is also referred to as ideal or “good-architecture”
conditions for transmission measurements (cf.
LIU et al. (1988)). Eventually, the relevance of broad-beam geometry for radiation attenuation particularly considering scattering is discussed in Chapter II–2.5. At this, e. g., MIDGLEY (2006) determines the maximum angular width of a more or less narrow beam considering an ac-ceptable amount of scattered radiation reaching the detector.
Contrary to beam collimation by apertures, par-ticular methods exist to actually focus or quasi-parallel align divergent X-rays. Principles of re-spective types of X-ray optics are attributed to particular wave-like characteristics of X-rays (cf.
ALS-NIELSEN, MCMORROW (2011)). Correspond-ing components are, however, commonly more elaborate compared to focussing of visible light, since radiation properties differ remarkably ow-ing to the energy range. Whereas simplistic col-limation via apertures is commonly applied for convenient and robust purposes, special beam optics are primarily utilised in laboratory environ-ments for analytical issues. Besides refractive X-ray lenses (cf. BRUNO et al. (2005)), capillary optics are common for beam focusing or collima-tion for different analytical setups, where BJEOUMIKHOV et al. (2005) provide an appropri-ate overview.
Capillary optics as capillary X-ray lenses are part of X-ray optical systems and further specified in VDI/VDE 5575-3 (2018). Accordingly, capillary optics for either beam focussing or collimation are methodically based on total external reflec-tion on smooth inner surfaces. Total refecreflec-tion was already demonstrated by COMPTON (1923) and RINDBY (1986) practically studied X-ray in-tensity after transmission through capillary glass fibres. Besides single capillaries, polycapillary optics are henceforth discussed and, however, shortly denoted as capillary optics. They consist of numerous hollow glass tubes within an array of certain shape, where multiple total reflections along each of the capillaries occur. For compre-hensive fundamentals, reference is made to GAO, JANSSENS (2004). The most significant pa-rameter for practical application is the critical an-gle 𝜃c [mrad] for total reflection without intensity loss, which depends on radiation energy and can
be approximated for convenient glass capillaries via
𝜃c≈ 30
𝐸 [keV] (II-7)
resulting in 𝜃c≈ 1 … 3 mrad for 𝐸 = 10 … 30 keV, i. e., < 0.2°. Within the considered energy range, X-rays under grazing incidence with angles be-low 𝜃c are totally reflected, where multiple repe-titions yield quasi-parallel beams with the diam-eter of the capillary array and divergence angle corresponding to 𝜃c. Consequently, capillary op-tics feature energy-dependent transmission effi-ciency, where their individual application is des-ignated for a corresponding energy range. GAO, JANSSENS (2004) exemplarily present transmis-sion efficiency as function of radiation energy due to critical angle energy dependence. Here, transmission efficiency drops beyond particular energy, which can individually be designed to a certain extent via capillary geometry with param-eters according to VDI/VDE 5575-3 (2018). Ow-ing to energy dependence of 𝜃c, RINDBY (1986) concludes capillary optics as appropriate for fil-tering of high-energy X-rays of the applied spec-trum. However, radiation intensity can signifi-cantly be enhanced at certain distance from ra-diation source compared to simple aperture col-limation with equivalent geometry in conse-quence of diminished divergence of quasi-paral-lelly collimated radiation by capillary optics.
Eventually, collimating capillary optics yield quasi-parallel beams, where their respective performance is particularly characterised by - output beam dimensions,
- output beam divergence angle, and - intensity gain.
The latter compares radiation intensity of colli-mated beam by capillary optics toward simple apertures of the same dimensions.
Beyond predominant round or hexagonal geom-etries, where BJEOUMIKHOV et al. (2009) pointed out recent developments, flat capillary optics ex-ist as applied by BERGSTEN et al. (2001) and CROUDACE et al. (2006) obtaining emitted beam dimensions < 0.2 × 200 mm2. Notwithstanding hitherto progress, ENGSTRÖM et al. (1996) point out controversies and unsolved problems re-garding actual processes inside the capillaries.
