DE2437529A1 - METHOD AND ARRANGEMENT FOR DISTORTION-FREE TOMOSYNTHESIS - Google Patents

Description

PHILIPS PATENTVERWALTUNG GMBH, Hamburg 1, Steindamm 94.

Method and arrangement for distortion-free tomosynthesis

The invention relates to a method and an arrangement for synthesis of any layers of a three-dimensional object through superposition of images, which through central projection of the object can be generated from different directions onto a curved radiation-sensitive layer.

It is known that by projecting a three-dimensional object from different directions onto a plane, radiation-sensitive Layer the image of a plane object layer parallel to the radiation-sensitive layer by shifted overlay of the can reconstruct individual projection images. (Lit .: D.G. Grant, Tomosynthesis: A Three-dimensional Radiographic Imaging Technique, IEEE, BME-19,1 (1972), 20-28 and E.R. Miller, E.M. McCurry, An infinite

Number of Laminograms from a finite Number of Radiographs, Radiology, 98, Feb. 1971, 249-255 _and K.Dümmling, Eine neue.Verfahren zum

PHD 74-140 Sh / sa ₅₀₉ 887/0667 ■

Multiple shifts with the help of television image storage, The radiologist 9, 37 (1969). The first object layer is created by not shifting Overlay of all individual images (primary layer). For a curved screen it was possible without loss of resolution only this primary layer can be reconstructed (Lit .: H.Vieten, on the dependence of the depicted object layer on the form the radiation-sensitive image layer, Stratigrafia, 2 (1957), 2-8).

The process of shifting object layers by superimposing them reconstruct has the disadvantage that one has to rely on a flat screen or that one has a considerable deterioration in the Resolving power receives. Radiation-sensitive layers with flat surfaces have too low a resolution, poor gradation (MicroChannel electron multiplier) or are too insensitive (Image converter). To set up an electronic tomosynthesis process therefore, an image intensifier must be used, which usually has a curved radiation-sensitive layer.

The object of the invention is to provide a tomosynthesis with a high resolution even when using powerful and highly sensitive To achieve image capture devices.

This object is achieved in that the individual projection images are scanned electronically, stored in a memory and then with an overlay in a medium, e.g. a

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Storage tube / electronically equalized so that all points a freely selectable object layer are mapped coincidentally, with a programmable, controlled by a process computer Equalization network when superimposed on the deflection voltages of the electronic sampling with the aid of two analog adding amplifiers For each of the two orthogonal deflection directions, additional correction voltages are added, those from the desired object slice depend, and these sums of the original deflection voltages with the associated correction voltages for the deflection of a write beam is used for the overlay medium.

The images of the individual projections are rectified in such a way that each object point is a desired slice in the Superposition of the individual images is always mapped into the same pixel, and each projection image is electronic Sampling before the superimposition by a programmable equalization electronically equalized with the help of the deflection voltages, e.g. of a storage tube.

The invention has the following advantages.

a) A quick recording sequence can be achieved, since the images of the individual projections are initially stored in a distorted manner will.

b) It can be done using the specified procedure by appropriate Programming of the equalization network any

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Object layer can be reconstructed (e.g. also a plane layer). The choice of the object layer is not restricted from the start, as is the case with rectification during the recording of the projection images.

c) The object slices to be reconstructed are suitably selected

(e.g. by moving the primary layer), the required non-linear corrections of the deflection voltages small compared to these themselves and the equalization network can accordingly can be easily set up.

d) If a rotationally symmetrical screen is assumed, there is a further advantage. By electrically rotating the coordinate system of the deflection voltages, the parameters that are required for programming the equalization network can be separated into those that only depend on the object slice to be reconstructed and a parameter that determines the rotation of the tomography device by a horizontal angle ( ^ P) describes. In the case of a circular blurring figure, only the parameter that describes this angle needs to be set anew before the superposition of a projection image during a synthesis.

e) The network also allows distortion errors in the image intensifier-camera system to be corrected without additional effort. If a rotationally symmetrical screen is used, and the rectification is carried out after the electronic rotation of the coordinate system, however, only rotationally symmetrical distortions can also be corrected will.

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f) The achievable resolution can be determined by a corresponding Complex equalization network can be increased in each case to such an extent that the overall resolution of a real system by the The influence of errors in other components is limited.

The invention is explained with reference to the figures. Show it
1 shows a schematic diagram of the method,

Fig.2 two examples of object layers that require small corrections the deflection voltages lead,

3 shows a block diagram of the entire equalization network.

Fig. 4 shows the equalization network, but without the required rotation and reverse rotation of the coordinate system and

Fig.5 shows a network for rapid electronic rotation of the
Coordinate system.

