Comparison between beam-stop and beam-hole array scatter correction techniques for industrial X-ray cone-beam CT

Nuclear Instruments and Methods in Physics Research B 269 (2011) 292–299

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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Comparison between beam-stop and beam-hole array scatter correction techniques for industrial X-ray cone-beam CT K. Schörner a,b,⇑, M. Goldammer a, J. Stephan a a b

Corporate Technology, Siemens AG, 81739 München, Germany Physik-Department, Technische Universität München, 85748 Garching, Germany

a r t i c l e

i n f o

Article history: Received 11 August 2010 Received in revised form 16 November 2010 Available online 26 November 2010 Keywords: X-ray cone-beam computed tomography Scatter Artifact removal Beam-stop array Beam-hole array Nondestructive testing

a b s t r a c t In industrial X-ray cone-beam computed tomography, the inspection of large-scale samples is important because of increasing demands on their quality and long-term mechanical resilience. Large-scale samples, for example made of aluminum or iron, are strongly scattering X-rays. Scattered radiation leads to artifacts such as cupping, streaks, and a reduction in contrast in the reconstructed CT-volume. We propose a scatter correction method based on sampling primary signals by employing a beam-hole array (BHA). In this indirect method, a scatter estimate is calculated by subtraction of the sampled primary signal from the total signal, the latter taken from an image where the BHA is absent. This technique is considered complementary to the better known beam-stop array (BSA) method. The two scatter estimation methods are compared here with respect to geometric effects, scatter-to-total ratio and practicability. Scatter estimation with the BHA method yields more accurate scatter estimates in off-centered regions, and a lower scatter-to-total ratio in critical image regions where the primary signal is very low. Scatter correction with the proposed BHA method is then applied to a ceramic specimen from power generation technologies. In the reconstructed CT volume, cupping almost completely vanishes and contrast is enhanced significantly. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction More than any other established non-destructive evaluation technique, industrial X-ray cone-beam computed tomography visualizes a sample’s internal structures precisely and allows for their inspection and quantitative analysis. Having become an increasingly important tool for industrial evaluation and inspection tasks, cone-beam CT has found many applications in different industrial fields [1], ranging from small parts (e.g. injector nozzles [2]) to rather large samples (e.g. turbine blades [3]). In cone-beam CT scanners, modern flat-panel detectors are used which provide complete 2D data acquisition at a time. While extending the volume coverage reduces the scan-time significantly, it also leads to an increased contribution of scattered radiation to the total detected signal [4–6]. Scattered radiation presents a major source of image degradation in cone-beam CT systems, resulting in artifacts such as cupping in homogeneous regions of material [5,6], reduction in contrast, and streaks between regions of high contrast [7,8]. Additionally, image noise increases when scattered radiation is detected [9]. Concerning dimensional ⇑ Corresponding author at: Corporate Technology, Siemens AG, 81739 München, Germany. E-mail addresses: [email protected], karsten.schoerner@ tum.de (K. Schörner). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.11.053

measurements, scatter negatively affects the surface detection step since it blurs sharp edges and renders flat surfaces bent [10]. Accordingly, for large-scale samples which are made of strongly scattering materials, these artifacts become even more severe [6]. In the field of medical CT, numerous approaches for scatter suppression as well as methods for scatter correction have been developed. The first aims at reducing the number of scattered photons reaching the detector, e.g. by use of an anti-scatter grid [9,11–13] or increased air gap [14,15]. While this can reduce the amount of detected scatter, it does not eliminate it completely. By contrast, scatter correction methods can be applied a posteriori to subtract the scatter contribution from the total detected signal. This requires precise knowledge of the scatter distribution in each projection. Several scatter estimation methods exist which can be divided into calculations based on analytical scatter models [16–19], Monte-Carlo simulations [4,20–22], and hybrid methods [23]. Analytical models rely on an approximated, global description of the physical scatter buildup. Point spread functions (PSF), either simulated or measured, are used for deconvolution of projections in Ref. [17]. Scatter distributions can be estimated by 2D convolution of weighted measured projections and scatter convolution kernels [19]. Monte-Carlo simulations are based on repeated tracking of individual photons undergoing scattering events. While presenting a powerful tool to explore scattering development (scatter

