Piezoelectric coefficient measurement method and system based on sinusoidal phase modulation laser interferometer

Abstract

The application provides a piezoelectric coefficient measurement method and system based on a sinusoidal phase modulation laser interferometer, and relates to the technical field of laser interferometry. The method comprises the following steps: obtaining driving signal data of a piezoelectric ceramic to be measured and interference light intensity signal data of a Michelson laser interference optical path; constructing the Michelson laser interference optical path; based on a sinusoidal phase modulation mode, applying phase modulation to the Michelson laser interference optical path, and performing phase modulation processing on the interference light intensity signal data input to the Michelson laser interference optical path to obtain phase-modulated interference light intensity signal data; performing photoelectric conversion processing on the phase-modulated interference light intensity signal data through a photodetector to obtain electrical signal data; performing phase demodulation processing on the electrical signal data to obtain displacement information data; performing piezoelectric coefficient calculation processing on the piezoelectric response relationship between the displacement information data and the driving signal data to obtain a piezoelectric coefficient measurement result.

Description

Technical Field

[0001] This invention relates to the field of laser interferometry technology, and in particular to a method and system for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer. Background Technology

[0002] The piezoelectric coefficient is a core physical quantity characterizing the mechanical and electrical energy conversion efficiency of piezoelectric materials. It is also a key parameter in the research, design, and application of piezoelectric functional devices, and its value directly affects the output performance of various piezoelectric devices. Piezoelectric coefficient measurement has become an important part of university physics experimental teaching and is widely used in many fields such as precision positioning stages, ultrasonic transducers, and adaptive optics systems. Nanoscale precision displacement components place even higher demands on the accurate calibration of the piezoelectric coefficient, making related measurement technologies of significant research and application value.

[0003] Currently, the quasi-static method and the resonance method are commonly used techniques in the field of piezoelectric coefficient measurement. Both methods have mature supporting measuring instruments that can complete routine piezoelectric coefficient testing. Laser interferometry, piezoelectric response force microscopy, and other techniques are also gradually being applied to high-precision piezoelectric coefficient characterization. These techniques enable effective detection of material micro-displacements and microscopic properties, providing strong technical support for piezoelectric material performance analysis and precision device development, and promoting the diversified development of piezoelectric material testing technology.

[0004] However, existing mainstream measurement equipment has a high degree of integration, making it difficult to fully demonstrate the measurement process. The application cost of some high-precision detection equipment is relatively high, which is not conducive to its widespread use in routine experimental scenarios. Summary of the Invention

[0005] To address the technical challenges of high integration in existing mainstream measurement equipment, making it difficult to fully demonstrate the measurement process, and the high cost of some high-precision detection equipment, which hinders its widespread use in routine experimental scenarios.

[0006] The technical solution provided by this invention is as follows: A first aspect of this invention proposes a method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer, comprising: S1: Acquire the driving signal data of the piezoelectric ceramic under test and the interference light intensity signal data of the Michelson laser interference optical path; S2: Construct the Michelson laser interference optical path; S3: Based on the sinusoidal phase modulation method, phase modulation is applied to the Michelson laser interference optical path, and the interference light intensity signal data input to the Michelson laser interference optical path is processed by phase modulation to obtain the phase-modulated interference light intensity signal data; S4: The phase-modulated interference light intensity signal data is processed by photoelectric conversion using a photodetector to obtain electrical signal data; S5: Perform phase demodulation processing on the electrical signal data to obtain displacement information data; S6: Perform piezoelectric coefficient calculation on the piezoelectric response relationship between displacement information data and drive signal data to obtain the piezoelectric coefficient measurement result.

[0007] A second aspect of the present invention provides a piezoelectric coefficient measurement system based on a sinusoidal phase-modulated laser interferometer, comprising: a processor and a memory; The memory stores programs or instructions that can run on the processor, which, when executed by the processor, implement the steps of the method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer as described in the first aspect.

