Abstract:
A method for generating a control signal is provided. The method includes the steps of decomposing a desired movement into two partial movements which are separately equalized, and the desired control signal is obtained by summing up the corrected components. The first movement is a slowly (mostly linear) changing long-period (period T 1 ) movement, and the second movement is a short-period (period T 2 ) movement, wherein the period T 1  is substantially longer than the period T 2 . The movements have to a large extent opposing temporal derivations which are nevertheless equal in magnitude so that their sum has a time derivative that is zero. In addition, a method is provided for operating a scanning unit periodically displaceable in an infeed direction by an infeed distance.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is claiming priority to German Application Nos. 10 2016 005 979.6, filed May 13, 2016, and 10 2016 211 373.9, filed Jun. 24, 2016, and the entire content of both applications is incorporated herein by reference. 
       TECHNICAL FIELD 
       [0002]    The present invention relates to a method for generating a control function and to a method for operating a scanning unit. 
       BACKGROUND 
       [0003]    In a scanning image capture, e.g. in laser scanning microscopes (LSMs), conventionally two 1D scanners or one 2D scanner are used. In this case, an object of which an image is to be created is scanned point by point and line by line (scanning). 
         [0004]    In the process, a scanning unit, for example a scanner, is placed at one end of a line to be scanned. The relevant line is scanned once or several times, and the scanning unit is placed at one end of another line to be scanned (line feed). 
         [0005]    For the line feed, the scanning unit is moved so that during a turnaround phase of the scanning movement (subsequently also referred to as turnaround area) the scanning unit is moved perpendicularly to the direction of the rapid scanning in the direction of the line (line scan), for example one line down. Afterwards, the scanning unit remains in this direction (infeed direction) at a constant position until the line scan is completed. 
         [0006]    Due to the limited reaction speed of a controlled scanning unit, at a higher scanning speed, the controlled scanning unit can no longer follow an intended nominal movement, which results in a position error for the line feed LF. The position error depends on the position in the rapid scanning direction and on the current direction of the line scan, e.g. forward scan or backward scan. The scanned image values result in a distorted image with additional image defects since image scanning and image representation do not match. 
         [0007]    Such distortions and image defects are particularly problematic in bidirectional scanning given that the image errors of even-numbered and odd-numbered lines differ and lines are no longer parallel to one another. In multi-spot scans in the line direction, the line interlaces are greater, are additionally emphasized by offsetting, and are significantly more visible to the human eye due to their structure. Problematic are also strong undersampling, scanning of every x-th line and offsetting (e.g. interpolation) of the pixels between them (line-step mode) as well as resonant scans with high speed in the line direction. 
         [0008]    One known solution for the problem is to reduce the useful area UA ( FIG. 1 ) of each scan curve SC in order to increase the turnaround area TA given that the sum of the useful area UA and turnaround area TA is always 100%. This leaves more time to move in the direction LD of the line feed LF. By enlarging the turnaround area TA from 16% (useful area UA 84%) to 48% (useful area UA 52%), the scan can be performed three times faster; by enlarging the turnaround area TA from 16% (useful area UA 84%) to 96% (useful area UA 4%), the scan can be performed six times faster, with the same position error in the feed direction, and thus already shows the limit of the method. The useful area UA becomes increasingly smaller and converges towards zero. 
         [0009]    In the scanning image capture, the scan is performed in the direction of the rapid scanning (line scan) with a temporally triangular scan trajectory in order to achieve a constant scanning speed over a useful area UA of a scan curve SC ( FIG. 1 ). 
         [0010]    In order to also compensate for remaining residual errors, a control function that is utilized for controlling the scanning unit must be pre-distorted for a scan at a constant scanning speed, as is known, for example, from U.S. Pat. No. 6,037,583. 
         [0011]    U.S. Pat. No. 6,037,583 describes a control system for a scanner drive, in particular for a laser scanning microscope. The scanner drive includes an oscillating motor for driving an oscillating mirror used for a linearly oscillating deflection of a beam. Furthermore, a control unit for supplying the oscillating motor with an exciting current is provided, which is variable with regard to the control frequency, the frequency curve and the amplitude. A function generator is provided, which is connected to the control unit. A measuring sensor serves to obtain a sequence of information about the deflection positions of the oscillating mirror. An arithmetic unit is configured for determining correction values for the exciting current from a comparison of actual and nominal values of the deflection position. In the arithmetic unit, arithmetic circuits are provided, which are configured for converting the information about the deflection positions of the oscillation mirror according to the amplitude and phase of the scanner based on a plurality of control frequencies. 
         [0012]    From the publication by John Giannini et al., “Driving MEMS mirrors for beyond their specification for fast, precise, synchronized laser scanning”, Focus on Microscopy 2015, a method is known, by which a pre-distorted control function for the line scan of MEMS devices is generated close to or above their resonance frequencies. To this end, a nominal function corrects and pre-distorts a control function with the deviations caused by the transmission function of the actual control function. 