K. Schörner et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 292–299

production and buildup), the drawback of Monte-Carlo simulations lies in the statistical nature of the simulation. A high number of photons have to be simulated, implying time-consuming computation, in order to yield a sufficiently smooth scatter image which is a prerequisite for accurate scatter correction. Reducing computational effort can be achieved by only simulating a small number of photons and consecutively denoising scatter images using the Richardson–Lucy algorithm [21]. Monte-Carlo based scatter correction is investigated in Refs. [4,20] for medical scanners and in Ref. [22] for industrial cone-beam CT. Hybrid methods also aim at reducing computational efforts by calculating first-order scatter deterministically which is much faster than a Monte-Carlo simulation. Scattering of higher-order is either assumed to have spatially uniform distribution and therefore is taken into account by a uniform background, or it is Monte-Carlo simulated by a small number of photons [23]. Apart from those software-based approaches, we want to point out two experimental methods which aim at measuring the scatter signal at a number of sampling points: the beam-stop array (BSA) and a complementary method using apertures which we call beam-hole array (BHA) method. In the first, highly absorbing elements (tungsten or lead), mostly in a cylindrical shape, are placed in front of the object on a regular grid. Total attenuation of the primary signal behind these cylinders is assumed and therefore, any signal detected there can be attributed to be scattered radiation. In this projection the sampled scatter signal is measured. For CT, a second projection without the beam-stop array is necessary to obtain the total image consisting of scatter plus primary image. Beam-stop based scatter correction in the medical field is investigated in Ref. [24] and for industrial CT in Ref. [25]. The beam-hole array method is complementary to the beamstop array method as it aims at measuring the sampled primary signal in a first projection and the total signal in a second. Sampling the primary signal is achieved by means of a lead sheet with small apertures whereby only small areas of the object and the detector are irradiated. Subtraction of the primary from the total signal yields the scatter contribution. This technique has been explored in the medical field for densitometric measurements [26,27] and is advantageous compared to beam-stop based methods as it reduces dose exposition to the patient. Few to no publications exist which cover beam-hole array scatter correction in the industrial environment. In this work, we propose the estimation of scatter within a beam-hole array measurement in the industrial CT framework to be suited for e.g. series inspection tasks. In Section 2, both the BSA and BHA methods are presented from a theoretical point of view. Section 3 describes the imaging system specifications as well as the employed BSA and BHA. Section 4 presents two comparison measurements of BSA and BHA where geometric effects and scatter-to-total ratios are investigated. In Section 5, the proposed beam-hole array correction method is applied to a large-scale, strongly scattering, industrial specimen. In Section 6 we discuss differences between the two methods and evaluate their performance for different possible applications.

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However, several secondary events P scat also contribute to the total detected signal at each pixel i of the detector:

Ptotal ðiÞ ¼ Pprim ðiÞ þ Pscat ðiÞ:

ð1Þ

Pscat ðiÞ comprises all secondary signals registered at pixel i, consisting of (i) X-ray scattered radiation and (ii) non-X-ray scatter and spread effects in the detector (detector internal effects), termed PDet: ðiÞ. Scattered radiation contributions stem from different scatter mechanisms and consist of components originating from the object, from the environment and from detector internal scatter events:

  Pscat ðiÞ ¼ c IObj: ðiÞ þ IEnv: ðiÞ þ IDet: ðiÞ þ PDet: ðiÞ:

