………….CT Physics - .CT Physics - ContinuedContinued

V.G.WimalasenaV.G.Wimalasena

PrincipalPrincipal

School of School of radiographyradiography

Correction for star artifacts - Correction for star artifacts - FilteringFiltering

A filter function is applied to each point A filter function is applied to each point along the attenuation profile to eliminate along the attenuation profile to eliminate these artifactsthese artifacts

Different filter functions are used to create Different filter functions are used to create sharper (higher resolution) or smoother sharper (higher resolution) or smoother (lower noise) images(lower noise) images

Attenuation profile

Filter function Filtered profile

Convolution?Convolution?

The process of applying the filter The process of applying the filter function to the attenuation profile is function to the attenuation profile is called CONVOLUTIONcalled CONVOLUTION

(Super imposition of the filter (Super imposition of the filter function and the attenuation profile)function and the attenuation profile)

Result of convolutionResult of convolution

The convolution minimizes the artifacts by The convolution minimizes the artifacts by changing the back projected information .changing the back projected information .

The dark and white bands in the illustration The dark and white bands in the illustration add up in such a way as to yield an image add up in such a way as to yield an image which accurately represents scanned objectwhich accurately represents scanned object

Impulse signals from linear traverses following angular rotations

1st back projection

2nd back projection

3rd back projection

Final back projection

Practical method of Practical method of Generation of Attenuation Generation of Attenuation

profilesprofiles Attenuation profiles are a recording of X-ray Attenuation profiles are a recording of X-ray

attenuation verses position in the object.attenuation verses position in the object. Attenuation is related to the ratio between Attenuation is related to the ratio between

incident intensity incident intensity (I(I00)) and transmitted intensity and transmitted intensity

(I(Itt))

I0It

X-ray intensity is measured by a X-ray intensity is measured by a DETECTOR which converts x-ray photons DETECTOR which converts x-ray photons to electrical currentto electrical current

The reference (Input) detector measures The reference (Input) detector measures the incident intensity the incident intensity (I(I00))

The output detector measures the The output detector measures the transmitted intensity transmitted intensity (I(It t ))

I0= incident intensity = tube output

It

II00 should remain constant should remain constant

IIt t will change depending on the attenuation will change depending on the attenuation of the object scanned (e.g. centered, round of the object scanned (e.g. centered, round object of uniform density)object of uniform density)

Io=1000

It=1000It

Calibration profileCalibration profile If the object scanned is a centered, round If the object scanned is a centered, round

water bath each attenuation profile is called a water bath each attenuation profile is called a CALIBRATION PROFILECALIBRATION PROFILE. . and the set of profiles and the set of profiles are calledare called the the Calibration File or Cal fileCalibration File or Cal file

DATA CalibrationDATA Calibration Subtraction Subtraction

of of calibration calibration filefile from the from the attenuation attenuation profilesprofiles of theof the object object called called data data calibrationcalibration

(consider an (consider an object object containing containing two areas of two areas of different different densities as densities as shown)shown)

Scan Data FileScan Data File

The The difference profiledifference profile are are stored asstored as numerical valuesnumerical values as a as a function of position in function of position in the profile.the profile.

This data is used in This data is used in the image the image reconstruction reconstruction processprocess

The set of difference The set of difference profiles for a complete profiles for a complete scan is called SCAN scan is called SCAN DATA FILE or DATA FILE or raw raw datadata

Back projection of scan Back projection of scan datadata

1.1. Back projection of Back projection of the corrected the corrected attenuation profiles attenuation profiles is accomplished by is accomplished by feeding the feeding the numerical values of numerical values of each point along each point along the profile into a the profile into a matrix. (Since the matrix. (Since the scanning motion is scanning motion is circular, the matrix circular, the matrix is usually round)is usually round) --

2.2. Close rays are Close rays are averaged to attain averaged to attain a pixel value from a pixel value from the ray that passes the ray that passes closest to its centerclosest to its center

3.3. Every pixel is Every pixel is assigned one value assigned one value per view.per view.

4.4. The final value is The final value is the sum of these the sum of these divided by the divided by the number of views number of views (as shown)(as shown)

6.6. When all the measurements have been When all the measurements have been projected back into the matrix and all pixel projected back into the matrix and all pixel values determined, the image can be displayedvalues determined, the image can be displayed

7.7. The number of The number of pixels in the image pixels in the image corresponds to the corresponds to the MATRIX SIZE. MATRIX SIZE.

This is given as 256 x This is given as 256 x 256, 320x 320, 512 256, 320x 320, 512 x 512. this refers to x 512. this refers to the number of the number of pixels across a pixels across a vertical or vertical or horizontal diameter horizontal diameter of the image.of the image.

8.8. The actual size of The actual size of a pixel is equal to a pixel is equal to the size of the the size of the area scanned, area scanned, called the FIELD called the FIELD OF VIEW (FOV) OF VIEW (FOV) divided by the divided by the matrix size.matrix size.

( Small pixel sizes ( Small pixel sizes helps to display helps to display small objects that small objects that can be resolved can be resolved by the system)by the system)

CT NumbersCT Numbers CT numbers are calculated from the CT numbers are calculated from the

measured attenuation values using the measured attenuation values using the equation given below.equation given below.

Range of CT numbersRange of CT numbers Tremendous range of attenuations that Tremendous range of attenuations that

might be displayed in a CT image requires might be displayed in a CT image requires a large number scale. +/- 1000 is a large number scale. +/- 1000 is commonly used and some systems have commonly used and some systems have extended this range further on the high extended this range further on the high end to differentiate bone densitiesend to differentiate bone densities

Limitation in display of CT numbersLimitation in display of CT numbers The The human eye can human eye can

distinguish only distinguish only aboutabout 20 levels of 20 levels of graygray in the gray in the gray scale and scale and cannot cannot appreciateappreciate the the large large range of informationrange of information contained in CT scancontained in CT scan

This is solved by This is solved by using the using the ‘window ‘window width’ & ‘window width’ & ‘window level’level’

WindowWindow width width This is the range of This is the range of

CT numbers that is CT numbers that is displayed using the displayed using the useful levels of gray useful levels of gray scalescale

Small window Small window separates one CT separates one CT number from another number from another

Large window Large window condenses more than condenses more than one CT number in one CT number in each of gray leveleach of gray level

Window levelWindow level This is the This is the centre of centre of

the range of CT the range of CT numbers displayed numbers displayed by the windowby the window

The level control The level control moves the visible moves the visible gray scale up and gray scale up and down the CT down the CT number scalenumber scale

Hounsfield unit system & Hounsfield unit system & CT numbersCT numbers

As an honour to Hounsfield who was As an honour to Hounsfield who was the pioneer of invention of CT the CT the pioneer of invention of CT the CT numbers are called Hounsfield units. numbers are called Hounsfield units.

The range of Hounsfield units Is The range of Hounsfield units Is from -1000 to +3000from -1000 to +3000

Standard reference points are -1000 Standard reference points are -1000 for Air and 0 for water.for Air and 0 for water.

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