Tunable F-P filter based on capacitance micro-displacement detection and control method

Abstract

The invention relates to a tunable F-P filter based on capacitance micro-displacement detection and a control method, and aims to solve the technical problems of low adjustment precision and stability of an interference cavity in the prior art. According to the tunable F-P filter based on capacitor micro-displacement detection, the reference capacitor and the five detection capacitors are arranged, two of the five detection capacitors form a differential circuit used for detecting the X-direction parallelism change of an interference cavity, and the other two detection capacitors form a differential circuit used for detecting the Y-direction parallelism change of the interference cavity. And the rest detection capacitor is adjacent to the reference capacitor, and the detection capacitor and the reference capacitor form a differential circuit which is used for detecting the Z-direction cavity length change of the interference cavity, so that the detection direction of the interference cavity is consistent with the adjustment direction of the piezoelectric ceramic to the interference cavity, and high-precision adjustment and high stability of the interference cavity are realized.

Description

TECHNICAL FIELD

[0001] The application relates to a tunable F-P filter, in particular to a tunable F-P filter based on capacitive micro-displacement detection and a control method. BACKGROUND

[0002] With the rapid development of the field of precision optics, there is an urgent requirement for extremely narrow bandwidth filters to meet the application demand of ultrahigh spectral resolution. A tunable Fabry-Perot (F-P) etalon becomes a key functional device in a spectral selection and imaging system due to its excellent wavelength selectivity, narrow-band transmissivity and high tuning accuracy, and is widely used in many technical fields such as hyperspectral imaging, laser wavelength control, environmental monitoring, industrial detection and biosensing. The tunable function of the F-P etalon is usually achieved by driving one of the mirrors to change the length of the interference cavity, so as to continuously adjust the center wavelength and thus narrow-band filter the specified wavelength signal. With the development of science and technology, the tuning accuracy and stability of the center wavelength need to reach the picometer level, and the size accuracy of the length and parallelism of the F-P etalon needs to reach the nanometer level, so the adjustment accuracy and stability of the interference cavity need to reach the sub-nanometer level.

[0003] The tunable F-P filter usually uses a piezoelectric ceramic to achieve sub-nanometer step adjustment of the interference cavity. However, due to the hysteresis, creep and nonlinearity of the piezoelectric ceramic, the positioning accuracy and stability accuracy of the piezoelectric ceramic are poor. By using a capacitive sensor to close-loop control the piezoelectric ceramic, the positioning accuracy and stability accuracy of the piezoelectric ceramic can be improved. The prior art usually uses three capacitive sensors to detect the direction and length of the interference cavity. There are capacitive measurement errors caused by electromagnetic interference, temperature, humidity and air pressure, which lead to differences between the detection direction of the capacitive sensor and the adjustment direction of the piezoelectric ceramic to the interference cavity, thereby affecting the closed-loop control of the piezoelectric ceramic, and resulting in low adjustment accuracy and stability of the piezoelectric ceramic to the interference cavity. SUMMARY

[0004] The application aims to solve the technical problem of low adjustment accuracy and stability of the interference cavity of the existing tunable F-P filter, and provides a tunable F-P filter based on capacitive micro-displacement detection and a control method.

[0005] To achieve the above-mentioned purpose, the technical solution provided by the application is as follows:

[0006] The application discloses a tunable F-P filter based on capacitive micro displacement detection, and has the characteristics that an upper reflecting plate is connected with a bottom plate through piezoelectric ceramics; a lower reflecting plate is arranged on the bottom plate, and the reflecting surface of the lower reflecting plate is arranged opposite to the reflecting surface of the upper reflecting plate; the upper reflecting plate and the lower reflecting plate are both cylindrical, and the diameter of the upper reflecting plate is larger than that of the lower reflecting plate; and the reflecting surfaces of the upper reflecting plate and the lower reflecting plate form an interference cavity for narrowband filtering of signals of a specified wavelength.

[0007] The piezoelectric ceramics include first piezoelectric ceramics P1, second piezoelectric ceramics P2 and third piezoelectric ceramics P3, which are uniformly distributed along the periphery of the lower reflecting plate, and one end of each of the piezoelectric ceramics is fixed on the upper reflecting plate, and the other end is connected with the bottom plate through a trimming pad; the center line of the second piezoelectric ceramics P2 and the third piezoelectric ceramics P3 is parallel to the X axis of the interference cavity, and is used for adjusting the X direction angle of the interference cavity; the first piezoelectric ceramics P1 is used for adjusting the Y direction angle of the interference cavity; and the three piezoelectric ceramics are used for adjusting the Z direction cavity length of the interference cavity.

[0008] The bottom plate is further provided with a reference capacitor and five detection capacitors which are distributed along the periphery of the lower reflecting plate; one detection capacitor is arranged near each piezoelectric ceramic; and the reference capacitor is arranged between any two piezoelectric ceramics; the center line of the detection capacitors near the second piezoelectric ceramics P2 and the third piezoelectric ceramics P3 is parallel to the X axis of the interference cavity, and the two detection capacitors constitute a differential circuit and are used for detecting the parallelism change of the X direction of the interference cavity; the center line of the detection capacitor near the first piezoelectric ceramics P1 and the remaining one detection capacitor is parallel to the Y axis of the interference cavity, and the two detection capacitors constitute a differential circuit and are used for detecting the parallelism change of the Y direction of the interference cavity; and the remaining one detection capacitor and the reference capacitor are adjacent, and the two detection capacitors constitute a differential circuit and are used for detecting the cavity length change of the Z direction of the interference cavity.

[0009] Further, the five detection capacitors are a first detection capacitor C X1 , a second detection capacitor C X2 , a third detection capacitor C Y1 , a fourth detection capacitor C Y2 and a fifth detection capacitor C Z2 ; the reference capacitor is defined as a reference capacitor C Z1 ; the fourth detection capacitor C Y2 and the first detection capacitor C X1 are sequentially arranged between the first piezoelectric ceramics P1 and the second piezoelectric ceramics P2, and the fourth detection capacitor C Y2 is arranged near the first piezoelectric ceramics P1, and the first detection capacitor C X1 is arranged near the second piezoelectric ceramics P2; the third detection capacitor C Y1 is arranged between the second piezoelectric ceramics P2 and the third piezoelectric ceramics P3; and the third detection capacitor C Y1and the fourth detection capacitor C Y2 The connecting line of the center point is parallel to the Y axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the Y direction of the interference cavity; the fifth detection capacitor C Z2 and the second detection capacitor C X2 , the fifth detection capacitor C Z2 is arranged close to the first piezoelectric ceramic P1, the second detection capacitor C X2 is arranged close to the third piezoelectric ceramic P3, and the second detection capacitor C X2 and the first detection capacitor C X1 The connecting line of the center point is parallel to the X axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the X direction of the interference cavity; the reference capacitor C Z1 is arranged between the fifth detection capacitor C Z2 and the second detection capacitor C X2 , and is arranged close to the fifth detection capacitor C Z2 , the reference capacitor C Z1 and the fifth detection capacitor C Z2 constitute a differential circuit for detecting the cavity length change of the Z direction of the interference cavity.

