reference will now be made in detail to the preferred embodiments of the present invention , examples of which are illustrated in the accompanying drawings , wherein like reference numerals refer to like elements throughout . fig1 shows an exemplary embodiment of a modulator field movement and an object movement relative thereto ; a movement or , as the case may be , an offset , which for example can be horizontal or vertical or diagonal , of the primarily modulating modulator field by half a period length per / 2 is provided , and moreover in such a way that two projections with modulator field offset by per / 2 are present for each angular position of the object that is to be tomographed . for that purpose the modulator field is not installed in a stationary manner , as disclosed according to u . s . pat . no . 7 , 463 , 712 b2 , but is provided on a motorized linear stage so as to be movable by at least half a period length . during a ct scan , the modulator field is then displaced by half a period length for each angular position α i ( i = 1 . . . n , where n signifies the number of angular positions to be recorded ) of the object that is to be tomographed after a first projection recording in a first modulator position 1 ( projection α i ( 1 )) in such a way that in the case of a checkerboard - like modulator field the dark fields come to lie where previously there were light fields , and vice versa . a second projection is then recorded ( at the second modulator position 2 ( projection α i ( 2 )), with the object that is to be tomographed not yet having been moved . for the next angular position α 1 + 1 of the object to be tomographed and all following positions , this twofold recording procedure with the first modulator field position 1 and the second modulator field position 2 is repeated in the same way . the vertical arrows are equivalent to a time bar . fig2 shows a first exemplary embodiment of a construction of a modulator - free overall image . by the offset by half a period length between the two modulator positions 1 and 2 it is possible in the proposed method to construct a modulator - free overall image for each angular position α i of the object that is to be tomographed , said overall image being in particular downsampled . this is illustrated in fig2 . toward that end , the light fields from the first projection α i ( 1 ) are transferred into a new image , in particular after a downsampling step . the dark fields from said projection cannot be used , and must therefore be replaced in order to generate a modulator - free image . as a result of the offset by half a period , however , light fields are located in the second projection , i . e . projection α i ( 2 ), at those positions where dark fields are to be found in the first projection α i ( 1 ). said light fields are likewise transferred into the new image , and moreover in particular after the downsampling step , thereby resulting in the modulator - free overall image . fig3 a to 3e show an exemplary embodiment of the proposed method for providing a scatter - corrected projection . with the modulator - free overall image , the high image frequencies caused by object edges and other high - contrast object details can subsequently be divided out . this is illustrated in fig3 a . the modulated projection image , which is in particular downsampled , is therefore divided by the modulator - free overall image , which is in particular downsampled , resulting in the ratio of measured modulation strength of the primary signal to the overall signal strength . a division of said type by the modulator - free overall image replaces the “ boundary detection ” step of u . s . pat . no . 7 , 463 , 712 b2 . this modulation image freed of object image frequencies is then high - pass filtered in the fourier domain , thereby removing the low - frequency scatter component . next there follows a demodulation by multiplication in the space domain by a modulator projection without sample . this is illustrated in fig3 b . the previously performed division by the modulator - free overall image , which is in particular downsampled , is reversed after the demodulation step by a corresponding multiplication of the in particular downsampled modulator - free overall image by the reconstructed primary image . this is illustrated in fig3 b . fig3 c shows how subsequently the modulator - free overall image is likewise used in order to generate the scatter image by subtraction of the reconstructed primary image . fig3 d shows how the calculated scatter image is subsequently subtracted from the original modulated ct projection , which is in particular not downsampled . then follows a pixel - by - pixel beam hardening correction , which is represented as operation bhc [.] in fig3 d and is described in greater detail in conjunction with fig7 . finally , in order to rectify the modulator pattern , the scatter - and beam - hardening - corrected image can be divided by a pure modulator projection , i . e . without object in the beam path . the steps described hereintofore , as illustrated in fig3 a to 3d , are performed for both projections α i ( 1 ) and α i ( 2 ) in the first modulator position 1 and the second modulator position 2 . as the object was not moved in these two projections , the scatter -, beam - hardening - and modulator - corrected projections , which are in each case the results of step 3 d , are averaged in order to improve the signal - to - noise ratio ( snr ). this is illustrated in fig3 e . fig4 shows a second exemplary embodiment of a modulator field movement and an object movement relative thereto . fig4 represents a second alternative of an offset of a primarily modulating modulator field . in this case an offset can be executed for example horizontally or vertically . other displacement directions are also possible . for example , the modulator field pattern can have been generated in such a way that an offset can be executed diagonally . according to this second exemplary embodiment , the primary modulator is offset by half a period length per / 2 from projection to projection , between which in each case an angle rotation increment of the object that is to be tomographed is carried out . toward that end the modulator field is not installed in a stationary manner , but is provided on a motorized linear stage to allow movability by at least half a period length . during a ct scan , the modulator field is then displaced as the primary modulator by half a period length from projection to projection in such a way that in the case of a checkerboard - like pattern of the modulator field the dark fields come to lie where previously there were light fields , and vice versa . this is illustrated in fig4 . the vertical arrows are equivalent