GCM-motivated Multidimensional Temperature Parametrization Scheme for Phase-curve Retrieval
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Ian Dobbs-Dixon↗
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Transport of intensity equation: a tutorial
When it comes to “phase measurement” or “quantitative phase imaging”, many people will automatically connect them with “laser” and “interferometry”. Indeed, conventional quantitative phase imaging and phase measurement techniques generally rely on the superposition of two beams with a high degree of coherence: complex interferometric configurations, stringent requirements on the environmental stabilities, and associated laser speckle noise severely limit their applications in optical imaging and microscopy. On a different note, as one of the most well-known phase retrieval approaches, the transport of intensity equation (TIE) provides a new non-interferometric way to access quantitative phase information through intensity only measurement. Despite the insufficiency for interferometry, TIE is applicable under partially coherent illuminations (like the Köhler’s illumination in a conventional microscope), permitting optimum spatial resolution, higher signal-to-noise ratio, and better image quality. In this tutorial, we give an overview of the basic principle, research fields, and representative applications of TIE, focus particularly on optical imaging, metrology, and microscopy. The purpose of this tutorial is twofold. It should serve as a self-contained introduction to TIE for readers with little or no knowledge of TIE. On the other hand, it attempts to give an overview of recent developments in this field. These results highlight a new era in which strict coherence and interferometry are no longer prerequisites for quantitative phase imaging and diffraction tomography, paving the way toward new generation label-free three-dimensional microscopy, with applications in all branches of biomedicine.
42 ENGINEERING↗
Hydrogen density mapping in biomolecular crystals through dynamic nuclear polarization
Many fundamental biological processes, including those in photosynthetic reaction centers and enzyme active sites, involve charge and energy transfer, bond cleavage, protonation and hydrogen bonding. Because H atoms play such central roles in these reactions, accurately determining their positions is essential. Yet, conventional X-ray crystallography primarily resolves the heavy atoms in biological structures and provides limited insight into hydrogen, even at atomic resolution. Neutron macromolecular crystallography (NMC) overcomes this limitation by offering exceptional sensitivity to hydrogen and deuterium. Here, we present a theoretical framework for the development of dynamic nuclear polarization NMC (DNP-NMC) techniques, which exploit the alignment of neutron and proton nuclear spins to enhance and tune the hydrogen signal contribution. The DNP-NMC approach advances the resolution of H atoms within biomolecular crystals, whether bound to protein residues or present in solvent. The method establishes key relationships for the coherent structure factor of polarized neutron scattering from hydrogenous matter. It theoretically achieves full accuracy in phase reconstruction and offers a path to improve neutron structure determination, achieving accuracies exceeding ≳80% by incorporating titration states. Using a variant of the hybrid input/output phase-retrieval algorithm, it allows recovery of the hydrogen density with ≳90% phase accuracy. In conclusion, we further discuss sources of experimental uncertainty for the upcoming DNP-enabled, quasi-Laue IMAGINE-X experiment at Oak Ridge National Laboratory's High Flux Isotope Reactor.
dynamic nuclear polarization↗
Complex imaging of phase domains by deep neural networks
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Wu, Longlong↗
High-sensitivity plasma density retrieval in a common-path second-harmonic interferometer through simultaneous group and phase velocity measurement
Precise measurements of the plasma density in ionized gas cells and discharged capillaries are critical to the design and operation of plasma-based accelerators, active plasma lenses, and plasma-based radiation sources. In this manuscript, a spectral-domain common-path second-harmonic interferometer is upgraded with the simultaneous measurement of the group and phase velocity, allowing for high-sensitivity density characterization (from the phase velocity advance) without the need for phase tracking from zero-density (enabled by the group velocity delay). The technique is applied to 1.5-cm-long plasma structures, without density ambiguity in parameter scans with >2π phase jumps. Finally, the single-shot sensitivity in phase retrieval is demonstrated at 63 mrad, equivalent to a density-length product of 1.8·10 15 cm -2 . This is an improvement of ×45 compared to group velocity analysis alone.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Phase measurements of EUV mask defects
Extreme Ultraviolet (EUV) Lithography mask defects were examined on the actinic mask imaging system, SHARP, at Lawrence Berkeley National Laboratory. Also, a quantitative phase retrieval algorithm based on the Weak Object Transfer Function was applied to the measured through-focus aerial images to examine the amplitude and phase of the defects. The accuracy of the algorithm was demonstrated by comparing the results of measurements using a phase contrast zone plate and a standard zone plate. Using partially coherent illumination to measure frequencies that would otherwise fall outside the numerical aperture (NA), it was shown that some defects are smaller than the conventional resolution of the microscope. We found that the programmed defects of various sizes were measured and shown to have both an amplitude and a phase component that the algorithm is able to recover.