ð2Þ

Here, IObj: , IEnv: , and IDet: represent incident X-ray scattered radiation (Compton and Rayleigh scatter events) caused by the sample, by environmental structures within the CT lab, including the mechanical CT system structure, and by the internal mountings within the detector, respectively. P Det: ðiÞ finally signifies an additional signal term at pixel i coming from adjacent pixels which contribute by non X-ray scatter mechanisms such as optical light spread and electronic crosstalk (diode leakage) in the detector. In order to list all different sources of secondary signals, here we have strictly differed between their origins, i.e. scattered radiation and detector internal effects P Det: . However, in the BSA/BHA methods presented in the following, all secondary signals are detected simultaneously, i.e. the measured signals represent the total of all secondary signal contributions. Thus in the following sections of the paper, secondary signals are termed scattered radiation and total scatter signal interchangeably if not noted otherwise. Considering the beam-stop method which we use to measure the amount of scattered radiation, the beam-stop array is placed between source and object as illustrated in Fig. 1. The lead cylinders totally block primary X-rays, so Pprim ðiÞ from Eq. (1) vanishes for shadowed pixels i and for those the detected signal only consists of P scat comprising all secondary signal contributions (X-ray scatter and detector effects) at once. This represents a direct measure of the quantity P scat at a number of sampling points. In the inverse situation, it is possible to measure only the primary signal with the beam-hole array method at given sampling points. The BHA, a lead plate with small apertures, is placed in between source and object, as shown in Fig. 2(a). The sample is irradiated only at very few and small spots, consequently almost no scattering occurs from the object and environmental structures. The same holds true for detector scatter events since most of the sensitive area of the detector is kept dark. In this configuration, only P prim is detected behind the apertures.

2. Theoretical considerations Reconstruction algorithms are based on the assumption that only primary radiation Iprim reaches the detector and thus, ideally, is the only contribution to the detected signal Pprim ðiÞ ¼ c  Iprim ðiÞ. Here, c is a linear conversion factor between the incident radiation intensity and the output signal. For simplicity, we only consider a one-dimensional detector here, with i ¼ 1 . . . N pixel . Further detector rows can be treated analogously.

Fig. 1. Schematic illustration of the working principle for scatter estimation with the BSA. The BSA is placed between sample and source where it totally blocks incident primary radiation at a number of sampling points. Therefore, any signal detected in the shadows of the lead cylinders of the BSA is considered to be scattered radiation or detector internal effects. Scattered radiation can originate from the object (object scatter), from the environment (environmental scatter) and from detector internal X-ray scattering (not shown in this schematic). Additionally, also electronic effects such as crosstalk from adjacent pixels add to the detected signal. This yields the total scatter estimate at the given sampling points.

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Fig. 2. Schematic for scatter estimation employing the BHA method: (a) in a first measurement with the BHA in place, almost all incident primary radiation is blocked except for very few and small apertures in the BHA. At these sampling points, it is assumed that only the primary signal is measured. In the first approximation this is true, since in this configuration, both object scatter and detector internal scatter effects are low due to the strongly reduced incident radiation. Environmental scatter, as illustrated, is also strongly reduced since it is either blocked by the BHA or not incident at the sampling points. In order to estimate the scatter contribution at the given sampling points, (b) a second, open-field projection is necessary. Here, the total signal, consisting of scatter plus primary signal, is measured at the same points. Subtraction of the primary signal from the total signal then yields the scatter estimate.

Now, in a second projection without the BHA, the entire signal P total is detected, see Fig. 2(b). Considering Eq. (1), subtraction of Pprim from Ptotal yields the quantity Pscat again for the given sampling points. The beam-hole array method is considered an indirect method for estimating the scatter as it is a differential measurement. At this point, let us mention an important experimental difference between the two methods. For the beam-stop array method, an acrylic plate (PMMA plate) serves as support for the lead cylinders. This acrylic plate is fully irradiated, and hence, it presents additional material that absorbs and scatters X-rays. On the one hand, this leads to smaller primary, and consequently, total signals as compared to the beam-hole method where an acrylic support is not necessary. On the other hand, we expect an additional scatter contribution IPMMA from the acrylic plate, extending Eq. (2) in case of the beam-stop method into

