CN117781851B - Multistage correction method for closed-loop piezoelectric driving phase shifter - Google Patents
Multistage correction method for closed-loop piezoelectric driving phase shifter Download PDFInfo
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Abstract
The invention discloses a multistage correction method for a closed-loop piezoelectric driving phase shifter, which comprises the following steps: performing closed-loop control on displacement output of a movable plate end of the phase shifter, so as to correct nonlinear errors of the displacement output speed of a movable end plate of the phase shifter; and inputting a motion planning curve of a preset period, performing closed-loop control on displacement output of each piezoelectric driver unit, shooting to obtain an interference image, analyzing the interference image to obtain the actual average speed of a specific point, thus obtaining a motion gesture corresponding to the phase shifter, scaling the previous motion planning curve based on the ratio of the ideal speed to the actual speed, obtaining a new motion planning curve until the difference between the actual speed of each specific point and the ideal speed is not greater than a preset tolerance, and completing correction of the spatial consistency of the displacement speed of the phase shifter and the error of the average speed. The multistage correction method provided by the invention provides a scheme for guaranteeing the precision of the phase shifter, and effectively reduces the error of phase shift.
Description
Technical Field
The invention relates to the technical field of phase shifters, in particular to a multistage correction method for a closed-loop piezoelectric driving phase shifter.
Background
The Fizeau interferometer is an optical instrument based on phase shift interference technology (PSI), and is widely applied to precise optical measurement and calibration and quality control of the interferometer. PSI was proposed in 1974, the core idea of PSI was to introduce a known phase shift to produce interference images with phase differences. By analyzing these interference images, performance parameters of the optical element or system, such as surface shape, displacement, refractive index, etc., can be accurately measured. The phase shifter is one of the core components of the Fizeau laser interferometer, and its function is to generate accurate movements on the order of micrometers so that the interference images produce accurate phase differences. For a Fizeau interferometer, the measurement error of PSI is largely dependent on the error of the phase shift, i.e. the shift error of the phase shifter.
Fig. 32 shows the working principle of the fei-cable interferometer. The monochromatic light beam emitted by the laser is expanded into a parallel light beam through a spectroscope and a collimating objective lens, and the parallel light beam is divided into a measuring light beam and a reference light beam at the lower surface (reference surface) of the reference mirror with a wedge shape. The two paths of light are reflected back through the reference mirror surface and the surface of the measured piece respectively, enter the ocular lens below through the spectroscope reflection, and see the interference fringes with equal thickness after proper adjustment. The piezoelectric stack in the phase shifter drives the reference mirror to generate tiny displacement of a fraction of a wavelength so as to change the phase of the reference light; the CCD camera collects the interferograms on the time sequence generated along with the phase change behind the ocular, then transmits and stores the interferograms into the computer, the computer obtains the phase values of each point of the surface to be measured according to a phase shift algorithm, and the appearance of the surface to be measured can be obtained through serial data processing.
In order to improve the accuracy of PSI measurement, two strategies are mainly adopted in the academia to correct errors introduced by the phase shifter: 1. the sensitivity to shifter errors is reduced using a phase shifting algorithm. 2. And the correction of the phase shifter is carried out, so that the movement precision of the phase shifter is improved.
Currently, the mainstream phase shifter mainly uses a piezoelectric stack (PZT) as a driving source, and drives the PZT in an open loop control manner. The PZT has the advantages of compact structure, high resolution, high precision and quick response. But the phase shifter of the open loop platform has a certain problem. Because PZT has the characteristic of hysteresis nonlinearity, hysteresis generally describes a non-smooth, memory-containing, nonlinear phenomenon between the input voltage and the output displacement, which is manifested not only in relation to the current input voltage, but also in relation to the past input voltage. The memory effect involved in hysteresis is a non-local memory effect, in particular, hysteresis causes the output displacement to be related to the peak of the past input voltage. This means that the output characteristics of the phase shifter will change over time even if the same voltage stimulus is given every cycle.