42 ENGINEERING↗
Parallel ptychographic reconstruction
Ptychography is an imaging method whereby a coherent beam is scanned across an object, and an image is obtained by iterative phasing of the set of diffraction patterns. It is able to be used to image extended objects at a resolution limited by scattering strength of the object and detector geometry, rather than at an optics-imposed limit. As technical advances allow larger fields to be imaged, computational challenges arise for reconstructing the correspondingly larger data volumes, yet at the same time there is also a need to deliver reconstructed images immediately so that one can evaluate the next steps to take in an experiment. Here we present a parallel method for real-time ptychographic phase retrieval. It uses a hybrid parallel strategy to divide the computation between multiple graphics processing units (GPUs) and then employs novel techniques to merge sub-datasets into a single complex phase and amplitude image. Results are shown on a simulated specimen and a real dataset from an X-ray experiment conducted at a synchrotron light source.
97 MATHEMATICS AND COMPUTING↗
Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis
Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.
36 MATERIALS SCIENCE↗
Advanced Wavefront Sensing and Control Testbed (AWCT)
The Advanced Wavefront Sensing and Control Testbed (AWCT) is built as a versatile facility for developing and demonstrating, in hardware, the future technologies of wave front sensing and control algorithms for active optical systems. The testbed includes a source projector for a broadband point-source and a suite of extended scene targets, a dispersed fringe sensor, a Shack-Hartmann camera, and an imaging camera capable of phase retrieval wavefront sensing. The testbed also provides two easily accessible conjugated pupil planes which can accommodate the active optical devices such as fast steering mirror, deformable mirror, and segmented mirrors. In this paper, we describe the testbed optical design, testbed configurations and capabilities, as well as the initial results from the testbed hardware integrations and tests.
active optics↗
Neutron sub-micrometre tomography from scattering data
Neutrons are valuable probes for various material samples across many areas of research. Neutron imaging typically has a spatial resolution of larger than 20 µm, whereas neutron scattering is sensitive to smaller features but does not provide a real-space image of the sample. A computed-tomography technique is demonstrated that uses neutron-scattering data to generate an image of a periodic sample with a spatial resolution of ∼300 nm. The achieved resolution is over an order of magnitude smaller than the resolution of other forms of neutron tomography. This method consists of measuring neutron diffraction using a double-crystal diffractometer as a function of sample rotation and then using a phase-retrieval algorithm followed by tomographic reconstruction to generate a map of the sample's scattering-length density. Topological features found in the reconstructions are confirmed with scanning electron micrographs. This technique should be applicable to any sample that generates clear neutron-diffraction patterns, including nanofabricated samples, biological membranes and magnetic materials, such as skyrmion lattices.
nanoscience↗
Simulation Studies of Forest Structure using 3D Lidar and Radar Models
The use of lidars and radars to measure forest structure attributes such as height and biomass are being considered for future Earth Observation missions. Large footprint lidar makes a direct measurement of the heights of scatterers in the illuminated footprint and can yield information about the vertical profile of the canopy. Synthetic Aperture Radar (SAR) is known to sense the canopy volume, especially at longer wavelengths and is useful for estimating biomass. Interferometric SAR (InSAR) has been shown to yield forest canopy height information. For example, the height of scattering phase retrieved from InSAR data is considered to be correlated with the three height and the spatial structure of the forest stand. There is much interest in exploiting these technologies separately and together to get important information for carbon cycle and ecosystem science. More detailed information of the electromagnetic radiation interactions within forest canopies is needed. And backscattering models can be of much utility here. As part of a NASA funded project to explore data fusion, a three-dimensional (3D) coherent radar backscattering model and a 3D lidar backscatter models were used to investigate the use of large footprint lidar, SAR and InSAR for characterizing realistic forest scenes. For this paper, we use stem maps and other forest measurements to develop a realistic spatial structure of a spruce-hemlock forest canopy found in Maine, USA. The radar and lidar models used measurements of the 3D forest scene as input and simulated the coherent radar backscattering signature and 1064nm energy backscatter, respectively. The relationships of backscatter derived forest structure were compared with field measurements. In addition, we also had detailed airborne lidar (Laser Imaging Vegetation Sensor, LVIS) data available over the stem map sites that was used to study the accuracies of tree height derived from modeled SAR backscatter and the scattering phase center retrieved from the simulated InSAR data will be compared with the height indices, or other structure parameters derived from the lidar data. These results will address the possible synergies between lidar and radar in data in terms of forest structural information.
