Displacement correction and rapid feedback control method based on grating interference signal

Abstract

The invention relates to a displacement correction and rapid feedback control method based on a grating interference signal. The method comprises the steps that 1, a lower computer outputs a voltage signal for driving a piezoelectric ceramic scanner according to an instruction of an upper computer; 2, the piezoelectric ceramic deforms, so that the grating of the grating interferometer generates corresponding displacement; 3, simultaneously uploading grating interference signals formed by frequency difference on the left side and the right side of the grating to an upper computer and a lower computer; 4, the upper computer and the lower computer carry out correction and calculation on the grating interference signal through an RANSAC-Heydemann algorithm which is jointly corrected by the upper computer and the lower computer, and actual displacement is obtained; and 5, the lower computer performs correction through a PID control model according to the actual displacement to obtain an accurate displacement value for driving the piezoelectric ceramic scanner. According to the invention, a mode of cooperative operation of the upper computer and the lower computer is adopted, the feedback period of the RANSAC-Heydemann grating interference signal correction algorithm is reduced, and the efficient and precise positioning capability of the flat-plate scanner is improved.

Description

Technical Field

[0001] This invention relates to a control method for a precision displacement measurement system, and in particular discloses a displacement correction and fast feedback control method based on grating interference signals, belonging to the field of optical precision measurement. Background Technology

[0002] Atomic force microscopy (AFM), a key tool for nanoscale measurement and characterization, relies heavily on scanner performance for its spatial resolution and positioning accuracy. In an AFM system, a high-precision flatbed scanner, driven by high voltage to deform piezoelectric ceramics and coupled with a flexible hinge mechanism, achieves nanoscale displacement positioning and is the core component of the entire system. Currently, laser interferometers, capacitive sensors, and grating encoders are the mainstream methods for precision displacement measurement. Among these, displacement sensors based on grating interferometers use the grating period as a length reference, exhibiting low sensitivity to environmental interference. Furthermore, their combination of high precision and ease of integration makes them an ideal choice for embedded feedback control. However, the inherent hysteresis and creep characteristics of piezoelectric ceramic materials, along with their high sensitivity to environmental factors, inevitably lead to significant nonlinear displacement errors during actual operation. Laser interferometer measurements are susceptible to changes in air refractive index, requiring complex calibration methods. Capacitive sensors, due to their limited measurement range and poor long-term stability, struggle to meet the high-precision requirements of nanometer-level positioning. Traditional commercial grating interferometers require calibration to trace their measurements back to the meter definition. Furthermore, most existing control systems based on grating interferometry employ a single-processor architecture, resulting in feedback cycles typically exceeding 50 ms, making it difficult to effectively suppress the effects of high-frequency environmental vibrations (10-20 nm). Traditional RANSAC-Heydemann grating signal correction algorithms suffer from excessively long single-point processing times, typically requiring 80 ms per point. This not only prolongs the feedback cycle and reduces control efficiency but may also introduce additional measurement errors due to environmental vibrations. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides a displacement correction and fast feedback control method based on grating interference signals, enabling precise real-time calibration of a high-precision flatbed scanner. This method achieves high-precision displacement control of a piezoelectric ceramic-based high-precision flatbed scanner (hereinafter referred to as the piezoelectric ceramic scanner) through collaborative work between a host computer and a slave computer. The host computer sends control parameters, which the slave computer converts into analog signals to drive the piezoelectric ceramic to deform, and the displacement of the scanning structure is transmitted through a flexible hinge. The grating moves with the scanner, generating an interference signal, which is transmitted to the processing unit after photoelectric conversion. The RANSAC-Heydemann grating signal correction algorithm is used to process the interference signal, calculating correction parameters to improve measurement accuracy. The slave computer obtains the actual displacement based on the received correction parameter signal and adjusts the output parameters in real time through a PID control model, forming a closed-loop feedback control system.