Disclosure of Invention
In order to eliminate the hysteresis nonlinearity of the phase shifter and improve the displacement output precision of the phase shifter, the invention provides a set of phase shifter precision guarantee scheme, and the error of phase shift is effectively reduced. In the system design, the displacement output of the phase shifter is subjected to closed-loop control by the built-in three high-precision capacitance displacement sensors, so that the nonlinear error of the phase shifter is reduced. In parameter calibration, the displacement output of the phase shifter is corrected by shooting interference images through the optical system of the interferometer, so that the average speed error and the space consistency error of the phase shifter are reduced.
In order to solve the technical problems, the invention adopts a technical scheme that:
The multistage correction method for the closed-loop piezoelectric driven phase shifter comprises a fixed end plate, a movable end plate connected to the top end surface of the fixed end plate and a rear cover plate fixedly connected to the bottom end surface of the fixed end plate, wherein coaxial through holes with the same diameter are formed in the centers of the fixed end plate, the movable end plate and the rear cover plate, an inner annular hinge capable of being flexibly deformed is integrally arranged on the inner wall of an annular hole of the movable end plate, an outer annular hinge capable of being flexibly deformed is integrally arranged on the outer wall of an inner annular side wall of the fixed end plate, and the top surface of the outer annular hinge is fixedly connected with the bottom surface of the inner annular hinge; a plurality of groups of piezoelectric driver units and capacitance displacement sensor units which are uniformly distributed around the axis of the through hole are embedded in the bottom end face of the fixed end plate;
The parameter calibration method comprises the following steps:
step 1, correcting nonlinear errors by using a capacitance displacement sensor, specifically:
Step 1.1, a platform test is built, displacement of an output point position of a phase shifter is tested by using a laser interferometer, 0V voltage and 150V maximum driving voltage are applied to each piezoelectric driving unit, displacement range of each point position is recorded by using the laser interferometer, corresponding indication range of each capacitance displacement sensor is recorded, and head-tail calibration is realized;
step 1.2 applying a voltage difference starting from 0V to each piezoelectric driver cell Each voltage value duration is/>Recording an output displacement curve by using a laser interferometer, recording corresponding readings of a capacitance displacement sensor, calculating nonlinear errors of the phase shifter, performing linear interpolation correction, and circularly correcting three-way locus output of the phase shifter until the nonlinearity of the phase shifter meets the requirement;
Step 2, correcting a space consistency error and an average speed error by utilizing an interference image, wherein the method specifically comprises the following steps:
Step 2.1, inputting a motion planning curve with a preset period of T, performing closed-loop control on displacement output of each piezoelectric driver unit, obtaining m x N interference images in m periods of T by using a Fizeau interferometer at a fixed frame rate of T/N, obtaining an actual average speed of a specific point corresponding to each piezoelectric driver unit by analyzing the interference images, thereby obtaining a motion gesture corresponding to the phase shifter, wherein N is the frame number of the Fizeau interferometer for shooting images in a single period of T, and m and N are positive integers, and ；
Step 2.2, if the difference value between the actual speed and the ideal speed of any specific point is larger than a preset tolerance, scaling the previous motion planning curve based on the ratio of the ideal speed to the actual speed to obtain a new motion planning curve;
And 2.3, replacing the previous motion planning curve with a new motion planning curve, and repeating the steps 2.1 and 2.2 in the same way until the difference value between the actual speed and the ideal speed of each specific point is not greater than a preset tolerance, thereby completing the correction of the spatial consistency and the average speed error of the displacement speed of the phase shifter.
