Correction of beam hardening in X-ray radiograms

Abstract

The intensity of a monochromatic X-ray beam decreases exponentially with the distance it has traveled inside a material; this behavior is commonly referred to as Beer-Lambert's law. Knowledge of the materialspecific attenuation coefficient µ allows to determine the thickness of a sample from the intensity decrease the beam has experienced. However, classical X-ray tubes emit a polychromatic bremsstrahlung-spectrum. And the attenuation coefficients of all materials depend on the photon energy: photons with high energy are attenuated less than photons with low energy. In consequence, the X-ray spectrum changes while traveling through the medium; due to the relative increase of high energy photons this effect is called beam hardening. For this varying spectrum, the Beer-Lambert law only remains valid if µ is replaced by an effective attenuation coefficient µ eff which depends not only on the material, but also its thickness x and the details of the X-ray setup used. We present here a way to deduce µ eff (x) from a small number of auxiliary measurements using a phenomenological model. This model can then be used to determine an unknown material thickness or in the case of a granular media its volume fraction.

Nondestructive Quantification of Heavy Elements Through the Analysis of Beam Hardening Artifacts Using Double-Exposure X-ray Computed Tomography: A Theoretical Consideration

“…This is analogous to the advantages of two-dimensional nuclear magnetic resonance (NMR) [25] compared to one-dimensional NMR, where using two dimensions significantly improves the ability to differentiate materials. However, a careful comparison between the image analysis methods proposed in this paper and the conventional double-exposure X-ray imagery [7,[26][27][28][29] should be performed in future. Additional directions for future research include the following four subjects.…”

“…(iv) This study is based on the physics of beam hardening that is derived from the non-linear relationship between the X-ray projection (logarithmic intensity of the attenuated X-ray) and the sample penetration depth [19]. Such non-linearity also occurs in X-ray radiography (not tomography) of a sample with an irregular shape [28]. Thus, the method of the present study could be potentially extended to the doubleexposure radiography [29], which is an economically more reasonable apparatus than tomography.…”

Granular Leidenfrost effect in microgravity

“…In fact, low frequencies are attenuated more than high frequencies such that the spectrum is shifted towards high frequencies. This phenomenon is referred to as beam hardening, and the measured thickness, , and, thus, the measured packing fraction in granular matter must be corrected for this effect [39,40].…”

“…To this end, (E, Z) in Eq. ( 1) is replaced by an effective attenuation coefficient, eff , which depends not only on the parameters of the radiographed material, but also on its thickness in the direction of the X-rays beam, , and on the specific properties of the X-rays and the detector used, for details see [39,40]. Again, stands for the extension of the granulate reduced by the voids between the grains.…”

Radiology and mammography standard X-ray spectra simulated with the Monte Carlo method

“…The Yu method, described in Equation 3, was initially established in high-energy beams, in the range of MeV; however, nowadays it is also used as a method of non-linear fit for beams with keV energies [12,13,14]. As seen in the literature, this method still produces residuals in a non-total uniform distribution [14], which could indicate the necessity of better fit models for attenuation curves in this low-energy range, producing smaller uncertainties to the parameters and for the results of 1 st HVL.…”