14 1 X-ray measuring systems Section II
Amongst others, capillary optics were compre-hensively investigated by BALAIC et al. (1995), BILDERBACK, FONTES (1997), VINCZE et al.
(1998), and BJEOUMIKHOV et al. (2005). How-ever, the only wood-related utilisation of capillary optics for sophisticated tree-ring analysis of drill-ing cores are attributed to BERGSTEN et al.
(2001). Several investigations exist (refer to tree-ring analysis in Chapter II–3.1) by means of the consequently applied X-ray scanner model based on the device introduced by RINDBY et al.
(1989) whereas CROUDACE et al. (2006) and fur-ther researchers employ the respectively adapted device for sediment core analyses. Not-withstanding that, SOLBRIG et al. (2010) report on the adaption of a respective device with capillary optics for measurements of the vertical raw den-sity profile on WBCs. Regardless of advanta-geous flat beam collimation, capillary optics ac-cordingly require demanding and repetitive maintenance of beam alignment.
2 Radiation-matter interaction
2.1 General radiation attenuation fundamentals
The intensity of ionising radiation is well-known to decrease along the beam path of propagation through matter in consequence of interaction be-tween radiation photons and the atomic electron shell with various mechanisms, i. e., in general absorption and scattering in the energy range with respect to wood and WBC applications. This radiation attenuation, in turn, depends on differ-ent parameters regarding both radiation and ma-terial, i. e., in general energy characteristics as well as thickness (penetration distance), density, and kind of matter. Considering that, fundamen-tal physics are available in textbooks such as EVANS (1955) or KOHLRAUSCH et al. (1996).
Terms and definitions are furthermore provided in standards and guidelines such as DIN 6814-2 (2000), IEC 60050-881 (1983) or ISO 5576 (1997). However, the attenuation of initial radia-tion intensity 𝐼0 [a. u.] within material layers of the thickness 𝑡 [mm, cm, m] yielding the transmitted intensity 𝐼T [a. u.] of the very same radiation beam is commonly quantified by the linear atten-uation coefficient 𝜇lin= 𝜇 [cm−1, m−1] and basi-cally described by exponential intensity decre-ment following well-known Beer’s10 law of atten-uation
𝐼T= 𝐼0∙ 𝑒−𝜇(𝐸)∙𝑡 (II-8)
with the energy-dependent linear attenuation co-efficient 𝜇(𝐸) = 𝜇lin as measure for the diminu-tion of radiadiminu-tion beam intensity along propaga-tion path through the absorber. Owing to its den-sity dependency, 𝜇lin is commonly related to the density 𝜌 [g cm⁄ 3, kg m⁄ 3] of the considered ma-terial, where
𝜇lin=𝜇
𝜌∙ 𝜌 (II-9)
10 Note, the shortest designation of this historically evolved physical law (cf. PERRIN (1948)) was chosen.
11 Note, henceforth in this thesis, the unit m2⁄kg is exclusively utilised for the mass attenuation coefficient 𝜇 𝜌⁄ , due to corre-spondence to area and raw density units kg m⁄ 2 and kg m⁄ 3, respectively, commonly applied in wood industry, notwithstand-ing that cm2⁄g is commonly to be found in 𝜇 𝜌⁄ tabulations.