The object 0 is made out of different by N X-ray flashes (F -... F) Directions illuminated by the associated horizontal

(VI.N)

angle 1 (P, ... J ^) and polar angle / be defined (Fig. 1). The image intensifier is adjusted in such a way that a connecting line from the center point of the image intensifier to the radiation source (central beam)
always goes through a point (Q). The positions of the image intensifier are identified in FIG. 1 by its center point (M -... M _n ). After electronic scanning by a television camera 2 with an optical system 3 and the intermediate storage by a

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Image memory 4 is the images in a superposition unit, e.g., a storage tube 5, with an electron write beam superimposed in such an equalized manner that only one object slice is sharply imaged. The equalization is done by adding to the deflection voltages (u ", u) of the deflection voltage generator 6 to-

x y

additional correction voltages (Au ", Λ, υ. ) by means of surgical

x y

amplifiers 6 ', 6 analogue added v / earth. The corrective tensions are generated in an equalization network 7. This equalization network is programmed by a process computer 8. The necessary Driver amplifiers for controlling magnetic deflection units are not specified separately in the circuit diagram.

The rectification is shown at a point (P) on any object slice to be reconstructed. _{The voltage pairs of the deflection voltages (u - ... u N} and ^u v1 * '* ^u vN ^ ^ ^{er Pernse} hcamera belong to this point (P) for the individual projection images (P' ... ΡΛ) / ... P ' \, which correspond to an object point (P), should be mapped coincidentally for all superimposed images on a point which should correspond to the deflection voltages u and 5 of the storage tube 5. The necessary correction voltages (Au = ΰ - u and Λ u = ü - u, η = 1 ... N) shown here as a function of an object point (P), after mathematical elimination of the coordinates of this point can be shown as functions of the deflection voltages themselves, ie

^Au xn ⁼ ^ x " ^u xn = ^x n ^(u x ' ^u y ^}
^ V = ⁵ y - ^u yn = ^Y n ^(u x ' ^u y>,

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The functions X- ... X and Y- ... Y are non-linear Functions of the deflection voltages. To the influence of errors in a circuit to keep the technical approximation of these functions small, they should themselves be small compared to the actual deflection voltages. Two measures are required for this.

a) The choice of a suitable mapping point a (u, u). This imaging point should be as central as possible in the area that is circumscribed by the deflection voltages of the individual images (u -... ti. ,, U -... u _N ). The point on which the object point (P) would be mapped in an axial central projection can be selected as a sensible mapping point. An overall distortion then remains in the synthesized image of the object layer, which corresponds to this axial central projection, including possible distortions of the image intensifier-camera system. In general, this overall distortion will be of no importance, but it can also be eliminated by means of fixed equalization networks on the camera deflection system. (Another possibility is the mean value of the voltages of all individual projections)

b) The choice of the desired object layer. Valid results, ie small correction stresses, are obtained, for example, by shifting the primary layer K ₁ (FIG. 2) or, in the case of a spherical cap-shaped primary layer, by concentric spherical surface sections K 2 (FIG. 2).

Taking into account points a) and b), the correction voltages (for a horizontal angle J = O) with sufficient accuracy

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approximate by simple functions, such as

^X n = ^a n ^{+ b} n < ^u x ~ ^c n> * ^{+ d} n «y * < ^u x ~ ^e n> ^Y n ^{= f} η ^u x * ^u y

The electronic generation of these correction voltages is shown in Fig. 4. Here DA. ,, ^D & 2 ' ^DA 3 ^D i9i ^ta l ~ ^Ana l ° 9 ~ ^Wan ^ l ^er r over which the network is programmed; S ₁ , S ₂ , S ₃ analog adders (for example adding amplifiers) j M ₁ , M2, M ₃ , M ^ are analog multipliers and Mr, Mg, My are multiplying digital-to-analog converters. However, these can also be replaced by a digital-to-analog converter in conjunction with an analog multiplier. The parameters with which the network is programmed (a _n ... £) are specified by the process computer 8. They can be saved there or they can be new

the

be calculated. The individual parameters depend on / geometric Imaging laws of an oblique central projection, on the shape of the radiation-sensitive layer, on the distortion of the image intensifier-camera system, on the required overall distortion and from the object layer to be imaged. Since each parameter depends on the stated circumstances or factors, must all be recalculated if one changes.

The rotation of the central ray (F _n QM _n , η = 1 ... N) by a horizontal _{angle (^ 1} ... J) is taken into account by the electronic rotation of the coordinate system (Fig. 3). The coordinate system of the deflection voltages is first rotated electronically

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then rectified by the horizontal angle (Fig. 3, k) as for the horizontal angle ° - 0 (Fig. 3, 1) and then rotated back again by the horizontal angle (Fig. 3, m). This rotation can be done, for example, by units that are known as resolvers in analog computing technology. For fast processing of the images (television standard), circuits according to Fig. 5 are suitable. Here / are Mg _f Mg, M ₁₀ , M ₁₁ multiplying digital-to-analog converters and S, and S, _ analog adders, the trigonometric functions of the angle of rotation are specified by the process computer via the digital inputs s-, s, and c, according to s ., = sin «- * , s ~ =" S ₁ , c = cos J. When turning back, the inputs s., and s _{2 have} to be swapped. With fixed discrete values the horizontal angle ( tf « ... J ^ _n ) the multiplying digital-to-analog converters can be replaced by resistor cascades with fixed taps. The process computer then controls the taps of the cascades.

