JOURNAL OF APPLIED PHYSICS 105, 094701 共2009兲
Performance characterization of microtomography with complementary
metal-oxide-semiconductor detectors for computer-aided defect inspection
Ho Kyung Kim,1,a兲 Seungman Yun,1 Jong Chul Han,1 Hanbean Youn,1 Min Kook Cho,1
Chang Hwy Lim,1 Sung Kyn Heo,2 Cheol-Soon Shon,2 Seong-Sik Kim,3
Bong Hae Cho,3 and Thorsten Graeve Achterkirchen4
1
School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan 609735, Republic of Korea
2
Sensor Business Division, E-WOO Technology Co., Ltd., Bora-dong, Giheung, Gyeonggi-do 449-904,
Republic of Korea
3
School of Dentistry, Pusan National University, Ami-dong, Seo-gu, Busan 602-739, Republic of Korea
4
Rad-icon Imaging Corp., Belick Street, Santa Clara, CA 95054-2404, USA
共Received 10 November 2008; accepted 26 March 2009; published online 6 May 2009兲
We developed a computer-aided defect inspection system based on computed tomography 共CT兲. The
system consists of a homemade small cone-beam CT 共CBCT兲 system and a graphical toolbox, which
is used to extract a computer-aided design 共CAD兲 model from the CT data. In the small CBCT
system, the x-ray imaging detector is based on a complementary metal-oxide-semiconductor
photodiode array in conjunction with a scintillator. Imaging performance of the detector was
evaluated in terms of modulation-transfer function, noise-power spectrum, and detective quantum
efficiency. The tomographic imaging performance of the small CBCT system was evaluated in terms
of signal-to-noise ratio and contrast-to-noise ratio. The graphical toolbox to support defect
inspection incorporates various functional tools such as volume rendering, segmentation,
triangular-mesh data generation, and data reduction. All the tools have been integrated in a
graphical-user interface form. The developed system can provide rapid visual inspection as well as
quantitative evaluation of defects by comparing the extracted CAD file with the original file, if
available, of an object. The performance of the developed system is demonstrated with experimental
CT volume data. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3124360兴
I. INTRODUCTION
X-ray computed tomography 共CT兲 is not only a well
recognized imaging modality in medicine1 but also an essential one in industrial quality control and nondestructive
evaluation.2,3 The recent cone-beam CT 共CBCT兲, enabling
three-dimensional 共3D兲 scanning in almost real time, pushes
further up the necessity in industry. Although the detailed
technologies in CBCT, such as imaging detectors, scanning
geometry, and image reconstruction algorithms, are still under development, the overall framework has been matured
enough for diverse applications. Recent developments in microfocus x-ray sources and large-area pixel detectors resulted
in the development of CBCT systems with resolving power
of the order of tens of micrometers; these CBCT systems are
called microtomography 共micro-CT兲 systems.4,5 Although
micro-CT has the same technology as conventional CT, and
thus, not a novel technology, the micro-CT has many new
potential applications in biological as well as materials
sciences.6–9
Moreover, with the 3D volume CT, the output voxel data
can be used for rapid prototyping 共RP兲 modeling, nondestructive testing and evaluation, and reverse engineering, etc.
In these aspects, the extraction of computer-aided design
共CAD兲 models of an object from CT data is essential.
a兲
Electronic mail: hokyung@pnu.edu.
0021-8979/2009/105共9兲/094701/8/$25.00
We developed a cost-effective laboratory micro-CT system as well as software to support the defect inspection of
small parts. The core of the micro-CT system is an x-ray
detector. Since the performance of the detector is mostly responsible for image quality and eventually the quality of the
tomographs, characterization of the detector is an important
issue. The imaging characteristics of the detector were evaluated in terms of modulation-transfer function 共MTF兲, noisepower spectrum 共NPS兲, and detective quantum efficiency
共DQE兲. Tomographic imaging performances of the system,
such as signal-to-noise ratio 共SNR兲 and contrast-to-noise ratio 共CNR兲, have also been evaluated by using quantitative
phantoms. The micro-CT system and software, which is the
integrated graphical toolbox for extracting CAD files in standard triangulation language 共STL兲 format from the voxel
data, are described in detail. The overall performance of the
developed toolbox is demonstrated with the experimental
volume CT data.
