A ray-trace analysis of X-ray multilayer Laue lenses for nanometer focusing

Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for X-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Bragg's law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions are provided of the fourth-order series expansions of the wavefront aberrations and transmissions of both axi-symmetric lenses and pairs of crossed lenses that each focuses in only one dimension like a cylindrical lens. We find that aplanatic zone-plate designs, whereby aberrations are corrected over a large field of view, can be achieved by axi-symmetric lenses but not the crossed lenses. We investigate the performance of 1 nm-resolution lenses with focal lengths of about 1 mm and show their fields of view are mainly limited by the acceptance angle of Bragg diffraction, and that aberrations can limit the performance of lenses with longer focal lengths. We apply the ray-tracing formalism for a tolerancing analysis of imperfect lenses and examine some strategies for the correction of their aberrations.Comment: 44 pages, 15 figure

Phase Retrieval with Application to Optical Imaging

This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art in this area, identify challenges, and suggest vision and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large, with applications in a variety of fields ranging from biology and chemistry to physics and engineering

DriftRec: Adapting diffusion models to blind JPEG restoration

In this work, we utilize the high-fidelity generation abilities of diffusion models to solve blind JPEG restoration at high compression levels. We propose an elegant modification of the forward stochastic differential equation of diffusion models to adapt them to this restoration task and name our method DriftRec. Comparing DriftRec against an $L_2$ regression baseline with the same network architecture and two state-of-the-art techniques for JPEG restoration, we show that our approach can escape the tendency of other methods to generate blurry images, and recovers the distribution of clean images significantly more faithfully. For this, only a dataset of clean/corrupted image pairs and no knowledge about the corruption operation is required, enabling wider applicability to other restoration tasks. In contrast to other conditional and unconditional diffusion models, we utilize the idea that the distributions of clean and corrupted images are much closer to each other than each is to the usual Gaussian prior of the reverse process in diffusion models. Our approach therefore requires only low levels of added noise, and needs comparatively few sampling steps even without further optimizations. We show that DriftRec naturally generalizes to realistic and difficult scenarios such as unaligned double JPEG compression and blind restoration of JPEGs found online, without having encountered such examples during training.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Ab Initio Spatial Phase Retrieval via Fluorescence Intensity Triple Correlations

A complete method for ab initio phase retrieval via spatial intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of classical incoherent emitters

Visualizing aerosol-particle injection for diffractive-imaging experiments

Delivering sub-micrometer particles to an intense x-ray focus is a crucial aspect of single-particle diffractive-imaging experiments at x-ray free-electron lasers. Enabling direct visualization of sub-micrometer aerosol particle streams without interfering with the operation of the particle injector can greatly improve the overall efficiency of single-particle imaging experiments by reducing the amount of time and sample consumed during measurements. We have developed in-situ non-destructive imaging diagnostics to aid real-time particle injector optimization and x-ray/particle-beam alignment, based on laser illumination schemes and fast imaging detectors. Our diagnostics are constructed to provide a non-invasive rapid feedback on injector performance during measurements, and have been demonstrated during diffraction measurements at the FLASH free-electron laser.Comment: 15 page

Continuous Diffraction of Molecules and Disordered Molecular Crystals

The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the continuous diffracted wave-fields from all objects gives rise to strong Bragg peaks that modulate the single-object transform. Wilson statistics describe the distribution of continuous diffraction intensities to the same extent that they apply to Bragg diffraction. The continuous diffraction obtained from translationally-disordered molecular crystals consists of the incoherent sum of the wave-fields from the individual rigid units (such as molecules) in the crystal, which is proportional to the incoherent sum of the diffraction from the rigid units in each of their crystallographic orientations. This sum over orientations modifies the statistics in a similar way that crystal twinning modifies the distribution of Bragg intensities. These statistics are applied to determine parameters of continuous diffraction such as its scaling, the beam coherence, and the number of independent wave-fields or object orientations contributing. Continuous diffraction is generally much weaker than Bragg diffraction and may be accompanied by a background that far exceeds the strength of the signal. Instead of just relying upon the smallest measured intensities to guide the subtraction of the background it is shown how all measured values can be utilised to estimate the background, noise, and signal, by employing a modified "noisy Wilson" distribution that explicitly includes the background. Parameters relating to the background and signal quantities can be estimated from the moments of the measured intensities. The analysis method is demonstrated on previously-published continuous diffraction data measured from imperfect crystals of photosystem II.Comment: 34 pages, 11 figures, 2 appendice

