Building Computerized Tomography Tools for Precision Additive Manufacturing

Robert Panas | 16-ERD-006


Additive manufacturing (AM) promises to open up the design space for fabricating complex three-dimensional parts with predetermined spatially varying material properties. Existing AM systems, however, have failed to deliver on this promise due in part to the presence of uncontrolled process variations. Uncertainty in the parts-fabrication process makes it difficult to integrate AM processes into fabrication efforts for field-specific applications. Computerized tomography provides a viable alternative to the existing manufacturing metrology techniques because it is ideally suited to provide metrology for AM parts. However, the utility of computerized tomography is limited by the uncertainty in a part’s measurements. The goal of this project was to take the first steps to produce new and better data for precision computerized tomography metrology of AM parts by studying these measurement uncertainties.

Background and Research Objectives

X-ray computed tomography (XCT) is an optimal technique to provide dimensional metrology for AM due to its ability to nondestructively measure internal features and multi-material components (Thompson et al. 2016). XCT is generally used for medical imaging, material analysis, and (more recently) dimensional metrology (Kruth et al. 2011). However, the use of XCT in manufacturing metrology has been slowed due to a lack of international standards for metrological testing and uncertainty assessment. The lack of standards is partly due to the difficulty involved in calculating uncertainty for computed tomography (CT) measurements compared to traditional measurement systems, such as coordinate measuring systems (CMMs). XCT is prone to develop uncertainties in its multiple complex components, experimental setup, and tomographic reconstruction algorithms. Some sources of errors that occur during data acquisition and reconstruction include temperature, mechanical vibrations, stage alignment errors, source emission profile, and detector sensing variability. These sources come from the environment and from all system components (such as the x-ray source and detector). Additionally, CT systems are used in many different measurement tasks, which leads to widely varying uncertainties. Our goal was to develop a consistent analytical framework for formulating a total uncertainty budget for x-ray images as a first step toward a total uncertainty budget for CT reconstructions.

A standardized method for calculating uncertainty in XCT measurements does not exist. In its place, several different approaches are used in practice, including the following: (1) analytical expressions for uncertainty budgets, (2) theoretical methods using simulations, (3) experimental methods, (4) expert knowledge and assessment, and (5) a combination of these approaches (Joint Committee for Guides in Metrology 2008). A need exists for new procedures and standards, not just for the specification of accuracy, but also for the identification of individual error components (Kruth et al. 2011). The goal of our project was to meet this need by characterizing and quantifying uncertainty in the XCT system’s individual acquisition components via Signal Variation Flow Graph (SVFG) techniques. We developed a new state-of-the-art uncertainty model that uses the dominant factors in each data acquisition hardware and software component. We followed a system performance approach, similar to the one presented by Panas et al. (2012) to develop a statistics-based uncertainty model that incorporates the behavior, noise, and sensitivity associated with each element of the XCT system while covering the nearly full parameter space of the system. Modeling all the subsystem components of XCT systems yielded new information enabling rapid optimization of all elements, which resulted in better measurements for metrology applications.

We developed the precision CT capability in conjunction with the study of AM parts fabricated using two-photon polymerization on a Nanoscribe three-dimensional micrometer-scale printer. The Nanoscribe provided an application-specific test case for developing quantitative precision CT metrology for AM parts. In combination, these two systems demonstrated the coupled fabrication–metrology approach to achieving precision AM.

We studied the measurement uncertainties in CT metrology by examining variations in radiographs. We developed a complete generalizable analytical uncertainty-propagation model for x-ray radiography, which was based on a new technique for modeling uncertainty called a Signal Variation Flow Graph (SVFG). The SVFG model generated in this project allows users to capture, quantify, and predict variations occurring in a system, moving the system toward rigorous x-ray metrology. Our research is the first step toward achieving full uncertainty modeling of CT reconstructions and provides insight into improving x-ray attenuation imaging systems. We used the SVFG framework to generate a complete basis set of functions describing the major sources of variation in radiographs. Five models were identified, covering variations in energy, intensity, length, blur, and position. Radiographic system experiments were defined to measure the parameters required by the SVFGs. Best practices were identified for these measurements.

We also developed a series of measurements of the internal state parameters of the x-ray metrology system, which included the following experimental measurements:

  • source-map measurement
  • dark-field measurement
  • detector spectral-sensitivity measurement
  • temperature-variation measurement
  • thermal-sensitivity measurement
  • electrical voltage- and current-variation measurements
  • blur measurement
  • pixel-dynamics measurement
  • mechanical-vibration measurement
  • alignment-error measurement

Impact on Mission

Our project supports the NNSA goal to advance the science, technology, and engineering competencies that are the foundation of the NNSA mission. Specifically, it enhances Lawrence Livermore National Laboratory's core competencies in advanced materials and manufacturing, as well as high-performance computing and data science.