[0004] This invention is implemented as follows: a displacement correction and fast feedback control method based on grating interference signals, comprising the following steps: Step 1: The host computer sends a displacement command to the slave computer. The slave computer sets the displacement parameters for the PID control model according to the displacement command. The digital signal of the output parameter is converted into an analog signal by the digital-to-analog converter. After amplification and bias processing by the auxiliary circuit, a voltage signal that can be input to the piezoelectric ceramic scanner is obtained. Step 2: The piezoelectric ceramic scanner receives the voltage signal sent in Step 1, the piezoelectric ceramic actuator deforms, and the deformation is transmitted through the flexible hinge of the bow structure, causing the flat scanning structure of the piezoelectric ceramic scanner to produce a corresponding displacement. Step 3: The grating of the grating interferometer integrated on the piezoelectric ceramic scanner moves accordingly, causing the coherent light carrying the grating period information to interfere on the left and right sides of the grating. The interference light is received by the photodetector to generate a grating interference analog signal. The grating interference analog signal is converted into a digital signal by the digital-to-analog converter in the signal acquisition module, and the grating interference signal is transmitted to the host computer and the slave computer. Step 4: The host computer and the slave computer use the RANSAC-Heydemann algorithm jointly corrected by the host computer and the slave computer to correct and solve the grating interference signal obtained in Step 3, and finally measure the actual displacement. Step 5: The lower-level machine adjusts the output parameters through proportional, integral and derivative operations using a PID control model based on the actual displacement obtained in step 4. Then, the output parameters are converted into analog signals by a digital-to-analog converter. After amplification and bias processing by auxiliary circuits, the voltage signal of the corrected piezoelectric ceramic is obtained, which finally enables the piezoelectric ceramic scanner to obtain an accurate displacement value.

[0005] In step 2, the flexible hinge of the piezoelectric ceramic scanner's bow-shaped structure includes a motion end face module and a hinge structure. The hinge structure has one or two degrees of freedom, and when subjected to force, it undergoes axial deformation, driving the displacement module to generate displacement.

[0006] The hinge structure has a single degree of freedom that generates working displacement in only one direction. It uses a double parallel four-bar linkage for transmission, with the moving end face module as the center and four bow-shaped hinges fixed in the upper, lower and left and right directions.

[0007] The hinge structure has two degrees of freedom, which generate working displacements in the X-axis and Y-axis directions. The X-axis and Y-axis are independent hinge structures with a single degree of freedom, and the entire X-axis module is nested into the motion end face module of the Y-axis.

[0008] In step 2, the piezoelectric ceramic actuator includes a piezoelectric ceramic manufactured using a low-pressure stacked co-fired process and a drive amplification structure made of carbon steel. When a voltage is applied to the two poles of the piezoelectric ceramic, it deforms, which guides the drive amplification structure to deform and generate a single degree of freedom of tension or thrust.

[0009] The specific steps in step 4 of the RANSAC-Heydemann algorithm, which is jointly corrected by the host computer and the slave computer, to finally measure the actual displacement are as follows: Step 4.1: The host computer performs DC cancellation processing on the grating interference signal obtained in step 3, subtracting the mean value of the original signal received by each photodetector and collected by the acquisition card to eliminate the synchronous DC bias under real-time measurement. Step 4.2: The host computer performs smoothing filtering on the grating interference signal obtained after DC cancellation processing in step 4.1, using the mean smoothing filtering method to filter the original signal; Step 4.3: The host computer calculates the parameters of the grating interference signal obtained by the smoothing and filtering process in step 4.2 based on the RANSAC-Heydemann algorithm, and sends the correction parameters to the slave computer. Step 4.4: The lower-level computer downsamples and filters out duplicate samples from the grating interference signal obtained in step 3 to save computing power; Step 4.5: The lower-level computer, in conjunction with the correction parameters received in Step 4.3, corrects the grating interference signal after downsampling and filtering out duplicate samples in Step 4.4; Step 4.6: The lower-level computer divides the grating interference signal corrected in step 4.5 into two parts: one part is the complete waveform acquired at this moment, and the other part is the waveform that has not completed a full cycle at this moment. Step 4.7: The lower-level machine obtains the number of integer cycles at this moment by counting the complete waveforms obtained in step 4.6, and performs arctangent decomposition on the incomplete waveforms to obtain the decimals; Step 4.8: The lower-level machine combines the integer and decimal obtained in step 4.7 and multiplies them by the grating period ratio to obtain the actual displacement, which is the accurate displacement value after correction at that moment.