       SUMMARY 
       [0013]    It is an object of the invention to provide methods for generating a control function and for operating a scanning unit that are improved in comparison with the related art. 
         [0014]    The method for generating the control function includes the following steps, wherein additional method steps can be performed. 
         [0015]    To generate the control function by a computer, a first function and a second function are derived, and the two functions are summed up to obtain a resulting control function. 
         [0016]    According to an aspect of the invention, the first function is, at least in sections, a linear function with a first frequency (and a first period), and the second function is a periodic function with a second frequency (and a second period). 
         [0017]    The first frequency is lower than the second frequency, the first function and the second function increase in directions opposite to each other over sections of their temporal progression, and the increases are of the same magnitude. 
         [0018]    A continuously linear function is considered as a function with a very low frequency. 
         [0019]    The counter-direction and the equality in magnitude is particularly important over sections in which at least one coordinate is to be kept constant by the control function. For example, the first function and the second function increase in directions opposite to each other over a useful area intended for acquiring image data, and the increases are equal in magnitude. 
         [0020]    The technical effect of the increases, which are in opposite or counter-directions in relation to each other, and which are equal in magnitude, is a mutual compensation which keeps at least one coordinate constant for the duration of the temporal section or the temporal sections, respectively. In a diagram in which the first and second functions are plotted over time, as a consequence of said compensation, the resulting function is parallel to the time axis. 
         [0021]    According to an aspect of the invention, a control function is provided, in particular in the form of a so-called step function, which is the sum of linear function(s), or functions that are linear at least in some sections, respectively, and of at least one periodic function, such as a sawtooth function, which together have an increase of zero in the useful area. These two portions of the resulting control function are separately equalized. Using the control function, control signals are generated, the execution of which generates the desired movement. 
         [0022]    It is an advantage that the first function has a comparatively low frequency and can be easily equalized. 
         [0023]    The second function is periodic and can be efficiently calculated by a suitable Fourier synthesis. 
         [0024]    The desired movement in the direction of the line scanning (pixel feed) can be continued to be achieved by harmonic synthesis as described in U.S. Pat. No. 6,037,583. The harmonic components are suitably to be chosen so that the desired movement (triangular movement or sawtooth movement) is performed. To this end, the harmonic components, for example, can be equalized in accordance with the transmission behavior of the scanners. 
         [0025]    The desired movement of the scanner in the direction of the image scanning (line feed) is decomposed into at least two movement components, one of which changes only slowly, usually linearly over time, and the other component(s) are temporally periodic movements. 
         [0026]    In the following, the terms movement components, component and components of the movement are used interchangeably. 
         [0027]    Both or more components of the movement are then equalized separately from one another by appropriate methods in each case and result in the respective components of the control signal. The sum of all components of the control signal constitutes the actual resulting control signal. 
         [0028]    According to an aspect of the invention, the first movement component is a long-period function usually changing slowly which can also contain short sections of rapid changes. These slowly changing areas are usually linear. 
         [0029]    The second and additional components, on the other hand, are short-period components and usually have a lower amplitude. They are determined by a harmonic approximation which minimizes the deviation of the component in the time domain during the image capture. The deviation is the difference between the actually desired nominal movement and the harmonic approximation. 
         [0030]    For the main application of the method described above, the temporal change in both movements (movement components) in some sections is equal in magnitude but opposite in sign so that the sum is constant in some sections. To achieve this property, the amplitude of the second component is proportional to the rate of change (including sign) of the first component. In principle, however, the method is suitable for any movements which do not possess this particular property. 
         [0031]    Equalization of the movement is understood to be the calculation of a control signal which leads to the desired movement. In this process, a transmission behavior of a device to be controlled, for example described by a transmission function, is advantageously taken into account. 
         [0032]    This can be achieved for the two components of the movement in the following ways:
       The first movement component is a low-frequency component and comparatively static in the areas(s) critical for the image capture. It either does not need to be equalized at all, or simple locally effective methods (e.g. lower-order location filters) are sufficient. This is numerically simple to carry out or avoids propagating errors from areas uncritical for the image capture.   The second component is a short-period component, which contains only a few and only higher-frequency spectral components, and except for their amplitude, these spectral components are not dependent on the low-frequency movement component. These spectral components are equalized with the inverse transmission function in the frequency space.       
 