 Pscat;BSA ðiÞ ¼ c IObj: ðiÞ þ I

Env: ðiÞ

 þ IDet: ðiÞ þ IPMMA ðiÞ þ P

Det: ðiÞ:

ð3Þ

Taking into account the former mentioned effect of attenuation caused by the acrylic plate only present in one of the two methods, it is necessary to introduce a quantity that renders the comparison measurements described in the following sections independent of this effect. We define the scatter-to-total ratio (STR), also denoted as scatter fraction, as the ratio of scatter signal P scat in a small circular region around pixel i on the detector to the total signal P total in an unobstructed-beam region (direct-beam), typically an outer region of the detector field where the object casts no shadow:

STRðiÞ ¼

Pscat ðiÞ : Ptotal ð direct-beamÞ

ð4Þ

With this definition, scatter fractions of both methods can be compared directly, even though their absolute signals (scatter and direct-beam) differ due to attenuation of the acrylic plate within the beam-stop method which is not present in the beamhole method. 3. Experimental setup and methods 3.1. Imaging system specifications Our cone-beam CT setup consists of an X-ray tube, a sample rotation table and a flat panel detector. The X-ray source is a microfocus transmission tube, model XT9225-TED manufactured by Viscom AG (Hanover, Germany). It is operated at 220 kVp, 320 lA

current and with prefilters of 3 mm copper and 0.5 mm tin employed in order to harden the spectrum. In this configuration, the focus of the tube is below 10 lm in diameter. The flat panel detector, a PerkinElmer XRD1621 AN14, is equipped with a DRZ-Plus scintillation screen; it has a resolution of 2048  2048 pixels with 200 lm pixel-size. The image is encoded in 16bit gray-values, frame times amount to 1.0 s here. Acquired images are all corrected for defect pixels and dark current as well as detector- and beam non-uniformity. The latter two are known as offset and (multi-)gain correction; all corrections are processed by the framegrabber board. 3D reconstructions are computed by a standard filtered-backprojection (FBP) algorithm which is implemented as a part of our own X-ray CT software. Here, a software-based correction of beam hardening effects (deterministic models of attenuation by step wedges for polychromatic spectra) is employed. Additionally, X-ray dose is measured for each projection in both beam-hole measurements (open-field and with BHA) with a dosimeter (Diados T11003, PTW Freiburg, Germany) installed between source and BHA but outside the field-of-view. This is necessary in order to detect fluctuations in the X-ray tube output and to compensate for them when subtracting the primary from the total signal in the BHA method. Therefore, all sampled measurements are normalized to a mean dose. Any uncompensated fluctuation here would lead to a deviation in the scatter estimate. 3.2. Definition of BSA and BHA In our setup, we use a commercially available beam-stop array produced by QRM (Quality Assurance in Radiology and Medicine, Möhrendorf, Germany). A matrix of 8  10 parallelly aligned lead cylinders with an interspacing of 20 mm is pressed into drilled holes in the support material, a 240  240 mm2 acrylic plate of 6 mm thickness. The lead cylinders are 3 mm in diameter and also 6 mm long, which yields an attenuation factor of 5  103 for 220 keV X-ray quanta [28]. Since the acrylic plate of the BSA absorbs and scatters X-rays itself, an acrylic plate without cylinders of same thickness has to be used in CT projections to be corrected with BSA measured scatter data in order to reproduce scatter conditions. A Monte-Carlo simulation was conducted to quantify attenuation and scattering of an acrylic plate with the specified dimensions placed 20 cm in front of the detector. All other X-ray parameters were chosen as specified in Section 3.1, including a polychromatic filtered X-ray spectrum, and the acrylic plate was

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(a)

1

10

(b) 1

11

11

21

21

31

31

41

41

51

51

61

61

71

71 0

20

40 mm

10

25000

0 0

20

40 mm

Fig. 3. Open-field projections with (a) BSA and (b) BHA. The geometric effect, by which off-centered lead cylinders are traversed by X-rays under a tilt-angle and their shadows are becoming larger whereas corresponding apertures are becoming smaller, can be clearly seen in the outermost cylinders (a) and apertures (b).

