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Results for “Phase retrieval”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Beyond Contrast Transfer: Spectral SNR as a Finite-Dose Metric for STEM Phase Retrieval

The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a finite-dose statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, finite-dose metric for assessing STEM phase retrieval methods.

STEM phase retrieval↗
DOE OSTI2024

Atomic resolution coherent x-ray imaging with physics-based phase retrieval

Coherent x-ray imaging and scattering from accelerator based sources such as synchrotrons continue to impact biology, medicine, technology, and materials science. Many synchrotrons around the world are currently undergoing major upgrades to increase their available coherent x-ray flux by approximately two orders of magnitude. The improvement of synchrotrons may enable imaging of materials in operando at the atomic scale which may revolutionize battery and catalysis technologies. Current algorithms used for phase retrieval in coherent x-ray imaging are based on the projection onto sets method. These traditional iterative phase retrieval methods will become more computationally expensive as they push towards atomic resolution and may struggle to converge. Additionally, these methods do not incorporate physical information that may additionally constrain the solution. In this work, we present an algorithm which incorporates molecular dynamics into Bragg coherent diffraction imaging (BCDI). This algorithm, which we call PRAMMol (Phase Retrieval with Atomic Modeling and Molecular Dynamics) combines statistical techniques with molecular dynamics to solve the phase retrieval problem. We present several examples where our algorithm is applied to simulated coherent diffraction from 3D crystals and show convergence to the correct solution at the atomic scale.

47 OTHER INSTRUMENTATION↗
NASA NTRS2012

Qualification of a Null Lens Using Image-Based Phase Retrieval

In measuring the figure error of an aspheric optic using a null lens, the wavefront contribution from the null lens must be independently and accurately characterized in order to isolate the optical performance of the aspheric optic alone. Various techniques can be used to characterize such a null lens, including interferometry, profilometry and image-based methods. Only image-based methods, such as phase retrieval, can measure the null-lens wavefront in situ - in single-pass, and at the same conjugates and in the same alignment state in which the null lens will ultimately be used - with no additional optical components. Due to the intended purpose of a Dull lens (e.g., to null a large aspheric wavefront with a near-equal-but-opposite spherical wavefront), characterizing a null-lens wavefront presents several challenges to image-based phase retrieval: Large wavefront slopes and high-dynamic-range data decrease the capture range of phase-retrieval algorithms, increase the requirements on the fidelity of the forward model of the optical system, and make it difficult to extract diagnostic information (e.g., the system F/#) from the image data. In this paper, we present a study of these effects on phase-retrieval algorithms in the context of a null lens used in component development for the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission. Approaches for mitigation are also discussed.

Bolcar, Matthew R.↗
NASA NTRS2003

Phase Retrieval Using a Genetic Algorithm on the Systematic Image-Based Optical Alignment Testbed

NASA s Marshall Space Flight Center s Systematic Image-Based Optical Alignment (SIBOA) Testbed was developed to test phase retrieval algorithms and hardware techniques. Individuals working with the facility developed the idea of implementing phase retrieval by breaking the determination of the tip/tilt of each mirror apart from the piston motion (or translation) of each mirror. Presented in this report is an algorithm that determines the optimal phase correction associated only with the piston motion of the mirrors. A description of the Phase Retrieval problem is first presented. The Systematic Image-Based Optical Alignment (SIBOA) Testbeb is then described. A Discrete Fourier Transform (DFT) is necessary to transfer the incoming wavefront (or estimate of phase error) into the spatial frequency domain to compare it with the image. A method for reducing the DFT to seven scalar/matrix multiplications is presented. A genetic algorithm is then used to search for the phase error. The results of this new algorithm on a test problem are presented.

Taylor, Jaime R.↗
DOE OSTI2026

The ABCs of phase retrieval: Connecting the acronyms of scanning transmission electron microscopy