[0008] The beneficial effects of the technical solution provided by this invention include: In this embodiment of the invention, addressing the issues of high integration, incomplete measurement process visualization, and high cost of high-precision equipment in existing devices, this solution utilizes a Michelson laser interferometry optical path and sinusoidal phase modulation to complete signal processing. It comprehensively presents all measurement stages from signal acquisition, phase modulation, photoelectric conversion, phase demodulation to coefficient calculation, providing a clear and intuitive view of the entire measurement process. The invention features a simple overall architecture, requires no dedicated high-end equipment, effectively reduces usage costs, and facilitates widespread application. The entire process relies on a predetermined optical path and signal processing logic to complete detection; the measurement link is clear and controllable, effectively measuring the piezoelectric coefficient while properly resolving the related problems existing in the prior art. Attached Figure Description

[0009] Figure 1 A schematic flowchart illustrating the piezoelectric coefficient measurement method based on a sinusoidal phase-modulated laser interferometer provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the Michelson interference optical path provided in an embodiment of the present invention; Figure 3 Analysis diagram of demodulation algorithm provided in embodiments of the present invention; Figure 4 A schematic diagram of the piezoelectric coefficient measurement system based on a sinusoidal phase modulation laser interferometer provided in an embodiment of the present invention. Detailed Implementation

[0010] Reference manual attached Figure 1 The diagram shows a flowchart of the piezoelectric coefficient measurement method based on a sinusoidal phase modulation laser interferometer provided in an embodiment of the present invention.

[0011] This invention provides a method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer, which may include the following steps: S1: Acquire the driving signal data of the piezoelectric ceramic under test and the interference light intensity signal data of the Michelson laser interference optical path.

[0012] The piezoelectric ceramic under test is a piezoelectric material exhibiting the inverse piezoelectric effect, which generates strain under the action of an applied electric field. The driving signal data is a voltage sequence used to drive the piezoelectric ceramic under test to produce displacement, generated by an STM32-controlled DDS and amplified by high voltage. The Michelson laser interferometer optical path is an optical structure composed of a laser, a beam splitter, a reference mirror, and a moving mirror, used to convert displacement into changes in interference light intensity. The interference light intensity signal data is the voltage signal corresponding to the light intensity output by the photodetector after the two reflected beams in the Michelson laser interferometer optical path are superimposed; it contains phase information caused by the displacement of the piezoelectric ceramic under test.

[0013] The interference light intensity signal data is obtained by the photodetector after initial electrical signal conversion during the acquisition process, and is sampled and processed synchronously with the driving signal data during acquisition.

[0014] Furthermore, synchronous sampling processing is implemented based on a unified clock signal to ensure the correspondence between the driving signal data and the interference light intensity signal data in the time dimension.

[0015] Optionally, the drive signal data is used to drive and control the piezoelectric ceramic under test so that the piezoelectric ceramic under test produces a displacement change, wherein there is a corresponding relationship between the drive signal data and the displacement change.

[0016] The displacement change is the axial elongation of the piezoelectric ceramic under test under an applied voltage. The corresponding relationship is described by the piezoelectric coefficient, i.e., the displacement produced per unit voltage.

[0017] Furthermore, piezoelectric materials exhibit the inverse piezoelectric effect, meaning that under an applied electric field, the material undergoes strain along its polarization direction. For piezoelectric ceramics polarized along their thickness direction, the relationship between their longitudinal strain and the electric field satisfies:

[0018] in, S 3 indicates longitudinal strain. d 33 Represents the longitudinal piezoelectric strain constant. E 3 represents an applied electric field.

[0019] Specifically, for a piezoelectric ceramic displacement device in practical use, axial displacement is generated under the action of an applied voltage, and the displacement and the piezoelectric coefficient satisfy the following relationship:

[0020] in, Δx This represents the displacement change produced by the piezoelectric ceramic under test. nIndicates the number of piezoelectric ceramic stack layers. V This indicates the driving voltage.

[0021] Furthermore, by acquiring the driving signal data and the corresponding displacement change data, the correspondence between the driving voltage and displacement can be established, providing basic data for subsequent piezoelectric coefficient calculation.

[0022] For example, when the driving voltage changes in a stepwise manner, the corresponding displacement change can be recorded synchronously, thereby constructing a displacement-voltage data sequence.

