 and 26: Chapter 2 Lateral shearing interfer
Page 27 and 28: 2. Lateral shearing interferometer
Page 39 and 40: P P 2. Lateral shearing interferome
Page 43 and 44: 3. Data processing If we look at th
Page 45 and 46: 3. Data processing term on the retr
Page 47: 3. Data processing mk1/33 (a) (b) k
Page 51 and 52: 3. Data processing 0.43 mk1/46 (a)
Page 53 and 54: 3. Data processing 3.3 Pupil positi
Page 55 and 56: 3. Data processing (a) (d) (g) (j)
Page 57 and 58: 3. Data processing 3.4 Phase recove
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Page 67 and 68: Chapter 4 Wavefront reconstruction
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Page 79 and 80: Chapter 5 Preliminary experiments 5
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Page 83 and 84: 5. Preliminary experiments dm1_no_w
Page 85 and 86: 5. Preliminary experiments bb_focus
Page 87 and 88: 5. Preliminary experiments the corr
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Page 91 and 92: 6. Tear topography dynamics experim
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6. Tear topography dynamics experim
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Chapter 7 Summary and discussion Th
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7. Summary and discussion The value
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7. Summary and discussion ao2_radia
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A. Preliminary study of feasibility
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B. Laser safety calculations B.1 MP
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Bibliography [1] T. Young. The Bake
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BIBLIOGRAPHY [22] P. Artal, S. Marc
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BIBLIOGRAPHY [44] Austin Roorda and
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BIBLIOGRAPHY [67] W.N. Charman and
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BIBLIOGRAPHY [89] J.P. Craig, P.A.
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BIBLIOGRAPHY [115] Frangois C. Delo
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Alfredo Dubra's PhD thesis - Imperial College London

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