Reconstruction algorithms for multispectral diffraction imaging

Thesis (Ph.D.)--Boston UniversityIn conventional Computed Tomography (CT) systems, a single X-ray source spectrum is used to radiate an object and the total transmitted intensity is measured to construct the spatial linear attenuation coefficient (LAC) distribution. Such scalar information is adequate for visualization of interior physical structures, but additional dimensions would be useful to characterize the nature of the structures. By imaging using broadband radiation and collecting energy-sensitive measurement information, one can generate images of additional energy-dependent properties that can be used to characterize the nature of specific areas in the object of interest. In this thesis, we explore novel imaging modalities that use broadband sources and energy-sensitive detection to generate images of energy-dependent properties of a region, with the objective of providing high quality information for material component identification. We explore two classes of imaging problems: 1) excitation using broad spectrum sub-millimeter radiation in the Terahertz regime and measure- ment of the diffracted Terahertz (THz) field to construct the spatial distribution of complex refractive index at multiple frequencies; 2) excitation using broad spectrum X-ray sources and measurement of coherent scatter radiation to image the spatial distribution of coherent-scatter form factors. For these modalities, we extend approaches developed for multimodal imaging and propose new reconstruction algorithms that impose regularization structure such as common object boundaries across reconstructed regions at different frequencies. We also explore reconstruction techniques that incorporate prior knowledge in the form of spectral parametrization, sparse representations over redundant dictionaries and explore the advantage and disadvantages of these techniques in terms of image quality and potential for accurate material characterization. We use the proposed reconstruction techniques to explore alternative architectures with reduced scanning time and increased signal-to-noise ratio, including THz diffraction tomography, limited angle X-ray diffraction tomography and the use of coded aperture masks. Numerical experiments and Monte Carlo simulations were conducted to compare performances of the developed methods, and validate the studied architectures as viable options for imaging of energy-dependent properties

Fourier ptychography: current applications and future promises

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either “zoom in” and image at high-resolution, or they can “zoom out” to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges

Joint Estimation of Attenuation and Scatter for Tomographic Imaging with the Broken Ray Transform

The single-scatter approximation is fundamental for many tomographic imaging problems. This class broadly includes x-ray scattering imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local events and nonlocal attenuation. Related applications typically focus on reconstructing one of two images: scatter density or total attenuation. However, both images are media specific. Both images are useful for object identification. Knowledge of one image aides estimation of the other, especially when estimating images from noisy data.Joint image recovery has been demonstrated analytically in the context of the broken ray transform (BRT) for attenuation and scatter-density images. The BRT summarizes the nonlocal affects of attenuation in single-scatter measurement geometries. We find BRT analysis particularly interesting as joint image recovery has been demonstrated analytically using only two scatter angles. Limiting observations to two scatter angles is significant because it supports joint reconstruction in two dimensions for anisotropic scatter modalities (e.g. Bragg, Compton). However, all analytic inversion strategies share two fundamental assumptions limiting their utility: nonzero scatter everywhere, and a deterministic data model.There are two themes to our work. First, we consider the BRT in a purely deterministic setting. We are the first to recognize the BRT as a linear shift-invariant operator. This linear-systems perspective motivates frequency-domain analysis both of the data and operator. Frequency-domain representations provide new insights on the operator and a common framework for contrasting recent inversion formulas. New algorithms are presented for regularized inversion of the BRT in addition to fast forward and adjoint operators. Second, we incorporate the BRT in a stochastic data model. Approximating the detectors as photon counting processes, we model the data as Poisson distributed. Our iterative algorithm, alternating scatter and attenuation image updates, guarantees monotonic reduction of the regularized log-likelihood function of the data. We are the first to consider joint image estimation from noisy data. Our results demonstrate a significant improvement over analytic methods for data sets with missing data (regions with zero scatter). In addition to joint image estimation, our approach can be specialized for single image estimation. With known attenuation, we can improve the quality of scatter image estimates. Similarly, with known scatter, we can improve the quality of attenuation image estimates.Through analysis and simulations, we highlight challenges for attenuation image estimation from BRT data, and ambiguity in the joint image recovery problem. Performance will vary with scaling of the problem. Total attenuation, detected counts, and scatter angle all affect the quality of image estimates. We are the first to incorporate both scatter density and attenuation in noisy data models. Our results demonstrate the benefits of accounting for both images, and should inform design of future measurement systems

Multi-Beam Scan Analysis with a Clinical LINAC for High Resolution Cherenkov-Excited Molecular Luminescence Imaging in Tissue.