[0023] In this embodiment of the invention, by synchronously acquiring the driving signal data of the piezoelectric ceramic under test and the interference intensity signal data of the Michelson laser interference optical path, the electrical drive and optical response are kept consistent in time, thereby establishing a correspondence between the driving signal and displacement change. At the same time, combined with the inverse piezoelectric effect principle of piezoelectric materials, a clear physical correlation is established between voltage change and material deformation, providing a stable data basis for subsequent piezoelectric coefficient calculation and improving the consistency and reliability of the measurement process.

[0024] S2: Construct the Michelson laser interference optical path.

[0025] The Michelson laser interferometer optical path includes a reference arm optical path and a measurement arm optical path. The measurement arm optical path corresponds to the displacement change of the piezoelectric ceramic under test. The reference arm optical path includes a fixed reflector. The measurement arm optical path includes a movable reflector attached to the piezoelectric ceramic under test; the displacement change of the piezoelectric ceramic under test causes a change in the optical path of the measurement arm.

[0026] Optionally, the Michelson laser interferometer optical path includes a reference arm optical path and a measurement arm optical path, wherein the measurement arm optical path corresponds to the displacement change of the piezoelectric ceramic under test.

[0027] Specifically, in the Michelson laser interferometer optical path, the He-Ne laser outputs linearly polarized light with a wavelength of 632.8 nm. This light is split into two orthogonally linearly polarized beams by a half-wave plate and a polarization beam splitter, which then enter the reference arm and the measurement arm, respectively. The reference arm incorporates a PM fiber phase modulator, which uses the electro-optic effect to perform high-frequency phase modulation on the reference light wave. The measurement arm has a stack of piezoelectric ceramics under test mounted at its end, with a high-reflectivity plane mirror attached to its free end.

[0028] Furthermore, the Michelson laser interferometer uses a beam-splitting method to divide the laser into a reference beam and a measurement beam. The two beams pass through the reference arm optical path and the measurement arm optical path respectively, and then are combined again to form interference.

[0029] Specifically, the reference light is directed toward a fixed reflector, and the measuring light is directed toward a moving reflector placed on the piezoelectric ceramic to be tested. The two reflected beams are superimposed at the beam splitter to form interference light.

[0030] Furthermore, the interference light intensity satisfies:

[0031] in, I Indicates the intensity of the interference light. I r This indicates the intensity of the reference light from the reference arm optical path. I m This indicates the intensity of the measuring light from the optical path of the measuring arm. cos Represents the cosine function. f This represents the phase difference between the reference light and the measurement light.

[0032] It should be noted that when the piezoelectric ceramic under test undergoes displacement... Δx At that time, the change in optical path of the measuring arm was 2. Δx The corresponding phase change satisfies:

[0033] in, Df This represents the change in the interference phase difference between the measuring arm and the reference arm. l Indicates the wavelength of the laser used. π It represents pi (π).

[0034] Furthermore, the expression for the interference light intensity can be obtained:

[0035] in, I ( t () indicates time t The received interference light intensity signal, I 0 represents the average light intensity. v Indicates interference contrast. f 0 Indicates the initial phase. Δx ( t The value represents the displacement change of the piezoelectric ceramic under test at time t.

[0036] For example, if a He-Ne laser with a wavelength of 632.8 nm is used, the displacement change corresponding to one interference fringe is approximately 316.4 nm.

[0037] Furthermore, the optical path of the reference arm and the optical path of the measuring arm form a closed interference structure in space to achieve stable detection of changes in optical path difference.

[0038] It should be noted that the displacement of the moving mirror in the optical path of the measuring arm directly causes a change in the phase of the interference fringes, thereby realizing the conversion of displacement into light intensity signal.

[0039] In this embodiment of the invention, by constructing a Michelson laser interference structure consisting of a reference arm optical path and a measurement arm optical path, the minute displacement generated by the piezoelectric ceramic under test can be converted into a change in optical path, and further manifested as a change in interference fringes, thereby achieving high-sensitivity optical detection of displacement, enabling nanoscale deformation to be effectively characterized, improving the resolution and stability of the overall measurement system, and enhancing the adaptability of the optical path structure to external disturbances.