[0010] Further, the reference capacitor includes a cover plate, a reference capacitor bottom plate, and a reference capacitor column and a reference capacitor trimming pad arranged on the reference capacitor bottom plate, the reference capacitor trimming pad is annular, and the reference capacitor column is located in the inner ring of the reference capacitor trimming pad; the cover plate is connected through the reference capacitor trimming pad and the reference capacitor bottom plate, the top surface of the reference capacitor column is arranged opposite to the bottom surface of the cover plate, and the bottom surface of the cover plate and the top surface of the reference capacitor column are both plated with electrodes, and a fixed capacitor gap is formed between the two, for correcting the fifth detection capacitor C Z2 during differential input.

[0011] Further, the detection capacitor is composed of two capacitor columns with different diameters, the two capacitor columns are coaxially arranged, one end of the capacitor column with a larger diameter is arranged on the bottom plate, and one end of the capacitor column with a smaller diameter is arranged on the bottom surface of the upper reflection plate, electrodes are plated on the other end of the capacitor column with a larger diameter and the other end of the capacitor column with a smaller diameter, and a capacitor gap is formed between the two, for detecting the parallelism change of the X direction and the Y direction of the interference cavity and the cavity length change of the Z direction.

[0012] Further, the stroke D of the piezoelectric ceramic satisfies the following conditions:

[0013] D≥D1+D2+D3

[0014] In the formula, D1 is the filter cavity length adjustment stroke, D2 is the initial installation error of the interference cavity, and D3 is the piezoelectric ceramic allowance.

[0015] Further, the relationship between the stroke D of the piezoelectric ceramic and the length L of the piezoelectric ceramic can be expressed as:

[0016] D=k P VL

[0017] In the formula, k P is the piezoelectric strain constant of the piezoelectric ceramic, and V is the maximum working voltage of the piezoelectric ceramic.

[0018] Meanwhile, the application also provides a control method of the tunable F-P filter based on the capacitive micro displacement detection, which adopts the tunable F-P filter based on the capacitive micro displacement detection, and has the following steps:

[0019] Step 1: when the F-P filter is used for the first time or at the preset calibration time, calibrate the F-P filter, detect the capacitance values of each detection capacitor and the reference capacitor after calibration, and obtain the voltage difference V X0 X of the X-direction differential circuit, the voltage difference V Y0 Y of the Y-direction differential circuit, and the voltage difference V Z0 Z of the Z-direction differential circuit after the capacitance values are processed by an external detection circuit, and take V X0 , V Y0 , and V Z0 as the correction voltages;

[0020] When the piezoelectric ceramic, the reference capacitor and the detection capacitor are working, the capacitance values of each detection capacitor and the reference capacitor are detected in real time, the output voltages of the X-direction differential circuit, the Y-direction differential circuit and the Z-direction differential circuit are obtained after the capacitance values are processed by an external detection circuit, and whether the difference between the output voltages and the correction voltages is zero is calculated to determine whether the cavity length of the Z-direction of the interference cavity and the parallelism of the X-direction and the Y-direction are at the ideal position, if the difference is 0, the cavity length of the Z-direction of the interference cavity and the parallelism of the X-direction and the Y-direction are at the ideal position, and the tunable F-P filter normally performs the filtering work, if the difference is not 0, step 2 is executed;

[0021] Step 2: detect the capacitance variation between the capacitance values of each detection capacitor and the reference capacitor and the standard capacitance value, obtain the output voltages of the X-direction differential circuit, the Y-direction differential circuit and the Z-direction differential circuit after the capacitance variation is processed by an external detection circuit, and calculate the difference V X , V Y , and V Z between the output voltages and the correction voltages, respectively, and take V X , V Y , and V Z as the voltage variation signals of the X-direction, the Y-direction and the Z-direction;

[0022] Step 3, according to the voltage change signal obtained in step 2, the angle adjustment amount of the interference cavity in X direction and Y direction, and the cavity length adjustment amount in Z direction are calculated;

[0023] Step 4, according to the angle adjustment amount of the interference cavity in X direction and Y direction, and the cavity length adjustment amount in Z direction obtained in step 3, the adjustment amount of each piezoelectric ceramic in Z direction is calculated;

[0024] Step 5, according to the adjustment amount of each piezoelectric ceramic in Z direction obtained in step 4, the corresponding driving voltage is output by the external piezoelectric ceramic driving circuit, and the piezoelectric ceramic is adjusted, so as to complete the adjustment of the X direction angle, Y direction angle and Z direction cavity length of the interference cavity;

[0025] Step 6, the capacitance values of the current detection capacitance and the reference capacitance are detected, and the output voltages of the X direction differential circuit, the Y direction differential circuit and the Z direction differential circuit are obtained after the capacitance values are processed by the external detection circuit. Whether the difference between the output voltage and the correction voltage is zero is calculated to determine whether the cavity length of the interference cavity in Z direction and the parallelism of the interference cavity in X direction and Y direction are in the ideal position. If the difference is 0, the cavity length of the interference cavity in Z direction and the parallelism of the interference cavity in X direction and Y direction are in the ideal position, the control of the tunable F-P filter is completed, and the tunable F-P filter normally performs filtering work. If the difference is not 0, return to step 2 until the cavity length of the interference cavity in Z direction and the parallelism of the interference cavity in X direction and Y direction are in the ideal position after adjustment, so as to complete the adjustment of the tunable F-P filter, and continuously monitor and keep the interference cavity in the ideal position, so that the tunable F-P filter normally performs filtering work.

[0026] Further, the output voltage V C of the differential circuit in step 2 is calculated as follows:

[0027] V C = k V C

[0028] C = C0 + ΔC

[0029] Wherein, k V is the voltage conversion coefficient of the capacitance detection circuit, C is the current capacitance value, C0 is the calibration capacitance value, and ΔC is the capacitance change amount. The calculation formula of ΔC is as follows:

[0030]

[0031] Wherein, A is the effective area of the detection capacitance, d c is the capacitance gap, ε0 is the vacuum dielectric constant, ε r is the relative dielectric constant of the medium in the capacitance gap, and Δd c is the capacitance gap change amount.