II. MATERIALS AND METHODS
A. Micro-CT system
We developed a cost-effective micro-CT system. As
shown in Fig. 1, the system consists of an x-ray source with
small focal spot, an object jig, and an x-ray imaging
detector.5 The source-to-object and source-to-detector distances 共SOD and SDD兲 are variables determining the imaging parameters, such as the geometrical magnification ratio,
105, 094701-1
© 2009 American Institute of Physics
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094701-2
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Kim et al.
FIG. 1. Schematic describing the developed micro-CT system. The x-ray
source continuously irradiates an object fixed onto a jig, which is rotated at
a constant angular velocity, and the 2D imaging detector acquires a projection view at a given integration time. All the operations of components are
computer controlled. The source status, such as potential and current, is
separately monitored. Two variable distances, SOD and SDD, determine the
system magnification factor, the actual cone-beam angle, and FOV of the
object.
actual cone-beam angles, and field-of-view 共FOV兲. A
computer-controlled rotation system was adopted in the object jig for the cone-beam mode scan. The precision of the
rotational motion was 0.036°.
The x-ray source 共Series 5000 Apogee, Oxford Instruments, USA兲 is a sealed tube with a 125-␮m-thick beryllium
exit window. A tungsten target produces x rays with energies
ranging from 4 to 50 kVp at 50 W. Imaging conditions can
be further enhanced by tailoring the x-ray beam profile with
additional filtration. The nominal focal spot size is 35 ␮m.
The emitted x-ray beam angle is about 22°. The x-ray source
continuously irradiates the sample to be imaged without any
shutters while the detector acquires two-dimensional 共2D兲
projection data at a given frame time 共or integration time兲.
The detector is based on a photodiode array in conjunction with a scintillator. A commercial phosphor screen 共MinR™, Carestream Health Care Inc., USA兲 was used as the
scintillator. The screen is mainly made of a terbium-doped
gadolinium oxysulfide 共Gd2O2S : Tb兲 showing an emission
spectrum with the main peak at 545 nm. The photodiode
arrays made by the complementary metal-oxidesemiconductor 共CMOS兲 process 共RadEye™, Rad-icon Imaging Corp., USA兲 were employed as the optical photon readout device.10 The CMOS photodiode array has a format of
512⫻ 1024 pixels with a pitch of 48 ␮m. Only one narrow
side of the CMOS photodiode array incorporates the readout
electronics to allow tiling of the CMOS photodiode array
into large mosaics. In this study, two CMOS photodiode arrays were tiled side by side and therefore the FOV was about
50⫻ 50 mm2. Two parallel voltage signals from the two
CMOS photodiode arrays are then simultaneously digitized
to 12-bit gray level through dual analog-to-digital converters
共ADCs兲 共PCI-6111, National Instruments, USA兲. The 12-bit
image data are converted into 16-bit form for postprocessing
and image reconstruction.
The frame time of the CMOS detector to acquire a single
projection could be variable and we normally operated the
detector with the frame time of 275 ms. Algorithms and software to acquire digital x-ray images, to apply postimage processing, and to reconstruct volumetric images were developed by using Microsoft Visual C⫹⫹®. When we operated
the system in the CT scan mode, the magnification factor
was usually set to about 2 and image data were obtained
through a 360° scan. For image reconstruction, we employed
the Feldkamp’s cone-beam algorithm11 to the projection data
filtered with a Ram-Lak filter 共or high-pass filter兲.12 The
Feldkamp’s algorithm is a simple extended version of the
conventional filtered backprojection method in longitudinal
direction by considering cone angles. Therefore, it is an approximate approach and may cause distortion when the cone
angle is wide. However, since Feldkamp’s algorithm is very
fast and easily applicable, it is mostly widely used in commercial CBCT systems. For a typical scan in this study,
the size of the acquired data was about 1 Gbyte
共=2 bytes/ pixel⫻ 10242 pixels/ projection
⫻ 500 projections兲.
