A self-calibration method based on planar two-dimensional time grating sensor

Abstract

The application discloses a self-calibration method based on a planar two-dimensional time grating sensor, which comprises an upper dynamic scale base and a lower fixed scale base, the fixed scale base is uniformly provided with exciting electrodes, and the dynamic scale base is provided with two sensing electrode groups along diagonal directions, each sensing electrode group is composed of a plurality of sensing electrode arrays arranged along X and Y directions. Equal-amplitude and same-frequency sinusoidal exciting voltages with a phase difference of pi / 2 are respectively applied to different categories of exciting electrodes, combination operation is conducted between the sensing electrodes of the sensing electrode groups, displacement signals of a single sensing electrode group along X and Y directions can be decoupled and output, combination operation is conducted between the output signals of the sensing electrode groups arranged along the moving direction, output signals containing measurement error information can be obtained, discrete Fourier transform is conducted on the processed data of the output signals, amplitude and phase parameters are calculated to construct an error function, and measurement errors of the sensor along X and Y directions are self-calibrated and corrected.

Description

Technical Field

[0001] This invention relates to an improvement in the structure of a linear displacement sensor, specifically to a self-calibration method based on a planar two-dimensional time grating sensor, belonging to the field of measurement and sensing. Background Technology

[0002] Two-dimensional planar sensors are widely used in semiconductors, precision machining, and precision displacement measurement. For example, Chinese invention patent CN109631735A, entitled "A Two-Dimensional Planar Time-Grating Displacement Sensor Based on Alternating Electric Field," boasts advantages such as high precision, high resolution, and non-contact measurement, showing strong potential for application in ultra-precision machine tools and dual-stage measurement and positioning systems for lithography machines. Capacitive two-dimensional planar time-grating sensors consist of a fixed scale and a moving scale. The main source of measurement error is crosstalk error from the electric field, which includes coupling errors in non-measurement directions and crosstalk errors between the excitation and sensing electrodes. Calibration is a commonly used and effective method to improve the measurement accuracy of two-dimensional planar time-grating sensors.

[0003] Currently, there are many calibration methods for planar two-dimensional sensors, including those using grating sensors, laser interferometers, and autocollimators. However, most of these methods rely on external measuring equipment as a reference for calibration. Self-calibration of capacitive planar two-dimensional time-grating sensors requires the use of a planar grating or laser interferometer. The sensor's measurement error periodicity is related to the manufacturing and design of the moving scale, necessitating calibration after replacing the moving scale or changing the relative orientation between the moving and fixed scales. This makes the calibration process overly cumbersome and time-consuming. Furthermore, if laser reading heads are used within the sensor's limited range, the more laser reading heads are deployed, the higher the cost of the self-calibration system. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing self-calibration technologies, the present invention aims to provide a self-calibration method based on a planar two-dimensional time grating sensor. This invention does not require external measuring equipment for reference calibration, nor does it require repeated calibration. It has low calibration costs, is not limited by measurement range, and is easy to maintain.

[0005] The technical solution of this invention is implemented as follows:

[0006] A self-calibration method based on a planar two-dimensional time grating sensor includes a movable scale base and a fixed scale base arranged parallel to each other with a gap. An excitation electrode is disposed on the upper surface of the fixed scale base, and a sensing electrode is disposed on the lower surface of the movable scale base. The sensing electrode on the movable scale base is directly opposite the excitation electrode on the fixed scale base. The excitation electrodes are arranged in 2m rows along the upper surface of the fixed scale base. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and their starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers.

[0007] In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4;

[0008] In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4;

[0009] All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group.

[0010] The sensing electrodes are two identical sets. Each set of sensing electrodes consists of four square sensing plates of the same size arranged in a 2×2 array to form a sensing electrode group. The side length of the sensing plates is I3. Adjacent sensing plates in each sensing electrode group have the same spacing I4. The two sensing electrode groups are located at two opposite corners on the lower surface of the moving ruler base. The distance between the centers of the two sensing electrode groups is L2 along the X direction and L1 along the Y direction.

