Self-calibration method based on planar two-dimensional time grating sensor

Abstract

The invention discloses a self-calibration method based on a planar two-dimensional time grating sensor, which comprises a movable ruler base body and a fixed ruler base body which are arranged up and down, excitation electrodes are uniformly arranged on the fixed ruler base body, and two induction electrode groups are arranged on the movable ruler base body along the diagonal direction. Each induction electrode group is composed of a plurality of induction electrode arrays arranged in the X direction and the Y direction. Equal-amplitude and same-frequency sine excitation voltages with the phase difference of pi / 2 are applied to different types of excitation electrodes respectively, and the induction electrodes of the induction electrode group are subjected to combined operation, so that displacement signals of the single induction electrode group in the X and Y directions can be decoupled and output; the method comprises the following steps of: performing combined operation on output signals among sensing electrode groups arranged along a moving direction to obtain an output signal containing measurement error information, performing discrete Fourier transform on data obtained after processing the output signal, solving amplitude and phase parameters to construct an error function, and calculating the measurement error of the sensing electrode groups. And self-calibration correction is carried out on measurement errors of the sensor along the X direction and the Y direction.

Description

Technical Field

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

[0002] Planar two-dimensional sensors are widely used in the fields of semiconductors, precision machining and precision displacement measurement. For example, the Chinese invention patent with the publication number CN109631735A and the invention name "A planar two-dimensional time-grating displacement sensor based on alternating electric field" has the advantages of high precision, high resolution, and non-contact measurement. It has great development potential in the application of ultra-precision machining machine tools and photolithography machine double worktable measurement and positioning systems. The capacitive planar two-dimensional time-grating sensor consists of a fixed scale and a moving scale. The measurement error of the sensor mainly comes from the crosstalk error of the electric field. The electric field crosstalk error includes the coupling error in the non-measurement direction, the crosstalk error between the excitation electrode and the induction electrode, etc. In order to improve the measurement accuracy of the planar two-dimensional time-grating sensor, calibrating the sensor is a common and effective means.

[0003] There are many calibration methods for planar two-dimensional sensors, including grating sensors, laser interferometers, autocollimators, etc. However, most of them are based on external measuring equipment as a reference for calibration. Self-calibration of capacitive planar two-dimensional time grating sensors requires calibration using planar gratings or laser interferometers. The periodic characteristics of the sensor's measurement error are related to the manufacture and design of the moving ruler. This requires calibration after replacing the moving ruler or changing the relative posture between the moving ruler and the fixed ruler. The calibration steps are too cumbersome and the calibration time is long. If the sensor is arranged with laser reading heads within a limited range, the more laser reading heads there are, the higher the cost of the self-calibration system. Summary of the invention

[0004] In view of the above-mentioned shortcomings of the existing self-calibration technology, the purpose of the present invention is to provide a self-calibration method based on a planar two-dimensional time grating sensor. The present invention does not require external measuring equipment for reference calibration, nor does it require multiple repeated calibrations. The calibration cost is low, it is not limited by the measuring range and is easy to maintain.

[0005] The technical solution of the present invention is achieved in this way:

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

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

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

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

[0010] The sensing electrodes are in two identical groups, each group of sensing electrodes is composed of four square sensing electrodes of the same size arranged in a 2×2 array to form a sensing electrode group; the side length of the sensing electrode is I3; adjacent sensing electrode pieces in each sensing electrode group have the same spacing I4; the two sensing electrode groups are arranged at two diagonal positions on the lower surface of the moving ruler substrate, and the spacing between the centers of the two sensing electrode groups along the X direction is L2, and the spacing along the Y direction is L1;

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

[0012] When the movable ruler substrate moves relative to the fixed ruler substrate along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each column signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction, the measurement signal of the two sensing electrode groups along the X direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L2 along the X direction is subtracted to obtain the difference of the measurement error along the X direction;

[0013] When the movable ruler substrate moves relative to the fixed ruler substrate along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each row signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction, the measurement signal of the two sensing electrode groups along the Y direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L1 along the Y direction is subtracted to obtain the difference of the measurement error along the Y direction;

[0014] The difference of measurement errors in the X and Y directions is transformed by Fourier transform 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 error value corresponding to the displacement measurement error function is subtracted from the actual measured displacement value, thus realizing self-calibration of the measurement errors along the X and Y directions.

