title: Modulator design for x-ray scatter correction using primary modulation: material selection.
abstract: OBJECTIVE
  An optimal material selection for primary modulator is proposed in order to minimize beam hardening of the modulator in x-ray cone-beam computed tomography (CBCT). Recently, a measurement-based scatter correction method using primary modulation has been developed and experimentally verified. In the practical implementation, beam hardening of the modulator blocker is a limiting factor because it causes inconsistency in the primary signal and therefore degrades the accuracy of scatter correction.
  
  
  METHODS
  This inconsistency can be purposely assigned to the effective transmission factor of the modulator whose variation as a function of object filtration represents the magnitude of beam hardening of the modulator. In this work, the authors show that the variation reaches a minimum when the K-edge of the modulator material is near the mean energy of the system spectrum. Accordingly, an optimal material selection can be carried out in three steps. First, estimate and evaluate the polychromatic spectrum for a given x-ray system including both source and detector; second, calculate the mean energy of the spectrum and decide the candidate materials whose K-edge energies are near the mean energy; third, select the optimal material from the candidates after considering both the magnitude of beam hardening and the physical and chemical properties.
  
  
  RESULTS
  A tabletop x-ray CBCT system operated at 120 kVp is used to validate the material selection method in both simulations and experiments, from which the optimal material for this x-ray system is then chosen. With the transmission factor initially being 0.905 and 0.818, simulations show that erbium provides the least amount of variation as a function of object filtrations (maximum variations are 2.2% and 4.3%, respectively, only one-third of that for copper). With different combinations of aluminum and copper filtrations (simulating a range of object thicknesses), measured overall variations are 2.5%, 1.0%, and 8.6% for 25.4 microm of copper, erbium, and tungsten, respectively. With and without 300 microm of copper in the beam, the measured variations for 25.4 microm of copper, erbium, and tungsten, 1 mm of aluminum, as well as 406 microm of copper, are 1.8%, 0.2%, 5.5%, 1.9%, and 7.5%, respectively.
  
  
  CONCLUSIONS
  The spatial variation in the effective transmission factor of the modulator blocker due to beam hardening caused by the modulator itself reaches a minimum when the K-edge of the modulator material is near the mean energy of the spectrum. An optimal modulator material selection using the K-edge discontinuity is therefore proposed.
authors.affiliation: Department of Radiology, Stanford University, California 94305, USA. heweigao@stanford.edu
authors.forename: Hewei
authors.initials: H
authors.lastname: Gao
authors.forename: Lei
authors.initials: L
authors.lastname: Zhu
authors.forename: Rebecca
authors.initials: R
authors.lastname: Fahrig
mesh_terms: D016477:Artifacts; D017076:Computer-Aided Design; D004867:Equipment Design; D019544:Equipment Failure Analysis; D008420:Manufactured Materials; D008422:Materials Testing; D011856:Radiographic Image Enhancement / Q000295:instrumentation*; D015203:Reproducibility of Results; D012542:Scattering, Radiation; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000295:instrumentation*; D014159:Transducers