METHOD FOR GENERATING A CONTROL FUNCTION AND METHOD FOR OPERATING A SCANNING UNIT

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 T1) movement, and the second movement is a short-period (period T2) movement, wherein the period T1 is substantially longer than the period T2. 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.

Claims

1. A method for generating a control function by using a computer, the method comprising: determining a first function and a second function, the first function being at least in some sections a linear function with a first frequency, the second function being a periodic function with a second frequency, the first frequency being lower than the second frequency, the first and second functions increasing over sections of temporal progression in directions opposite to one another, and increases of the first and second functions being of a same magnitude; and generating the control function by summing up the first function and the second function.

2. A method for generating a control signal, the method comprising: decomposing a desired movement into a first movement and at least one second movement, the desired movement being a sum of the first movement and the at least one second movement, the first movement being a slowly changing movement with a first period, the second movement being a periodic movement with a second period, and a duration of the second period being shorter than a duration of the first period; separately generating a first control component of the first movement and at least one second control component of the at least one second movement; separately equalizing the first control component of the first movement and the at least one second control component of the at least one second movement; and generating the control signal by summing up the first control component and the at least one second control component.

3. A method for operating a scanning unit that is periodically displaceable in an infeed direction by an infeed distance, the method comprising: generating the control function according to claim 1; and generating a control signal by utilizing the control function.

4. A method for operating a scanning unit periodically displaceable in an infeed direction by an infeed distance, the method comprising: generating the control signal according to claim 2 as a function of the desired movement; and controlling the scanning unit by the control signal.

5. The method according to claim 1, wherein: the first movement is a slow, continuous, and long-period movement, and the first period of the first movement has a duration that corresponds to a single image duration during unidirectional image scanning.

6. The method according to claim 1, wherein: the first movement is a slow, continuous, and long-period movement, and the first period of the first movement has a duration that is twice the image duration during bidirectional image scanning.

7. The method according to claim 1, wherein: the second movement is a fast, short-period movement, and a duration of the second period corresponds to a temporal distance between two image lines.

8. The method according to claim 1, wherein the second movement includes a number of harmonic frequency components which are determined such that deviations from the nominal function are minimized.

9. The method according to claim 2, wherein the first movement and the at least one second movement are equalized independent of each other and result in the first and the at least one second control components which correct a transmission behavior of a scanning unit and based on which the control signal is generated.

10. The method according to claim 2, further comprising: controlling an infeed of a scanning unit having a plurality of scanning directions and being configured as a scanner, the infeed being controlled by respective control signals in one of the scanning directions of the scanning unit.

11. The method according to claim 10, further comprising: controlling a plurality of scanning units by respective control signals in order to achieve a multi-dimensional scanning of an object, a space, or the object and the space.

12. The method according to claim 1, further comprising: acquiring location-resolved image values by a scanning unit; and providing the location-resolved image values for image generation.

13. The method according to claim 2, further comprising: decomposing the desired movement, generating the first and the at least one second control components, and equalizing the first and the at least one second control components for more than two dimensions.

14. The method according to claim 13, further comprising: performing a synthesis with respective moving components for scanning axes, wherein coordinate axes of a multi-dimensional movement and the scanning axes do not coincide.

Description

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 M1 is determined (e.g. identified) in the form of a line and a second movement component M2 in the form of a sawtooth function. The increases in the two components M1, M2 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 M1 is a linear sawtooth function in some sections with a negative increase and a first period T1. The second movement component M2 is a sawtooth function having the second period T2 with T1>T2.

[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 M1 with the first period T1 of an image scanning (image frequency) and the rapid component M2 with the second period T2 of a line scanning. The first movement component M1 is a sawtooth function with the image frequency. In additional design possibilities, the first component M1 is a triangular function with half the image frequency. Due to the smaller first period T1, the first movement component M1 is to be equalized by simple methods.

[0066] A frequency of the image scanning (image frequency) is calculated based on=1/T1, a frequency of the line scanning is calculated based on=1/T2.

[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: [0068] not to equalize the first movement component M1 at all; [0069] to subject the first movement component M1 to a compensation of the group delay, or [0070] to equalize the first movement component M1 by filtering in the local area; [0071] to equalize the first movement component M1 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 M2, its harmonic approximation hA and the pre-distorted control component C2.

[0073] For the second movement component M2, 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 M1 (e.g. FIGS. 2, 3), M2 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 M2 in the useful area UA, or by another method.

[0076] With the harmonic approximation hA of the movement component M2, a band-limited representation of the high-frequency movement M2 is now available. Using the transmission function of the system, the control signal can be calculated from this movement. Various options are available: [0077] filtering in the frequency space with the reciprocal frequency response of the system, [0078] local area filtering by convolution with inverse system response, and [0079] compensation of the group delay.

[0080] This can take place in the following locations: [0081] (calculated) nominal input signal of the controlled scanner, and/or [0082] pre-control in the module of the controlled scanner.

[0083] The transmission function [0084] can be measured directly or [0085] can be determined indirectly by optimizing the image quality.