B. Imaging characteristics of the CMOS detector
The performance of the CMOS detector has been evaluated in terms of MTF, NPS, and DQE, which are fundamental metrics describing the physical imaging characteristics of
an imaging system. The MTF describes the contrast transfer
efficiency as a function of an object detail, hence the resolving power of an imaging system. The NPS measures the
change in the noise amplitude as a function of spatial frequency and bridges the noise power and spatial resolution in
an image. The DQE is a measure of the square of the SNR
共SNR2兲 transfer and measures the fraction of the incident
x-ray fluence contributing to image quality. Therefore, the
DQE represents the performance of an imaging system. A
detailed description of measurement procedures can be found
in a previous study.13 Briefly, the presampling MTF was
measured using the slanted-slit method to avoid aliasing14
and the NPS was determined by 2D Fourier analysis of white
images.15,16 Gain and offset corrections were performed on
all images used to obtain the MTF and NPS. We actually
measured a normalized NPS 共NNPS兲 to avoid the additional
measurement of the detector gain. A 45 kVp x-ray spectrum
tailored by a 0.5-mm-thick aluminum filter was used for all
measurements. The DQE was then assessed from the measured MTF, NPS, and the estimated photon fluence q̄ as
DQE共f兲 =
MTF2共f兲
q̄ ⫻ NNPS共f兲
,
共1兲
where f denotes the spatial frequency. The fluence was calculated using the experimentally measured exposure and
half-value layer, and the computational program for x-ray
spectral analysis.17 The exposure rate at the entrance surface
of the detector was measured by replacing the detector with a
calibrated ion chamber 共Victoreen 6000–528, Inovision,
USA兲 while keeping the same distance.
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094701-3
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Kim et al.
D. Graphical toolbox to extract CAD files from CT
data
FIG. 2. 共Color online兲 Homemade phantoms to evaluate the tomographic
imaging performance of the micro-CT system. 共a兲 The cylindrical acrylic
vessel, which contains water, is scanned for the estimation of the voxel noise
and SNR. 共b兲 Low-contrast inserts, which are immersed in water inside the
cylindrical acrylic vessel and scanned for the estimation of CNR. Each
insert has three different diameters: 1.5, 3.0, and 5.0 mm.
C. Tomographic imaging performances of the microCT system
Tomographic imaging performance of the developed
micro-CT system was evaluated with homemade quantitative
phantoms as shown in Fig. 2. A water-filled cylindrical
acrylic vessel having a diameter of 30 mm was used in
evaluating the voxel signal and noise characteristics. The
CNR was evaluated with the contrast phantom, which consists of six low-contrast inserts. The contrast phantom is
completed when the inserts are immersed in the water vessel.
As shown in Fig. 2共b兲, each insert was made of commercial
electronic density phantoms 共Model 76-430, Nuclear Associates, NY, USA兲 and it had three different diameters; 1.5, 3.0,
and 5 mm. The insert materials are plastic water
nylon
共1.15 g / cm3兲,
polyethylene
共1.03 g / cm3兲,
3
acryl
共1.18 g / cm3兲,
polystyrene
共0.95 g / cm 兲,
共1.11 g / cm3兲, and polycarbonate 共1.18 g / cm3兲, and their
densities are similar to that of water. From the crosssectional images obtained with the contrast phantom, the
CNR was calculated by18
CNRi =
兩S̄i − S̄w兩
冑␴2i + ␴w2 ,
共2兲
where S̄ and ␴ are the mean signal and standard deviation of
the voxel values, respectively. The subscripts i and w denote
the inserts and the background water region in the contrast
phantom, respectively. The CNR was analyzed in terms of
various imaging conditions, such as dose, diameter of inserts,
and slice thickness.
Radiation doses, addressed in this study, are based on the
exposure measurement in air at the axis-of-rotation 共AOR兲.19
To take into account the dose, the measured exposure was
converted to the kerma in air using the exposure-to-kerma
conversion factor of 8.736 mGy/R for the x-ray spectrum of
45 kVp, which was interpolated with tabulated data between
40 and 50 kVp.20
In this study, we used two approaches for defect inspection. One is a simple visual inspection of three-dimensionally
reconstructed image data. The other is the defect inspection
based on CAD data. In these regards, we developed a graphical toolbox capable of visualizing 3D data as well as extracting CAD files from the CT data. Main functional tools incorporated in the developed toolbox are the volumetric
rendering of the reconstructed 3D data, the segmentation of
region-of-interests 共ROIs兲, the generation of triangular-mesh
data of the segmented ROIs, and the smoothening and reduction of mesh data.