         [0035]    The control signal generated according to an aspect of the invention is advantageously usable in a method for operating a scanning unit that is periodically displaceable in an infeed direction by an infeed distance, for example as an element of an image capture unit. To this end, the control signal is determined, control signals are generated depending on the desired movement, and the control signals are utilized to control the scanning unit. 
         [0036]    According to an aspect of the method, the first movement (e.g. first movement component) is a sawtooth or triangular movement each having a linear slope time corresponding to the capture time of an image. Times for returning back to the beginning of the image or reversing the movement direction may be added. 
         [0037]    The second movement (e.g. second movement component) is, for example, a sawtooth function with a period corresponding to the gross capture time of an image line. The sawtooth function has a constant increase in the area of the net capture time of an image line. The amplitude is proportional to the respective increase in the first movement. 
         [0038]    To generalize, it can be said that the first movement (representable by the first function, wherein a function is a mathematical calculation rule, for example of the general form f(x)) and the second movement (representable by the second function) can be pre-distorted independently of each other by a transmission function of the scanning unit. 
         [0039]    The scanning unit is controlled with the generated control function. A feed undesirably occurring in infeed direction by the first component is compensated for by the second component. 
         [0040]    According to an aspect of the invention, the control function is used for controlling the line feed of a scanning unit configured as a scanner. 
         [0041]    If more than two dimensions are scanned, the method can also be used for this purpose. Movements other than rapid line scanning are produced by slow, piecewise linear movements an average speed of which is equal to the speed at which the dimension is scanned. Undesired movement during the scanning of low dimensions is compensated for by the method, already known from 2D scanning, by adding harmonic functions compensating for the slow constant movement during the actual image scanning of low dimensions and thereby performing the actual position change between the image scanning. 
         [0042]    This can, for example, be performed for a Z scanner which requires a comparatively small amount of time to step (to be adjusted) between the planes, and thus steps without usual waiting periods between the planes. 
         [0043]    This is necessary, in particular, for bi-directional Z scans, since the image planes for the two scanning directions (e.g. down and up) otherwise have an opposing oblique position. 
         [0044]    The method is to be performed in an equivalent manner for higher dimensions. 
         [0045]    If the image capture is performed with a turned scanning field in regard to the scanning directions of the scanner, the individual dimensions are no longer served by separate scanners. Instead, the dimensions are scanned proportionately by multiple scanners. Feed and line scans are decomposed proportionally according to the scanning direction of the scanner. The previously described method for the pre-distortion for the components of the line movement and the feed in the different dimensions is performed in accordance with the earlier described methods. The transmission behavior of the corresponding scanner can be used for the pre-distortion. The pre-distorted components are summed separately for each scanner, and the scanner is thereby controlled. 
         [0046]    The method can also be used for multiple scanning of a line which is applied both in the multiple scanning of a line for the purpose of averaging and for the purpose of scanning a line with varying illumination. The sawtooth component is calculated here for a frequency which is lower by the factor of the multiple scanning. The harmonic approximation is different in this case due to other scanning ranges. 
         [0047]    According to a further aspect of the invention, the pre-distortion can also be performed, instead of a control or a pre-distortion, respectively, of a scanning unit, for example of a controlled scanner, at the input of the nominal position of the controller, at another location of the controller as an actuating signal or completely uncontrolled. In this case, the frequency response of the scanner relative to the signal is simply to be used at this location. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0048]    The invention will now be described with reference to the drawings wherein: 
           [0049]      FIG. 1  shows a schematic overview of possible deviations of actual scan curves from nominal functions; 
           [0050]      FIG. 2  illustrates schematically a first exemplary embodiment of a method for decomposition of the components of the line feed for a section of a 2D scan; 
           [0051]      FIG. 3  illustrates schematically a second exemplary embodiment of the method with useful areas and turnaround areas for a time-recurrent 2D scan; 
           [0052]      FIG. 4  illustrates schematically a third exemplary embodiment of the method with a pre-distorted control function; 
           [0053]      FIG. 5  illustrates schematically a fourth exemplary embodiment of the method with a pre-distorted control function with a double scan of a line (multi-track); 
           [0054]      FIG. 6  illustrates schematically a fifth embodiment of the method with a pre-distorted control function with different line feed and direction; 
           [0055]      FIG. 7  illustrates schematically the unidirectional image scan (+ bidirectional in the rapid scanning direction) with the slow first movement component (top), the rapid second movement component (center) and the resulting movement (bottom) in the direction of the image feed; 
           [0056]      FIG. 8  illustrates schematically the bidirectional image scan (+ bidirectional in the rapid scanning direction) with the slow first movement component (top), the rapid second movement component (center) and the resulting movement (bottom) in the direction of the image feed; 
           [0057]      FIG. 9  illustrates schematically the complete movement of the scanners (top) for a rotated image scan relative to the scanner axes, the movement components for the horizontally scanning scanner (center) and the vertically scanning scanner (bottom); and 
           [0058]      FIG. 10  illustrates schematically the complete movement of the scanners for a 3D scan aligned with the scanner axes, with the XY view of the movement (top), the X component (top center), the Y component (bottom center) and the Z component of movement (bottom), in which a complete slice (time 0-80) is used for the method of the Z scanner at the first Z position (Z position  40 ). 
       
