CA1141471A - Method of making planigrams of three- dimensional object - Google Patents

Abstract

ABSTRACT.
"Method of making planigrams of a three-dimensional object."

In order to make planigrams of a three-dimensional object, the object is irradiated from different directions in order to form a superposition image which consists of separate perspective images, Multiple imaging of the super-position image is realized by means of an imaging matrix, the individual perspective images being superposed in a zone which is situated behind the imaging matrix and in which, for example, a ground glass plate can be arbitrarily positioned for the imaging of layer images. During the superposition of the individual perspective images by means of the associated imaging elements of the imaging matrix, however, artefact images are caused by the transmission of perspective image, by inappropriare imaging elements. These artefact images are suppressed in that on each artefact image a correction perspective image, derived from a perspective image, is superposed via an additional imaging element in order to compensate for the artefact image.

Description

The invention relates to a method of and a device for making planigrams of a three dimensional object which i5 irradiated by a large number of radiation sources which are arranged in one plane in order to form a superposition image which is composed of separate primary perspective images, said superposition image subsequently being imaged by means of an optical imaging matrix whose imaging ele-ments are distributed in accordance with the distribution of the radiation sources, the imaging elements being positioned wi~h respect to the primar~ perspective images so that central rays of radiation beams which transmit the primary perspective images via the associated imaging elements intersect behind the imaging matrix in a point situated on an optical axis which is directed perpendi-cularly to the imaging matrix, in the superposition zoneo the radiation beams there being ormed a real image of the object wherefrom planigrams can be formed b~ means of a record carrier.
In a known method, an object is simultaneously irradiated from different directions by means of a source matrix which consists of a plurality of radiation sources which are arranged in one plane, separate perspective images forming a superposition image on, for example, a film plate. During a subsequent decoding step, reconstruc-tion takes place by means of the superposition image inorder to form separate planigrams of the three-dimensional objectO
The decoding can be illustrated as follows: in order to make an image of a given, arbitrary flat slice of the object, the superposition image is shifted and summed a number of times which equals the number of sources used for the irradiation of the object. The superposition image .,

2 PHD 79 028 is then shifted so that al] associated primary perspect-ive images are made to register in order to obtain a planigram.
A decoding step of this kind can be performed, for example, by means of an imaging matrix which is arranged in front of a superposition image which is illum-inated from the rear, the distribution of the imaging ele-ments of the imaging matrix corresponding to the distri-bution of the separate radiation sources of the source matrix. Each separate primary perspective image is then transmitted by an associated imaging element so that the central rays of the radiatiorl beams which transmit the primary perspective images via the associated imaging elements intersect behind the imaging matrix in a point on an optical axis which extends perpendicularly through the imaging matrix, in the superposition zone of khe radiation beams there being formed a real image of the object wherefrom layer images can be derived by means o~, for example, a ~round glass plate. The central rays are to be understood to mean the ra~s which extend through the centres o~ the primary perspective images as well as through the centres of the imaying elements. However, primary perspective images are not only transmitted by means of the associated imaging elements, but also at the same time by inappropriate imaging elemen~s, so that -these primary perspective images are imaged as artefact images together with the desired layer image, in an image plane in the superposition zone.
Therefore, the invention has for its obj~ct to provide a method which enables the formation of arbitrary planigrams of a three-dimensional object which are arte-fact-poor at least at their centre.
This object i5 achieved in accordance with the invention in that, in order to obtain planigrams which are artefact-poor at least in their cen-tre, artefact images which are caused by transmission of primary perspective images inappropriate imaging elements are suppressed by means of additional elements in that on each artefact image '~

3-3~1980 3 PHD 79 02g a correction perspective image derived from a primary perspec-tive image is superposed, each time via an addi-tional imaging element so that the artefact image is com-pensated for. ' The c'orrection perspective images derived frorn the primary perspective images are superposed on the arte-fact images by means of additional imaging elements which are included in the imaging matrix and which are arranged each time in the beam path between an artefact image to be l compensated for and a suitable primary perspective image.
Obviously, these image-transmitting imaging elements also transmit correction perspective images to locations where there are no artefact images to be compensated for. At these areas new artefact images are formed which are com-15 pensated for by means of imaging elements, -to be included in the imaging matrix, and primary perspective images which serve as correction perspective images. The magnitude of the area in which the artefact images in the reconstruct-ed layer image can be compensa-ted for can be chosen at 20 random and is dependent only of -the magnitude of the :imagirlg ma-trix or of -the structure and the number ot' imaglng ele-men-ts of the imaging Inatrix.
:Cn a preferrecL em'bodiment in accordance with the inven-tion, lenses are used for t,he imaging eLements and a 25 len~ matrix is used as the imaglng matrix9 a first f'il-ter being arranged in the beam path of the lenses used fo:r transmitting -the primary perspective images, a second filter which dif~ers f`rom the first filter being arranged in the beam path of the Lenses used for transmitting the 30 correc-tion perspective images, the radiation passing through the filters being detected by image pick-up tubes, a first input filter which co~re$ponds to the first fil-ter being arranged in front of -the one tube, and a seconcl inpu-t filter ~rhich corresponds to the second filter being 35 arranged in front of the other t-ube. The video signals of -the image pic'k-up tubes are sub-trac-ted frorn each o`ther in order to obtain layer images.
The different filters in the relevant bearrl path3 3-3-198O L~ P~ID 79 ~28 ensure tha-t only a single superposition image consist:ing of primary perspective images has to be made. The forma-tion of a superpositio,n image consisting of correction perspec-tive images can thus'be dispensed with. I~hen the super-position image is irradiated from the rear, fo-r example, by means of white light, two different colour filters can be used, for example, a red filter and a blue filter. The red filters are then arranged, for example, in the beam path of the lenses -transmitting the primary perspective images, whilst the blue filters are arranged in the beam path of the lenses which serve to superpose the correction perspective images on the artefact images. The image pick~up - tubes, comprising corresponding input filters, each time detect only one colour in order to make corresponding colour images which are electronically subtracted from each ~other in order to form artefact-free layer images.
Said filters and input filters, however, may also be other filters, for example, polari~ation filters.
Embodiments .Ln acco:rdance with the invention 20 will 'be described in detail hereinafter with re~rence to the accompanying diagrammatic d:rawing.
. :Figure 'I shows the recording of a superposit:i.on image consisting o~ primary perspecti.ve images, Figure 2 shows the reconstruction of a layer image 25 from the superposi-tion image by means of a lens matrix and the compensation of artefact images, Figures 3a-g illustrate a recordi.ng code consis-ting of two points and the s-tep-wise building up of a com-pensation distribution which is correlated to the recording 30 code, Figures L~a-i show 1 recorcling cocle consisting of three points and the step-wise building up of a further compensa-tion dis-tribu-tion which is correla-ted to the re cording code, Figure 5 shows a three-point recording cocle w:hich is correlated -to a di.stribu-tion which corresponds to -the recording cocde, L?igure 6 shows a dev-ice for making la-,ver :images 7~