[0010] The displacement correction and fast feedback control method based on grating interference signals mainly includes three parallel while loop modules: a grating interference signal displacement calculation module, a scanner displacement feedback module, and a result display module. The grating interference signal displacement calculation module continuously retrieves the original grating interference signal data and Z-axis height data from register two, and downsamples the original grating interference signal data. The Z-axis height data is provided by a technologically mature optical lever principle probe and directly imported into register one. The downsampled grating interference signal data is then sent to RANS by the host computer. The AC-Heydemann parameters are corrected, and then the results carrying decimals are solved by integer wave counting and arctangent calculation to obtain the absolute integer wave count after power-on and the relative displacement after the most recent integer wave count. Finally, the absolute displacement of the piezoelectric ceramic scanner is obtained through joint processing and stored in register one. The scanner displacement feedback module generates the set displacement in real time through the display lookup table of the lower computer and adjusts the set displacement according to the absolute displacement of the piezoelectric ceramic scanner read from register one using the PID control model. The adjusted set displacement is stored in register two. The result display module transmits the data stored in register one to the upper computer for display in real time.

[0011] This invention significantly improves the accuracy and stability of displacement control through digital signal processing and real-time feedback mechanisms, and can be widely applied in fields such as precision instruments and microelectronics manufacturing.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The RANSAC-Heydemann grating signal correction algorithm was applied to displacement feedback control, which improved the precision positioning capability of the piezoelectric ceramic scanner and filled the technical gap of applying grating interference signal feedback control to high-precision flat panel scanner positioning.

[0013] 2. By combining upper-level computer fitting with lower-level computer correction, the feedback cycle of the RANSAC-Heydemann grating signal correction algorithm is reduced, effectively suppressing the influence of high-frequency environmental vibration and effectively reducing the generation of measurement errors. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the process steps of the displacement correction and fast feedback control method based on grating interference signals described in this invention.

[0015] Figure 2This is a block diagram of the lower-level machine program logic in this invention.

[0016] Figure 3 This is a schematic diagram of the process steps of a specific embodiment of the present invention.

[0017] Figure 4 This is a simplified structural diagram of the repeatability positioning accuracy testing system in a specific embodiment of the present invention.

[0018] Figure 5 This is a schematic diagram of the motion waveform of the displacement stage during a partial test in a specific embodiment of the present invention.

[0019] In the diagram: 1. Piezoelectric ceramic scanner; 2. Reflector; 3. Grating; 4. Signal generator; 5. User computer; 6. A / D conversion module. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] According to the appendix Figure 1 This invention relates to a displacement correction and fast feedback control method based on grating interference signals, comprising the following steps: Step 1: The host computer sends a displacement command to the slave computer. The slave computer sets the displacement parameters for the PID control model according to the displacement command. The digital signal of the output parameter is converted into an analog signal by the digital-to-analog converter. After amplification and bias processing by the auxiliary circuit, a voltage signal that can be input to the piezoelectric ceramic scanner is obtained.

[0022] Step 2: The piezoelectric ceramic scanner receives the voltage signal sent in Step 1. The piezoelectric ceramic actuator deforms and transmits the deformation through the flexible hinge of the bow structure, causing the flat scanning structure of the piezoelectric ceramic scanner to produce a corresponding displacement.

[0023] Step 3: The grating of the grating interferometer integrated on the piezoelectric ceramic scanner moves accordingly, causing the coherent light carrying the grating period information to interfere on the left and right sides of the grating. The interference light is received by the photodetector to generate a grating interference analog signal. The grating interference analog signal is converted into a digital signal by the digital-to-analog converter in the signal acquisition module, and the grating interference signal is transmitted to the host computer and the slave computer.