12 HOLLOWAY, BAKER (1972) report on origin of the barn as unit for cross-sections defined as 10−24 cm2.
defines the mass attenuation coefficient 𝜇 𝜌⁄ [cm2⁄ mg, 2⁄kg], which is preferably applied as material constant11 due to its theoretical inde-pendence from density. Consequently, eq. (II-8) turns into
𝐼T= 𝐼0∙ 𝑒−
𝜇
𝜌(𝐸)∙𝜌∙𝑡 (II-10)
and with 𝜌A= 𝜌 ∙ 𝑡 it becomes 𝐼T= 𝐼0∙ 𝑒−
𝜇
𝜌(𝐸)∙𝜌A (II-11)
where 𝜇 𝜌⁄ (𝐸) is still an energy-dependent ma-terial constant. Moreover, the mass attenuation coefficient is defined by means of the atomic cross-section12 𝜎𝑎 [m2, barn] as common meas-ure for interaction probability of a radiation beam with an absorber such that
𝜇 𝜌=𝑁𝐴
𝑀∙ 𝜎𝑎 (II-12)
with Avogadro’s number 𝑁𝐴 and molar mass 𝑀 [kg mol⁄ ], where the product is also referred to as total or macroscopic interaction cross-section Σ [cm−1, m−1] per mass unit (cf. KRIEGER (2012)). Note, beyond linear and mass attenua-tion coefficients, there exist the mass energy-transfer coefficient 𝜇tr⁄ [cm𝜌 2⁄ ] and the mass g energy-absorption coefficient 𝜇en⁄ [cm𝜌 2⁄ ]. g The values take energy transfer from radiation on the charged particles of the attenuating mate-rial into account These quantities are, thus, ra-ther of dosimetric interest and considered as less relevant in terms of material testing.
Radiation attenuation along the beam path through the object under investigation occurs due to interaction of photons with matter, where, e. g., TSOULFANIDIS (1995) fundamentally de-scribes the interaction processes and their indi-vidual dependencies on photon energy 𝐸 and atomic number 𝑍 of the material (referred to as low-𝑍 matter). Here, PARETZKE (1987) provides
16 2 Radiation-matter interaction Section II
the theory of radiation track structures, which is important particularly in case of material with low atomic numbers 𝑍. Therefore, GROSSWENDT (1999) presents a summary of “[…] the physical background of photon interactions with matter from the point of view of track structure formation in water”, and thus provides basic aspects of ra-diation propagation through matter. For detailed fundamentals of mechanics, kinematics, and cross-sections of radiation-matter interaction ref-erence is made to HUSSEIN (2007). Aspects of radiation propagation, interaction mechanisms, and attenuation as well as their dependencies are comprehensively reviewed and summarised in further textbooks such as
- ATTIX (2004),
- LEROY, RANCOITA (2004),
- ALS-NIELSEN, MCMORROW (2011), - HUSSEIN (2011),
- KRIEGER (2012), and - RUSSO (2018).
Beyond attenuation as consequence of radia-tion-matter interaction, FENGEL, WEGENER (1983) report on changes of structural, chemical, physical, and mechanical wood properties initi-ated by ionising radiation of rather high energy and dose rates, which has, however, no rele-vance in case of NDE owing to low dose rates and short irradiation duration, where no impact on transmission measuring results is expected.
In an energy range of 𝐸 = 5 … 100 keV with re-spect to wood and WBCs, three relevant interac-tion mechanisms occur, which are exemplarily il-lustrated in Figure II-3 for two distinct chemical elements, i. e.,
- photoelectric absorption (photo),
- coherent, i. e., elastic, scattering (coh), also referred to as Rayleigh scattering, and - incoherent, i. e., inelastic, scattering (incoh),
also referred to as Compton scattering, where only photoelectric absorption is consid-ered to remove the attenuated radiation portion from the beam of certain extent whereas scatter-ing solely changes the direction and partly the energy of the respective photons. Obviously, scattering occurs as an elastic (coherent) or ine-lastic (incoherent) process, where the prior is
as-sociated without and the latter with release of en-ergy from the incident and subsequently scat-tered photon (cf. DIN 6814-2 (2000)). Thus, the energy of scattered radiation 𝐸′ from incoherent Figure II-3: Total mass attenuation coefficients 𝜇 𝜌⁄ (𝐸) over radiation energy 𝐸 incl. single attenua-tion processes photoelectric absorpattenua-tion, coherent and incoherent scattering, as well as scattering (scat = coh + incoh) of the elements carbon 6C (top, equal to Fig-ure VII-30, with corresponding data in Table VII-4) and copper 29Cu for a practice-oriented energy range de-termined via XCOM (2010).
0.0001 0.001 0.01 0.1 1 10
0 25 50 75 100
E[keV]
tot photo
coh incoh
scat
C 0.004
0.035 0.066
22 24.5 27
0.001 0.01 0.1 1 10 100
0 25 50 75 100
E[keV]
tot photo
coh incoh
scat
Cu 0.004
0.035 0.066
22 24.5 27