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Transverse tomography with incoherent optical reconstruction
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1978 Phys. Med. Biol. 23 90 (http://iopscience.iop.org/0031-9155/23/1/008) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.239.1.231 This content was downloaded on 26/08/2015 at 20:17
Please note that terms and conditions apply.
PHYS. MED. BIOL.,
1978, VOL. 23,
NO.
1, 90-99.
@
1978
Transverse Tomography with Incoherent Optical Reconstruction PAUL EDHOLM,t LARS GiiSTA HELLSTRiiMS and BERTIL JACOBSON$ t Department of Diagnostic Radiology, Linkoping University, The Medical School, S-581 85 Linkoping, Sweden 3 Department of Medical Engineering, Karolinska Institute, S-104 01 Stockholm 60, Sweden Received 2 1 April 1977
ABSTRACT. A thin layer of an object can be imaged by reconstruction from a so-called sinogram. It is produced by an X-ray fan beam rotating around the object while a recording film is moved in a direction perpendicular to the plane of the fan beam. Before reconstruction the sinogram image is convoluted according to a special function to remove artifacts consisting of spurious shadows between different object elements. Thereconstruction is donefrom the convoluted sinogram by means of a back projector, which operates according t o a principle that is the reverse of the recording of the original sinogram. Tomograms of phantoms, pork chops and the head of a dog show that the process is capable of high spatial resolution but is limited by low contrast.
1. Introduction
Computed tomography (CT) ischaracterised by highcontrastresolution but limited geometric resolution. Techniques theoretically similar to CT are possible using film as recording medium and incoherent optical methods for image reconstruction (Peters 1973, Edholm and Jacobson 1975, Gordon and Barrett 1975). Since suchmethodsshould not involve the same geometric limitations the present experimental study was undertaken. 2. Principleandmethod
The tomography comprises three processes: (i) recording of the intensity objectduring rotation, distribution of radiationtransmittedthroughthe which corresponds to the scanning process in CT; (ii) convolution, analogous to that in C T ; and (iii) back projection for reconstruction of the desired tomogram, corresponding t o the formation and display of the image matrix in CT. 2.1. Recording
Lateral projections of a one millimetre thick layer through the object was imaged on a 350 mm x 350 mm film by means of a collimated X-ray fan beam (fig. 1). The beam divergence is 0.14 radians. The energy used varied between 80 and 110 kV, tubecurrent was 10mA and the film-focus distance was 1220 mm. During rotation of the object the film was moved in a direction parallel to the axis of rotation. Thus each object element in the projected
Tomography with
Optical Reconstruction
91
layer was recorded as a sine-like curve on the film; therefore,the image obtained istermeda ‘sinogram’. The sinogram formsarhomboidwith an angle of 86O, length 306 mm and height 170 mm, In the sinogram the w-axis denotes the direction parallel to the translation of the film, and the u-axis the perpendicular direction. It should be observed that animage element inthe sinogram represents a lineararray of object elements,and that an array of image elements represents the whole layerin oneprojection. Aswill be discussed under section 2.3.1 this projected array of image elements is approximately linear.
y..@e 3
Dodger
,”&
il.
Focus Colilmotor
..-;--..S .
,’
~
._
-.._ ”_
,
..
ob,ect
FIIm
”,
. l.
’/
Fig. 1. System for recording information from an object layer on a film to produce a sinogram.
During scanning the object rotated 7~ radians plus the divergence of the beam 0.14 radians, altogether 3.28 radians. The distance between the axis of rotation and the film was 120 mm. The scanning time varied between 1.8 and 3.5 min. The power source was a DC servomotor and steel wires were used for transmission. Excellent mechanical stability and very smooth movement was found to be important. 2.2. Convolution
A convoluted sinogramwas obtained by superimposing a compensation mask on the original. The mask is a transformed negative sinogram with a spatial frequency filtering in the u-direction only. The convoluted sinogram obtained is a ramp-filtered band-passed image of the original sinogram. The procedure compensates for the artifacts consisting of spurious shadows between different object elements usually encountered in tomography, and it corresponds to the image processing in CT (Edholm 1977). The mask was produced in the compensator shown in fig. 2. The sinogram was exposed by light from a 100 W incandescent lamp controlled by a function generator. An unexposed film of the same size as the sinogram with a gamma value close to one was placed under the sinogram and pressed close to it. The distance between the lamp and the film is 730 mm. During illumination the new film was moved in the u-direction a t a speed of 2.9 mm S-l. The degree of translational movement controlled the function generator. The nature of the compensation function will be discussed below.
Paul Edholm et al.
92
Thedigitalfunctiongeneratormultiplexes between 55 voltage levels t o produce the desired convolution function. A light intensity proportional to the convolutionfunctionisproduced by acontrolcircuitcomparing the lamp output with a signal proportional to the function. The clock frequency in the function generator can be chosen between 3 Hz and 3 MHz making it possible to change the width of the curve. The overall amplitude was set by a trim potentiometer in order to obtain the right exposureof the film.