High-resolution scanning transmission electron microscopy (S/TEM) is an indispensable tool for characterizing the structure and properties of materials down to the atomic scale. Conventional S/TEM imaging, however, is limited by the phase problem, whereby the phase of the electron exit wave is lost upon detection. Recent advances in diffractive imaging and 4D-STEM have enabled a range of phase-retrieval techniques that computationally reconstruct the missing information encoded in the phase of the transmission function. These approaches offer improved dose efficiency and enhanced sensitivity to weakly scattering signals, extending quantitative imaging to beam-sensitive materials composed of light elements. In this work, we introduce the phase problem in electron microscopy and survey the diverse landscape of phase-retrieval techniques used in the field. Despite their many acronyms and algorithmic variations, these techniques share a common physical and mathematical foundation. We present a unified framework that connects these seemingly distinct methods, from parallax imaging and tilt-corrected bright-field (tcBF-STEM), to aberration-corrected bright-field (acBF-STEM), optimum bright-field (OBF-STEM) and single-sideband (SSB) ptychography, as well as first-moment integrated center of mass techniques (iCOM) and iterative ptychographic algorithms. Based on these insights, we discuss the opportunities and practical limitations of applying these methods across different materials systems, detector designs, and microscope configurations.Graphical abstractRepresentative electron microscopy configurations used for phase retrieval and diffractive imaging in S/TEM: (a) Zernike phase-contrast transmission electron microscopy (TEM), (b) small-convergence-angle four-dimensional scanning transmission electron microscopy (4D-STEM) for nanobeam-based phase reconstruction methods, and (c) large-convergence-angle 4D-STEM for ptychographic and related diffractive imaging techniques reviewed in this work.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Phase retrieval camera for testing NGST optics

The NGST Phase Retrieval Camera (PRC) is a portable wavefront sensor useful for optical testing in high-vibration environments. Primary applications of the PRC are testing and experimenting with NGST technology demonstrator mirrors, along with exploring other wavefront sensing and control problems not easily studied using WCT. An overview of the hardware and testing results will be presented.

NGST↗
DOE OSTI2023

Single-shot, phase-diversity phase retrieval for high-energy beam focal-spot diagnostics

A single-shot, phase-diversity phase-retrieval method is demonstrated for directly characterizing the on-target focal spot at kilojoule energy in the OMEGA 60-beam laser. A 2D holographic grating that introduces diversity focal spots is installed in an existing on-target focal-spot diagnostic to obtain a single-shot diversity focal-spot image. A nonlinear optimization phase-retrieval algorithm with four diversity focal spots is employed to determine modal coefficients for the incident wavefront. The agreement between the measured and calculated focal spots is excellent. Furthermore, this approach can be easily adapted for other high-energy focal-spot diagnostics.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Combined speckle- and propagation-based single shot two-dimensional phase retrieval method

Single-shot two-dimensional (2D) phase retrieval (PR) can recover the phase shift distribution within an object from a single 2D x-ray phase contrast image (XPCI). Two competing XPCI imaging modalities often used for single-shot 2D PR to recover material properties critical for predictive performance capabilities are: speckle-based (SP-XPCI) and propagation-based (PB-XPCI) XPCI imaging. However, PR from SP-XPCI and PB-XPCI images are, respectively, limited to reconstructing accurately slowly and rapidly varying features due to noise and differences in their contrast mechanisms. Herein, we consider a combined speckle- and propagation-based XPCI (SPB-XPCI) image by introducing a mask to generate a reference pattern and imaging in the near-to-holographic regime to induce intensity modulations in the image. We develop a single-shot 2D PR method for SPB-XPCI images of pure phase objects without imposing restrictions such as object support constraints. It is compared against PR methods inspired by those developed for SP-XPCI and PB-XPCI on simulated and experimental images of a thin glass shell before and during shockwave compression. Reconstructed phase maps show improvements in quantitative scores of root-mean-square error and structural similarity index measure using our proposed method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Ptychographic phase retrieval by proximal algorithms

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 10 4 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Phase retrieval for the Hubble Space Telescope using iterative propagation algorithms

Phase retrieval algorithms, including the iterative transform algorithm and gradient search algorithms, were generalized to include the effects of propagation through a complicated optical system and to discount the effects of bad CCD pixels. For the gradient search algorithms, analytic gradients were derived that greatly speed up the computation over finite difference methods. For the Hubble Space Telescope (HST), the aperture function was reconstructed and the phase errors were retrieved. This information is useful to design correction optics for the telescope and for the deconvolution of blurred images from the HST.

