fig1 is a schematic representation of a magnetic resonance imaging apparatus for generation of a nuclear magnetic resonance image of a subject according to the present invention . the design of the magnetic resonance tomography apparatus corresponds to the design of a conventional tomography apparatus , with the differences noted below . a basic field magnet 1 generates a temporally - constant strong magnetic field for polarization or alignment of the nuclear spins in the examination region of a subject such as , for example , of a part of a human body to be examined . the high homogeneity of the basic magnetic field necessary for the magnetic resonance measurement ( data acquisition ) is defined in a spherical measurement volume m into which the parts of the human body to be examined are introduced . for this purpose , the patient lies on a mobile patient bed ( movable table ) that is introduced into the basic field magnet in order to place the region of the patient to be examined into the homogeneity volume . to support the homogeneity requirements , and in particular to eliminate temporally invariable influences , what are known as shim plates made from ferromagnetic material are mounted at a suitable location . temporally variable influences are eliminated by shim coils 2 that are activated by a shim power supply 15 . a cylindrical gradient coil system 3 that has a number of windings ( known as sub - windings ) is used in the basic field magnet 1 . each sub - winding is supplied with current from an amplifier 14 for generation of a linear gradient field in the respective direction of the cartesian coordinate system . the first sub - winding of the gradient field system 3 thereby generates a gradient g x in the x - direction , the second sub - winding generates a gradient g y in the y - direction and the third sub - winding generates a gradient g z in the z - direction . each amplifier 14 includes a digital - analog converter that is activated by a sequence controller 18 for accurately timed generation of gradient pulses . located within the gradient field system 3 is a radio - frequency antenna 4 that converts the radio - frequency pulses emitted by a radio - frequency power amplifier into an alternating magnetic field for excitation of the nuclei and alignment of the nuclear spins of the subject to be examined or of the region of the subject to be examined . the radio - frequency antenna 4 includes one or more rf transmission coils and a number of rf acquisition coils in the form of the advantageously linear arrangement of component coils already described . the alternating field originating from the precessing nuclear spins ( i . e . normally the nuclear spin echo signals caused by a pulse sequence composed of one or more radio - frequency pulses and one or more gradient pulses ) is also converted by the rf acquisition coils of the radio - frequency antenna 4 into a voltage that is supplied via an amplifier 7 to a radio - frequency acquisition channel 8 of a radio - frequency system 22 . the radio - frequency system 22 furthermore has a transmission channel 9 in which are generated the radio - frequency pulses for the excitation of the nuclear magnetic resonance . the respective radio - frequency pulses are thereby digitally represented in the sequence controller 18 as a series of complex numbers based on a pulse sequence predetermined by the system computer 20 . this number series is respectively supplied as a real part and an imaginary part via an input 12 to a digital - analog converter in the radio - frequency system 22 and from this to a transmission channel 9 . in the transmission channel 9 the pulse sequences are modulated on a radio - frequency carrier signal whose basic frequency corresponds to the resonance frequency of the nuclear spins in the measurement volume . this signal is amplified in rf amplifier 16 . the switch - over from transmission mode to acquisition mode ensues via a transmission - reception diplexer 6 . the rf transmission coil of the radio - frequency antenna 4 radiates the radio - frequency pulses for excitation of the nuclear spins into the measurement volume m and samples resulting echo signals via the rf acquisition coils . the correspondingly - acquired nuclear magnetic resonance signals are phase - sensitively demodulated on then intermediate frequency in the acquisition channel 8 ′ ( first demodulator ) of the radio - frequency system 22 and digitized in an analog - digital converter ( adc ). this signal must be demodulated to the frequency 0 . the demodulation to frequency 0 separation into real part and imaginary part occurs in the digital domain in a second demodulator 8 after the digitization . an image is reconstructed by an image computer 17 from the measurement data so acquired . the administration of the measurement data , the image data and the control programs ensues via the system computer 20 . based on a requirement with control programs , the sequence controller 18 monitors the generation of the respective desired pulse sequences and the corresponding sampling of k - space . the sequence controller 18 thereby in particular controls the time - accurate switching of the gradients , the emission of the radio - frequency pulses with defined phase and amplitude and the acquisition of the nuclear magnetic resonance signals . the time base for the radio - frequency system 22 and the sequence controller 18 is provided by a synthesizer 19 . the selection of corresponding control programs for generation of a nuclear magnetic resonance image as well as the presentation of the generated magnetic resonance image ensues via a console 21 that has a keyboard as well as one or more screens . it is the goal of the present invention to distinctly increase the effectiveness of slice - selective or , respectively , spatially - selective multi - slice excitations in mrt imaging . slice - selective or spatially - selective 3d imaging in mrt is severely impaired via non - ideal excitation profiles . an ideal rf excitation profile ( according to the depiction in fig2 a ) is characterized by