Modulation transportation map ( MTF ) is a method of depicting “ the extent to which a piece of equipment degrades the images created in it or go throughing through it. ”[ 1 ]Therefore it can be said that MTF is a step of the ability of the imagination system to manage contrast as a map of spacial frequence, the greater the MTF of a system, at high spacial frequences, the more adept it is at capturing all right item.
MTF= transition in image at a peculiar spacial frequence
transition in object at the same spacial frequence
MTF is merely defined for a additive system where the end product is linearly relative to the input. Additionally “ an object whose brightness ( I ) varies sinusoidally with a frequence of ( L ) lines/mm is imaged through the optical system. The transition of the object ( Mo ) is defined as Mo = ( IMAX – Imam ) / ( IMAX + Imam ) , where IMAX = maximal strength, Imam = minimal strength. The image can be measured utilizing the same process, where transition of the image ( Mi ) is defined as Mi = ( IMAX – Imin ) / ( IMAX + Imin ) . ”[ 2 ]
Figure 1: The top image shows an object whose brightness ( I ) varies sinusoidally with a frequence of ( L ) lines/mm. The bottom image is a secret plan of the transition transportation factors at assorted spacial frequences
The undermentioned describes a method to find the MTF in an x-ray system. “ An x-ray beam that varies sinusoidally in infinite is created by agencies of a spatially modulated attenuator, and falls on the screen. The ensuing form of visible radiation is mapped by scanning the screen with a light metre or by exposing the movie. The MTF at this frequence is the ratio of the end product and input transitions. After the MTF for this spacial frequence is obtained the procedure is repeated at other frequences. ”[ 3 ]
( two ) Typical values for the MTF for:
Type of system
MTF
Mammography
Chest skiagraphy
Fluoroscopy
Question 2
Definition of contrast
“ Radiographic contrast refers to the extent to which the assorted different tissue constructions within the organic structure are displayed as different sunglassess of Grey in the image. ”[ 4 ]It is determined by the belongingss of the tissues, thickness, denseness and chemical composing.
Factors which determine contrast
X-ray tubing end product: High energy beams from the x-ray tubing consequence in radiation spread in the organic structure. This consequences in a low contrast image. To cut down the affects of spread the beam energy is low. This produces an image of high contrast but consequences in a higher radiation dosage to the patient.
The patient: As the x-ray beam base on ballss through the patient ‘s organic structure, it undergoes Compton dispersing. This sprinkling reduces the contrast of the image. Besides the dilutant the patient the less dose required when compared to a thicker patient which requires an increased dosage in order to obtain images.
Image receptor: is “ the ability of a movie or screen-film combination to gaining control and depict contrast is determined by the rate at which the optical denseness alterations with the logarithm of the exposure or comparative exposure, or of air kerma, by the incline of the characteristic curve, vitamin D ( optical denseness ) / vitamin D ( log_10 kerma ) . ”[ 5 ]
Method to bespeak the contrast in an image
To obtain an indicant of the contrast the simplest method uses a particular saloon apparition. The saloon apparition contains holes of different diameters and which have been preset at certain contrast degree. The trial measures the systems ability to decide low contrast objects.
Figure 2: This image shows a saloon apparition with holes of different diameters and at preset at certain contrast degree.
Question 3
Show how the constructs of Fourier analysis can be used to find the size of the focal topographic point of an x-ray system.
Whirl is used to mathematically depict the blurring of an image under certain premises. In bend this can be used to find the focal topographic point size. The premise is made that “ the focal topographic point of the X-ray beginning is non point-like. It is extended in a plane which is parallel to the surface of the sensor system. ”[ 6 ]
Figure 3: shows the apparatus assumed and relates variables to the corresponding objects.
Whirl characterizes image blurring and this blurring can be removed by deconvolution. Using the above equation can happen that the “ deconvolution of T with gd outputs an estimation of degree Fahrenheit. ”[ 7 ]
Describe in some item an experimental process to get at this
The focal topographic point size can be determined by utilizing a pinhole camera which takes an image of the focal topographic point. Using a gold/platinum home base, a little hole is drilled into it, approximately 75I?m in diameter, this is the pinhole camera. This pinhole is so inserted into lead, so that the X raies which do non go through through the hole are absorbed. The image of the focal topographic point is projected onto movie. To acquire the effectual focal topographic point, the x-ray tubing must be horizontal, when the pinhole is straight below the focal topographic point and in a plane analogue to the axis. In order to minimise mistakes the image of the focal topographic point is magnified ( M=d2/d1 ) . The image below shows the geometry for finding the size of the focal topographic point.
Figure 4: Geometry for the finding of focal-spot sizes utilizing a pinhole
d2
d1
Pinhole
Finite -size focal topographic point
Image of focal topographic point
Question 4
Why do you believe that such a apparition can give a incorrect estimation of the true focal topographic point size?
A saloon apparition indirectly measures the acuteness of an image. To accomplish an accurate focal topographic point size, a saloon apparition which contains a series of line braces of decreasing separation is required. The lines braces should run parallel and perpendicular to each other ; this allows the breadth and length of the focal topographic point to be estimated. The undermentioned image shows a standard saloon apparition.
Figure 5: This image shows a standard saloon apparition with every bit spaced lines.
The saloon apparition given in the inquiry does non incorporate line braces of equal separation. Line pairs in this apparition are running in merely one way. If this saloon apparition was used, it would ensue in a incorrect estimation of the focal topographic point size as the right length and breadth of the focal topographic point size would be unable to be determined.