[0011] During self-calibration, sinusoidal excitation voltages with equal amplitude and frequency and a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode groups A, B, C, and D.

[0012] When the moving scale base moves relative to the fixed scale base along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of each column of signals of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction. The displacement of the measurement signal of the two sensing electrode groups along the X direction is calculated and output. The difference between the displacement values ​​output by the two sensing electrode groups is then processed and the distance L2 along the X direction is subtracted to obtain the difference of measurement error along the X direction.

[0013] When the moving scale base moves relative to the fixed scale base along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of the signals of each row of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction. The displacement of the measurement signal of the two sensing electrode groups along the Y direction is calculated and output. The displacement values ​​output by the two sensing electrode groups are then subtracted from the distance L1 along the Y direction to obtain the difference of measurement error along the Y direction.

[0014] Fourier transforms are performed on the difference between measurement errors in the X and Y directions respectively, and the amplitude and phase values ​​of the error difference spectrum are extracted. Then, a displacement measurement error function is constructed through inverse Fourier transform. The actual measured displacement value is subtracted from the error value corresponding to the displacement measurement error function, thus realizing self-calibration of the measurement errors along the X and Y directions.

[0015] Furthermore, let the width of the induction electrode group be W, then W = 4(I1 + I2) = 2(I3 + I4).

[0016] Furthermore, the specific self-calibration steps are as follows:

[0017] Step 1: Within the measurement range of the moving scale base, according to the measurement step length of the sensor, set a number of measurement points in advance along the X and Y directions corresponding to the measurement step length within one excitation cycle;

[0018] Step 2: When measuring along the X and Y directions, read the displacement values ​​of the two induction electrode sets at each measurement point;

[0019] Step 3: Store the displacement values ​​of the two sensing electrode groups at each measurement point along the X and Y directions until all measurement points of one excitation cycle have been collected;

[0020] Step 4: Subtract the displacement values ​​of each measurement point of the two sensing electrode groups along the X and Y directions, and subtract the corresponding spacing in the X and Y directions to obtain discrete data of the measurement error difference corresponding to each measurement point.

[0021] Step 5: Perform a discrete Fourier transform on the discrete data of the measurement error difference between the two sensing electrode groups along the X and Y directions to obtain the frequency and the corresponding amplitude and phase.

[0022] Step 6: Perform inverse Fourier transform on the obtained frequencies, corresponding amplitudes and phases to construct the displacement measurement error function of the moving scale substrate and store it as compensation data;

[0023] Step 7: Subtract the error value corresponding to that measurement point in the displacement measurement error function from the actual displacement value of a certain measurement point of the induction electrode group to obtain the calibrated displacement value and output it.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] This invention arranges the sensing electrode group diagonally, enabling multiple sensor probes to simultaneously measure the X and Y directions without requiring external measuring equipment for reference calibration. The calibrable sensing electrode group is integrally designed and molded onto a moving scale substrate using PCB technology. All electrodes have identical error characteristics, eliminating the need for repeated calibration. The calibrable sensing electrode group on the moving scale substrate consists of a simple geometric array of sensing electrodes, resulting in a simple, compact, and low-cost calibration structure that is not limited by measurement range and is easy to maintain. Attached Figure Description

[0026] Figure 1 This is a schematic diagram showing the correspondence between the fixed-length base and the moving-length base in Example 1.

[0027] Figure 2 This is a schematic diagram of the structure of the fixed-length base in Example 1.

[0028] Figure 3 This is a schematic diagram of the structure of the moving ruler base in Example 1.

[0029] Figure 4 This is a schematic diagram of the displacement signal calculation and error self-calibration process in Embodiment 1 of the present invention;

[0030] Figure 5 This is a schematic diagram of the structure of the moving ruler base in Example 2.

[0031] Figure 6 This is a schematic diagram of the structure of the moving ruler base in Example 3. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0033] See Figures 1-3The present invention discloses a self-calibration method based on a planar two-dimensional time grating sensor, comprising a movable scale base 2 and a fixed scale base 1 arranged parallel to each other with a gap between them. An excitation electrode 1-1 is provided on the upper surface of the fixed scale base 1, and an induction electrode 2-1 is provided on the lower surface of the movable scale base 2. The induction electrode on the movable scale base is directly opposite to the excitation electrode on the fixed scale base.

