Patent Publication Number: US-11036038-B2

Title: Closed-loop control of a scanner with frequency-space analysis of a system deviation

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. § 119 to German Patent Application No. 102018109055.2, filed on Apr. 17, 2018, the disclosure of which is incorporated herein in its entirety by reference. 
     TECHNICAL FIELD 
     Various embodiments of the invention relate to techniques for closed-loop control of a scanner. In particular, various embodiments of the invention relate to techniques for taking account of error components in an input signal, which is indicative for a system deviation, in the control in the case of closed-loop control. 
     BACKGROUND 
     Scanners for deflecting light are employed in different fields of technology. By way of example, scanners are used for scanning in laser scanning microscopes (LSMs). 
     Scanners typically comprise a scanning module with a deflection unit, which is configured to deflect light. The light is deflected differently depending on the position and/or orientation of the deflection unit. This defines a scanning angle. As a result, light can be emitted in different directions. It may also be possible to receive light from different directions. 
     For the purposes of probing the sample, the scanners typically travel over defined curves, which are sometimes also referred to as scanning angle curves. Deviations from these target curves cause image distortions or double contours in LSMs, for example. Therefore, it is desirable to travel the scanning angle curves with a high spatial and temporal accuracy. 
     One technique for setting the scanning angle with a high accuracy employs a control loop. Here, a TARGET pose of the deflection unit can be predetermined and a deviation of a measured ACTUAL pose of the deflection unit from the TARGET pose can be minimized. A corresponding exemplary technique is described in, for instance, DE 10 2005 047 200 A1. 
     SUMMARY 
     There is a need for improved techniques for a closed-loop control of a scanner. In particular, there is a need for techniques which control the scanner both reliably and with a high accuracy. 
     This object is achieved by the features of the independent patent claims. The features of the dependent patent claims define embodiments. 
     A method for closed-loop control of a scanner comprises the reception of an input signal. The input signal is indicative for a time dependence of a system deviation between an ACTUAL pose and a TARGET pose of a deflection unit of the scanner. The method also comprises the expansion of the input signal into a multiplicity of error components at a plurality of frequencies. Further, the method comprises, for each of the multiplicity of error components, the determination of a corresponding correction signal component on the basis of a respective frequency response component of a predetermined reciprocal frequency response. Further, the method comprises the output of a control signal on the basis of a combination of the correction signal components. 
     Thus, it is possible for a receiver of an input signal to be present, with the input signal supplying the ACTUAL pose of the scanner. Then, the system deviation can be determined with the inclusion of the TARGET pose of the deflection unit, which is supplied to a regulator. The system deviation can be expanded into a multiplicity of error components at different frequencies. A corresponding correction signal component can be determined for each of the multiplicity of error components on the basis of the error component and the reciprocal frequency response of the system at the frequency of the respective correction signal component. Further, it may be possible to output a control signal on the basis of a combination of the correction signal components. 
     By way of example, it would be possible for the aforementioned steps—reception, expansion, determination and output—to be respectively repeated for a plurality of regulating processes, for example according to a controller clock cycle. 
     Thus, the error components can describe the system deviation in the frequency space. 
     Taking account of the various components may correspond to an analysis of the system deviation in the frequency space. 
     A control loop, in particular, can be implemented by receiving the input signal and outputting the control signal. 
     A particularly reliable and robust closed-loop control of the scanner can be obtained by implementing a control loop with an analysis of the system deviation in the frequency space. In particular, it is possible to correct errors that no longer can be corrected by conventional (PID) controllers. By way of example, scanning angle curves can be implemented particularly accurately. 
     By way of example, a corresponding method could be implemented by a controller for a scanner, wherein the controller may have a memory and a logic component, for example. 
     The controller can be part of an LSM, for example. 
     A computer program product or a computer program comprises program code, which can be loaded by a logic component. Then, the logic component can execute the program code. Executing the program code causes the logic component to carry out a method for closed-loop control of a scanner. The method comprises a reception of an input signal. The input signal is indicative for a time dependence of a system deviation between an ACTUAL pose and a TARGET pose of a deflection unit of the scanner. The method also comprises the expansion of the input signal into a multiplicity of error components at a plurality of frequencies. Further, the method comprises, for each of the multiplicity of error components, the determination of a corresponding correction signal component on the basis of a respective frequency response component of a predetermined reciprocal frequency response. Further, the method comprises the output of a control signal on the basis of a combination of the correction signal components. 
     The features set out above and features that are described below may be used not only in the corresponding combinations explicitly set out, but also in further combinations or in isolation, without departing from the scope of protection of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  schematically illustrates a scanner comprising a controller in accordance with various examples. 
         FIG. 2  is a schematic illustration in relation to a control loop, which is implemented by the controller in accordance with various examples. 
         FIG. 3  is a flowchart of one exemplary method. 
         FIG. 4  illustrates the time curve of a movement of a deflection unit of the scanner and the sampling of the movement of the scanner and a system deviation in accordance with various examples. 
         FIG. 5  schematically illustrates an analysis of the system deviation in the frequency space in accordance with various examples. 
         FIG. 6  is a flowchart of one exemplary method. 
     