Further, in step 2.1, the method for obtaining the actual speed of a specific point is as follows:
The light intensity expression at any position on the interference image is:
（1）
Wherein, 、/>For two beams of coherent light at the point/>Light intensity at the spot; /(I)The initial optical path difference between the reference mirror and the measured mirror comprises the surface morphology information of the measured mirror; /(I)Is a specific phase amount that varies with time;
If ideal phase change between two adjacent frames of images is taken For/>The ideal displacement between the corresponding two adjacent frames of images is:
（2）
Ideal displacement between two adjacent frames of images Generated by the displacement of the output of the phase shifter, the ideal speed of the phase shifterThe method comprises the following steps:
（3）
Wherein, Is the wavelength of the light source,/>For image capture frame rate value,/>Is the time interval between two adjacent frames;
respectively taking gray values of specific points corresponding to each piezoelectric driver unit on the interference image as ordinate, taking the sequence number of a shooting frame as abscissa, and drawing to obtain a discrete graph after subtracting the respective average value;
performing cubic spline curve interpolation on the gray value points to simulate that the intersection point of the continuous gray value change curve and the horizontal axis is Then dot/>The average time period of the dark change at is/>：
（4）
The average time interval between two adjacent frames of images is：
（5）
The actual average speed of the phase shifter at this point is available in combination with (2)The method comprises the following steps:
（6）。
compared with the prior art, the invention has the following beneficial effects:
1. The invention adopts the closed-loop control phase shifter of the capacitive displacement sensor, and eliminates the hysteresis and creep characteristics of the piezoelectric driver driving the phase shifter in principle, so that the displacement output of the phase shifter has very good linearity (time consistency). The corrected phase shifter has the advantages that the speed characteristic of the corrected phase shifter does not drift along with time, and the speed characteristic of the corrected phase shifter does not change due to power-on and power-off, so that the reliability, stability and repeated positioning accuracy of the output displacement of the phase shifter are further improved. In addition, the closed-loop control also improves the damping and rigidity of the phase shifter, reduces the influence of external vibration, and ensures that the motion is more stable.
2. In the practical application scene of the phase shifter, the complex problems of expansion/shrinkage of the structure of the phase shifter, replacement of lenses with different masses, posture change of the interferometer in a flat and hoisting mode, metal creep of an internal annular hinge, ageing of piezoelectric stack materials, long-distance transportation and the like are faced with temperature change. The optical system of the Fizeau interferometer is utilized to correct the phase shifter in real time, and systematic errors generated in the situations can be eliminated together. The correction method greatly widens the use scene of the phase shifter while ensuring the output precision of the phase shifter, and improves the long-time stability, the anti-interference capability and the repeatability of the measurement result of the whole Fizeau interferometer.
3. The correction process adopted by the invention is efficient and convenient, does not need additional instruments for auxiliary correction, can be used after the assembly of the phase shifter is completed, and is beneficial to large-scale mass production in commercial environments.
Drawings
FIG. 1 is a schematic perspective view of a phase shifter according to the present invention;
FIG. 2 is a schematic diagram showing a second three-dimensional structure of the phase shifter according to the present invention;
FIG. 3 is a schematic diagram of a three-dimensional exploded structure of a phase shifter according to the present invention;
FIG. 4 is a schematic cross-sectional view of a phase shifter according to the present invention;
FIG. 5 is an enlarged schematic view of the portion A in FIG. 4;
FIG. 6 is a schematic perspective view of the fixed end plate;
FIG. 7 is a second perspective view of the fixed end plate;
FIG. 8 is one of the schematic perspective views of the movable end plate;
FIG. 9 is a second perspective view of the movable end plate;
FIG. 10 is one of the schematic perspective views of the piezoelectric driver unit;