the only object included in the scenario. For the central detector region where simulated object scatter is maximal, attenuation amounts to 10.0% and scatter contribution results in a scatter-toprimary ratio (SPR) of 2.7% in this case. Being manufactured to order, the beam-hole array is a 6 mm thick plate of lead with apertures arranged in the same way as the lead cylinders are on the beam-stop array: apertures are also 3 mm in diameter and their spacing amounts to 20 mm. The total size of the BHA is the same as for the BSA for comparability. Attention has to be paid to dimensions and interspacings between lead cylinders and apertures, respectively, as well as to their number. Analysis of influence of aperture diameters and interspacings on the detected signal is reported in Refs. [26,27], a similar examination for BSA shadows can be found in Ref. [29]. In this work, the total shadowed area by the BSA lead cylinders amounts to less than 1.5% of the total sensitive area of the detector in a typical CT situation (same for BHA), so underestimation of scatter in this respect is negligible. 4. Comparison measurements

and less to environmental scatter, which is in full agreement with the results published in Ref. [25]. As presented in Fig. 4, the dependence of the scatter-total ratio (STR) on shadow size of the aperture/cylinder can be clearly recognized. For the central aperture (BHA) and cylinder (BSA), cast shadows are of the same size. Both methods yield nearly the same STR in this case. On the one hand, the more displaced a cylinder (BSA) is from the center (meaning its shadow size increases), the less the STR becomes. On the other hand, the contrary holds for the BHA method as the imaged apertures become smaller when increasing their tilt angle in respect to the traversing X-rays. In the BHA measurement, differences in the STR between apertures are greater than in the BSA measurement indicating that the STR is more accurately measured at small apertures and underestimated at bigger apertures whereas the BSA-based STRs are all underestimated tendentially. Smaller apertures in the BHA and smaller lead cylinders in the BSA would improve the accuracy of scatter estimation. However, the geometric effect always leads to underestimation of scatter with the BSA in off-centered lead cylinders whereas with the BHA method the accuracy of scatter estimation increases off-center.

4.1. Geometric effects In this initial comparison of both methods, no further object apart from beam-stop and beam-hole array, respectively, is imaged, see Fig. 3. At first, the BSA is placed at a source-to-object distance (SOD) of 50 cm with the detector at a source-to-detector distance (SDD) of 100 cm. In this configuration, the outermost lead cylinders are traversed by X-rays with a tilt angle of 12° and thus will be image tilted and with a bigger shadow than the central cylinder, see Fig. 3(a). Without any further object an open field image is taken. Exactly the same parameters, including SOD and SDD, are used in projections with the beam-hole array, see Fig. 3(b), and openfield projections. Additionally, X-ray dose is measured for each projection with a dosimeter as described in Section 3.1. For both methods, the scatter-total ratio, see Eq. (4), is calculated. In this step, P scat is determined by taking the mean gray-value in a small circle area (diameter of 10 pixels) in the shadow of a cylinder, or aperture, respectively, whereas the total incident signal is taken as mean gray-value from an open-field region. Measured scatter-total ratios for each cylinder and aperture are displayed in Fig. 4, where the numbering is as given in Fig. 3. The two measurements show that scattering occurs and amounts to 11–14% of the total incident signal, even in this situation where no object is imaged. The scatter signal is due to detector scatter

Fig. 4. Comparison of BSA and BHA method without any sample: the STRs are shown for each BHA aperture and BSA cylinder (numbering is as in Fig. 3). For central apertures and cylinders, STRs of both methods are about the same. Offcentered apertures have greater STRs than their BSA counterparts which is due to a geometric effect illustrated in Fig. 3.