Volume rendering is a discrete representation and visualization of objects as sampled data, of not only the surface
but also the entire inner of an object, in three dimensions. We
independently considered two different methods, such as ray
casting and maximum intensity projection 共MIP兲.21 Ray casting is a direct volume rendering that sums the intensity values of voxels based on the light absorbed as it propagates
from back to front through the 3D voxel data set. On the
other hand, in the MIP method, the shade of gray of a voxel
having maximum intensity is chosen in the 3D voxel data
encountered along the projection line.
We consider the STL format as a CAD file, which is
mesh data containing geometrical information that details the
object.22 It consists of vectors designating three vertices of a
triangle and its surface normal vector. The procedure to extract a STL file from the voxel data mainly consists of two
steps: segmentation of voxel data in binary form and triangulation of the segmented volume data. Segmentation, the
most important procedure, is very sensitive to each voxel
value and largely responsible for the reliability of the mesh
data. We basically incorporate the thresholding method based
on histogram analysis. The threshold is determined by a
simple calculation that maximizes the variance of the intensities between the user-defined ROI and the other regime in
the histogram.23 This approach can be easily realized with
effective computation.
In order to generate triangle meshes, we employed the
well-known marching cube algorithm.24 A virtual cube is defined by eight-pixel 共or eight-vertex兲 values between two
vertically consecutive slices of the segmented volume data.
Therefore, this algorithm determines how the slice surfaces
intersect the cube by comparing the vertex values, which are
prescribed as unities, with the segmented data. Since possible triangles 共256 cases兲 are already prepared as a look-up
table, the triangulation is automatic. The cube marches to the
next location and the process is repeated. However, since the
number of triangles that could be generated per cube is limited to four,24 the degree of surfaces that should be expressed
is restricted. Reducing the gap between slices or a higherorder interpolation method might be a way to overcome this
restriction, but it entails computational cost. It is completed
when the triangulated meshes are exported according to the
STL file format.
Since the file size of the mesh data extracted by the
marching cube algorithm is normally large, it is often necessary to remove unnecessary meshes and merge the meshes in
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J. Appl. Phys. 105, 094701 共2009兲
coplanar planes.25 This data reduction process should preserve the original topology and approximate the original geometry reasonably. We employed various mesh-data reduction algorithms, such as mesh decimation, quadric
decimation, and quadric clustering.25
Most of the algorithms describing each tool were coded
by using Microsoft Visual C⫹⫹®. For user convenience, the
toolbox was developed in an integrated graphical user interface 共GUI兲 form.
E. Experimental simulation
In order to implement the developed toolbox, we designed a chessman, bishop, in STL file format using a commercial CAD software, Pro/Engineering™ and manufactured
an RP sample using optical stereolithography 共SLA 350, 3D
Systems, USA兲 with SL-51902 resin. The manufactured RP
bishop sample was then scanned by the developed micro-CT
system and a 3D image was reconstructed in voxel size of
0.096⫻ 0.096⫻ 0.096 mm3. By using the developed toolbox, we extracted the STL file from the scanned CT voxel
data and used the developed toolbox to compare the extracted STL file with the original one. The bishop sample
was designed to have a height of 67.44 mm and the manufactured RP sample was measured to 67.58 mm. Both the
imaging FOV of the CMOS detector and the introduction of
magnification in imaging geometry restricted the sample
height to be imaged to about 34.69 mm.
III. RESULTS
FIG. 3. Fourier analyses for the imaging characteristics of the CMOS detector. 共a兲 The measured system MTF and theoretical MTFs representing
physical parameters affecting the overall MTF, the focal spot of x-ray
source, the pixel aperture of detector, and the width of slit camera. 共b兲 The
measured NNPS and the least-squares fits to analyze the NNPS. 共c兲 The
measured DQE.
A. Radiographic imaging performance
Fourier analysis of the radiographic imaging performance of the detector equipped in the micro-CT system is
summarized in Fig. 3. The measured MTF is plotted in Fig.
3共a兲. At 10% of MTF, the spatial resolution is about
10.5 mm−1. We could easily resolve 10 lp/mm of the highresolution line-pair phantom from a separate measurement as
shown in Fig. 4.
Figure 3共b兲 describes the NNPS as a function of the
spatial frequency. There is a noticeable increase in noise
power around zero frequency due to large-scale gain variation across the detector, which would normally be eliminated
by the gain correction procedure. In order to remove or reduce the large-scale nonuniformity, a 2D second-order polynomial fit to an image is used and is subtracted from the
corresponding image. In this study, however, we subtracted
the mean value of the image instead. The measured NPS
shows essentially white-noise property with respect to the
spatial frequency. The higher MTF performance might reflect
this white-noise property in part because the noise is also
transferred through the MTF as a signal.26 A previous study
pointed out that in a detector employing a thin phosphor, the
extra noise due to the direct absorption of x-ray photons in
the photodiode is white.5 Together with the measured MTF
and NNPS, the DQE was calculated and the result is shown
in Fig. 3共c兲.