3-3-1980 - 5 PH~ ~9 02 which are artefact-free at leas-t in their centre, Figure 7 shows a further device for making layer images with separate optieal and electronic channels, Figure 8 shows a deviee eomprising separate op-tieal ehannels and a eommon eleetronie ehannel, Figure 9 shows a device for making artefaet-~ree layer images by way of holography, and Figure 10 shows a table of eharaeteristie numbers.
The foregoing deseription, and also the follow-ing deseription, is given with referenee to X-ray super-position images. IIowever, images of partiele radiation ean also be proeessed aceording to this method without restrie-tion as normal optieal as well as eleetronie images. Ar-ti-ficial images ealeulated by a eomputer ean also be proeessed 15 by the method in aecordance with the invention.
Figures 1 and 2 serve to illustrate the principle of the method in aeeordance with the invention. Figure 1 shows a multiple radiation souree 1 whieh eomprises, ~or example, three separate radiation sources 2, 3 ancl 4 -which 20 are arranged in a plane 1a ancl whose distrib~tion in -the plane la is described b~v a so-termed point-irnage function whieh lndicates -th'e positions of the separate rac1iation sourees.
The separa-to radiation sources 2, 3 and 4, wh:ich 25 ean be simultaneously ~lashed, emi-t X-ray beams 6, 7, ~
whieh are stopped by apertures 5 and which intersect on an optical axis 10, extending perpendicularly with respect to the plane-of the radia-tion sources, in order to irradiate an object 11 to be examined. The objec-t 11 is thus recorded 30 in a coded manner in t'hat separate primary perspective images 12, 13, 14 are imaged, for example, on a single ~ilm 15.
Figure 2 shows the decoding step. The separate primary perspeetlve images 12, 13, 14 on the f'ilm 15 are 35 irradia-ted b~ means of a light box 16, whieh com~prises, f`or example,a flat ground gla.ss plate 17 a-t its front, and are imaged by means of a lens ma-trix 1~ 80 that -the central ra~s 12b, 13b, 14b of the radiation beams trans-3-3-l980 PHD 79 028 mitting the primary images 12, 13, 1L~ intersec-t each ot'her behind the lens matrix 8 in a point on the optical axis 18a which extends perpendicularly through the lens matrix 18, the radiation beams being superposed in a zone 1g.
The primary perspective images 12, 13, 1L~ are then imaged by means of the associated lenses 12a, 13a, 1L~a. In the superposition zone 19 there may also be arranged a scatter disc 21, or a similar device, which can be arbitrarily positioned in order to make the layer images 21 o~ the object 11 vislble, so that oblique layers of the object 11 can also be reproduced.
An artefact image in the imaging plane 20 is formed because the separate primary perspective images 12, 13, 14, for example, being positive, are also transmitted 15 by the inappropriate lenses. For example, the primary perspective image 12 is also transmitted, via the lens 13a, by way of a beam 22, so that in the imaging plane 20 an ar-tefact image 23 is produced which corresponds to -the primary perspec-tive image '12. In order to compensate fo:r 20 this artefact image 23, an additional lens 2L~ :is incl~lcLecL
in -the imaging matrix 18. Via this adcLitional le.ns 2L~, a correct.ion perspeotLve image 25 ~nega-tive), derived f:rorn -the primary perspective image 'l4, :Ls transmi-t-ted by way of a beam 26 and is superposed on the artefact image 23, so' 25 that they cancel each other. The correction perspective image 25 can be obtained from the primary perspective image 14 or from the -total superposition image 15.
The additional lens 24 also transmits further correcti.on perspective images 27 which are situated in the 30 imaging plane 20, for example, via a beam 28, and which are produced in conjunction with the compensation of the arte-fact .image 23 by the correc-tiOn perspective image 25.
This is because the correction perspec-tive image 25 was obtained from -the superposition irnage ~15, -thus :from -the 35 primary perspec-tive image 13.
The correc-tion perspecti~e image 27 (for example, a negative :Lmage) i-tself is -t'hen compensated for by means of a :further lens 29 introduced i.nto -the lens matrix 18, ~4~