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In order to reduce this purely geometric effect, either a focused BSA/BHA with lead cylinders/apertures aligned parallel to the Xrays is used or the tilt angle is reduced by placing the BSA/BHA very close to the detector. The first is possible but limited to certain imaging geometries (SOD, SDD) thus representing a non-universal beam-stop array which is also more difficult to manufacture. Placing the BSA/BHA closer to the detector often is undesirable since it limits magnification, and additionally, for the BSA as will be shown in the next section, it also leads to a greater amount of scattered radiation and therefore to higher STRs.

4.2. Scatter estimates from complete CT-scan Now, the scatter-total ratios (STRs) of both methods are examined in an imaging situation with a large-scale phantom sample, as can be seen in Fig. 5 where the first projection of the sample plus beam-stop array is displayed. The dimensions of the aluminum block are 185  185  40 mm3; thin notches are incised laterally. In this comparison measurement, the object is at SOD = 65 cm, the detector at SDD = 100 cm, and the BSA/BHA is placed right in front of the object, i.e. at xBSA=BHA ¼ 55 cm, as shown in Fig. 5. The scatter measurements are conducted in the same way as described above, the object is rotated and a total of 360 projections in 1°steps are recorded. In Fig. 6, the STRs of the central aperture and cylinder (no. 41) for both the BHA and BSA methods are shown as a function of projection angle. For the central cylinder and aperture, the geometric effects discussed above are negligible. In all projections, the measured STR is larger when using the BSA, a fact we ascribe to increased scattered radiation caused by the PMMA plate, cf. Eq. (3). Particularly, the difference in STRs between the two methods is the greatest in those projections where the object is rotated 90° and 270°, respectively, i.e. where scattered radiation from the PMMA plate is less hindered by the object to reach the detector. These projection angles are important in respect of being maximally scatter- and noise-reduced since the primary signal is low at these length scales (minimally 185 mm of aluminum) when using a 225 kV X-ray tube as in our setup. Analogously to the examination at the center, Fig. 7 presents the measured STRs at the outermost corner, i.e. for cylinder and aperture no. 1 in the top-left corner, in dependence on the projection angle. Here, the geometric effect is maximal and leads to the

Fig. 6. Central cylinder/aperture (no. 41) which is shadowed by the sample in all projections: the measured STRs are permanently higher within the BSA measurements which is due to a greater amount of scattered radiation by the PMMA plate (directly and indirectly scattered onto the detector).

Fig. 7. Top-left cylinder/aperture (no. 1) which is direct-beam in all projections: The measured STRs are permanently larger within the BHA measurement which is due to the geometric effect (smaller size of aperture).

greatest deviation of about 0.03 in the scatter estimates between the BSA and BHA method. The scatter estimates by the BHA method in both figures show a higher noise level than those measured with the BSA, which can be clearly recognized in Fig. 7 for the STR of a permanent open field region. Since in the BHA method two potentially high-level signals are subtracted,

Pscat;BHA ðiÞ ¼ Ptotal ðiÞ  Pprim ðiÞ;

ð5Þ

the corresponding noise level, given by

DPscat;BHA ðiÞ ¼

Fig. 5. First projection (0°-projection angle) of large-scale aluminum sample and BSA. Lateral and top lead cylinders are exposed to the direct-beam in all projections, whereas the central cylinder is always shadowed by the sample. STRs of both topleft (no. 1) and central (no. 41) cylinders/apertures are compared in Figs. 6 and 7.

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 2 ðDP total ðiÞÞ þ DP prim ðiÞ ;

ð6Þ

is consequently higher than in the situation of a BSA measurement where the scatter estimate is measured directly and the signal itself is much lower (noise level is assumed to be dominated by quantum noise, i.e. Poisson-distributed and thus proportional to square root pffiffiffiffiffiffiffiffiffi of signal, here Pscat ). In order to improve the signal-to-noise ratio (SNR) for BHA-measured scatter estimates, one has to average over

