Deep-tissue large field of view imaging by Fourier conjugate adaptive optics

Light microscopy enables multifunctional imaging of biological specimens at unprecedented depths and resolutions. However, the performance of all optical methods degrades with the imaging depth due to sample-induced aberrations. Methods of adaptive optics (AO) are aimed at pre-compensation of these distortions but state-of-the-art adaptive optics still provides a limited field of view and imaging depth. Here I propose a new approach to overcome these limitations: Fourier image plane conjugate AO. Two possible experimental designs of the new approach are investigated and an accurate comparison between proposed and previously used methods of AO is presented. We see that Fourier conjugate AO provides a significantly larger field of view, which can only be limited by the angular optical memory effect, as well as it is simpler in practical realization for large imaging depth and allows the optimal use of resolution of spatial light modulator.Comment: 4 pages, 3 figure

Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.Comment: 13 pages, 7 figure

A sparse reconstruction framework for Fourier-based plane wave imaging

International audienceUltrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared with traditional delay and sum methods. Motivated by the success of compressed sensing techniques in other Fourier imaging modalities, like magnetic resonance imaging, we propose a new sparse regularization framework to reconstruct high-quality ultrasound (US) images. The framework takes advantage of both the ability to formulate the imaging inverse problem in the Fourier domain and the sparsity of US images in a sparsifying domain. We show, by means of simulations, in vitro and in vivo data, that the proposed framework significantly reduces image artifacts, i.e., measurement noise and sidelobes, compared with classical methods, leading to an increase of the image quality

Fourier Optics in the Classroom

Borrowing methods and formulas from Prof. Goodman's classic Introduction to Fourier Optics textbook [1], I have developed a software package [2] that has been used in both industrial research and classroom teaching [3]. This paper briefly describes a few optical system simulations that have been used over the past 30 years to convey the power and the beauty of Fourier Optics to our students at the University of Arizona's College of Optical Sciences.Comment: 2 pages, 5 figures, 3 references, Published in the Proceedings of the Optical Society of America's Imaging & Applied Optics Congress, Orlando, Florida (June 2018

A Reconstruction Algorithm for Photoacoustic Imaging based on the Nonuniform FFT

Fourier reconstruction algorithms significantly outperform conventional back-projection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.Comment: 22 pages, 8 figure

A Laboratory Demonstration of High-Resolution Hard X-ray and Gamma-ray Imaging using Fourier-Transform Techniques

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard x-ray and γ-ray imaging, with particular emphasis on possible applications to high-energy astronomy. We discuss considerations for the design of a Fourier-transform imager and describe the instrumentation used in the laboratory studies. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented

Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging

Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction process (for contour completion) proposed by Mumford. This paper presents a thorough study and comparison of the many numerical approaches, which, remarkably, is missing in the literature. Existing numerical approaches can be classified into 3 categories: Finite difference methods, Fourier based methods (equivalent to $SE(2)$-Fourier methods), and stochastic methods (Monte Carlo simulations). There are also 3 types of exact solutions to the PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in previous works by Duits and van Almsick in 2005. Here we provide an overview of these 3 types of exact solutions and explain how they relate to each of the 3 numerical approaches. We compute relative errors of all numerical approaches to the exact solutions, and the Fourier based methods show us the best performance with smallest relative errors. We also provide an improvement of Mathematica algorithms for evaluating Mathieu-functions, crucial in implementations of the exact solutions. Furthermore, we include an asymptotical analysis of the singularities within the kernels and we propose a probabilistic extension of underlying stochastic processes that overcomes the singular behavior in the origin of time-integrated kernels. Finally, we show retinal imaging applications of combining left-invariant PDE-evolutions with invertible orientation scores.Comment: A final and corrected version of the manuscript is Published in Numerical Mathematics: Theory, Methods and Applications (NM-TMA), vol. (9), p.1-50, 201