FIG. 11 is a schematic diagram showing a second perspective structure of the piezoelectric driver unit;
Fig. 12 is a schematic view of a perspective exploded structure of the piezoelectric driver unit;
FIG. 13 is a schematic perspective view of the back cover plate;
FIG. 14 is a schematic diagram of the capacitive displacement sensor unit;
FIG. 15 is a schematic diagram of a three-dimensional structure of the capacitive displacement sensor probe;
FIG. 16 is a schematic view of a three-dimensional exploded structure of the capacitive displacement sensor probe;
FIG. 17 is a schematic view of the mounting position of the capacitive displacement sensor probe on a stationary endplate;
Fig. 18 is a schematic perspective view of the lead switching PCB board;
FIG. 19 is a schematic diagram of a closed-loop control loop of a phase shifter according to the present invention;
FIG. 20 is a schematic diagram of the correct actual displacement curves of two phase shifters;
FIG. 21 is a schematic diagram of a multistage correction process of a phase shifter according to the present invention
FIG. 22 is a schematic diagram of the displacement output of the phase shifter of the present invention;
FIG. 23 is a schematic illustration of nine frame interference images obtained in an eight step phase shift method;
FIG. 24 is a graph of a continuous gray value curve simulated by cubic spline interpolation of gray value points in the present invention;
FIG. 25 is a schematic diagram of a 3D model of a DPM Platform experimental Platform constructed for phase shifter performance testing in the present invention;
FIG. 26 is a schematic diagram of a test platform for phase shifter spatial uniformity and average speed in accordance with the present invention;
FIG. 27 is a plot of excitation voltage and resulting single-point displacement versus time for an open-loop phase shifter non-linearity test performed in accordance with the present invention;
FIG. 28 is a graph of motion planning and displacement versus time for a single point of the phase shifter obtained for a closed loop phase shifter non-linearity test in accordance with the present invention;
FIG. 29 is a graph of motion planning and resulting phase shifter displacement versus time for a phase shifter closed-loop resolution test performed in accordance with the present invention;
FIG. 30 is an interference image before shifter speed correction in an embodiment;
FIG. 31 is an interference image after the phase shifter velocity correction in the embodiment;
fig. 32 is a schematic diagram of the operation of the fei-cable interferometer.
In the figure: the device comprises a fixed end plate 1, an inner circular side wall 101, a rear cover plate sinking groove 102, a swelling sleeve mounting hole 103, a probe embedding groove 104, a lead plate embedding groove 105, a cable perforation 106, a movable end plate 2, an outer circular side wall 201, a circular hole 202, a slot 203, a rear cover plate 3, a piezoelectric driver unit 4, a piezoelectric stack positioning sleeve 41, a mounting hole 411, a sleeved hole 412, a 413-tooth sheet-shaped protection ring, a 414 lead groove, a 42 piezoelectric stack, a 43 piezoelectric stack jacking column, a 44 swelling sleeve, a 45 swelling bolt, a 5 inner circular hinge, a 6 pin shaft, a 7-capacitor displacement sensor probe 71 a first pole piece mounting seat, a 72 second pole piece mounting seat, a 73 target pole plate, a 74 fixed pole plate, 75 contacts, an 8-lead switching PCB board, a 9 outer circular hinge, a 10-cable protection sleeve, an 11-hoop wire device, a 121-phase shifter body 122 metal support, a 123 metal hanging plate, a 124 reflector, a 125 spectroscope, a 126 Raney-80 laser, a 127 air table, a 131 two-dimensional adjusting frame, a 132 reference mirror and a 133 test mirror.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making clear and defining the scope of the present invention.
Referring to fig. 1 to 5, a piezoelectric driven mechanical phase shifter integrated with a high-precision capacitive displacement sensor includes a fixed end plate 1, a movable end plate 2 fixedly connected to the top end surface of the fixed end plate 1, and a back cover plate 3 fixedly connected to the bottom end surface of the fixed end plate 1. The outline of the fixed end plate 1, the movable end plate 2 and the back cover plate 3 are similar, and coaxial through holes with equal diameters are formed in the centers of the fixed end plate 1, the movable end plate 2 and the back cover plate 3, so that a column structure with uniform outline can be formed after the three through holes are sequentially overlapped.