K. Schörner et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 292–299

297

Fig. 8. Comparison of BSA and BHA method for the first projection (i.e. angle 0°). Scatter-total ratios are shown for each cylinder and aperture of BSA/BHA. Amount of scatter is larger for object covered sampling points within the BSA measurement.

more projections which is more time-consuming but poses no general constraint to this method. In Fig. 8, the STR is reported for all cylinders and apertures within the first projection (projection angle 0°). A greater amount of scattered radiation caused by the PMMA plate in the BSA method is observed in all cylinders’ shadows that cover the object in the projection. On the contrary, underestimation is reduced in the apertures which are direct-beam when using the BHA method (i.e. apertures 1–10, 18, 19, 27, 28, 36, 37, 45, 46, 54, 55, 63, 64, 72). Also, the relevance of internal detector scatter can be deduced from this figure. The measured scatter level (for both the BHA and BSA method) is significantly higher in regions of unobstructed impinging radiation than in regions which are covered by the sample (attenuated X-rays), a finding already presented in Ref. [25]. This is contrary to MC-simulations which we conducted considering only object scatter. In such a simulated scenario, the maximum scatter level is found at the center of the object.

Fig. 9. Photograph of the tomographed ceramic specimen employed in power generation technologies. Samples, such as the one shown here, are to be inspected for inner cracks, voids, and dimensional tolerances with CT. The specimen’s dimensions are 192  190  38 mm3 .

5. Beam-hole array scatter correction applied to CT of a ceramic specimen As a first demonstration of the proposed scatter correction, the beam-hole array method is applied to a highly scattering, industrial sample, a ceramic specimen from the field of power generation technology. A photograph of the tomographed sample is presented in Fig. 9. The specimen’s dimensions are 192  190  38 mm3, it is manufactured from an aluminum-oxide based ceramic. Samples, such as the one examined here, are to be inspected for inner cracks, voids, and dimensional tolerances with CT. As for the actual CT parameters, SOD was set to 80 cm and SDD to 100 cm. In the beam-hole array measurements, the latter was put in front of the specimen at xBHA ¼ 60 cm. The specimen itself was mounted on the rotating table as shown in the 0°-projection in Fig. 10, i.e. tilted by approximately 45°. By this tilting, the top and bottom parts of the specimen expose less material to the imaging X-ray cone-beam for CT and are thus better penetrated within projections where long penetration lengths occur in the central region of the specimen, i.e. around angles of 90° and 270°. For these projections, this results in relatively high primary signals in the mentioned parts of the specimen compared to a situation where it is not tilted and penetration lengths are critical yielding only extremely small primary signals for the entire object.

Fig. 10. First projection (0° angle) from the CT of the ceramic specimen demonstrating the tilted mounting in order to have shorter penetration lengths in the top and bottom part of the specimen, indicated by red boxes. Here, primary signals are relatively high and these parts can be reconstructed – after correction for scatter and beam hardening – with very little artifacts. In the central part, however, penetration lengths become too long around 90° and 270° projections to measure a reasonable primary signal. Consequently, this part shows severe artifacts in the reconstructed CT volume. The blue dashed line indicates the position of the reconstructed slices presented in Fig. 12. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The tilted imaging configuration in combination with our 225 kV X-ray tube allows for good inspection of at least the regions of interest indicated in Fig. 10. A second CT with the specimen rotated by 90° would be necessary to also tomograph the remaining regions of interest, i.e. the other two notch-halves. Generally,

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Fig. 11. (a) Interpolated, smoothed scatter image for first projection (0°) and (b) the corresponding line profile (red graph). Scatter signals are a direct function of primary signals (blue graph). The SPR (green) calculates to 78% in the object center. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 12. (a) Slice z = 172 (cf. Fig. 10, blue dashed line) from the scatter-corrected CT-volume of the ceramic specimen, (b) shows the corresponding slice from the uncorrected CT-volume. Corresponding line profiles are indicated and shown in (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