Mantle heat flow

A map of the heat flux out of the earth's mantle has been prepared by subtracting the heat flow arising in the earth's crust from the surface heat flow. In continental areas the crustal contribution of the enriched zone is determined from the parameters of the linear heat flow-heat production relationship q0 = q* + bA0 in areas where such data exist. Where heat flow-heat production data are not available, a new empiricism relating reduced heat flow q* to the mean heat flow of a province , is used to estimate the reduced heat flow, and the depth parameter b is assigned an average value of 8.5 km. The oceanic crustal heat flow contribution includes both heat liberated by cooling, which is a function of the age of the ocean floor, and a small radiogenic component. A spherical harmonic analysis to degree 18 of the computed 5[deg] x 5[deg] mantle heat flow values yields a mean of 48 mW m-2; the degree variance spectrum has prominent strength at degrees 1,4 and 5. Continent-ocean differences are more apparent in the mantle heat flow than in the surface heat flow. However, contrasting surface heat flow patterns within continents, such as in central and western Australia, which arise from different surficial radioactivity distributions, do not appear in the mantle heat flow. Mantle heat flow is positively correlated with the geopotential and negatively correlated with the topography of the earth. However, correlation of heat flow with a "normalized" topography, in which the base line elevation difference between oceans and continents is suppressed is significantly positive, in accordance with observation that ocean floor topography is thermally controlled.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22966/1/0000533.pd

On the regional variation of heat flow, geotherms, and lithospheric thickness

Geotherm families in which surface heat flow is the principal independent variable have been constructed for continental and oceanic lithospheres. The continental model is characterized by geotherms in which surface heat flow is in equilibrium with heat flowing into the lithosphere at its base plus heat generated by radioactive decay within the lithosphere. The model accommodates the regional variation of the surface heat flow with proportional variations in the radioactivity of the surficial enriched zone and in the deeper heat flow. The proportionality is dictated by a new and general linear relationship between reduced heat flow and mean heat flow for a region (), which enables both q* and the mean heat production of the enriched zone to be estimated from knowledge of the mean surface heat flow of a province. The oceanic model is characterized by the transient cooling of a semi-infinite medium with an initial temperature gradient and some near-surface radiogenic heat production. The model yields a heat flow in satisfactory agreement with observations in the oldest ocean basins. The depth at which both the oceanic and continental geotherms reach ~0.85 of the melting temperature is shown to be a consistent estimator of the depth to the top of the low-velocity channel, or the thickness of the high-velocity lid overlying the channel. We identify the lid as synonymous with the lithosphere, and produce a global map of lithospheric thickness based on the regional variation of surface heat flow. The lithosphere is less than 100 km thick over most of the globe, but thickens appreciably and becomes more viscous beneath the Precambrian shields and platforms, regions of low heat flow. These characteristics of shields are consistent with recently reported models of the driving mechanisms of the plate system, which require greater retarding forces beneath plates with large continental areas.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22955/1/0000522.pd

Heat flow and heat production in Zambia: Evidence for lithospheric thinning in central Africa

Heat-flow results from eleven widely spaced sites in central and western regions of the Republic of Zambia range between 54 and 76 mW m-2. Ten of the sites are located in late Precambrian (Katangan) metasediments or Kibaran age basement, while one site is located in Karroo age sandstone. Compared to the global mean of 39 +/- 7 (sd) mW m-2 for Precambrian provinces elsewhere, these heat-flow results are anomalously high by some 25 mW m-2. Heat-production measurements on borehole core samples indicate that enhanced radioactivity of an enriched surface zone can account for only half of the observed anomaly. The remaining anomalous heat flow must have a deeper source, and can be interpreted as a flux from the asthenosphere, providing the overlying lithosphere has been thinned to less than 60 km. Such an interpretation supports the existence of an incipient arm of the East African rift system trending southwest from Lake Tanganyika into the central African plateau.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22858/1/0000420.pd