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Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗

BEACON—automated aberration correction for scanning transmission electron microscopy using Bayesian optimization

Aberration correction is an important aspect of modern high-resolution scanning transmission electron microscopy. Most methods of aligning aberration correctors require specialized sample regions and are unsuitable for fine-tuning aberrations without interrupting on-going experiments. Here, we present an automated method of correcting first- and second-order aberrations called BEACON, which uses Bayesian optimization of the normalized image variance to efficiently determine the optimal corrector settings. We demonstrate its use on gold nanoparticles and a hafnium dioxide thin film showing its versatility in nano- and atomic-scale experiments. BEACON can correct all first- and second-order aberrations simultaneously to achieve an initial alignment and first- and second-order aberrations independently for fine alignment. Ptychographic reconstructions are used to demonstrate an improvement in probe shape and a reduction in the target aberration.

techniques and instrumentation↗

Analysis and fringe field scaling of a legacy set of electrostatic deflector aberration formulas [Chapter Seven]

In this work we performed an analysis of the derivation of first and second order analytic aberration formulas by Wollnik (1965) for the case of electrostatic deflectors in the horizontal plane. We found that these aberration formulas are valid for the main field of the deflector; however, they do not account for any fringe field effects. To address this issue, we modified the aberration formulas from Wollnik (1965) for a hard edge fringe field by scaling the particle inclinations at the entrance and exit edges of the deflector. These modified aberration formulas fully agree with electrostatic aberration formulas derived by Valetov and Berz (2020), as well as with differential-algebraic (DA) calculations of electrostatic deflector aberrations using the code COSY INFINITY.

43 PARTICLE ACCELERATORS↗

Fourier-based three-dimensional multistage transformer for aberration correction in multicellular specimens

High-resolution tissue imaging is often compromised by sample-induced optical aberrations that degrade resolution and contrast. Although wavefront sensor-based adaptive optics (AO) can measure these aberrations, such hardware solutions are typically complex, expensive to implement and slow when serially mapping spatially varying aberrations across large fields of view. Here we introduce AOViFT (adaptive optical vision Fourier transformer)—a machine learning-based aberration sensing framework built around a three-dimensional multistage vision transformer that operates on Fourier domain embeddings. AOViFT infers aberrations and restores diffraction-limited performance in puncta-labeled specimens with substantially reduced computational cost, training time and memory footprint compared to conventional architectures or real-space networks. We validated AOViFT on live gene-edited zebrafish embryos, demonstrating its ability to correct spatially varying aberrations using either a deformable mirror or postacquisition deconvolution. By eliminating the need for the guide star and wavefront sensing hardware and simplifying the experimental workflow, AOViFT lowers technical barriers for high-resolution volumetric microscopy across diverse biological samples.

Alshaabi, Thayer [Howard Hughes Medical Institute,↗

High-resolution cryo-EM reconstructions in the presence of substantial aberrations

Here, an analysis is performed of how uncorrected antisymmetric aberrations, such as coma and trefoil, affect cryo-EM single-particle reconstruction (SPR) results, and an analytical formula quantifying information loss owing to their presence is inferred that explains why Fourier-shell coefficient-based statistics may report significantly overestimated resolution if these aberrations are not fully corrected. The analysis is validated with reference-based aberration refinement for two cryo-EM SPR data sets acquired with a 200 kV microscope in the presence of coma exceeding 40 µm, and 2.3 and 2.7 Å reconstructions for 144 and 173 kDa particles, respectively, were obtained. The results provide a description of an efficient approach for assessing information loss in cryo-EM SPR data acquired in the presence of higher order aberrations, and address inconsistent guidelines regarding the level of aberrations that is acceptable in cryo-EM SPR experiments.

3D reconstruction and image processing↗

Automating STEM Aberration Correction via Bayesian Optimization

Multipole aberration correctors have given scanning transmission electron microscopes (STEM) the ability to produce high-quality, atomic-resolution images, enabling STEM to be a key tool in material sciences for characterizing the structure and composition of materials. However, the process of correcting these aberrations typically requires human input and is accomplished using scanned STEM or Ronchigram images at different focii and beam tilts. In this work, we demonstrate an automated on-sample aberration correction system using Bayesian Optimization. We have developed a Python-based server able to communicate with the CEOS DCOR aberration corrector and the Thermo Fischer microscope scripting interface. This server allows us to change aberrations, acquire images and perform basic image analysis.