[0024] Step 4: The host computer and the slave computer use the RANSAC-Heydemann algorithm, which is jointly corrected by the host computer and the slave computer, to correct and solve the grating interference signal obtained in Step 3, and finally measure the actual displacement. The specific steps are as follows: Step 4.1: The host computer performs DC cancellation processing on the grating interference signal obtained in step 3, subtracting the mean value of the original signal received by each photodetector and collected by the acquisition card to eliminate the synchronous DC bias under real-time measurement.

[0025] Step 4.2: The host computer performs smoothing filtering on the grating interference signal obtained after DC cancellation processing in step 4.1, using the mean smoothing filtering method to filter the original signal.

[0026] Step 4.3: The host computer calculates the parameters of the grating interference signal obtained by the smoothing and filtering process in step 4.2 based on the RANSAC-Heydemann algorithm, and sends the correction parameters to the slave computer.

[0027] Step 4.4: The lower-level computer performs downsampling and duplicate sample filtering on the grating interference signal obtained in step 3 to save computing power.

[0028] Step 4.5: The lower-level computer, in conjunction with the correction parameters received in Step 4.3, corrects the grating interference signal after downsampling and filtering out duplicate samples in Step 4.4.

[0029] Step 4.6: The lower-level computer divides the grating interference signal corrected in step 4.5 into two parts: one part is the complete waveform acquired at this moment, and the other part is the waveform that has not completed a full cycle at this moment.

[0030] Step 4.7: The lower-level machine obtains the number of integer cycles at that moment by counting the complete waveform obtained in step 4.6, and performs arctangent calculation on the incomplete waveform to obtain the decimal.

[0031] Step 4.8: The lower-level machine combines the integer and decimal obtained in step 4.7 and multiplies them by the grating period ratio to obtain the actual displacement, which is the accurate displacement value after correction at that moment.

[0032] Step 5: The lower-level machine adjusts the output parameters through proportional, integral and derivative operations using a PID control model based on the actual displacement obtained in step 4. Then, the output parameters are converted into analog signals by a digital-to-analog converter. After amplification and bias processing by auxiliary circuits, the voltage signal of the corrected piezoelectric ceramic is obtained, which finally enables the piezoelectric ceramic scanner to obtain an accurate displacement value.

[0033] Example: To verify the capability of the displacement correction and fast feedback control method based on grating interference signals described in this invention, a metrological atomic force microscope (AFM) was used to conduct a repeatability positioning accuracy experiment on the method of this invention.

[0034] In this embodiment, the lower-level machine adopts the PCI extensions for instrumentation (PXI) system from National Instruments (NI). This device has two transceivers with Butterworth filters and two accompanying Kintex-7 core FPGA modules, driven by a controller with Thunderbolt 3 ports. It can achieve 100 Ms / s 8-channel synchronous 18-bit input and 200 Ms / s 8-channel 18-bit synchronous output capabilities. The main program logic block diagram of the displacement feedback control method based on grating interference signals compiled on the PXIe-7971 architecture is shown below. Figure 2 As shown, the system mainly consists of three parallel while-loop modules: a grating interference signal displacement calculation module (loop 1), a scanner displacement feedback module (loop 2), and a result display module (loop 3). The grating interference signal displacement calculation module continuously retrieves the original grating interference signal data and Z-axis height data from register two, and downsamples the original grating interference signal data. The Z-axis height data is provided by a mature optical lever principle probe and directly imported into register one. The downsampled grating interference signal data is corrected by RANSAC-Heydemann parameters issued by the host computer. The result, carrying decimal values, is then used to calculate the absolute integer number (integer) after power-on and the relative displacement (decimal) after the most recent integer number. Finally, after joint processing, the absolute displacement of the piezoelectric ceramic scanner is obtained and stored in register one. The scanner displacement feedback module generates the set displacement in real time through a 203,800-entry lookup table on the PXIe-7971 lower-level computer. Based on the absolute displacement of the piezoelectric ceramic scanner read from register one, it adjusts the set displacement using a PID control model. The adjusted set displacement is then stored in register two. The result display module transmits the stored data from register one to the upper-level computer for display in real time.