Fienup, J. R.↗
DOE OSTI2024

Phase retrieval for refraction-enhanced x-ray radiography using a deep neural network

X-ray refraction-enhanced radiography (RER) or phase contrast imaging is widely used to study internal discontinuities within materials. The resulting radiograph captures both the decrease in intensity caused by material absorption along the x-ray path, as well as the phase shift, which is highly sensitive to gradients in density. A significant challenge lies in effectively analyzing the radiographs to decouple the intensity and phase information and accurately ascertain the density profile. Conventional algorithms often yield ambiguous and unrealistic results due to difficulties in including physical constraints and other relevant information. We have developed an algorithm that uses a deep neural network to address these issues and applied it to extract the detailed density profile from an experimental RER. To generalize the applicability of our algorithm, we have developed a technique that quantitatively evaluates the complexity of the phase retrieval process based on the characteristics of the sample and the configuration of the experiment. Accordingly, this evaluation aids in the selection of the neural network architecture for each specific case. Beyond RER, the model has potential applications for other diagnostics where phase retrieval analysis is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2013

System and method for phase retrieval for radio telescope and antenna control

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for radio phase retrieval. A system practicing the method gathers first data from radio waves associated with an object observed via a first aperture, gathers second data from radio waves associated with the object observed via an introduced second aperture associated with the first aperture, generates reduced noise data by incoherently subtracting the second data from the first data, and performs phase retrieval for the radio waves by modeling the reduced noise data using a single Fourier transform. The first and second apertures are at different positions, such as side by side. This approach can include determining a value Q which represents a ratio of wavelength times a focal ratio divided by pixel spacing. This information can be used to accurately measure and correct alignment errors or other optical system flaws in the apertures.

Dean, Bruce H.↗
DOE OSTI2026

Adaptively coupled phase retrieval in multi-peak Bragg coherent diffraction imaging

Recent advances in Bragg coherent diffraction imaging (BCDI) experimental techniques permit routine measurement of multiple Bragg peaks from a single crystalline grain. The resulting images contain the full lattice distortion vector field which can be differentiated to provide lattice strain and rotation. With the advent of fourth-generation synchrotron light sources, such multi-peak datasets are produced at high rates, facilitating the need for rapid phase retrieval of the multiple peaks and subsequent image analysis. Here we describe and demonstrate a new implementation of a coupled phase retrieval technique for multi-peak BCDI which simultaneously treats each Bragg peak of the dataset and produces a three-dimensional image of the crystal's morphology and lattice distortion field. In addition, this method uses the redundant information contained in the various Bragg diffraction patterns to detect and suppress spurious signal appearing on the detector in a subset of the measurements. Compared with manual data editing, adaptive coupling produces a more consistent phase profile in reciprocal space and sharper surfaces in direct space, with no significant difference in computational cost. These improvements reduce the need for manual preprocessing and enable robust high-throughput analysis of multi-peak BCDI data, supporting near-real-time strain microscopy at modern synchrotron facilities.

36 MATERIALS SCIENCE↗
NASA NTRS2012

Sampling and Reconstruction of the Pupil and Electric Field for Phase Retrieval

This technology is based on sampling considerations for a band-limited function, which has application to optical estimation generally, and to phase retrieval specifically. The analysis begins with the observation that the Fourier transform of an optical aperture function (pupil) can be implemented with minimal aliasing for Q values down to Q = 1. The sampling ratio, Q, is defined as the ratio of the sampling frequency to the band-limited cut-off frequency. The analytical results are given using a 1-d aperture function, and with the electric field defined by the band-limited sinc(x) function. Perfect reconstruction of the Fourier transform (electric field) is derived using the Whittaker-Shannon sampling theorem for 1<Q<2. The Fourier transform is constructed by periodic extension, i.e., by spacing copies of the transform in a definite way, recognizing that no aliasing occurs for values of the sampling ratio such that 1<Q<2, which can be used to advantage in the application of phase retrieval estimation. A method was developed for propagating the electro magnetic field with no aliasing, which has been extended to 2-d optical apertures.

Dean, Bruce↗
NASA NTRS2012

Method for utilizing properties of the sinc(x) function for phase retrieval on nyquist-under-sampled data

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for simulating propagation of an electromagnetic field, performing phase retrieval, or sampling a band-limited function. A system practicing the method generates transformed data using a discrete Fourier transform which samples a band-limited function f(x) without interpolating or modifying received data associated with the function f(x), wherein an interval between repeated copies in a periodic extension of the function f(x) obtained from the discrete Fourier transform is associated with a sampling ratio Q, defined as a ratio of a sampling frequency to a band-limited frequency, and wherein Q is assigned a value between 1 and 2 such that substantially no aliasing occurs in the transformed data, and retrieves a phase in the received data based on the transformed data, wherein the phase is used as feedback to an optical system.

Dean, Bruce H.↗
DOE OSTI2024

Predicting ptychography probe positions using single-shot phase retrieval neural network

Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of 10 2 pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

47 OTHER INSTRUMENTATION↗