DE2842518A1 - TOMOGRAPHIC DEVICE AND USE OF THIS DEVICE - Google Patents

Description

Cologne, September 27, 1978 Applicant Ohio-Nuclear, Inc My reference »0 22/10

Tomograf laugh device and use, this device

The invention relates to a topographical device and on the use of this device. In particular, the invention relates to a method and a device for reconstructing objects and / or tomographic binders from them Projections. This invention finds particular application in the field of medical computer-controlled tomography.

There is a constant trend towards faster and more accurate computer-controlled tomographic scanners. The previous known medical scanners consisted of a radiation source, for example for X-rays, and a detector. The radiation source and detector were moved linearly in the transverse direction over the body to be examined, then around a few Just turned, and the crossing was repeated. Several minutes were required to obtain a sufficient number of readings for the reconstruction of a tomographic image. This long period of time was undesirable for medical tomography. She meant the patient and that too examining organ had to be kept completely still for this period of time. This known system thus made it possible to scan relatively stationary organs, such as the brain, for example. However, it was not suitable for making of cross-sectional images of fast moving organs such as the heart. A system of this type is described in U.S. PS 3,778,614 shown.

In search of higher speed, one came across a fan-shaped jet. This illuminates several detectors at the same time. See, for example, U.S. Patent 3,881,110. With such an arrangement, the transverse movement can be switched off and the only movement would be the rotation of the radiation

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source and the detectors. With this arrangement, the speed, but also the number of detectors would increase. A detector is a very expensive component. Furthermore, different detectors would take the measurements through the different parts of the body. For a total of these measurements it was essential that each detector is equally sensitive and remains equally sensitive. Otherwise the impression _T arises that more or less radiation is absorbed by this part of the body.

The next step in increasing the speed was to have all of the detectors stationary in a single rotating one Arrange radiation source. This increases the speed. However, it will be necessary to place the detectors on an arc of 360 ° over the patient. Other variations in the arrangement of stationary detectors have also been attempted. See, for example, US Pat. No. 4,031,395. The arrangement according to FIG. 3 of this US-PS has fixed detectors on an arc of 360 °, fixed X-ray tubes on an arc of 360 ° and one rotating collator. The geometry of this system lies in the fact that it is a real system with transverse and rotary motion 1st. But since the detectors and the X-ray tubes are stationary, it can be done much faster than the earlier systems with transverse and Rotary motion work in which the detector and the radiation source moved. However, this system also needs detectors on an »arc of 360 °. But as stated on page 7 of the article Reconstruction from Divergent Ray Data by A.V. Lakshaminarayanan in "Technical Report No. 92", State University by New York at Buffalo, Department of Computer Science, January 49 1973, it is suggested that any image generation system as described above has & views on an arc of 360 ° and requires a sufficient number of detectors to encompass the full 360 ° of the patient's scanning circle, among other things.

The present invention "represents a major breakthrough. With it it is recognized for the first time that views over an arc of 360 ° when using the Geoaetrle of a divergent

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Beams are not needed. Instead, she recognizes According to the present invention, each point in the area to be examined need only be viewed from an angle of 180 ° in order to obtain a complete set of projection data. That The system, in turn, can work much faster, since the x-ray source only has to scan a little over one hundred and eighty degrees, and almost half of the detectors are superfluous, that you would need in a 360 ° scanning system.

The speed at which the patient was scanned was not the only concern for medical applications used early computer-controlled tomographic devices. The first devices were very slow at taking pictures and the images they produced were not as sharp and clear as as one would have liked. The early transverse and rotary motion systems actually took a whole lot of transverse motion Series of density measurements and then filled several columns of a matrix with the successive density measurements A second matrix was then filled with further turning and lateral movements of the system. These matrices were then stacked, rotated by their respective angle relative to each other and the strengths at the corresponding point of each matrix, i.e. each vertical strength column, was summed up. This was a very slow system and less than accurate.

It was then determined that each image could be improved if each strength was aggregated by those around it Strengths has been modified to a certain extent. However, this method took even more time and required as many as fifteen to convert the data into a tomographic image Minutes.

The next step towards increasing the speed of processing the data into images was to modify the intensity at each detector by the intensities read on the surrounding detectors before entering the intensity values into the matrix. As an example, consider See U.S. Patent 3,924,129. The system shown shows a

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Number of geometrically derived approximations to achieve of these modifications. A large number of papers have subsequently appeared in which a theory of convolution was used to express the intensity at each point as a function to modify the points surrounding it. With these considerations, the intensity data are at a given point with a Faftmgsfunktlon modified whose values with intensities can be determined, which in turn are read at surrounding points. These intensity data are then stored in matrices for further processing in an image representation. The convolution method is faster than the geometric method because the functions are brought together as a unit and not as a series of individual point calculations. As stated above, however, it has hitherto been believed that the FaI-tunga interval must extend from 0 to 2ίΓ radians, that is, that the absorption intensities would have to be read off over the circle surrounding the body through all 360 °. Here too it can again be said that the present invention reduces the image processing time since it only worked with views must be that surround every point of the object to be viewed over 180 °.