[0034] The excitation electrodes are arranged in 2m rows along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and their starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers.

[0035] In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4.

[0036] In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4.

[0037] All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group.

[0038] The sensing electrodes 2-1 are two identical sets. Each set consists of four identical square sensing plates arranged in a 2×2 array to form a sensing electrode group. The side length of the sensing plates is I3. Adjacent sensing plates in each sensing electrode group have the same spacing I4. The two sensing electrode groups are located at two opposite corners on the lower surface of the moving ruler base. The distance between the centers of the two sensing electrode groups is L2 along the X direction and L1 along the Y direction.

[0039] Let the width of the induction electrode group be W, which satisfies W = 4(I1 + I2) = 2(I3 + I4).

[0040] During self-calibration, sinusoidal excitation voltages with equal amplitude and frequency and a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode groups A, B, C, and D.

[0041] When the moving scale base moves relative to the fixed scale base along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of each column of signals of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction. The displacement of the measurement signal of the two sensing electrode groups along the X direction is calculated and output. The difference between the displacement values ​​output by the two sensing electrode groups is then processed and the distance L2 along the X direction is subtracted to obtain the difference of measurement error along the X direction.

[0042] When the moving scale base moves relative to the fixed scale base along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of the signals of each row of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction. The displacement of the measurement signal of the two sensing electrode groups along the Y direction is calculated and output. The displacement values ​​output by the two sensing electrode groups are then subtracted from the distance L1 along the Y direction to obtain the difference of measurement error along the Y direction.

[0043] Fourier transforms are performed on the difference between measurement errors in the X and Y directions respectively, and the amplitude and phase values ​​of the error difference spectrum are extracted. Then, a displacement measurement error function is constructed through inverse Fourier transform. The actual measured displacement value is subtracted from the error value corresponding to the displacement measurement error function, thus realizing self-calibration of the measurement errors along the X and Y directions.

[0044] In this embodiment, all the sensing electrodes in the two sensing electrode groups are integrally molded onto the moving scale substrate using PCB technology, so that all sensing electrodes have the same error characteristics.

[0045] The following examples are provided to further illustrate the present invention.

[0046] Example 1: As Figures 1 to 4 As shown, the upper surface of the fixed-length base and the lower surface of the movable-length base are installed parallel to each other, with a gap of h = 3mm.

[0047] like Figure 2As shown, the excitation electrodes are arranged in 48 rows along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of 24 identical square excitation electrodes evenly arranged along the X-axis. The distance between two adjacent square excitation electrodes is I2 = 2.6 mm, which is greater than the width of the square excitation electrode I1 = 2.4 mm. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2 = 0.1 mm, and the starting positions along the X-axis are staggered by (I2+I1) / 2 = 2.5 mm. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same.

[0048] This invention divides all excitation electrodes into two arrays: all odd-numbered rows of excitation electrodes form one 24×24 array, and all even-numbered rows of excitation electrodes form another 24×24 array.

[0049] In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming 24 row excitation groups. Starting from the first row below, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3, and row excitation group Y4. Example 1 yields a total of 6 row excitation groups of Y1, Y2, Y3, and Y4.

[0050] In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming 24 column excitation groups. Starting from the first column on the left, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3, and column excitation group X4. Similarly, in Example 1, a total of 6 column excitation groups X1, X2, X3, and X4 are obtained.

[0051] Then, all the X1 column excitation groups and all the Y1 row excitation groups are connected to form the A-phase excitation electrode group; all the X2 column excitation groups and all the Y2 row excitation groups are connected to form the B-phase excitation electrode group; all the X3 column excitation groups and all the Y3 row excitation groups are connected to form the C-phase excitation electrode group; and all the X4 column excitation groups and all the Y4 row excitation groups are connected to form the D-phase excitation electrode group, thus obtaining the A, B, C, and D four-phase excitation electrode groups.