[0040] S3: Based on the sinusoidal phase modulation method, phase modulation is applied to the Michelson laser interference optical path, and the interference light intensity signal data input to the Michelson laser interference optical path is processed by phase modulation to obtain the phase-modulated interference light intensity signal data.

[0041] Sinusoidal phase modulation is a technique that uses a high-frequency sinusoidal signal to drive a phase modulator to apply a known phase modulation to a reference light. This is used to load the slow phase change caused by the displacement being measured onto a high-frequency carrier. Phase modulation processing is the process of changing the carrier phase in the interference light signal. The phase-modulated interference light intensity signal data is the output signal of the photodetector after modulation processing, and its expression includes a Bessel function expansion.

[0042] Optionally, the sinusoidal phase modulation method specifically involves generating a sinusoidal function from the phase modulation signal to obtain a sinusoidal modulation signal, and then inputting the sinusoidal modulation signal into the Michelson laser interference optical path.

[0043] The phase modulation signal is the electrical signal used to drive the phase modulator. The sine function generation process is the process of generating a sine wave by the DDS module. The sine modulation signal is a high-frequency sine wave with programmable frequency and amplitude.

[0044] Optionally, the sinusoidal modulation signal is input as a carrier signal to the phase modulation channel of the Michelson laser interference optical path.

[0045] The carrier signal is a high-frequency sine wave carrying the displacement information to be measured. The phase modulation channel is a pathway containing a PM fiber phase modulator and its driving circuit, used to apply phase carrier modulation to the reference arm optical path.

[0046] Furthermore, the sinusoidal modulation signal and the interference light intensity signal data are correlated through time synchronization to ensure the synchronization of the phase modulation process and the signal acquisition process. The sinusoidal modulation signal is used as a phase carrier signal to apply high-frequency phase modulation to the reference arm optical path, so that the low-frequency phase change caused by the measured displacement is modulated onto the high-frequency carrier.

[0047] In one possible implementation, S3 specifically includes sub-steps S301 to S304: S301: Generates periodic sinusoidal modulated signals based on sinusoidal phase modulation.

[0048] The periodic sinusoidal modulation signal is generated by a digital signal generation module and output after being controlled by a microcontroller unit.

[0049] Specifically, the digital signal generation module generates a sine wave signal based on direct digital frequency synthesis, and the microcontroller unit is used to control the output timing of the sine wave signal.

[0050] S302: Loads a periodic sinusoidal modulation signal into the phase modulation channel of the Michelson laser interference optical path.

[0051] The phase modulation channel includes an optical fiber phase modulator and a driving circuit.

[0052] Specifically, a periodic sinusoidal modulation signal is loaded onto the fiber phase modulator via a driving circuit to apply phase modulation to the reference arm optical path.

[0053] Furthermore, during the process of loading the periodic sinusoidal modulation signal into the phase modulation channel, the modulation depth can be stabilized at approximately 2.4 rad by adjusting the output amplitude. The calculation formula is as follows:

[0054] in, C Indicates the phase modulation depth. V pp This represents the peak-to-peak voltage of the modulated signal. V π This represents the half-wave voltage of the fiber optic phase modulator.

[0055] Reference manual attached Figure 2 The diagram shows a schematic of the Michelson interference optical path provided in an embodiment of the present invention.

[0056] Specifically, Figure 2 In the diagram: Laser is the laser source. P and H are polarization control elements. PBS is a polarization beam splitter. OC1 and OC2 are fiber couplers. PM is a fiber phase modulator. BS is a beam splitter. PZT is the piezoelectric ceramic under test. PD is a photodetector.

[0057] Furthermore, in terms of their components, the system comprises six main parts: a laser emitting unit, a polarization control unit, an interference beam splitting unit, a phase modulation unit, a measurement and reference arm, and a photoelectric detection unit. In terms of connectivity, the laser output from the laser passes sequentially through the P and H arms before entering the PBS. The PBS splits the light into two paths: one path couples through OC1 into the PM, and then outputs through OC2 to the BS. The other path is directly transmitted to the BS, forming an interference structure between the reference arm and the measurement arm. The BS splits the interference beam, one path entering the PD, and the other entering the PZT. After reflection from the PZT, the beam returns to the BS and superimposes with the reference arm light, forming a dynamic interference signal.