Another advantage of the present invention is that it contains a faster rear projection system. The rear projector works old the data in the same order as the convolver, since the rear projector projects the data back into the image memory when they exit the convolver.

Another advantage of the present system is that each detector collects absorbance data along pathways throughout the body. So if all If detectors do not have the same sensitivity, the differences will be detected without affecting the final tomographic analysis Image an error occurs, compensated.

Another advantage of the system according to the invention is that that it contains a new Convolver (convolution *) function, which is used by fewer views, greater resolution, faster processing

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processing and simpler invoices.

The invention thus relates to an X-ray type tomographic system containing an X-ray source, which creates an x-ray fan. This compartment is wide enough to include the patient group. The system further includes means to rotate the x-ray source at a constant rate by less than a full Rotation around the patient circle. There is also a partial ring consisting of detectors, which surrounds the patient's circle by an angle of 180 ° plus the angle of the Ray fan plus the angle between adjacent detectors surrounds. In the preferred embodiment, these are with a patient circle of 50 cm about € 5r 215 °. The attenuation data from the detectors is entered into the attenuation data detector bins. This data is then processed with a convolver function. This data is then stored in returned an image memory and displayed on a monitor.

The invention will now be described further using the example of the embodiments shown in the drawing. In the drawing is *

j ^; ig. 1 is a block diagram of the entire arrangement according to the invention,

2 shows a representation of the geometry of the detectors, the X-ray source and the radiation fan,

3 shows a representation of the beam coverage of an arbitrary arranged detector,

4 shows a block diagram of the processing devices sub

Converting the projection data into convolved data and their subsequent projection into the image memory,

5A shows the Cartesian coordinate system of the Image memory,

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FIG. 5B is a representation of a rotated Cartesian coordinate system for any selected radiation fan,

6 is a block diagram of the rear projection system,

7 shows the representation of the geometry of the 180 ° plus the beam fan,

8 shows a geometrical representation of a change in the coordinates and

9 is a geometric representation of another change in the coordinates,

Fig. 1 shows generally the physical structure of the device according to the invention. The device for performing the actual physical test consists of a stationary frame 10 on which a plurality of X-ray detectors 12 are mounted are. These detectors are either single scintillation crystals or photomultiplier tubes or the ends of Light tubes, which have one or more detector stations with a single photomultiplier tube or an illumination crystal associate. The detectors 12 contain means for converting the detected X-rays into an electrical signal which indicates the strength of the X-ray beam striking the detector. The strength of the X-rays at the radiation source is known. The strength of the X-rays impinging on a specific detector is therefore a measure of the attenuation of the X-ray beam · on its way between the radiation source and the detector «that is, a measure of the absorption of the body sections located on this path. The electrical signal indicating this strength is generated by the individual detectors Entered into the processing device via electrical lines 14.

The arrangement also includes a single X-ray source 16. This creates a single fan-shaped bundle of X-rays. The opening angle of the fan should be at one

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y / inkel, which is determined by two lines running from the radiation source to the possible tangent points of the patient's circle, since radiation outside this angle exposes only the patient and the operators to additional radiation without improving the results; a device 24 is provided, to rotate the X-ray source around the patient's circle at a constant speed. A device 18 ensures that the rotation of the X-ray source is limited to an arc segment along the circumference of a circle. For this it can be seen that the detectors Λ1 are arranged only on part of the circumference of this device. The x-ray source only rotates along a similar angular arc over the patient's circle.

consideration of Fig. 2, the exact geometry of the Device now much clearer. In accordance with the present invention, it has been found that testing every point of the Object over an arc of 180 ° all data for producing a tomographic flat image results. The exam any point over an angle of more than 180 ° only leads to redundant data that needs to be removed. The geometry of the arrangement should therefore be made so that the point 26 on the circumference of the patient's circle over all 180 °, but is examined over no more angular degrees. For this to happen, the x-ray source must move counterclockwise au3 move their starting position 16 over the patient circle into their end position 16 ·. Similarly, only enough detector elements 12 be provided so that they have data over 180 ° from all points take up. It can be seen without further ado that the detectors are only from a point 28 on the outer edge of the device must extend to point 30. All detectors on a lower side of the circle between points 30 and 28 would be redundant Generate views that only have to be filtered out before further processing of the signals. One can see that the exact number of angular degrees on the outer circumference at which detectors have to be arranged, with the geometry d · »Systeaea is changeable. It changes with the relative diameters of the patient circle and the detector circle as well as the

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Circle around which the X-ray source rotates. If the The diameter of the patient circle approximates UuIl, the Number of degrees over which detectors must be placed, 180 °. You can also see that with a fan of rays X-rays in which the angle 22 is just sufficient to cover the entire patient's angle, that is, if the radius is around the the x-ray source rotates, the same as the radius around which the detectors are arranged that the detectors are then arranged on an arc of 160 ° on the circumference plus the angle 22 of the X-ray source. The X-ray source rotates around a radius slightly smaller than that radius i3t on which the detectors are arranged. The number of degrees on which the detectors are then arranged must be, is then just a little more than 180 ° plus the angle of the fan beam. As a practical matter was still noted that the detectors do not form a continuous row, but a succession of discrete points. One Rotation by an additional angular amount, which is equal to the angular distance between two i) detector elements, may then be necessary so that there are views of at least one hundred and eighty degrees at every point in the patient circle. Trap the Detectors are, for example, 4 ° apart and if the X-ray source has then just been rotated far enough » in order to expose the point 26 to radiation from 180 different angular degrees, it is possible that the data are only received from an angular range of 176 ° due to the distance of 4 ° between each two detectors.