[0052] like Figure 3As shown, the lower surface of the moving scale base 2 is provided with two sets of sensing electrodes, a and b, arranged diagonally. Each set of sensing electrodes consists of four sensing electrodes 2-1 arranged in two columns and two rows along the X and Y directions, respectively referred to as a1, a2, a3, a4, b1, b2, b3, and b4. The width of each sensing electrode is I3 = 9.9 mm, and they are identical in shape and size with the same spacing I4 = 0.1 mm. The distance between the two sets of sensing electrodes is L2 = 26 mm along the X direction and L1 = 26 mm along the Y direction. The width of one set of sensing electrodes is W = 2(I3 + I4) = 20 mm, and it corresponds spatially to the width of one set of excitation electrodes, i.e., W = 4(I1 + I2).

[0053] In Embodiment 1 of the present invention, the distance between the two sensing electrode groups along the X and Y directions is equal, but the distance is not an integer multiple of the width of the sensing electrode group, that is, L1=L2≠k2W, k2=1,2,3,4.......

[0054] like Figure 4 As shown, during measurement, sinusoidal excitation voltage signals U with equal amplitude and same frequency, and a phase difference of π / 2, are sequentially applied to the four-phase excitation electrode groups A, B, C, and D. A =U0sinωt,U B =U0cosωt,U C =-U0sinωt,U D =-U0cosωt. When the moving scale base moves parallel to the fixed scale base along the X direction, the output signals of the sensing electrodes a1, a2, a3, and a4 in the sensing electrode group a along the X direction are Uxa1, Uxa2, Uxa3, and Uxa4; the output signals of the sensing electrodes b1, b2, b3, and b4 in the sensing electrode group b along the X direction are Uxb1, Uxb2, Uxb3, and Uxb4. The output signals Uxa1, Uxa2, Uxa3, and Uxa4 of the sensing electrodes are processed to obtain the output signal Uxa of sensing electrode group a along the X direction. The output signals Uxb1, Uxb2, Uxb3, and Uxb4 of sensing electrodes are processed to obtain the output signal Uxb of sensing electrode group b along the X direction. When the moving scale base moves parallel to the fixed scale base along the Y direction, the output signals Uya1, Uya2, Uya3, and Uya4 of sensing electrodes a1, a2, a3, and a4 in sensing electrode group a along the Y direction are obtained. The output signals Uyb1, Uyb2, Uyb3, and Uyb4 of sensing electrodes b1, b2, b3, and b4 in sensing electrode group b along the Y direction are obtained. The output signals Uya1, Uya2, Uya3, and Uya4 of the sensing electrodes are processed to obtain the output signal Uya of sensing electrode group a along the Y direction. The output signals Uyb1, Uyb2, Uyb3, and Uyb4 of sensing electrodes are processed to obtain the output signal Uyb of sensing electrode group b along the Y direction. The specific calculation is shown in the following formula:

[0055] Uxa=Uxa2+Uxa4-Uxa1-Uxa3=K e U0sin(wt+2π(x+e a (x)) / W)

[0056] Uxb=Uxb2+Uxb4-Uxb1-Uxb3=K e U0sin(wt+2π(x+L2+e b (x+L2)) / W)

[0057] Uya=Uya1+Uya2-Uya3-Uya4=K e U0sin(wt+2π(y+L1+e a (y+L1)) / W)

[0058] Uyb=Uyb1+Uyb2-Uyb3-Uyb4=K e U0sin(wt+2π(y+e b (y)) / W) (1)

[0059] The excitation voltage amplitude U0 = 26V, the frequency f = 20KHz, and the angular frequency ω = 2πf = 4 × 10⁻⁶V. 4 π, K e e is the electric field coupling coefficient. a (x), e b (x+L2), e a (y+L1), e b (y) represents the measurement error when the induction electrode groups a and b on the moving scale substrate measure along the X and Y directions, respectively, which can be expanded into a Fourier series as follows:

[0060]

[0061] Where i is the harmonic frequency, a i The amplitude for the corresponding frequency. This represents the phase at the corresponding frequency.