3-3~1980 7 PHD 79 028 so that, via a beam 29a, the primary perspective image 14 (posi-tive) is superposed, vla the lens 28, on the correction perspective image 27, so that the two images l~ and 27 cancel each other. Ob'viously, the primary perspective 5 images and the correction perspective images are not trans-mitted in succession. For example, during a first step all primary perspective images 12, 13, 14 can be simul-taneously transmitted via the lenses 12a, 13a, 1~a and 29, whilst the correction perspective images 25 and 27 are transmitted, by 10 way of the beams 26 and 28 during a second step~ via the lens 24. Bo-th transmissions can also be simultaneously per-formed; this will be elaborated hereinafter.
Using the method in accordance with the invention, therefore, within a layer image representing a given object 15 layer the artefact images are cornpensated for which were produced during the reconstruction 'by -transmission of primary perspective irnages from the correspondirlg object layer.
The Figures 3a-g and 4a-:i clearly il:L~lstra-te hol~r 20 the posit:ions o:l~ the lenses 21~ ancl 29 in Figure Z are determ:ined.
As has alreacly 'been sta-ted, the Lenses 12a, 13a, l~a, are arranged in -the plane la in accordance wi-th '-the distribution of the radia-'ion sources 2, 3 and 4 1.e.
~5 distributed in accordance with the image-point function of -the recording geometry (radiation source array) in the lens matrix 18.
- Figure 3a shows a so-termed recording code S' wherefrom a compensating code ~' (Figure 3f) can be derived 30 which contains the recording code S', the compensating code ~' being correlated to the recording cocle A' in order -to obtain layer images which are artefact-poor at least in -their centre (Figure 3g).
~o ena'ble a clear i]lustration of the si-tua-tion, 35 it is assur~ed that t'he object I1 consists onLy of a po-int P' (not shown) and -that two X-ray sources (not shownj having the same intensity are used for irradiating the object 1I. O'bviously, the object 11 may alterrlatively ha-ve 3-3-1980 ~ 8 PHD 7g 028 a shape other than that of a point. For example, it ma~
form part of a human body, for example, a human organ.
The first phase o~ the method consists in the re-cording of -the object- (point) on a separate recording material by means of the two X-ray sources. On the recording material there are produced two points P1 and P2 whose distribution corresponds to the distribution of the X-ray sources. Figure 3a shows such a distribution of two points P1 and P2 in a coordinate system X, Y which have the coor-dina-te (X,Y) = (-1, O) and (+1, O) and each tiMe an ampli-tude (for example, density) of ~1. A point distribution of this kind is referred to hereina~ter as the recording code S'.
From thls recoding code S' -there is derived a l5 compensating code K' (Figure 3f) which in this case con-sists of a line of points. To -this end, a generator G' is defined which is shown in Figure 3b and which consists of two circles a and b having the coordinates (~l, O) ancl (1, O). Wh~n this generator Cr~ is positioIlecl on the re-20 cording co~e S' and is subsequentl~ shifted in the pos~tiveor negative X direct:ion until a point ot`-the recording cocle S' arrives :Ln a circle a or b of -the genera-tor G', a new point is de-termined each time in the free generator circle 7 the amplitude o~ said new point being the negative amplitude 25 of the point of the recording code S~ which is situated in the other generator circle. Superposition of the two generator circles with both points o~ the recording code S' is then precluded.
In Figure 3c, the generator G' has been shifted 30 in the positive ~ direction (to the right). In the genera-tor circle b, therefore, a point having the amplitude -I
is situated. In Figure 3d, the generator has been shifted one step further -to the right. '~he generator circle a -then covers a point having the amplitude -1, so that in -the 35 genera-tor circle b a point having -the amplitude -~1 is situated, e-tc. ~Ln Figure 3e, the genera-tor G' has been shif-ted in -the nerative x direc-tion. :[n the circle a o~
-the genera-tOr G~, now pertorming a translator~ movement, 3-3-lg~o 9 RHD 79 028 a point having the amplitude -1 is situated, because a point having the amplitude ~1 is situated in the generator circle b. Further shifting of the genera-tor to the left produces an additional point having the amplitude ~1 in the generator circle a (Figure 3f). The formation of the com-pensating code K', shown in Figure 3f, which still contains the recording code (the two inner poin-ts P3 and P4 must be interrupted at this point.
~hen this compensating code K' is correlated to the recording code S' as shown in ~igure 3g, i.e. the operation K' ~ S', a quasi-one dimensional image B' is obtained of the point P' having the amplit~de 2 and also two secondary points P5 and P6, each -time having th.e ampli-tude ~1, which are sitùated comparatively far from the 15 centre of the image B'. These secondary points represent the artefact images which, however, can be readily pushed to the ou-tside by enlargement of the compensating code K'.
The centre of the image :~' therefore, is free of artefacts.
The opera-tion K' ~ S' ~ = co:rrelation) only rneans -t:hat 20 the compensating code K' i.s sh-if`ted with respcct -Io i-t~cl:L~
so that each tirne an inner poin-t P3, :P~I is made -to register w:ith an other po:int. Subsequent.L~, all regi..sterillg po:ints are sumrned arld the image B' is obtained. The number o~ shifts of the compellsating code ~', therefore, is de-termined on 25 the basis of the n points in the recording code S'. In the above example, therefore, n-1 shifts are performed. Alter-natively, n shifts can be performed if both inner points P3s P4 of-the compensating code K' are shifted over only half the mutual dis-tance with respect to each o-ther, after 30 which they are macLe to register.
The correla-tion ~ need not be necessarily exe-cuted by the shifting of a cornpensat:ing code K' in the form of a point irnage. The compensating code K' can alter-na-tively be realized by a one dimensional row of lenses which are 35 situated at the poin-ts of the code K'. :Referring to Figure 2, theref`ore, the compensa-tinp~ code ~K' could be realizecL
:in the lens matr:ix 18 and the recording code S' wou.Ld correspond to.the superposition image -l5. ~ further exarnp:Le 3-3-1980 10 P~ID 79 OZc~

