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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗
DOE OSTI2025

Code Verification of Multiple Physics-Fidelity Models in Hypersonic Aerodynamics

Hypersonic aerodynamics models exist across a range of physics fidelities with associated computational expenses. These models may be run independently or in a multifidelity framework that leverages their complementary strengths of speed for lower-fidelity and accuracy for higher-fidelity models. This work presents applied code verification of two lower-fidelity models contained within the Sandia hypersonic aerodynamics code. Each model has a different form that requires individualized verification approaches, including comparison to analytical solutions as well as manufactured solutions with order-of-accuracy testing. In conclusion, results of this effort include the identification and resolution of code errors and shortcomings, as well as the demonstration of code correctness and consistency for both models.

Aerodynamics↗
DOE OSTI2024

Jemima Plate Characterization

The HEU Jemima plates have been utilized in numerous International Criticality Safety Benchmark Evaluation Project (ICSBEP) evaluations. ICSBEP evaluations are a vital com ponent of nuclear data validation for applications across the nuclear community. In the past, different combinations of mass, caliper measurements, and drawing dimensions have been used to define the HEU Jemima plates in ICSBEP evaluations. Some of these combinations result in large density ranges (17 g/cm 3 to 19 g/cm 3 ) or unrealistic densities (greater than 19 g/cm 3 ). Additionally, oxidation of the plates has led to questioning the flatness of each plate, which can add additional gaps in experiment configurations. This work proposes a standardized method of defining the commonly used HEU Jemima plates across different experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Magnetic cores with high reluctance differences in flux paths

Embodiment of the present invention includes a magnetic structure and a magnetic structure used in a direct current (DC) to DC energy converter. The magnetic structure has an E-core and a plate, with the plate positioned in contact or in near contact with the post surfaces of the E-core. The E-core has a base, a no-winding leg, a transformer leg, and an inductor leg. The no-winding leg, the transformer leg, and the inductor leg are perpendicular and magnetically in contact with the base. The plate is a flat slab with lateral dimensions generally larger than its thickness. The plate has a plate nose that overlaps a top no-winding leg surface of the no-winding leg with a no-winding gap area to form a no-winding gap with a no-winding gap reluctance. The plate also has a plate end that overlaps a top inductor leg surface of the inductor leg with an inductor gap area to form an inductor gap with an inductor gap reluctance. In some embodiments, e.g., where the duty cycle is less than 50 percent, the inductor gap reluctance will be designed to be less than the no-winding gap reluctance. In these cases, the majority of the magnetic flux that passes through the transformer leg will return through the inductor leg, instead of through the no-winding leg. The inductor and no-winding gap reluctances can he adjusted, so that the electromotive force applied to a charge passing through the inductor will partially cancel the electromotive force applied by the transformer secondary. The gap reluctance ratio can be defined, so that the difference in secondary and inductor electromotive forces is equal to the output voltage defined by an optimal no-ripple duty cycle. In this way no changing current is required through the inductor to create a dI/dt inductive voltage drop across the output inductor. Zero output current ripple is achieved.Various embodiments of the plate, plate shape, and no-winding leg are disclosed. These embodiments allow achieving a high ratio of no-winding gap reluctance to inductor gap reluctance, for practical, affordable magnetic material structures and aspect ratios. A high gap reluctance ratio enables zero output current ripple for the high transformer turns ratios that are needed to achieve high input to output voltage ratios. The embodiments therefore allow achieving low output current ripple for 48 V or higher input voltages, 1 V or lower output voltages, and high output currents.

Yao, Yuan↗
DOE OSTI2020

Report Documenting Activity for Second Alloy 709 Commercial Heat

SUMMARY Qualification of the advanced austenitic stainless steel material Alloy 709 for use in Section III Division 5 of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code is being pursued by the US Department of Energy Advanced Reactor Technology Program. Qualification of this alloy will allow its use in design and construction of components for elevated temperature nuclear reactor systems. Code qualification requires extensive characterization of three commercial scale heats of the alloy. This report describes progress in procuring the second of three required heats of Alloy 709 plate from ATI Flat Rolled Products.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Magnetostrictive EMAT for Nuclear Spent Fuel Canisters