irradiation can be improved and penetration lengths increased when employing X-ray tubes with higher voltage. In order to generate scatter images, a total of 3  2 equidistantly horizontally and vertically shifted BHA-sets, each comprising 360 projections, were recorded. Shifting the BHA yields a finer sampling grid of primary signals which is necessary to detect the high spatial-frequency content in the scatter distribution of the image, a fact which was pointed out in Ref. [25] using a BSA. The total signals at the given sampling points were extracted from the original CT projection set, whereby scatter estimates according to Eq. (5) can be calculated. For all measurements, dose was recorded as described in Section 3.1 in order to compensate dose fluctuations. Scatter images were generated by a bicubic spline interpolation algorithm in Matlab and smoothed by a median filter afterwards. In Fig. 11, both the interpolated scatter image for a projection angle of 0° and the corresponding line profile – as indicated in the scatter image – are shown. As can be seen in Fig. 11(b), the scatter fraction is a direct function of the primary signal, including high spatial frequencies where object edges are present, see [25]. The calculated

scatter-to-primary ratio (SPR) along the given line profiles is 75– 80% in central regions covered by the object, whereas it can exceed 450% in critical projections around 90° and 270°. We then subtract the interpolated, smoothed scatter images from the original CT projections. Two different volume reconstructions are then performed, one with the uncorrected projections and the other with the scatter-corrected projections. In both reconstructions, a beam hardening correction is performed as described in Section 3.1. For comparison, a 2D slice extracted from each of the volumes is presented in Fig. 12(a) for the beam-hole array scattercorrected case and in Fig. 12(b) for the uncorrected. While the uncorrected volume shows strong artifacts such as cupping and streaks, particularly dark ones along the corners and a bright one along the notch region, these vanish almost completely in the scatter-corrected volume. Also, overall contrast is enhanced as can be seen in the corresponding line profiles in Fig. 12(c). Here, e.g. in the mid region, local contrast of the void (see red arrows) is increased from 70% to more than 94%. This will also improve the ability to detect smaller cracks within the reconstructed notch regions

K. Schörner et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 292–299

of the specimen. Furthermore, reconstructed voxel gray-values in the uncorrected volume outside the object are not zero as they should be, cf. the long tail of the line profile for the uncorrected volume inside the notch region, see Fig. 12(c). For dimensional measurement tasks, this leads to deviations in the surface detection process. Finally, edge sharpness is improved significantly in the scatter-corrected volume, see Fig. 12(c).

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effort is worthwhile in series measurements since the beam-hole method helps reducing overall scatter and noise by not having to insert an additional acrylic plate as with the beam-stop method. Acknowledgements We would like to thank Peter Böni of Technische Universität München for helpful discussions.

6. Conclusions References In this work, a scatter correction method employing a beamhole array (BHA) has been proposed for large-scale samples in the industrial field which are strongly scattering X-rays. This method represents an alternative to the more common beam-stop array (BSA) correction method. Although equivalent from a theoretical point of view, in practice the BHA and BSA methods differ in certain aspects which have been addressed in this paper. Firstly, the different geometric behavior for apertures (BHA) and lead cylinder shadows (BSA) of same size leads to a more accurate scatter estimate within the beam-hole method, especially in off-centered regions. Secondly, no additional scattering material as in the beamstop method has to be used, which was shown to reduce overall scatter. This is important for large industrial samples where primary signals are often weak in certain projections and where it is thus preferable to reduce noise as well as scatter-to-primary ratios. An example for such conditions is a ceramic specimen from the power generation technology field. For this specific sample, we have proved successful application of the beam-hole array method. Additionally, the CT was also beam hardening corrected and the reconstructed CT volume allows for inspection tasks in the regions of interest, i.e. the notches of the specimen. We think beam-hole array correction procedures are particularly suited for series inspection tasks. In order to create accurate scatter images, a greater effort than with a beam-stop array is needed, since scatter estimation with the BHA represents an indirect method and thus is more sensitive to dose fluctuations as well as quantum noise within the image. For this reason, dose recording and a higher level of averaging are necessary. An initially greater

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