When looking at the system from the image field of one of the detectors 21, see FIG. 3, it can be seen that the detector 21 receives the X-rays during the entire time during which the X-ray source 16 is located between the positions 23 and 25. In the case of digital processing devices such as the preferred embodiment is used, a continuous ratio of strength to tent is not processed. The amount of attenuation of the X-rays that hit detector 21 occurs, therefore becomes periodic during the movement of the X-ray source on the arc between points 23 and 25

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and each i * ies & utt & represents the ochväehunt »along a Jahn on the patient circle. The "inkeltbatand of these tracks." determines the resolution in the final toaographic flat image, and the lanes can be as close together as the physical capabilities of the processing device allow In other words, every detector can continuously generate data about the x-ray attenuation, the data processing device only records a discrete number of measurements about the x-ray attenuation at each detector.

Every time a detector is interrogated, the attenuation data are sent from the radiated detector on one of the lines 14 to the atensail device 32, where they digitize the logical output voltage of each detector. were esaiainelt along eiuer dei ¹ tracks in the fan-shaped Continuum of the tracks i UF, which ihrtr & eite of any "detected element have been received, as was described above in connection ait FIG · 3 will be described. The second signal on line 15, which indicates the angular position of the X-ray source "is also entered into the data and ammeleinrichtung 32" so that each weakening state is coordinated with the angle at which it aa

When used to zoom in, the data is considered to be logical The expression of the intensity is temporarily stored in the mass memory 40 until one of the detectors has recorded all the monitoring data that it is going to record At this point, the aorting device 34 begins, the distribution of the data to the detector beam bundles, that is to say to the seeds Attenuation data collected by a single detector over all angles. The data are then sent with the Blast hardness correction device 36 corrected. Dieae forms the Average value of several places at the end of each detector compartment and subtracts the average value from the entire compartment, whereby the detector is corrected with respect to an amplifier drift Modified non-linear optrator to correct the beam depth and input to an interpolator 38. DIt device 36 Interpolates the data in equal tangents (sltht dlt

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following equation 17) and feeds this information into the projection data memory 42 a. This process is repeated until all detector beams have been processed. A The rear projector 44, together with an image memory 46, converts the data contained in the memory 42 into a sequence of intensity representations for each point of the scan of the video monitor 48 in the raster direction. The image memory 46 can also another camera 50 of the type sold by the applicant under the trade name "Delta-Mat", be connected. In addition, another storage or display device can also be used at the discretion of the user 52 can be connected to the system.

Figure 4 is a block diagram of the reconstruction process system. It can be seen that the path of each beam can be described solely by its angular position in relation to the detector that detected it, and by the angle within the detector fan. This angle can also be expressed as a function of this angle, for example its tangent. The device 54 receives two input signals. <r shows the angular position of the detector and λ. the tangent of the angle of the path in this detector fan. The projection data h, that is to say the intensity or the attenuation of the radiation on this beam path, are entered into the projection data memory 42. A time sequence T1 to T4 pushes this data through the circuit. In this time sequence, each cer successive value of λ for a given angle Ct is entered together with the corresponding projection data h and processed until each Λ has been processed for a given fan. At this point the system moves to the next detector, takes a new angle oC and starts moving the λ- and h through the system again. The projection data memory 42 contains the projection data which are designated by the angle <SL and λ, the tangent of the angle in the fan beam. In a typical case, this memory would be a RAM that contains all beam; lenbündel could store, or in the one case in which the \ data storage is slower than the processing speed I, a double buffer would be used. The establishment ~ 8 Ö 9 8 U / 1 0 5 S

AT-

addresses the et and λ values stored in the projection data memory 42 are entered, which in turn supplies the appropriate attenuation data 1ι '(λ, <£.) To the multiplier 56.

The memory 58 is preprogrammed with a Jacobian table and is addressed by Λ. For each value of Λ a value is stored in this table. For the mathematical function selected for use in this particular preferred embodiment, the Jacobian equals Cos (arctan (λ / D)), where D is the distance between the vertex of the detector beam and the center of the patient's circle. The multiplier 56 multiplies the projection data h '(A, ^a ) by the Jacobian taken from the Jacobian table 58.

The read-only memory 60 contains a table of arctangents. The read-only memory 60 is addressed by each X and generates a value at its output which is equal to the -Arctan (λ / D). The addition stage 62 combines the angle &. with the output of read only memory 60 and generates the sum that is equal to et - Arctan Λ / D,

As already stated above, every point within the patient's circle should be viewed from only 180 ° and no more. The redundant data would produce an excess of values which would cause errors in the final tomographic projection. As a result, the excess values must be filtered out. The geometry of the system clearly shows that certain values of <£ - Arctane λ / D represent a redundant value, while other values are not redundant. Thus, a window function memory 64 is provided. ^; This yields a window function ψ * (λ, α), which is as follows | can be written:

π + F Ψ * (λ, α) = J

- Ti *

! where ψ (λ, β) '= 1 if 0 <j3-arctan £ <*

« 0 otherwise

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See the following discussion of equation 24. β is like <λ die Angular displacement around the body, however, ß can be continuous Assume sequence of values, while oc only those discrete Can assume values that correspond to the detector positions. An example of a useful interpolation function is like follows:

sin (TT (a, B) / b)
TT (a, ß) / b

where b is the distance between the views.