As shown in fig. 6 and 7, the bottom of the fixed end plate 1 is an annular flat plate structure, and the inner side edge of the top surface of the annular flat plate structure is integrally provided with an inner circular annular side wall 101. As shown in fig. 8 and 9, the top of the movable end plate 2 is an annular flat plate structure, an outer annular side wall 201 is integrally arranged at the outer edge of the bottom surface of the annular flat plate structure, and the movable end plate 2 is integrally in a shell-shaped structure. The step surface with the same width as the wall thickness of the outer annular side wall 201 is formed on the top surface edge of the annular flat plate structure of the fixed end plate 1, so that the outer annular side wall 201 can be movably fastened on the step surface, the movable end plate 2 is fastened and connected on the fixed end plate 1, the movable end plate 2 can axially move relative to the fixed end plate 1 in a certain displacement range, a reference mirror support of the phase shifter is connected with the movable end plate 2, a reference mirror 131 is arranged in the reference mirror support (not shown in the figure), and the reference mirror 131 is used for following synchronous movement of the movable end plate 2, so that the phase shifting function of the phase shifter is realized. As shown in fig. 13, the back cover plate 3 is a sheet punched member. The bottom surface of the annular flat plate structure of the fixed end plate 1 is provided with a rear cover plate sinking groove 102 matched with the outline of the rear cover plate 3, and the rear cover plate 3 can be completely embedded in the rear cover plate sinking groove 102 and is fixedly connected with the groove top surface of the rear cover plate sinking groove 102 through bolts. The fixed end plate 1 is connected with a main body of the Fizeau laser interferometer.
The outer wall of the inner circular side wall 101 of the fixed end plate 1 is integrally provided with a flexibly deformable outer circular hinge 9 (the thickness is 1 mm), the outer circular hinge 9 is coaxially positioned on the outer side of the inner circular side wall 101, and the inner radius size of the outer circular hinge 9 is equivalent to the aperture size of the circular hole 202 of the circular flat plate structure of the movable end plate 2. An inner annular hinge 5 (with the thickness of 1 mm) capable of flexibly deforming is integrally arranged on the inner wall of the annular hole 202 of the movable end plate 2, the inner annular hinge 5 is coaxially positioned on the inner side of the annular hole 202 (the radial direction which is radial from the central axis to the periphery is defined as the direction from inside to outside), the inner annular hinge 5 and the inner annular side wall 101 are butted to form a hollow cylinder structure with equal diameter and equal wall thickness, and an annular gap is reserved between the end part of the inner annular hinge 5 and the inner end face of the through hole of the movable end plate 2. When the movable end plate 2 is buckled on the fixed end plate 1, the bottom surface of the inner annular hinge 5 is propped against the top surface of the annular side wall of the fixed end plate 1, and is inserted and positioned through the pin shaft 6 positioned between the bottom surface of the movable end plate 2 and the top surface of the annular side wall of the fixed end plate 1, and is fixedly connected through bolts which are arranged in the bottom surface of the fixed end plate 1 and penetrate through the inner annular side wall 101; meanwhile, the top surface of the outer annular hinge 9 abuts against the bottom surface of the movable end plate 2, which is located outside the annular hole 202, and is fixedly connected through bolts arranged in the top surface of the movable end plate 2 and penetrating through the side wall of the annular hole 202. In this way, in the initial assembled state of the movable end plate 2 and the fixed end plate 1, the inner annular hinge 5, the inner annular side wall 101, the outer annular hinge 9, and the annular hole 202 side wall may form an annular quadrangular hinge structure having a hollow structure of quadrangular cross section, as shown in fig. 5. When the movable end plate 2 is slightly moved vertically upwards by the external force, the inner wall of the annular hole 202 drives the outer annular hinge 9 to slightly move upwards synchronously (the part of the bottom of the outer annular hinge 9 connected with the inner annular side wall 101 is obliquely deformed), and the inner annular hinge 5 moves downwards relative to the inner wall of the annular hole 202 under the fixing action of the inner annular side wall 101 (the part of the top of the inner annular hinge 5 connected with the annular hole 202 is obliquely deformed). This parallelogram structure minimizes the stiffness of the phase shifter along the optical axis. In this way, the primary displacement output of the piezoelectric actuator is converted into an output of the moving part on the optical axis.
