Geometric calibration of a cone-beam
computed tomography system and medical
linear accelerator
Youngbin Cho1, Douglas J. Moseley1, Jeffrey H. Siewerdsen2, and David A. Jaffray1
1
2
Department of Radiation Oncology, Princess Margaret Hospital, Toronto, Ontario, Canada
Ontario Cancer Institute, Princess Margaret Hospital, Toronto, Ontario, Canada
Abstract
Cone-Beam CT (CBCT) systems have been developed to provide in-situ imaging for the purpose of
guiding radiation therapy. Geometric calibration involves the estimation of a set of parameters that fully
describe the geometry of the system, and is essential for accurate image reconstruction and precise
radiation treatment. We developed an efficient and accurate calibration method for such systems in which
a kV X-ray imager is incorporated on the treatment machine. The sensitivity and accuracy of the method
are proven to be excellent with an uncertainty of 0.02o and 0.1mm. The method is used to provide a
complete calibration of a medical linear accelerator in this paper, including source position, portal
imaging device position and tilt angles, couch motion, mechanical axis of collimator, and motion of jaw
and MLC at every gantry angle. Since this method is highly automated and integrated, acceptance testing,
as well as annual and daily machine QA for precision radiation therapy such as stereotatic, IMRT, CBCT
on linear accelerator can be done accurately and frequently. Combining the information of the MV
treatment system and kV CBCT system will greatly facilitate precise radiation therapy.
Keywords
Geometric calibration, cone-beam CT, linear accelerator, image-guided radiation therapy, crosscalibration
Introduction
The development of volumetric imaging systems
for the purpose of guiding radiation therapy has
been a major interest of research in radiation
therapy1-6. Medical linear accelerators with kilo
voltage (kV) CBCT system orthogonal to the
Mega voltage (MV) source are currently
available (See figure 1). Such systems are
capable of producing images of soft tissue with
excellent spatial resolution (full width at half
maximum of 0.6mm)5 at acceptable imaging
doses (3cGy)7. Integrating this technology with
the medical linear accelerator offers a highly
promising platform for high-precision, imageguided radiation therapy.
Geometric calibration is essential for accurate
image reconstruction. We developed a
calibration phantom and an analytic method for
the estimation of the geometric parameters of the
kV CBCT scanner including CBCT on medical
linear accelerator, C-arm, and lab bench. The
sensitivity and accuracy of the method, applied
to calibration of the kV CBCT system has been
Rotation of gantry
MV source
90o
KV source
w
x
yw
-90o
zw
World
coordinate, w
i
z
y
Detector
coordinate, i
i
Portal Imaging
Device
x
i
Piercing
point
(Uoffset
Figure 1. Illustration of system incorporating
cone
Voffset)
beam CT on medical linear accelerator
shown to be excellent with an uncertainty of
0.02o and 0.1mm8.
Geometric calibration of the MV system is also
important for accurate dose delivery for highly
precise dose delivery technique such as IMRT,
stereotactic radiosurgery and therapy. The
calibration method developed for the kV CBCT
system, which has been proven to be efficient
and accurate, is applied to calibrating the
medical linear accelerator. We used a portal
imaging device to acquire images of the
calibration phantom. Machine parameters
include source position, portal imaging device
position and tilt angles, couch motion,
mechanical axis of the collimator, motion of
jaw, stability of the beam position and MLC
motion at every gantry angle.
Material and methods
A. CBCT geometry
To describe the geometry of the scanner, three
right-handed Cartesian coordinate systems are
introduced. Coordinate systems of world (w),
and virtual detector (i) are shown in Figure 1.
Objects, such as the calibration phantom and
patient, and CT reconstruction are based on the
world coordinate system. The virtual detector
coordinate system describes the ideal detector,
which is the same as the real detector system
except that it has no tilt. The real detector
coordinate system considers detector tilt and
rotation from the ideal orientation. The
algorithm used herein works accurately when
the detector tilt is less than 45 degrees.
B. Calibration phantom
The calibration phantom consists of 24 steel ball
bearings precisely located in two circular
trajectories in a plastic cylinder as shown in
Figure 2. In each circular pattern, twelve steel
ball bearings (BBs) are spaced evenly at 30
degrees. Each ball bearing is 3mm in diameter.
Precision of the ball bearing location in the
phantom is important.