Cherenkov-excited luminescence scanned imaging (CELSI) is achieved with external beam radiotherapy to map out molecular luminescence intensity or lifetime in tissue. Just as in fluorescence microscopy, the choice of excitation geometry can affect the imaging time, spatial resolution and contrast recovered. In this study, the use of spatially patterned illumination was systematically studied comparing scan shapes, starting with line scan and block patterns and increasing from single beams to multiple parallel beams and then to clinically used treatment plans for radiation therapy. The image recovery was improved by a spatial-temporal modulation-demodulation method, which used the ability to capture simultaneous images of the excitation Cherenkov beam shape to deconvolve the CELSI images. Experimental studies used the multi-leaf collimator on a clinical linear accelerator (LINAC) to create the scanning patterns, and image resolution and contrast recovery were tested at different depths of tissue phantom material. As hypothesized, the smallest illumination squares achieved optimal resolution, but at the cost of lower signal and slower imaging time. Having larger excitation blocks provided superior signal but at the cost of increased radiation dose and lower resolution. Increasing the scan beams to multiple block patterns improved the performance in terms of image fidelity, lower radiation dose and faster acquisition. The spatial resolution was mostly dependent upon pixel area with an optimized side length near 38mm and a beam scan pitch of P = 0.33, and the achievable imaging depth was increased from 14mm to 18mm with sufficient resolving power for 1mm sized test objects. As a proof-of-concept, in-vivo tumor mouse imaging was performed to show 3D rendering and quantification of tissue pO2 with values of 5.6mmHg in a tumor and 77mmHg in normal tissue

Spectral LADAR: Active Range-Resolved Imaging Spectroscopy

Imaging spectroscopy using ambient or thermally generated optical sources is a well developed technique for capturing two dimensional images with high per-pixel spectral resolution. The per-pixel spectral data is often a sufficient sampling of a material's backscatter spectrum to infer chemical properties of the constituent material to aid in substance identification. Separately, conventional LADAR sensors use quasi-monochromatic laser radiation to create three dimensional images of objects at high angular resolution, compared to RADAR. Advances in dispersion engineered photonic crystal fibers in recent years have made high spectral radiance optical supercontinuum sources practical, enabling this study of Spectral LADAR, a continuous polychromatic spectrum augmentation of conventional LADAR. This imaging concept, which combines multi-spectral and 3D sensing at a physical level, is demonstrated with 25 independent and parallel LADAR channels and generates point cloud images with three spatial dimensions and one spectral dimension. The independence of spectral bands is a key characteristic of Spectral LADAR. Each spectral band maintains a separate time waveform record, from which target parameters are estimated. Accordingly, the spectrum computed for each backscatter reflection is independently and unambiguously range unmixed from multiple target reflections that may arise from transmission of a single panchromatic pulse. This dissertation presents the theoretical background of Spectral LADAR, a shortwave infrared laboratory demonstrator system constructed as a proof-of-concept prototype, and the experimental results obtained by the prototype when imaging scenes at stand off ranges of 45 meters. The resultant point cloud voxels are spectrally classified into a number of material categories which enhances object and feature recognition. Experimental results demonstrate the physical level combination of active backscatter spectroscopy and range resolved sensing to produce images with a level of complexity, detail, and accuracy that is not obtainable with data-level registration and fusion of conventional imaging spectroscopy and LADAR. The capabilities of Spectral LADAR are expected to be useful in a range of applications, such as biomedical imaging and agriculture, but particularly when applied as a sensor in unmanned ground vehicle navigation. Applications to autonomous mobile robotics are the principal motivators of this study, and are specifically addressed

A full degree-of-freedom photonic crystal spatial light modulator

Harnessing the full complexity of optical fields requires complete control of all degrees-of-freedom within a region of space and time -- an open goal for present-day spatial light modulators (SLMs), active metasurfaces, and optical phased arrays. Here, we solve this challenge with a programmable photonic crystal cavity array enabled by four key advances: (i) near-unity vertical coupling to high-finesse microcavities through inverse design, (ii) scalable fabrication by optimized, 300 mm full-wafer processing, (iii) picometer-precision resonance alignment using automated, closed-loop "holographic trimming", and (iv) out-of-plane cavity control via a high-speed micro-LED array. Combining each, we demonstrate near-complete spatiotemporal control of a 64-resonator, two-dimensional SLM with nanosecond- and femtojoule-order switching. Simultaneously operating wavelength-scale modes near the space- and time-bandwidth limits, this work opens a new regime of programmability at the fundamental limits of multimode optical control.Comment: 25 pages, 20 figure