concerning a three-point recording code S" and the making of a corresponding compensating code K" will be described with reference to the Figures 4a-i.
For the clari-ty of the description a point-like object P" is again chosen instead of a part of, for e~ample, a human body. This object P" is recorded by means of X-ray sources (not shown) which are situated in one plane at the corners of a right-angled triangle. After the recording of the object P", therefore, a point image is obtained on a single recording material, the points P7, P8 and P9 thereof being situated on the record carrier in accordance with the distribution of the X-ray sources. The points P7, P8 and P9 are situated, for example, at the coordinates (-1, +1), (-1, -1) and (+1, -1~ within the coordinate s~stem X, Y and all have the same amp]itude +1 (~or example, density).
~ corresponding generator G" then has generator points a, b and c which are also situated at the coordinates ~-1, +1),(-1, -1) and (-~l, -1) tÇF`igure 4b). In order to form a compensating code K", this gene:rator G" i.s accurate-20 ly positioned on the recorcling codff S" and is shifted withrespect thereto by transla-tory movements. ~ s:imultaneous superposition Or -the gen~rator points a, b and c on all po:Lnts P7 -to P9 of the recording code S" is again precludecl.
The genera-tor c.rcle a, b or c in which each time 25 a point i9 inserted for -the building up of the condensating code K" is determined by the shifting of the generator ~"
with respect to the recording code S".
I. For shifts of the generator G" to the right (+x), downwards -to the right or downwards (-y), the gene-30 rator circle c is used, II. for shlfts in the upwards direction (+y) or upwards to the left, the generator ciecle a i9 used, III. for sh:ifts -to -the le~t (-x) or downwards -to the left, the genera-tor circle b is used, :CV. in the case of shifts upwards -to the right, the genera-tor C" does no-t cover points of the recording code S", so that in this case no poin-ts which contribu-te to the forma-tiOn of a compengating code K~ are f`ormed in the first quadrant of the coordinate system.
As is shown in ~igure 4c, the generator G" is shifted in the positive x-direction so that the generator circle b thereof surrounds the poin-t P9 of the recording code S". In this case it is laid down that in the ge~erator circle c a point is inserted having an amplitude which is the negative sum of the amplitudes of the points situated in the other generator circles a and b. The generator circle c thus obtains a point having the amplitude -1 In Figure 4d the generator is shifted upwards (~y), so that in the generator circle a a point having the amplitude -1 is inserted, whilst in the generator shifted to the left in Figure l~e a point having the amplitude -1 is also inserted in the generator circle b. A downwarcds 15 shift ~-y) of the generator as shown in Figure l~f produces a point having the amplitude -1 in the generator circle c.
A further upwards shift -to the left in figure 4g prod~ces a poin-t having the amplitude -1 in the generator circle a.
A downwards shift to the lef-t (Figure 4b) prod~tces a fllr-20 ther point having the amplitude -~1 in the generato.r c:ircle b.
Figure ~i clear:ly shows the compen.sa-ting code K"
again. Obviously, this code can ~e increased as desired by shifti.ng the genera-tor G" approxima-tely counter-clock-25 wise in the described manner in order to find new pointsfor building up a larger compensating code. In order to make layer images B" which are artefact-poor at least in their centre, the compensation code K" thus obtained is correlated to the recording code S". The operation K" @~ S"
30 means that each -time the to-tal compensating code K" is shifted so that the poin-ts P10 and P12 are positioned on the P11 and are summed. The fur-ther points of the compen-sating code K" regis-tered during thi.s shif-t are also surrlmecl, so that the image B" is forrrled. This image internall~ has 35 a point P"ha~ing the amplitude -~3, -whils-t around -thi~s po:int P" an arte~`act_free area is presen-t. ~rhe seconclary poin-ts (artefact images) are situa-tecL mo:re or less in the vicinit~
of -the edge o.f the :image and can be shif-ted ar~:itrar-i:ly . .

.