[0035] According to the appendix Figure 3 The specific processing steps for applying the method described in this invention to a metrological atomic force microscope (AFM) are as follows: Step 1: The host computer sends a displacement command (X-axis displacement value X, Y-axis displacement value Y) to the slave computer. The slave computer then sets the displacement parameters for the PID control model according to the displacement command (correspondingly setting the X-axis displacement parameter value to X, and the Y-axis displacement parameter value to Y, etc.). Figure 3In subsequent steps, corresponding data processing and system components are further differentiated by X and Y axes. A digital-to-analog converter converts the digital signal of the output parameter into an analog signal. After amplification and biasing by auxiliary circuitry, a voltage signal capable of being input to the piezoelectric ceramic scanner is obtained, and then output as a voltage signal through a signal generator. The host computer can simultaneously send displacement commands for both the X-axis and Y-axis displacement values ​​to the slave computer, or it can choose to send one of the two axis displacement values. Accordingly, the subsequent data processing in the displacement correction and fast feedback control method based on grating interference signals described in this invention processes the sent displacement commands step by step.

[0036] Step 2: The piezoelectric ceramic scanner receives the voltage signal sent in Step 1. The piezoelectric ceramic actuator deforms and transmits the deformation through the flexible hinge of the bow structure, causing the flat scanning structure of the piezoelectric ceramic scanner to produce a corresponding displacement.

[0037] The piezoelectric ceramic actuator includes a piezoelectric ceramic manufactured using a low-pressure stacked co-fired process and a drive amplification structure made of carbon steel. When a voltage is applied to the two poles of the piezoelectric ceramic, it deforms, which guides the deformation of the drive amplification structure to generate a single degree of freedom of tension or thrust.

[0038] The aforementioned bow-shaped flexible hinge includes a motion end-face module and a hinge structure. The hinge structure has one or two degrees of freedom, and under force, it undergoes axial deformation, driving the displacement module to generate displacement. The single degree of freedom generates working displacement in only one direction, transmitted using a double parallel four-bar linkage, with four bow-shaped hinges fixed at the center of the motion end-face module (up, down, left, and right). The two degrees of freedom generate working displacement in both the X and Y axes. The X and Y axes are independent hinge structures with single degrees of freedom each. The entire X-axis module is nested within the Y-axis motion end-face module, i.e., the part pushed / pulled by the piezoelectric ceramic and flexible hinges, also known as the scanner's motion module.

[0039] Step 3: The grating of the grating interferometer integrated on the piezoelectric ceramic scanner moves accordingly, causing interference between the coherent light carrying grating period information hitting the left and right sides of the grating. The interference light is received by a photodetector to generate a grating interference analog signal. This analog signal is converted into a digital signal by the digital-to-analog converter in the signal acquisition module, and simultaneously transmitted to the host computer and the slave computer. The relationship between the light intensity signal and displacement of the grating interferometer is as follows: (1), In this process, two perpendicularly polarized diffracted beams are proportionally split into two paths by a non-polarizing beamsplitter (NPS). These paths are then incident on a quarter-wave plate W1 with its fast axis at a 45° angle to the incident plane, and a half-wave plate W2 with its fast axis at a 22.5° angle to the incident plane. After passing through PBS2 and PBS3, the perpendicularly polarized portion is transmitted into photodetectors PD2 and PD4 and received, while the horizontally polarized portion is reflected into photodetectors PD1 and PD3 and received, forming four interference light intensity signals with phase differences of 3λ / 4, λ / 4, λ, and λ / 2 from the initial phase, respectively. Differencing PD1 with PD2 and PD3 with PD4 yields two interference sine wave signals with a 90° phase difference and twice the amplitude of their original values.