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0059]      FIG. 1  shows possible deviations of actual scan curves SC from the nominal functions NF. The actually realized scan curves SC are shown as solid lines, and the nominal functions NF are shown as dashed lines. A line feed LF occurs in an infeed direction FD which coincides with the direction of a Y-axis Y of a two-dimensional XY coordinate system. The realized infeed distance ID for each performed line feed LF is constant. 
         [0060]    At the beginning and at the end of each line scan, a directional change of a scanning unit (not shown) performing a line scan in the rapid scanning direction (here, e.g., X) occurs in a turnaround area TA. Between the turnaround areas TA, the scanning unit passes through a useful area UA over whose duration over time image values can be acquired. Taking into account, for example, current values of the orientation of the scanner and/or using measurements, location data can be assigned to each image value so that location-resolved image values are obtained. 
         [0061]    As can be seen in  FIG. 1 , large deviations occur between the scan curves SC and the nominal movement functions NF, which to a large extent can be attributed to the line feed LF being offset in time with respect to the line scan to which it occurs in a lagging manner. As a result, a zigzag-shaped scan occurs in the XY plane (real deflection). 
         [0062]    In a first exemplary embodiment of the invention ( FIG. 2 ), a first movement component M 1  is determined (e.g. identified) in the form of a line and a second movement component M 2  in the form of a sawtooth function. The increases in the two components M 1 , M 2  are opposite to each other over sections of their time profile and are equal in magnitude so that no movement M occurs in the direction of the image feed.  FIG. 2  shows the movement in the image-feed direction (e.g. Y, see for example  FIG. 1 ). The scanning field is scanned from −1 to +1 in this direction. 
         [0063]    The principle discussed in  FIG. 2  is also applied in the second exemplary embodiment of the method according to the invention shown in  FIG. 3 . Here, the first movement component M 1  is a linear sawtooth function in some sections with a negative increase and a first period T 1 . The second movement component M 2  is a sawtooth function having the second period T 2  with T 1 &gt;T 2 . 
         [0064]    In  FIG. 3 , the useful areas UA and the turnaround areas TA are plotted, the latter shown as black bars. The turnaround areas TA represented by wide bars represent turnaround areas during which an image return occurs. The control function CF is shown schematically and depicted in the useful areas UA. 
         [0065]    The desired infeed or feed movement, for example of the scanning unit, from one scanned line to the next line to be scanned, is decomposed into two components, the slow component M 1  with the first period T 1  of an image scanning (image frequency) and the rapid component M 2  with the second period T 2  of a line scanning. The first movement component M 1  is a sawtooth function with the image frequency. In additional design possibilities, the first component M 1  is a triangular function with half the image frequency. Due to the smaller first period T 1 , the first movement component M 1  is to be equalized by simple methods. 
         [0066]    A frequency of the image scanning (image frequency) is calculated based on=1/T 1 , a frequency of the line scanning is calculated based on=1/T 2 . 
         [0067]    Subsequently, equalization refers to the correction of the nominal signal in order to generate a good agreement with the nominal movement component. Depending on frequency and directionality, the following methods can be considered:
       not to equalize the first movement component M 1  at all;   to subject the first movement component M 1  to a compensation of the group delay, or   to equalize the first movement component M 1  by filtering in the local area;   to equalize the first movement component M 1  using the inverse transmission function of the scanner in the frequency response.       
 