[0032] Further, the angle adjustment amount R of the interference cavity in the X direction in step 3 is calculated X The formula is as follows:

[0033]

[0034] V X = k V (C X2 -C X1 )- V X0

[0035] In the formula, k d is a coefficient for converting voltage to displacement amount, V X0 is a calibration voltage of the X direction differential circuit of the calibrated filter, C X1 is a capacitance value of the first detection capacitor C X1 , C X2 is a capacitance value of the second detection capacitor C X2 , and L X1 is a distance between the center points of the first detection capacitor C X1 and the second detection capacitor C X2 .

[0036] The angle adjustment amount R of the interference cavity in the Y direction is calculated Y The formula is as follows:

[0037]

[0038] V Y = k V (C Y2 -C Y1 )- V Y0

[0039] In the formula, V Y0 is a calibration voltage of the Y direction differential circuit of the calibrated filter, C Y1 is a capacitance value of the third detection capacitor C Y1 , C Y2 is a capacitance value of the fourth detection capacitor C Y2 , and L Y1 is a distance between the center points of the third detection capacitor C Y1 and the fourth detection capacitor C Y2 .

[0040] The cavity length adjustment amount T of the interference cavity in the Z direction is calculated Z The formula is as follows:

[0041] T Z = k d V Z + Δd z

[0042] VZ =k V (C Z2 -C Z1 )-V Z0

[0043] In the formula, V Z0 C is the calibration voltage for the Z-axis differential circuit of the calibrated filter. Z1 Reference capacitor C Z1 The capacitance value, C Z2 The fifth detection capacitor C Z2 The capacitance value, Δd z This is the adjustment amount of the cavity length relative to the zero position.

[0044] Further, in step 4, the adjustment amount [d1, d2, d3] of the piezoelectric ceramic (6) in the Z direction is calculated using the following formula:

[0045]

[0046] In the formula, A -1 Let A be the inverse transformation matrix of the forward transformation matrix A. The forward transformation matrix A is:

[0047]

[0048] In the formula, L X2 L is the distance between the center points of piezoelectric ceramics P2 and P3. Y2 L is the distance between the center points of piezoelectric ceramics P2 and P1. X3 For piezoelectric ceramic P1 and fifth detection capacitor C Z2 The distance L between the centers Y3 For piezoelectric ceramic P3 and the fifth detection capacitor C Z2 The distance between the center points.

[0049] The beneficial effects of this invention are:

[0050] 1. The present invention provides a tunable FP filter based on capacitor micro-displacement detection. The capacitor micro-displacement detection circuit, composed of a detection capacitor and a reference capacitor, together with the piezoelectric ceramic drive, forms a high-precision closed-loop control circuit, enabling the tunable FP filter to have good tuning accuracy and stability.

[0051] 2. The present invention provides a tunable FP filter based on capacitor micro-displacement detection. The differential detection circuit composed of detection capacitors can compensate for capacitance measurement errors caused by electromagnetic interference, temperature, humidity and air pressure. Furthermore, the structural dimensions, materials and capacitor gaps of each detection capacitor are consistent, and the thermal characteristics of the detection capacitors are consistent, which makes the parallelism of the interference cavity of the tunable FP filter very stable.

[0052] 3. The tunable F-P filter based on the capacitance micro displacement detection, the temperature stability of the reference capacitance is very good, the fifth detection capacitance C Z2 The reference capacitance C Z1 is calibrated, so that the stability of the cavity length of the tunable F-P filter approaches the stability of the reference capacitance, and the capacitance change caused by the cavity length adjustment is also very small under the influence of temperature, so that the cavity length tuning accuracy reaches the sub-nanometer level.

[0053] 4. The control method of the tunable F-P filter based on the capacitance micro displacement detection, the capacitance change amount of the detection capacitance is calculated to obtain the adjustment amount required by the parallelism of the interference cavity and the cavity length, and the adjustment amount of the piezoelectric ceramic can be conveniently obtained through the deduced inverse conversion matrix, so that the adjustment accuracy and stability of the interference cavity reach the sub-nanometer level, and finally the tuning accuracy and stability of the tunable F-P filter reach the picometer level. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 It is a structure schematic view of the embodiment of the tunable F-P filter based on the capacitance micro displacement detection.

[0055] Figure 2 It is a distribution schematic view of the piezoelectric ceramic, the detection capacitance and the reference capacitance in the embodiment of the tunable F-P filter based on the capacitance micro displacement detection.

[0056] Figure 3 It is a structure schematic view of the reference capacitance in the embodiment of the tunable F-P filter based on the capacitance micro displacement detection.

[0057] Figure 4 It is a principle schematic view of the control method of the tunable F-P filter based on the capacitance micro displacement detection.

[0058] The reference signs are explained as follows: 1 - upper reflection plate, 2 - lower reflection plate, 3 - bottom plate, 4 - reference capacitance, 41 - cover plate, 42 - reference capacitance column, 43 - reference capacitance trimming pad, 44 - reference capacitance bottom plate, 5 - detection capacitance, 6 - piezoelectric ceramic, 7 - trimming pad. DETAILED DESCRIPTION

[0059] The application will be further described below in combination with the drawings and embodiments.

[0060] As Figure 1 and Figure 2As shown, the tunable F-P filter based on capacitive micro displacement detection of the present application comprises an upper reflecting plate 1 and a bottom plate 3, the upper reflecting plate 1 is connected with the bottom plate 3 through a piezoelectric ceramic 6; the bottom plate 3 is provided with a lower reflecting plate 2, the reflecting surface of the lower reflecting plate 2 is oppositely arranged with the reflecting surface of the upper reflecting plate 1, the upper reflecting plate 1 and the lower reflecting plate 2 are both cylindrical and the diameter of the upper reflecting plate 1 is larger than that of the lower reflecting plate 2, the reflecting surfaces of the upper reflecting plate 1 and the lower reflecting plate 2 form an interference cavity for narrowband filtering of signals of specified wavelengths.