One approach for mitigation of stainless steel (SS) spent fuel canisters (SFCs) is to coat the welds or even the entire SFC with a cold-sprayed nickel coating. The coating can serve as a magnetostrictive interface between an electromagnetic acoustic transducer (EMAT) and the SS plate material. The EMAT can send ultrasound into the canister and “listen” for reflections caused by chloride-initiated stress corrosion cracking (CISCC) or other damage mechanisms that may lead to leaks if undetected and unmitigated. Here, this project outlines an approach for monitoring the integrity of SFCs using magnetostrictive EMAT sensors, which emit and detect discontinuity-initiated reflections indicative of pits or cracks likely arising from CISCC. Flat 13 mm SS plates with welds similar to actual canister welds were prepared, with flat-bottom holes 3 mm and 6 mm deep and 6 mm in diameter placed within the weld heat-affected zone (HAZ). The most effective sensor configurations were able to detect critical discontinuities more than 2 m away. Although a single sensor could be robotically deployed, the large volume covered by each sensor could support a small number of permanently mounted sensors, equipped with an external connector for periodic interrogation. The HAZ of a hypothetical SFC cylindrical surface could be effectively monitored with just 16 sensors.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

A User’s Guide to the PLTEMP/ANL Code

PLTEMP/ANL V4.3 is a program that obtains a steady-state flow and temperature solution for a nuclear reactor core, or for a single fuel assembly. It is based on an evolutionary sequence of codes originally used for plate temperatures, hence “PLTEMP”, developed at Argonne National Laboratory over several decades. Fueled and non-fueled regions are modeled. Each fuel assembly consists of one or more plates or tubes separated by coolant channels. The fuel plates may have one to five layers of different materials, each with heat generation. The width of a fuel plate may be divided into multiple longitudinal stripes, each with its own axial power shape. Depending upon the heat transfer method selected, the temperature solution is effectively 2-dimensional or 3-dimensional (Appendix XV). It begins with a solution across all coolant channels and fuel plates or tubes within a given fuel assembly, at the entrance to the assembly. The temperature solution is repeated for each axial node along the length of the fuel assembly. The geometry may be either slab or radial, corresponding to fuel assemblies made of a series of flat (or slightly curved) plates, or of nested tubes. A variety of thermal-hydraulic correlations are available to determine safety margins such as onset-of-nucleate boiling ratio(ONBR), departure from nucleate boiling ratio (DNBR), and onset of flow instability ratio (OFIR). Coolant properties for either light or heavy water are obtained from FORTRAN functions rather than from tables. The code is intended for thermal-hydraulic analysis of research reactor performance in the sub-cooled boiling regime. Both turbulent and laminar flow regimes can be modeled. Options to calculate both forced flow and natural circulation are available. A general search capability is available (Appendix XII) to greatly reduce the reactor analyst’s time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A User’s Guide to the PLTEMP/ANL Code (V.4.3)

PLTEMP/ANL V4.3 is a program that obtains a steady-state flow and temperature solution for a nuclear reactor core, or for a single fuel assembly. It is based on an evolutionary sequence of codes originally used for plate temperatures, hence “PLTEMP”, developed at Argonne National Laboratory over several decades. Fueled and non-fueled regions are modeled. Each fuel assembly consists of one or more plates or tubes separated by coolant channels. The fuel plates may have one to five layers of different materials, each with heat generation. The width of a fuel plate may be divided into multiple longitudinal stripes, each with its own axial power shape. Depending upon the heat transfer method selected, the temperature solution is effectively 2-dimensional or 3-dimensional (Appendix XV). It should be noted that for a 3-dimensional solution the axial power shape is modeled without accounting for axial heat conduction. It begins with a solution across all coolant channels and fuel plates or tubes within a given fuel assembly, at the entrance to the assembly. The temperature solution is repeated for each axial node along the length of the fuel assembly. The geometry may be either slab or radial, corresponding to fuel assemblies made of a series of flat (or slightly curved) plates, or of nested tubes. A variety of thermal-hydraulic correlations are available to determine safety margins such as onset-of-nucleate boiling ratio(ONBR), departure from nucleate boiling ratio (DNBR), and onset of flow instability ratio (OFIR). Coolant properties for either light or heavy water are obtained from FORTRAN functions rather than from tables. The code is intended for thermal-hydraulic analysis of research reactor performance in the sub-cooled boiling regime. Both turbulent and laminar flow regimes can be modeled. Options to calculate both forced flow and natural circulation are available. A general search capability is available (Appendix XII) to greatly reduce the reactor analyst’s time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

