Coherent diffractive imaging (CDI) methods are techniques that image a sample by illuminating it with a coherent beam and recording the intensity diffraction pattern produced by the wavefront outgoing from the sample. These are lensless methods that are not limited in resolution by the physical characteristics of an objective lens, and therefore are versatile and increasingly popular, especially in the ptychography form factor. Conversely, they depend on a computational inversion of the recorded intensity patterns, which requires the solution of the challenging phase retrieval problem, and is typically achieved through a gradient-based optimization method. As CDI methods grow in complexity, the corresponding inversion problem become more challenging, and manually calculating these gradients can require complex mathematics that is both difficult and tedious. It is therefore worthwhile to consider solution methods that remove such inconvenience and thereby truly unlock the utility of these imaging techniques. In this dissertation we propose the use of the automatic differentiation (AD) method as a framework to solve the coherent diffractive imaging problem. In this framework, we only need to specify the physics-based forward model for a specific imaging application; the gradients are automatically calculated. We show that the AD method is easy to use and convenient to adapt for changing experimental demands, and can even enable the design of optimization algorithms that outperform state-of-the-art manually derived methods. We then leverage this versatility to apply AD for imaging in the ``multi-peak Bragg ptychography'' (MPBP) CDI modality, so that the algorithm we use for the MPBP reconstruction is just an extension of the basic approach we develop for ptychography. Our numerical experiments demonstrate that this AD-based MPBP method can directly reconstruct the vector-valued crystal lattice displacement profiles, rather the just the scalar-valued phase maps, from intensity diffraction data alone. Moreover, the algorithm we propose is more robust and data-efficient than any existing technique in the literature. We expect that the AD-based MPBP method, and the AD method in general, will find application for the imaging of real-world functional materials.

Creator

• Kandel, Saugat

DOI

• https://doi.org/10.21985/n2-631x-vk62

Subject

• Applied physics
• Physics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15629
• etdadmin_upload_830433

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright