A method for determining a correction value, a method for determining a corrected phase value, a device for determining a correction value, and a device for determining a corrected phase value.

Abstract

This invention relates to a method for determining a correction value, a method for determining a corrected phase value, a device for determining a correction value, and a device for determining a corrected phase value. [Solution] A method for determining a correction value, etc., which determines at least one correction value for an actual phase value, and includes the following steps: (a) A step of determining an actual phase value for two or more sampling locations, wherein the sampling locations are spaced apart from each other by an integer multiple of the signal period length; (b) A step of determining an estimated curve of the phase value trajectory corresponding to the actual phase value; (c) A step of determining a target frequency distribution of the phase value corresponding to the estimated curve; (d) A step of determining the actual frequency distribution of the actual phase value; (e) A step of determining a target phase value such that it has the same cumulative frequency as the cumulative frequency determined based on at least one selected actual phase value, determining the difference between the target phase value and the actual phase value as a difference value unique to the actual phase value, and determining a correction value corresponding to the difference value.

Description

Technical Field

[0001] The present invention relates to a method for determining a correction value, a method for determining a corrected phase value, a device for determining a correction value, and a device for determining a corrected phase value. More specifically, the present invention relates to a method for determining at least one correction value for correcting a phase value determined based on two orthogonal signals, a method for determining a corrected phase value (hereinafter sometimes simply referred to as a corrected phase value) which is a phase value corrected based on such a correction value, a device for determining such a correction value, and a device for determining a corrected phase value.

Background Art

[0002] Position sensors or distance sensors used in the present invention, particularly interference-based or encoder-based sensors, are known to generate output signals based on the so-called orthogonal method. Generation methods using such sensors are described in, for example, Patent Document 1 and Non-Patent Document 1.

[0003] Here, in an ideal flow (scenario) in the generation method as described above, it is preferable to generate norm signals of sine waves centered on zero and shifted from each other by 90 degrees to form a so-called orthogonal signal pair (hereinafter sometimes simply referred to as a signal or a signal pair). That is, in an ideal scenario, when the amplitude value (displacement amount) of the first signal of the signal pair forms the value on the horizontal axis (x value) and the corresponding amplitude value (displacement amount) of the second signal of this signal pair forms the value on the vertical axis (y value), the measurement points based on the orthogonal signal pair will be located within a circle over the length of the signal period. This is also called a Lissajous figure and is shown in FIG. 2. In other words, Lissajous figures refer to the geometric patterns (curvilinear figures) that are drawn over time when two simple sine waves vibrating in mutually perpendicular directions are combined. Discovered by the French physicist Lissajous, these figures exhibit a variety of shapes, such as circles, ellipses, straight lines, or complex patterns, depending on the frequency ratio and phase difference of the two signals, and are particularly used in oscilloscopes to visually analyze the relationship between the frequencies and phases of signals. In this case, using the arctangent function, the period-specific phase value (ph) can be determined based on equation (1) as follows: However, which signal is used as the x-value and which as the y-value can be changed as appropriate depending on the situation in which the phase value becomes zero.

[0004]

number

[0005] Furthermore, the period-dependent phase value can take values ​​in the range of 0 to 360 degrees, or 0 to 2π. On the other hand, the period-independent cumulative phase value (PH) is preferably determined based on equation (2) as follows.

[0006]

number

[0007] Here, the symbol u in equation (2) represents the number of execution cycles that have already been completed.

[0008] This type of phase value (ph, PH) can be converted into positional information (sometimes simply referred to as position) corresponding to that phase value. Therefore, changes in the phase value (ph, PH) can be converted into changes in position. And such corresponding assignments can be determined, for example, by calibration. For example, they can be determined based on equation (3) as follows.

[0009]

number

[0010] Here, Delta_s indicates the change in position, and Delta_PH, or Delta_ph, indicates the change in phase value. Furthermore, the proportionality constant k is a value that depends on various variables, such as the wavelength of the laser light used and the periodicity of the optical grating.

[0011] The problem with this method of determination is that the Lissajous figure is not necessarily an ideal circle. Therefore, there were problems such as the inability to calculate the phase value (ph, PH) using inverse trigonometric functions (arctangent), or a decrease in the measurement accuracy of the values ​​obtained for this type of calculation. In particular, in this case, periodic measurement errors may occur. For example, in the case of interferometer sensors, under unfavorable conditions, the error can exceed 10 nm, which posed a problem of excessive inaccuracy, especially when measuring predetermined dimensions in the semiconductor field.

[0012] As described above, there are many reasons why Lissajous figures become non-circular, including detector mismatch, multiple reflections within the measurement cavity, and crosstalk between measurement channels.

[0013] Specifically, in the practically relevant special case of elliptical Lissajous figures, to put it simply, it is known that there are multiple correction approaches to convert an ellipse into a circle. These approaches can utilize, for example, modified or extended methods of the method described in the paper "P. Heydemann, Measurement and Correction of Orthogonal Fringe Measurement Errors in Interferometers, Applied Optics (USA), 20(19), 3382 (1981)." However, these correction methods had a problem: they didn't work for irregular Lissajous figures, especially those that weren't elliptical. Specifically, these types of irregularly shaped residuum figures are generated, for example, when a Fabry-Perot interferometer is used as a measurement cavity and multiple reflections occur in the measurement arm, or when an orthogonal signal pair is generated by modulating the laser wavelength using electricity. And, although not desirable at that time, irregularly shaped residuum figures will occur when, for example, an inherent intensity modulation occurs.