Figure 6: Image given in the inquiry.
Question 5
A
Describe the basic building of a modern CT scanner and supply a tabular array with the most of import public presentation specifications of such a device
The CT scanner comprises of 3 chief subdivisions ; x-ray tubing, gauntry and the sensor. CT imaging requires the usage of high energy X raies in order to obtain accurate images. For this ground the x-ray tubing of a CT scanner must be able to manage utmost chilling and warming. The x-ray tubing of coiling CT scanner ( “ technique that involves uninterrupted motion of the patient through the scanner with the ability to scan faster and with higher definition of internal constructions. ”[ 8 ]) experiences big volumes of heat, for this ground an anode of high heat capacity and rapid chilling is necessary. Whereas translate -rotate CT scanners ( “ uses both interlingual rendition and rotary motion of a tubing sensor assembly to roll up the projection informations for each piece. ”[ 9 ]) have an oiled-cooled stationary x-ray tubing.
Figure 7: This image shows the chief constituents of a CT scanner
In recent old ages CT x-ray tubing designs have incorporated Cu and black lead blocks in the tungsten anode. In order to minimise sampling clip, a revolving anode x-ray tubing with an revolutions per minute of 10,000 and pulsed x-ray beams are used to make higher X ray end products. The gauntry houses the x-ray tubing and the sensors which are placed opposite each other. An aperture in the gauntry allows a patient to be moved through the scanner. To revolve the gauntry faux pas rings are used. “ The faux pas ring allows electric power to be transferred from a stationary power beginning onto the continuously revolving gauntry. State of the art CT scanners with slip rings can now revolve continuously and do non hold to decelerate down to get down and halt. ”[ 10 ]The CT scanner uses solid-state sensors, which are arranged in multiple rows, with the Numberss in each row changing with different industries. The sensors used require certain belongingss and are “ chosen for their sensing efficiency, short response clip, and stableness of operation ”[ 11 ]
The Following is a tabular array of the most of import public presentation specifications for a Siemens SOMATOM AR, STAR[ 12 ]
Performance Specification
Heat storage, hu ( X-ray tubing anode )
1750000
Tube chilling ( X-ray tubing anode ) :
Closed-loop, oil/air
Heat dissipation rate, hu/min ( X-RAY TUBE )
300,000 ( 3.7kW )
Number and type of sensors ( GANTRY )
512, deep-chamber Xe
Geometry ( GANTRY )
Continuous rotate-rotate, low- electromotive force faux pas ring
X-ray fan beam angle, AA° ( GANTRY )
52
Gantry gap, centimeter ( GANTRY )
60
Bacillus
Supply a description of the mathematics of image Reconstruction in CT
Reconstruction Algorithm is necessary for image Reconstruction. There are a figure of mathematical techniques used to cipher the piece of the image.
Fourier transform ( FT ) ; the x-ray fading at each angular place is divided into frequence constituents at changing amplitudes. Using the frequence component the image is created in frequence infinite, into a spatially right image and can so be reconstructed utilizing an opposite Fourier transform.
Iterative techniques ; x-ray fading at one angular orientation is compared to similar fading at a different place. The difference in x-ray fading at the changing places is added. This is so repeated at all angular waies. To guarantee the convergence of the reconstructed informations diminishing sums of the fading difference is added each clip. This technique is slow and has been replaced by other more efficient methods of image Reconstruction.
Cardinal piece theorem ; is a cardinal construct in image Reconstruction. “ This theorem states that the 1-D FT of the projection of an object is the same as the values of the 2-D FT of the object along a line drawn through the centre of the 2-D FT plane. ”[ 13 ]
Filtered back projection ; normally referred to as the whirl method. It uses a one dimensional built-in equation for the Reconstruction of the image. “ In the whirl method of utilizing built-in equations, a de-blurring map is combined ( convolved ) with the x-ray transmittal informations to take most of the blurring before the informations are back projected. ”[ 14 ]The de-blurring map is a filter that removes the frequence that causes film overing in the composite image. The image can be reconstructed while the information is being collected.
Figure 8: This image, gives image Reconstruction procedure, can be expressed compactly in the above equation, where the footings have been grouped to reflect the “ filtered-back-projection ” attack
C
Standard tests a medical physicist would execute on a CT scanner.
The followers are some of the criterion trials performed on a CT scanner.
CT figure ; truth is measured by scanning a H2O filled apparition. If the CT figure varies somewhat it can be adjusted by utilizing a rectification factor for the pel value.
Noise ; evaluated by taking the standard divergence of CT Numberss. The standard divergence can be determined by utilizing the CT Numberss obtained by scanning the H2O filled apparition.
Resolution ; if scanning apparitions returns a low contrast declaration ; it can bespeak alterations in component public presentation as it affects noise.
Patient dosage ; this is measured utilizing ionisation Chamberss. These Chamberss determine the dosage by ciphering the exposure conditions such as the x-ray beam and piece thickness used in the CT scan.
The following tabular array shows the standard trials and the frequence at which they are performed.[ 15 ]
Measurement
Frequency
CT figure, Accuracy
Monthly
CT figure, Constancy
Daily
Noise, Evaluation
Semi-annually
Noise, Constancy
Daily
Resolution
Monthly
Patient dosage
Semi-annually