This means that all the values of the equation are known. With the predetermined program for each value of cc-arctan λ, / D becomes thus generating a value for ψ * (λ, α).

The window function of ψ * enters the multiplier 66. The output of the multiplier 56 is multiplied by the window function and generates the product of the projection data, multiplied by the Jacobian and the window function, that is: _η · (λ, α) J (A) ψ * (λ, α). For the sake of simplicity, this product is called H (λ / α).

It has already been stated that the buffer 68 is only used selectively and can then be omitted if the data storage speed is not below the processing speed. The convolver 70 is a conventional convolver, the input of which can be double-buffered with the buffer 68 in order to allow an overlapping K convolution and a back projection. The adding force 72 changes the angle ot to (cc-1), that is to say that it returns the angle cc to the angle of the previous} scanning beam. The buffer 68 is addressed with λ: and the convolver 70 receives the input voltage indicating (<cc-1). The memory 74 contains a table of values for a ^{filter function called G (λ 1} -λ), which for different! Values of (A. ¹ - A) is addressed by the convolver 70 in order to! to form an output function G (λ ¹ - λ) which is fed to the convolver 70 with the function H (A, dC). j

i The value of H for a certain value of λ and <X is compared with the

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-γζ-

Value of H for the same specific value of λ, at each of the possible detector positions. As will be derived in the following:

G (M-N) «1 if M-N» 0

»-X—- 5 if M-N is odd

Tt ² (MN) ²

»0 if M-N is even,

where M is the number of the detector position whose data is being processed and N is the number of each of the previous detector positions.

That is, the value of H for a given X in the detector fan of the M-th detector position, H (A, M) is convoluted and thus becomes H (A ¹ , M), where

H (X ¹ , M) = H (X, M) G (MM) + H (X, MI) G (I) +

H (X, M-2) G (2) + H (X, M-3) G (3) +

= H (X, M) + 4H (X, MI) ₊ 0 ₊ 4H (X, M-3) ^ , τι ² 9π ²

It is noticeable that the data for every second detector position is not taken into account and that the data from detector positions that are withheld are increasingly weighted less heavily as the detector position is further out. : The addition stage 80 leads the (oil - 2) addressing signal to the; Convolver 70 too. Similar addition stages can be added to supply the (et-3) etc. addresses. One can see, however, I that the proportion for the further from located detector positions j decreases rapidly so that only a few need to be addressed. ;

The data from the convolver 70 is addressed and placed in the buffer 76. This is used together with the rear projector 78. The working method of the rear projector is connected are explained in more detail with FIGS. 5 and 6.

There are several ways of performing the rear projection, ¹ see, for example, US Pat. No. 3,924,129

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Conduct algorithms, i.e. algorithms in which the position of the matrix element is the independent variable. at the procedure described here is not just one such algorithm are used, but no arctangent calculations are required. The present invention develops a- ■ A simple set of linear relationships between the data relating to the detector beams and the image matrix. This makes it possible for the back projection to be described with a set of differential equations which can be described with have a minimum of arithmetic work done. The minimization of the computational work is very important because the back projection requires numerous iterations and is generally the most time consuming part of the reconstruction. Under With reference to the following mathematical derivation, it should be said that a description of the reconstruction process now follows:

f (γ, Φ) = jT Σ Σ h '(X, a) cos (arctan £) G (X'-X) ψ * (λ, et) a = - »X = -p *

since one over (<cos y) ^{2 is} a function of only R, φ and ole, it can be extracted from the inner summation. The ι equation can thus be written in the following way, where; the inner summation has already been carried out in the convolver 70;

became: ;

P *

# ^? w h '(X, a) cos (arctan κϋ) (ί <λ · -λ) ψ * (λ, α)

^(Γ ' ^Φ) ^ L (F ₊ A) ^{(KCOS μ)} ' λ = "Ρ *

5A and 5B show the relationship between the carte i forensic image matrix and the geometry of FIG. 9. This proportionality 'nis is another Cartesian in Fig. 5B by superposition! The coordinate system (s, t) has been simplified, which has been rotated until it is aligned with the dlvergent system. The description of K (r ₍ <j?, * 0 and jju {f. Φ, <£) is simplified by converting from the (x, y) coordinate system to the (s, t) coordinate system. Using these systems . in the gezeig th in Figure 5B relationship, the above equation can be written in these variables as follows:

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Zn

π + F + A

E (x, y, a) = D + χ sin α + y cos α λ ¹ = (χ cos α - y sin ct) / E (x, y, a)

Equations 27 to 29 naturally describe the operations to be carried out by the rear projector. One recognises, that the system operates with transverse and rotary scanning as described in US Pat. No. 3,924,129. Best suited however, it is an X-ray source with a fan-shaped beam.