[0061] The piezoelectric ceramic 6 comprises a first piezoelectric ceramic P1, a second piezoelectric ceramic P2 and a third piezoelectric ceramic P3, which are uniformly distributed along the outer periphery of the lower reflecting plate 2 respectively, one end of each is fixed on the upper reflecting plate 1 and the other end is connected with the bottom plate 3 through a trimming pad 7, the trimming pad 7 is used for compensating the height of the piezoelectric ceramic 6 and can compensate the initial installation accuracy of the interference cavity, the connecting line of the center points of the second piezoelectric ceramic P2 and the third piezoelectric ceramic P3 is parallel to the X axis of the interference cavity, which is used for adjusting the X direction angle of the interference cavity, the vertical distance from the center point of the first piezoelectric ceramic P1 to the connecting line is parallel to the Y axis of the interference cavity, which is used for adjusting the Y direction angle of the interference cavity, the piezoelectric ceramic P2 and the piezoelectric ceramic P3 are adjusted simultaneously and the adjustment amount is opposite, the position of the midpoint of the piezoelectric ceramic P2 and the piezoelectric ceramic P3 is kept unchanged, the X direction and the Y direction are orthogonal, the adjustment of the piezoelectric ceramic P1 will not affect the parallelism of the X direction of the interference cavity, the piezoelectric ceramic P1, the piezoelectric ceramic P2 and the piezoelectric ceramic P3 are adjusted simultaneously and the adjustment amount is consistent, the three piezoelectric ceramics are used together for adjusting the Z direction cavity length of the interference cavity.

[0062] The bottom plate 3 is further provided with a reference capacitor 4 and five detection capacitors 5 which are distributed along the outer periphery of the lower reflecting plate 2, the detection capacitor 5 is composed of two capacitive columns with different diameters, the two capacitive columns are coaxially arranged, one end of the capacitive column with larger diameter is arranged on the bottom plate 3 and one end of the capacitive column with smaller diameter is arranged on the upper reflecting plate 1, electrodes are plated on the other end of the capacitive column with larger diameter and the other end of the capacitive column with smaller diameter, the end surface area of the other end of the capacitive column with smaller diameter is the effective sensing area of the capacitor, a capacitor gap is formed between the two, which is used for detecting the parallelism changes of the X direction and the Y direction of the interference cavity and the cavity length changes of the Z direction; the structure size, material, capacitor gap and other parameters of each detection capacitor 5 are consistent, the thermal characteristics of each detection capacitor 5 are consistent, the parallelism of the X direction and the Y direction is respectively calculated by differential operation of two detection capacitors, after the filter is calibrated, the closed loop control loop of the piezoelectric ceramic 6 maintains the constant capacitor difference, so that the parallelism of the interference cavity of the filter has very good stability.

[0063] The five detection capacitors 5 are respectively a first detection capacitor C X1 , a second detection capacitor C X2 , a third detection capacitor C Y1 , a fourth detection capacitor C Y2 and a fifth detection capacitor CZ2 The reference capacitor 4 is defined as the reference capacitor C. Z1 The fourth detection capacitor C is sequentially disposed between the first piezoelectric ceramic P1 and the second piezoelectric ceramic P2. Y2 and the first detection capacitor C X1 And the fourth detection capacitor C Y2 The first detection capacitor C is positioned close to the first piezoelectric ceramic P1. X1 The third detection capacitor C is positioned close to the second piezoelectric ceramic P2; the third detection capacitor C is positioned between the second piezoelectric ceramic P2 and the third piezoelectric ceramic P3. Y1 And the third detection capacitor C Y1 and the fourth detection capacitor C Y2 The line connecting the center points is parallel to the Y-axis of the interference cavity, and the two form a differential circuit used to detect changes in the parallelism of the interference cavity in the Y direction; the fifth detection capacitor C is sequentially arranged between the first piezoelectric ceramic P1 and the third piezoelectric ceramic P3. Z2 Second detection capacitor C X2 The fifth detection capacitor C Z2 The second detection capacitor C is positioned close to the first piezoelectric ceramic P1. X2 It is positioned close to the third piezoelectric ceramic P3, and the second detection capacitor C X2 and the first detection capacitor C X1 The line connecting the center points is parallel to the X-axis of the interference cavity, and the two form a differential circuit used to detect changes in the parallelism of the interference cavity in the X-axis; the reference capacitor C Z1 Set in the fifth detection capacitor C Z2 Second detection capacitor C X2 Between, and close to the fifth detection capacitor C Z2 Set the reference capacitor C. Z1 and the fifth detection capacitor C Z2 A differential circuit is constructed to detect the change in cavity length in the Z direction of the interference cavity.

[0064] like Figure 3 As shown, the reference capacitor 4 includes a cover plate 41, a reference capacitor base plate 44, and a reference capacitor post 42 and a reference capacitor trimming pad 43 disposed on the reference capacitor base plate 44. The reference capacitor trimming pad 43 is annular, and the reference capacitor post 42 is located in the inner ring of the reference capacitor trimming pad 43. The reference capacitor trimming pad 43 is used to adjust the capacitance gap between the reference capacitor 4 and the detection capacitor 5 to be approximately the same. The cover plate 41 is connected to the reference capacitor base plate 44 through the reference capacitor trimming pad 43. Electrodes are plated on the bottom surface of the cover plate 41 and one end face of the reference capacitor post 42, forming a capacitance gap between them. The reference capacitor C Z1 Approaching the fifth detection capacitor C Z2 Configure the fifth detection capacitor C. Z2 Perform calibration. Reference capacitor C Z1The material is quartz with low expansion coefficient, and the reference capacitor 4 is a fixed gap, for example, the quartz expansion coefficient is 0.5x10 -6 , the capacitor gap is 0.1mm, and the thermal stability of the capacitor gap is 0.05nm / ℃. It can be considered that the capacitor gap of the reference capacitor 4 is very stable.

[0065] Generally, a single detection capacitor 5 can achieve sub-nanometer resolution micro-displacement detection, but the detection capacitor 5 and the reference capacitor 4 are extremely sensitive to electromagnetic interference, temperature, humidity, air pressure and other factors, and it is difficult to achieve long-period sub-nanometer stable detection. Through differential correction of the detection capacitor 5 and the reference capacitor 4, sub-nanometer stable detection can be achieved. The center line of the first detection capacitor C X1 and the second detection capacitor C X2 is parallel to the X axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the X direction of the interference cavity. The center line of the third detection capacitor C Y1 and the fourth detection capacitor C Y2 is parallel to the Y axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the Y direction of the interference cavity. The reference capacitor C Z1 and the fifth detection capacitor C Z2 constitute a differential circuit for detecting the cavity length change of the Z direction of the interference cavity. After the filter is calibrated, the piezoelectric ceramic closed-loop control circuit maintains the constant capacitor difference, which can make the stability of the filter interference cavity length close to the stability of the reference capacitor C Z1 , so that the interference cavity length reaches the sub-nanometer level, and the capacitance change caused by the adjustment of the interference cavity length is also very small, so that the tuning accuracy of the filter interference cavity length reaches the sub-nanometer level.