[0058] It should be noted that this optical path converts the micro-displacement of PZT into interference light intensity changes that can be detected by PD through fiber phase modulation and Michelson interference structure, achieving sub-nanometer displacement resolution and providing a stable optical signal basis for subsequent high-precision demodulation of piezoelectric coefficient.

[0059] S303: Based on the phase modulation channel, perform phase response processing on the interference light intensity signal data.

[0060] Phase response processing includes mixing, low-pass filtering, and differential cross-multiplication.

[0061] Specifically, the interference light intensity signal data, under phase modulation, forms a modulated signal containing a carrier term and sideband terms, the expression of which is:

[0062] in, f ( t () indicates time t The corresponding phase difference to be measured, oh 0 represents the angular frequency of the sinusoidal modulation signal, that is, the angular frequency of the carrier signal.

[0063] Further expansion yields:

[0064] in, J 0( C ) represents the zeroth-order Bessel function of the first kind. J 1( C () represents the first-order Bessel function of the first kind. J 2( C ) represents the second-order Bessel function of the first kind, and sin represents the sine function.

[0065] Optionally, phase response processing is performed based on the phase change relationship between the periodic sinusoidal modulation signal and the interference light intensity signal data.

[0066] The phase change relationship is described by the modulation depth and the Bessel function, which determines the amplitude of each harmonic component. The modulated signal formed by phase response processing contains multiple harmonic components, and the amplitude of each harmonic component is determined by the modulation depth parameter.

[0067] In one possible implementation, S303 specifically includes sub-steps S3031 and S3032: S3031: Based on the phase modulation process, phase change mapping processing is performed on the interference light intensity signal data.

[0068] Among them, the phase change mapping process is an operation that superimposes the phase difference caused by the displacement to be measured onto the modulation phase to generate a composite phase term.

[0069] Specifically, by interacting the interference optical signal with the carrier signal, the phase information to be measured is superimposed on the modulation phase.

[0070] S3032: Perform phase response processing on the phase change mapping results.

[0071] The phase change mapping result is a composite phase function that includes the carrier phase and the phase to be measured.

[0072] Specifically, by performing calculations on the mapped signal, a response result containing phase information is obtained.

[0073] S304: Based on the phase response processing results, output phase-modulated interference light intensity signal data.

[0074] The interference light intensity signal data is converted into an electrical signal output by a photodetector.

[0075] Specifically, the photodetector is used to convert light intensity signals into voltage signals and output them to the phase demodulation processing module.

[0076] In this embodiment of the invention, by introducing a sinusoidal phase modulation method, the phase change to be measured is superimposed on the high-frequency carrier signal, so that the originally slowly changing displacement information is moved to the high-frequency signal region for processing, thereby effectively avoiding low-frequency noise interference. In addition, the phase information is separated and extracted by combining the multi-frequency component structure of the signal, so that weak displacement signals can be stably identified in complex background noise, improving the system's anti-interference ability and phase resolution stability.

[0077] S4: The phase-modulated interference light intensity signal data is processed by photoelectric conversion using a photodetector to obtain electrical signal data.

[0078] The photodetector is a device that converts light intensity signals into voltage signals, and a high-speed silicon photodetector is used. Photoelectric conversion processing is the process of converting incident light power into an electrical signal. The electrical signal data is the analog voltage value output by the detector, which includes DC bias, high-frequency carrier, and low-frequency interference terms.

[0079] S5: Perform phase demodulation processing on the electrical signal data to obtain displacement information data.

[0080] Phase demodulation is a technique for extracting phase changes caused by displacement from interference signals, employing a phase-generated carrier demodulation method. The displacement information data is the axial elongation value of the piezoelectric ceramic under test.

[0081] In one possible implementation, S5 specifically includes sub-steps S501 to S505: S501: Performs low-pass filtering on electrical signal data.

[0082] Low-pass filtering is an operation that removes high-frequency components from the signal. A Butterworth low-pass filter is used to remove the second harmonic carrier component.