    
    
     DETAILED DESCRIPTION 
     The properties, features and advantages of this invention described above and the way in which they are achieved will become clearer and more clearly comprehensible in association with the following description of the exemplary embodiments which are explained in greater detail in association with the drawings. 
     The present invention is explained in greater detail below on the basis of preferred embodiments with reference to the drawings. In the figures, identical reference signs designate identical or similar elements. The figures are schematic representations of different embodiments of the invention. Elements illustrated in the figures are not necessarily depicted as true to scale. Rather, the different elements illustrated in the figures are reproduced in such a way that their function and general purpose become comprehensible to the person skilled in the art. Connections and couplings between functional units and elements as illustrated in the figures may also be implemented as an indirect connection or coupling. A connection or coupling can be implemented in wired (electric or optical) or wireless (electromagnetic, magnetic, optical, mechanical) fashion. Functional units can be implemented as securely wired hardware, hardware that is configurable and controllable by means of software or a combination of both. 
     Techniques for scanning light are described below. A corresponding scanner comprises a scanning module with a deflection unit. The scanning module may also comprise a mounting for the deflection unit, and an actuator. The actuator can be configured to exert a force on the mounting of the deflection unit and thus move the deflection unit. In the process, the pose of the deflection unit can be varied, as a result of which the scanning angle is varied. 
     As a general rule, different types of scanner can be used in the various examples described herein. Examples comprise: resonant scanners with free or forced resonance; non-resonant scanners, galvano scanners, MEMS scanners, incrementally moved scanners, continuously moved scanners, rotating scanners with ball bearings, etc. The mechanism with which the deflection unit is moved can vary depending on the employed type of scanner. In particular, a degree of freedom of the movement of the deflection unit can also vary. By way of example, the deflection unit could rotate in some examples, tilt in further examples, be deflected in transverse fashion in further examples, etc. Overlaid movements are also possible. Therefore, reference is made in general below to a variation of the position and/or the orientation (pose) of the deflection unit which, in principle, can describe all such degrees of freedom of the movement, either on their own or in combination with one another. The pose can be defined in a reference coordinate system which also determines the pose of the optical unit, i.e., a pose of a light source and/or a detector, for example. 
     In particular, scanners that implement periodic or quasi-periodic movement of the deflection unit can be used in the various examples described herein. 
     The techniques for scanning of light described herein can be used in different fields of technology. By way of example, corresponding scanners can be used in conjunction with an LSM. In the process, a sample object is sensed or scanned by a laser beam focused in punctiform fashion. Light that is scattered or reflected or re-emitted at the sample object is imaged on a pinhole. The light passing through the pinhole is captured by a detector, optionally after spectral splitting on the detector. In order to capture an image of a layer of the sample object, the laser beam is guided approximately line-by-line over the sample object by varying the scanning angle. Other examples comprise, e.g., laser micro-machining or printers or projectors, etc. 
     There is a closed-loop control of the scanner in the examples described herein. By way of example, a control loop can be implemented by a controller (closed-loop control). Then, the scanning angle can be set particularly accurately. A system deviation between a TARGET pose of the deflection unit and an ACTUAL pose of the deflection unit can be reduced efficiently and quickly and accurately, even in cases where other regulators no longer permit stable regulation. 
     This is based on the discovery that a conventional PID control loop is interested in the response characteristic of the system over broad frequency ranges, even if the actuation signal itself does not have any components there. This is different in the various examples described herein. If set correctly, the control loop only regulates where signal components are present. Furthermore, the feedback for each of these components can be set directly and independently of the other components. 
     The techniques described herein can be scaled flexibly. By way of example, it is possible to control a multiplicity of scanners in different channels. By way of example, a multiplicity of actuators can also be controlled per scanner. This be helpful for 2D scanning, for example, where light sequentially passes through a plurality of deflection units, which are actuated separately. 
     Various examples of the invention are based on an analysis of a system deviation between an ACTUAL pose of the deflection unit and a TARGET pose of the deflection unit. Here, the system deviation in real space is analysed as a component in frequency space. By way of example, the system deviation can be analysed at a plurality of discrete frequencies. 
     In order to carry out such an analysis of the system deviation in the frequency space, it may be desirable to receive a time-resolved input signal over a certain time interval; here, the input signal may comprise a plurality of data points, with each data point being indicative for the system deviation at a corresponding time. 
     By considering the system deviation over an integer multiple of its periodicity, it is possible to reliably detect system deviations of integer harmonics of its periodicity. 
       FIG. 1  illustrates aspects in relation to the scanner  100 . By way of example, the scanner  100  could be part of an LSM, which furthermore comprises a light source, an objective lens, a sample stage, etc. (not illustrated in  FIG. 1 ). 
     The scanner  100  comprises a deflection unit  112 , which may be implemented by a mirror or a prism, for example. Incident light  130  is deflected through a scanning angle  131 . The scanning angle  131  can be varied by varying the pose of the deflection unit  112 . 
     The light  130  can originate both from a light source (for instance, a laser or an LED) and from a scattering or fluorescent test object or from a sample. 
     The scanner  100  also comprises an actuator  111 . The actuator  111  is configured to modify the pose of the deflection unit  112 , as a result of which the scanning angle  131  is also varied. Very different types of actuators  111  can be used in the various examples described herein, for instance piezo-actuators, capacitive actuators or magnetic actuators. 
       FIG. 1  also illustrates a control signal  121 , which is output to the actuator  111  by a controller  101 . The control signal  121  should bring about a periodic movement of the deflection unit  112  in accordance with a TARGET pose of the deflection unit  112 . 
     Nevertheless, deviations may arise between the desired TARGET pose of the deflection unit  112  and the real ACTUAL pose of the deflection unit  112  on account of disturbing influences—for instance, heating, humidity, an external shock, ageing, material fatigue, partly unknown disturbing influences, etc. A sensor  113  is provided to capture such deviations. The sensor  113  is configured to output a measurement signal  122 , which is indicative for the measured pose of the deflection unit  112 . Hence, the measurement signal  122  is also indicative for the system deviation. 
