Roadmap on optical security

Postprint (author's final draft

When holography meets coherent diffraction imaging

Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner.Comment: 22 pages, 7 figure

Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion

We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal’s expansion in distance-dependent waveletlike Fresnelet bases. We show results from simulations and experimental situations that confirm its applicability

Numerical techniques for Fresnel diffraction in computational holography

Optical holography can produce very realistic virtual images due to its capability to properly convey the depth cues that we use to interpret three-dimensional objects. Computational holography is the use of digital representations plus computational methods to carry out the holographic operations of construction and reconstruction. The large computational requirements of holographic simulations prohibit present-day existence of real-time holographic displays comparable in size to traditional two-dimensional displays. Fourier-based approaches to calculate the Fresnel diffraction of light provide one of the most efficient algorithms for holographic computations because this permits the use of the fast Fourier transform (FFT). The limitations on sampling imposed by Fourier-based algorithms have been overcome by the development, in this research, of a fast shifted Fresnel transform. This fast shifted Fresnel transform was used to develop a tiling approach to hologram construction and reconstruction, which computes the Fresnel propagation of light between parallel planes having different resolutions. A new method for hologram construction is presented, named partitioned hologram computation, which applies the concepts of the shifted Fresnel transform and tiling

Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

High-resolution ab initio three-dimensional X-ray diffraction microscopy

Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.Comment: 22 pages, 11 figures, submitte

Digital hologram recording systems: some performance improvements

The work presented in this thesis was performed under the EU's Framework 7 (FP7) project, 'REAL3D'. The aim of this project is to develop methods based on digital holography for real time capture and display of 3D objects. This thesis forms a small subset of all the work done in this project. Much of the research work was aimed towards fullling our part of the requirements of the REAL3D project. The central theme of the research presented in this thesis is that of improving the performance of the digital holographic imaging system for its use in 3D display. This encompasses research into speed up of reconstruction algorithms, understanding the in uence of noise and developing techniques to increase resolution and angular perspective range in reconstructions. The main original contributions of this research work presented in this thesis are: A computer-interfaced automatic digital holographic imaging system employing `phase shifting' has been built. This system is capable of recording high-quality digital holograms of a real world 3D object. The object can be rotated on a rotational stage and a full 360 range of perspectives can be recorded. Speckle reduction using moving diusers can be performed to improve the image quality of the reconstructed images. A LabView based user friendly interface has been developed. Novel methods based on space-time tradeo and xed point arithmetic have been developed and implemented for speed- ing up the reconstruction algorithm used in digital holography. This has resulted in the publication of one peer-reviewed journal pub- lication and one conference proceeding [1, 2]. The in uence of additive noise, particularly quantization noise in digital holography has been studied in detail. A model has been developed to understand the in uence of noise on the re- constructed image quality. Based on this model, a method has been developed to suppress quantization noise in a memory ecient man- ner. This work led to the publication of two peer-reviewed journal publications [3, 4]. A novel method of removing the twin image has been devel- oped. Methods to increase the perspectives in holography based on synthetic aperture have been implemented. Apart from these primary contributions, the author of this thesis has also contributed in the form of assisting in experiments, creating gures for various papers, writing computer programs and discussions during group meetings. In total, 6 peer-reviewed journal papers (3 being primary author) have been published and 6 conference proceedings (3 being primary author) have been published. Additionally, 2 talks have been given at international conferences

Improvements in Digital Holographic Microscopy

The Ph.D. dissertation consists of developing a series of innovative computational methods for improving digital holographic microscopy (DHM). DHM systems are widely used in quantitative phase imaging for studying micrometer-size biological and non-biological samples. As any imaging technique, DHM systems have limitations that reduce their applicability. Current limitations in DHM systems are: i) the number of holograms (more than three holograms) required in slightly off-axis DHM systems to reconstruct the object phase information without applying complex computational algorithms; ii) the lack of an automatic and robust computation algorithm to compensate for the interference angle and reconstruct the object phase information without phase distortions in off-axis DHM systems operating in telecentric and image plane conditions; iii) the necessity of an automatic computational algorithm to simultaneously compensate for the interference angle and numerically focus out-of-focus holograms on reconstructing the object phase information without phase distortions in off-axis DHM systems operating in telecentric regime; iv) the deficiency of reconstructing phase images without phase distortions at video-rate speed in off-axis DHM operating in telecentric regime, and image plane conditions; v) the lack of an open-source library for any DHM optical configuration; and, finally, vi) the tradeoff between speckle contrast and spatial resolution existing in current computational strategies to reduce the speckle contrast. This Ph.D. dissertation is motivated to overcome or at least reduce the six limitations mentioned above. Each chapter of this dissertation presents and discusses a novel computational method from the theoretical and experimental point of view to address each of these limitations