[0062] During self-calibration, when the moving scale base moves relative to the fixed scale base along the X direction for self-calibration, the output signals Uxa and Uxb of the sensing electrode groups a and b are input to the shaping circuit through the signal acquisition system to form square waves. The square wave signals are then input to the FPGA signal processing system for phase comparison with a fixed reference square wave Ur of the same frequency. The phase difference between the comparisons is interpolated and counted using high-frequency pulses, and the linear displacement value x is obtained by conversion of the interpolation count value. a x b Using the same processing method, the output displacement value y when measured along the Y direction can be obtained. ay b The displacement signal calculation and error self-calibration process in Embodiment 1 of this invention is as follows: Figure 4 As shown. Output displacement value x a x b y a y b The specific calculation formula is shown below.

[0063]

[0064] When measuring along the X direction, the measured value x of the sensing electrode group b is... b Subtract the measured value x of the sensing electrode group a a The difference in measurement error Δe along the X direction is obtained by considering the distance L2 along the X direction and the distance L2 along the X direction. x When measuring along the Y direction, the measured value y of the sensing electrode group a is... a Subtract the measured value y of the sensing electrode group b b The difference in measurement error Δe along the Y direction is obtained by considering the distance L1 along the Y direction and the distance L1 along the Y direction. y As shown below,

[0065]

[0066] Δe x and Δe y Rewritten in series form as a standard sine function:

[0067]

[0068] The difference Δe between the measurement errors of the induction electrode groups a and b when measuring along the X and Y directions, respectively. x and Δe y The amplitude A of the corresponding frequency i i Phase θ i With measurement error e a (x) and e b The amplitude a of the corresponding frequency i of (y) i Phase The relationship can be represented as:

[0069]

[0070] The difference Δe between the errors in the X and Y directions respectively x and Δe y After performing a Fourier transform, the amplitude A corresponding to frequency i in the spectrum of the error difference is extracted. i and phase θ i Substituting this into formula (6) yields the displacement measurement error e. a (x) and e b The amplitude a of (y) iSum of phases Then, substitute the obtained amplitude a i and the sum of phases into Equation (2), that is, construct the displacement measurement error through the inverse Fourier transform, so as to construct the measurement error functions e a (x) and e b (y) of the induction electrode groups a and b along the X and Y directions. Subtract the corresponding values of the measurement error functions e a 、y b from the actual measured displacement values x a (x) and e b (y) of the induction electrode groups a and b, and output the calibrated displacement values.

[0071] Embodiment 2: The measurement principle and most of the structures of Embodiment 2 are the same as those of Embodiment 1. The difference is that, as Figure 5 shown, the induction electrode groups on the moving scale base are arranged diagonally. The distances between the two induction electrode groups along the X and Y directions are not equal and L2>L1. At the same time, the distance is not an integer multiple of the width of the induction electrode group, that is, L1≠k2W, L2≠k2W, k2 = 1, 2, 3, 4......

[0072] Embodiment 3: The measurement principle and most of the structures of Embodiment 3 are the same as those of Embodiment 1. The difference is that, as Figure 6 shown, the induction electrode groups on the moving scale base are arranged diagonally. The distances between the two induction electrode groups along the X and Y directions are not equal and L2<L1. At the same time, the distance is not an integer multiple of the width of the induction electrode group, that is, L1≠L2≠k2W, k2 = 1, 2, 3, 4......