3-~-1980 '12 P~D 79 028 further outwards by increasing the compensating code K".
Again it is not necessary to perform the corre-lation ~ by the. shifting of a compensating code K" in the form of a point image. The correlation can be realized instead by means of a lens matrix whose lenses are situatcd at the points of the compensating code K".
The lenses which are si-tuated at the points of positive amplitude of a compensa-ting code thus -transmit the primary perspective images, whilst the lenses which are situated at the points of negati~e amplitude of the compensating code transmit the correction perspective images which are superposed on the artefact images. O'b-viously, a compensating code may also comprise points having an amplitude other than 1, for example, ~2. The lens to be situated at this point must then be so large that it ,can transmit a corresponding amount of light f'or compensa-tion of the artefact images.
Figure 5 shows an autocorrelation of the recor-ding code S" for -the purpose of compar.ison. The shift.Lng 20 and summing of -the i.ndividual points (or irnages) produces a principal poi:nt P"' wh:ich i9 surrouncled by ~urther poin-ts which repr~sent artefact innages and which are situ-ated substan-tial~ nea:rer to the centre of -the :image P"' than the artefact images in the image B" of Figure 4i.
The arithme-tical determination of a compansating code K for a predetermined recording code S will be des-cribed in detail hereinafter.
~irst of all, the following general matrices are defined:
30 a) Smn = recording code (S', S") Kmn = reconstruction code (compensa-ting code K', K"), 'Tmn = Kmn - Smn = compensation part of` the reconstruct code, Amn = ~ ~ ` Sm~j, n~k, SJk = S ~ S =
j=_~ k=-autocor:relation of the record-ing code (1 ,: , ~ r~

3-3-lg80 13 PHD 79 028 c~ ~ ~
Bmn = ~ / Sm+j, n+k Kij = S ~K =
j=_~ k=-~
crosscorrelation o~ recording code and reconstruc-tion code (2) ~ 6~
Cmn = ~ ~ Sm+j, n+k, Tij = S ~ T =

crosscorrelation o~ the recording code and the compensation part of the recons-truction code (3).
The characteristic numbers _ and n are integer numbers (m, n=o, +1, +2j ...), while the symbol ~ each time characterizes conjugated complex ~uantities.
b) The codes used (Smn, Kmn, Tmn) are represented as a ~lat 15 distribution o~ points, the points of the polnt distribution being elements of a matrix.
The position of the points within the matrix is determined b~ the characteristic numbers m, n resulting from the coordinates of the points, divided by -the la-ttice 20 distance of -the matrix. The dimensions of -the matr:Lx e:le-ments determine, for example, the intensity of -the points.
For the further description, an oxampLe is use(l in the form of a point distribution which represents a recording code gmn and which consists of two points. Both points have the 25 value or the intensity ~1, whilst the coordinates thereof 1 ~ Y1 mm) and (x2 - -0.1 mm y 0 These coordinates correspond to the posi-tion coordina-tes of the radiation sources used to irradia-te an object. They have only been reduced bv the same factor. When a suitable 30 la-t-tice distance is chosen for the matrix, for example, 0.1 mm and if the zero point of the matrix is determined as (xO = 0. mm, yO = 0.0 mm), the -two poin-ts can be deno-ted 1,0 = 1 and S_1 0 = 1- All other elementS
of the matrix have the value 0.
35 c) The cen-tre of -the arte~act--~ree recons-truction :image is situa-ted :in the poin-t ~l = 0, n = 0. The intensi-ty of th-is point is given by -the matrix elemen-t BQ 0. All other eLe-ment~s Bmn which are no-t ~ero~ represent artefacts, ~.e ' ~

3-3-1980 1/~ PHD 79 028 Bmn is the extent of an artefact at the lattice poin-t (m, n) (see the Figures 3g and 4i).
The aim lS to create an artefact-poor area around an artefact-~ree reconstruction centre by means of a compensation code. A quadratic area having sides of a length 2mO is chosen by way o~ example. The lattice con-stants in the x direc-tion and the y direction are the same.
All matrix elements Bmn must be zero in this area, that is to say Bmn = 0 ~or all /m/ ~ mO or /n/ ~ mO ~n e~cep-10 tion in this respect is formed by the elemen-t Bo 0 for which 0,0 ~ ' d) The reconstruction code Kmn (compen5ating code) con-sists of two parts: the recording code Smn and the com-15 pensation part Tmn o~ the reconstruction code Kmn.
Kmn = Smn ~ Tmn (L~)Therefore, the matrlx Bmn also consists of two parts Bmn= ,~ > Sm~,n-~k Sjk -~ ~ ~ Srn-~j,n-~lc Tjl~ (5) Je~ s= ~ J=-~' kY-~

~rnn -~ Cmn = S ~ S ~ S ~ T (~,ee equat:ions 1-3).
The ma-trix Amn contains the position and the ex-tent of the po:in-ts reconstructed without disturbance, but 25 also the position and the exten-t of artef`acts ~or example, see ~igure 5)u The ma-trix Cmn, however, only contains arte-~acts of reverse sign. When Amn ancl Cmn are summed, the artefacts in the preselected area disappear. Thus, the aim is -for:
30 Cmn = -Amn, where /m/ ~ mO ~ /n/ ~ nO and (rn,n) ~ (0,0).
This requiremen-t can be satisfied by sequential solu-tion ~or the compensation part of -the reconstruc-tion code Tmn.
e) In order -to ob-tain this solution, firs-t the corner points of the recording code Smn are define~0 The corner points 35 contain the indices ~/u~ ) f`or do~nwards lef-t, (/u2, ~ ~) for clownwards right, (/u~ ) for upwarcls righ-t, and (/u~ L~) for upwards le~t. Movernent to -the right means that _ increases, whils-t up-wards mo-vement means -that _ increases.

. . .
.