C. Calibration
Since the calibration is based on the location of
the ball bearings in an image, portal image of the
phantom should show all the ball bearings
clearly. The calibration algorithm needs only
one image of the phantom to determine the
source position, portal imaging device position
and tilt angles, and couch position with respect
to the world coordinate system located at the
center of the phantom. When those machine
parameters are changing with gantry angle, the
(a)
(b)
Xw
Zw
Yw
Figure 2. Two circle BB phantom for
geometric calibration.
calibration can be repeated at every gantry
angle. Calibration is done by the following
procedures:
1) Place the phantom close to machine isocenter. Although location of the
phantom does not affect the calibration
result, it is preferred to put the phantom
close to iso-center to reduce the chance
that any ball bearing is outside the field
of view.
2) Acquire a portal image of the phantom.
3) Identify all the ball bearings in the
image. This procedure was done
automatically using image processing.
4) Solve for the system geometry using the
method described in the literature8.
Position of BB in imaging plane is the
function of geometric parameters and
3D coordinate in the world coordinate
system. Since the coordinate of the BB
is known and position of BB is found in
step 3), geometric parameters can be
determined. See the reference 8 for
detail.
Results and discussion
The sensitivity of the calibration algorithm on
the inaccuracy of ball bearing identification due
to limitations of image quality or limited
accuracy of the phantom dimension is analyzed.
Table 1 shows the uncertainty of the calibration
parameter due to the 0.5 pixel error. It has been
shown that the pixel error of the BB position in
kV image is less than 0.1 pixels for this
phantom. However, the poor quality of the portal
image compared to the kV diagnostic image
gives poorer estimation and pixel error seems to
be about 0.5 pixels on average. Effort to
improve the image quality needs to be given.
The current phantom consists of small size ball
Source position
Piercing point position
0
1000
Y [mm]
1
5
0.5
0
-1000
X [mm]
-1500
Z [mm]
7
0
-1
-1000
-0.1
0
Y [mm]
0.1
0.2
0.3
0.4
0.5
0
-1
t= -90
-3
0
X [mm]
-1.5
-0.2
1000
t= 90
-2
t= -90
-3
-0.3
0
X [mm]
1
-2
-1
-0.4
-1000
2
t= 90
1
6
-2
-0.5
0
-500
-1000
1000
Z [mm]
Z [mm]
2
4
500
8
0
-0.5
1000
0
-2
-1000
1.5
1500
2
Y [mm]
2
calculated at each angle. Figure 4 shows the
nominal gantry angle reported by the linear
accelerator console and measured gantry angle
from the calibration. Maximum error of the
gantry angle is always less than 0.1 degree as
shown in Figure 4.
Figure 5 shows the MV source position and
piercing point on the detector in 3 dimensional
spaces. Average source to iso-center distance
(SAD) is 1003.2mm and source to detector
distance is 1600.4mm. The maximum deviation
of the beam position from the ideal trajectory of
a perfect circle is found at gantry angles of –90
degree and 90 degree. The MV source moves
toward the gantry by 1.2mm and toward the
couch by 1.2mm again at gantry angle of –90
and 90 degree, respectively. This movement is
also found from the analysis of piercing point
movement as a function of gantry angle (not
shown here).
Figure 6 shows the alignment of collimator
rotational axis to the MV source position. The
Z,gantry axis [mm]
bearing, which was originally designed for kV
CBCT calibration. Larger ball bearings and
higher MU can be used to make better portal
images of the phantom. Better image processing
algorithm also can be helpful.
Megavoltage beam stability is tested first. At
fixed gantry angle, nine images of phantom are
taken continuously. The position of the electron
beam on the target was found to vary over the
first nine images. Figure 3 shows the trajectory
of the electrons on the target, where the Z-axis is
the direction pointing out from iso-center away
from gantry. Since the first couple of images and
the last image are extremely poor, those images
couldn’t be used. The beam position is
controlled very well in the direction of cross
plane (Y axis). Range of motion in Y and Z
direction is about 0.3 mm and 1.5 mm,
respectively.
The nominal gantry angle and measured gantry
were compared. 36 portal images were taken at
gantry angles spaced at 10 degrees. 10 MU are
given at each gantry angle. Geometric
parameters such as source position, detector
position and tilt angle, and gantry angle were
1000
-1000
0
Y [mm]
1000
Figure 5. Movement of the MV X-ray source
Figure 3. Stability test. Position of the electron
beams on the target.
3
2.5
100
0.1
0
-100
-200
-200
0
Measured
-150
-0.1
-100
-50
0
50
100
Nominal Gantry Angle [degree]
150
-0.2
200
Figure 4. Nominal gantry angle vs measured
gantry angle
Y [mm]
0.2
Difference [degree]
Gantry Angle [degree]
2
200
1.5
1
0.5
0
3
3.5
4
4.5
5
X [mm]
5.5
6
6.5
Figure 6. Movement of MV source relative to
the collimator rotational axis.
