Radon Transformation - Digital Signal Processing for Medical Imaging Using Matlab - page 10

Fig. 1.8 Illustration of reconstruction of the image obtained by cumulative summation of original
parallel beam backprojected images

1.3 Fanbeam Projection

The parallel beam projection technique based CT Scan takes more scanning time.
Hence Fanbeam projection technique based CT Scan is used. The Geometry for the
Fan beamprojection is as mentioned in the Fig. 1.12 . The single X-ray source (S) kept
in the y-axis at the distance D from the origin is subjected to the slice of the test body
and the multiple detectors (D1-D5 ) kept at the circumference of the sector (obtained
with S as the centre) are used to capture the attenuated signal along the ray of paths.
Mathematically this is proportional to the line integrals taken along the ray of paths.
This arrangement helps in reducing the scanning time. This corresponds to the angle
β = B in the anticlockwise direction

and the corresponding attenuated signals are captured. This is repeated for

0. Further the source is tilted by an angle β =

β ranging

from 0 to 2 radians. Positions of the detectors are described by the angle measured

from reference line segment SD to the line segment joining the source(S) and the
detector in the anticlockwise direction. This angle is represented as

π

δ . Detector 1

(refer Fig. 1.12 ), is kept at an angle − δ max and the detector 5 is kept at an angle

+ δ max .