to a time bar according to fig1 . as a result of the offset by half a period length from projection to projection it is possible according to the exemplary embodiment to construct an approximated modulator - free overall image for each projection . this is illustrated in fig5 . toward that end the light fields from the current projection , designated as projection i , are transferred into a new image , and moreover in particular after the downsampling step . the dark fields from said projection i cannot be used , and must therefore be replaced in order to generate a modulator - free image . as a result of the offset by half a period , however , light fields are located in the preceding projection ( i − 1 ) and in the succeeding projection ( i + 1 ) at those positions where dark fields are to be found in the current projection i . by a simple interpolation , approximated grayscale value signals can be found for said fields ; depending on object composition and increment size of the sample or object rotation angle , these grayscale value signals represent a very good approximation to the actual grayscale value signals which , though , have not been measured here . an interpolation can be provided for example by a uniform weighting in the case of neighboring projections , for example with an equal weighting of 0 . 5 . fig5 shows a second exemplary embodiment of a construction of an approximated modulator - free overall image . in this case the modulator - free overall image is merely approximated . according to this embodiment variant , each time a modulator field is offset or shifted by half a period length between the two modulator positions 1 and 2 , an angular position α i of the object to be tomographed is changed , with the result that on this basis a modulator - free overall image , which is in particular downsampled , can only be approximated . this is illustrated in fig5 . toward that end the light fields from a current projection ( i ) are transferred into a new image , in particular after a downsampling step . the dark fields from this projection cannot be used , and must therefore be replaced in order to approximate a modulator - free image . as a result of the offset by half a period , however , light fields are located in a preceding projection ( i − 1 ) where dark fields are to be found in the current projection ( i ). in a following projection ( i + 1 ) light fields are likewise located where dark fields are to be found in the current projection ( i ). the preceding and succeeding projections can be combined and weighted relative to each other , for example by a factor of 0 . 5 in each case . these light fields of the three projections ( i − 1 , i , i + 1 ) are transferred into the new image , and moreover in particular after the downsampling step , thereby producing the approximated modulator - free overall image as result . fig6 a to 6d show the second exemplary embodiment of the proposed method for calculating a scatter - corrected projection . according to this exemplary embodiment , in contrast to the first exemplary embodiment , an approximated modulator - free overall image is used instead of a modulator - free overall image . with this approximated modulator - free overall image the high image frequencies caused by object edges and other high - contrast object details can now be divided out in a subsequent step . this is illustrated in fig6 a . the modulated projection image , which is in particular downsampled , is therefore divided by the approximated modulator - free overall image , thereby yielding the ratio of measured modulation strength of the primary signal to the overall signal strength as result . this division by the approximated modulator - free overall image replaces the “ boundary detection ” step of u . s . pat . no . 7 , 463 , 712 b2 . this modulation image freed of object image frequencies is then high - pass filtered in the fourier domain , as a result of which the low - frequency scatter component is removed and subsequently demodulated accordingly by multiplication in the space domain by a modulator projection without object . this is illustrated in fig6 b . the above - performed division by the approximated modulator - free overall image is reversed after the demodulation step by a corresponding multiplication of the approximated modulator - free overall image by the reconstructed primary image . this is illustrated in fig6 b . fig6 c shows that the approximated modulator - free overall image is used to obtain the scatter image by a subtraction of the reconstructed primary image performed thereby . this is illustrated in fig6 c . the following method according to fig6 d largely corresponds to the first exemplary embodiment . according to the second exemplary embodiment , in contrast to the first exemplary embodiment , a ct projection is generated per angle rotation increment of the object , such that averaging according to the first exemplary embodiment is dispensed with . fig7 shows an exemplary embodiment of a correction of beam hardening effects , also referred to simply as beam hardening . a simple beam hardening correction is carried out for dark fields , such a correction already being applied in a similar manner for conventional ct , though in that case for complete ct projections . in the case of primary modulation , a more severe beam hardening effect occurs at the positions of the dark fields , since here the additional material , which can be for example copper or tungsten , causes an additional hardening of the beam which does not occur in the case of the light fields . by a simple simulation it is possible to simulate theoretically exact attenuation curves for specific recording parameters ( see also [ 1 ]). a well - known restriction of this method is that in the subsequently described correction the theoretical exactness applies only to monomaterials , i . e . only to objects to be recorded that are formed of one material , which can be for example aluminum . if objects is formed of a plurality of materials , referred to as multimaterials , are examined , a more or less great discrepancy exists in respect of the hardening effects actually occurring . fig7 shows two attenuation curves i / i 0 for the example of the following recording parameters : tube voltage 200 kv , tube - side preamplifier of 2 mm copper and object material aluminum . in this case the two curves show the ratio of the recorded signal to the overall signal , a normalization to 1 having been performed in each case . the ratio of the recorded signal to the overall signal is plotted against the increasing radiation penetration depth through an aluminum wedge . in the left - hand graph the lower curve shows the case of the light fields , in which the prefiltering of the spectrum actually includes only 2 . 