Advances in 3D single particle localization microscopy

The spatial resolution of conventional optical microscopy is limited by diffraction to transverse and axial resolutions of about 250 nm, but localization of point sources, such as single molecules or fluorescent beads, can be achieved with a precision of 10 nm or better in each direction. Traditional approaches to localization microscopy in two dimensions enable high precision only for a thin in-focus layer that is typically much less than the depth of a cell. This precludes, for example, super-resolution microscopy of extended three-dimensional biological structures or mapping of blood velocity throughout a useful depth of vasculature. Several techniques have been reported recently for localization microscopy in three dimensions over an extended depth range. We describe the principles of operation and typical applications of the most promising 3D localization microscopy techniques and provide a comparison of the attainable precision for each technique in terms of the Cramér-Rao lower bound for high-resolution imaging

IMAGING INTERFEROMETRIC MICROSCOPY TO THE LIMITS OF AVAILABLE FREQUENCY SPACE

Imaging interferometric microscopy (IIM) is a synthetic aperture approach offering the potential of optical resolution to the linear systems limit of optics (~lambda/4n). IIM allows one to resolve structures not accessible in a conventional illumination setup, while using a low NA microscope objective and thus keeping the large working distance, depth of focus and field of view associated with the lower NA. The goal of this dissertation is to reach ultimate resolution limits of non-fluorescent microscopy by using IIM in new optical configurations realizing a solid immersion technique with immersion materials employed in advanced regimes unsuitable in other systems. The immersion advantages of IIM can be realized if the object is in close proximity to a solid-immersion medium. Illumination through the substrate involves photons propagating at angles beyond total internal reflection, collection of high frequencies, and decoupling this radiation by a grating on the medium surface opposite to the object. The spatial resolution as a function of the medium thickness and refractive index as well as the field-of-view of the optical system is derived and applied to simulations. Structural illumination technique allows aliasing high spatial frequency into the low frequency range and using conventional microscopes at high resolution. This technique may be useful for broad swath of technical applications, biological and medical research

Super Resolution of Wavelet-Encoded Images and Videos

In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images

Quantitative optical microscopy of colloids : The legacy of Jean Perrin

When the discontinuous structure of matter was yet an intriguing hypothesis, Jean Perrin performed a set of elegant and pioneering experiments that marked the birth of what today we consider quantitative optical microscopy. Picking up the baton from Perrin, today microscopists face incredible challenges, aiming to extract quantitative information from the increasingly content-rich and complex images made available by modern microscopy techniques. Here, I provide an overview of these challenges and describe the solutions adopted to succeed in this complex task when investigating colloidal systems or systems in which colloidal particles are embedded as microrheological probes

Quantitative optical microscopy of colloids : The legacy of Jean Perrin

When the discontinuous structure of matter was yet an intriguing hypothesis, Jean Perrin performed a set of elegant and pioneering experiments that marked the birth of what today we consider quantitative optical microscopy. Picking up the baton from Perrin, today microscopists face incredible challenges, aiming to extract quantitative information from the increasingly content-rich and complex images made available by modern microscopy techniques. Here, I provide an overview of these challenges and describe the solutions adopted to succeed in this complex task when investigating colloidal systems or systems in which colloidal particles are embedded as microrheological probes

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light’s diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we’ve termed the interpretation problem

Light, the universe and everything – 12 Herculean tasks for quantum cowboys and black diamond skiers

The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mind-boggling to recognize how the concepts presented at these conferences have transformed scientific understanding and human society. In January 2017, the participants of PQE were asked to consider the equally important prospects for the future, and to formulate a set of questions representing some of the greatest aspirations in this broad field. The result is this multi-authored paper, in which many of the world’s leading experts address the following fundamental questions: (1) What is the future of gravitational wave astronomy? (2) Are there new quantum phases of matter away from equilibrium that can be found and exploited – such as the time crystal? (3) Quantum theory in uncharted territory: What can we learn? (4) What are the ultimate limits for laser photon energies? (5) What are the ultimate limits to temporal, spatial and optical resolution? (6) What novel roles will atoms play in technology? (7) What applications lie ahead for nitrogen-vacancy centres in diamond? (8) What is the future of quantum coherence, squeezing and entanglement for enhanced super-resolution and sensing? (9) How can we solve (some of) humanity’s biggest problems through new quantum technologies? (10) What new understanding of materials and biological molecules will result from their dynamical characterization with free-electron lasers? (11) What new technologies and fundamental discoveries might quantum optics achieve by the end of this century? (12) What novel topological structures can be created and employed in quantum optics