[0083] S502: Perform orthogonal component extraction processing on the filtered electrical signal data to obtain orthogonal components.

[0084] The orthogonal component extraction process involves multiplying the signal with the reference signal and its 90-degree phase-shifted signal, and then low-pass filtering them to obtain a pair of mutually orthogonal signal components.

[0085] Specifically, after low-pass filtering, two orthogonal signals are obtained, namely... P and Q The expressions are as follows:

[0086]

[0087] in, P This represents the sinusoidal quadrature signal components in the phase generation carrier demodulation process. Q This represents the cosine quadrature signal component in the phase generation carrier demodulation process.

[0088] S503: Perform differential processing on orthogonal components.

[0089] Among them, differential processing involves differentiating and cross-multiplying the orthogonal components to construct the expression for the phase difference.

[0090] Furthermore, through the analysis of P , Q Phase information data can be obtained by performing differentiation, cross-multiplication, subtraction, and integration. The calculation formula is as follows:

[0091] in, arctan Represents the arctangent function. Represents cosine quadrature signal components Q The differential, Represents sinusoidal orthogonal signal components P The differential.

[0092] Reference manual attached Figure 3 The diagram shows the demodulation algorithm analysis provided in the embodiments of the present invention, namely (a) differential cross-multiplication PGC demodulation algorithm and (b) arctangent PGC demodulation algorithm.

[0093] Specifically, Figure 3 The meanings of each module are as follows: carrier signal I'm sorry. c t , cos2ω c t The reference signal is used. The multiplier is used for mixing. LPF is a low-pass filter. DIF↓ is the differentiating and downsampling module. SUB is the subtraction module. INT is the integration module. HPF is a high-pass filter. DIV is the division module. Arctan is the arctangent operation module. i e To demodulate the output phase signal.

[0094] Furthermore, in terms of inclusion relationships, Figure 3 It includes two PGC demodulation processes, both consisting of mixing, low-pass filtering, core demodulation computation, and post-stage filtering. Regarding connectivity: In (a), the input interference signal is multiplied by the two carrier signals respectively. After being low-pass filtered by LPF, the signal enters the DIF↓ module for differentiation. After cross-multiplication, it is subtracted by SUB, integrated by INT, and filtered by HPF to output the time domain signal spectrum.

[0095] (b) The input signal is mixed by two channels and filtered by LPF, then enters DIV phase division, and then passes through Arctan operation and HPF filtering to output the demodulated phase signal \(\theta_e\).

[0096] It should be noted that, Figure 3 Two complementary PGC demodulation implementation paths are provided, which can effectively suppress environmental noise and light intensity disturbances, achieve high-resolution phase demodulation, and provide reliable algorithm support for subsequent high-precision calculation of piezoelectric ceramic displacement and hysteresis characteristics.

[0097] S504: Perform arctangent operation on the differential processing result to obtain phase information data.

[0098] The arctangent operation involves calculating the arctangent of the ratio of the orthogonal components to obtain the enclosed phase value. The phase information data is the change in interference phase difference caused by the displacement to be measured, expressed in radians.

[0099] It should be noted that the wrapped phase can be extracted through arctangent operation, and the calculation formula is as follows:

[0100] in, DO This represents the wrapped phase value, which is directly obtained from the arctangent operation and ranges from [value missing]. Phase difference within.

[0101] Furthermore, by combining this with a phase unwrapping algorithm, the phase change caused by the PZT displacement can be extracted at high resolution. .

[0102] S505: Displacement information data is calculated based on phase information data.

[0103] The displacement information is calculated by multiplying the phase difference by the laser wavelength and dividing by four times pi. The formula is: displacement equals phase difference multiplied by wavelength divided by four times pi.

[0104] Specifically, using the calibrated wavelength parameters, the program converts the phase change into actual displacement, and the calculation formula is as follows:

[0105] in, ΔL This represents the actual displacement generated by the piezoelectric ceramic (PZT) under test, 4 π This represents a fixed coefficient determined by the round-trip propagation characteristics of the Michelson interferometer optical path.