     Here,  FIG. 1  shows an example in which the sensor  113  determines the pose by measuring a physical observable in conjunction with the deflection unit  112 . In other examples, it would also be possible, as an alternative or in addition thereto, to measure a physical observable in conjunction with the actuator  111  (dashed arrow in  FIG. 1 ). 
     The controller  101  receives the measurement signal  122  and processes the latter. In particular, the controller  101  can implement a control loop on the basis of the measurement signal  122 . 
     To this end, the controller  101  can be implemented by securely wired hardware, hardware that is configurable and controllable by means of software or a combination of both. 
     By way of example, the controller  101  could be implemented in time-discrete fashion with a digital circuit. By way of example, the controller  101  could be implemented as a field programmable gate array (FPGA), application-specific integrated circuit (ASIC) or microcontroller.  FIG. 1  illustrates a corresponding logic component  102 , which is sometimes also referred to as a functional unit (FU), and a memory  103 . By way of example, the logic component  102  could load program code from the memory  103  and could then implement the control loop. 
     The functionality of the logic component  102  is also described in conjunction with  FIG. 2 . 
       FIG. 2  illustrates aspects in relation to the closed-loop control of a scanner. In particular,  FIG. 2  illustrates aspects in conjunction with a control loop  170 . 
     The logic component  102  (regulator of the control loop) is functionally arranged between TARGET pose signal  126 , P target  (reference variable of the control loop), ACTUAL pose signal or measurement signal  122 , F actual  (feedback of the control loop) and an actuation signal  125 , A that is optional as a matter of principle. The ACTUAL pose signal  122  is obtained from an analogue-to-digital converter  113 - 1 , which is coupled to the sensor  113 . 
     As a general rule, different types of sensors  113  (measuring member of the control loop) are conceivable, for instance: magnetic field sensors; optical sensors; capacitive sensors; etc. The type of sensor  113  can vary with the actuated degree of freedom of the movement of the deflection unit  112 . 
     The difference between the TARGET and ACTUAL pose signal P target −P actual  (system deviation)—indicated by the input signal  127 —is used to modify the predetermined actuation signal  125 , A to form a corrected actuation signal  121 , A corr  (manipulated variable of the controller). The control signal  121  is transferred to the actuator  111  (actuating element of the control loop) via a digital-to-analogue converter  111 - 1 . 
     The actuation signal  121 , A corr  produces a movement B of the deflection unit  112  and feeds back—by means of the sensor  113 —a measurement signal  122 , P actual  that has a fixed relationship with this movement B (controlled variable of the control loop). In general, it is possible to measure the pose of the deflection unit  112  which is determined by the movement B. 
     It is possible to correct changes in the properties of the actuator  111 , i.e., the influence of the actuation signal  121 , A corr  on B, if the properties of the sensor  113 , i.e., the influence of B on the measurement signal  122 , P actual , are known. 
     The logic component  102  can resort to the frequency response  129 , F, which mediates between the control signal  121 , A corr  output at the actuator  111  and the measurement signal  122 , P actual . By way of example, the frequency response  129 , F and/or the reciprocal of the frequency response  129 , F could be stored in the memory  103 . The frequency response  129 , F can correspond to a transfer function. 
     The logic component  102  is configured to correct periodic or almost periodic movements with a period T if the TARGET pose signal  126  is known as well as the frequency response  129 , F. An optional (default) actuation signal  125 , A is helpful. By way of example, the actuation signal  125 , A can map certain technical boundary conditions of the actuator  111 , for instance a certain minimum voltage in the case of piezo-actuators, etc. 
     The actuating signal  125 , A is modified to form the corrected actuation signal  121 , A corr  such that the ACTUAL pose signal  122 , P actual  approaches the predetermined TARGET pose signal  126 , P target . Thus, the system deviation of the control loop is minimized. 
     To this end, the difference of TARGET and ACTUAL pose signal  122 ,  126  is combined by calculation over a preferably integer number of oscillation periods in various examples described herein. 
     The difference is correlated with an orthogonal basis over the period T (e.g., cos 2πm t/T and sin 2πm t/T) over an integer number of oscillation periods, where m is an integer, non-negative number such as, e.g., m=1 and m=2 and specifies the correlated harmonic. These correlated entities are combined by calculation using the complex-value frequency response F at points that correspond to the harmonic frequencies of the period T (i.e., m/T). The coefficients thus calculated describe the amplitude of a harmonic correction of the observed errors. The—optionally weighted—sum of all harmonic corrections yields ΔA; A CORR =A+ΔA is used as a corrected actuation signal. 
     In general, other orthogonal basis functions instead of cosine and sine can also be taken into account for the expansion. 
       FIG. 2  illustrates that the logic unit  102  can process a plurality of channels 1, 2, . . . n. As a result, the correction of a plurality of movements and a plurality of actuators is possible. 
     Thus, e.g., periodic control signals  121  are generated, which are output to the actuator. By way of example, this can be implemented—as illustrated in  FIG. 2 —by producing a correction signal  121  on the basis of a predetermined basis signal  125 . 
     Here, the logic component can trigger correction commands at defined times, in respect of which an update of the control signal  121  is implemented (regulating process). This can be implemented periodically or in event-related fashion. The logic component  102  could trigger a regulating process independently or in event-related fashion by producing the corresponding command. By way of example, a time interval between regulating processes can correspond to the controller clock cycle. In general, the controller clock cycle can vary over time. This means that the regulating processes can be carried out in not strictly periodic fashion or with a varying periodicity. 
     In general, there can be a parametrized analysis of the system deviation. Here, certain properties of the closed-loop control can be modified. By way of example, the parametrization can be undertaken by a register interface, the controller  101  or, in particular, the FU  102 . As a result of the parametrizable analysis, it is possible, for instance, to flexibly choose the number of data channels to be analysed and data points of the measurement signal  122 , with the data channels corresponding to the input and the output channels. 
     An exemplary implementation of the control loop  170  is described below. 
     The control loop  170  is subdivided into the modules (I) analysis, 
     (II) coefficient calculation and (III) synthesis, which produces the corrected actuation signal  121 . 
     All calculations below can be carried out multiple times and independently for different channels, which are indexed below by 1 . . . n. However, the index n is not listed explicitly everywhere below for reasons of clarity. 
     (I) Analysis Module (ana): 
     The difference of ACTUAL pose signal  122  (also referred to as measurement signal) and TARGET pose signal  126  is determined for each data point:
 
