The seismic method has many applications. It is important in the critical sector of energy. Besides being used in imaging oil and gas reservoirs, it is also utilized in other sectors of energy such as geothermal energy exploration and development. It also plays a role in extracting other resources such as minerals or in the process of monitoring CO2 sequestration to reduce the carbon footprint of humankind. While seismic waves can occur naturally, their study gives insight in analysing the occurrence of and mitigating risks related to earthquakes. As far as active-source seismic is concerned: seismic images make it possible to see what is in the subsurface with minimal expensive and invasive operations such as drilling unnecessary holes in the subsurface — similar to what medical professionals use ultrasound or X-ray images for. Several methods have been proposed to analyze seismic data. A popular method nowadays is full waveform inversion (FWI), for instance, which attempts to fit all the recorded waveformwith amodel. This process solves, in fact, a very complicated highly non-linear inverse problem. Another process that uses such inversion process, but which tries to separate classes of parameters to reduce non-linearity, is joint migration inversion (JMI), in which scattering properties of the subsurface are separated from the propagation properties of seismicwaves. Currently those two methods, FWI and JMI, are generally model-dependent — that is they have been formulated to fit specific physics model such as isotropic acoustic media, transversally isotropic media with or without absorption. Hence, they would tend to have biases towards those particular models. Another paradigmis the so-called data-driven paradigm, or data-adaptive paradigm, and since it is formulated in terms of operators, one could also refer to it as operatorbased. Since it contains less biases towards a particular physics model or require no detailed knowledge of model parameters, beforehand, some also refer to it as modelindependent, as it does not need to force the data to fit a specific model, rather the process adapts to the model contained within the data. A process such as surface-related multiple elimination follows this paradigm. Another process, which is also shown in this dissertation, separates the surface multiples scattering-order-by-scattering-order without the need to assume a specific physics model. The process is referred to as scattering order decomposition. So, this dissertation looks into the problem of extending the inversion process to the model-independent or the operator-based paradigm. This dissertation looks first into the theoretical underpinning of this problem, where integral representations are used to study it. These representations are divided into four categories: first model-based representations are derived and presented as directional and non-directional. So, it places in context those theories. Next, the operator-based representations are also divided into directional and non-directional. Finally, four representations are derived, in this dissertation, which have the potential for applications in modeling, inversion and various seismic data analysis processes. Modeling is needed before any inversion since the inverse problem is ill-posed or illconditioned and hence no unique solutions exist but rather preconditioned or regularized solutions to these problems are normally used. Moreover, the inverse problem uses modeling iteratively and also back-projects the data residuals with the forward modeling mechanism. Therefore, the next chapters study operator generation and the subsequent modeling of wavefields with these derived operators...@en

Localization microscopy has circumvented the diffraction limit by sequentially imaging individual light emitting molecules at a time. The position of these individual molecules can be determined and a super-resolution reconstruction is made with improved resolution. Normally freely rotating emitters are used such that the point spread function (PSF) is rotationally symmetric and only minor errors in the localization process are made by approximating the PSF with a Gaussian. The precision with which the individual emitters can be localized scales with the 1/√N, N the number of detected photons so that more detected photons leads to a better localization precision. However, the emission of fluorescent molecules is limited by photobleaching, a light induced chemical reaction to a permanent non-fluorescent state. In this thesis we investigate the effect of cooling the sample to cryogenic temperatures with liquid nitrogen. This reduces the chemical reaction rates and improves photostability more than 100 fold. To use localization microscopy it is necessary to switch the fluorescent molecules between an on-state and off-state, this turns out to be difficult at cryogenic temperatures. Standard methods used at room temperature in aqueous media do not work. As the molecules are frozen in place at cryogenic temperatures we use polarized light to selectively image molecules with certain orientations at a time. To realize this it is necessary to generate pure linear polarization with an arbitrary orientation in the sample plane. By calibrating the phase difference induced by the dichroic mirrors this can be achieved, effectively modulating the fluorescence of fixed dipole emitters at cryogenic temperatures. The addition of an orthogonal linearly polarized stimulated emission depletion (STED) beam narrows the orientational distribution of fluorescing molecules. This method does induce some degree of sparsity, however, it is not enough for localization microscopy of dense biological samples. Furthermore, the STED process reduces the photon yield of single molecules. This is presumably caused by the long dark-state recovery measured on fluorescent molecules in vacuum and at cryogenic temperatures. Localization microscopy of fixed or orientationally constrained emitters has long been avoided as the orientation of individual molecules leads to bias in the localizations. There are various ways to eliminate this bias but they reduce the amount of information that can be extracted from the sample. By fixing the orientation of fluorescent emitters to biomolecules of interest they become reporters for the orientation of the biomolecules. We have devised the so-called Vortex PSF with which the orientation, 3D position and degree of rotational constraint can be extracted from a single image. Alternatively the orientation of single-molecules can be probed with varying polarization states over multiple frames achieving a better precision with less photons. @en