[0015] Furthermore, assuming that the width of the sensing electrode group is W, W=4(I1+I2)=2(I3+I4) is satisfied.

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

[0017] Step 1: Within the measuring range of the moving ruler substrate, according to the measuring step length of the sensor, a number of measuring points corresponding to the measuring step length are pre-set along the X direction and the Y direction within one excitation cycle;

[0018] Step 2: When measuring along the X direction and the Y direction, read the displacement values ​​of the two sensing electrode groups at each measuring point respectively;

[0019] Step 3: storing the displacement values ​​of the two sensing electrode groups at each measuring point along the X direction and the Y direction until all measuring points of an excitation cycle are collected;

[0020] Step 4: Perform differential processing on the displacement values ​​of each measuring point of the two sensing electrode groups along the X direction and the Y direction, and subtract the corresponding spacing in the X direction and the Y direction to obtain discrete data of the difference of the measurement errors corresponding to the measuring points one by one;

[0021] Step 5: Perform discrete Fourier transformation on the discrete data of the difference in measurement errors of the two sensing electrode groups along the X direction and the Y direction to obtain the frequency and the corresponding amplitude and phase;

[0022] Step 6: Perform inverse Fourier transform on the obtained frequency and the corresponding amplitude and phase, construct the displacement measurement error function of the moving ruler substrate and store it as compensation data;

[0023] Step 7: Subtract the error value corresponding to the measurement point in the displacement measurement error function from the actual displacement value of a measurement point of the sensing 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] The present invention arranges the sensing electrode group diagonally, so that multiple sensor probes can measure the X direction and the Y direction at the same time, and no external measuring equipment is required for reference calibration. The calibrable sensing electrode group is integrated on a moving ruler substrate by PCB process, and its error characteristics are the same, so it does not need to be calibrated repeatedly; the calibrable sensing electrode group on the moving ruler substrate is composed of a simple sensing electrode geometric array, and the calibration structure is simple and compact, low cost, not limited by the measuring range and easy to maintain. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the corresponding relationship between the fixed-size substrate and the movable-size substrate in Example 1.

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

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

[0029] Figure 4 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 structural diagram of the movable ruler base in Example 2.

[0031] Figure 6 This is a schematic diagram of the structure of the movable ruler base in Example 3. DETAILED DESCRIPTION

[0032] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] See also Figure 1-Figure 3The present invention discloses a self-calibration method based on a planar two-dimensional time-grating sensor, comprising a movable ruler base 2 and a fixed-length base 1 which are arranged in parallel with each other with a gap, an excitation electrode 1-1 is arranged on the upper surface of the fixed-length base 1, and a sensing electrode 2-1 is arranged on the lower surface of the movable ruler base 2, and the sensing electrode on the movable ruler base is directly opposite to the excitation electrode on the fixed-length base.

[0034] The excitation electrodes are arranged in 2m rows side by side along the upper surface of the fixed-length substrate, and each row of excitation electrodes is composed of n identical square excitation electrode pieces uniformly arranged along the X-axis direction, and the spacing I2 between two adjacent square excitation electrode pieces is greater than the width I1 of a square excitation electrode piece; the spacing between two adjacent rows of excitation electrodes along the Y-axis direction is (I2-I1) / 2, and the starting positions along the X-axis direction are staggered by (I2+I1) / 2; the starting positions of the excitation electrodes in odd rows along the X-axis direction are the same, and the starting positions of the excitation electrodes in even rows along the X-axis direction are the same; wherein n=4k1, m=4k2, and k1 and k2 are both positive integers.