 P   DIFF   :=P   ACTUAL   −P   TARGET   (1)
 
     This corresponds to the input signal  127 , P DIFF . Forming the difference of Equation (1) is carried out iteratively for a plurality of data points, as a result of which each data point of the input signal  127 , P DIFF  is indicative for the system deviation at a corresponding time. 
     The data points for the ACTUAL pose signal  122  are received with a sampling clock cycle. By way of example, the sampling clock cycle can be predetermined by the sensor  113  and/or the ADC  113 - 1 . Typically, the sampling clock cycle is substantially greater than the period duration T of the movement of the deflection unit  112 , e.g., by a factor of 100 or 500 or 1000. Moreover, the sampling clock cycle is typically substantially greater than the controller clock cycle, for example by a factor in the range of between 200 and 10000, with this factor however also being able to reach orders of magnitude of 10{circumflex over ( )}7 . . . 10{circumflex over ( )}9, for example if scanners that move particularly slowly are regulated. 
     In each computer clock cycle, the data points of the input signal  127 , P DIFF  are multiplied by a sine and cosine of a predetermined frequency—for example, harmonics/harmonic oscillation 1 . . . m, respectively for each channel—and are summed for each computer clock cycle in an accumulating variable ΔC m , ΔS m :
 
Δ C   m   :=ΔC   m   +P   DIFF  cos  N   m φ  (2a)
 
Δ S   m   :=ΔS   m   +P   DIFF  sin  N   m φ  (2b)
 
m indicates the various frequencies. This processing is operated with the computer clock cycle of the FU  102  in order to process a plurality of data points between two regulating processes. That is to say Equations (2a) and (2b) are carried out repeatedly with the computer clock cycle. As a result, different frequencies can be taken into account sequentially for each data point by varying m. Optionally, it is also possible to take account of the plurality of channels.
 