[0066] In addition to the piezoelectric ceramic 6, the materials of the remaining elements are all selected from quartz materials with low expansion coefficient. The upper reflection plate 1 and the bottom plate 3 are supported by three piezoelectric ceramics for adjusting the length and parallelism of the interference cavity. The stroke D of the piezoelectric ceramic 6 is selected to satisfy:

[0067] D≥D1+D2+D3

[0068] In the formula, D1 is the filter cavity length adjustment stroke, D2 is the initial installation error of the interference cavity, and D3 is the piezoelectric ceramic excess. Generally, the filter cavity length adjustment stroke needs to satisfy the adjustment of 3-5 free spectral ranges, the initial installation accuracy of the interference cavity needs to reach the micron level, and the piezoelectric ceramic excess accounts for 20% of the total stroke of the piezoelectric ceramic;

[0069] The relationship between the stroke D of the piezoelectric ceramic 6 and the length L of the piezoelectric ceramic 6 can be expressed as:

[0070] D=k P VL

[0071] In the formula, k Pdenoted as ρ, where ρ is the piezoelectric strain constant of the piezoelectric ceramic, and V is the maximum operating voltage of the piezoelectric ceramic.

[0072] This embodiment presents a control method for a tunable FP filter based on capacitor micro-displacement detection, such as... Figure 4 As shown, its working principle is as follows: based on the first detection capacitor C in the tunable FP filter... X1 Second detection capacitor C X2 The third detection capacitor C Y1 Fourth detection capacitor C Y2 Fifth detection capacitor C Z2 and reference capacitor C Z1 The capacitance value corresponding to each capacitance gap is calculated, and each capacitance value is converted into a first voltage signal V by an external detection circuit. CX1 Second voltage signal V CX2 Third voltage signal V CY1 Fourth voltage signal V CY2 Fifth voltage signal V CZ1 and the sixth voltage signal V CZ2 The calibrated compensation voltage V X0 V Y0 and V ZO Correction is performed to obtain the corrected voltage V. X V Y and V Z According to the corrected voltage V X V Y and V Z Calculate the X-axis angle adjustment R of the interference cavity X Y-axis angle adjustment amount R Y Z-axis cavity length adjustment T Z The adjustment amount is transformed by the inverse transformation matrix A -1 After processing, the adjustment values ​​d1, d2 and d3 of piezoelectric ceramics P1, P2 and P3 are obtained. The external piezoelectric ceramic driving circuit outputs driving voltages V1, V2 and V3 according to the adjustment values ​​d1, d2 and d3. The driving voltages V1, V2 and V3 drive the piezoelectric ceramics to be adjusted to the appropriate position.

[0073] This embodiment presents a control method for a tunable FP filter based on capacitance micro-displacement detection. The method employs the aforementioned tunable FP filter based on capacitance micro-displacement detection and includes the following steps:

[0074] Step 1, when the F-P filter is assembled for the first time or at a preset calibration time, use a laser with a known wavelength as a calibration light source, vertically incident on the F-P filter through a collimating mirror, and use a detector to collect an interference image for judgment. After manually adjusting the piezoelectric ceramic 6 to achieve the desired parallelism and cavity length, the energy transmitted reaches a maximum, and the F-P filter calibration is complete. After the current detection capacitors 5 and the reference capacitor 4 are processed by an external detection circuit, the voltage differences V X0 , V Y0 , and V Z0 of the X, Y, and Z differential circuits are obtained. X0 Y0 Z0 as the correction voltage;

[0075] When the control circuit is working, the capacitance values of the current detection capacitors 5 and the reference capacitor 4 are detected in real time. After the capacitance values are processed by an external detection circuit, the output voltages of the X, Y, and Z differential circuits are obtained. By calculating whether the difference between the output voltages and the correction voltage is zero, it is determined whether the cavity length of the Z direction and the parallelism of the X and Y directions of the interference cavity are at the ideal position. If the difference is 0, the cavity length of the Z direction and the parallelism of the X and Y directions of the interference cavity are at the ideal position, and the tunable F-P filter can perform normal filtering work. If the difference is not 0, step 2 is executed.

[0076] Step 2, detect the capacitance change between the current detection capacitors 5 and the standard capacitor value. After the capacitance change is processed by an external detection circuit, the difference V X , V Y , and V Z between the output voltages of the three differential circuits and the correction voltage are obtained as the voltage change signals in the three directions. The formula for converting the capacitance value to the voltage signal is as follows:

[0077] V C = k V C

[0078] C = C0 + ΔC

[0079] where k V is the voltage conversion coefficient of the capacitance detection circuit, C is the current capacitance value, C0 is the calibration capacitance value, and ΔC is the capacitance change. The calculation formula of ΔC is as follows:

[0080]

[0081] where A is the effective area of the detection capacitor 5, d c is the capacitance gap, ε0 is the vacuum dielectric constant, and ε r ​​is the relative dielectric constant of the medium in the capacitor gap, and Δd is the change in the capacitor gap c is the change in the capacitor gap

[0082] The capacitance value of the detection capacitor 5 and the reference capacitor 4 can be expressed as:

[0083]

[0084] The capacitance value is proportional to the effective area of the capacitor and inversely proportional to the capacitor gap. When the effective area of the capacitor is constant, reducing the capacitor gap increases the initial value of the capacitor, and the change in the capacitance value is significantly affected by the displacement. For example, when the capacitor gap is 0.1 mm, the effective diameter of the capacitor is 10 mm, and the effective area of the capacitor is 78.5 mm 2 , the dielectric constant of vacuum is 8.85 x 10 -12 F / m, and the relative dielectric constant of air is 1. The corresponding initial capacitance is 79 aF when the capacitor gap changes by 1 nm.

[0085] Step 3: According to the corrected voltage change signal obtained in step 2, calculate the angle adjustment amount of the interference cavity in X direction and Y direction, and the cavity length adjustment amount in Z direction; calculate the angle adjustment amount R X of the interference cavity in X direction, which is calculated as follows:

[0086]

[0087] V X = k V (C X2 -C X1 )- V X0

[0088] In the formula, k d is the coefficient for converting voltage to displacement, V X0 is the calibration voltage of the calibrated filter X direction differential circuit, C X1 is the capacitance value of the first detection capacitor C X1 , C X2 is the capacitance value of the second detection capacitor C X2 , and L X1 is the distance between the center points of the first detection capacitor C X1 and the second detection capacitor C X2 .

