ProcIEEE_Kak_computerized_tomography_with_xray_emission_ultr(8)

tubespec-

[-I]P(x,y,E)ds

(27)

In the energyrangesused for diagnostic examinations the linear attenuation coefficient for many tissues decreases with energy. For a propagating polychromatic X-ray beam this causes the low energy photons to be preferentially absorbed, so that the remaining beam becomes proportionately richer’Althoughone may takea verylarge number of samplesineach projection,“useful information” would now be limited by the width of thefocalspot on the X-ray tube andby thesize of thedetector aperture. In discussing polychromatic X-ray photons one has to bear i mind n typesof detectors 1881. The thatthere are basicallythreedifferent output of a detector may be proportional to the total number of on it; or it may be proportional to total photon photons incident energy; or it may respond to energydeposition per unit Most countingtypedetectors are of thefirst type, mostscintillation type detectors are of the second type, while most ionization detectors are of the third type. In determining the output of a detector one must also take into account the dependence of detector sensitivity on photon energy. In this paper, we w assume, for the sake of simplicity, that

l i over the energy range of interest the detector sensitivity is constant.

in high energy photons. In other words, the mean energy associated with the exit spectrum Sexit(E), is higher than that associated with the incident spectrum Si,(E). This phenomenon is called beam hardening. Given the fact that X-ray sources in CT scanning are polychromaticand that the attenuation coefficient is energydependent, the following question arises:What parameter does an X-ray CT scanner reconstruct?To answer t i question hs McCullough[ 871,[ 881 has introduced the notion effective of energy o f a CT scanner. It is d e f i e d as that monochromatic energy a t which a given material will exhibit the same attenuation coefficient as is measured by the scanner. McCullough e t al.[ 871 showed empirically that for the original EM1 head scanner the effective energy is 72 keV when the X-ray tube is operated at 120 kVp. (See[ 921 for a practical procedure for determining the effective energy of a CTscanner.) The concept of effective energy is valid only under the condition that the exit spectra are the same for all the rays used in the measurement of projection data. (When the exit specfra are not the same, the result is the appearance o f beam hardening artifacts discussed in thenextsubsection.) It follows from the work byMcCullough[881 that it is a good assumption thatthe measured atknuation coefficient, h e a s u r e d, at a point in a cross section is related to the actual attenuationcoefficient p(E) at that pointby

T i expression applies only when the output of the detectors hsis proportional to the total number of photons incident on them. McCullough has given similar expressions when detectors measure total photon energy and when they respond to total energy depositionlunit mass. Effective energy of a scanner depends not only on the X-ray tube spectrum but a s lo on the nature of photon detection. Although it is customary to say that a CT scanner calculates the linear attenuation coefficient of tissue (at some effective

mass.

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KAK: COMPUTERIZED TOMOGRAPHY

1255

energy), the numbersactually putoutbythecomputerattached to the scanner are integers that usually range in values from - 1000 to 1000. These integers have been given the name Hounsfield units and are denoted by H . The relationship between the linear attenuation coefficient and the corresponding Hounsfield unit isH=

Cl - Clwater x loooPwater

(29)

where p water is the attenuation coefficient of water, the value of both p and ClWter are taken at the effective energy of the scanner. The value H= 0 corresponds to water; and thevalue H= - 1000 corresponds to p= 0, which is assumed t o be the attenuation coefficient of air. Clearly, if ascanner wasperfectly calibrated it would give a valueof zero for water and - 1000 for air. Under actual operatin

g conditions this is rarely the case. However, if the assumption of linearity between the measured Hounsfield units and the actual view of the attenuation coefficient (at the effective energy of the scanner) is valid, one mayuse the following relationship to convertthe measured numberH, into theideal numberH H=Hm

- Hm, water(30)

x

1000

H m, water- H w, air

where Hm,water and Hm,& are, respectively, the measured Hounsfield units for water and air, respectively. (This relationship may easily be derived by assuming that/I= aHm+ b, cal. culating a and b in terms ofHm, water, Hm, air, and Pwater, and then using (29).) Brooks[ 181 has used (28) to show that theHounsfield unit H a t a point in a image may be expressed as CT

A:

Polychromatic case

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