47 OTHER INSTRUMENTATION↗

Meiotic susceptibility for induction of sperm with chromosomal aberrations in patients receiving combination chemotherapy for Hodgkin lymphoma

Improvements in survival rates with gonad-sparing protocols for childhood and adolescence cancer have increased the optimism of survivors to become parents after treatment. Findings in rodents indicate that chromosomal aberrations can be induced in male germ cells by genotoxic exposures and transmitted to offspring and future generations with effects on development, fertility and health. Thus, there is a need for effective technologies to identify human sperm carrying chromosomal aberrations to assess the germ-line risks, especially for cancer survivors who have received genotoxic therapies. The time-dependent changes in the burden of sperm carrying structural chromosomal aberrations were assessed for the first time in a cancer setting, using the AM8 sperm FISH protocol which simultaneously detects abnormalities in chromosomal structure and number in sperm. Nine Hodgkin lymphoma (HL) patients provided 20 semen samples before, during, and after NOVP therapy (Novantrone, Oncovin, Velban and Prednisone) and radiation therapy that produced scattered gonadal doses from <0.05 to 0.6 Gy. Late meiosis was found to be the most sensitive to NOVP treatment for the production of sperm with chromosomal abnormalities, both in structure and number. Earlier stages of spermatogenesis were less sensitive and there was no evidence that therapy-exposed stem cells resulted in increased frequencies of sperm with abnormalities in chromosomal structure or number. This indicates that NOVP therapy may increase the risks for paternal transmission of chromosomal structural aberrations for sperm produced 32 to 45 days after a treatment with these drugs and implies that there are no excess risks for pregnancies conceived more than 6 months after this therapy. This clinical evaluation of the AM8 sperm FISH protocol indicates that it is a promising tool for assessing an individual’s burden of sperm carrying chromosomal structural aberrations as well as aneuploidies after cancer therapy, with broad applications in other clinical and environmental situations that may pose aneugenic or clastogenic risks to human spermatogenesis.

60 APPLIED LIFE SCIENCES↗

A polypeptide model for toxic aberrant proteins induced by aminoglycoside antibiotics

Aminoglycoside antibiotics interfere with the selection of cognate tRNAs during translation, resulting in the synthesis of aberrant proteins that are the ultimate cause of cell death. However, the toxic potential of aberrant proteins and how they avoid degradation by the cell’s protein quality control (QC) machinery are not understood. Here we report that levels of the heat shock (HS) transcription factor σ32 increased sharply following exposure of Escherichia coli to the aminoglycoside kanamycin (Kan), suggesting that at least some of the aberrant proteins synthesized in these cells were recognized as substrates by DnaK, a molecular chaperone that regulates the HS response, the major protein QC pathway in bacteria. To further investigate aberrant protein toxic potential and interaction with cell QC factors, we studied an acutely toxic 48-residue polypeptide (ARF48) that is encoded by an alternate reading frame in a plant cDNA. As occurred in cells exposed to Kan, σ32 levels were strongly elevated following ARF48 expression, suggesting that ARF48 was recognized as a substrate by DnaK. Paradoxically, an internal 10-residue region that was tightly bound by DnaK in vitro also was required for the ARF48 toxic effect. Despite the increased levels of σ32, levels of several HS proteins were unchanged following ARF48 expression, suggesting that the HS response had been aborted. Nucleoids were condensed and cell permeability increased rapidly following ARF48 expression, together suggesting that ARF48 disrupts DNA-membrane interactions that could be required for efficient gene expression. Our results are consistent with earlier studies showing that aberrant proteins induced by aminoglycoside antibiotics disrupt cell membrane integrity. Insights into the mechanism for this effect could be gained by further study of the ARF48 model system.

36 MATERIALS SCIENCE↗

High-resolution bandpass x-ray imaging with crystal reflectors: Overcoming geometric aberrations

The imaging problem of a specular reflector is revisited. Retaining terms through the second order in the reflector surface expansion, we derive the form of the aberration-limiting aperture for arbitrary magnification, assuming no bandwidth limitations. A permissible relative aperture size of the reflector is limited by a set relative aberration tolerance and scales with the tangent of the central glancing angle of incidence. These limiting aberrations become practically insignificant near backscattering. The results extend to x-ray diffracting crystals in symmetric Bragg geometry shaped as an ellipsoid of revolution. This geometry permits polychromatic imaging for hard x-rays over a bandwidth defined by the accepted range of Bragg angles, thereby suppressing aberrations of higher orders. We assess ellipsoidal crystal imagers using ray tracing simulations for two high-magnification designs with Bragg angles far from and close to backscattering. Finally, in both cases, the ellipsoidal crystals produce images of higher quality compared to those formed by equivalent toroidal crystal imagers.