The system must calculate and ^{insert λ 1} into the convolved data H (X ¹ , ot), which are weighted with 1 / E and summed up in the corresponding matrix point. It can be seen that with the determination of E and \ 'there is a simple linear relationship. Indeed, equations 28 and 29 can be manipulated with finite differences to reduce the multiplications required.

For example, to scream through the matrix in the X-direction equations 28 and 29 would look like this:

^E J + 1 ^{= E} J ⁺ §1 i

⁵ yrs ₊ I " ⁸ yrs

§ £ = .sin α; § | = cos α

Similar equations result when the matrix is traversed in the Y direction. Figure 6 is a block diagram of the back projector system. All work steps are shown in a sequential way. When using locking

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Successfully, however, the work steps can also be carried out in one direction, which then results in multiplications and memory accesses overlap. This increases the speed of these work steps considerably.

A basic processor inputs the value ac, which describes the orientation of a single projection line, into registers 92 and. The values s _Q and Eq are determined using the above calculations.

For each detector position, that is to say each viewing angle, the multiplexers 98 and 104 are triggered with the input I and the s., Register 110 and the E., Register 112 are cleared. During operation, the ^H R "input for the multiplexers 98 and 104 is selected so that the s.» Register 110 and the E ^ register 112 can be set. The timing and regulating device 128 then triggers this process each time, if it advances the address in the image memory to a position of the contents of s, -... the register 110 and the e, - register 112 are projected so that they progressively, the values of Sq, S _1, S _2, etc., and Eq , E ₁ , E ₂ , etc. Memories 116 and 118 may be ROM or RAM memory, and if RAM is used, the basic processor could change the geometry of the processor by entering other tables

change ρ. These memories are reciprocal tables for E and E. For for each value of E, memory 116 gives the value of eim over E.

ρ and the memory 118 outputs the value of one through E.

The multiplier 114 performs the multiplication given in Equation 29 above. That is, it converts the address X ¹ into the projection data. The memory 16 is a RAM memory which contains the projection data H (A. ¹ , oc) supplied by the convolver 70 from FIG. 4. These projection data can be fed into the memory 120 directly from the convolver 70 or by a basic processor.

As was the case for the processing device shown in Fig. 4, the rear projector processes each of the possible for each predetermined angle ac, that is to say for a predetermined detector position

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Beam paths λ. within the viewing angle before moving to the next angle oc. This means that the rear projector does not have to wait until the convolver has processed the data for all angles of oc, but rather only has to wait until the processing of a certain angle <x has ended before it makes the rear projection entries in the image memory 124. For this predetermined detector position oc, each time the memory 120 is ^{addressed by A 1} , the memory generates an output signal which indicates the convolved data Η (λ ', oc).

The multiplier 122 multiplies the output of the memory 120 by the output of the memory 118. This becomes the projection beam Η (λ ', oc) weighted by one over E. One over E is the value that is superimposed on a given matrix point will. The addition stage 126 combines this value with the respective one Content of the matrix position. This process continues until all projection data is collected and stored in the Image memory have been back-projected. At this point in time, the content of the image memory actually represents the tomography of the affected cross-section.

It is useful for the image memory 46 to have the same number of X-lines as it does on a standard television monitor There are scan lines, i.e. 512, and that it contains as many matrix points on each X-line as there are on each scan raster of the standard television monitor are pixels. This is used to convert the contents of the image memory into a Video point just a digital to analog converter and a standard television monitor needed.

In some cases it is desirable to view the projection data during; to interpolate the rear projection. This can be done by address-i sizing the two closest points in the Η (λ.) memory by obtaining addresses with fractions and using another addition stage and another multiplier for Be-f effect a linear interpolation at the output of the memory. So-y however, this can be costly in terms of both the facilities required and the turnaround time.

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A simpler way is to have H (A, et) in the basic processor pre-interpolated. This creates a longer series of data. The corresponding high-precision addresses are then entered in the Memory 120 given. Although this requires more memory, it has computational advantage and interpolation occurs only once per image instead of about once per image line per image.

In some cases, the rear projector can be many times faster than generally make large image memory. This results in the processor being thrown out of step. This problem can be solved in that several groups of projection data are buffered in a high-speed memory and a or several image buffer lines are buffered in the fast memory. This way you can have multiple images in project each line of the image before making a transfer to the image memory. This increases the effective speed of the image memory by an amount that is proportional to the number of buffered projection lines.

The next section describes the math behind the convolution function used in the preferred embodiment stands. It should also be pointed out that the device described in FIG. 4 can of course also be used with others Convolution functions can work, although this involves changing values in some of the tables in some of the memories may require, and the convolution function to be described can also be used with other facilities. For example, a general purpose digital computer or a microprocessor can be used use. The rear projection system can also be independent of the convolution function or that shown in FIG Use switching devices and vice versa, the rear projectors can also use the switching devices shown in FIG functions and / or the convolu-j tion function to be described below.