         [0072]    With reference to  FIG. 4 , a configuration of a third exemplary embodiment of the invention is explained in more detail.  FIG. 4  shows the useful areas UA, the turnaround areas TA, the high-frequency second movement component M 2 , its harmonic approximation hA and the pre-distorted control component C 2 . 
         [0073]    For the second movement component M 2 , a harmonic approximation hA is calculated ( FIG. 4 ). This consists in the minimum of the odd-numbered multiples of the image feed frequency (1, 3, 5 . . . ), the image feed frequency being the reciprocal of the period between two feed movements. The frequency thus depends on the frequency of the line scanning, the directionality of the line scanning, and, when appropriate, the number of multiple line scanning. Both movement components M 1  (e.g.  FIGS. 2, 3 ), M 2  compensate each other in the useful area UA, so that no or only a minimal movement occurs in feed direction FD ( FIG. 1 ) during this time. 
         [0074]    For the sufficiently accurate calculation of the line feed LF ( FIG. 1 ) in the direction of the Y-axis Y, only a limited number of multiples of the fundamental frequency (harmonic) is required. 
         [0075]    This function referred to as harmonic approximation hA can be determined by direct Fourier decomposition, by optimization to an optimum agreement of the sawtooth function of the second movement component M 2  in the useful area UA, or by another method. 
         [0076]    With the harmonic approximation hA of the movement component M 2 , a band-limited representation of the high-frequency movement M 2  is now available. Using the transmission function of the system, the control signal can be calculated from this movement. Various options are available:
       filtering in the frequency space with the reciprocal frequency response of the system,   local area filtering by convolution with inverse system response, and   compensation of the group delay.       
 