Prior Art Documents

Patent Documents

[0014]

Patent Document 1

Non-Patent Documents

[0015]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0016] Therefore, the technical problem of the present invention is to provide a method for determining a correction value for providing at least one correction value for the actually measured phase value to be corrected, a method for determining a corrected phase value corrected by at least one correction value, and a determination device for these, thereby accurately determining the corrected phase value and the like. That is, particularly, to provide a preferable determination method and the like that can be used even when the measured values (amplitudes) of the orthogonal signal pair form an irregular residuum figure and are not arranged in an arc shape or an elliptical arc shape.

[0017] Therefore, the technical problems in this invention can be solved, and are the objectives of this invention, by a method for determining a correction value, a method for determining a modified phase value, a device for determining a correction value, and a device for determining a modified phase value, each consisting of the components described in the independent claims of the patent claims. Furthermore, more advantageous configurations of the present invention are described in the dependent claims for a method for determining a correction value, a method for determining a modified phase value, a device for determining a correction value, and a device for determining a modified phase value, and the aim is to provide these. [Brief explanation of the drawing]

[0018] [Figure 1] This figure is provided to illustrate an example of the signal curves for an orthogonal signal pair. [Figure 2] This diagram illustrates the difference between an ideal Lissajous figure and a distorted Lissajous figure. [Figure 3] This schematic diagram is used to explain the measured phase values ​​and estimated curves specific to the sampling location. [Figure 4] This is a schematic diagram used to explain the target frequency distribution and the actual frequency distribution. [Figure 5] This is a schematic diagram used to explain the correction values ​​in Lissajous plots. [Figure 6] This is a schematic block diagram used to illustrate the apparatus according to the present invention. [Modes for carrying out the invention]

[0019] Furthermore, the method for determining the correction value, the method for determining the corrected phase value, the device for determining the correction value, and the device for determining the corrected phase value of the present invention will be described in more detail by exemplary embodiments as shown in the figures, but will be described more specifically below with reference to the drawings as appropriate.

[0020] [First Embodiment] A first embodiment of the present invention is a method for determining a correction value, which determines at least one correction value for a measured phase value to be corrected. As explained at the beginning, this measured phase value can directly represent positional information, or it can be used to calculate positional information. In particular, the change in the measured phase value can directly represent the change in position, or it can be used to calculate the change in position. Therefore, it is preferable to determine the movement information in response to the change in the phase value, and thus, it is preferable that such movement information includes information regarding the direction of movement and the movement path / angle. Furthermore, as explained at the beginning, it is preferable that the measured phase value is either in a state where it can be determined from the orthogonal signal pair, or in a state where it has been determined from the orthogonal signal pair. Furthermore, it is preferable that this orthogonal signal pair includes at least a first signal and a second signal. In addition, it is preferable that at least one of these signals is a detection signal from a sensor, or a measurement signal obtained by converting such a detection signal. Furthermore, it is preferable that both the first signal and the second signal are measurement signals of these types. However, it is also preferable that at least one signal is mathematically determined in correspondence to a measurement variable different from the signal. Ideally, the first signal is proportional to a sine function, and the second signal is proportional to a cosine function. Known techniques for generating such orthogonal signal pairs include, for example, the generation of phase-shifted signals using polarization degrees of freedom and sinusoidal wavelength modulation. More ideally, the first and second signals are preferably sinusoidal normalized signals centered at zero and shifted 90 degrees from each other.

[0021] Therefore, the proposed correction method is characterized by being carried out including at least the following steps (a) to (e).

[0022] 1. Process (a) First, step (a) is typically the first step, characterized in that a measured phase value unique to each sampling location is determined for at least two sampling locations. Furthermore, these sampling locations are spaced apart from each other by a multiple of the signal period length. In this case, it is preferable that the sampled signals have the same period length. Furthermore, the multiple of the period length is preferably 1, but it is also preferable that it be greater than 1. In other words, it is preferable that the measured phase value is determined for multiple sampling locations. Furthermore, it is preferable that the measured phase values ​​specific to these sampling locations be stored in the memory of a correction value determination device that determines at least one correction value. The reason for this configuration is that it allows the measured phase values ​​to be saved and used according to the method assigned to each sampling point.

[0023] Furthermore, it is preferable that, for example, a relative movement occurs between the device that generates or provides orthogonal signal pairs and the target, and that the orthogonal signal pairs are provided during this relative movement. The reason for this is that, as mentioned above, the measured phase value determined from the orthogonal signal pair, or the amount of change thereof, allows for the calculation or direct representation of movement information related to the performed relative movement.

[0024] Therefore, it is preferable to determine the measured phase value during relative movement. Furthermore, it is preferable to assign time information (e.g., a timestamp) representing the time of generation to these measured phase values. In other words, it is preferable that the measured phase values ​​are weighted differently, for example, in accordance with the time interval from the previous measured phase value and / or the subsequent measured phase value. Furthermore, it is preferable that the measured phase values ​​are generated at a constant sampling rate and / or given the same weighting. Furthermore, it is preferable that the measured phase values ​​are generated over at least one predetermined number of periods, for example, less than 10 or greater than 10. Then, it is preferable to determine the unique measured phase values ​​at the sampling location from the number of measured phase values ​​determined in this way. In addition, the sampling point is preferably selected as the point where the arctangent function described at the beginning is either 0, or the point where it has the maximum or minimum value. The reason for this is that by making this selection, the sampling location can be determined easily and reliably.

