Characterization of resolution performance of novel high energy X-CT : eXTRACT

Characterization of resolution performance by means of MTF for a newly developed high-energy and high-resolution X-ray CT system : eXTRACT is performed. eXTRACT has shown the unique characteristics such as the averaged X-ray energy of 1 MeV and demonstrates the structural resolution performance of 0.1 mm in case line and space periodical structure built by metal and air were scanned. The current study reports the characterization result of the modulation transfer function (MTF). A cylindrical feature made of aluminum is scanned and the MTF is evaluated under several different modes of scan on eXTRACT. A series of experimental data show almost satisfactory results in the spatial resolution performance except for the mode of operation supposed to realize the highest resolution performance. The source of the imperfect performance is identified and solved by redesigning the supporting structure of tungsten wire target built in the X-ray source. The improvement in the resolution performance is experimentally verified. It realizes 29.2 line pair par cm when 1/3 and 3/8 offset scan mode is applied on field of view size of 300 mm in the diameter.


Introduction
Technical trend in coordinate metrology has shifted from the discrete point measurement using conventional tactile CMMs to point cloud measurement realized by a huge number of points using e.g.optical scanners.Furthermore, X-ray computed tomography (X-ray CT) has attracted interest of manufacturing industry today to evaluate not only the external geometrical features but also the internal features of the products which cannot be measured by the existing technologies.To meet the requirements to measure larger objects, X-ray source having significantly higher penetration capability is required.A linear electron accelerator (linac) has been used for this purpose and classified as high energy X-ray CT.Even tomographic scan of a whole body of automobiles is trialed by increasing the acceleration voltage [1].In addition to the penetration capability, the performance to resolve fine structure of the object is also demanded.Accounting for the demand, authors have developed a high-energy high-resolution X-ray CT named eXTRACT realizing both the penetration capability and the resolution performance at the same time as illustrated in Fig. 1 by a rectangular area bounded by red solid line, which is difficult for existing X-ray CT.To overcome the inevitable limitation, authors has adopted a new X-ray source based on bremsstrahlung utilizing a target with the dimension of 100 µm in the diameter equivalent to the intended focal size of the X-ray.By limiting physical dimension of the target down to the intended focus dimension, X-ray focal size equivalent to the dimension of the target is realized in principle.However, adoption of smaller size of the target for electron linac results in difficulties in the other technical aspects.I.e., majority of electrons may not hit the target and discarded uselessly, and the discarded electron may generate unintended X-ray when it hits other part of the X-ray source.Authors intend to solve the above problem by adopting a compact sized synchrotron which works as an electron accumulation ring.The synchrotron with the circular electron orbit is used to accumulate and re-use electron, however generation principle of X-ray does not rely on the synchrotron radiation but on the bremsstrahlung.The X-ray source is called as Mirrorcle [4] and continues the development.A 5 µs electron pulse is bundled into 10 pulses signals.The bundled signal is generated 300 times a second and used as the master sampling signal for the developed X-ray CT system.

X-ray detector
The developed X-ray system is designed as the fan beam CT with the horizontal beam angle width of ±15 degree.The X-ray detector having the structure of a linearly allocated one-dimensional detector allay is developed.The 970 channels of detector are positioned with equi-angular distanced each other across the horizontally formed X-ray fan beam.The respective detector made of Silicon semiconductor is designed by sufficient longitudinal dimension to keep sensitivity even for high energy X-ray in the order of a few MeV.Once X-ray plunges in the X-ray detector, a corresponding electrical charge may be generated by a certain probability.The charge accumulated during bundled 10 pulses of X-ray is converted from current to voltage, and then A/D converted by the front end signal processor closely located with the X-ray detector to enhance the signal-to-noise ratio.The digital data is transmitted to the data processing PC.

Image reconstruction
The modified offset scanning method [5] with two different mode operations is adopted while conventional filtered back projection algorithm is applied to perform image reconstruction.The operation mode-1 offset scan is performed with 1/4 pixel offset of the rotary stage in the transversal direction against the center position of X-ray line detector.Sinogram is collected for 360 degree rotation of the rotary stage.The image reconstruction result shows two times higher resolution than the conventional method in theory.The operation mode-2 offset scan is performed with 1/8 as well as 3/8 pixel offset of the rotary stage in the transversal direction against the center position of X-ray line detectors.Sinogram is collected for 720 degree rotation of the rotary stage.The image reconstruction result shows four times larger pixel number in theory than the conventional scanning method.Unintended systematic variation, e.g.deviation caused by the X-ray source in time, inhomogeneous sensitivity of the X-ray line detector, and so on, are software compensated in advance.

Initial testing of MTF on eXTRACT
MTF is evaluated in accordance with ISO 15708-1:2002 [6].
A series of experimental studies is performed by introducing a cylinder object having the nominal diameter of 50 mm made of aluminum.The cylinder is scanned by eXTRACT under respective scanning modes and the derived MTF is experimentally demonstrated.
A simulation study is also performed before building eXTRACT to predict its reachable performance.The simulation is fully conforming to ISO 15708-1:2002, clause 7.3.A one dimensional Fourier transform approximating MTF of a point spread function at a boundary of a rotation symmetric object such as a cylinder is expressed by multiplication of following terms: ・ Fourier transform of the convolution function of filtered back projection, ・ Fourier transform of width of X-ray beam emitted from X-ray source, ・ Fourier transform of data integration factor corresponding to evaluation of incremental moving of X-ray source, ・ Fourier transform of linear interpolation function in the image reconstruction, and ・ Fourier transform of displaying function corresponding to interpolated value determination.Figure 4 and 5 show the evaluation result of MTF, the former obtained by 1/4 offset scan mode with the pixel number of 3,000 by 3,000 results 16.8 line pair par centimeter, the former obtained by 1/8and 3/8 offset scan mode with the pixels number of 4286 by 4286 pixels results 25.9 line pair par centimeter.The former experimental result on 1/4 offset scan mode conforms well with the corresponding simulation result.However, the latter does not.The experimental result implies that a significant error source should exist with in eXTRACT.