7~

3-3-19~0 15 PHD 79 028 The matrix element S/u1, ~ 1 thus represents the point which is situated furthest to the bottom le-ft.
f) Subsequently, a coupling is required between the charac-teristic numbers of the matrix Amn and the corner points of the recording code Smn. This coupling is necessary be-cause for a sequential solution for the compensation part of the reconstruc-tion code Tmn matrix elements are chosen from Smn which are dependent of the characteristic numbers of the rnatrix elements Amn. To this end, an image is defined:
(~u1, ~1) for m ~ 0 n ~ 0 (~ m~ mn) = (/u2~ 23 for m~ n ~ 0 (6) (/u3,~ 3) for m ~ 0 n ~ 0 (/u4~ 4) for m~ 0 n ~ 0 Example:
m = 1, n = 2. Therefrom it follows -that: m~ 0, n >0, so ( ~12' ~ 12) (/ 1 g) Furthermore, -the matrix elements Amn mus-t be arranged. In Figurc 10 a sequence of numbers ls arrangecd at polnts of in-tersectlon of a quadratic latt:ice, s-tarting 20 in the centre ~0) and proceeding counter-clockwlse. Af-ter each revolution, a new star-t :is made at a point w:l-t~l m~ 0, n _ 0. This arrangemen-t enables the determinat:ion of a separate pair of chnracteristic numbers (m, n) by a nwrl-ber N, and hence of a matrix elemen-t Amn. Example:
25 Assuming that (m, n) = (2, 1), N = N (m, n) = N (2~ 1) = 10-Using the arrangement according to Figure 10,the matrix Amn can be determined by an index N. A (N) - Amn.
h) Finally, -the matrix elements Tmn are arranged.
Therefore, it is defined that T(N) = T ~ mn ~ m~ ~ mn Example:
(mjn) = (1,2). I-t follows therefrom that ( ~ 1 2' 1~2) = (/U1 and N = (/u~
35 and T(N) = ~r(/U1 - 1 ~ ~ 1 - 2)-i) The equa-tion to be solved was:

:``

7~

G~ cO
Cmn = ~ ~ Sm~j, n-~k TJk = -Amn (7) j=_~ k=-.~
for /m/C mO~ /n/ ~ nO and (m~n) ~ 0.
j) A sequential solution is T(0) = 0 T(N) = ~ LAmn + ~ Sm-~j, n+k T(N')~ / S~ mn' ~ mn ( ) 0~ N'C N
10 where Tjk = T(N') for N' ~ N.
k) . A two-point distribution as described with reference to the Figures 3a-g is used as an example. For the recording code Sm, S1 0 = 1 and S_1,0 = ~1, o Smn = 0.
15 As a result, Ao 0 = 2, A2 o = 1, A 2 o = 1 (formule 1).
0 CN ~ 24 (see Figure 10) is found for an arte-fact-free area with -3 ~ m ~ 3, -3~ n ~ 3.
The corner points of` the ma-trix Smn are (/U1 ' ~ 'I ) = (-1 ,0) 20 (/u2, ~ 2) = (1, 0) (9) (/u3, ~ 3) = (1, 0) (/U4, ~ 4) = (-1 ~ O)-The solut:ion of -the formula (8) can be determined as ~hown in -the folLowing table:
;L5 N (m~n) ( ~ , ~ ) ( ~ ~m, ~n) T(N) 0 T(0)=0 1 (1,0) (-1,0) (-2,0) T(1)=-(A1 0~O)/S 1,0=
2 (1,1) (-1,0) (-2,-1) T(2)=0 3 (0~1) (1,0) (1,-1) T(3)=0 30 4 (-1,1) (1,0) (2,-1) T(4)=o (-1,0) (1,0) T(5)=0 6 (-1,-1) (1,0) T(6)=o 7 (0,~ 1,0) T(7)=0 ( 1 ,~ -I ,o) T(8)=o 35 9 (2,0) (-1,0) (-3,0) (9) (~2,() )/ -1,0 =-1=T 3 0 . _ , .. !