[0073] On the fixed scale base of the present invention, excitation electrodes are uniformly arranged along the X and Y directions. On the moving scale base, induction electrode groups are arranged diagonally. Each induction electrode group is composed of multiple induction electrodes uniformly arrayed along the X and Y directions. Apply sinusoidal excitation voltages with the same amplitude and frequency and a phase difference of π / 2 to different types of excitation electrodes. Perform a combined operation between the induction electrodes of the induction electrode group to decouple and output the displacement signals of a single induction electrode group along the X and Y directions. Perform a combined operation on the output signals between the induction electrode groups arranged along the moving direction to obtain an output signal containing measurement error information. Perform a discrete Fourier transform on the processed data of the output signal, obtain the amplitude and phase parameters to construct an error function, and perform self-calibration and correction on the measurement errors of the sensor along the X and Y directions.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the applicant has described the present invention in detail with reference to preferred embodiments, those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A self-calibration method based on a planar two-dimensional time grating sensor, the planar two-dimensional time grating sensor comprising a movable scale base and a fixed scale base arranged parallel to each other with a gap, wherein an excitation electrode is disposed on the upper surface of the fixed scale base, and a sensing electrode is disposed on the lower surface of the movable scale base, the sensing electrode on the movable scale base being directly opposite the excitation electrode on the fixed scale base; characterized in that: The excitation electrodes are arranged in 2m rows along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and their starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers. In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4; In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4; All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group. The sensing electrodes are two identical sets. Each set of sensing electrodes consists of four square sensing plates of the same size arranged in a 2×2 array to form a sensing electrode group. The side length of the sensing plates is I3. Adjacent sensing plates in each sensing electrode group have the same spacing I4. The two sensing electrode groups are located at two opposite corners on the lower surface of the moving ruler base. The distance between the centers of the two sensing electrode groups is L2 along the X direction and L1 along the Y direction. During self-calibration, sinusoidal excitation voltages with equal amplitude and frequency and a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode groups A, B, C, and D. When the moving scale base moves relative to the fixed scale base along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of each column of signals of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction. The displacement of the measurement signal of the two sensing electrode groups along the X direction is calculated and output. The difference between the displacement values ​​output by the two sensing electrode groups is then processed and the distance L2 along the X direction is subtracted to obtain the difference of measurement error along the X direction. When the moving scale base moves relative to the fixed scale base along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal. The sum of the signals of each row of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction. The displacement of the measurement signal of the two sensing electrode groups along the Y direction is calculated and output. The displacement values ​​output by the two sensing electrode groups are then subtracted from the distance L1 along the Y direction to obtain the difference of measurement error along the Y direction. Fourier transform is performed on the difference between the measurement errors in the X and Y directions respectively, and the amplitude and phase values ​​of the error difference spectrum are extracted. Then, the displacement measurement error function is constructed by inverse Fourier transform. The actual measured displacement value is subtracted from the error value corresponding to the displacement measurement error function, thus realizing self-calibration of the measurement error along the X and Y directions. Let the width of the induction electrode group be W, which satisfies W=4(I1+I2)=2(I3+I4); All the sensing electrodes in the two sensing electrode groups are integrally molded onto the moving scale substrate using PCB technology to ensure that all sensing electrodes have the same error characteristics.

2. The self-calibration method based on a planar two-dimensional time grating sensor according to claim 1, characterized in that: The specific self-calibration steps are as follows: Step 1: Within the measurement range of the moving scale base, according to the measurement step length of the sensor, set a number of measurement points in advance along the X and Y directions corresponding to the measurement step length within one excitation cycle; Step 2: When measuring along the X and Y directions, read the displacement values ​​of the two induction electrode sets at each measurement point; Step 3: Store the displacement values ​​of the two sensing electrode groups at each measurement point along the X and Y directions until all measurement points of one excitation cycle have been collected; Step 4: Subtract the displacement values ​​of each measurement point of the two sensing electrode groups along the X and Y directions, and subtract the corresponding spacing in the X and Y directions to obtain discrete data of the measurement error difference corresponding to each measurement point. Step 5: Perform a discrete Fourier transform on the discrete data of the measurement error difference between the two sensing electrode groups along the X and Y directions to obtain the frequency and the corresponding amplitude and phase. Step 6: Perform inverse Fourier transform on the obtained frequencies, corresponding amplitudes and phases to construct the displacement measurement error function of the moving scale substrate and store it as compensation data; Step 7: Subtract the error value corresponding to that measurement point in the displacement measurement error function from the actual displacement value of a certain measurement point of the induction electrode group to obtain the calibrated displacement value and output it.

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