Single molecule localization microscopy is a powerful tool that delivers high contrast and imaging specificity at a resolution beyond that of conventional microscopes. To obtain a super-resolved image, one needs to image at least hundred thousand camera frames and estimate the position of millions of molecules with nanometer precision. The tremendous amount of data that needs to be analyzed is one of the challenges scientists face when applying single molecule localization techniques. For this reason, a maximum likelihood estimation method is proposed in this thesis that attains the Cramer-Rao Lower Bound and estimates the position of single molecules in parallel on a GPU to achieve near real-time processing with high precision. A major drawback of current methods that detect single molecules is that the number of false positives is unknown. Therefore, a generalized likelihood ratio test is proposed here, which can control both the number of false positives and true positives withminimal user input. This target is stably achieved in the experiment over a large range of signal to background conditions. A key application of single molecule localization microscopy can be found in in vivo RNA imaging. In this thesis two RNA studies are presented: i) The nuclear pore complex structures and the kinetic interaction with mRNA are investigated, where a point mutation of mex67p triggered the nuclear export efficiency to drop significantly; and ii) A study on the mobility and occupation of mRNA within the nucleus is performed by instantaneously imaging the whole three-dimensional volume ofmRNAs in the nucleus of a living cell. Fromthis study, no evidence was obtained for exclusion or enrichment of the heterochromatin by mRNAs. For the general applicability of singlemolecule localization microscopy, the two-dimensionalmethods will need to be extended to three-dimensions. In threedimensional imaging small aberrations will become significant when imaging away from focus and therefore need to be compensated or calibrated. This thesis shows that one can extend single molecule localization into three-dimensions, or even a fourth-dimension such as color when the point spread function of a microscope is correctly distorted. Additionally, an adaptive optics strategy is presented that can correct for sample induced aberrations, and a method is proposed to encode emission color of the single molecule into the measurement.@en

In optical imaging, image quality is not only determined by the system itself but also by the media in which light traverse. Differences in the refraction index of the media encountered by a light wavefront produces phase aberrations which distort the image received from the original object. Currently, there are two main approaches for solving this problem: adaptive optics, which rely on deformable mirrors and wavefront sensors for correcting the phase aberration before it reaches the imaging sensor; and post-processing techniques, which try to estimate the object after receiving distorted images. MFBD methods are a family of algorithms that are capable of reconstructing the object by fusing the information carried by a set of differently aberrated images. These techniques are widely used in current optical systems, allowing a notable increase in image quality in most situations. However, there are cases in which they are not applicable; for example, looking at a dynamic object (e.g., a bird flying) or looking through static aberrations (e.g., in microscopy applications); but certain modifications in the optical system can be used for solving this problem. Actual optical devices have only one aperture, thus creating one full-size image on the imaging sensor but, by segmenting the pupil, several images can be retrieved at the same time with different aberrations (i.e., light follows a distinct path for each aperture). However, using a multi-aperture system implies that there is less imaging sensor area available for each aperture, thus obtaining images with less resolution. Nonetheless, MFBD algorithms can usually be extended in order to support SR, a technique that allows the increase of the object resolution by retrieving extra information from the displacement between images. This thesis is focused on the development of a functional prototype of a multi-aperture optical system that can do real-time object reconstruction. As a MFBD technique is needed, the novel TIP algorithm (developed at Delft Center for Systems and Control) is selected. In order to achieve a fast and reliable reconstruction, the algorithm is: modified for increasing its robustness against noise, expanded in order to support SR and implemented efficiently in both CPU and GPU. Finally, the system is tested in a real environment, showing promising results.