Bragg reflection↗

Analysis of the effect of spherical aberrations on a solenoid scan

Solenoid scans are often used to determine the beam emittance of an intense relativistic electron beam (IREB). In a solenoid scan, the beam size is measured at a location downstream of the solenoid as a function of the strength of the solenoid magnetic field. The emittance is then inferred using a beam optics model of the transport of the beam through the solenoid magnet to the imaging location. This requires precise knowledge of the field strength and shape as a function of the current supplied to the solenoid. The beam optics model for an IREB needs to include an accurate model of the magnetic field. Unfortunately, most beam optics models do not include the effect of spherical aberrations which are inherent in a solenoid magnet. Spherical aberrations are manifested as an essentially quadratic increase in the solenoid magnetic field as a function of radius. One consequence of this is that the focal length will be dependent on the beam radius. This note examines the sensitivity of a typical solenoid scan performed on DARHT axis 2 to spherical aberrations. The sensitivity to spherical aberrations is examined as a function of the beam envelope size and the drift distance from the solenoid magnet to the imaging station.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy

Abstract In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Correcting aberrations of a transverse-field neutron resonance spin echo instrument

Neutron resonance spin echo (NRSE) technique has the potential to increase the Fourier time and energy resolution in neutron scattering by using radio frequency (rf) neutron spin-flippers. However, aberrations arising from variations in the neutron path length between the rf flippers reduce the polarization. Here, we develop and test a transverse static-field magnet, a series of which are placed between the rf flippers, to correct for these aberrations. The prototype correction magnet was both simulated in an NRSE beamline using McStas, a Monte Carlo neutron ray-tracing software package, and measured using neutrons. The results from the prototype demonstrate that this static-field design corrects for transverse-field NRSE aberrations.

47 OTHER INSTRUMENTATION↗

Multidimensional images and aberrations in STEM

Recent advances in scanning transmission electron microscopy (STEM) have led to increased development of multi-dimensional STEM imaging modalities and novel image reconstruction methods. This interest arises because the main electron lens in a modern transmission electron microscope usually has a diffraction-space information limit that is significantly better than the real-space resolution of the same lens. This state-of-affairs is sometimes shared by other scattering methods in modern physics and contributes to a broader excitement surrounding multidimensional techniques that scan a probe while recording diffraction-space images, such as ptychography and scanning nano-beam diffraction. However, the contrasting resolution in the two spaces raises the question as to what is limiting their effective performance. Here, we examine this paradox by considering the effects of aberrations in both image and diffraction planes, and likewise separate the contributions of pre- and post-sample aberrations. In conclusion, this consideration provides insight into aberration-measurement techniques and might also indicate improvements for super-resolution techniques.

Hoglund, Eric R.↗

Spherical Aberrations - Final Focus and Solenoid Scans

Conclusions: Spherical aberrations in solenoids are unavoidable and problematic whenever the beam is focused; It may be possible to include a spherical aberration correction to the analysis of a solenoid scan in the manner described above although more accurate 2D PIC models should be studied to determine the accuracy of the very simple model used above. This correction would have to be iterated as the beam size in the solenoid is iterated; A quadrupole triplet final focus would not have aberrations (preliminary analysis shows improvement in spot size, very difficult to tune).

