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Artifact-suppressing reconstruction for X-ray near-field holography
Citation Link: https://doi.org/10.15480/882.16702
Publikationstyp
Doctoral Thesis
Date Issued
2026
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-06-03
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2026)
X-ray near-field holography is an excellent tool for imaging objects with a resolution in the nanometer range. Full-field measurements with a lens-free microscopic measurement setup allow holograms of objects to be recorded at multiple magnifications. Unfortunately, these holograms can only be measured as an integral over a certain period of time. The phase information of the hologram is lost and only the intensities are recorded, commonly known as the phase problem. To recover the phase information, a spatial support and/or the recording of several holograms at different detector distances are usually used as additional information in reconstruction approaches. However, both constraints are only feasible for a very closed set of experiments, require time consuming optimization of hyper-parameters and a lot of computation time. Avoiding both techniques is a necessity to enable in-situ/operando measurements but, in doing so, reconstruction artifacts appear. Another challenge is the Autofocus problem. For the reconstruction of holographic data, the numerical focus of the measurement setup is part of the forward model and must be known very precisely. If the numerical focus is inaccurately embedded in the forward model of the reconstruction algorithm, it will generate artifacts or result in blurred reconstructed images. In practice, it is often difficult to accurately determine the Fresnel number for a good reconstruction. In the following work, the origin of possible artifacts as described above is investigated in detail and countermeasures are developed by adjusting the raw data preprocessing, by adjusting the reconstruction and by an automatic optimization of the forward model.
The first part of this thesis addresses reconstruction artifacts with respect to a reference method, a projected gradient decent approach, using a Nesterov accelerated gradient. The reconstruction artifacts have the following identified causes: Truncation artifacts are caused by the limited field of view of the detector. The real hologram is cut off and as a result, the acquired image contains inconsistent areas at the borders. Mirroring the hologram in all directions in combination with a modified window function is derived as a countermeasure to reduce the impact of truncation edges. Low frequency artifacts are identified to be mainly caused by a global normalization error in the empty beam normalization or flat-field-correction. The normalization is corrected by introducing a constant offset parameter into the reconstruction. Other artifacts are overestimation artifacts, mainly caused by the Nesterov acceleration. The forward model amplifies this effect, which is sensitive to high spatial frequencies. To reduce the overestimation of the phase and absorption values, a regularization of the absorption values is applied, which is sufficient for both parameters simultaneously. The insensitivity of the forward model to low spatial frequencies leads to weak reconstruction artifacts. These are therefore reconstructed slowly since they have a small impact on the reconstruction loss. A newly introduced frequency-dependent Nesterov momentum and iterations on multiple grids explicitly accelerate the reconstruction of low frequencies. Both techniques also reduce an overestimation of high spatial frequencies. The combination of all described methods is summarized in a new artifact-suppressing reconstruction method (ASRM). Compared to the reference algorithm, it suppresses all artifacts mentioned above and reduces the reconstruction time significantly.
The second part of the thesis proposes a solution to the autofocus problem with an approach to automatically optimize the Fresnel number. The approach consists of three problems to be solved. An error metric is required that quantifies the distance between the estimated forward model and the correct one. A global optimization has to be defined, which has to be solved by an appropriate solver. As an error metric, a model fit error (MFE) metric is derived from data inconsistencies that are introduced when a non-negative electron density constraint is applied to a defocused wave-field. The novel error metric is evaluated by simulation and experimental results and finally compared with other error metrics from the literature. On simulated data, the MFE metric performs similarly to comparative error metrics and significantly better on experimental data. For an automated solution of the autofocus problem, a global optimization problem with respect to the numerical focus is formulated. The expected uncertainty of the setup geometry is added as a constraint to the target function. Since the gradients of the target function are not trivially accessible, a gradient-less downhill simplex method is chosen as a solver. As fine tuning, the parameters for the ASRM algorithm are adjusted so that the MFE behaves optimally.
The first part of this thesis addresses reconstruction artifacts with respect to a reference method, a projected gradient decent approach, using a Nesterov accelerated gradient. The reconstruction artifacts have the following identified causes: Truncation artifacts are caused by the limited field of view of the detector. The real hologram is cut off and as a result, the acquired image contains inconsistent areas at the borders. Mirroring the hologram in all directions in combination with a modified window function is derived as a countermeasure to reduce the impact of truncation edges. Low frequency artifacts are identified to be mainly caused by a global normalization error in the empty beam normalization or flat-field-correction. The normalization is corrected by introducing a constant offset parameter into the reconstruction. Other artifacts are overestimation artifacts, mainly caused by the Nesterov acceleration. The forward model amplifies this effect, which is sensitive to high spatial frequencies. To reduce the overestimation of the phase and absorption values, a regularization of the absorption values is applied, which is sufficient for both parameters simultaneously. The insensitivity of the forward model to low spatial frequencies leads to weak reconstruction artifacts. These are therefore reconstructed slowly since they have a small impact on the reconstruction loss. A newly introduced frequency-dependent Nesterov momentum and iterations on multiple grids explicitly accelerate the reconstruction of low frequencies. Both techniques also reduce an overestimation of high spatial frequencies. The combination of all described methods is summarized in a new artifact-suppressing reconstruction method (ASRM). Compared to the reference algorithm, it suppresses all artifacts mentioned above and reduces the reconstruction time significantly.
The second part of the thesis proposes a solution to the autofocus problem with an approach to automatically optimize the Fresnel number. The approach consists of three problems to be solved. An error metric is required that quantifies the distance between the estimated forward model and the correct one. A global optimization has to be defined, which has to be solved by an appropriate solver. As an error metric, a model fit error (MFE) metric is derived from data inconsistencies that are introduced when a non-negative electron density constraint is applied to a defocused wave-field. The novel error metric is evaluated by simulation and experimental results and finally compared with other error metrics from the literature. On simulated data, the MFE metric performs similarly to comparative error metrics and significantly better on experimental data. For an automated solution of the autofocus problem, a global optimization problem with respect to the numerical focus is formulated. The expected uncertainty of the setup geometry is added as a constraint to the target function. Since the gradients of the target function are not trivially accessible, a gradient-less downhill simplex method is chosen as a solver. As fine tuning, the parameters for the ASRM algorithm are adjusted so that the MFE behaves optimally.
Subjects
X-ray microscopy
Near-field holography
Synchrotron radiation
Inverse problems
Image reconstruction
Autofocusing
DDC Class
530: Physics
519: Applied Mathematics, Probabilities
Funding(s)
Funding Organisations
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