B. Tomographic imaging performance
Cross-sectional images of the contrast phantom with respect to various parameters, such as the diameter of the lowcontrast inserts, the dose and the slice thickness, are shown
in Fig. 5. We applied narrow threshold windows to clearly
differentiate the inserts. The default voxel size is 0.139
⫻ 0.139⫻ 0.278 mm3. The voxel heights or the slice thicknesses of the images shown in Figs. 5共f兲 and 5共g兲 are 0.556
and 1.112 mm, respectively.
FIG. 4. Radiograph of the line-pair test phantom, which supports the result
of measured MTF.
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094701-5
Kim et al.
J. Appl. Phys. 105, 094701 共2009兲
FIG. 7. The SNR, calculated from the images obtained for the water phantom, as a function of dose. The solid lines show a trend curve proportional
to the square root of the dose.
FIG. 5. Cross-sectional images of the contrast phantom with respect to
various imaging parameters, such as the dose, the diameters of inserts, and
the slice thickness. Reference images of 共a兲–共c兲 depict the effect of the insert
diameter, 共d兲 and 共e兲 the effect of the dose, and 共f兲 and 共g兲 the effect of the
slice thickness. Note that ␾ and t denote the insert diameter and the slice
thickness, respectively.
For three different diameters of inserts 关see Figs.
5共a兲–5共c兲兴, no severe change in contrast was observed, even
down to the diameter of 1.5 mm, for each insert material.
The acquired images also showed similar CNR values and
tendencies as a function of dose for the three different diameters of inserts. For the inserts having a diameter of 1.5 mm,
the calculated CNR as a function of the dose at the AOR is
plotted in Fig. 6. The CNR was found to be proportional to
the square root of the dose.27
Figure 5共a兲, 5共d兲, and 5共e兲 demonstrate the effect of dose
on visual impact. In general, the image quality of a radiograph is mainly dependent on the number of detected photons and it is definitely increased as the number of incident x
rays is increased. The tomograph becomes poorer as the dose
FIG. 6. The CNR, calculated from the images obtained for low-contrast
inserts having a diameter of 1.5 mm, as a function of dose. The dotted lines
are trend curves that are proportional to the square root of the dose.
decreases. For a given dose, the increase in the slice thickness has the same effect as an increased number of detected
photons, as shown in Figs. 5共a兲, 5共f兲, and 5共g兲.
In all the measurements, the worst CNR was observed
with the insert made of acrylic. The minimum resolvable
CNR with the naked eye was approximately 1 and the voxel
noise of the water phantom corresponding to this CNR value
was about 250 CT numbers.
The SNR, calculated from the measured cross-sectional
image of the water phantom, as a function of dose is shown
in Fig. 7. Like the CNR, the SNR is also dependent on the
square root of dose. At the dose of 83 mGy, the SNR is about
6, and the corresponding voxel noise is 295 CT numbers.
C. Graphical toolbox and the extraction of CAD files
from CT data
Figure 8 describes the main frame of the developed
graphical toolbox. The toolbar at the top of the main frame
contains various symbolic buttons, which are used to run the
corresponding functions, such as loading of the volume data
or STL data, handling of visualization and cropping, the ex-
FIG. 8. 共Color online兲 Screenshot of the main window describing the developed graphical toolbox.
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094701-6
Kim et al.
J. Appl. Phys. 105, 094701 共2009兲
the approximate Feldkamp’s algorithm for cone angle could
produce an error,11 the generated error for small cone angle
or small sample volume would be negligible. For the reliable
performance evaluation of the developed system, the error
should be quantitatively analyzed in terms of each contributing factor.