[0025] 2. Process (b) Next, step (b) is a second step, characterized by determining an estimated curve of the phase value trajectory based on the unique measured phase value at the sampling location. Such an estimated curve is also called an estimated trajectory, and it is particularly preferable that it represents, or approximates, the curve of the measured phase value over time during the described relative motion. The reason for this is that the estimation curve allows us to determine the estimated phase values ​​that are not located at the aforementioned sampling points. In other words, it is preferable that the estimation curve is one that minimizes the deviation between the measured phase value specific to the sampling location and the corresponding estimated phase value of the estimation curve.

[0026] 3. Process (c) Next, step (c) is a third step, characterized by determining the target frequency distribution of phase values ​​(hereinafter sometimes referred to as the target intensity distribution of phase values) in correspondence with the estimation curve. In other words, this target frequency distribution is preferably normalized with respect to the number of phase values ​​determined over one or more period lengths. Here, this corresponds to the probability density and is a relative target frequency distribution. Therefore, the target frequency distribution is preferably the frequency distribution of estimated phase values ​​determined over one or more period lengths of the signal. In particular, the target frequency distribution is preferably determined as a histogram generated in response to estimated phase values ​​generated / determined from an estimation curve using a predetermined sampling rate. On the other hand, it is also preferable to determine the target frequency distribution by applying kernel density estimation or by processing the estimation curve using a properly trained machine learning model. The target frequency distribution determined in this way is sometimes referred to as the theoretically expected frequency distribution of the phase values.

[0027] 4. Process (d) Next, step (d) is a fourth step, characterized by determining the actual frequency distribution of phase values ​​(hereinafter sometimes referred to as the actual intensity distribution of phase values). In other words, this actual frequency distribution is also preferably normalized with respect to the number of phase values ​​determined over one or more period lengths. Here, such normalization corresponds similarly to probability density and exists as a relative actual frequency distribution. Furthermore, this actual frequency distribution, also known as the experimentally observed frequency distribution, is preferably determined not by relying on the estimation curve, but by relying particularly on the measured phase values ​​provided by the corresponding instrument. Therefore, as described above, the measured phase values ​​can be determined, for example, using a predetermined sampling rate over a predetermined period, and in this case, it is preferable that the actual frequency distribution is determined as a histogram that depends on these measured phase values. Therefore, the actual frequency distribution is preferably the frequency distribution of measured phase values ​​determined over one or more period lengths of the signal. On the other hand, as mentioned above, it is also preferable to apply other methods to determine the actual frequency distribution with respect to the theoretically predicted frequency distribution. Furthermore, it is preferable that the number of period lengths considered in determining the target and the actual frequency distribution are the same. However, it is also preferable that the number of period lengths and the actual frequency distribution are different. Furthermore, while it is preferable that the target frequency distribution, the measured phase value for determining the actual frequency distribution, and the sampling rate for determining the estimated phase value are all the same, it is also preferable that they may be different.

[0028] 5. Process (e) Next, step (e) is a fifth step, which includes determining a target phase value (ph_target) such that it has the same cumulative frequency as the cumulative frequency intrinsic to the phase value, determined based on at least one selected measured phase value (ph_actual). In other words, it is characterized by determining the difference between the target phase value (ph_actual) and the measured phase value (ph_actual) as a difference value specific to the measured phase value, and determining a correction value corresponding to this difference value. Furthermore, the target phase value is preferably the phase value of the estimated curve. In other words, the cumulative frequency unique to the measured phase value or target phase value is identified by the corresponding frequency distribution, and it is preferable to determine it by calculating the frequency assigned to different measured phase values ​​or target phase values ​​(hereinafter sometimes referred to as estimated phase values) by accumulating the frequency from a phase value of zero up to the measured phase value or target phase value. This can be done, for example, by summing the frequency values ​​specified by the histogram.

[0029] In this case, it is preferable to select the target phase value such that the cumulative frequency inherent to the target phase value matches the cumulative frequency inherent to the measured phase value. And this can be expressed mathematically as follows:

[0030]

number

[0031] Here, in equation (4), φ true φ is the target phase value. NL This represents the measured phase value. The variable ρ NL The variable ρ represents the (normed) actual frequency distribution, and the variable ρ represents the (normed) target frequency distribution. Furthermore, equation (4) can be solved using equations (5) to (7) below, by utilizing the exact monotonicity of P in relation to the target phase value.

[0032]

number

[0033]

number

[0034]

number

[0035] Furthermore, it is preferable to calculate the difference between the target phase value and the measured phase value as a correction value specific to the measured phase value. In other words, it is preferable to determine the correction value specific to the measured phase value in this manner. Furthermore, it is preferable that correction values ​​specific to the measured phase value are stored as data records, as described above.

[0036] Furthermore, a key feature is that the correction value for the measured phase value to be corrected is determined in accordance with the difference value inherent to the measured phase value. In this case, two scenarios can be distinguished. In other words, if the measured phase value to be corrected is the same as the selected measured phase value, or if the deviation from the selected measured phase value is less than a predetermined value (including cases where it is less than a predetermined amount), it is preferable to use a correction value specific to the measured phase value as the correction value. On the other hand, if the measured phase value to be corrected differs from the selected measured phase value, particularly if the difference is greater than or equal to a predetermined value (including cases where it differs by a predetermined amount or more), it is preferable to determine the correction value by interpolation, for example, corresponding to a correction value specific to the measured phase value. This will be discussed later.

[0037] The proposed correction method has the advantage of being able to determine a correction value for a specific measured phase value quickly and easily. A particular advantage is that, as explained at the beginning, determining this type of correction value does not require any preconditions regarding the shape of a Lissajous figure, such as an ellipse. Therefore, error correction over a wide range of applications becomes possible in a favorable manner. Furthermore, the proposed method has the advantage of being simple, which means it has low hardware requirements for the computing device that runs it. In particular, since the method can be run on an integrated circuit, such as a circuit implemented on an FPGA chip, or a circuit integrated into an FPGA chip, it enables particularly fast implementations.

[0038] 6. Example Configuration (1) Configuration Example 1 Furthermore, in the present invention, it is preferable that, as Configuration Example 1, signals can be generated, provided, and / or received from an orthogonal signal pair, and that the measured phase value is preferably determined from the signal values ​​of the orthogonal signal pair.

[0039] (2) Configuration Example 2 Furthermore, as another configuration example 2 of the present invention, it is preferable to determine the estimation curve by interpolation. Here, in the sense of the present invention, interpolation may also include extrapolation. Therefore, it is preferable to determine the estimated phase value by interpolation from the measured phase value specific to the sampling location. The reason for this is that this method allows for the determination of the estimation curve to be performed easily and with sufficient accuracy.

[0040] (3) Configuration Example 3 Furthermore, as another configuration example 3 of the present invention, it is preferable to determine the estimation curve using a Kalman filter. In this case, the measured phase value specific to the sampling location is preferably a so-called observed quantity. That is, the estimated phase value is preferably determined as a system state variable, especially before applying new observed values. This is because it allows for a more accurate determination of the estimation curve.

[0041] (4) Configuration Example 4 Furthermore, as another configuration example 4 of the present invention, it is preferable to determine the estimation curve using a machine learning model. In this case, it is preferable that the amount of measured phase value specific to the sampling location forms the input data points of the machine learning model, and the estimation curve, i.e., the amount of estimated phase value, forms the output data points of the machine learning model. In addition, it is preferable that the machine learning model be trained using an appropriate combination of training data, including training input data points and training output data points, particularly in multiple training stages. It is preferable that this type of training data combination is generated by an expert generating or specifying an estimated curve of estimated phase values ​​as training output data points for the amount of measured phase values ​​specific to the sampling locations used as training input data points. For example, if the target trajectory curve of the relative movement is already known because a calibration relative movement has been performed, it is preferable to determine the estimated phase value in accordance with the target trajectory curve. This is also called annotation. That is, during the learning phase, it is preferable that the parameters of the machine learning model, in particular the weights and / or links, be adjusted in the learning model so that the deviation between the output data points generated by the machine learning model with respect to the learning input data points is as small as possible from the learning output data points. And for this purpose, it is preferable that at least one parameter of the machine learning model is changed after each learning step. On the other hand, it is also preferable that the machine learning model (MLM) is a model generated through a supervised learning process. This is preferably a DL model, particularly a neural network, especially a CNN (Convolutional Neural Network), RNN (Recurrent Neural Network), LSTM (Long Short-Term Memory) network, or a Transformer family model (Transformer model). However, it is also preferable that the MLM is generated by an unsupervised learning process, a semi-supervised learning process, or a self-supervised learning process. The reason for this is that it also allows for a very accurate determination of the estimation curve, and as a result, an accurate determination of the correction value.

[0042] In particular, it is preferable to determine such estimated phase values ​​by interpolation, Kalman filtering, or machine learning models. In other words, the estimated phase value is preferably a value between the measured phase values ​​specific to the sampling location, a value greater than the maximum measured phase value specific to the sampling location, or a value less than the minimum measured phase value specific to the sampling location.

[0043] (5) Configuration Example 5 Furthermore, as another configuration example 5 of the present invention, it is preferable that the measured phase value unique to the sampling location is determined as a unique measured phase value corresponding to the scanning point, and it is preferable that such scanning point lies within a predetermined range of the sampling location. Furthermore, in order to determine the measured phase value specific to the sampling location, it is preferable that, as described above, the orthogonal signal pair and the corresponding current measured phase value arising therefrom are provided during relative movement using a predetermined sampling rate. In this case, if none of these scanning points correspond to a predetermined sampling location, it is preferable that the measured phase value unique to the sampling location is determined as a unique phase value at a scanning point determined, for example, as an average, particularly a weighted average, within a predetermined value range around the sampling location. This is because it allows for a more accurate determination of the unique measured phase value at the sampling location.

[0044] (6) Configuration Example 6 Furthermore, as another configuration example 6 of the present invention, it is preferable that the determination of the target frequency distribution of phase values ​​dependent on the estimation curve is performed only when the quality of the estimation curve has been determined and at least one predetermined quality criterion has been met. In particular, it is preferable that a quality index dependent on the estimation curve determined in the second determination step is determined. This quality index is a value that represents the quality of the estimation curve, for example, its precision.

[0045] (7) Configuration Example 7 Furthermore, as another configuration example 7 of the present invention, it is preferable to predict an estimated phase value specific to the sampling location based on the estimated curve and compare it with the actually measured phase value that occurs. Here, the predicted estimated phase value is preferably a phase value that is adjusted according to the estimated curve in the future or during the continuation of the relative motion described earlier. In particular, such a predicted estimated phase value is preferably an estimated phase value that is adjusted over a predetermined prediction period, for example, a period-specific period. Here, the period-specific period is preferably the period required for the arctangent function described at the beginning to be executed and for the period-specific phase value to be generated.

[0046] Furthermore, it is preferable to determine that the quality standard is met, for example, when an index representing the deviation is smaller than a predetermined value. Similarly, if this indicator is above a predetermined value, it is preferable to determine that the predetermined quality standards are not met. If the quality criteria are not met, it is preferable to re-determine the estimated curve. That is, for this purpose, it is preferable to repeat the second step (b), and even more so to repeat the sequence of the first step (a) and the second step (b). This is because it allows for the accurate determination of the estimation curve, and consequently, the accurate determination of the correction value.

[0047] (8) Example of configuration 8 Furthermore, as another configuration example 8 of the present invention, it is preferable that the deviation between the estimated curve, particularly the predicted estimated curve, and the measured curve is determined, and that the quality standard is met if the deviation is smaller than a predetermined value. This point and related advantages have already been described.

[0048] In another configuration example, it is preferable that the orthogonal signal pairs are generated by an interferometry system. Specifically, it is preferable that the interferometry system be a Michelson interferometer or a Fabry-Perot interferometer. Furthermore, it is naturally preferable to use other types of interference measurement systems. Alternatively, the orthogonal signal pair is preferably generated by an optical encoder. Specifically, the optical encoder preferably comprises, for example, a light source, one or more detectors, and an optical grating, wherein the detectors are movable relative to the optical grating, thereby generating a first signal and / or a second signal, and providing orthogonal signals.

[0049] For example, it is preferable that the light generated by the light source is irradiated through or onto an optical lattice that can be designed based on glass or plastic. Here, it is preferable that the optical lattice is configured such that, at specific relative positions between the lattice and the detector, light generated by the light source can be detected by the detector, while at other relative positions, the light is blocked (i.e., not detected). The reason for this is that in both cases, the simple and reliable generation / provision of orthogonal signal pairs is advantageously realized. Consequently, the accuracy of information generated using an interferometric measurement system or optical encoder, particularly motion information, can be advantageously improved.

[0050] (9) Configuration example 9 Furthermore, as another configuration example 9 of the present invention, it is preferable that the correction value is stored in a readable manner, and in particular in a manner that assigns it to a phase value selected as the target of correction, or to an actual measured phase value. In particular, it is preferable that the correction value is assigned to a period-specific phase value as described at the beginning. The reason for this is that, if the measured phase value specific to this period is later determined again, the corresponding correction value can be easily read out and used to correct the measured phase value. Furthermore, this is advantageous because it allows for the correction of measured phase values, which can be performed quickly and easily, or the determination of corresponding correction values, which can be easily and rapidly updated.

[0051] (10) Configuration Example 10 Furthermore, as another configuration example 10 of the present invention, it is preferable to determine a correction value as an element of the combination of correction values ​​for each measured phase value of a combination of phase values ​​consisting of at least two selected measured phase values, according to the above formula (4) corresponding to step (e). In other words, it is preferable that a correction value specific to the measured phase value is determined as a combination element of the correction value.

[0052] Furthermore, if the measured phase value is other than the measured phase value selected as a combination element of phase values ​​(i.e., does not belong to the combination element of phase values), it is preferable that the correction value for the measured phase value other than that combination element is determined without going through step (e) based on the above-mentioned combination element of correction values, i.e., the correction value specific to the measured phase value. Specifically, it is preferable that correction values ​​for measured phase values ​​other than those belonging to the combination of phase values ​​(measured phase values ​​that do not belong to the combination of phase values) are determined by interpolation, a Kalman filter, or a machine learning model. Please refer to the explanation above for details. The reason for this is that a correction value for the measured phase value can be determined quickly, and this correction value is sufficiently accurate, thus allowing for the determination of a sufficiently accurate corrected measured phase value. Furthermore, if the measured phase value to be corrected belongs to this combination of phase values, it is preferable to determine the correction value assigned to the measured phase value within the combination of phase values ​​as the desired correction value. It is also preferable that these phase values ​​of the combination of phase values ​​and the correction values ​​assigned to them be stored in the form of a LUT (Lookup Table).

[0053] (11) Configuration Example 11 Furthermore, as another configuration example 11 of the present invention, it is preferable to determine the correction value corresponding to the combination element of the correction value by interpolation. This point and related advantages have already been described.

[0054] 7. Implementation Conditions Therefore, the correction method, etc. of the present invention can be particularly preferably used when at least one of the following assumptions is met as an implementation condition.