[0040] Step 4: The host computer and the slave computer use the RANSAC-Heydemann algorithm, jointly corrected by the host and slave computers, to correct and solve the grating interference signal obtained in Step 3, and finally measure the actual displacement. The specific steps are as follows: Step 4.1: The host computer performs DC cancellation processing on the grating interference signal obtained in step 3, subtracting the mean value of the original signal received by each photodetector and collected by the acquisition card to eliminate the synchronous DC bias under real-time measurement.

[0041] Step 4.2: The host computer performs smoothing filtering on the grating interference signal obtained after DC cancellation processing in step 4.1, using the mean smoothing filtering method to filter the original signal.

[0042] Step 4.3: The host computer calculates the parameters of the grating interference signal obtained by the smoothing and filtering process in step 4.2 based on the RANSAC-Heydemann algorithm, and sends the correction parameters to the slave computer.

[0043] Step 4.4: The lower-level computer performs downsampling and duplicate sample filtering on the grating interference signal obtained in step 3 to save computing power.

[0044] Step 4.5: The lower-level computer, in conjunction with the correction parameters received in Step 4.3, corrects the grating interference signal after downsampling and filtering out duplicate samples in Step 4.4.

[0045] Step 4.6: The lower-level computer divides the grating interference signal corrected in step 4.5 into two parts: one part is the complete waveform acquired at this moment, and the other part is the waveform that has not completed a full cycle at this moment.

[0046] Step 4.7: The lower-level machine obtains the number of integer cycles at that moment by counting the complete waveform obtained in step 4.6, and performs arctangent calculation on the incomplete waveform to obtain the decimal.

[0047] Step 4.8: The lower-level machine combines the integer and decimal obtained in step 4.7 and multiplies them by the grating period ratio to obtain the actual displacement, which is the accurate displacement value after correction at that moment.

[0048] Step 5: The lower-level machine adjusts the output parameters through proportional, integral, and derivative operations using a PID control model based on the actual displacement obtained in Step 4.

[0049] Let S(k) be the displacement measured by the direct-source grating interferometer at time k. Ideally, the displacement-to-piezoelectric ceramic conversion ratio is α. Then, the process variable in the lower-level machine at this time is s(k) = S(k) / α. Therefore, the lower-level machine output parameter u(k) at time k through the PID control model is: (2), Among them, K p K represents the proportional gain. i K represents the integral gain. d Let represent the differential gain, 'a' represent the filtering coefficient, 'SP' represent the setpoint, 'beta' represent the proportional weight, 'gamma' represent the differential weight, 'e'(k) is the error signal based on the proportional weight 'beta', 'e''(k) is the error signal based on the differential weight 'gamma', 'e''(k-1) is the error signal based on the differential weight 'gamma' at time (k-1) (i.e., the previous time step), and 'u'(k-1) is the error signal based on the differential weight 'gamma'. D (k-1) is the perturbation output at time (k-1) (i.e. the previous time), used to compensate for perturbations that are not modeled.

[0050] After processing by the PID control model, the output parameters are converted into analog signals by a digital-to-analog converter. After amplification and biasing by auxiliary circuits, the voltage signal of the corrected piezoelectric ceramic is obtained, which ultimately enables the piezoelectric ceramic scanner to obtain accurate displacement values.

[0051] Figure 4 This is a simplified structural diagram of a repeatability positioning accuracy testing system for a displacement feedback control device and method based on grating interference signals. This embodiment uses a quDIS type FP laser interferometer manufactured by quTools (Germany) and calibrated by the National Institute of Metrology (China) (Test Certificate: CDjc2024-01942) as the reference device. (See attached diagram.) Figure 4The laser interferometer and the grating interferometer are connected to a digital-to-analog converter (DAC) 6, which is connected to a user computer 5. The piezoelectric ceramic scanner 1 is connected to a signal generator 4. The normal of the laser interferometer's mirror 2 is collinear with the vector direction of the grating 3. The voltage signal output from the signal generator 4 drives the piezoelectric ceramic scanner 1 to perform corresponding displacement movements. The voltage signal output from the signal generator 4 is adjusted to 0-130V through a bias circuit and an amplification circuit, and a displacement of approximately 10 μm is obtained through feedback control of the grating interferometer. The data measured by the laser interferometer and the grating interferometer are simultaneously sampled by the NI-5783 DAC 6 and converted into digital signals for transmission to the host computer for processing.