Lcrnp
Y"l
m$
F,lm
Sinogram
generator;
U
Posltlon
lndlcator
Fig. 2 . System for producing compensation masks to obtain convoluted sinograms.
It is necessary that the positioning of the sinogram and the mask can be accurately reproduced after development. Therefore two register marks consisting of hairline crosses on the sinogram were automatically projected on the mask by twominiatureincandescentlampsactuatedforashorttime interval when the convolution function passed its axis of symmetry. 2.3. Back projection
The reconstruction of the image of the layer was done during a translation of the convoluted sinogram in the w-direction (fig. 3 ) . Each image element in the sinogram was projected by means of a cylindrical lens,power 7.85 m-l and length 90 mm, as a line on a new film. The distance between sinogram and lens was 265 mm and between lens and film 240 mm. The approximately linear array of image elements corresponding to one projection of the object layer was illuminated by a slit light source consisting of a rod-shaped 11200 lumen incandescent halogen lamp and a cylinder lens, power 20 m-1. The illuminated width, z 0.2 mm, was then projected as a rectangle on a new film, 300 mm x 300 mm. During the translational movement the new film is rotated in a way that corresponds to the rotation during therecording process. A reconstructed tomogram of the layer is obtained after completed rotation, which amounts 60 S. To avoidblurringdue to vibrationsand to 3.28 radiansandtakes geometricalerrorshigh precision mechanics was necessary;all parts were mounted on two parallel optical benches.
Tomography with Optical Reconstruction
W
93
Lamp
p-
, ,
Transformed sinogram
- / c
e:-'. &l ,,c
\
Slit shaped stop
Lens
"
Image under construction on new fllm
Rotating dlsc
..
/h
L
Electrlc motor
-. -
Fig. 3. Back projector to reconstruct a tomographic image.
2.3.1. Compensation for distortion. Due to the divergence 6 of the radiation, each projection q of the layer is distorted in the sinogram (fig, 4). In the
w-direction the distortion occurs as parallel linear arrays qi of object elements in a layer are imaged by rays pi during different angular positions W of the object. With the notations given in fig. 4 the equation U = f t a n (W - w 0 )
41%;
represents the projections si of the object layer by parallel rays. Thus each layer is projected along a tan-shaped curve; the deviation from linearity is s
1
u
Sinogram
50
WO
W
6=W,-W0
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About
Contact us
My IOPscience
Transverse tomography with incoherent optical reconstruction
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1978 Phys. Med. Biol. 23 90 (http://iopscience.iop.org/0031-9155/23/1/008) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.239.1.231 This content was downloaded on 26/08/2015 at 20:17
Please note that terms and conditions apply.
PHYS. MED. BIOL.,
1978, VOL. 23,
NO.
1, 90-99.
@
1978
Transverse Tomography with Incoherent Optical Reconstruction PAUL EDHOLM,t LARS GiiSTA HELLSTRiiMS and BERTIL JACOBSON$ t Department of Diagnostic Radiology, Linkoping University, The Medical School, S-581 85 Linkoping, Sweden 3 Department of Medical Engineering, Karolinska Institute, S-104 01 Stockholm 60, Sweden Received 2 1 April 1977
ABSTRACT. A thin layer of an object can be imaged by reconstruction from a so-called sinogram. It is produced by an X-ray fan beam rotating around the object while a recording film is moved in a direction perpendicular to the plane of the fan beam. Before reconstruction the sinogram image is convoluted according to a special function to remove artifacts consisting of spurious shadows between different object elements. Thereconstruction is donefrom the convoluted sinogram by means of a back projector, which operates according t o a principle that is the reverse of the recording of the original sinogram. Tomograms of phantoms, pork chops and the head of a dog show that the process is capable of high spatial resolution but is limited by low contrast.
1. Introduction
Computed tomography (CT) ischaracterised by highcontrastresolution but limited geometric resolution. Techniques theoretically similar to CT are possible using film as recording medium and incoherent optical methods for image reconstruction (Peters 1973, Edholm and Jacobson 1975, Gordon and Barrett 1975). Since suchmethodsshould not involve the same geometric limitations the present experimental study was undertaken. 2. Principleandmethod
The tomography comprises three processes: (i) recording of the intensity objectduring rotation, distribution of radiationtransmittedthroughthe which corresponds to the scanning process in CT; (ii) convolution, analogous to that in C T ; and (iii) back projection for reconstruction of the desired tomogram, corresponding t o the formation and display of the image matrix in CT. 2.1. Recording
Lateral projections of a one millimetre thick layer through the object was imaged on a 350 mm x 350 mm film by means of a collimated X-ray fan beam (fig. 1). The beam divergence is 0.14 radians. The energy used varied between 80 and 110 kV, tubecurrent was 10mA and the film-focus distance was 1220 mm. During rotation of the object the film was moved in a direction parallel to the axis of rotation. Thus each object element in the projected
Tomography with
Optical Reconstruction
91
layer was recorded as a sine-like curve on the film; therefore,the image obtained istermeda ‘sinogram’. The sinogram formsarhomboidwith an angle of 86O, length 306 mm and height 170 mm, In the sinogram the w-axis denotes the direction parallel to the translation of the film, and the u-axis the perpendicular direction. It should be observed that animage element inthe sinogram represents a lineararray of object elements,and that an array of image elements represents the whole layerin oneprojection. Aswill be discussed under section 2.3.1 this projected array of image elements is approximately linear.
y..@e 3
Dodger
,”&
il.
