Flying Focal Spot (FFS) in Cone–Beam CT
Marc Kachelrieß, Michael Knaup, Christian Penßel, Willi A. Kalender
Fig. 1. A rotating envelope tube with focal spot deflection capability.
Abstract — In the beginning of 2004 medical spiral-CT
scanners that acquire up to 64 slices simultaneously became
available. Most manufacturers use a straightforward acqui-
sition principle, namely an X–ray focus rotating on a circular
path and an opposing cylindrical detector whose rotational
center coincides with the X–ray focus. The 64–slice scanner
available to us, a Somatom Sensation 64 spiral cone–beam
CT scanner (Siemens, Medical Solutions, Forchheim, Ger-
many), makes use of a flying focal spot that allows for view–
by–view deflections of the focal spot in the rotation direc-
tion (αFFS) and in the z–direction (zFFS). The FFS feature
doubles the sampling density in the channel direction and
in the longitudinal direction. Up to four detector readings
contribute to one view (projection). A significant reduction
of in–plane aliasing and of aliasing in the z–direction can be
expected. Especially the latter is of importance to spiral CT
scans where aliasing is known to produce so–called windmill
artifacts. We have derived and analyzed the optimal focal
spot deflection values ∂α and ∂z as they would ideally occur
in our scanner. Based upon these we show how image recon-
struction can be performed in general. A simulation study
showing reconstructions of mathematical phantoms further
provides evidence that image quality can be significantly
improved with the FFS. Aliasing artifacts, that manifest as
streaks emerging from high–contrast objects, and windmill
artifacts are reduced by almost an order of magnitude with
the FFS compared to a simulation without FFS.
I. Introduction
C
ORRECT sampling requires to satisfy the Nyquist
condition: at least two sample points should be taken
per spatial resolution element (Shannon sampling theo-
rem). In many cases this situation is not easy to achieve.
In CT the spacing of the detector samples is slightly
Institute of Medical Physics (IMP), University of Erlangen–
N¨urnberg, Henkestr. 91, 91052 Erlangen. Corresponding author: PD
Dr. Marc Kachelrieß, E–mail: marc.kachelriess@imp.uni–erlangen.de.
larger than the active width of the detector pixels —
far from sampling the active detector area twice. One
workaround is the quarter detector offset. During a 360
◦
rotation each ray is measured twice and the data are re-
dundant. Shifting the detector array (channel direction)
by one quarter of the detector sampling distance pays out
since opposing rays interlace and, by combining opposing
views, one effectively doubles the sampling [1]. However,
for cone–beam scans and for spiral scans this kind of data
redundancy is not really available since opposing rays do
not exist; they rather differ by their tilt–angle wrt the ro-
tation axis and by their z–position. Further, the quarter
shift does not improve the sampling in the detector row
direction (z–direction).
An alternative is deflecting the focal spot between ad-
jacent detector read–outs (figure 1) as it is done in our
tube [2]. This flying focal spot can be used to double the
sampling density in both directions regardless of the cone–
angle and the spiral trajectory. In this paper we specify
the FFS deflection values, we clarify the geometry, we in-
troduce the subfan approximation, we present the way we
store FFS data in a view–based (opposed to a reading–
based) format and we demonstrate the effect of the FFS in
a simulation study.
II. Source and Detector Geometry
With R
F
being the distance of the undeflected focal spot
to the isocenter, d being the table increment per rotation,
¯d = d/2π and α being the view angle let us define the spiral
source trajectory as
s(α, ∂α, ∂z)=
(R
F
+ ∂R
F
)sin(α + ∂α)
−(R
F
+ ∂R
F
)cos(α + ∂α)
¯dα+ ∂z
.
The vector s(α)=s(α, 0, 0) is the source trajectory vec-
tor of a spiral CT scanner without FFS. The additional
parameters ∂α and ∂z are the focal spot deflection angle
and deflection length that are used to improve the in–plane
and the axial sampling properties of CT. These deflection
parameters are of very small magnitude. Using the small
angle approximation (first order Taylor series in the two de-
flection parameters) is justified and will be implicitly used
below when deriving the ideal values for ∂α and ∂z.The
remaining parameter ∂R
F
is not independent. It accounts
for small variations in the radius of the true focal spot to
the isocenter. Since the rotation axis of the X–ray tubes
is parallel to the scanner’s rotation axis a focal spot de-
flection ∂z in the z–direction will effectively change R
F
by
∂R
F
= ∂z/tan φ where φ is the anode angle (in our case
7
◦
). Note that the variation in R
F
due to ∂α is of second
order in ∂α and therefore negligible.
0-7803-8701-5/04/$20.00 (C) 2004 IEEE