[0052] The displacement motion of the piezoelectric ceramic scanner 1 has 11 measurement positions evenly distributed throughout its entire stroke, denoted as p. i (i=1,2,3,…,11), where p1 is the extreme position of the reverse direction of the journey, p 11 The travel distance is the positive limit position. The reading is reset to zero each time the movement reaches p1, and the measurement is repeated 5 times. Discarding the first point, the bidirectional average measurement value at the i-th measurement position is obtained. for: (3), in, This is the i-th positive average measurement value of the scanner. Let be the i-th reverse repeated measurement value. Then the forward repeatability and reverse repeatability of the i-th point are: (4), in Let be the i-th and j-th forward average measurement value of the scanner. Let be the i-th and j-th reverse repeated measurement value, and m be the number of measurements. Finally, take... To ensure the repeatability of the piezoelectric ceramic scanner.

[0053] Test using the method described above. Figure 5 This is a partial test waveform diagram of the displacement stage in an embodiment of the displacement feedback control device and method based on grating interference signals described in this invention. The complete test results for the X and Y axes are shown in Tables 1 and 2, respectively. Table 1 shows the X-axis repeatability test results of the scanner, and Table 2 shows the Y-axis repeatability test results of the scanner.

[0054] The measurement results show that the repeatability of the flatbed scanner at full scale (100 μm) is 0.038 μm for the X-axis and 0.046 μm for the Y-axis. Since the testing system did not strictly control environmental noise during the test, even better results would be achieved when the piezoelectric ceramic scanner is integrated into a metrological atomic force microscope (AFM) with strict environmental noise control.

Claims

1. A displacement correction and fast feedback control method based on grating interference signals, characterized in that... The displacement correction and fast feedback control method includes the following steps: Step (1): The host computer sends a displacement command to the slave computer. The slave computer sets the displacement parameters for the PID control model according to the displacement command. The digital signal of the output parameter is converted into an analog signal by the digital-to-analog converter. After amplification and bias processing by the auxiliary circuit, a voltage signal that can be input to the piezoelectric ceramic scanner is obtained. Step (2): The piezoelectric ceramic scanner receives the voltage signal sent in step (1), the piezoelectric ceramic actuator deforms, and transmits the deformation through the flexible hinge of the bow structure, causing the flat scanning structure of the piezoelectric ceramic scanner to produce a corresponding displacement. Step (3): The grating of the grating interferometer integrated on the piezoelectric ceramic scanner moves accordingly, causing the coherent light carrying the grating period information on the left and right sides of the grating to interfere. The interference light is received by the photodetector to generate a grating interference analog signal. The grating interference analog signal is converted into a digital signal by the digital-to-analog converter in the signal acquisition module, and the grating interference signal is transmitted to the host computer and the slave computer at the same time. Step (4): The host computer and the slave computer use the RANSAC-Heydemann algorithm jointly corrected by the host computer and the slave computer to correct and solve the grating interference signal obtained in step (3), and finally measure the actual displacement. Step (5): The lower computer adjusts the output parameters through the proportional, integral and derivative functions of the PID control model according to the actual displacement obtained in step (4), and then converts the output parameters into analog signals through the digital-to-analog converter. After amplification and bias processing by the auxiliary circuit, the voltage signal of the corrected piezoelectric ceramic is obtained, so that the piezoelectric ceramic scanner can obtain the accurate displacement value.

2. The displacement correction and fast feedback control method based on grating interference signals according to claim 1, characterized in that: In step (2), the piezoelectric ceramic scanner's bow-shaped flexible hinge includes a motion end face module and a hinge structure. The hinge structure has one or two degrees of freedom, and when subjected to force, it undergoes axial deformation, driving the displacement module to generate displacement.