This project resulted in two specific improvements: (1) the improved operation of Lawrence Livermore National Laboratory's two-photon polymerization equipment to produce better nanoscale structures, such as targets for the National Ignition Facility, and (2) an improvement in the Laboratory's capability to measure and model x-ray metrology systems, such as blur reduction. This research is in the process of being integrated into both ongoing two-photon polymerization work as well as x-ray metrology research and modeling efforts. The x-ray metrology improvements are being further developed with DOE Strategic Partnership Projects funding.


Joint Committee for Guides in Metrology. 2008. "Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement." JCGM 100.

Kruth, J. P., et al. 2011. "Computed Tomography for Dimensional Metrology." CIRP Annals - Manufacturing Technology 60(2): 821–842. doi: 10.1016/j.cirp.2011.05.006.

Panas, R. M., et al. 2012. "Design of Piezoresistive-Based MEMS Sensor Systems for Precision Microsystems." Precision Engineering 36(1): 44–54. doi: 10.1016/j.precisioneng.2011.07.004.

Thompson, A., et al. 2016. "X-Ray Computed Tomography for Additive Manufacturing: A Review." Measurement Science and Technology 27(7): 072001. doi: 10.1088/0957-0233/27/7/072001.

Publications and Presentations

Cole, J. A., et al. 2018. "Surface Roughness Estimation by X-Ray Reflectivity." Proceedings of the 2018 Winter Topical Meeting of the American Society for Precision Engineering: Precision Engineering for Micro and Nanotechnology, Livermore, CA, February 2018. LLNL-ABS-742396.

Cuadra, J .A. and R. M. Panas. 2016. "A Systems Approach to Quantifying Uncertainty in X-Ray Systems for Metrology." ASPE 2016 Summer topical meeting on Dimensional Accuracy and Surface Finish in Additive Manufacturing, Raleigh, NC, June 2016. LLNL-ABS-692077.

——— . 2016. "Uncertainty Quantification of an X-Ray System Via a 0D Model Using a Systems Approach." Proceedings of the Annual Meeting of the American Society for Precision Engineering 31st Annual Meeting, Portland, OR, October 2016. LLNL-ABS-702326.

——— . 2017. "Uncertainty Quantification of an X-Ray Computed Tomography System." EUSPEN 2017 Special Interest Group Meeting: Additive Manufacturing, Leuven, Belgium, October 2017. LLNL-CONF-733872.

Cuadra, J. A., et al. 2017. "Error Budgeting Analysis for X-Ray Systems Using a 0D Uncertainty Model." Proceedings of the Annual Meeting of the American Society for Precision Engineering 32nd Annual Meeting, Charlotte, NC, October 2017. LLNL-CONF-738286.

——— . 2016. "An Uncertainty Model For X-Ray Computed Tomography Metrology Using A Systems Approach." JOWOG 39/ 46th Weapons Agency Nondestructive Testing Organization (WANTO), Sandia Laboratories, Albuquerque, NM, April 20116. LLNL-ABS-687039.

——— . 2016. "A Systems Approach to Quantifying Uncertainty in X-Ray Systems for Metrology." ASPE 2016 Summer topical meeting on Dimensional Accuracy and Surface Finish in Additive Manufacturing, Raleigh, NC, June 2016. LLNL-ABS-692077.

Dooraghi, A., et al. 2016. "Computed Tomography to Evaluate Large Area Projection Micro-Stereo-Lithography (LAPµSL)." ASPE 2016 Summer topical meeting on Dimensional Accuracy and Surface Finish in Additive Manufacturing, Raleigh, NC, June 2016. LLNL-ABS-687139.

Mohan, K. A., et al. 2018. "Modeling Blur in X-Ray Radiography Using a Systems Approach." 22nd Annual Signal & Image Sciences Workshop for the Center for Advanced Signal and Imaging Sciences, Livermore, CA, May 2018. LLNL-PRES-751512.

——— . 2018. "A Systems Approach to Prediction and Mitigation of Radiographic Blur." ASPE 2018 Summer Topical Meeting on Advancing Precision in Additive Manufacturing, Berkeley, CA, July 2018. LLNL-ABS-749879.

Saha, S. K., et al. 2016. "Part Damage Due to Proximity Effects During Sub-Micron Additive Manufacturing Via Two-Photon Lithography." Proceedings of the 2016 Manufacturing Science and Engineering Conference, MSEC2016, Blacksburg, VA, June 2016. LLNL-CONF-679759.

——— . 2016. "Process and Equipment Driven Limits to the Performance of Two-Photon Polymerization Based Submicron Additive Manufacturing." Proceedings of the Annual Meeting of the American Society for Precision Engineering 31st Annual Meeting, Portland, OR, October 2016. LLNL-ABS-687320 and LLNL-PRES-706346.

——— . 2017. "Effect of Proximity of Features on the Damage Threshold During Submicron Additive Manufacturing Via Two-Photon Polymerization." Journal of Micro and Nano-Manufacturing 5(3): 031002-031002–10. doi: 10.1115/1.4036445. LLNL-JRNL-694037.

——— . 2018. "Kinematic Fixtures to Enable Multi-Material Printing and Rapid Non-Destructive Inspection During Two-Photon Lithography." Precision Engineering 54: 131–137. LLNL-JRNL-736107.