Focus Colilmotor
..-;--..S .
,’
~
._
-.._ ”_
,
..
ob,ect
FIIm
”,
. l.
’/
Fig. 1. System for recording information from an object layer on a film to produce a sinogram.
During scanning the object rotated 7~ radians plus the divergence of the beam 0.14 radians, altogether 3.28 radians. The distance between the axis of rotation and the film was 120 mm. The scanning time varied between 1.8 and 3.5 min. The power source was a DC servomotor and steel wires were used for transmission. Excellent mechanical stability and very smooth movement was found to be important. 2.2. Convolution
A convoluted sinogramwas obtained by superimposing a compensation mask on the original. The mask is a transformed negative sinogram with a spatial frequency filtering in the u-direction only. The convoluted sinogram obtained is a ramp-filtered band-passed image of the original sinogram. The procedure compensates for the artifacts consisting of spurious shadows between different object elements usually encountered in tomography, and it corresponds to the image processing in CT (Edholm 1977). The mask was produced in the compensator shown in fig. 2. The sinogram was exposed by light from a 100 W incandescent lamp controlled by a function generator. An unexposed film of the same size as the sinogram with a gamma value close to one was placed under the sinogram and pressed close to it. The distance between the lamp and the film is 730 mm. During illumination the new film was moved in the u-direction a t a speed of 2.9 mm S-l. The degree of translational movement controlled the function generator. The nature of the compensation function will be discussed below.
Paul Edholm et al.
92
Thedigitalfunctiongeneratormultiplexes between 55 voltage levels t o produce the desired convolution function. A light intensity proportional to the convolutionfunctionisproduced by acontrolcircuitcomparing the lamp output with a signal proportional to the function. The clock frequency in the function generator can be chosen between 3 Hz and 3 MHz making it possible to change the width of the curve. The overall amplitude was set by a trim potentiometer in order to obtain the right exposureof the film.
Lcrnp
Y"l
m$
F,lm
Sinogram
generator;
U
Posltlon
lndlcator
Fig. 2 . System for producing compensation masks to obtain convoluted sinograms.
It is necessary that the positioning of the sinogram and the mask can be accurately reproduced after development. Therefore two register marks consisting of hairline crosses on the sinogram were automatically projected on the mask by twominiatureincandescentlampsactuatedforashorttime interval when the convolution function passed its axis of symmetry. 2.3. Back projection
The reconstruction of the image of the layer was done during a translation of the convoluted sinogram in the w-direction (fig. 3 ) . Each image element in the sinogram was projected by means of a cylindrical lens,power 7.85 m-l and length 90 mm, as a line on a new film. The distance between sinogram and lens was 265 mm and between lens and film 240 mm. The approximately linear array of image elements corresponding to one projection of the object layer was illuminated by a slit light source consisting of a rod-shaped 11200 lumen incandescent halogen lamp and a cylinder lens, power 20 m-1. The illuminated width, z 0.2 mm, was then projected as a rectangle on a new film, 300 mm x 300 mm. During the translational movement the new film is rotated in a way that corresponds to the rotation during therecording process. A reconstructed tomogram of the layer is obtained after completed rotation, which amounts 60 S. To avoidblurringdue to vibrationsand to 3.28 radiansandtakes geometricalerrorshigh precision mechanics was necessary;all parts were mounted on two parallel optical benches.
Tomography with Optical Reconstruction
W
93
Lamp
p-
, ,
Transformed sinogram
- / c
e:-'. &l ,,c
\
Slit shaped stop
Lens
"
Image under construction on new fllm
Rotating dlsc
..
/h
L
Electrlc motor
-. -
Fig. 3. Back projector to reconstruct a tomographic image.
2.3.1. Compensation for distortion. Due to the divergence 6 of the radiation, each projection q of the layer is distorted in the sinogram (fig, 4). In the
w-direction the distortion occurs as parallel linear arrays qi of object elements in a layer are imaged by rays pi during different angular positions W of the object. With the notations given in fig. 4 the equation U = f t a n (W - w 0 )
41%;
represents the projections si of the object layer by parallel rays. Thus each layer is projected along a tan-shaped curve; the deviation from linearity is s
1
u
Sinogram
50
WO
W
6=W,-W0