3. The displacement correction and fast feedback control method based on grating interference signals according to claim 2, characterized in that: The hinge structure's single degree of freedom generates working displacement in only one direction, which is transmitted using a double parallel four-bar mechanism. The four bow-shaped hinges, one above the other and one to the left and right, are fixed around the moving end face module.

4. The displacement correction and fast feedback control method based on grating interference signals according to claim 2, characterized in that: The hinge structure has two degrees of freedom, which generate working displacements in the X-axis and Y-axis directions. The X-axis and Y-axis are independent hinge structures with a single degree of freedom, and the entire X-axis module is nested into the motion end face module of the Y-axis.

5. The displacement correction and fast feedback control method based on grating interference signals according to claim 1, characterized in that: In step (2), the piezoelectric ceramic actuator includes a piezoelectric ceramic manufactured using a low-pressure stacked co-fired process and a drive amplification structure made of carbon steel. When the voltage is applied to the two poles, the piezoelectric ceramic deforms, which guides the drive amplification structure to deform and generate a single degree of freedom of tension or thrust.

6. The displacement correction and fast feedback control method based on grating interference signals according to claim 1, characterized in that: The specific steps in step (4) of the RANSAC-Heydemann algorithm, which is jointly corrected by the host computer and the slave computer, to finally measure the actual displacement are as follows: Step (4.1): The host computer performs DC cancellation processing on the grating interference signal obtained in step (3), subtracts the mean value of the original signal received by each photodetector and collected by the acquisition card, and eliminates the synchronous DC bias under real-time measurement. Step (4.2): The host computer performs smoothing filtering on the grating interference signal obtained after DC elimination processing in step (4.1), and uses the mean smoothing filtering method to filter the original signal; Step (4.3): The host computer performs parameter calculation on the grating interference signal obtained by the smoothing and filtering process in step (4.2) based on the RANSAC-Heydemann algorithm, and sends the correction parameters to the slave computer; Step (4.4): The lower-level machine performs downsampling and duplicate sample filtering on the grating interference signal obtained in step (3) to save computing power; Step (4.5): The lower-level machine combines the correction parameters received in step (4.3) to correct the grating interference signal after downsampling and filtering out duplicate samples in step (4.4); Step (4.6): The lower computer divides the grating interference signal corrected by step (4.5) into two parts: one part is the complete waveform acquired at this moment, and the other part is the waveform that has not completed the cycle at this moment. Step (4.7): The lower-level machine obtains the number of integer cycles at this moment by counting the complete waveform obtained in step (4.6), and performs arctangent decomposition on the incomplete waveform to obtain the decimal; Step (4.8): The lower-level machine combines the integer and decimal obtained in step (4.7) and multiplies them by the grating period ratio to obtain the actual displacement, which is the accurate displacement value after correction at that moment.

7. The displacement correction and fast feedback control method based on grating interference signals according to claim 1, characterized in that: The displacement feedback control method based on grating interferometric signals mainly includes three parallel while loop modules: a grating interferometric signal displacement calculation module, a scanner displacement feedback module, and a result display module. The grating interferometric signal displacement calculation module continuously retrieves the original grating interferometric signal data and Z-axis height data from register two, and downsamples the original grating interferometric signal data. The Z-axis height data is provided by a technologically mature optical lever principle probe and directly imported into register one. The downsampled grating interferometric signal data is then sent by the host computer to the RANSAC-Heydemann parameter. The result is corrected, and then the result carrying the decimal is solved by integer wave counting and arctangent calculation to obtain the absolute integer wave count after power-on and the relative displacement after the most recent integer wave count. Finally, the absolute displacement of the piezoelectric ceramic scanner is obtained through joint processing and stored in register one. The scanner displacement feedback module generates the set displacement in real time through the display lookup table of the lower computer, and adjusts the set displacement according to the absolute displacement of the piezoelectric ceramic scanner read from register one using the PID control model. The adjusted set displacement is stored in register two. The result display module transmits the data stored in register one to the upper computer for display in real time.

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