0 mm copper . the upper curve , in contrast , depicts the case of the dark fields , where an overall filter , formed of 2 . 7 mm copper , is assumed . in other words , in addition to the tube - side prefilter of 2 . 0 mm thickness , the additional material of the modulator in the dark fields , in this case 0 . 7 mm copper , is taken into account . the input intensities , in other words the intensities that are present after the modulator , but before the object , are smaller for the dark fields than for the light fields . nonetheless , the spectra of the radiation behind the dark fields are on average more energy - rich , i . e . more severely hardened , than the corresponding spectra behind the light fields . because of this difference between the spectra , the radiation behind the dark fields penetrates the following object material more effectively , and moreover relatively , i . e . referred to the same input intensity . this influencing factor is subsequently taken into account in that for the dark fields this effect is compensated by calculation . the result for the more strongly filtered 2 . 7 mm cu spectrum ( upper curve ) is a smaller attenuation , considered relatively , than with a more weakly filtered 2 . 0 mm cu spectrum ( lower curve ). according to a first embodiment variant , a beam hardening correction is performed prior to the scatter estimation . the dark fields of the modulated projection image are corrected for beam hardening in the downsampling step , i . e . the value uncorrval ( m , n ) measured in a dark field ( m , n ) is corrected by a value corrval , which is calculated as follows : firstly , an approximated scatter value approxscatterval ( m , n ), which is generated from the most recently calculated scatter image of the preceding projection , is subtracted from the measured value uncorrval ( m , n ). this value is searched for in the attenuation curve for the dark fields ( upper curve ); it corresponds to a certain radiation penetration depth . a corresponding attenuation value for the light fields ( lower curve ) can now be found at this radiation penetration depth . this step is represented in the equation as function bhc [.]. finally , the approximated scatter signal approxscatterval ( m , n ) is also added to said beam - hardening - corrected value once again . this means that theoretically the beam hardening effect is fully compensated for the treated dark field ( m , n ). in addition to the attenuation curves in a coordinate system with radiation - penetrated aluminum depth of arbitrary unit along the abscissa and i / i 0 as normalized projection intensity along the ordinate , fig7 shows a second graph which indicates the correction values for the dark fields , i . e . the difference between the two above - described attenuation curves , in grayscale values versus an original grayscale value in a dark field . analogously it is also possible from the second graph , starting from an original grayscale value in a dark field , to correct this by subtracting the correction value . according to another advantageous embodiment variant , the correction of beam hardening effects can also be carried out after the scatter estimation and prior to the division by the pure modulator image . toward that end the following steps must also be performed after the scatter estimation in order to obtain a fully corrected ct projection . the just calculated scatter image is subtracted from the original modulated ct projection . this is illustrated in fig3 d and 6d . a beam hardening correction is then carried out pixel by pixel for the dark fields , as described in conjunction with formula ( 1 ). in this case it is taken into account for each pixel individually , how much additionally hardening material is present due to the modulator or modulator field . according to the exemplary embodiment this is between 0 . 0 and 0 . 7 mm of additional copper . in this way , when a cone - beam computed tomography system is used , the boundary pixels of the dark fields can likewise be optimally corrected , for with such a system geometry the boundaries of the dark fields are not sharply delimited , in particular for non - centrally located fields , but rather have a gradual grayscale value progression . fig8 shows an exemplary embodiment of the proposed device . x - ray radiation , represented as a triangle , of a primary x - ray source 1 passes through a modulator field 3 having a repetitive pattern of areas with different x - ray radiation attenuation . the radiation then passes through an object 5 that is to be imaged and is positioned so as to be rotatable about an axis of rotation 9 . the result is an original amplitude - modulated projection on a detector 7 . fig9 shows exemplary embodiments of the proposed modulator field 3 from the direction of the primary x - ray source 1 . a linear motor 12 moves a linear stage 11 , which positions the modulator field 3 . the modulator field 3 contains a repetitive pattern of areas having two different x - ray radiation attenuation coefficients . a first half of the repeating pattern is congruent with a second half , wherein mutually congruent areas of the two halves have mutually opposite x - ray radiation attenuation coefficients , the pattern is repeated along at least one repetition line 13 , and a length of the pattern along the repetition line 3 corresponds to a period length per . fig9 shows that in a displacement movement of the modulator field 3 from a first position to a second position along the repetition line 13 by , for example , half a period length , modulator field areas having small x - ray beam attenuation coefficients and in comparison therewith modulator field areas having relatively large x - ray beam attenuation coefficients are reciprocally interchanged . according to the present application , all patterns that provide the above - described interchange are possible in principle . patterns including polygons are particularly suitable . fig9 shows exemplary embodiments of modulator field patterns , such as parallelograms , rhombuses and hexagons for example . when polygons are used it is furthermore possible to use halves of the pattern that have arbitrary shapes inside the polygons in each case . the invention has been described in detail with particular reference to preferred embodiments thereof and examples , but it will be understood that variations and modifications can be effected within the spirit and scope of the invention covered by the claims which may include the phrase “ at least one of a , b and c ” as an alternative expression that means one or more of a , b and c may be used , contrary to the holding in superguide v . directv , 69 uspq2d 1865 ( fed . cir . 2004 ).