         [0080]    This can take place in the following locations:
       (calculated) nominal input signal of the controlled scanner, and/or   pre-control in the module of the controlled scanner.       
 
         [0083]    The transmission function
       can be measured directly or   can be determined indirectly by optimizing the image quality.       
 
         [0086]    The corrected second component C 2  of the second movement component M 2  and the optionally also corrected first component C 1  of the first movement component M 1  (not shown) are adapted to each another so that the resulting movement M compensates in the useful area(s) UA (see for example also  FIG. 2 ). For this purpose, the amplitude of the second component C 2  is to be adapted to the line spacing of the scan, i.e. to the image height and number of lines. 
         [0087]    With the resulting control signal, the scanning unit is controlled in the image feed direction (usually Y-axis), and at least one image is acquired. 
         [0088]    One example for the performing of the method for pre-distortion of the second control component C 2  for single-track recording of an image is now described with reference to  FIG. 5 :
       1. The desired movement curve M is decomposed into a high-frequency portion M 2  (second component M 2 ) and a continuous low-frequency portion M 1  (first component M 1 , see for example  FIG. 2 ). The low-frequency portion M 1  includes an active useful area of the image with a slow constant image feed and a passive return phase with a faster image return.   2. For the second movement component M 2 , the harmonic approximation hA is generated with a predetermined number of harmonics H (see below). In the case of simple bi-directional single-track scans, only the straight-line harmonics (h i =2, 4, 6, . . . ) are created because the function is twice the fundamental frequency of the line scanning, since, in each case after one half-oscillation, a change-over to the next line is performed.   3. The harmonic approximation hA is optimized to the least possible deviation from the nominal function NF (second component M 2 ) within the useful area UA. The harmonic approximation hA with H_LF (t) is described by:       
 
         [0000]    
       
         
           
             
               H_LF 
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                 ( 
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             = 
             
               
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                 with 
                  
                 
                     
                 
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         [0092]    The following values are given as an example for optimized parameters: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
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                 0 
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                 b i  [rad] 
                 0 
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                 a i  [a.u] 
                 0 
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                 0.127 
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                 0.096 
               
               
                   
               
             
          
         
       
       
         
           
             4. The frequency components of the harmonic approximation hA are corrected with the frequency response of the controlled scanner AS(f)=c(f)—c(f)·e jvd(f) . Here, c describes the amplitude frequency response, and d the phase frequency response. For the pre-emphasized line feed HPE_LF (t), the harmonic approximation hA is corrected with the reciprocal frequency response. 
           
         
       
     
         [0000]    
       
         
           
             
               HPE_LF 
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             5. The normalized first control component C 1  is generated and, possibly, the scanner behavior is also corrected (here without correction): 
           
         
       
     
         [0000]    
       
         
           
             
               BV 
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             6. Subsequently, the pre-emphasized second control component C 2  is summed with the optionally pre-emphasized control component C 1  and scaled to the field to be scanned in infeed direction ID of the line feed LF (“feed direction”) and scaled to the set image size with a factor VV A  and an offset VV O  in: 
           
         
       
     
         [0000]        VVs ( t )= VV   O   +VV   A ·( BV ( t )+ HPE _ LF ( t ))
       7. The scanning unit and the image capture are controlled with the thus calculated control signal.       
 