In the case of a circular blurring figure (i.e. all positions of the radiation source F ... F (Fig. 1) lie on a circle) in the case of superposition, only the parameters of the horizontal angle in the electronic rotation for each individual projection image of the coordinate system can be reset. The other parameters (a ... f) are not changed, whether the screen or the one to be displayed Object layer is rotationally symmetrical.

Claims Ϊ

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Claims (15)

Claims ϊ / 1 ./Verfahren any of synthesizing layers of a three-dimensional object by superposition of images, which are generated by central projection of the object from different directions on an arbitrarily curved radiation sensitive layer, characterized net gekennzeich that the individual projection images electronically scanned, stored in a memory and then, when superimposed in a medium, e.g. a storage _{tube f, are} electronically equalized in such a way that all points of a freely selectable object layer are mapped coincidentally analog editing amplifier adds additional correction voltages for the two orthogonal deflection directions, which depend on the desired object layer, and these sums of the original deflection voltages with the associated correction r voltages for deflecting a write beam for the overlay medium • can be used. 2. The method according to claim 1, characterized in that Object layers are mapped, which in the case of size are continuous pass into the primary layer, with the primary layer being the Layer applies whose points without correction:.; Tensionun at the The superposition is mapped coincidentally and which is a layer similar to the radiation-sensitive layer. 5 0 9 8 {· .j 7 ~ ' ¹ 3. The method according to claim 2, characterized in that object layers mapped v / ground, which are determined by the displacement of the primary layer in the axial direction. 4. The method according to claim 2, characterized in that in the case of a spherical cap-shaped radiation-sensitive layer, object layers which are concentric spherical surfaces and have the same center as the primary layer. 5. The method according to claim 1, characterized in that for small correction voltages compared to the deflection voltages the individual pixels of a desired object layer coincidentally superimposed with such corrected deflection voltages which are in the range that is limited by the deflection voltages that are used when reading out the various Projection images were assigned to the individual object points. 6. The method according to claim 5, characterized in that the Image points are superimposed with such corrected deflection voltages that are derived from the mean values of all the individual Ob j ect points assigned in the various projection images Deflection voltages are formed. 7. The method according to claim 5, characterized in that the pixels are superimposed with such corrected deflection voltages that would be assigned to them in an axial Kentrai projection. - 12 - ^ 09887 / 0BB7 8. The method according to claim 5, characterized in that the Image points with such corrected deflection voltages are superimposed, which are determined by the mean values from the deflection voltages the actual oblique central projection and the deflection voltages of the oblique central projection from the opposite one Direction can be defined. 9. The method according to claim 1, characterized in that with a rotationally symmetrical radiation-sensitive layer the rotation of the central ray around a point of rotation with a horizontal angle through the electrical rotation of the coordinate system of the deflection voltages by the same horizontal angle, a remaining equalization and subsequent reverse rotation is compensated and the remaining equalization network works without parameters that depend on the rotation about this horizontal angle depend. 10. The method according to claim 9, characterized in that for the correction of the deflection voltage, which corresponds to a direction perpendicular to the plane of the central beam axis of rotation (y-direction), a voltage is chosen that corresponds to the weighted product of the two deflection voltages corresponds, and that for the correction of the orthogonal deflection voltage (x-direction) a voltage is chosen that corresponds to the sum of the weighted square of the deflection voltage in the x-direction plus a constant one Voltage and the weighted square of the deflection voltage of the y-direction multiplied by the voltage of the x-direction - 13 5 0 9 8 R 7/0 ß B 7 plus a constant voltage and an additional constant voltage. 11. The method according to claim 10, characterized in that in the 'Equalization network' further higher products or mixed products the deflection voltages generated and added to this v / ground for correction. 12. The method according to claim 1 or the following, characterized in, that the analog operations are carried out with currents instead of voltages. 13. Arrangement for performing the method according to claim 9, characterized in that for components and for the weighting factors Digital-to-analog converter with subsequent analog Multipliers or multiplying digital-to-analog converters are used, while the constant voltages are via digital-to-analog converters with subsequent analog summation are specified. 14. Arrangement for performing the method according to claim 9, characterized characterized in that for electronic rotation and reverse rotation of the coordinate system by four rapid multiplying Digital-to-analog converters or four digital-to-analog converters with subsequent analog multipliers are provided, which Multiply the actual deflection voltages with the trigonometric functions + sin, cos of the angle of rotation and then - 14 - 509887/0 667 by analogous addition of these products, the deflection voltages for a rotated coordinate system are generated, according to the mathematical formulas u,,. = u cos ^ - u sin & , x, rotated χ y u -, .. = u sin ^ "+ u cos J, where the trigonometric y, rotated Yy Values of the angle of rotation are given digitally by the process computer. 15. The arrangement according to claim 14, characterized in that at fixed angles of rotation the multiplying digital-to-analog converters are replaced by resistance voltage dividers with fixed taps. 509887/0667