     Equations (2a) and (2b) correspond to an incremental expansion because the subsequent iteration builds on the result of the preceding iteration. The computer clock cycle—with which such calculations as are described in Equations (2a) and (2b) are carried out—is typically substantially greater than the controller clock cycle, e.g., by a factor of 10 or 100. A factor of, e.g., 20 (such as, e.g., presently in the case of the controller clock cycle=5 MHz, computer clock cycle=100 MHz) allows processing of, e.g., 20 harmonics of one axis or respectively 10 harmonics of two axes per execution unit; this will still be explained in more detail below. 
     Equations (2a) and (2b) correspond to expanding the input signal  127  in a multiplicity of error components at the plurality frequencies 1 . . . m. By virtue of selecting the computer clock cycle to be sufficiently high, Equations (2a) and (2b) can be calculated for a data point for all frequencies 1 . . . m before the next data point is obtained according to the sampling clock cycle. That is to say, the expansion of the input signal  127  can be implemented in real time. 
     Here, Equations (2a) and (2b) describe the decomposition of the input signal  127  in cosine and sine described as a basis in exemplary fashion. In general, other orthogonal basis functions instead of cosine and sine can also be taken into account for the expansion. 
     Equations (2a) and (2b) implement this expansion in the error components by multiplying each data point of the input signal  127 , P DIFF  by a first reference data point cos N m φ and a second reference data point sin N m φ. Here, the first reference data point corresponds to the value of a first basis function of the corresponding frequency and phase—cosine in the example—and the second reference data point corresponds to the value of a second basis function of the corresponding frequency and phase—sine in the example. In general, other orthogonal, periodic functions can also be used instead of cosine and sine. The corresponding result values are then added to the values of the variables ΔC m  and ΔS m . These values are calculated sequentially for each data point, e.g., adapted iteratively. 
     By way of example, it would be possible for the corresponding data point P DIFF  to be discarded following the addition of Equations (2a) and (2b). In this way, it is not necessary to keep a particularly large memory for all data points that are received between two correction commands. In general, the data point can be discarded after multiplying the corresponding data point P DIFF  by the first reference data point and after multiplying the corresponding data point P DIFF  by the second reference data point, but before the end of the corresponding controller clock cycle—i.e., before the next regulating process. 
     The variables ΔC m  and ΔS m  are reset when a regulating process is implemented i.e., for example, if a correction commando (apply_accu_derivation) is received, and so subsequent data points are summed anew.
 
Δ C   m :=0  (3a)
 
Δ S   m :=0  (3b)
 
     In conclusion, the analysis module thus facilitates the expansion of the input signal in a multiplicity of error components at the various frequencies. Thus, this means that the system deviation can be quantified in frequency-resolved fashion. The coefficient calculation module can be carried out after the analysis module. 
     (II) Coefficient Calculation Module (calc_coe) 
     The coefficient calculation module can render possible the facilitation of the adaptation of the control signal for reducing the system deviation at the various frequencies. To this end, the frequency response  129 , F is taken into account. The adaptation of the control signal is described by coefficients (see  FIG. 2 , ΔA). These correspond to a corresponding correction signal component of the correction signal  121 . 
     In particular, this includes the inverse/reciprocal frequency response of the system. The frequency response is typically complex valued, i.e., it describes the relationship between control signal  121  and a measurement signal  122  in relation to the amplitude ratio and phase difference as a function of the considered frequency. The frequency response used here describes the relationship between electric response of the position detector as a function of the frequency of the actuation signal. Thus, in the example, the frequency response is given by:
 
 F:A   corr   →P   actual .
 
     The reciprocal frequency response is given by:
 
 F   −1   :P   actual   →A   corr .
 
     The frequency response is a complex-valued function. From it, it is possible to determine, inter alia, the response of the system in the case of the harmonic m of the considered oscillation. 
     These are described below as Re(F −1   m ) and Im(F −1   m ). Re(F −1   m ) and Im(F −1   m ) describe the real and complex component of the frequency response of the m-th harmonic of the currently regulated periodic movement. By way of example, it is possible that Re(F −1   m ), Im(F −1   m ) are stored in the memory  103  for all currently required harmonics m. 
     The results are summed in a variable and made available to the subsequent module (synthesis). 
     By way of example, the coefficient calculation can be carried out when a corresponding command is received. In addition to calculating new coefficients, further actions can be triggered by the command. 
     The APPLY_ACCUMULATED_DERIVATION command applies these two registers for all harmonics N m :
 
 C   m   :=C   m +Re( F   −1   m )Δ C   m   /p −Im( F   −1   m )Δ S   m   /p   (4a)
 
 S   m   :=S   m +Re( F   −1   m )Δ S   m   /p +Im( F   −1   m )Δ C   m   /p   (4b)
 
     This corresponds to determining components of the correction signal for the different error components. Here, p is the number of summed data points in the summation of ΔS m  and ΔC m . 
     Using modified sine and cosine functions (period length 2 32  or 2 64  instead of 2π), (4a) or (4b) can also be carried out as integer arithmetic. 
     The RESET_ONLINE_CORRECTION command resets the registers:
 
 C   m :=0  (5a)
 
 S   m :=0  (5b)
 
     In conclusion, the coefficient calculation module thus facilitates the determination of correction signal components as coefficients for the correction signal  121  at the various frequencies. Then, the correction signal can be produced—proceeding from these correction signal components—in the following synthesis module. 
     (III) Synthesis Module (syn) 
     The corrected actuation signal  121  is generated in the synthesis module and emerges from the combination, e.g., the weighted or unweighted sum, of all correction signal components. Here, the current coefficients from the coefficient calculation module (calc_coe) are loaded again for each regulating process and said current coefficients are multiplied by sine and cosine in order to facilitate the transformation into the time-space.
 
Δ A   m   =C   m  cos  N   m   φ+S   m  sin  N   m φ,  (6)
 
where cos N m φ and sin N m φ were already calculated in (2a) and (2b).
 
     Equation (6) once again corresponds to the calculation of the plurality of data points of the correction signal. 
     The various frequency contributions are added.
 
