Reconstruction of multiple point sources by employing a modified Gerchberg-Saxton iterative algorithm

Habool Al-Shamery, Maitham (2018) Reconstruction of multiple point sources by employing a modified Gerchberg-Saxton iterative algorithm. Doctoral thesis (DPhil), University of Sussex.

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Abstract

Digital holograms has been developed an used in many applications. They are a technique by which a wavefront can be recorded and then reconstructed, often even in the absence of the original object. In this project, we use digital holography methods in which the original object amplitude and phase are recorded numerically, which would allow these data be downloaded to a spatial light modulator (SLM).This provides digital holography with capabilities that are not available using optical holographic methods.The digital holographically reconstructed image can be refocused to different depths depending on the reconstruction distance. This remarkable aspect of digital holography as can be useful in many applications and one of the most beneficial applications is when it is used for the biological cell studies. In this research, point source digital in-line and off-axis digital holography with a numerical reconstruction has been studied. The point source hologram can be used in many biological applications. As the original object we use the binary amplitude Fresnel zone plate which is made by rings with an alternating opaque and transparent transmittance. The in-line hologram of a spherical wave of wavelength, λ, emanating from the point source is initially employed in the project. Also, we subsequently employ an off-axis point source in which the original point-source object is translated away from original on-axis location. Firstly, we create the binary amplitude Fresnel zone plate (FZP) which is considered the hologram of the point source. We determine a phase-only digital hologram calculation technique for the single point source object. We have used a modified Gerchberg-Saxton algorithm (MGSA) instead of the non-iterative algorithm employed in classical analogue holography. The first complex amplitude distribution, i(x, y), is the result of the Fourier transform of the point source phase combined with a random phase. This complex filed distribution is the input of the iteration process. Secondly, we propagate this light field by using the Fourier transform method. Next we apply the first constraint by modifying the amplitude distribution, that is by replacing it with the measured modulus and keeping the phase distribution unchanged. We use the root mean square error (RMSE) criterion between the reconstructed field and the target field to control the iteration process. The RMSE decreases at each iteration, giving rise to an error-reduction in the reconstructed wavefront. We then extend this method to the reconstruction of multiple points sources. Thus the overall aim of this thesis has been to create an algorithm that is able to reconstruct the multi-point source objects from only their modulus. The method could then be used for biological microscopy applications in which it is necessary to determine the position of a fluorescing source from within a volume of biological tissue.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering > TK5101 Telecommunication Including telegraphy, telephone, radio, radar, television > TK5102.9 Signal processing
Depositing User: Library Cataloguing
Date Deposited: 08 Nov 2018 09:32
Last Modified: 08 Nov 2018 09:32
URI: http://sro.sussex.ac.uk/id/eprint/79826

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