Table 1. Uncertainty in geometric parameters for different number of ball bearings and 0.5 pixel error in BB localization .
N
12
16
20
24
32
40
60
source position
Ysi
Zsi
[mm]
[mm]
1.1925 9.4450
0.8545 7.5175
0.7620 6.7150
0.6955 6.1295
0.6025 5.3085
0.5385 4.7480
0.4400 3.8770
detector position
Ydi
Zdi
[mm] [mm]
0.7180 5.7435
0.5155 4.5890
0.4595 4.0990
0.4195 3.7420
0.3635 3.2405
0.3250 2.8985
0.2655 2.3665

detector angle
[deg]
0.4515
0.5420
0.4660
0.4425
0.3730
0.3370
0.3015
collimator rotational axis can be found by
attaching the phantom to the collimator. 36
images are taken by rotating collimator with the
phantom. 10 MU is given to each image. The
source position in the rotating coordinate system
fixed in the phantom will stay at a point when
the source is at the axis of collimator rotation. If
the source is at distance from the axis of
collimator rotation, the source position follows
circular trajectory around the axis of collimator
rotation. Thin lines with small circle represent
the raw data of source positions in rotating
coordinate system of the phantom. The axis of
rotation can be found by averaging the source
position. The average distance of the source
positions from the center indicates the distance
between source position and the axis of
collimator rotation. Thick line represents the
average motion of the source around collimator
axis. It was found to be 0.9mm.
A new method has been proposed for calibration
of CBCT and medical linear accelerator. This
method is robust, easy to implement and
efficient. The calibration algorithm uses a linear
parameter-estimation approach (fast and
accurate computation) and produces a complete
solution (all the calibration parameters are
found) using a calibration phantom consisting of
24 steel ball bearings precisely located in two
circular trajectories in a cylindrical plastic
phantom.
Conclusions
A general and reliable method for geometric
calibration of a CBCT system and medical linear
accelerator is developed. Using this algorithm,
characterization of kV and MV source,
detectors, jaws, MLC, and couch system are
possible. Once the MV system, kV system, and
couch system are characterized and calibrated,


[deg]
0.4430
0.3840
0.3435
0.3135
0.2715
0.2430
0.1980
[deg]
0.0400
0.0485
0.0435
0.0390
0.0340
0.0315
0.0265
gantry
angle, t
[deg]
0.0760
0.3840
0.3385
0.3020
0.2660
0.2465
0.2110
Magnification
Zsi/(Zsi-Zdi)
[percent]
0.0465
0.0405
0.0360
0.0330
0.0285
0.0255
0.0210
precise image-guided radiation therapy is
possible. Overall, a robust and convenient
method has been developed and demonstrated
for an accurate geometric calibration of these
systems.
References
1.
D.A. Jaffray, J.H. Siewerdsen, J.W. Wong, and
A. A. Martinez. “Flat-panel cone-beam
computed tomography for image-guided
radiation therapy.” Int. J. Radiat Oncol Biol
Phys. 53, 1337-1349 (2002)
2. B.A. Groh, L. Spies, B.M. Hesse, T. Bortfeld,
“Megavoltage computed tomography with an
amorphous silicon detector array.” International
Workshop on Electronic Portal Imaging.
Phoenix, AZ, 93–94 (1998)
3. M. Uematsu, A. Shioda, K. Tahara K, et. al.
”Focal, high dose, and fractionated modified
stereotactic radiation therapy for lung carcinoma
patients: A preliminary experience.” Cancer, 82,
1062-1070, (1998)
4. Y. Cho, and P. Munro, “Kilovision : Thermal
modelling of a kilovoltage x-ray source
integrated into a medical linear accelerator.”
Med. Phys. 29, 2101-2108 (2002)
5. D.A. Jaffray, J.H. Siewerdsen, “Cone-beam
computed tomography with a flat-panel imager:
initial performance characterization.” Med. Phys.
25, 1493–501 (1998)
6. D.A. Jaffray, D. Drake, M. Moreau, et. al. “A
radiographic and tomographic imaging system
integrated into a medical linear accelerator for
localization of bone and soft-tissue targets.” Int.
J. Radiat Oncol Biol Phys., 45, 773-789 (1999)
7. B.A. Groh, J.H. Siewerdesen, D.G. Drake, J.W.
Wong, and D.A. Jaffray, “A performance
comparison of flat-panel imager-based MV and
KV cone-beam CT”, Med. Phys. 29, 967-975
(2002)
8. Y. Cho, D. Moseley, J. Siewerdsen, and
D.Jaffary, “Geometric calibration of a cone-
beam computed tomography system” submitted
to Med. Phys. for publication.