Sun, Guoqing↗
Demonstration of on Sky Contrast Improvement Using the Modified Gerchberg-Saxton Algorithm at the Palomar Observatory
We have successfully demonstrated significant improvements in the high contrast detection limit of the Well-Corrected Subaperture (WCS) using the Autonomous Phase Retrieval Calibration (APRC) software package developed at the Jet Propulsion Laboratory (JPL) for the Palomar adaptive optics instrument (PALAO). APRC utilizes the Modified Gerchberg-Saxton (MGS) wavefront sensing algorithm, also developed at JPL. The WCS delivers such excellent correction of the atmosphere that non-common path (NCP) wavefront errors not sensed by PALAO but present at the coronagraphic image plane begin to factor heavily as a limit to contrast. We have implemented the APRC program to reduce these NCP wavefront errors from 110 nm to 35 nm (rms) in the lab, and we have extended these exceptional results to targets on the sky for the first time, leading to a significant suppression of speckle noise. Consequently we now report a contrast level of very nearly 1x10(exp -4) at separations of 2 lambda/D before the data is post processed. We describe here the major components of our instrument, the work done to improve the NCP wavefront errors, and the ensuing excellent on sky results, including the detection of the three exoplanets orbiting the star HR8799.
mgs↗
Proof-of-concept Talbot–Lau x-ray interferometry with a high-intensity, high-repetition-rate, laser-driven K-alpha source
Talbot–Lau x-ray interferometry is a grating-based phase-contrast technique, which enables measurement of refractive index changes in matter with micrometric spatial resolution. The technique has been established using a variety of hard x-ray sources, including synchrotron, free-electron lasers, and x-ray tubes, and could be used in the optical range for low-density plasmas. The tremendous development of table-top high-power lasers makes the use of high-intensity, laser-driven K-alpha sources appealing for Talbot–Lau interferometer applications in both high-energy-density plasma experiments and biological imaging. To this end, we present the first, to the best of our knowledge, feasibility study of Talbot–Lau phase-contrast imaging using a high-repetition-rate laser of moderate energy (100 mJ at a repetition rate of 10 Hz) to irradiate a copper backlighter foil. The results from up to 900 laser pulses were integrated to form interferometric images. A constant fringe contrast of 20% is demonstrated over 100 accumulations, while the signal-to-noise ratio continued to increase with the number of shots. Phase retrieval is demonstrated without prior ex-situ phase stepping. Instead, correlation matrices are used to compensate for the displacement between reference acquisition and the probing of a PMMA target rod. The steps for improved measurements with more energetic laser systems are discussed. The final results are in good agreement with the theoretically predicted outcomes, demonstrating the applicability of this diagnostic to a range of laser facilities for use across several disciplines.
Bouffetier, V. (ORCID:0000000160791260)↗
Measuring an ultrashort, ultraviolet pulse in a slowly responding, absorbing medium
Frequency-resolved optical gating (FROG) is a common technique for measuring ultrashort laser pulses using an instantaneous, nonlinear-optical interaction as a fast time-gate to measure the pulse intensity and phase. But at high frequencies, materials are often absorbing and it is not always possible to find a medium with a fast nonlinear-optical response. Here we show that an ultrashort, ultraviolet (UV) pulse can be measured in a strongly absorbing medium, using the absorption as the nonlinear-optical time-gate. To do this, we build on our recent implementation of FROG, known as induced-grating cross-correlation FROG (IG XFROG), where an unknown, higher-frequency pulse creates a transient grating that is probed with a lower-frequency, more easily detectable reference pulse. We demonstrate this with an 800 nm reference pulse to characterize 400 nm or 267 nm pulses using ZnS as the nonlinear-optical medium, which is absorptive at and below 400 nm. By scanning the delay between the two UV pulses which create the transient grating, we show that the phase-sensitive instantaneous four-wave-mixing contribution to the nonlinear signal field can be detected and separated from the slower, incoherent part of the response. Measuring a spectrally-resolved cross-correlation in this way and then applying a simple model for the response of the medium, we show that a modified generalized projections (GP) phase-retrieval algorithm can be used to extract the pulse amplitude and phase. We test this approach by measuring chirped UV pulses centered at 400 nm and 267 nm. Since interband absorption (or even photoionization) is not strongly wavelength-dependent, we expect IG XFROG to be applicable deeper into the UV.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
High-speed 3D shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system
In this study, we propose a high-speed 3D shape measurement technique based on the optimized composite fringe patterns and stereo-assisted structured light system. Stereo phase unwrapping, as a new-fashioned method for absolute phase retrieval based on the multi-view geometric constraints, can eliminate the phase ambiguities and obtain a continuous phase map without projecting any additional patterns. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which limits the accuracy of 3D measurement. To solve this problem, we develop an optimized method for designing the composite pattern, in which the speckle pattern is embedded into the conventional 4-step phase-shifting fringe patterns without compromising the fringe modulation, and thus the phase measurement accuracy. We also present a simple and effective evaluation criterion for the correlation quality of the designed speckle pattern in order to improve the matching accuracy significantly. When the embedded speckle pattern is demodulated, the periodic ambiguities in the wrapped phase can be eliminated by combining the adaptive window image correlation with geometry constraint. Finally, some mismatched regions are further corrected based on the proposed regional diffusion compensation technique (RDC). These proposed techniques constitute a complete computational framework that allows to effectively recover an accurate, unambiguous, and distortion-free 3D point cloud with only 4 projected patterns. Experimental results verify that our method can achieve high-speed, high-accuracy, robust 3D shape measurement with dense (64-period) fringe patterns at 5000 frames per second.