an exactly horizontal plateau 25 which is bounded by exactly vertical edges 24 . by contrast , a non - ideal ( thus a real ) excitation profile 26 ( according to the depiction in fig2 b ) exhibits angled edges 27 whose steepness is essentially limited by the specific absorption rate ( sar ). the plateau 28 has a central non - linearity that causes no artifacts but disruptive intensity fluctuations in the later reconstructed image . in order to be able to measure larger patient segments , in particular given short measurement volumes m ( limited by magnet bores growing ever shorter ( engl . : decreasing bore lengths )) segment - by - segment ( block - by - block ) scanning is necessary that ensues during either a continuous or a likewise per - segment table displacement . the per - segment scanning ensues such that at least two spatial regions displaced counter to one another along a spatial direction ( table displacement direction , i . e . in the direction of the patient longitudinal axis ) and respectively inherently bound are excited and measured . the contrary displacement advantageously ensues ( as can be seen from fig3 ) such that a best possible excitation of the respective plateau fovs 28 of the rf excitation profiles s of the respective spatial regions ob is given since only the plateau width actually corresponds to the fov of interest . however , this causes an overlapping of the respective edge regions 27 of the one slab profile s 2 with the corresponding edges of the adjoining plateau regions of the adjacent slab profiles s 1 , s 3 which , given phase or spatial coding alone in the fovs of interest ( in the plateau regions ), generates severe foldovers of the edges 27 in the border region of a fov displaced by one fov or a number of fovs ( which , in the case of very flat edges , as such sweep over a number of fovs ). ultimately , such foldovers lead to extremely disruptive image inhomogeneities in the aforesaid spatial direction , and in fact in all combined plateau segments , i . e . thus over the entire fov ( composed from all partial fov segments ) of the entire plateau region of interest . the procedure according to the prior art in order to reduce or to eliminate the foldovers ( and therewith these image inhomogeneities ) was presented in detail in the specification preamble . by contrast , the present invention now exists in replacing the oversampling of all rf excitation profiles s necessary for artifact elimination with setting up and solving an algebraic equation system that reflect or describes the imaging problem . the mathematical solution of this equation system leads to a set of folding - free target values that can ultimately map to the desired fov combination free of folding . the algebraic equation system represents a linear equation system and can be written as z is the coordinate in the spatial coding direction , table displacement direction as well as phase coding direction , s ( z ) is the slice profile ( modulating the target values ) of the rf excitation pulse ( also designated as a slab profile or modulation function ), i ( z ) represents the intensity of the foldover - free target values , i . e . the desired artifact - free image , across all partial fovs . j n ( z ) is the measured intensity value belonging to the block n or to the slice n , inclusive of the foldings due to overlapping of adjacent fov measurement values ; however , j n ( z ) extends only over a range of the overlapping itself is taken into account in the sum over wherein m - values ≧ 2 are only reasonable for slab profiles whose overlapping extends over more than two adjacent fovs due to very flat edges . j n ( z ) are the actual measurement values that comprise the nuclear magnetic resonance signals of the respective fov profile which , however , are modulated with the rf slice profile ( slab profile s ( z )). due to the deviation from a precise rectangular profile 23 , the slab profile experiences an expansion beyond the actual central fov and modulates ( influences ) further slices n , which is accounted for by the further sum terms due to its modulating character , the rf slice profile or slab profile is generally designated in the following as a “ modulation function ”. as long as the number of measurement values corresponds to at least the number of the folding - free target values i ( z ) that are unknown ( and therefore to be determined ), as long as the equation system it solvable , the modulation function s ( z ) is assumed to be known . how the modulation function s ( z ) is determined need not be described herein . it is noted , however , that such a modulation function does not exclusively have to be given by the slice profile ( the flip angle distribution ) of a spatially - selective rf excitation pulse ; rather , by all means other modulating units of other technical provenance can also be superimposed . such units can be , for example , sensitivity profiles of participating local transmission and / or acquisition coils ( possibly arranged in a coil array ) in the corresponding spatial region ob , as they are also used in conventional ppa imaging methods for measurement time reduction via reduction of time - consuming phase coding steps . in order to determine the slice profile units of a modulation function s , for example , it would be possible to oversample a single rf slice profile . since the rf slice profiles ( slab profiles ) of the different slices n differ only slightly , it is reasonable and efficient to use a slab profile determined once as a modulation function for all further slices . furthermore , it is noted that it can be advantageous in the calculation of the foldings to take into account the knowledge of redundant subject information in the overlap regions or . in principle , the rf slice profile can also be analytically determined via the employed rf pulse shape . furthermore , it is conceivable that , via the use of information from a plurality of rf acquisition channels , a simultaneous estimation of i ( z ) and s ( z ) is possible using methods analogous to parallel imaging .