IV. DISCUSSIONS AND CONCLUSION
FIG. 9. 共Color online兲 Experimental simulation with a chessman, bishop,
using the developed toolkit. 共a兲 Original CAD data, which were as an input
file for the RP machine, and the manufactured RP bishop sample. 共b兲 3Drendered images of voxel data obtained from the CT scan. Two different
visualizations, ray casting, and MIP, are shown. 共c兲 Extracted CAD files
from the voxel data by using the developed toolkit. The left is the extracted,
as is, and the right is after decimation and smoothening processes. 共d兲 A map
describing the difference between the original and the extracted CAD files.
traction of STL files from the volume data including segmentation and triangulation, etc. The loaded 3D CT or STL image is displayed on four subwindows. The large window
renders a 3D view of an object. In this window, cropping and
free rotation of the 3D view for any axis can help the inner
and surface investigations. The small three subwindows describe the cross-sectional views of the object parallel to x, y,
and z, and those are synchronized with one anther so that we
can simultaneously identify the inner investigation for the
three axes.
Figure 9 shows the results of the experimental simulation. Figure 9共a兲 shows the original CAD file 共left兲 used as
the input file for the RP machine and the photograph of the
manufactured RP bishop sample 共right兲. 3D-rendered images
of the CT-scanned voxel data are shown in Fig. 9共b兲. Two
different visualizations, i.e., ray casting 共left兲 and MIP 共right兲
are shown. Figure 9共c兲 shows the extracted CAD files from
the developed toolbox and two images are distinguished
from each other by the degree of data reduction and smoothing. As designated by magnifiers, the right image was obtained after about 30% reduction in the number of meshes.
Figure 9共d兲 shows a difference map of geometries and dimensions between the original and extracted CAD files. The
scale bar designates the degree of difference in dimension in
the unit of millimeter. As shown in Fig. 9共d兲, the difference is
as large as 1 mm, but this is not purely resulted from the
manufacturing error. The most significant factor affecting the
errors is presumed to misalignment in imaging geometry,
which was not characterized in this study. Another cause that
may provide an error is probably the threshold-based segmentation procedure because the threshold determined from
histogram already has some extent of uncertainty.23 Although
The overall MTF of the detector system is affected by
various physical parameters such as the x-ray focal spot size,
the slit width, the magnification ratio, and the inherent detector resolving power.19 The inherent resolving power of the
detector employed in this study is mainly determined by the
optical photon scattering in the phosphor screen and the pixel
aperture size of the CMOS photodiode array. Since the SDD
was set to 200 mm when measuring MTF with a slit camera
having a 10-␮m-width slit aperture and made of the 1.5-mmthick tantalum28 and the slit camera was in contact with the
entrance surface of the detector, we neglected the magnification of focal spot and slit width. The theoretical MTF due to
an aperture function can be expressed by the “sine cardinal”
or simply “sinc” function. Accounting for the onedimensional 共1D兲 geometries of the focal spot, the slit aperture, and the detector pixel, the theoretical MTFs are plotted
in Fig. 3共a兲. The pixel MTF was estimated with consideration of the geometric pixel fill factor of 0.87. From the
results, the overall MTF was seemed to be mostly determined by the resolving power of the phosphor screen; in
other words, the dominant blurring factor was the optical
photon scattering within the phosphor screen.
On the other hand, tomography is obtained with a certain
magnification factor, i.e., the ratio of SDD to SOD. Therefore, there is a compromise between the magnification of
details in an object and the blur due to the magnified focal
spot size. In addition, image reconstruction is another blurring factor in tomography.29 In the previous study on the
development of a microtomography system incorporating a
focal spot size of 10 ␮m and a pixel pitch of 50 ␮m,19 the
system total MTF was mostly determined by the detector
resolving power at the magnification factor of 2. We assumed
that the system MTF of our micro-CT system would be similar. However, the MTF in tomography should be measured
for optimal and reliable use.
As long as the additive electronic noise is not exceptionally large, the NPS of an imaging system is mainly governed
by the stochastic variation of information-carrying quanta
introduced in various image-forming states. Typical examples are the interaction of x-rays in a scintillator, the absorption of its energy, the conversion of x-ray to optical photons, the spread of an optical photon burst, and the escape of
optical photons, and, in a photodiode, the collection of optical photons, the conversion of optical photons to electronic
charges, and the spread of electronic charges. This stochastic
variation increases the noise at the output, and whose effect
can be seen by examining the NPS. According to
Rossmann,26 because the spatial-frequency dependence of
the signal transfer is described by MTF共f兲, the NPS would
behave as MTF2共f兲. However, as shown in Fig. 3共b兲, the
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094701-7
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Kim et al.