[0089] The angle adjustment amount R Y of the interference cavity in Y direction is calculated as follows:

[0090]

[0091] V Y = k V (C Y2 -C Y1) - V Y0

[0092] wherein V Y0 is the calibration voltage of the filter Y-direction differential circuit after calibration, C Y1 is the capacitance value of the third capacitor C Y1 , C Y2 is the capacitance value of the fourth detection capacitor C Y2 , L Y1 is the center point connecting distance of the third detection capacitor C Y1 and the fourth detection capacitor C Y2 ;

[0093] The cavity length adjustment amount T Z of the interference cavity in the Z-direction is calculated according to the following formula:

[0094] T Z = k d V Z + Δd z

[0095] V Z = k V (C Z2 - C Z1 ) - V Z0

[0096] wherein V Z0 is the calibration voltage of the filter Z-direction differential circuit after calibration, C Z1 is the capacitance value of the reference capacitor C Z1 , C Z2 is the capacitance value of the fifth detection capacitor C Z2 , and Δd z is the adjustment amount of the cavity length relative to the zero position.

[0097] Step 4, according to the angle adjustment amounts of the interference cavity in the X-direction and the Y-direction and the cavity length adjustment amount in the Z-direction obtained in step 3, the adjustment amount of the piezoelectric ceramic 6 in the Z-direction is calculated.

[0098] The adjustment amount [d1, d2, d3] of the piezoelectric ceramic 6 in the Z-direction is calculated according to the following formula:

[0099]

[0100] wherein A -1 is the inverse conversion matrix, and the calculation process is as follows:

[0101] Step 4.1, according to the adjustment amount [d1, d2, d3] of the piezoelectric ceramic 6 in the Z-direction, the angle adjustment amount of the interference cavity in the X-direction, the angle adjustment amount in the Y-direction, and the cavity length adjustment amount in the Z-direction are defined according to the following formula:

[0102]

[0103] In the formula, L X2 L is the distance between the center points of the piezoelectric ceramic P2 and the piezoelectric ceramic P3, Y2 L is the distance between the center points of the piezoelectric ceramic P2 and the piezoelectric ceramic P1, X3 L is the distance between the center points of the piezoelectric ceramic P1 and the fifth detection capacitor C Z2 L is the distance between the center points of the piezoelectric ceramic P2 and the fifth detection capacitor C Y3 L is the distance between the center points of the piezoelectric ceramic P3 and the fifth detection capacitor C Z2 L is the distance between the center points of the piezoelectric ceramic P2 and the fifth detection capacitor C

[0104] Step 4.2, the definition formula of step 4.1 is expressed in matrix form:

[0105]

[0106] Step 4.3, determine the positive conversion matrix A through the matrix form of step 4.2:

[0107]

[0108] Step 4.4, according to the positive conversion matrix A, the inverse conversion matrix A -1 ;

[0109] Step 5, the external piezoelectric ceramic driving circuit outputs the corresponding driving voltage according to the adjustment amount of the piezoelectric ceramic 6 in the Z direction obtained in step 4, and adjusts the piezoelectric ceramic 6, thereby completing the adjustment of the X direction angle, the Y direction angle and the Z direction cavity length of the interference cavity;

[0110] Step 6, detect the capacitance values of the current detection capacitors 5 and the reference capacitors 4, and obtain the output voltages of the X direction differential circuit, the Y direction differential circuit and the Z direction differential circuit after the capacitance values are processed by the external detection circuit. By calculating whether the difference between the output voltage and the correction voltage is zero, it is judged whether the cavity length of the interference cavity in the Z direction and the parallelism of the X direction and the Y direction are in the ideal position. If the difference is 0, the cavity length of the interference cavity in the Z direction and the parallelism of the X direction and the Y direction are in the ideal position, the control of the tunable F-P filter is completed, and the tunable F-P filter normally performs filtering work. If the difference is not 0, return to step 2 until the cavity length of the interference cavity in the Z direction and the parallelism of the X direction and the Y direction are in the ideal position after adjustment, thereby completing the adjustment of the tunable F-P filter and continuously monitoring to keep the interference cavity in the ideal position, so that the tunable F-P filter normally performs filtering work.

[0111] The bottom surface of the upper reflecting plate 1 and the top surface of the lower reflecting plate 2 are coated with a reflecting film, and the two reflecting surfaces form an interference cavity. Light enters the interference cavity and produces interference phenomenon through multiple reflections and transmissions. The optical path difference Δ of two adjacent reflected beams is Δ = 2nhcosθ, and the phase difference The transmission function T(θ, λ) of the filter is:

[0112]

[0113] where λ is the wavelength, θ is the incident angle, F is the fineness coefficient, n is the refractive index of the medium in the interference cavity, and h is the thickness of the interference cavity.

[0114] The transmittance of the filter is different for different wavelengths at the same incident angle, forming a comb filter, and the interval of each spectral line transmittance peak is equal to the free spectral range FSR, which can be expressed as:

[0115]

[0116] The spectral resolution of the filter is equal to the bandwidth FWHM of the spectral line transmittance peak, which can be expressed as:

[0117]

[0118] The wavelength variation Δλ can be expressed as:

[0119]

[0120] For example, the operating wavelength λ of the filter is 1000 nm, the fineness of the F-P filter is 50, the free spectral range is 0.5 nm, the spectral resolution is 0.01 nm, the refractive index of the air in the interference cavity is 1, and the thickness of the interference cavity is 1 mm; to achieve a center wavelength tuning accuracy of 1 pm, the adjustment amount of the interference cavity is 1 nm; the actual adjustment accuracy and stability of the interference cavity need to reach sub-nanometer level to achieve center wavelength tuning accuracy and stability better than 1 pm.