43 PARTICLE ACCELERATORS↗

Aberration corrected RF flipper for high resolution neutron spectroscopy

Project Summary Company: Adelphi Technology, Inc. Title: Aberration-corrected High Frequency RF Flipper for High-Resolution Neutron Spectroscopy PI: Dr. Jay Theodore Cremer Topic: C55-11 Enhancement of Scattering Instrumentation Technology Used at Pulsed and Continuous Sources Subtopic: d. Other Statement of the problem or situation that is being addressed. The quest to understand heterogeneous and hierarchical materials is gathering momentum, as described in a 2015 report by the Basic Energy Sciences Advisory Committee on Challenges at the Frontiers of Matter and Energy. For the past 40 years a technique called neutron spin echo (NSE) has been used to probe molecular motions in such non-crystalline materials over time scales from 10’s of picoseconds to 100’s of nanoseconds. The method has provided unique information about the dynamics of soft heterogeneous materials, including confirmation of the de Gennes model of polymer reptation and quantitative measurement of bending constants of biologically relevant lipid membranes. However, scientists continue to clamor for even higher resolution than NSE can provide. Biomaterials, polymers, glasses, and artificially nanostructured materials all manifest slow molecular motions because of weak or competing interactions between subunits and are amenable to study with neutrons, provided sufficiently long dynamical correlation times can be achieved. All these materials have important applications to advanced technologies so understanding them is key to technological progress. General statement of how this problem is being addressed. We will address the need for high-resolution neutron spectroscopy by using a technique called Neutron Resonance Spin Echo (NRSE). While similar to NSE in many respects, this method has the potential to exceed the NSE capabilities, if 2 technical hurdles can be overcome. The major impediments to successful high-resolution NRSE are the availability of two technologies: a very high frequency, efficient, radiofrequency (rf) flipper for neutrons and a method to correct certain magnetic aberrations. Based on previous STTR support and follow-on research we have developed a suitable rf flipper and we have invented a method to correct the magnetic aberrations. Both technologies need refinement to make them suitable for implementation at a neutron source such as the Oak Ridge National Laboratory nuclear reactor. In this proposal we seek to perfect the two technologies and to combine them into a single, operationally convenient device. Commercial Applications and Other Benefits In view of the increasing demand for the unique scientific information that high resolution neutron spectroscopy can provide, we expect several major instrumentation upgrades at both U.S. and foreign neutron centers will require make use of the NRSE method over the coming decade, creating a market for the devices we will design. These components will enhance scientists’ abilities to probe the time dependence of density fluctuations in a wide range of hierarchical and heterogeneous materials many of which are vital to existing and future technologies. Key Words – Polarized Neutrons, Neutron Spin Echo, Neutron Scattering, advanced materials. Summary for Members of Congress Neutron beams are a powerful materials-science probe that provide unique information about the structure of matter. The proposed devices will accelerate scientific discoveries required to achieve national goals for new technological materials.

36 MATERIALS SCIENCE↗

Secondary-electron imaging of bulk crystalline specimens in an aberration corrected $\text{STEM}$

Atomic-scale electron microscopy traditionally probes thin specimens, with thickness below 100 nm, and its feasibility for bulk samples has not been documented. Here in this study, we explore the practicality of scanning transmission electron microscope (STEM) imaging with secondary electrons (SE), using a silicon-wedge specimen having a maximum thickness of 18 μm. We find that the atomic structure is present in the entire thickness range of the SE images although the background intensity increases moderately with thickness. The consistent intensity of secondary electron (SE) images at atomic positions and the modest increase in intensity in between (background) observed in silicon suggest a limited contribution from SEs generated by backscattered electrons, a conclusion supported by our multislice calculations. We conclude that achieving atomic resolution in SE imaging for bulk specimens is indeed attainable using aberration-corrected STEM and that an aberration-corrected scanning electron microscope (SEM) may have the capacity for atomic-level resolution, holding great promise for future strides in materials research.

25 ENERGY STORAGE↗

Mitigating challenges in aberration-corrected electron-beam lithography on electron-opaque substrates

Aberration-corrected electron-beam lithography (AC-EBL) using ultra-thin electron transparent membranes has achieved single-digit nanometer resolution in two widely used electron-beam resists: poly (methyl methacrylate) (PMMA) and hydrogen silsesquioxane. On the other hand, AC-EBL implementation on thick, electron-opaque substrates is appealing for conventional top-down fabrication of quantum devices with nanometer-scale features. To investigate the performance of AC-EBL on thick substrates, we measured the lithographic point spread function of a 200 keV aberration-corrected scanning transmission electron microscope by defining both positive and negative patterns in PMMA thin films, spin-cast on thick SiO 2 /Si substrates. We present the problems encountered during pre-exposure beam focusing and discuss methods to overcome them. In addition, applying some of these methods using commercial 50 nm thick SiN X membranes with thick Si support frames, we printed arrays of holes in PMMA with pitches around 26 nm on SiN X /Si substrates with increasing Si thickness. Here, our results show that proximity effects from even 50 nm thick SiN X membranes limit hole arrays to 20 nm pitch; however, down to this limit, the effect of the substrate thickness on the pattern quality is minimal. These results highlight the need for novel resists less susceptible to proximity effects, or resists which can be used directly, after development, as the dielectric material in periodic gates in 2D quantum devices.

2D quantum devices↗

Laser aberration signatures in expelled electrons from a tenuous gas

We describe a mechanism by which the aberration content of a focused, multiterawatt laser is imprinted upon the forward angular distribution of electrons ionized within and ponderomotively expelled from the focal volume. In our experiments, the laser aberration type and magnitude are controllably varied, and the measured electron distributions are correspondingly modified in a way consistent with predictions from numerical simulations. This imprint mechanism shows potential for enabling the development of accurate focal-spot characterization of intense lasers when fired at full power and is being developed for extension to petawatt laser systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