[0106] It should be noted that the formula for calculating displacement information data based on phase information data is:

[0107] in, f ( t () indicates time t The corresponding continuous phase information data.

[0108] It should be noted that this formula converts the phase difference change into the actual displacement of the piezoelectric ceramic, achieving sub-nanometer displacement resolution.

[0109] In this embodiment of the invention, phase demodulation processing is performed on the electrical signal to extract phase change information caused by displacement from the modulated complex signal, and the phase change process is recovered by utilizing the relationship between orthogonal signal components, thereby converting the interference signal into continuous displacement information. This enables the signal that was originally affected by noise to be effectively restored to a stable displacement change curve, improving the accuracy and continuity of phase extraction, and enhancing the resolvability under weak signal conditions.

[0110] S6: Perform piezoelectric coefficient calculation on the piezoelectric response relationship between displacement information data and drive signal data to obtain the piezoelectric coefficient measurement result.

[0111] The piezoelectric response is a function curve of displacement versus voltage, including rise and fall curves. The piezoelectric coefficient calculation involves linearly fitting the displacement-voltage curve to determine its slope. The piezoelectric coefficient measurement result is a parameter characterizing the electromechanical conversion efficiency of the piezoelectric material, expressed in nanometers per volt.

[0112] Furthermore, by combining the voltage values ​​at each step, the slope is automatically calculated using least-squares linear fitting, yielding the piezoelectric coefficient and the linearity of the fit. The formula for calculating the linearity is:

[0113] in, R 2 The linearity (coefficient of determination) of the displacement-voltage curve is used to measure how well the displacement response of a piezoelectric ceramic fits the ideal linear relationship. SS res This represents the sum of squares of the residuals, which is the sum of the squares of the differences between each measured displacement value and the corresponding displacement value of the fitted line. SS tot It represents the total sum of squares, that is, the sum of the squares of the differences between each measured displacement value and the average displacement value.

[0114] For example, the system can calculate the nonlinear hysteresis using a standardized hysteresis metric formula. The calculation process is as follows:

[0115] in, H This represents the nonlinear hysteresis of piezoelectric ceramics, used to quantitatively describe the degree of deviation between the rise and fall of the displacement-voltage curve. ΔL diff This represents the maximum difference between the lift and return displacements under the same driving voltage. ΔL max This indicates the maximum displacement generated by the piezoelectric ceramic within the driving voltage range.

[0116] For example:

[0117] It should be noted that the continuity equations for the lift and return displacements can be obtained separately through polynomial fitting, for example:

[0118]

[0119] in, The displacement response equation represents the voltage rise phase, i.e., the displacement as a function of voltage as the driving voltage increases. The displacement response equation represents the voltage return phase, i.e., the displacement as a function of voltage change when the driving voltage decreases. U Indicates the driving voltage value. m This indicates the order of the polynomial fit. a k The polynomial fitting coefficients represent the lift curve. b k The polynomial fitting coefficients represent the return curve.

[0120] For example:

[0121]

[0122] Furthermore, by differentiating the fitted lift and return curves, the lift piezoelectric coefficient and return piezoelectric coefficient can be obtained, respectively, and their calculation formulas are as follows:

[0123]

[0124] in, This represents the transient piezoelectric coefficient during the voltage rise phase, i.e., the rate of change of displacement with respect to voltage as the driving voltage increases. This represents the transient piezoelectric coefficient during the voltage return phase, i.e., the rate of change of displacement with respect to voltage as the driving voltage decreases. The equation representing the lift-displacement response is as follows: The equation representing the return displacement response is as follows: k Indicates the order index of a polynomial term.

[0125] For example:

[0126]

[0127] Furthermore, to quantitatively describe the degree of hysteresis, a hysteresis degree H can be defined, and its calculation formula is as follows:

[0128] in,U max Indicates the maximum value of the driving voltage. ΔL max This indicates the maximum displacement produced by the piezoelectric ceramic within the driving voltage range. This represents absolute value operations.