Imaging by inversion of acoustic or electromagnetic wave fields have applications in a wide variety of areas, such as non-destructive testing, biomedical applications, and geophysical explorations. Unfortunately, each modality suffers from its own application specific limitations, typically being difficulties in distinguishing different materials or tissues from each other in the case of acoustic wave fields and a low spatial resolution in the case of electromagnetic wave fields. To exploit the advantages of both imaging modalities, methods to combine them include image fusion, usage of spatial priors and application of joint or multi-physics inversion methods. The latter can be based on empirical relations between acoustic and electromagnetic medium properties or on structural similarity. In this work, two joint inversion algorithms based on structural similarity are presented. To account for the structural similarity the error-functional of standard Born inversion is extended with an additional penalty term. This additional term is either based on the L2-norm of the cross-gradient (CG), i.e. the cross product of the gradients of the acoustic and electromagnetic contrasts or on the L2-norm of the gradient difference (GD), i.e. the difference between the normalized gradients of both contrasts. To test the proposed methods, two synthetic models are considered; one with the gradients of the contrasts pointing in the same direction and one where the gradients point in opposite directions. Results show that the GD constraint significantly improves the resolution for the electromagnetic reconstruction compared to separate BI. The mean square errors (MSE) of the reconstructed profiles for the separate BI are 0.12 for the acoustic and 0.51 for the electromagnetic case, and for the joint GD inversion, 0.09 for the acoustic and 0.46 for the electromagnetic case. The joint GD inversion fails when using the model with the gradients of the contrasts pointing in opposite directions. The joint CG inversion does not enhance the reconstructed images, but shows similar performances for the different models. In conclusion, joint inversion based on structural constraints is shown to improve the electromagnetic resolution, especially using the GD constraint. Further research needs to be conducted to extend the functionality of the GD constraint to acoustic and electromagnetic contrasts with opposite contrast gradient directions.

The time taken to generate a super-resolution image and the quality of the final synthetic image depends on the performance of the localization algorithm which is used in the localization microscopy pipeline. The most precise and accurate algorithms are mostly iterative and they take a long time to generate the localization list while the faster ‘one-shot algorithms’ are not very accurate and precise. A deep learning method smNet (single-molecule Net) was developed by Zhang et al which was claimed to perform one-shot localization with precision close to the theoretical limit and very accurately, along with performing aberration estimation and dipole-emitter orientation angle estimation. The deep learning model smNet was trained either by augmenting experimental data or using simulated data generated with an erroneously simplified simulation model and a phase retrieval method. The purpose of this work was to characterize the performance of smNet when it was trained with simulated images generated using an accurate vector model for a range of physical conditions. Along with the characterization of smNet’s performance in doing 3D localization and aberration estimation with the accurate vector model, a pipeline was also designed which made the training process of smNet more efficient and computationally cheaper while performing accurate and precise 3D localization and aberration estimation. The pipeline was designed to implement the concept of simulator learning where a smNet model could be trained on simulated data and used to perform 3D localization and aberration estimation directly on experimental data without any retraining or domain adaptation techniques.

A limiting factor with regard to resolution in OPT is the limited depth of field (DoF) due to light detection with a Gaussian beam profile. The further a source in the sample is removed from the centre of rotation in the focal plane, the more distorted the image is in tangential direction due to the limited DoF. The goal of this research is to extend the depth of field in Optical Projection Tomography. The DoF limitations due to diffraction are mainly caused by the Gaussian beam shape and its inherent limitations such as a small high intensity spot and a small region of focus. An alternative to Gaussian beams is found sporadically in the literature in the form of non-diffracting beams. Non-diffracting beams are beams that propagate without diffraction and show regenerative properties after obstruction. The Bessel beam is a non-diffracting beam that is rotationally symmetric and displays a transversal high-intensity core. It can be generated without energy loss with a lens shaped like a rotationally symmetric prism, called an axicon. A propagation simulation of the axicon generated Bessel beam, using the Hankel transform as a rotationally symmetric alternative to the 2D Fourier transform, is performed and used to verify the analytic description of the axicon generated Bessel beam. A numerical OPT simulation shows that OPT reconstructions of point sources show virtually no blurring, but do show concentric rings due to the intensity distribution of the Bessel beam. These rings can be removed by deconvolution of the projection or deconvolution of the reconstruction of simulated OPT results with the imaging point spread function (PSF) of the axicon-generated Bessel beam. The PSF describes the response of the imaging system to a point source. Practical work is presented with the imaging set-up of an axicon with an objective lens as described earlier. The resolution of the PSF is analysed over paraxial distance from the objective lens for both coherent and incoherent illumination. The same is done for a resolution target in transmission. Comparison of the Bessel system with Gaussian models show that the DoF increase shown by the Bessel system is significant in all cases. It is found that for sources with spatially narrow intensity distributions (near-point source) the PSF resolution matches theoretical predictions. However, as the spatial light source distribution increases slightly, Bessel distributions overlap spatially. This creates artefacts and deteriorates the resolution It is concluded that extended depth of field in OPT can be achieved with non-diffracting axicon generated Bessel beams. However, for objects larger than point sources the resolution deteriorates. Furthermore, the means of illumination are a major influence on the resulting images when using an axicon. Further research on the optimization of illumination is recommended. Additionally, recommendations for further research on the significance of self-regeneration are made. Recommended applications for use of Bessel beams in optical imaging are those where a large DoF is desired and high resolution is less of a priority, or imaging and OPT of very sparse but large samples.