A User’s Guide to the PLTEMP/ANL Code

PLTEMP/ANL V4.4 is a program that obtains a steady-state flow and temperature solution, in geometrical extent, for a nuclear reactor core, or a single fuel assembly, including the effect of manufacturing and modelling uncertainties by the means of hot channel factors. It is based on an evolutionary sequence of codes originally used for calculating plate temperatures, hence “PLTEMP”, developed at Argonne National Laboratory over the past 30 years. Fueled and non-fueled regions are modeled. Each fuel assembly consists of one or more plates or tubes separated by coolant channels. The fuel plates may have one to five layers of different materials, each with heat generation. The width of a fuel plate may be divided into multiple longitudinal stripes, each with its own axial power shape. Depending upon the heat transfer method selected, the temperature solution is effectively 2-dimensional or 3-dimensional. The geometry may be either slab or radial, corresponding to fuel assemblies made of a series of flat (or slightly curved) plates, or of nested tubes. A variety of thermal-hydraulic correlations are available to determine safety margins such as onset of nucleate boiling ratio (ONBR), departure from nucleate boiling ratio (DNBR), and onset of flow instability ratio (OFIR). Coolant properties for either light or heavy water are obtained from FORTRAN functions rather than from tables. The code is intended for thermal-hydraulic analysis of research reactor performance in the sub-cooled boiling regime. Both turbulent and laminar flow regimes can be modeled. Options to calculate both forced flow and natural circulation are available. A general search capability for select design and safety parameters is available to greatly reduce the reactor analyst’s time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

9. Support, Raft, Brim, and Skirt Pathing

The previous chapters discussed the primary path types in additive manufacturing: perimeter, inset, skeleton, skin, and infill. In addition to those distinct primary path types, regions of primary paths can be assigned secondary path types: support, raft, brim, and skirt. Support paths are used to enable the printing of features that would otherwise have nothing underneath to print atop, such as overhangs. Raft paths are used to level the build plate and provide a flat surface on which to construct the object. Brim toolpaths are used to increase the footprint of the object to improve bed adhesion and reduce first layer delamination. The last path type, the skirt, is used to prime the extruder at the start of the print. These four types of path regions are created using a combination of closed-loop, open-loop, and space-filling toolpaths. This chapter will discuss how to find and generate the pathing for each region.

Roschli, Alex↗
DOE OSTI2024

Failure investigation and mitigation after experimental research reactor fuel plate deformation in an irradiation device

Experimental research reactor fuel testing is conducted in the Belgian Reactor 2 (BR2) of the Belgian Nuclear Research Centre (SCK CEN) in dedicated irradiation vehicles or rigs. One such vehicle allows flat full-size fuel plates to be irradiated by inserting them into slotted baskets that captures a narrow portion of the longitudinal edges of the plates. The motion of the fuel plates within the baskets is possible within the narrow slots and thus, the plate is considered to be unattached. The design intentionally omits fixing mechanisms of the fuel plates to the baskets to facilitate the inspection and repositioning of the plates between the irradiation cycles and the accommodation of thermal expansion of the plates in the lateral direction. However, loosely inserted fuel plates have weak structural boundary conditions allowing for larger out-of-plane deflections caused by hydrodynamic loads exerted by the flowing coolant, as compared to those of fixed plates. Unexpected large deformations of plates occurred in several irradiation cycles that further resulted in a loss of cladding integrity. These deformations could not be attributed to a single source. This triggered a series of thermal hydraulic, structural, and fluid-structure interaction analyses aiming at understanding the observed phenomenon. The analyses revealed that, for a certain combination of unfavorable manufacturing and assembly tolerances, fuel plate edges could escape out of the slots in the irradiation basket due to the hydrodynamic load. Subsequently, the plate could become wedged inside the basket coolant channel opening. This resulted in reduced coolant flow and accelerated temperature increase and thermal expansion of the plate while under irradiation. This unfavorable feedback loop could then lead to excessive plate surface temperatures, deformed plates and cladding failure, as was observed in the experiments. These analyses not only provided a probable cause of the fuel plate failures, but also resulted in a new and improved design of the irradiation basket to avoid these issues in the future. In conclusion, a series of recent successful irradiations confirm that the sources of failures were identified correctly, and the implemented mitigations were adequate.

BR2↗
DOE OSTI2020

(U) Endpoint Energy and Scintillator Geometry Effects on the Swank Factor, Quantum Efficiency, and DQE(0) for High-Energy Radiography

High-energy radiography is used to image imploding materials to better understand weapon design and performance. The Enhanced Capabilities for Subcritical Experiments (ECSE) is a new facility proposal that aims to collect radiographic images of nuclear material. As part of the facility design, we aim to optimize data quality and radiographic performance by investigating different detector designs. We addressed design decisions by simulating different scintillator designs using M CNP6 and calculated the quantum efficiency, Swank factor, and detective quantum efficiency at zero-frequency (DQE(O)). First, we investigated the effects of the x-ray endpoint energy on the detector response. We generated three x-ray spectra with endpoint energies of 20 MeV, 22 MeV, and 24 MeV. The three raw spectra were filtered using the Dual-Axis Radiographic Hydrodynamic Test facility (DARHT) line-of-sight materials along with 1) flat field filtration using 7 cm tungsten alloy in the bullnose and 2) an FTO with 4 plates. The scatter-to-direct radiation ratio was much larger for FTO with 4 plates (50-60%) compared to the flat field with 7 cm of bullnose material (8%). We used these filtered spectra to calculate the detector response for the original DARHT segmented scintillator design. We found that the endpoint energy and filtration had a negligible effect on the detector response. The quantum efficiency was 0.63, the Swank factor was 0.84, and the DQE(O) was 0.53 for all six spectra.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