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IS

Mathematical derivation

In this mathematical derivation, the system is viewed from the point of view of a detector element such as the one in FIG detector 21 shown. If one now, as shown in Fig. 8, a line perpendicular to the middle If a ray of the bundle of rays were to draw, then all rays of this bundle would intersect this line. Every ray within of the beam has a single value indicating the attenuation in the beam path. If this value to the line h in Fig. 8 is applied to the point at which each beam crosses it, then one would get a line, on which there would be a series of amplitudes indicating the attenuation along the beam that the line on it Point crosses. These individual discrete amplitudes can be interpolated into a smooth continuous function. In this way it can then be said of the line h that it is the data line for this bundle view of the object to be examined Represents the object. The value for each point on line h can be addressed by knowing the vertex of the Detector beam (i.e. the detector position), which is determined by the angle ß and the angle in the fan that of the definition is equivalent to a position on the line h.

In prior tomographic systems, a cross-and-rotate system is used in which the detector detected the attenuation along one group of parallel beam paths, then rotated and detected another group of parallel beam paths at some angle to the first group, and so on. For each given object, the projection data in the transverse and rotation system are the same as the projection data from the system with the rotating beam. The individual data points are different. However, the entirety of the data provides the same picture. Where ρ (Ζ, θ) supplies the projection data for the 'transverse and rotational system, the relationship between- ' can be found. see the transverse and the rotation system and the system with the rotating fan of rays as follows:

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(1) p (i, θ) = η (λ, Ρ)

A simple geometry leads to the following relationships when looking at FIG. 1:

(2) θ = B + tan ~ ¹ (X / D)

(3) I = Xcos tan " ¹ (λ / D)

This allows the projection data for the system with the rotating fan beam to be expressed as follows:

(4) h (X, B) = ρ (Xcos (tan " ¹ (λ / D), B + tarT ¹ (X / D))

From the theorem for the central section it is known that the following applies to a point to be reconstructed:

π <= °
(5) f (r, 4>) = / J | R | F (R, 8) exp [27riRr cos <8- <j>}] dRde

O-oo

Here, f (r,) is a two-dimensional image in the real space to be reconstructed, and r and φ are the polar coordinates for the points in the real space, and F (R, Θ) is a Fourier transform, where R and θ are the polar coordinates in Fourier space. It can be seen that the theorem of the central section is expressed with different limits than those explained in the above-mentioned paper by AV Lakshminarayanan. The following proof shows that the author is right in his assumption that integrating only from 0 to IC and not from 0 to 21t, as Lakshminarayanan explains on page 7 of his essay. It goes without saying that the integrals in polar coordinates from 0 to 21t for the angular displacement and from 0 to infinity for the radial displacement is the equivalent of an integration of 0 to 2iC for the angular displacement and minus infinity to plus infinity for the radial displacement, since '■ both kinds of integrals all scan the same points.

·; The Fourier transform of ί (τ, φ) is related to the projection in the ratio given by the following equation:

42518

or substituting the relationships given in equations 2, 3 and 4 into equation 6, which is then written as follows:

The following then applies: ρ is the radius of the object to be tested in real space, γ * jst is the equivalent of the radius of the object to be tested in Fourier space and J (X) is the Jacobian of the transformation and in this case the partial derivative of Z compared to %, whereby the following applies even more precisely:

As stated above, the angle corresponds to ρ in the data line h (A »p) the detector position, and da a discrete number from detectors is present, h in is not continuous. Since h (A ,, ß) is keyed in (3, a continuum is required in β. It follows that h must be interpolated into a continuous function in β. This can be done by using an interpolation function A, which can be any of a number of interpolation functions. An example of an Interpola-j tion function that could be used is as follows:;

Hence, h (A, ß), which is continuous in ß, can be as follows to write:

j Here, cc means the discrete angle corresponding to the detector positions in physical reality and β is the con-

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tinuum the angle corresponding to J. Included:

(9a) cf'U) «= scanner (for example

(9b) b »Angular shift between the views

Other interpolators and samplers can of course be used, provided that only the compatibility between them is maintained.

By introducing a Fourier filter function B (R, θ) which is within of the equivalent of the patient circle is 1 in Fourier space and 0 outside of it, by substituting the equations in equation 7 and 9 equivalents found in equation 5 and by changing the integration order, this equation 5 can be as follows to write:

F is one half of the angle of the detector beam

and where γ ( ^ ₁ ^) is a window function in order to cut out the redundancies determined by the following equation:

(JlJ

0 on the other hand

It has already been stated that for viewing each point of the patient's circle from at least 180 °, a few points from more ' must be viewed as 180 °. So that superfluous j readings are not used twice and thus the | Computing the final tomographic image values for use lead to incorrect sums, these extra views must be removed. Therefore this function brings the weakening « data that are received along the superfluous beam paths and

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projected onto the data line is zero. Since the redundant angular views have now been removed by the function Ψ and since h has been made continuous in ß in equation 9, it is now possible to change the variable of the integration from £> to ß. By changing the variables of integration in equation 10 from θ to β and by changing the order of integration, equation 10 can be written as follows:

or by changing the order of integration again:

"F.