NPS of our detector system shows behavior close to that of a
white noise spectrum except at the very low frequency band,
probably due to the imperfect removal of the fixed-pattern
noise during the gain-offset correction procedure. For comparison, a best fit function, proportional to MTF2共f兲, is plotted in Fig. 3共b兲. A large discrepancy is observed in the high
spatial-frequency region. From Lubberts,30 the NPS generally falls off more slowly at high frequency than the MTF2
because of the stochastic variation caused by the depthdependent interaction of x rays within a phosphor screen and
the fluctuation of processes at the corresponding depth.
Badano et al.31 demonstrated the Lubberts’ effect on a phosphor screen by estimating the Lubberts fraction, L共f兲
= MTF2共f兲 / NNPS共f兲 based on Monte Carlo simulation.
However, their result on the phosphor screen having a similar thickness as that employed in our detector is quite different. Our measurement and analysis showed a much stronger
effect than Lubberts’ effect, indicating another factor affecting the NPS degradation. A previous study5 pointed out that
in a detector employing a thin phosphor, the extra noise due
to the direct absorption of x-ray photons in the photodiode
has a white spectrum. The direct x rays are those that are
unattenuated from the phosphor screen and that directly interact with the photodiode. This additional white noise can
further raise the spectral density in the high spatial frequency
band. The proof that the NNPS due to the direct x rays is
white is shown in Ref. 32. Considering this additional white
noise, we analyzed the measured NPS with a least-squares fit
of the form aMTF2共f兲 + b, where a and b are the constants
obtained from the numerical fit and plotted the resultant fit in
Fig. 3共b兲. This analysis was directly applied to the DQE result as shown in Fig. 3共c兲. The analysis reasonably agreed
with the measured DQE data. The degradation of NPS due to
the direct x-ray absorption noise decreased the DQE performance, especially in the high frequency region.
Not only do direct x rays affect the image quality or the
detector performance, such as NPS and DQE, but they also
can give rise to a change in the characteristics of the active
devices in the photodiode array, such as the leakage current
of a photodiode and the threshold voltage of a switching
transistor. The radiation-induced increase in the dark signal
and noise can result in the gradual reduction in the dynamic
range and enhance the fixed-pattern noise in digital
radiography.33 Therefore, a phosphor screen must be designed or selected optimally. In digital radiography, the offset
and gain correction is typically performed. With carefully
updated and applied correction during the operation of
CBCT, the detrimental effects of increased dark current on
NPS and DQE can be overcomed.33
The applicability of the developed system is somewhat
limited by the FOV of the detector. If magnified images and
tomograms are needed for a detailed analysis of an object to
be scanned, FOV becomes a more serious problem. The detector can extend the tiling approach of the CMOS photodiode array used in this study to a larger dimension, for example, the FOV of about 100⫻ 100 mm2 with 2 ⫻ 4
arrangements of the photodiode array. Moreover, commercial
large-area flat-panel detectors are available. With an undersized detector, the extension of the reconstructed volume
with mechanical motion or a smart image reconstruction algorithm is another approach that can be used to overcome
the restricted FOV of a detector. Spiral motion, which is
typical in medicine, on a long object is an example. For a
wide object, by shifting a detector laterally so that data from
at least half the width of the object are acquired for each
view, the image reconstruction based on the estimation of the
missing rays through the unprojected part of the object from
the redundant rays can be used to enlarge the reconstructed
volume in laterally.34
A series of algorithms to realize computer-aided defect
inspection has been integrated in a GUI form. The developed
graphical toolkit was used to extract CAD files from the
scanned CT volume data of an RP sample. In the serial procedures, the most important procedure is the segmentation.
An object containing various inner structures with similar
material properties, such as density and atomic number, requires the implementation of more elaborate segmentation
algorithms. However, the segmentation algorithm used in
this study is reasonable for typical industrial applications because most industrial parts are composed of a few materials.
Although the developed system is somewhat restricted in
FOV, it can be used for diverse industrial applications, such
as the inspection of solder joins in electronic components
and reverse engineering of small parts, and for biological
applications, such as small-animal imaging, tissue engineering, etc.
ACKNOWLEDGMENTS
This research was performed for the Nuclear R&D Programs 共Grant No. M20609000107-06B0900-10710兲 and the
Korea Science and Engineering Foundation 共KOSEF兲 共Grant
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