         [0097]      FIG. 5  shows the harmonic approximation hA of the second component M 2 , the pre-emphasized second control component C 2 , the nominal function NF as well as the distribution in time of the useful areas UA and the turnaround areas TA for a double multi-track. A first useful area UAL illustrated by way of example, is scanned with a first illuminating radiation and a second useful area UA 2 , likewise illustrated by way of example, is scanned with a second illuminating radiation before a line feed LF occurs. 
         [0098]    Another exemplary embodiment of the method for pre-distorting the second function F 2  for a multi-track capture of an image with two captures is now described with reference to  FIG. 5 . 
         [0099]    This correction differs from the exemplary embodiment discussed above with regard to  FIG. 5  in the following: 
         [0100]    The line number L (L=1, 2, 3 . . . ) can also be odd. The track number T is here T=2. 
         [0101]    The number of harmonic components of the harmonic approximation hA is, for example, for a minimal deviation: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 h i   
                 0 
                 2 
                 4 
                 6 
                 8 
                 10 
                 12 
                 14 
                 16 
               
               
                   
               
               
                 b i  [rad] 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 a i  [a.u] 
                 0 
                 0.316 
                 0.155 
                 0.100 
                 0.072 
                 0.054 
                 0.042 
                 0.032 
                 0.026 
               
               
                   
               
             
          
           
               
                 h i   
                 18 
                 20 
                 22 
                 24 
                 26 
                 28 
                 30 
                 32 
               
               
                   
               
               
                 b i  [rad] 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 a i  [a.u] 
                 0.000 
                 0.004 
                 0.004 
                 0.004 
                 0.004 
                 0.003 
                 0.003 
                 0.003 
               
               
                   
               
             
          
         
       
     
         [0102]    All other steps correspond to the third exemplary embodiment. Thus, for a change in the track number T, the number of coefficients for the harmonic approximation hA and its coefficients must be adapted, and the frequency response must be known at a larger number of support points and at other frequencies. 
         [0103]      FIG. 6  shows, in a fifth exemplary embodiment of the invention, a first component M 1  which is linear in some sections, a second component M 2 , and a movement M obtained by summation. 
         [0104]    The increase in the first component M 1  changes at t=100 (halving, interval I: 100−&lt;200) and t=200 (change in sign and tripling, interval I: 200-300). The amplitude of the second component M 2  is adapted accordingly, so that the desired plateaus are formed. With varying increases in the first component M 1 , the amplitude and/or the profile of the second component M 2  is to be correspondingly adapted. 
         [0105]    Such an exemplary embodiment of the method is, for example, suitable for achieving a pre-distortion of the line feed LF with a varying resolution of line groups. 
         [0106]    In a further exemplary embodiment of the invention, it is also possible for the line feed LF to be implemented with an alternating direction between two images in order to achieve a high frame rate even at high second frequencies f 2  (line scan frequencies) and a small number L of scanned lines. See in this respect  FIG. 8 . 
         [0107]    The sequence of the method is further subdivided into the following steps:
       1. The feed movement is decomposed into a long-period (period T 1 ) movement M 1  for the image feed and a short-period (period T 2 ) movement M 2  for the line feed LF (see for example  FIG. 2 ).   2. The first component M 1  is constructed from a slow steady phase for the actual image capture and a faster phase for the image return. Optionally, the low-frequency part (first component M 1 ) can also be pre-emphasized, e.g. by an IIR or FIR filter.   3. The high-frequency periodic portion M 2  (second component M 2 ) for the line feed LF is in turn decomposed into a certain number of harmonic frequency components which are optimized for a minimal deviation from the nominal function NF (harmonic approximation hA of the line feed LF).   4. The frequency components of the harmonic approximation hA of the high-frequency portion M 2  of the line feed LF are corrected with the frequency response of the scanning unit.   5. A control signal C 1 , C 2  of the different frequency components of the line feed LF is generated, and these components are summed up. When the scanning unit is controlled with the control signal thus obtained, it moves effectively with the desired movement M of the harmonic approximation hA.   6. The corrected first and second functions C 1  and C 2  (control components C 1  and C 2 ; line feed function and image feed function) are summed up and scaled to the image section while taking into account an amplitude and/or an offset.   7. The total control signal C=C 1 +C 2  is to be calculated for each scanner/scanning unit, respectively. In the process, at least the signals Cx and Cy are created, and possibly signals from additional scanners (Cz, . . . ).   8. The scanning unit is controlled with the calculated control signals Cx and Cy and possibly additional scanners. In the process, the actual image capture occurs.       
 