To achieve a filter function that is like a convolution function looks, it is advisable to change the coordinates in such a way that every point within the patient's circle is through its distance from the vertex of the beam and by the angle between the center of the beam and one Line connecting the vertex to the point. This distance is called K and the angle. Fig. 9 shows the relationship between (K, //) and (r, <p). At introduction With this change in coordinates, the filter function B can be written as follows:

If scanning in λ along the data line at intervals of a, where a is some positive constant, that is, evaluating h (A, ß) for values of λ equal to Na. A definition of the last integral of Equation 13 as g (A'-A) and substitution for Λ * and φ according to the equations 10a and 10b and then with a change in the limits of the integration according to equation 14, then write this last integral as follows:

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This equation can be written as follows:

The following applies:

As a result, the integral from equation 16 can be evaluated. By performing the integration and selecting λ equals Na, where a is the sampling integral and N is an integer is, it results:

The following applies:

-N) = 1 if (M-N) = 0

—5 ^ ^- if MN is odd

^ (MN) ²

= 0 if M-N is even

Where M is the scanned projection and N is the total number of the projections. By inserting g (A'-A) into the Equation 13 and exchanging the integrals for discrete summations (janter with reference to Fig. 9) results in the following:

9 oll ίϊ 4 / TÖ5 5

In order to obtain a spatially invariant and thus a computationally usable convolution function, g (A .'- / t) must be removed from the integral, but g is the function of (β, r, <p). It should be said, however, that the interpolator A (oL, ß) is a very narrow function which weights g (A'-A) very strongly for small values of oL-ß. For systems with an adequate viewing distance, errors of less than 0.1 % result from the following approximation.

This means that g can be calculated as a function of the discrete angle ole with detectors close enough to one another, which marks the position of the discrete detectors rather than that of the continuous angle β. In this approximation, will g is therefore always regarded as the closest detector point. This means that g can be removed from the integral. With With this approximation, equation 19 can be written as follows?

The following definition applies:

Ψ * is simply a convolution of the interpolator A with the window function ψ. It can be viewed as a weighting function for the projection data, and since the kernel functions can be made stationary, ψ * only needs to be calculated once and pushed into the appropriate position on the projection data as determined by oil. The summation limits on α from minus infinity to infinity are difficult to calculate. Since the interpolator is narrow, t * is

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essential but remain at right angles similar to ψ. If, however, one chooses any distance A from the point at which it becomes zero and at which Ψ * is sufficiently close to zero, then the limits on equation 23 shift from between minus infinity and infinity to between -FA and 1Γ + Q + A. Practice has shown that excellent results can be achieved with A equal to zero. Equation 23 can thus be written as follows:

F is equal to half the detector fan angle. The resulting Algorithm is thus simply a convolution and back projection with the addition of a weighting function that in front of the convolution is applied to the projection data.

Conclusion

It can thus be seen that the density for each point within the patient circle can be calculated using equation 25. A two-dimensional density image f (r, qp) can thus be calculated for all r and <p within the patient group and a tomographic image is obtained. The above system only requires sufficient detectors so that every point in the patient's circle can be viewed from 180 ° in order to incorporate the attenuation data into the tomographic image. It is readily apparent that other mathematical approximations can be made and other interpolation functions can be used to arrive at the equation to be evaluated. The invention is not limited to a single interpolation function or approximation. The above interpolation functions and approximations are given as examples only. It is also apparent that the switching devices for the processing and rear projection can also assume other embodiments in addition to the embodiments disclosed above, for example in the form of a digital computer.

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Claims (1)