~ r,~

3-3-1980 17 P~ID 79 028 10 (2,1) (-1,0) (-3,-1) T(10)=-(~2 1+T_3~0S-1 7 1 )/ -1 ~
11 (2,2) (-1,0) T(11)=0 12 (1,2) (-1,0) 13 (0,2) (1,0) 14 (1-,2) (1,0) (-2~2~ (1,0) 16 (-2,1) (1,0) 17 (-2,0) (1,0) (3~ ) T(17)=-(A_2 o~T_3~oS_5tO/ 1,0 -1 = T3 0 T(18) to T(48) = 0 49 (4,0 ) (-1,0) (-5,o) T(49) ~( 4jo ~-3,o +1,0 3,0 T(50) 'to T(64) = o 65 (~49) (1,0) (59) T(65)=-( _4 o~T_3,0S-7,0 3,o S 1 o~T s~ ) /
= +1 = ~ 5 0 The values ( ~ ,~ ) and (~ mn, ~ mn) are obtained ~rom the ~ormule (6) in comb:lnation wlth the ~ormule (9). For pre-determined (m, n), the f`ormu].e (6) is ~Ised to fincl the associated (/u ~ ) with w'hich the values :in the f'ormule (9) are associatecl.
The compensa-tion cocLe is then Kmn = Smn ~ Tmn Theref'ore, for this example:
25 K1 0 = 1 ~ Predetermined by Smn, because the compensation K ; 1~ code Kmn contains -the recording code Smn.
K 3 0 = -1 determined from Tmn 3,0 1) K 5 0 = 1 t determined from Tmn 5, This compensation code Kmn is shown in Figure 3g as the compensating code K'.
For other recording distributions, f'or example, the three-point distribu-tiOn of' F`igure 4a or distribu-tions comprising 5 more points (~or example, 24 poin-ts)9 compensation codes Kmn can be de-term-ined in a simi]ar manner.
The solution stepY are always:
1) Selection o;~ a recording distribution Smn and conversion into the form of a matrix.
2) ~etermination and indication of the corner points of the recordi.ng distribution Smn.
3) Successive application of the solution for~ule ~8) with the aid of Figure 10.
During the calculation of T(N) a) ~ ~ and ~ - m, ~ -n are determined, and mn' mn ~mn mn b) (m+j, n+k) are calculated for all (j9k), where Tjk = T(N') for N' ~ N.
The.Figures 6 to 9 show various devices for ob-taining planigrams which are artefact-poor at least in their centre by means of the method in accordance with the in-vention.
In Figure 6, a light box 30 irradiates a super-15 position image 31, for example, with white light. A lensmatrix 32 wherethrough an optical system axis 33 extends perpendicularly produces a real -th:ree-dimensional image 3L~
in the superposition zone 35. Using a ground glass pla-te 26, which can be displaced at randoln within the image 34, a 20 relevant slice of the object ls imaged for e.~ample, an oblique slice. The ground glass plate 36 may :furthermo.re be connected to a FresneL lens 36a which acts as a field :Lens in order -to -increase the brightness of -the Layer image.
The individual Lenses of the lens matrix, being L5 arranged in accordance with the point distribution of the compensating code, for example, the code I~i' of Figure 4i, are covered by different colour filters 32a, h. For example, the lenses arranged at the points of the code ~" having the amplitude ~1 are covered by red filters, whilst the lenses 30 which are arranged at the points of the code ~" having the amplitude -1 are covered by blue :filters. A beam splitter 38 which is displaceable in the direction of the optical axis 33 and which is arranged behind the ground glass plate 36 spli-ts the light intwo -two beams 7 one of which extends 35 parallel whilst the other extends perpendicularly to the optical axis 33. Using two objectives 39 and ~0, -the im~ge of the ground glass plate is each time projected on a tele vision camera L~l, 42~ one camera comp:rislng a red f-il-ter L~

3-3-1980 ~ 19 PHD 79 0~8 as an input filter, whilst the other camera comprises a blue filter 44 as the input filter.
Thus, the camera 41 receives only red :radiation, whilst the camera 42 receives only blue radiation. By syn-chronous scanning of the two images and by subtrac-tion of the video output signals of the two cameras l~1 and l~2 by means of a subtractor 45, layer images can be made which are artefact-poor at least in their centre and which can be displayed, for example, on a monitor 46.
Figures 7 and 8 each time show a two-channel construction. On two optical axes 47 and 48 which extend parallel with respect to each other two light boxes 30 are arranged, superposition images 31 and negative superposition images 31a being present in front of each box. ~ lens matrix 49 in this case only comprises the lenses which are arranged at points of posi-tive amplitude +l of a compensat-ing code, for example, the code ~". A second lens matrix 50 only comprises the lenses which are situated at points o~ negative amplltude 1. In Figur~ 7, the images obtained 20 by means of the arbitrarily but synchronously movable gro~nd glass plate 36 are projected, via F:resnel lenses 36a whi.ch act as field lenses and which a:re rig.idly connec-ted to the gro-~1nd glass plates ~6, and vla objectives 51 and 52, each tlme on a t0levi.sion camera 53, 54. ~he image synchronized 25 output s~gnals of the two cameras 51 and 52 are then addecl in an adder 55 in order to obtain artefact-free layer images which are displa~ed on a monito:r 56.
In Figure 8, the images obtained by means of the ground glass plates 36 are projected onto a television 30 camera 60 by means of a Plat mirror 57 and t~ semitrans-parent plate 58 which are d-isplaceable in the d.irection. of the optical axis 47 and 485 respectively, via a separa.te objective 59, said tele-vision camera being connectecL to a monitor 61 for a display and to a memory 6~ for the storage 35 o~ -the layer images.
F-lgure ~ shows a holographic co~struc-t.io:n ~or per-forming the rnethod in accordance l~ith -the inven-tion. On an op-tical axis 63 there is si-tuated a lens 6~ which con-7~

verts a parallel, monochromatic radiation beam 65 in-to a converging radiation beam. At the point of convergence there is present a ~ourier hologram H in which the Fourier transform of a compensating code is presen-t, for example, that of the code K". Between the hologram H and the lens 64 there is present the superposition image 31 which is projected, via a second lens 66 which is situated behind the hologram H, in an image plane 67. The superposition image 31, the lens 66 and the image plane 67 are mechani-10 cally interconnected via a system of rods 68 and can bedisplaced parallel with respec-t to the optical axis 63 (arrow 69) for the display of different layer images.
The hologram H can be produced by means of a hole diaphragm which is irradiated from the rear b~ means of 15 coherent light and a reference beam, the dlstribution of .the holes in the hole diaphragm corresponding to the dis~
tribution o~ the points of a compensating code (or the dis-trib~ltion of the imaging elements). ~-uring the record-ing of the hologram, the holes which generate the imaglng elernents 20 whereby correction perspective irnages are supe:rpos~d on the artefact images, are covered l~-~ t:ra:nsparent plates for the formation o~ a phase diff`e:rence amounting to an odd multipll3 of half the waveleng-th ~ of the coherent light.
Therefore, the thickness d of -the plates is (j~ /2).n, 25 where rl ~ 1, 35 S, ... The imaging elemen-ts generated by the covered holes in the hologram -then correspond to irnaging elements, for example, lenses, which are arranged at the points of-negative amplltude of a compensating code, for example, of the code K" in l~igure 4i.
Obviously, the hologram ~I can also be obtained by means o~ a computer which calculates the hologram from a predetermined compensa.t:ing code.