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

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

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

[0038] The sensing electrodes 2-1 are two identical groups, each group of sensing electrodes is composed of four square sensing electrodes of the same size arranged in a 2×2 array to form a sensing electrode group; the side length of the sensing electrode is I3; the adjacent sensing electrode pieces in each sensing electrode group have the same spacing I4. The two sensing electrode groups are arranged at two diagonal positions on the lower surface of the moving ruler substrate, and the spacing between the centers of the two sensing electrode groups along the X direction is L2, and the spacing along the Y direction is L1.

[0039] Assuming that the width of the sensing electrode group is W, W=4(I1+I2)=2(I3+I4) is satisfied.

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

[0041] When the movable ruler substrate moves relative to the fixed ruler substrate along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each column signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction, the measurement signal of the two sensing electrode groups along the X direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L2 along the X direction is subtracted to obtain the difference of the measurement error along the X direction;

[0042] When the movable ruler substrate moves relative to the fixed ruler substrate along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each row signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction, the measurement signal of the two sensing electrode groups along the Y direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L1 along the Y direction is subtracted to obtain the difference of the measurement error along the Y direction;

[0043] The difference of measurement errors in the X and Y directions is transformed by Fourier transform 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 error value corresponding to the displacement measurement error function is subtracted from the actual measured displacement value, thus realizing self-calibration of the measurement errors along the X and Y directions.

[0044] In the embodiment, all the sensing pole pieces in the two sensing electrode groups are integrally formed on the moving ruler substrate by PCB process, so that the error characteristics of all the sensing pole pieces are the same.

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

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

[0047] like Figure 2As shown, the excitation electrodes are arranged in 48 rows side by side along the upper surface of the fixed-size substrate, and each row of excitation electrodes is composed of 24 identical square excitation electrode pieces uniformly arranged along the X-axis direction. The spacing between two adjacent square excitation electrode pieces is I2=2.6mm, which is larger than the width of the square excitation electrode pieces I1=2.4mm; the spacing between two adjacent rows of excitation electrodes along the Y-axis direction is (I2-I1) / 2==0.1mm, and the starting positions along the X-axis direction are staggered by (I2+I1) / 2=2.5mm; the starting positions of the odd-numbered rows of excitation electrodes along the X-axis direction are the same, and the starting positions of the even-numbered rows of excitation electrodes along the X-axis direction are the same.

[0048] The present invention divides all the excitation electrodes into two arrays, wherein all the excitation electrodes in odd rows form a 24×24 array, and all the excitation electrodes in even rows form another 24×24 array.

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

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

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

[0052] like Figure 3As shown, the lower surface of the movable ruler substrate 2 is provided with two sensing electrode groups a and b arranged along the diagonal line. Each sensing electrode group is composed of four sensing electrodes 2-1 arranged in 2 columns and 2 rows along the X direction and the Y direction, which are respectively called a1, a2, a3, a4, b1, b2, b3, and b4. The width of each sensing electrode is I3=9.9mm, the shape and size are the same and there is the same spacing I4=0.1mm. The spacing between the two sensing electrode groups along the X direction is L2=26mm, and the spacing along the Y direction is L1=26mm. The width of a sensing electrode group is W=2(I3+I4)=20mm, and corresponds to the width of an excitation electrode group in terms of spatial position, that is, W=4(I1+I2).