Claims

1. A tunable F-P filter based on capacitive micro displacement detection, characterized in that: it comprises an upper reflecting plate (1) and a bottom plate (3), the upper reflecting plate (1) is connected with the bottom plate (3) through piezoelectric ceramics (6); a lower reflecting plate (2) is arranged on the bottom plate (3), the reflecting surface of the lower reflecting plate (2) is arranged opposite to the reflecting surface of the upper reflecting plate (1), the upper reflecting plate (1) and the lower reflecting plate (2) are both cylindrical, and the diameter of the upper reflecting plate (1) is larger than that of the lower reflecting plate (2), the reflecting surfaces of the upper reflecting plate (1) and the lower reflecting plate (2) form an interference cavity for narrowband filtering of signals of a specified wavelength; the piezoelectric ceramics (6) comprise a first piezoelectric ceramic P1, a second piezoelectric ceramic P2 and a third piezoelectric ceramic P3, the three piezoelectric ceramics (6) are uniformly distributed along the outer periphery of the lower reflecting plate (2), one end of each piezoelectric ceramic (6) is fixed on the upper reflecting plate (1), and the other end is connected with the bottom plate (3) through a trimming pad (7), the center line of the second piezoelectric ceramic P2 and the third piezoelectric ceramic P3 is parallel to the X axis of the interference cavity, for adjusting the X direction angle of the interference cavity, the first piezoelectric ceramic P1 is for adjusting the Y direction angle of the interference cavity, and the three piezoelectric ceramics (6) are collectively for adjusting the Z direction cavity length of the interference cavity; the bottom plate (3) is further provided with a reference capacitor (4) and five detection capacitors (5) distributed along the outer periphery of the lower reflecting plate (2), one detection capacitor (5) is arranged near each piezoelectric ceramic (6), and the reference capacitor (4) is located between any two piezoelectric ceramics (6); the center line of the detection capacitors (5) near the second piezoelectric ceramic P2 and the third piezoelectric ceramic P3 is parallel to the X axis of the interference cavity, and the two form a differential circuit for detecting the parallelism change of the X direction of the interference cavity, the center line of the detection capacitor (5) near the first piezoelectric ceramic P1 and another detection capacitor (5) is parallel to the Y axis of the interference cavity, and the two form a differential circuit for detecting the parallelism change of the Y direction of the interference cavity, and the remaining one detection capacitor (5) and the reference capacitor (4) are adjacent, and the two form a differential circuit for detecting the cavity length change of the Z direction of the interference cavity.

2. The tunable F-P filter based on capacitive micro displacement detection according to claim 1, characterized in that:

3. The tunable F-P filter based on capacitive micro displacement detection according to claim 2, characterized in that: The five detection capacitors (5) are respectively a first detection capacitor C X1 , a second detection capacitor C X2 , a third detection capacitor C Y1 , a fourth detection capacitor C Y2 and a fifth detection capacitor C Z2 , the reference capacitor (4) is defined as a reference capacitor C Z1 ; the fourth detection capacitor C Y2 and the first detection capacitor C X1 are arranged between the first piezoelectric ceramic P1 and the second piezoelectric ceramic P2 in sequence, the fourth detection capacitor C Y2 is arranged close to the first piezoelectric ceramic P1, and the first detection capacitor C X1 is arranged close to the second piezoelectric ceramic P2; the third detection capacitor C Y1 is arranged between the second piezoelectric ceramic P2 and the third piezoelectric ceramic P3, and the center line of the third detection capacitor C Y1 and the fourth detection capacitor C Y2 is parallel to the Y axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the Y direction of the interference cavity; the fifth detection capacitor C Z2 and the second detection capacitor C X2 are arranged between the first piezoelectric ceramic P1 and the third piezoelectric ceramic P3 in sequence, the fifth detection capacitor C Z2 is arranged close to the first piezoelectric ceramic P1, the second detection capacitor C X2 is arranged close to the third piezoelectric ceramic P3, and the center line of the second detection capacitor C X2 and the first detection capacitor C X1 is parallel to the X axis of the interference cavity, and the two constitute a differential circuit for detecting the parallelism change of the X direction of the interference cavity; the reference capacitor C Z1 is arranged between the fifth detection capacitor C Z2 and the second detection capacitor C X2 , and is arranged close to the fifth detection capacitor C Z2 , the reference capacitor C Z1 and the fifth detection capacitor C Z2 constitute a differential circuit for detecting the cavity length change of the Z direction of the interference cavity.

4. The tunable F-P filter based on capacitive micro displacement detection according to claim 3, characterized in that: The reference capacitor (4) comprises a cover plate (41), a reference capacitor bottom plate (44), and a reference capacitor column (42) and a reference capacitor trimming pad (43) arranged on the reference capacitor bottom plate (44), the reference capacitor trimming pad (43) is annular, the reference capacitor column (42) is located in the annular of the reference capacitor trimming pad (43), the cover plate (41) is connected through the reference capacitor trimming pad (43) and the reference capacitor bottom plate (44), the top surface of the reference capacitor column (42) is arranged opposite to the bottom surface of the cover plate (41), and the bottom surface of the cover plate (41) and the top surface of the reference capacitor column (42) are both plated with electrodes, and a fixed capacitor gap is formed between the two, which is used for correcting the fifth detection capacitor C Z2 in the differential input process. the detection capacitor (5) is composed of two capacitive columns with different diameters, the two capacitive columns are coaxially arranged, one end of the capacitive column with a larger diameter is arranged on the bottom plate (3), one end of the capacitive column with a smaller diameter is arranged on the bottom surface of the upper reflecting plate (1), and electrodes are plated on the other end of the capacitive column with a larger diameter and the other end of the capacitive column with a smaller diameter, a capacitive gap is formed between the two, and the capacitive gap is used for detecting the parallelism changes of the X direction, the Y direction and the cavity length change of the Z direction of the interference cavity.

5. The tunable F-P filter based on capacitive micro displacement detection according to claim 4, characterized in that: ​ The stroke D of the piezoelectric ceramic (6) satisfies the following condition: D≥D1+D2+D3 In the formula, D1 is the adjustment stroke of the filter cavity length, D2 is the initial installation error of the interference cavity, and D3 is the piezoelectric ceramic (6) allowance.

6. The tunable F-P filter based on capacitive micro displacement detection according to claim 5, wherein: the stroke D of the piezoelectric ceramic (6) and the length L of the piezoelectric ceramic (6) are related as follows: The method comprises the following steps: D = k P VL where k P is the piezoelectric strain constant of the piezoceramic (6) and V is the maximum operating voltage of the piezoceramic (6).