AX Farm and A Farm Third Retrieval Technology Chemical Dissolution Options Evaluation

In response to DOE-ORP direction to prepare a Practicability Evaluation for Waste Tank AX-102, and to address the Washington State Department of Ecology recommendation to evaluate the use of acid reagents for chemical dissolution, an Integrated Project Team (IPT) consisting of retrieval, process chemistry, corrosion, closure and laboratory subject matter experts was assembled to evaluate chemical dissolution options. This document provides a summary of these efforts and is intended to aid in the evaluation and third retrieval technology decision process not only for AX-102, but for all the AX and A Farm tanks, since the tanks contain similar waste and are flat-bottomed with uneven bottom plates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Numerical Simulations of Flow-Induced Deflections in MITR LEU Fuel Plate Due to Channel Size Disparity

The hydromechanical stability of the fuel plates in parallel coolant channels of a Materials Testing Reactor (MTR) fuel element design is of great importance to the safety of research and test reactors. Previous analytical, experimental, and numerical efforts focused on parallel channels with the same or similar size; also, in the prior numerical simulations, the fuel plate was often assumed to be perfectly flat. This work presents the results of a fluid-structure interaction simulation performed to evaluate the flow-induced deflections of the fuel plates in the low-enriched uranium (LEU, <20 wt% 235 U) fuel element design for the conversion (from highly enriched uranium) of the Massachusetts Institute of Technology Reactor (MITR-II, also referred to as MITR). Various manufacturing and assembly tolerances of the MITR LEU elements are considered in the analysis, and the effects of channel size disparity, nonideal plate shape, and flow rate uncertainty are investigated. Results show that, for all cases analyzed, the deflection occurs toward the larger channel, and the change in any channel stripe remains small (less than 0.021 mm) compared to fabrication tolerances. In addition to simulation work, a hydraulic performance test of the MITR LEU fuel element is currently planned to support conversion to the use of LEU fuel.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods

The three involute plate research reactors RHF, HFIR, and FRM II have expressed an interest in using computational software to carry their steady-state safety analysis. Since these tools represent a significant departure from the methods used currently (one-dimensional), the acceptability of the new approach by regulators requires thorough verification and validation of these tools. Therefore, Argonne National Laboratory and the three involute-plate reactors formed an informal group called the Involute Working Group aiming at qualifying computational tools to perform steady-state safety analysis. The present report focuses on a comparison of finite volume and finite element methods to model solids in fluid-structure interaction problems with the goal to estimate the coolant flow-induced fuel plate deflections obtained with the two methods. The finite volume method will be obsoleted in STARCCM+ by the end of 2021, nevertheless, this evaluation is important because the method was used by ANL researchers to model the response of the fuel plates, despite its drawbacks, which are discussed in the report. It was essential to check how those estimates compare to the results obtained with the finite element method that is considered superior for structural analysis. Various geometries, i.e., flat, cylindrical and circle-involute fuel plates, as well as coolant flow speed, were considered. The comparison shows that, independently of the plate geometry, the finite volume method significantly underestimates the deflection as compared to finite element method for coarser meshes. When the discretization is developed as a result of a mesh sensitivity study using finite element method, the result obtained using finite volume method can be a few times smaller than the corresponding finite element method solution. A code-to-code comparison , between STAR-CCM+ and LS-DYNA was included in the analysis. Within the LS-DYNA models, two types of finite element formulations were used: solid and shell finite elements. Mesh sensitivity study showed that both approaches converge to a similar value that was obtained with STAR-CCM+ finite element solver. The evaluation of the computational solvers was extended by adding two benchmark cases from the STAR-CCM+ Verification Suite and presented in the Appendix A. The selected cases are: (1) bending of a cantilever beam under external load, and (2) cylindrical shell deformation analysis, known in the literature as ‘Scordelis-Lo roof’. The problems were solved with finite volume, and finite element methods, and the results confirmed the previously discussed findings. The analysis shows that the finite element solver is superior to the finite volume solver in terms of representation of model geometry and estimating the structural behavior of fuel plates. Depending on the ratio of the load to the flexibility of the plate, the finite volume solver can greatly under- or overestimate the structural response if a very carefully selected mesh is not used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Sizing comingled CF/PA 6 fibers with cellulose nanofibrils for enhanced performance properties