[0129] In this embodiment of the invention, by establishing the correspondence between displacement change and driving voltage, the lift and return data are modeled and analyzed separately to obtain the response characteristics of piezoelectric materials under different driving conditions. By comparing the differences between lift and return, the hysteresis characteristics of the material are quantitatively described, so that the calculation results of the piezoelectric coefficient can more comprehensively reflect the actual performance of the material and improve the completeness and engineering applicability of piezoelectric parameter evaluation.

[0130] Reference manual attached Figure 4 The diagram shows a schematic of the piezoelectric coefficient measurement system based on a sinusoidal phase modulation laser interferometer provided in an embodiment of the present invention.

[0131] This invention provides a piezoelectric coefficient measurement system 20 based on a sinusoidal phase-modulated laser interferometer, comprising: a processor 201 and a memory 202; The memory 202 stores programs or instructions that can run on the processor 201. When the program or instructions are executed by the processor 201, they implement the steps of the above-described method for measuring the piezoelectric coefficient of a laser interferometer based on sinusoidal phase modulation, and achieve the same technical effect. To avoid repetition, the present invention will not elaborate further.

[0132] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer, characterized in that, include: S1: Acquire the driving signal data of the piezoelectric ceramic under test and the interference light intensity signal data of the Michelson laser interference optical path; S2: Construct the Michelson laser interference optical path; S3: Based on the sinusoidal phase modulation method, phase modulation is applied to the Michelson laser interference optical path, and the interference light intensity signal data input to the Michelson laser interference optical path is subjected to phase modulation processing to obtain phase-modulated interference light intensity signal data; S4: The phase-modulated interference light intensity signal data is processed by photoelectric conversion using a photodetector to obtain electrical signal data; S5: Perform phase demodulation processing on the electrical signal data to obtain displacement information data; S6: Perform piezoelectric coefficient calculation on the piezoelectric response relationship between the displacement information data and the driving signal data to obtain the piezoelectric coefficient measurement result.

2. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 1, characterized in that, The driving signal data is used to drive and control the piezoelectric ceramic under test so that the piezoelectric ceramic under test produces a displacement change, wherein there is a corresponding relationship between the driving signal data and the displacement change.

3. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 1, characterized in that, The Michelson laser interferometer optical path includes a reference arm optical path and a measurement arm optical path, wherein the measurement arm optical path corresponds to the displacement change of the piezoelectric ceramic under test.

4. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 1, characterized in that, The sinusoidal phase modulation method specifically involves generating a sinusoidal function from the phase modulation signal to obtain a sinusoidal modulation signal, and then inputting the sinusoidal modulation signal into the Michelson laser interference optical path.

5. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 4, characterized in that, The sinusoidal modulation signal is input as a carrier signal to the phase modulation channel of the Michelson laser interference optical path.

6. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 1, characterized in that, S3 specifically includes: S301: Based on the sinusoidal phase modulation method, generate a periodic sinusoidal modulation signal; S302: The periodic sinusoidal modulation signal is applied to the phase modulation channel of the Michelson laser interference optical path; S303: Based on the phase modulation channel, perform phase response processing on the interference light intensity signal data; S304: Based on the phase response processing results, output phase-modulated interference light intensity signal data.

7. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 6, characterized in that, The phase response processing is based on the phase change relationship between the periodic sinusoidal modulation signal and the interference light intensity signal data.

8. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 6, characterized in that, Specifically, S303 includes: S3031: Based on the phase modulation process, the interference light intensity signal data is subjected to phase change mapping processing; S3032: Perform phase response processing on the phase change mapping results.

9. The method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer according to claim 1, characterized in that, S5 specifically includes: S501: Perform low-pass filtering on the electrical signal data; S502: Perform orthogonal component extraction processing on the filtered electrical signal data to obtain orthogonal components; S503: Perform differential processing on the orthogonal components; S504: Perform arctangent operation on the differential processing result to obtain phase information data; S505: Based on the phase information data, the displacement information data is calculated.

10. A piezoelectric coefficient measurement system based on a sinusoidal phase-modulated laser interferometer, characterized in that, include: Processor and memory; The memory stores programs or instructions that can run on the processor, which, when executed by the processor, implement the steps of the method for measuring the piezoelectric coefficient based on a sinusoidal phase-modulated laser interferometer as described in any one of claims 1 to 9.

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