Problem identification and enhancement of resolution performance
A successive radiographs observation is made for identification of the error source by locating the cylinder object described in the previous section at the fixed position in respect with the X-ray source and the X-ray detector.Distance between the cylinder object and the focal point of the X-ray source is set to 280 mm that is a position practically possible to realize the highest optical magnification.Stability of radiographs which might influence score of MTF is evaluated by center position of two boundaries between the cylinder and the air projected on respective radiographs.Figure 6 shows a record of the center position of the cylinder observed on the X-ray detector.The X-ray source is turned on from the cold state at 0 minute of the abscissa of Fig. 6.The X-ray source is turned on three times from 0 to 53 minutes, from 71 to 128 minutes, and from 142 minutes to 176 minutes.The X-ray source is turned off two times from 53 minutes to 71 minutes, and from 128 minutes to 142 minutes.Lack of experimental data between 22 minutes and 34 minutes is caused by an accidental failure of data collection during the experiment.

Thermal drift of target
It is evident that the radiograph drifts in the order of 0.1 mm by spending more than hour.The initial observation results imply significant spatial drift in position of tungsten wire target.The tungsten wire is supported by a target supporting frame (TSF) designed to have the effective length of 250 mm and made of SUS316 having coefficient of thermal expansion of 16x10 -6 .
The TSF is installed in vacuum chamber where circular electron orbit is realized within the X-ray source.It is believed to be natural to consider the TSF is heated up while X-ray is turned on, although cooled down while X-ray is turned off.Accumulation of heat into TSF while X-ray is turned on occurs only by incoming heat caused by hit of electron or X-ray to the TSF.Accumulation of heat into the TSF does not take place while X-ray is turned off.On the other hand, heat dissipation from the TSF to elsewhere driven by spatial temperature gradient between the TSF and elsewhere, independent from turned on/off state of X-ray source.
A simple simulation model as schematically drawn in Fig. 7 is built based on the above mentioned consideration on heat transfer relative to the TSF.It assumes: ・ Heat dissipation from the TSF is linearly dependent of temperature raising of the TSF, ・ Heat accumulation to the TSF is made by balance of incoming heat and the above heat dissipation, and ・ Incoming heat while X-ray source turned on is constant.The model and the boundary conditions presented in Table 2 is applied to the experimental data depicted on Fig. 6.It yields dissipation heat of 1.8 J/(K min.)and incoming heat of 76 J/min.Figure 8 depicts target drift experimentally measured versus that derived from the simulation result.Target drift shown in Fig. 8 is calculated by the source-object-distance of 280 mm and the source-detector-distance of 2033 mm.It is fair to say the simple simulation model describing heat transfer of the TSF is able to approximate target drift observed by the X-ray detector of eXTRACT.

Alternative material choice of target supporting frame
Thermal expansion of TSF plays dominant role on target drift observed by X-ray detector.The material property is reconsidered with intention to replace TSF material to minimize these influences.Within various low expansion material against temperature variation, SiC is chosen by recognizing its low coefficient of thermal expansion of 2.6x10 -6 K -1 , which is less than 1/5 of that of SUS316, as well as its specific electrical resistance of 10 3 Ohm cm,   which is believed to be sufficient to avoid charging up during X-ray source operation.The representative indices the TSF made of SiC is depicted in Table 3.The model depicted in Fig. 7 and the boundary conditions presented in Table 3 are applied to predict drift of TSF when the material is replaced from SUS316 to SiC with the identical geometrical properties.

Verification of improved MTF
The target supporting frame is reproduced by using SiC as the material with the same dimension to that made of SUS316.Its outlook is shown in Fig. 10.Drift of target is again verified after installation of TSF made of SiC.The result is shown in Fig. 11.It results in drift of target suppressed down to 0.02 mm or less.
The MTF is evaluated again.The result shows 29.2 line pair par centimeter when 1/8 and 3/8 offset scan mode is applied.The value is close to 30 line pair par centimeter predicted through the simulation as the theoretical upper limit of MTF.The accomplishment of this study is summarized as shown in Table 4.

Summary
Spatial resolution performance of newly developed high-energy high-resolution X-ray CT is verified and then tried to be enhanced.The verified resolution performance is believed to become a cutting-edge performance within the state of the art Xray CT in the high-energy X-ray range.

Fig. 1 :
Fig. 1 : Trade off relationship between resolution and X-ray energy representing penetration capability.

Fig. 7 :
Fig. 7 : Simulation model of temperature variation of target supporting frame.

Figure 9
Figure 9 shows the predicted drift of the target by the broken green line which indicates drift of the target suppressed down to 0.02 mm or less.Figure 9 also indicates drift of the target observed by the experiment described in the above and stitched each other by applying Model-Xray-off characteristics depicted in Fig. 8.

Fig. 10 :
Fig. 10 : Outlook of target supporting frame made of SiC.

Table 1 :
Summary of accomplished performance indices of eXTRACT.

Table 2 :
Representative indices of target supporting frame made of SUS316.

Table 3 :
Representative indices of target supporting frame made of SiC.