Reconstruction Algorithms in Undersampled AFM Imaging

This software was used for producing the simulation results for the paper "Reconstruction Algorithms in Undersampled AFM Imaging", published in IEEE Journal of Selected Topics in Signal Processing: http://dx.doi.org/10.1109/JSTSP.2015.2500363. This deposition consists of a number of Python scripts, some of which were used for producing the results in the accompanying data set available at http://dx.doi.org/10.5281/zenodo.32958 and some of which can be used to extract data and images from said data set. The deposition further contains a README file explaining the purpose and use of the individual files as well as MD5 and SHA checksums of the files for validating the integrity of the files after download. The scripts are licensed under the BSD 2-Clause license (http://opensource.org/licenses/BSD-2-Clause). The scripts perform and analyse results from simulations using images, and reconstructed versions of these, originally published in the data set available at http://dx.doi.org/10.5281/zenodo.17573

Magni: A Python Package for Compressive Sampling and Reconstruction of Atomic Force Microscopy Images

Magni is an open source Python package that embraces compressed sensing and Atomic Force Microscopy (AFM) imaging techniques. It provides AFM-specific functionality for undersampling and reconstructing images from AFM equipment and thereby accelerating the acquisition of AFM images. Magni also provides researchers in compressed sensing with a selection of algorithms for reconstructing undersampled general images, and offers a consistent and rigorous way to efficiently evaluate the researchers own developed reconstruction algorithms in terms of phase transitions. The package also serves as a convenient platform for researchers in compressed sensing aiming at obtaining a high degree of reproducibility of their research

Image processing techniques for high-speed atomic force microscopy

Atomic force microscopy (AFM) is a powerful tool for imaging topography or other characteristics of sample surfaces at nanometer-scale spatial resolution by recording the interaction of a sharp probe with the surface. Dispute its excellent spatial resolution, one of the enduring challenges in AFM imaging is its poor temporal resolution relative to the rate of dynamics in many systems of interest. This has led to a large research effort on the development of high-speed AFM (HS-AFM). Most of these efforts focus on mechanical improvement and control algorithm design. This dissertation investigates a complementary HS-AFM approach based on the idea of undersampling which aims at increasing the imaging rate of the instrument by reducing the number of pixels in the sample surface that need to be acquired to create a high-quality image. The first part of this work focuses on the reconstruction of images sub-sampled according to a scheme known as μ path patterns. These patterns consist of randomly placed short and disjoint scans and are designed specifically for fast, efficient, and consistent data acquisition in AFM. We compare compressive sensing (CS) reconstruction methods with inpainting methods on recovering μ-path undersampled images. The results illustrate that the reconstruction quality depends on the choice of reconstruction methods and the sample under study, with CS generally producing a superior result for samples with sparse frequency content and inpainting performing better for samples with information limited to low frequencies. Motivated by the comparison, a basis pursuit vertical variation (BPVV) method, combing CS and inpainting, is proposed. Based on single image reconstruction results, we also extend our analysis to the problem of multiple AFM frames, in which higher overall video reconstruction quality is achieved by pixel sharing among different frames. The second part of the thesis considers patterns for sub-sampling in AFM. The allocation of measurements plays an important role in producing accurate reconstructions of the sample surface. We analyze the expected image reconstruction error using a greedy CS algorithm of our design, termed simplified matching pursuit (SMP), and propose a Monte Carlo-based strategy to create μ-path patterns that minimize the expected error. Because these μ path patterns involve a collection of disjoint scan paths, they require the tip of the instrument to be repeatedly lifted from and re-engaged to the surface. In many cases, the re-engagements make up a significant portion of the total data acquisition time. We therefore extend our Monte Carlo design strategy to find continuous scan patterns that minimize the reconstruction error without requiring the tip to be lifted from the surface. For the final part of the work, we provide a hardware demonstration on a commercial AFM. We describe hardware implementation details and image a calibration grating using the proposed μ-path and continuous scan patterns. The sample surface is reconstructed from acquired data using CS and inpainting methods. The recovered image quality and achievable imaging rate are compared to full raster-scans of the sample. The experimental results show that the proposed scanning combining with reconstruction methods can produce higher image quality with less imaging time

Doctor of Philosophy

dissertationOptics is an old topic in physical science and engineering. Historically, bulky materials and components were dominantly used to manipulate light. A new hope arrived when Maxwell unveiled the essence of electromagnetic waves in a micro perspective. On the other side, our world recently embraced a revolutionary technology, metasurface, which modifies the properties of matter-interfaces in subwavelength scale. To complete this story, diffractive optic fills right in the gap. It enables ultrathin flat devices without invoking the concept of nanostructured metasurfaces when only scalar diffraction comes into play. This dissertation contributes to developing a new type of digital diffractive optic, called a polychromat. It consists of uniform pixels and multilevel profile in micrometer scale. Essentially, it modulates the phase of a wavefront to generate certain spatial and spectral responses. Firstly, a complete numerical model based on scalar diffraction theory was developed. In order to functionalize the optic, a nonlinear algorithm was then successfully implemented to optimize its topography. The optic can be patterned in transparent dielectric thin film by single-step grayscale lithography and it is replicable for mass production. The microstructures are 3?m wide and no more than 3?m thick, thus do not require slow and expensive nanopatterning techniques, as opposed to metasurfaces. Polychromat is also less demanding in terms of fabrication and scalability. The next theme is focused on demonstrating unprecedented performances of the diffractive optic when applied to address critical issues in modern society. Photovoltaic efficiency can be significantly enhanced using this optic to split and concentrate the solar spectrum. Focusing through a lens is no news, but we transformed our optic into a flat lens that corrects broadband chromatic aberrations. It can also serve as a phase mask for microlithography on oblique and multiplane surfaces. By introducing the powerful tool of computation, we devised two imaging prototypes, replacing the conventional Bayer filter with the diffractive optic. One system increases light sensitivity by 3 times compared to commercial color sensors. The other one renders the monochrome sensor a new function of high-resolution multispectral video-imaging