         [0116]    The steps 1 to 2 only need to be performed once. Step 3 must be performed once per system. For multi-track capture and single-track capture, different high-frequency components are necessary for the line feed LF. Only the steps 4 to 7 have to be recalculated prior to an image capture for the settings for the number of support points for the controlling per line, the second period T 2 , the number of lines, and the number of empty oscillations. 
         [0117]      FIG. 7  shows two movement components M 1  and M 2  of the line feed signal (usually Y-axis) for unidirectional image scanning, in which the individual image lines are always scanned in the same sequence. The unidirectional image scan (bidirectionally in the rapid scan direction) with the slow first movement component M 1  (top), the fast second movement component M 2  (center), and the resulting movement M (bottom) in the direction of image advance are shown. 
         [0118]      FIG. 8  shows, in contrast to  FIG. 7 , the two movement components M 1  and M 2  of the line feed signal (usually Y-axis) for a bidirectional image scanning in which the individual image lines are scanned alternately from top to bottom and then from bottom to top to reduce the dead time at the end of an image. To this end, the high-frequency component M 2  is to be inverted from one image to the other (see  FIG. 8 , center). 
         [0119]      FIG. 9  shows a rotated image scan as compared to the native scanner axes. The upper view shows the movement of the scanning in the XY plane, the two representations below show the temporal representation of the movements of the two scanners. Both scanners are each subjected to parts of line scanning and image scanning. The image scanning is in turn composed of the two components M 1  and M 2  so that the movement of the two scanners is composed of three components each. This is a schematic representation of the complete movement of the scanners (top) for a rotated image scan relative to the scan axes, the movement component (Mx) for the horizontally scanning scanner (center) and the movement component (My) of the vertically scanning scanner (bottom). 
         [0120]      FIG. 10  shows an unrotated XYZ-3D scan in which, by the composition of a slow component M 1  and a rapid component M 2 , both the image scanning (mostly Y scanners) and the batch scanning (usually Z scanners) allows the scanning of non-tilted rows and panes. The principle can be extended to any number of scanners (not shown), and also multi-dimensional scans can be rotated as desired as shown in  FIG. 9 . It illustrates schematically the complete movement of the scanners for a 3D scan aligned with the scanner axes, with the XY view of the movement (top), the X component Mx (top center), the Y component My (bottom center), and the Z component Mz of movement (third component M 3 ) (bottom). Here, a complete slice (time 0-80) is used for the method of the Z scanner at the first Z position (Z position  40 ). 
         [0121]    It is understood that the foregoing description is that of the exemplary embodiments of the invention and that various changes and modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims. 
       LIST OF REFERENCE NUMERALS 
       [0000]    
       
         C 1  component  1  of control signal C 
         C 2  component  2  of control signal C 
         Cx control signal of the first scanner (usually x) 
         Cy control signal of the second scanner (usually y) 
         Cz control signal of the third scanner (usually z) 
         SC scan curve 
         M movement (of the scanner) 
         M 1  first component (of the scanner movement); first function 
         M 2  second component (of the scanner movement); second function 
         Mn n-th component (of the scanner movement) 
         Mx movement of the first scanner (usually x) 
         My movement of the second scanner (usually y) 
         Mz movement of the third scanner (usually z) 
         T 1  first period (period length of image scanning) 
         T 2  second period (period length of line scanning) 
         UA useful area 
         UA 1  first useful area 
         UA 2  second useful area 
         hA harmonic approximation 
         I interval 
         NF nominal function 
         t time 
         TA turnaround area 
         FD infeed direction 
         ID infeed distance 
         LF line feed 
         X X-axis 
         Y Y-axis 
         Z Z-axis