7. A control method of a tunable F-P filter based on capacitive micro displacement detection, using the tunable F-P filter based on capacitive micro displacement detection according to any one of claims 1 to 6, characterized in that, When the piezoelectric ceramic (6), the reference capacitor (4) and the detection capacitor (5) are working, the current capacitance values of each detection capacitor (5) and the reference capacitor (4) are detected in real time, the capacitance values are processed by an external detection circuit to obtain output voltages of X-direction differential circuit, Y-direction differential circuit and Z-direction differential circuit respectively, whether the difference between the output voltages and the correction voltages is zero is calculated, whether the cavity length in the Z direction and the parallelism in the X direction and the Y direction of the interference cavity are in the ideal position is judged, if the difference is zero, the cavity length in the Z direction and the parallelism in the X direction and the Y direction of the interference cavity are in the ideal position, the tunable F-P filter normally performs filtering work, if the difference is not zero, step 2 is performed; Step 1: When the FP filter is used for the first time after assembly or at a preset calibration time, the FP filter is calibrated. The capacitance values ​​of each detection capacitor (5) and reference capacitor (4) of the FP filter after calibration are detected. The capacitance values ​​are processed by an external detection circuit to obtain the voltage difference V of the X-direction differential circuit. X0 The voltage difference V in the Y-axis differential circuit Y0 and the voltage difference V of the Z-axis differential circuit. Z0 V X0 V Y0 V Z0 As a correction voltage; Step 3: according to the voltage change signal obtained in step 2, the angle adjustment amount of the interference cavity in the X direction and the Y direction and the cavity length adjustment amount in the Z direction are calculated; Step 2, detecting the capacitance variation between the capacitance value of each detection capacitor (5) and the standard capacitance value of the reference capacitor (4), and obtaining the output voltage of the X-direction differential circuit, the Y-direction differential circuit, and the Z-direction differential circuit after the capacitance variation is processed by an external detection circuit, and calculating the difference V between the output voltage and the correction voltage respectively X Y Z V X Y Z as the voltage variation signals of the X-direction, the Y-direction, and the Z-direction.​​​​ Step 4: according to the angle adjustment amount of the interference cavity in the X direction and the Y direction and the cavity length adjustment amount in the Z direction obtained in step 3, the adjustment amount of each piezoelectric ceramic (6) in the Z direction is calculated; Step 5: according to the adjustment amount of each piezoelectric ceramic (6) in the Z direction obtained in step 4, the corresponding driving voltage is output by the external piezoelectric ceramic driving circuit, the piezoelectric ceramic (6) is adjusted, and thus the adjustment of the X direction angle, the Y direction angle and the Z direction cavity length of the interference cavity is completed; Step 6: the capacitance values of each detection capacitor (5) and the reference capacitor (4) are detected, the capacitance values are processed by an external detection circuit to obtain output voltages of X-direction differential circuit, Y-direction differential circuit and Z-direction differential circuit respectively, whether the difference between the output voltages and the correction voltages is zero is calculated, whether the cavity length in the Z direction and the parallelism in the X direction and the Y direction of the interference cavity are in the ideal position is judged, if the difference is zero, the cavity length in the Z direction and the parallelism in the X direction and the Y direction of the interference cavity are in the ideal position, the control of the tunable F-P filter is completed, the tunable F-P filter normally performs filtering work, if the difference is not zero, step 2 is returned, until the cavity length in the Z direction and the parallelism in the X direction and the Y direction of the interference cavity are in the ideal position after adjustment, and thus the adjustment of the tunable F-P filter is completed, and the interference cavity is continuously monitored to stably keep in the ideal position, so that the tunable F-P filter normally performs filtering work. C=C0+ΔC 8. The control method of the tunable F-P filter based on the capacitive micro displacement detection according to claim 7, characterized in that, The output voltage V of the differential circuit in step 2 C The calculation formula is as follows: V C = k V C 9. The control method of the tunable F-P filter based on capacitive micro displacement detection according to claim 8, wherein: In the formula, k V is the voltage conversion coefficient of the capacitance detection circuit, C is the current capacitance value, C0 is the calibration capacitance value, and ΔC is the capacitance change amount, and the calculation formula of ΔC is as follows: where A is the effective area of the detection capacitor (5), d c is the capacitance gap, ε0is the vacuum permittivity, ε r is the relative permittivity of the medium in the capacitance gap, Δd c is the capacitance gap variation. In step 4, the adjustment amount [d1, d2, d3] of the piezoelectric ceramic (6) in the Z direction is calculated, and the formula is as follows: The angle adjustment amount R of the interference cavity in the X direction in step 3 is calculated X The formula is as follows: V X = k V (C X2 -C X1 )-V X0 wherein k d is a coefficient of voltage converted to displacement amount, V X0 is a calibration voltage of the post-calibration filter X to the difference circuit, C X1 is a capacitance value of the first detection capacitor C X1 , C X2 is a capacitance value of the second detection capacitor C X2 , L X1 is a center point connecting distance of the first detection capacitor C X1 and the second detection capacitor C X2 ​ The angle adjustment amount R of the calculation interference cavity in the Y direction Y The formula is as follows: V Y = k V (C Y2 -C Y1 )-V Y0 In the formula, V Y0 is the calibration voltage of the post-amplifier Y-direction differential circuit, C Y1 is the capacitance value of the third detection capacitor C Y1 , C Y2 is the capacitance value of the fourth detection capacitor C Y2 , L Y1 is the center point connecting distance of the third detection capacitor C Y1 and the fourth detection capacitor C Y2 ; The cavity length adjustment amount T of the computing interference cavity in the Z direction Z The formula is as follows: T Z = k d V Z + Δd z V Z = k V (C Z2 -C Z1 )-V Z0 wherein V Z0 is the calibration voltage of the post-filter Z- direction difference circuit, C Z1 is the capacitance value of the reference capacitor C Z1 is the capacitance value of the fifth detection capacitor C Z2 is the capacitance value of the fifth detection capacitor C Z2 is the capacitance value of the fifth detection capacitor C z is the adjustment amount of the cavity length relative to the zero position.

10. The control method of the tunable F-P filter based on the capacitive micro displacement detection according to claim 9, characterized in that, ​ In the formula, A -1 is the inverse conversion matrix of the positive conversion matrix A, and the positive conversion matrix A is: wherein L X2 is the distance of the center point connecting line of the piezoelectric ceramic P2 and the piezoelectric ceramic P3, L Y2 is the distance of the center point connecting line of the piezoelectric ceramic P2 and the piezoelectric ceramic P1, L X3 is the distance of the center point connecting line of the piezoelectric ceramic P1 and the fifth detection capacitor C Z2 is the distance of the center point connecting line of the piezoelectric ceramic P1 and the fifth detection capacitor C Y3 is the distance of the center point connecting line of the piezoelectric ceramic P3 and the fifth detection capacitor C Z2 is the distance of the center point connecting line of the piezoelectric ceramic P3 and the fifth detection capacitor C

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