42 ENGINEERING↗
Iterative reconstruction of magnetic induction using Lorentz transmission electron tomography
Intense ongoing research on complex nanomagnetic structures requires a fundamental understanding of the 3D magnetization and the stray fields around the nano-objects. 3D visualization of such fields offers the best way to achieve this. Lorentz transmission electron microscopy provides a suitable combination of high resolution and ability to quantitatively visualize the magnetization vectors using phase retrieval methods. In this paper, we present a formalism to represent the magnetic phase shift of electrons as a Radon transform of the magnetic induction of the sample. Using this formalism, we then present the application of common tomographic methods particularly the iterative methods, to reconstruct the 3D components of the vector held. We present an analysis of the effect of missing wedge and the limited angular sampling as well as reconstruction of complex 3D magnetization in a nanowire using simulations.
Phatak, C.↗
CERES MODIS Cloud Product Retrievals for Edition 4--Part I: Algorithm Changes
The Edition 2 (Ed2) cloud property retrieval algorithm system was upgraded and applied to the MODerate-resolution Imaging Spectroradiometer (MODIS) data for the Clouds and the Earth's Radiant Energy System (CERES) Edition 4 (Ed4) products. New calibrations for solar channels and the use of the 1.24-μm channel for cloud optical depth (COD) over snow improve the daytime consistency between Terra and Aqua MODIS retrievals. Use of additional spectral channels and revised logic enhanced the cloud-top phase retrieval accuracy. A new ice crystal reflectance model and a CO₂-channel algorithm retrieved higher ice clouds, while a new regional lapse rate technique produced more accurate water cloud heights than in Ed2. Ice cloud base heights are more accurate due to a new cloud thickness parameterization. Overall, CODs increased, especially over the polar (PO) regions. The mean particle sizes increased slightly for water clouds, but more so for ice clouds in the PO areas. New experimental parameters introduced in Ed4 are limited in utility, but will be revised for the next CERES edition. As part of the Ed4 retrieval evaluation, the average properties are compared with those from other algorithms and the differences between individual reference data and matched Ed4 retrievals are explored. Part II of this article provides a comprehensive, objective evaluation of selected parameters. More accurate interpretation of the CERES radiation measurements has resulted from the use of the Ed4 cloud properties.
54 ENVIRONMENTAL SCIENCES↗
Randomized probe imaging through deep k-learning
Randomized probe imaging (RPI) is a single-frame diffractive imaging method that uses highly randomized light to reconstruct the spatial features of a scattering object. The reconstruction process, known as phase retrieval, aims to recover a unique solution for the object without measuring the far-field phase information. Typically, reconstruction is done via time-consuming iterative algorithms. In this work, we propose a fast and efficient deep learning based method to reconstruct phase objects from RPI data. The method, which we call deep k-learning, applies the physical propagation operator to generate an approximation of the object as an input to the neural network. This way, the network no longer needs to parametrize the far-field diffraction physics, dramatically improving the results. Deep k-learning is shown to be computationally efficient and robust to Poisson noise. The advantages provided by our method may enable the analysis of far larger datasets in photon starved conditions, with important applications to the study of dynamic phenomena in physical science and biological engineering.
Guo, Zhen (ORCID:0000000213473451)↗