[0055] (1) When the measurement error is periodic, that is, it is repeated every execution over a certain period of time, or every number of executions over a certain period of time (e.g., 10 times or less). (2) The relative motion between the quadrature signal pair, or the device for providing measured phase values, and the target is sufficiently smooth and can be described or represented by a differentiable trajectory in particular. (3) If all measured phase values ​​are timestamped or detected at a known time. Here, it is preferable that the weighting of individual measurement points is proportional to the time interval between preceding or succeeding measured phase values. Furthermore, it is preferable to use a constant sampling rate with equal weighting for all individual measurements.

[0056] 8. Detailed explanation based on the diagram Hereafter, the same reference number will indicate a component having the same or similar technical characteristics. Furthermore, the detailed explanation based on the following diagram applies not only to the first embodiment but also to the second to fourth embodiments described later, unless there are any particular inconsistencies.

[0057] Figure 1 shows schematic curves of the first signal S1 and the second signal S2 that form an orthogonal signal pair. These signals are generated, for example, using an interferometric measurement system or an optical encoder, during the relative movement between the device providing signals S1 and S2 and the target (neither of which are shown). The curves of the two signals S1 and S2 are shown over different distances between the target and, for example, one or more detectors of the device providing the corresponding signals S1 and S2. Furthermore, it is clear that signals S1 and S2 are sinusoidal norm signals centered at zero and shifted 90 degrees relative to each other. The distance-specific orthogonal signal pair includes, as a first value, the distance-specific amplitude value of the first signal S1, and as a second value, the distance-specific amplitude value of the second signal S2. When the amplitude value of the first signal S1 is given as the horizontal axis value, and the amplitude value corresponding to the second signal S2 is given as the vertical axis value, the Lissajous figure shown in Figure 2 is obtained. Here, the ideal Lissajous figure L1 is circular, especially when the amplitudes of signals S1 and S2 are the same and there are no off-peak combinations. Figure 2 similarly shows a non-ideal Lissajous figure L2, which occurs especially when periodic measurement errors occur. Furthermore, Figure 2 shows the period-specific measured phase value (ph), which is obtained as the arctangent of the ratio of the amplitude value of the second signal S2 to the amplitude value of the first signal S1, as shown in process (d).

[0058] Furthermore, Figure 3 shows schematic curves of the measured phase values ​​PH_actual1, PH_actual2, PH_actual3, and PH_actual4, which are specific to the sampling location. Here, the actual curve iV of the measured phase value PH_actual is shown as a dashed line, and these measured phase values ​​are determined using a predetermined sampling rate during the relative movement between the quadrature signal pair or the devices generating the measured phase value PH_actual.

[0059] In other words, as is clear from Figure 3, the measured phase values ​​PH_actual1, ..., PH_actual4, which are specific to the sampling location, are selected measured phase values ​​PH_actual that are generated during relative movement over time. Here, it is shown that the measured phase values ​​PH_actual1, ..., PH_actual4, which are unique to each sampling location, are spaced apart from each other by a period length of 2π. The measured phase values ​​PH_actual1, ..., PH_actual4, which are unique to each sampling location, are determined and stored up to the first time point t1.

[0060] Furthermore, the estimated curve gV of the phase value trajectory is shown as a solid line. This phase value trajectory is determined, for example, using interpolation, based on the measured phase values ​​PH_actual1, ..., PH_actual4 which are specific to the sampling location. Therefore, for example, the estimated phase values ​​specific to the scanning points of this estimation curve can be determined by interpolation based on the measured phase values ​​PH_actual1, ..., PH_actual4 specific to the sampling locations. In particular, for each scan point or selected scan point of the actual curve iV of the measured phase value, the corresponding estimated phase value of the estimated curve can be determined. In other words, the estimated phase value can be determined in correspondence with the estimated curve gV, and the estimated phase value is adjusted in correspondence with the estimated curve using a predetermined sampling rate over a predetermined period. Here, the predetermined period can be, in particular, the period over which the scan value is determined over integer multiples of the signal period length according to the estimated curve gV. However, this is not mandatory.

[0061] Furthermore, Figure 3 also shows the predicted estimated phase value (pPH) specific to the sampling location, which is preferably determined by extrapolation, for example, based on the already determined measured phase values ​​(PH_actual1, ..., PH_actual4) specific to the sampling location. This predicted estimated phase value (pPH) is then used to evaluate the quality of the estimated curve gV. In particular, at a second time point t2, which is later than the first time point (t1), the measured phase value specific to the sampling location can be obtained and compared with the predicted estimated phase value (pPH) specific to the sampling location. Furthermore, if the current measured phase value specific to the sampling location deviates by only a predetermined amount from the predicted estimated phase value (pPH) specific to the sampling location, it can be determined that the quality standard is met.

[0062] Furthermore, Figure 4 shows a schematic diagram of the frequency distribution, i.e., the target frequency distribution (HV_target) of the phase value of the estimation curve (gV) (see Figure 3), that is, the frequency distribution of the estimated phase value over a period corresponding to a specific period, particularly a period-specific period, or the sum of multiple period-specific periods. Here, Figure 4 similarly shows the actual frequency distribution (HV_actual) of the measured phase values ​​for the same period. These frequency distributions (HV_target, HV_actual) can be determined, for example, by generating histograms over all sampling-point-specific values ​​of the estimated curve gV and the actual curve iV, also shown in Figure 3, for the specified period.