Δ A=ΔA   1   +ΔA   2   + . . . +ΔA   m   (7)
 
and the control signal  121 , A CORR  is calculated on the basis of the correction contribution from Equation (7) and the predetermined default control signal  125 :
 
 A   CORR   =A+ΔA.   (8)
 
     In a further variant, the result can also be written in a plurality of accumulating output variables in order to facilitate a mixture or duplication of results. To this end, use can be made of one hot coding, for example. 
     (IV) Generalities: 
     In (2a) and (2b), and also (6), φ denotes the current phase. Proceeding from the last correction command RESET_ONLINE_CORRECTION, RESET_ACCUMULATED_DERIVATION or APPLY_ACCUMULATED_DERIVATION, the data points are counted (value p; see also Equations (4a) and (4b)) and the current phase φ is determined as:
 
φ:=2π p/k   (9a)
 
which can also be calculated as
 
φ:=2π( p  MOD  k )/ k   (9b)
 
     How the aforementioned techniques can be implemented in the FU  102  using few resources will be described below 
     If the computer clock cycle—with which the various calculations according to the aforementioned equations can be carried out by the FU  102 —is substantially higher than the sampling clock cycle, with which the data points of the input signal  127 , P Diff  are obtained, the computational resources of the FU  102  can be employed multiple times in sequence in each sampling clock cycle. Here, different options are conceivable for designing the resources management of the computational resources of the FU  102 . Time slices are used in one example: Then, e.g., u harmonic time slices are assigned to each input channel n, said time slices dividing the resource allocation of the computational resources of the FU  102 . These time slices are activated in sequence; the calculation for a time slice is carried out in full or in part with each computer clock cycle. Thus, a time slice can have a length of one or more computer clock cycles. The time slices can be considered to be place holders for computational slots which are divided among the number of channels |n| and the number of frequencies |m| of the respective channel. 
     The following boundary conditions emerge from the time slice processing: The computational operations (1)-(9b) assigned to the various time slices are processed in sequence. Further, the possible number of time slices present per data point is determined by the system and emerges, in particular, from the ratio of computer clock cycle to sampling clock cycle. Typically, the computer clock cycle is greater than the sampling clock cycle by at least a factor of 20. This ensures that the processing of an entire time slice clock cycle—i.e., of the analysis module—is completed before the next data point. The time slice clock cycle emerges from the temporal sequence of all time slices 1 . . . u, wherein the sequence thereof need not necessarily be increasing. By way of example, in order to ensure this, the number of error components |m| could be determined on the basis of the ratio of the computer clock cycle to the sampling clock cycle. Optionally, the number of channels could also be taken into account. This is described on the basis of a specific example: 13 usable time slices emerge per data point in the case of a sampling clock cycle of 5 MHz and a computer clock cycle of 66 MHz. Accordingly, the number of error components can be up to |m|=13 in the case of one channel, and, e.g., respectively |m|=6 per channel in the case of two channels. 
       FIG. 3  is a flowchart of one exemplary method. By way of example, the flowchart can be carried out by the FU  102 . 
     Initially, an input signal is received in block  1001 . The input signal is indicative for a time dependence of a system deviation between an ACTUAL pose and a TARGET pose of a deflection unit of a scanner. By way of example, the input signal  127  of  FIG. 2  could be received. This also corresponds to Equation (1). 
     Here, the input signal  127  may comprise a multiplicity of data points. By way of example, these data points are received sequentially with a sampling clock cycle signal. Different data points describe the ACTUAL pose at different times. The sampling rate can correspond to a time resolution of a corresponding sensor, for example. These days, typical sampling clock cycle signals lie in the range of 1 kHz and 10 MHz. What this can achieve is that the input signal indicates the system deviation in time-resolved fashion. 
     As a general rule, it is not necessary for the data points to be received according to an unchanging, strictly periodic sampling clock cycle between two regulating processes. Temporal fluctuations of the sampling clock cycle are also possible. Where necessary, these would have to be taken into account in the frequency space analysis of the input signal by way of taking into account the changeable time intervals between adjacent data points. 
     This is followed by an analysis of the input signal in the frequency space. To this end, the input signal is expanded into a multiplicity of error components in block  1002 . Such an expansion of the input signal into respective error component comprises the decomposition of the input signal into orthogonal basis functions of the corresponding frequency. The different error components have different frequencies. By way of example, this corresponds to the calculation in Equations (2a) and (2b). Thus, in general, the expansion of the input signal for each data point can be implemented in sequence in relation to the multiplicity of error components, specifically, for example, in conjunction with Equations (2a) and (2b) by varying the index m. Different time slices can be used in the process. The calculation of the sum of Equation (2a) or the sum of Equation (2b) for a certain error component or frequency and for a certain channel can be assigned to different time slices in each case. The available computational resources can be managed by the time slices. 
     The expansion of the input signal can be implemented, in particular, sequentially for each data point of the multiplicity of data points, directly after the arrival thereof or, in general, in reaction to the reception of a data point with a computer clock cycle. By way of example, Equations (2a) and (2b), specifically, can be carried out for a newly obtained data point before a further data point is received with the sampling clock cycle. Consequently, it is not necessary to store the data points or build up the calculations. The input signal can be expanded in real time, in particular incrementally for each data point. As a result, the following can be achieved: (i) low storage requirements, independently of the number of data points of the input signal. (ii) continuous combining by calculation without load peaks (no build up). (iii) an instantaneous regulating process or a regulating process with only a few sampling cycles delay is possible, directly after completion of the analysis; there are very low time requirements, independently of the number of processed data points. 
     Subsequently, the corresponding correction signal component is determined in block  1003  for each error component. By way of example, this is based on a respective frequency-related frequency response component of a predetermined reciprocal frequency response. A corresponding implementation is illustrated, for example, in Equations (4a) and (4b). 
     Then, the various correction signal components can be combined in block  1003 ; see Equation (7), for example. Subsequently, an appropriate control signal can be output in block  1004 ; see Equation (8), for example. 
       FIG. 4  illustrates aspects in relation to a controller clock cycle  201 . In particular,  FIG. 4  illustrates the desired, periodic movement  200 , B of the deflection unit  112 . This periodic movement  200  is indicated by the measurement signal  122 , which specifies the ACTUAL pose of the deflection unit  112 . 
     It is evident from  FIG. 4  that the controller clock cycle  201  corresponds to the clock cycle of the TARGET operating frequency of the movement  200  of the deflection unit  112 . That is to say, the controller clock cycle  201  corresponds the period duration T P  of the movement that should be regulated. To this end, the correction command  290 —which triggers a regulating process, see, e.g., Equations (6)-(8)—can be output with the controller clock cycle  211  in each case. 
     As a general rule, the controller clock cycle can be chosen to be fixed and unchanging over time, or else it could be adapted over time. By way of example, a check as to whether the controller clock cycle  201  should be adapted can be carried out with the output of a correction command  290 . Such an adaptation of the controller clock cycle over time renders it possible to resolve a trade-off between (i) image aberrations on account of regulation that is too slow and (ii) image aberrations on account of an erroneous, unnecessary or bothersome correction of the movement on account of uncertainties or signal noise in the measurement signal. Thus, for example, it may be expedient to regulate more quickly at the start of the movement or at the start of using the control loop in order to quickly compensate large deviations or fast drifts; with continuing movements, it may be expedient to subsequently lengthen the time intervals between the correction commands  290  in order, for example, to reduce the noise of the sensor and hence to reduce jitter as a result of this noise. 
     The subsequent table illustrates an example for adapting the controller clock cycle over time, specifically together with the correction command  290  in each case. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Adapting the controller clock cycle 201 over time 
               