[0086] The corrected second component C2 of the second movement component M2 and the optionally also corrected first component C1 of the first movement component M1 (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 C2 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 C2 for single-track recording of an image is now described with reference to FIG. 5: [0089] 1. The desired movement curve M is decomposed into a high-frequency portion M2 (second component M2) and a continuous low-frequency portion M1 (first component M1, see for example FIG. 2). The low-frequency portion M1 includes an active useful area of the image with a slow constant image feed and a passive return phase with a faster image return. [0090] 2. For the second movement component M2, 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.sub.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. [0091] 3. The harmonic approximation hA is optimized to the least possible deviation from the nominal function NF (second component M2) within the useful area UA. The harmonic approximation hA with H_LF (t) is described by:

[00001]$\mathrm{H\_LF}.Math.\left(t\right)=a_0+\underset{h_i}{\overset{H}{.Math.}}.Math.a_i.Math.\cos \left(2.Math..Math.\pi .Math..Math.h_i.Math.f_s.Math.t/T-b_i\right)$$\mathrm{with}.Math..Math.h_i=2.Math.k,k\in {\mathbb{N}}_0,$

[0092] The following values are given as an example for optimized parameters:

TABLE-US-00001 h.sub.i 0 2 4 6 8 10 12 14 16 b.sub.i [rad] 0 0 0 0 0 0 0 0 0 a.sub.i [a.u] 0 0.311 0.127 0.142 0.172 0.175 0.157 0.127 0.096 [0093] 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).Math.e.sup.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.

[00002]$\mathrm{HPE\_LF}.Math.\left(t\right)=a_0+\underset{h_i}{\overset{H}{.Math.}}.Math.\frac{a_i}{c\left(f_s/T.Math.h_i\right)}.Math.\cos \left(h_i.Math.2.Math..Math.\pi .Math.f_s/T.Math.t-b_i+d\left(f_s/T.Math.h_i\right)\right)$$.Math.\mathrm{with}.Math..Math.h_i=2.Math.k,k\in {\mathbb{N}}_0,$ [0094] 5. The normalized first control component C1 is generated and, possibly, the scanner behavior is also corrected (here without correction):

[00003]$\mathrm{BV}\left(t\right)=\left(Z+L\right).Math.\left(-\frac{1}{2}-\frac{4}{\pi }.Math.\underset{z_i}{\overset{\infty }{.Math.}}.Math.{\left(2.Math.z_i+1\right)}^{-1}.Math.\cos \left(\frac{z_i.Math.2.Math..Math.\pi .Math.f_s/T.Math.t}{\left(Z+L\right)}\right)\right)$$\mathrm{with}.Math..Math.z_i\in \mathbb{N}.$ [0095] 6. Subsequently, the pre-emphasized second control component C2 is summed with the optionally pre-emphasized control component C1 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.sub.A and an offset VV.sub.O in:

VVs(t)=VV.sub.O+VV.sub.A.Math.(BV(t)+HPE_LF(t)) [0096] 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 M2, the pre-emphasized second control component C2, 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 UA2, 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 F2 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:

TABLE-US-00002 h.sub.i 0 2 4 6 8 10 12 14 16 b.sub.i [rad] 0 0 0 0 0 0 0 0 0 a.sub.i [a.u] 0 0.316 0.155 0.100 0.072 0.054 0.042 0.032 0.026 h.sub.i 18 20 22 24 26 28 30 32 b.sub.i [rad] 0 0 0 0 0 0 0 0 a.sub.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 M1 which is linear in some sections, a second component M2, and a movement M obtained by summation.

[0104] The increase in the first component M1 changes at t=100 (halving, interval I: 100−<200) and t=200 (change in sign and tripling, interval I: 200-300). The amplitude of the second component M2 is adapted accordingly, so that the desired plateaus are formed. With varying increases in the first component M1, the amplitude and/or the profile of the second component M2 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 f2 (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: [0108] 1. The feed movement is decomposed into a long-period (period T1) movement M1 for the image feed and a short-period (period T2) movement M2 for the line feed LF (see for example FIG. 2). [0109] 2. The first component M1 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 M1) can also be pre-emphasized, e.g. by an IIR or FIR filter. [0110] 3. The high-frequency periodic portion M2 (second component M2) 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). [0111] 4. The frequency components of the harmonic approximation hA of the high-frequency portion M2 of the line feed LF are corrected with the frequency response of the scanning unit. [0112] 5. A control signal C1, C2 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. [0113] 6. The corrected first and second functions C1 and C2 (control components C1 and C2; 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. [0114] 7. The total control signal C=C1+C2 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, . . . ). [0115] 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 T2, the number of lines, and the number of empty oscillations.

[0117] FIG. 7 shows two movement components M1 and M2 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 M1 (top), the fast second movement component M2 (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 M1 and M2 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 M2 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 M1 and M2 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 M1 and a rapid component M2, 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 M3) (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

[0122] C1 component 1 of control signal C [0123] C2 component 2 of control signal C [0124] Cx control signal of the first scanner (usually x) [0125] Cy control signal of the second scanner (usually y) [0126] Cz control signal of the third scanner (usually z) [0127] SC scan curve [0128] M movement (of the scanner) [0129] M1 first component (of the scanner movement); first function [0130] M2 second component (of the scanner movement); second function [0131] Mn n-th component (of the scanner movement) [0132] Mx movement of the first scanner (usually x) [0133] My movement of the second scanner (usually y) [0134] Mz movement of the third scanner (usually z) [0135] T1 first period (period length of image scanning) [0136] T2 second period (period length of line scanning) [0137] UA useful area [0138] UA1 first useful area [0139] UA2 second useful area [0140] hA harmonic approximation [0141] I interval [0142] NF nominal function [0143] t time [0144] TA turnaround area [0145] FD infeed direction [0146] ID infeed distance [0147] LF line feed [0148] X X-axis [0149] Y Y-axis [0150] Z Z-axis