Cologne, September 21, 1978 vA. Applicant: Ohio-Nuclear, Inc. My reference: 0 22/10 PATENT CLAIMS C 1oyTomographic device for exposing a body to penetrating radiation, characterized by the following features: a radiation source that can rotate relative to the object, an arrangement of detectors which are arranged in the circumferential direction along an arc of a circle surrounding the object are, the array of detectors encompassing an angle of less than 360 ° on the sheet. 2. Apparatus according to claim 1, characterized in that the radiation source generates a fan-shaped radiation beam. 3ο device according to claim 2, characterized in that devices are provided that define an image circle that encloses the object to be exposed to radiation. 4. Apparatus according to claim 3, characterized in that the radiation source encloses such an angle that the Edges of the radiation fan are tangent to the image circle. 5. Apparatus according to claim 1, characterized in that the Detectors an angle greater than 180 ° but less than '■ enclose 300 °. Detector arrangement an arc of less than 250 °, but more 6 "Device according to claim 1, characterized in that the ^; detector
than 190 ° encloses. 9098U / 1055 7. The device according to claim 1, characterized in that the detector arrangement has an arc of more than 200 °, but less than 230 ° encloses. 8. The device according to claim 1, characterized in that the detectors have an arc of more than 210 °, but less than
Enclose 220 °. 9. The device according to claim 1, characterized in that the detector arrangement has an arc of more than 220 °, but less than 230 ° encloses. 10. The device according to claim 4, characterized in that the detector arrangement has an arc ν
of the bundle of rays. Detector arrangement an arc of 180 ° plus the angle 11. The device according to claim 4, characterized in that the detector arrangement plus an arc of more than 180 °
the angle of the radiation fan, but less than 190 plus the angle of the radiation fan encloses _o 12. The device according to claim 1, characterized in that the detector device encloses an arc of 180 ° plus a number of degrees which lie between two lines
both starting from the same point on the detector arc, and each line being at a different point tangent to the image circle. 13. Apparatus according to claim 12, characterized by Devices for generating an electrical signal,
ι that shows the intensity of the radiation received by each detector element,
Devices for generating an electrical signal, which indicates the position of the X-ray beam, and
Devices for processing the electrical signals indicating the intensity and the position in order to
! To indicate the position of the density of the object in the layer through which the radiation passes. 9098 U / 1055 14. Use of the device according to claims 1 to 13 for producing a representation of the fluctuating absorption of a planar layer of a body against penetrating radiation, characterized by the following steps: a) Formation of a plurality of groups of beam data signals, the signals of each group having the absorption of a represent corresponding group of rays emanating from a radiation source in a fan-shaped scheme through the whole Diverge plane of the layer, b) rearranging the data into data groups that represent the absorption of a corresponding group of all rays, which pass through the body and converge to a single point, this array of rays being a would be a fan-shaped arrangement, the apex of which lies in this single point, c) Interpolation of the discrete absorption values corresponding to each ray within one of the groups of the converging ones Beam data for a continuous function, d) sampling a plurality of points along the function for each of the converging ray data groups, e) Deriving a value for a window function from the Angular position of the vertex of the fan-shaped arrangement and the angular position of the beam that corresponds to the scanned point corresponds to the function, f) Multiplication of the value of the sampled point of the Function with the value for the window function, g) convolving each sampled intensity with a convolving function that defines the sampled intensity as sets a function of the intensity values of the other of the converging beam data groups; h) back projection of the convolved absorption data in | an image memory. ι (ι I. , i j15. Use according to claim 14, characterized by the following j the steps:! a) Exposing the body to fan-shaped radiation source, b) Rotation of the fan-shaped radiation source with respect to the body at a constant speed until each Point in the body has been exposed to radiation from 180 °, c) detecting the radiation that penetrates the body, d) converting the detected radiation into electrical signals that indicate the absorption of radiation, e) processing the signals into a representation of the variation in absorption of the planar layer of the body " 16. Use according to claim 15, characterized in that the Signals are filtered to remove any signals generated by any point in the body of a Exposure to radiation from more than 180 °. 17. Use according to claim 15 »characterized in that the Radiation is detected at a plurality of discrete detection points which are arranged around the body. 18. Use according to claim 17, characterized in that the signals detected by a first detection point are convolved with a function which results from the signals at other detection points detected signals determined. 19. Use according to claim 18, characterized in that the signals detected at a predetermined detection point with Signals received at the Nth neighboring detection point, but only if N is an odd number. 20. Use according to claim 18, characterized in that the Convolving stage has the following characteristics: , Addition to the signal that corresponds to the absorption along the i ι beam path that is applied to the N-th detector point under, an angle λ. to the imaginary line between the detector '4 j point and the body meets, to the product of! and the signal corresponding to absorption along a beam path having a detection point M below the same 90 "9TIi 7 1 Corresponds to the angle λ relative to the imaginary line between the M-th detection point and the center of the body, if M-N is odd, and if M-N is even, nothing is added to the signal. 21. Use according to claim 14, characterized by the following Steps: Acquisition of a plurality of groups of beam data signals, the signals of each group having the absorption of a corresponding one Represent arrangement of x-rays converging to a point Interpellating any discrete signals so that each group of beam data signals is a continuous function, so that for each beam reaching the detection point which has traversed at an angle / L relative to an imaginary line between the center of the body and the detector point, an absorption data signal corresponding to some angle X is present for each detection point, Convolve the data received at each detection point with the data received at the other detection points. 22. Use according to claim 21, characterized in that the data of the N-th detector point with each other detection point M can only be convolved if M-N is odd. 23. Use according to claim 21, characterized in that when convolving for each angle λ G (MN) -fold a function of the beam data signal is added which corresponds to the absorption of a beam at an angle λ in each of the M groups of the data beam signals, wherein G (M-N) = 1 if M-N is 0 | G (M-N) - -5—- ^, if M-N is odd, and! TT ^ (M-N) ^ i G (M-N) - 0 if M-N is even. 24. Use according to claim 21, characterized in that the back projection of the convolved data into a matrix system with image coordinates has the following steps: Selection of a point (X, Y) in the image coordinate system, for one of the data groups the angle λ. is determined who corresponds to a ray that would pass through the point in the body corresponding to point (X, Y), Determine the distance from the point to the point according to the point (X, Y) and project this distance onto a line starting from this point and passing through the center of the body, Set the signal that corresponds to the convolved attenuation data for that angle of λ and this Data group by a function of the ratio of the distance between the point and the center of the body and the projected distance, Repeat this process for each detection point, Sum the resulting value for each data group and Repeat the process for each point (X, Y) of the matrix system the image coordinates. 25. Use according to claim 24, characterized in that the Function of the ratio of the distance between the detection point and the center of the body and the projection distance is as follows: D ² where D is the distance from the detection point to the center of the body, E is the projection distance, and a is the distance in the body which is the distance between adjacent matrix points in the matrix system of image coordinates is equivalent to. 9Q98U / 1055