            
           
           
               
               
               
               
            
               
                   
                 Regulating interval, 
                 Duration of the regulating 
                 Noise of the 
               
               
                 LSM 
                 i.e., correction 
                 interval, i.e., controller 
                 measurement 
               
               
                 image 
                 command 290 
                 clock cycle 201 
                 signal 121 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Image 1 
                 1 
                 from 0 * T P  to 1 * T P   
                 100% 
               
               
                   
                 2 
                 from 1 * T P  to 3 * T P   
                 70% 
               
               
                   
                 3 
                 from 3 * T P  to 7 * T P   
                 50% 
               
               
                   
                 4 
                 from 7 * T P  to 15 * T P   
                 35% 
               
               
                   
                 5 
                 from 15 * T P  to 31 * T P   
                 25% 
               
               
                   
                 6 
                 from 31 * T P  to 63 * T P   
                 18% 
               
               
                   
                 7 
                 from 63 * T P  to 95 * T P   
                 18% 
               
               
                   
                 8 
                 from 95 * T P  to 127 * T P   
                 18% 
               
               
                   
                 ( . . . ) 
               
               
                   
                 12  
                 223 * T P  to 255 * T P   
               
               
                 Image 2 
                 1-8 
                 Respectively 32 T P   
               
               
                 Image 3 
                 1-8 
                 Respectively 32 T P   
               
               
                 Image 4 
                 ( . . . ) 
                 ( . . . ) 
               
               
                   
               
            
           
         
       
     