[0053] In the first embodiment of the present invention, the spacing between the two sensing electrode groups along the X direction and the Y direction is equal, but the spacing is not equal to 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 the measurement, a sinusoidal excitation voltage signal U with equal amplitude and frequency and a phase difference of π / 2 is applied to the four-phase excitation electrode groups A, B, C, and D in sequence. A =U0sinωt,U B =U0cosωt,U C =-U0sinωt,U D =-U0cosωt. When the movable ruler substrate moves parallel to the fixed ruler substrate along the X direction, the sensing electrodes a1, a2, a3, and a4 in the sensing electrode group a output signals along the X direction as Uxa1, Uxa2, Uxa3, and Uxa4; the sensing electrodes b1, b2, b3, and b4 in the sensing electrode group b output signals along the X direction as Uxb1, Uxb2, Uxb3, and Uxb4. The output signals Uxa1, Uxa2, Uxa3 and Uxa4 of the sensing electrodes are calculated to obtain the output signal Uxa of the sensing electrode group a along the X direction, and the output signals Uxb1, Uxb2, Uxb3 and Uxb4 of the sensing electrode group b along the X direction are calculated to obtain the output signal Uxb; when the movable scale substrate moves in parallel with the fixed scale substrate along the Y direction, the output signals Uya1, Uya2, Uya3 and Uya4 of the sensing electrodes a1, a2, a3 and a4 of the sensing electrode group a along the Y direction are output by the sensing electrodes b1, b2, b3 and b4 of the sensing electrode group b along the Y direction are output by the sensing electrodes Uyb1, Uyb2, Uyb3 and Uyb4. The output signals Uya1, Uya2, Uya3 and Uya4 of the sensing electrodes are calculated to obtain the output signal Uya of the sensing electrode group a along the Y direction. The output signals Uyb1, Uyb2, Uyb3 and Uyb4 of the sensing electrodes are calculated to obtain the output signal Uyb of the 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 4 π, K e is the electric field coupling coefficient. a (x), e b (x+L2), e a (y+L1), e b (y) is the measurement error of the sensing electrode groups a and b on the moving ruler substrate when measuring along the X direction and Y direction respectively, which is expanded into the following form according to the Fourier series:

[0060]

[0061] Where i is the harmonic frequency, a i is the amplitude of the corresponding frequency, is the phase of the corresponding frequency.

[0062] During self-calibration, when the movable ruler substrate moves relative to the fixed ruler substrate in the X direction for self-calibration, the output signals Uxa and Uxb of the sensing electrode groups a and b are input into the shaping circuit through the signal acquisition system to form a square wave, and the square wave signal is input into the FPGA signal processing system for phase comparison with the fixed reference square wave Ur of the same frequency. The compared phase difference is interpolated and counted by high-frequency pulses, and the interpolated count value is converted to obtain the linear displacement indication x. a 、x b ; By the same processing method, the output displacement indication y when measuring along the Y direction can be obtained a,y b The displacement signal calculation and error self-calibration process in Embodiment 1 of the present invention is as follows: Figure 4 Output displacement indication 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 and the spacing L2 along the X direction, the difference in measurement error Δe along the X direction is obtained 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 and the spacing L1 along the Y direction, the difference in measurement error Δe along the Y direction is obtained y : As shown below,

[0065]

[0066] Δe x and Δe y Rewritten as a series of standard sine functions:

[0067]

[0068] The difference in measurement error when the sensing electrode groups a and b are measured along the X direction and the Y direction is Δe x and Δe y The amplitude A of the corresponding frequency i i , phase θ i With the measurement error e a (x) and e b The amplitude a of (y) corresponding to frequency i i , Phase The relationship can be expressed as:

[0069]

[0070] The difference between the X-direction and Y-direction errors Δe x and Δe y After Fourier transform, the amplitude A of the error difference spectrum corresponding to frequency i is extracted i and phase θ i , and then substitute it into formula (6) to obtain the displacement measurement error e a (x) and e b The amplitude of (y) is a 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 inverse Fourier transform, thereby constructing 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 (x) and e a (y) from the actual measured displacement values x b of the induction electrode groups a and b, and output the calibrated displacement values.