Compatibility between the reinforcing phase and the polymer matrix is critical to achieving the desired mechanical and thermal performance of composite materials. Several mechanisms can enhance this interfacial interaction, including surface treatments (e.g., oxidation, plasma, or irradiation), in-situ nanoparticle deposition, and fiber sizing. Here, in this study, cellulose nanofibrils (CNF) were employed as a sustainable sizing agent to modify the interface in commingled carbon fiber (CF)/polyamide 6 (PA 6) yarns, in which CF and PA6 filaments are intimately blended to enable simultaneous consolidation. A 0.25 wt% CNF aqueous suspension was applied under bath sonication to ensure uniform dispersion and minimize agglomeration. CNF-sized and unsized yarns were used to fabricate unidirectional composite plates via filament winding on a flat mandrel, followed by compression molding. Scanning electron microscopy confirmed CNF presence on both CF and PA6 filaments. CNF-sized composites exhibited increments in interlaminar shear strength (ILSS) by 50%, flexural strength by 11%, and tensile strength by 2.5% compared to unsized composites. Thermal analysis showed minimal changes in degradation temperature and crystallinity. These findings demonstrate that CNF sizing enhances interfacial bonding and mechanical performance, offering a scalable and environmentally friendly strategy for thermoplastic composite manufacturing along with yarn/tow handleability.

Cellulose nanofibrils (CNF)↗
DOE OSTI2026

Effect of macroscopic surface defects on dynamic damage: An experimental and numerical study

This study examines the impact of macroscopic surface defects on the dynamic ductile damage behavior of polycrystalline metals using plate-impact experiments. Defects of various shapes (flat, round, and point) were manufactured on the free or impact surfaces of annealed copper specimens. The experiments were diagnosed with photon Doppler velocimetry measurements and soft recovery techniques. The experimental results revealed that defect shape and location significantly affect velocity–time profiles and void distribution. In order to understand the dynamics of shock propagation and corresponding ductile damage evolution within the target specimens, the impact experiments were modeled with a calibrated Tepla model, a dynamic ductile damage model for polycrystalline metals [Nguyen et al., Int. J. Solids Struct. 329, 113833 (2026)]. Overall, our resulting simulated velocity showed good agreement with measured velocity, and our simulated porosity distributions qualitatively matched experimental data. Based on our simulation results, defects on the free surface were found to distort rarefaction waves and therefore the corresponding spall planes. On the other hand, defects on the impact surface generated a delayed shock when the flyer plate and the defected target area were in contact, leading to distortion of the spall plane. The distortion of the spall plane resulted in a non-uniform distribution of voids within the defected specimens. Lastly, we examined the role of local work hardening due to the defect manufacturing process on the velocity and porosity distribution, using Tepla simulations with a simplified representation of local hardening. This investigation highlights the importance of defect geometry, location, and local hardening associated with defect generation in dynamic ductile damage processes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Image Alignment and Flat-Field Correction of Film and Computed Radiography Images on the LLNL Flash Testbed

Computed radiography (CR) imaging plates and film are used in HEAF firing tanks and in the NDE group. The imaging plates allow for the creation of high-resolution digital images with flash X-ray (FXR). A typical treatment of flash X-ray radiographs is flat-field correction, where the image from an experiment is normalized by a “flat-field” or “bright-field” image. This flat-field image is taken in an identical configuration to the experimental image, but without the object or experiment in the field of view (FOV). This treatment reduces spatial effects from the FXR spot size and detector misalignment, as each pixel value in the corrected image represents a ratio of collected radiation with the object in FOV to the collected radiation without the object in FOV. One challenge in the creation of a corrected image is the misalignment of the CR plate or film pack between capturing the flat-field image and the experimental image. Fiducial structures can remedy this issue. Small (3.18mm) stainless steel ball bearings serve as good fiducial structures due to their small size and high radiographic contrast. Spheres are view-agnostic geometry, always presenting a circular cross section no matter the orientation. This process was developed for images from the flash X-ray testbed. The flash testbed was used to compare the X-ray transmission at different thicknesses of aluminum and copper step wedges. Each step wedge section is a rectangular shape, so evaluation is made much simpler if the rectangles are not rotated with respect to the image. This alignment process aligns the object and flat-field images together and leaves the rectangles of each step aligned with the image.

36 MATERIALS SCIENCE↗