       FIG. 4  also illustrates aspects in relation to a sampling clock cycle  211 . The sampling clock cycle  211  is substantially greater than the controller clock cycle  201 . As a general rule, the sampling clock cycle  211  could be greater than the controller clock cycle  201  by at least a factor of 500. Data points  301  of the measurement signal  122 —and hence also of the input signal  127 —are received with the controller clock cycle  201  to ensure that; see Equation (1). Therefore, the sampling clock cycle  211  corresponds to a time resolution of the input signal  127 . 
       FIG. 4  also illustrates the input signal  127 . The input signal  127  is indicative for the system deviation  200 A. It is evident from  FIG. 4  that, typically, the system deviation  200 A has a substantially smaller amplitude than the amplitude of the movement  200  itself. Typically, the regulating target is set in respect of minimizing the system deviation  200 A. 
       FIG. 5  illustrates aspects in relation to analysing the input signal  127  in frequency space. In particular,  FIG. 5  illustrates aspects in relation to frequencies of an expansion of the input signal  127  or the decomposition of the input signal into components of different frequencies  311 - 314 . 
       FIG. 5  illustrates that an expansion of the input signal  127  into error components is implemented for four frequencies  311 - 314 . The frequency  311  (m=1) corresponds to the controller clock cycle  201  (illustrated in frequency space in  FIG. 5  and therefore denoted there by  201 ′; illustrated in time-space in  FIG. 4 ). The frequency  312  (m=2) in this case corresponds to twice the controller clock cycle  201 , the frequency  313  (m=3) corresponds to four times the controller clock cycle  201  and the frequency  314  (m=4) corresponds to six times the controller clock cycle  201 . This is one example. In other examples, it would be possible, for example, to regulate the controller clock cycle itself, three times the controller clock cycle, five times the controller clock cycle and seven times the controller clock cycle. 
     When matching the controller clock cycle  201  to the TARGET operating frequency of the movement  200  (cf.  FIG. 4 ), this corresponds to a harmonic series of the TARGET operating frequency of the movement  200 . As a general rule, the frequencies could thus be the multiple of the base frequency. The base frequency is the frequency f, and so the movement or the actuation signal repeats cyclically after the 1/f. Firstly, this achieves regulation of only components that are present in the system and that may occur. Secondly, these signals are orthogonal to one another. 
     The choice of the frequencies in  FIG. 5  is exemplary and, in general, other, fewer or more frequencies may be selected. 
       FIG. 5  also illustrates the contribution of the various error components  710 - 713  to the input signal  127 . 
     The greatest contribution is supplied—in the non-limiting example of  FIG. 5 —by the error component  711  at the TARGET operating frequency of the movement  200 . The error components  711 - 713  supply smaller contributions. The amplitude of the error components  710 - 713  corresponds to sqrt(C m   2 +S m   2 ) of Equations (6a) and (6b). 
     In general, the amplitude of the error components  710 - 713  can vary. Strong used signals need not necessarily produce the strongest corrections, even if these promote the latter. Higher frequencies of the error components tend to produce more regulation because a possibly also still present PID controller or PD controller corrects such high frequencies to substantially worse extent. Components in the region of the resonant frequency of the PID controller also tend to produce relatively large deviations since small changes in the parameters there significantly change the phase frequency response. 
       FIG. 6  is a flowchart of one exemplary method. The flowchart according to  FIG. 6  corresponds to a correction clock cycle. By way of example, the correction clock cycle could start when the operation of a scanner is started. Hence, the control loop is initialized. 
     Initially, there is a reset in block  1101 . This may correspond to setting the values of the variables according to Equations (3a), (3b), (5a) and (5b) to zero. 
     Then, a new data point  301  of the input signal  127  is received in block  1102 . The data point  301  is indicative for the system deviation  200 A at a certain time. By way of example, the data point  301  could be obtained by the calculation according to Equation (1) from the TARGET pose signal  126  and the measurement signal  122 —which corresponds to the ACTUAL pose signal. 
     Then, a current error component is selected in block  1103  and the corresponding variable is adapted in conjunction with the expansion of the input signal into the corresponding error component in block  1104 . This may correspond to a scalar product with two orthogonal basis functions of the corresponding frequency and can be implemented, for example, by Equations (2a) and (2b). Appropriate time slices can be used by taking account of the available computer clock cycle in order to carry out these calculation operations. 
     Blocks  1103  and  1104  may correspond to the analysis module, as described above. 
     Then, a check is carried out in block  1105  as to whether a calculation for further error component  710 - 713  should be carried out. If this is the case, blocks  1103  and  1104  are carried out again in further time slices. 
     Otherwise, a check is carried out in block  1106  as to whether a further data point  301  should be received before the end of the controller clock cycle or before emitting a correction command  290  for triggering a regulating process. 
     If the expansions are carried out in real time, it is possible to ensure that block  1106  is carried out before the next data point of the input signal  127  is received in the next iteration of block  1102 . So that the expansion can be implemented in real time, the computer clock cycle—with which blocks  1103  and  1104  can be carried out in the different time slices—can be compared to the sampling clock cycle, which defines the time interval between the reception of sequential data points. Then, it would be possible, for example, to determine the number of error components, i.e., the number of iterations of blocks  1103  and  1104  per iteration of block  1102 , from the ratio between computer clock cycle and sampling clock cycle. 
     If it is determined in block  1106  that no further data point should be received, the control signal  121  is determined in block  1107 . By way of example, this may comprise carrying out the coefficient calculation and synthesis modules, i.e., carrying out Equations (4a), (4b), (5a), (5b) and (6)-(8). Block  1107  can be carried out particularly quickly—on account of the already previously implemented iterative adaptation of the variables; cf. Equations (2a) and (2b). The resource-intensive expansion was already undertaken previously, for example in real time. 
     The controller clock cycle is optionally adapted in block  1108 ; cf. Table 1. By way of example, it may be expedient to reduce the frequency of regulation, i.e., the controller clock cycle, when the regulation target is approached—i.e., for example, depending on the size of the system deviation and/or with increasing number of iterations of block  1108 . This may serve to reduce the effects of errors of the sensor  113 , in particular non-systematic errors, on the corrected scanner movement. 
     It goes without saying that the features of the embodiments and aspects of the invention described above can be combined with one another. In particular, the features can be used not only in the combinations described but also in other combinations or on their own without departing from the scope of the invention. 
     By way of example, examples described above are described in conjunction with LSMs. However, corresponding techniques can also be used for other applications.