.. .. . .

Claims (11)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. Apparatus for decoding a recording of a coded superposition image which is composed of a large number of separate primary perspective images of an object and was formed by irradiating the object with radiation from a plurality of radiation sources which were distributed in a geometric configuration in a plane comprising:
a white light source disposed to irradiate the recording;
a lens matrix, disposed parallel to the record-ing, for transmitting light received from the recording, the lens matrix including primary lenses which are dis-tributed in the matrix in a geometric configuration which corresponds to the configuration of the radiation sources and correction lenses which are distributed in the matrix to produce compensating images over artefact images pro-duced by the primary lenses;
first color filters disposed to filter light transmitted through each of the primary lenses;
second color filters, having light transmission characteristics which differ from the first color filters disposed to filter light transmitted through each of the correction lenses;
beam splitter means disposed to receive light from the recording which is transmitted through the lens matrix for splitting that light into a first beam and a second beam;
a first input filter, having the same light transmission characteristics as the first color filters, disposed to filter the first beam;
a second input filter, having the same light transmission characteristics as the second color filters, disposed to filter the second beam, first image pick-up tube means for receiving the filtered first beam and producing a first electrical sig-nal corresponding thereto;

second image pick-up tube means for receiving the filtered second beam and producing a second electrical sig-nal corresponding thereto; and subtractor means for subtracting the second elec-trical signal from the first electrical signal to produce an output electrical signal which corresponds to a cor-rected decoded image.

2. In an apparatus for decoding a recording of a coded superposition image which was formed by irradiating an object with radiation from a plurality of radiation sources distributed in a geometric configuration in a plane and recording the superposed separate primary perspective images thus produced, of the type which comprises:
a light source disposed to illuminate the record-ing; a matrix of a like plurality of primary imaging ele-ments which are disposed in a plane in a geometric con-figuration which corresponds to the configuration of the radiation sources; and image detecting means for recording and/or visualizing a primary decoded image formed by light which is transmitted from the recording, through the matrix; the improvement, for reducing artefacts produced by the primary imaging elements, in at least a central portion of the decoded image, which comprises:
an additional matrix of compensating imaging ele-ments for projecting a correction perspective image derived, from the recording onto each artefact in at least in the central portion of the decoded image, whereby those arte-facts are at least partially cancelled.

3. The apparatus of claim 2 wherein the means for recording and/or visualizing comprise first television pick-up tube means for receiving the primary image and pro-ducing a first electrical signal corresponding thereto;
second television pick-up tube means for receiving the cor-rection image and producing a second electrical signal corresponding thereto and means for combining the first electrical signal and the second electrical signal to pro-duce an output electrical signal corresponding to the com-pensated decoded image.

4. The apparatus of claim 3 wherein the matrix of primary elements and the additional matrix are disposed in a plane in a common optical path and further comprising:
first color filters disposed to filter light transmitted by the primary imaging elements and light received by the first television pick-up means;
second color filters, which have light trans-mission characteristics which differ from those of the first color filters, disposed to filter light transmitted by the compensating image element means and light received by the second television pick-up means; and means for splitting light transmitted through the primary imaging elements and second imaging elements into two separate beams and projecting those beams, res-pectively, for reception by the first and second television pick-up means.

5. The apparatus of claim 3 wherein the matrix of primary elements and the first pick-up tube means are dis-posed on a first optical path and the additional matrix and second pick-up tube means are disposed on a second, separate optical path.

6. The apparatus of claim 2, 3 or 4 wherein the imaging elements comprise lenses.

7. The apparatus of claim 2 or 3 wherein the imaging elements comprise one or more holograms.

8. In a method for making planigrams of a three-dimensional object which comprises the steps of:
irradiating the object with radiation from a plurality of radiation sources, which are configured in a plane, to form a coded superposition image which is com-posed of a like plurality of separate primary perspective images;
making a recording of the superposition image;
and subsequently decoding the superposition image by imaging the recording through a matrix which comprises a like plurality of imaging elements, which are distributed in a geometric configuration which corresponds to the con-figuration of the radiation sources, to form a decoded image; the improvement comprising the steps of:
further imaging the recording through an addit-ional matrix of imaging elements to form correction per-spective images over at least some artefacts in the decoded image and subtracting the correction perspective images from the decoded image to compensate for the artefacts, at least in the center of the decoded image.

9. The method of claim 8 further comprising the steps of detecting the decoded image and the correction images on one or more television pick-up tubes to produce corresponding output signals and wherein the subtracting step comprises subtracting one of the output signals from another.

10. The method of claim 8 wherein the recorded super-position image is imaged by illuminating it with white light and further comprising the steps of filtering the light transmitted through the primary imaging elements with a first color filter and filtering the light transmitted through the correction imaging elements with a second color filter.

11. The method of claim 10 wherein two pick-up tubes are utilized in the decoding step and further comprising the step of filtering light detected by pick-up tubes with filters which correspond to the first and second filters respectively.