[0063] Furthermore, Figure 4 also shows the period-specific measured phase value (ph_actual), and the cumulative frequency specific to this period-specific measured phase value (ph_actual) is visualized as a dashed crosshatch region below the actual frequency distribution from zero measured phase value to the period-specific measured phase value (ph_actual). On the other hand, the period-specific target phase value (ph_target) and the cumulative frequency specific to that target phase value are similarly shown in Figure 4 as solid cross-hatch regions below the target frequency distribution (HV_target) from zero measured phase value to the period-specific target phase value (ph_target). Furthermore, it is preferable that the target phase value (ph_target) be determined such that the region described under the target frequency distribution (HV_target) matches the area described under the actual frequency distribution (HV_actual). In other words, it is preferable that the cumulative frequency inherent to the phase value is the same. That is, it is preferable to determine the difference between the target phase value (ph_target) and the measured phase value (ph_actual) as the correction value.

[0064] Furthermore, such correction values ​​can only be determined for selected measured phase values, particularly measured phase values ​​specific to a selected period, and based on these correction values, correction values ​​for further measured phase values ​​can be determined. Therefore, for example, correction values ​​for each measured phase value, particularly period-specific measured phase values, can be determined as combination elements of correction values. In other words, for measured phase values ​​specific to other periods that are not part of a combination of phase values, it is preferable to determine the correction values ​​by interpolation, for example, in correspondence with the combination of correction values.

[0065] Furthermore, Figure 5, corresponding to Figure 4, shows the period-specific measured phase value (ph_actual) and the period-specific target phase value (ph_target) represented by Lissajous figures. For example, if at least one of the signals (S1, S2) is prone to errors when compared to the mean value, and the period-specific measured phase value (ph_actual) is determined according to equation (4), it is preferable to use the proposed method to determine the target phase value (ph_target) after assuming a corresponding target signal value.

[0066] Furthermore, Figure 6 shows a schematic block diagram of the apparatus 1 for determining at least one correction value for the measured phase value (ph_actual) (see Figure 4) that can be determined from an orthogonal signal pair including the first signal (S1) and the second signal (S2). Here, it is preferable that such device 1 includes a receiving interface 2 for receiving orthogonal signal pairs, particularly two signals (S1, S2). Furthermore, it is preferable that such device 1 further comprises an evaluation device 3, and the receiving interface 2 is shown to be part of the evaluation device 3. Furthermore, the measured phase value and the corresponding correction value can be determined by the evaluation device 3. Similarly, the corrected phase value can be determined by correcting the measured phase value (ph_actual) determined from the signals (S1, S2) using the correction value, using the evaluation device 3.

[0067] Furthermore, Figure 6 also shows a memory device 4, which can store measured phase values ​​(PH_actual1, ..., PH_actual4) specific to the sampling location, and correction values ​​specific to the measured phase values. As a result, the evaluation device 3 can determine an estimated curve (gV) (see Figure 3) based on the stored measured phase values ​​(PH_actual1, ..., PH_actual4) specific to the sampling location. Furthermore, the evaluation device 3 can also determine a correction value based on a correction value specific to the measured phase value stored in the memory device 4.

[0068] [Second Embodiment] A second embodiment of the present invention is a method for determining the corrected phase value of an orthogonal signal pair consisting of a first signal and a second signal by correcting the measured phase value to be corrected based on the correction value determined in the first embodiment. Furthermore, this method is characterized by including at least the following steps (b1) to (b2). (b1) A step to determine the measured phase value to be corrected. (b) A step of determining a corrected phase value by correcting a measured phase value that is corrected using a correction value determined using one of the methods of the first embodiment described above.

[0069] This makes it advantageous to determine the corrected phase value with great precision, especially when the Lissajous figure described at the beginning does not have a specific shape.

[0070] [Third Embodiment] A third embodiment of the present invention is an apparatus for determining at least one correction value for a measured phase value to be corrected by performing the correction value determination method of the first embodiment. Furthermore, it is preferable that this at least one correction value is determined from an orthogonal signal including a first signal and a second signal. Preferably, the device comprises at least one first receiving interface for receiving orthogonal signal pairs, particularly a first signal and / or a second signal, and an evaluation device. Furthermore, it is preferable that such an evaluation device be designed as a computing device. Furthermore, such a computing device may be designed as a microcontroller or an integrated circuit, or preferably includes either of these. In addition, the correction value determination device is preferably configured to perform a method for determining at least one correction value for an actual phase value, according to one of the embodiments described in this disclosure. The reason for this is that having such a configuration provides the aforementioned advantages.

[0071] [Fourth Embodiment] Furthermore, a fourth embodiment of the present invention is a device for determining at least one corrected phase value for an orthogonal signal pair including at least a first signal and a second signal. Furthermore, the apparatus is characterized by comprising a device for determining at least one correction value for an actual phase value according to one of the first embodiments described herein. Furthermore, the determination device is characterized by being configured to perform a method for determining a corrected phase value according to at least one of the steps described in the first and second embodiments described herein. In particular, it is preferable that the correction of the measured phase value be performed using the correction value by the evaluation device.