[0071] Embodiment 2: The measurement principle and most of the structure of Embodiment 2 are the same as those of Embodiment 1. The differences are as follows: 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 structure of Embodiment 3 are the same as those of Embodiment 1. The differences are as follows: 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 a plurality of 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 amplitude and phase parameters to construct an error function, and perform self-calibration 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 solution of the present invention rather than to limit it. Although the applicant has described the present invention in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that modifications or equivalent substitutions of the technical solution of the present invention without departing from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A self-calibration method based on a planar two-dimensional time-grating sensor, comprising a movable ruler substrate and a fixed-length substrate arranged in parallel with each other with a gap, an excitation electrode is arranged on the upper surface of the fixed-length substrate, and a sensing electrode is arranged on the lower surface of the movable ruler substrate, and the sensing electrode on the movable ruler substrate is directly opposite to the excitation electrode on the fixed-length substrate; characterized in that: The excitation electrodes are arranged in 2m rows side by side along the upper surface of the fixed-length substrate, and each row of excitation electrodes is composed of n identical square excitation electrode pieces uniformly arranged along the X-axis direction, and the spacing I2 between two adjacent square excitation electrode pieces is greater than the width I1 of a square excitation electrode piece; the spacing between two adjacent rows of excitation electrodes along the Y-axis direction is (I2-I1) / 2, and the starting positions along the X-axis direction are staggered by (I2+I1) / 2; the starting positions of the excitation electrodes in odd rows along the X-axis direction are the same, and the starting positions of the excitation electrodes in even rows along the X-axis direction are the same; wherein n=4k1, m=4k2, and k1 and k2 are both positive integers; In the excitation electrode array composed of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form a row excitation group, thereby forming m row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called Y1 row excitation group, Y2 row excitation group, Y3 row excitation group and Y4 row excitation group; In the excitation electrode array composed of all excitation electrodes in even rows, all excitation electrodes in each column are connected to form a column excitation group, thereby forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called X1 column excitation group, X2 column excitation group, X3 column excitation group and X4 column excitation group; All X1 column excitation groups and all Y1 row excitation groups are connected to form an A phase excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form a B phase excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form a C phase excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form a D phase excitation electrode group; The sensing electrodes are in two identical groups, each group of sensing electrodes is composed of four square sensing electrodes of the same size arranged in a 2×2 array to form a sensing electrode group; the side length of the sensing electrode is I3; adjacent sensing electrode pieces in each sensing electrode group have the same spacing I4; the two sensing electrode groups are arranged at two diagonal positions on the lower surface of the moving ruler substrate, and the spacing between the centers of the two sensing electrode groups along the X direction is L2, and the spacing along the Y direction is L1; During self-calibration, sinusoidal excitation voltages of equal amplitude and frequency with a phase difference of π / 2 are applied to the four-phase excitation electrode groups A, B, C, and D in sequence; When the movable ruler substrate moves relative to the fixed ruler substrate along the X direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each column signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the X direction, the measurement signal of the two sensing electrode groups along the X direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L2 along the X direction is subtracted to obtain the difference of the measurement error along the X direction; When the movable ruler substrate moves relative to the fixed ruler substrate along the Y direction, each sensing electrode of the two sensing electrode groups senses and outputs a corresponding signal respectively; the sum of each row signal of the two sensing electrode groups is subtracted to obtain the measurement signal of the two sensing electrode groups along the Y direction, the measurement signal of the two sensing electrode groups along the Y direction is subjected to displacement calculation to obtain the displacement value and output it, and then the displacement value output by the two sensing electrode groups is subjected to difference processing and the spacing L1 along the Y direction is subtracted to obtain the difference of the measurement error along the Y direction; The difference of measurement errors in the X and Y directions is transformed by Fourier transform 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 error value corresponding to the displacement measurement error function is subtracted from the actual measured displacement value, thus realizing self-calibration of the measurement errors along the X and Y directions.

2. The self-calibration method based on a planar two-dimensional time-grating sensor according to claim 1, characterized in that: Assume that the width of the sensing electrode group is W, satisfying W=4(I1+I2)=2(I3+I4).

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

4. The self-calibration method based on a planar two-dimensional time-grating sensor according to claim 3, characterized in that: All the sensing pole pieces in the two sensing electrode groups are integrally formed on the moving ruler substrate by PCB technology, so that the error characteristics of all the sensing pole pieces are the same.

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