Astigmatic phase retrieval of lightfields with helical wavefronts
AuthorHenderson, Clare Anne
AffiliationSchool of Physics
Document TypePhD thesis
Access StatusOpen Access
© 2012 Clare Anne Henderson
The controlled use of coherent radiation has led to the development of a wide range of imaging methods in which aspects of the phase are enhanced through diffraction and propagation. A mathematical description of the propagation of light allows us to determine the properties of an optical wavefield in any plane. When a sample is illuminated with coherent planar illumination and its diffracted wavefield is recorded in the far-field of propagation, a direct inverse calculation of the phase can be quickly performed through computational means – the fast Fourier transform. Algorithmic processing is required, however, because only the intensity of the diffracted wavefield can be recorded. To determine structural information about the sample, some other information must be known about the experimental system. What is known, and how it is processed computationally, has led to the development and successful application of a broad spectrum of phase reconstruction iterative algorithms. Vortices in lightfields have a helical structure to their wavefront, at the core of which exists, necessarily, a screw-discontinuity to their phase. They have a characteristic intensity distribution comprising a radially symmetric bright ring around a dark core which, for either handedness of the rotation of the vortex, appears identical. Observation of a vortex is, therefore, ambiguous in its ability to determine its true direction of rotation. The ubiquitous presence of vortices in all lightfields hinder the success of phase reconstruction methods based on planar illumination and, if successful, render any reconstruction of the phase non-unique, due to the ambiguity associated to their helicity. The presence of a controlled spherical phase distortion can break the symmetry of the appearance of the vortices and, hence, remove the ambiguity from the system and drive algorithms to a solution. For the pathological case of an on-axis vortex, however, spherical distortion will not break the radial symmetry. The astigmatic phase retrieval method separates the spherical distortion into cylindrical distortion in two orthogonal directions. This form of phase distortion breaks the symmetry of a vortex allowing a unique determination of the phase. The incorporation of such use of cylindrical distortion into an iterative phase reconstruction algorithm forms the basis for the astigmatic phase retrieval (APR) method. Presented in this thesis is the creation and propagation of lightfields with helical wavefronts, produced through simulation and experiment. Observation of the effects of cylindrical distortion on vortices is explored in detail, particularly for split high-charge vortices where their positions can inform the type and strength of the applied phase distortion. Experimentally, onaxis vortices are created and distorted for the purposes of astigmatic phase retrieval in both visible light and X-ray wavefields. This thesis presents the first experimental demonstration of the astigmatic phase retrieval (APR) method, successfully applied optically with a simple test sample. The method is also applied to lightfields with helical wavefronts. The successful unambiguous reconstruction of on-axis chargeone and charge-two visible light vortices are presented, which is the first experimental demonstration on the unique phase reconstruction of an on-axis vortex from intensity measurements alone. Experiments are then performed to apply the method to vortices created in X-ray wavefields. The parameters of the experiment and the data have not, however, allowed for a successful reconstruction in this case. It is demonstrated through extensive simulation analysis that the APR method is a fast and robust imaging method. It is also shown that, through observation of the error metric, experimental parameters can be corrected or even determined, making the method successful even if there is no a priori knowledge of the experimental system. The application of the APR method as a general imaging technique for use in high-resolution X-ray diffraction experiments is, therefore, is a logical extension of the work of this thesis.
Keywordsoptical physics; coherent diffractive imaging; optical vortex; phase retrieval
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