[0072] In other words, this device is preferably part of a path measurement device. This method and device are particularly preferred for applications requiring a path measurement accuracy of 1 nanometer or less. For example, this correction method / device is preferably used in the positioning system of a lithography apparatus, and is also preferably a component of such a positioning system. In this case, path measurement is preferably performed to ensure positional control of the movable components of such apparatus during movement.

[0073] Furthermore, the proposed method / device is preferably designed to provide a corrected measurement signal from an interferometric measurement system or an optical encoder, or to be a component of such a system / encoder.

[0074] Similarly, the proposed apparatus / method is also preferable for positioning monochromators for synchrotrons. Furthermore, it is preferable to use it for vibration measurement and, for example, mass measurement using a watt balance.

[0075] Furthermore, if the positioning system consists of multiple axes, for example three axes, and particularly enables positioning along multiple axes oriented perpendicular to each other, axis-specific path / position information can be determined based on the phase value determined for a particular axis. In other words, for each axis, it is possible to determine axis-specific correction values, and consequently, axis-specific phase values. This has the advantage that the (periodic) errors of the measurement axes are generally independent of each other and depend on position, thus enabling accurate position measurement specific to each axis. [Explanation of Symbols]

[0076] 1: Device 2: Receiving Interface 3: Evaluation device 4: Storage devices gV: Estimated curve iV: Real curve HV_actual: Actual frequency distribution HV_target: Target frequency distribution L1: Ideal Lissajous figure L2: Non-ideal Lissajous figure Ph_actual: Measured phase value Mor_target: Target phase value PH_actual1, ..., PH_actual4: Measured phase values pPH: Predicted estimated phase value specific to the sampling location S1: First signal S2: Second signal t1: First point in time t2: Second point in time

Claims

1. A method for determining a correction value for an actual phase value (ph_actual), characterized by including the following steps a) to e). a) A step of determining the unique measured phase value at at least two sampling locations, wherein the sampling locations are spaced apart from each other by an integer multiple of the period length of the signals (S1, S2), and the measured phase value is used as the measured phase value. b) A step of determining an estimated curve (gV) of the phase value trajectory corresponding to the measured phase value. c) A step of determining the target frequency distribution (HV_target) of the phase value in accordance with the estimation curve (gV) d) A step to determine the actual frequency distribution (HV_actual) of the measured phase values. e) A step of determining a target phase value (ph_target) such that it has the same cumulative frequency as the cumulative frequency intrinsic to the phase value determined based on the measured phase value (ph_actual), taking the difference between the target phase value (ph_actual) and the measured phase value (ph_actual) as the difference value intrinsic to the measured phase value, and determining the correction value corresponding to the difference value.

2. The method for determining the correction value according to claim 1, characterized in that the estimation curve (gV) is determined by interpolation or by a Kalman filter or a machine learning model.

3. The method for determining a correction value according to claim 1 or 2, characterized in that a unique measured phase value (PH_actual1, ..., PH_actual4) at the sampling location is determined as a unique measured phase value at the scanning point, and the scanning point is located within a predetermined range around the sampling location.

4. A method for determining a correction value according to claim 1 or 2, characterized in that a predetermined characteristic of the estimation curve (gV) is determined, and further, only when a quality criterion for at least one predetermined characteristic is met, the determination of the target frequency distribution (HV_target) of the measured phase value, which depends on the estimation curve (gV), is performed.

5. The method for determining a correction value according to claim 4, characterized in that the deviation between the estimated curve (gV) and the actual curve (iV) is determined, and the quality standard is considered to be met if the deviation is less than a predetermined value.

6. The method for determining a correction value according to claim 1 or 2, characterized in that the signal is a pair of orthogonal signals, and the signal as such an orthogonal signal pair is generated by an interferometric measurement system or an optical encoder.

7. The method for determining a correction value according to claim 1 or 2, characterized in that the correction value is stored as data in a predetermined location in a searchable manner and in a manner assigned to the measured phase value.

8. The method for determining a correction value according to claim 1 or 2, characterized in that, in a combination of phase values ​​consisting of at least two measured phase values, the correction value for each selected measured phase value is determined as a combination element of the correction value according to step e), while when the measured phase value is not an element of the combination of phase values, the correction value for the measured phase value is determined based on the combination element of the correction value.

9. The method for determining a correction value according to claim 8, characterized in that the correction value determined in correspondence with the combination elements of the correction value is determined by interpolation.

10. A method for determining a corrected phase value of an orthogonal signal pair including a first signal (S1) and a second signal (S2), characterized by comprising the following steps. a) A step in determining the measured phase value (ph_actual) to be corrected. b) A step of determining a corrected phase value by correcting the measured phase value (ph_actual) using the correction value determined by the method for determining the correction value described in claim 1 or 2.

11. A correction value determination device that determines at least one correction value for the measured phase value (ph_actual) that can be determined from an orthogonal signal pair including a first signal (S1) and a second signal (S2) by performing the correction value determination method described in claim 1 or 2, wherein the correction value determination device comprises at least one receiving interface for receiving the orthogonal signal pair and an evaluation device.

12. A device for determining a corrected phase value, comprising the correction value determination device according to claim 11, characterized in that it determines at least one corrected phase value of an orthogonal signal pair including a first signal (S1) and a second signal (S2).

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