The bottom end face of the fixed end plate 1 is embedded with a plurality of (3 in this embodiment) groups of piezoelectric driver units 4 uniformly distributed around the axis of the through hole according to the shell shape structure setting of the phase shifter, and the outer side of the inner circular side wall 101 of the fixed end plate 1 is fixedly embedded with a capacitance displacement sensor probe 7 which is positioned below the outer circular hinge 9 and positioned at the inner side of the piezoelectric driver units 4, as shown in fig. 5.
Specifically, as shown in fig. 10 to 12, the piezoelectric driver unit 4 includes a piezoelectric stack positioning sleeve 41 fixedly embedded in the bottom end face of the movable end plate 2, a piezoelectric stack 42 movably sleeved in the top of the piezoelectric stack positioning sleeve 41, a piezoelectric stack top column 43 movably sleeved in the piezoelectric stack positioning sleeve 41 and propped against the bottom end of the piezoelectric stack 42, and a expansion sleeve 44 movably sleeved outside the bottom end of the piezoelectric stack top column 43, wherein the expansion sleeve 44 is embedded in the bottom end face of the fixed end plate 2, and after the expansion bolts 45 are screwed, the outer circumference of the expansion sleeve 44 expands and deforms to be fixed in the fixed end plate 2 (as shown in fig. 4). The mounting hole 411 matched with the piezoelectric pile 42 is formed at one end of the piezoelectric pile positioning sleeve 41 matched with the movable end plate 2, the piezoelectric pile 42 is positioned in the mounting hole 411, the sleeving hole 412 matched with the piezoelectric pile jack-up column 43 is formed at the other end of the piezoelectric pile positioning sleeve 41, and the piezoelectric pile jack-up column 43 is positioned in the sleeving hole 412, so that the axes of the piezoelectric pile jack-up column 43 and the piezoelectric pile 42 after being assembled in the piezoelectric pile positioning sleeve 41 are coincident or parallel, the rapid automatic alignment of the piezoelectric pile jack-up column 43 and the piezoelectric pile 42 in the piezoelectric pile positioning sleeve 41 can be realized, and the fact that the acting force of the piezoelectric pile jack-up column 43 on the piezoelectric pile 42 is perpendicular to the end face of the piezoelectric pile 42 and the contact acting force is uniformly distributed when the piezoelectric pile jack-up column 43 is pressed and pre-tightly pressed subsequently can be ensured; the piezoelectric pile 42 is applied with a certain axial force through the piezoelectric pile top column 43, and the shaft end of the piezoelectric pile top column 43 is fixed through the shrinkage deformation of the inner circumference of the expansion sleeve 44, so that the positioning and pre-tightening fixation of the piezoelectric pile 42 can be realized, the pre-tightening force is controllable, the universality is good, and the overall production cost of the phase shifter is reduced; by providing a pre-tightening force to the piezoelectric stack 42, the piezoelectric stack 42 can only bear forward pressure and cannot be damaged by forces or moments in other directions during use.
The bottom end face of the movable end plate 2 is provided with embedded slots 203 (as shown in fig. 9) matched with the end parts of the piezoelectric stack positioning sleeves 41, the bottom end face of the fixed end plate 1 is provided with expansion sleeve mounting holes 103 (as shown in fig. 6 and 7) matched with the expansion sleeves 44, the number of the embedded slots 203 and the expansion sleeve mounting holes 103 is 3, and the embedded slots and the expansion sleeve mounting holes 103 are uniformly distributed around the axis circumference of the through hole in pairs. Preferably, the outer circumferential surface of the end of the mounting hole 411 of the piezoelectric stack positioning sleeve 41 is integrally provided with the uniformly distributed toothed guard rings 413, so that after the toothed guard rings 413 are assembled with the embedded slot 203, the outer side of the end of the piezoelectric stack positioning sleeve 41 has certain flexible shrinkage performance, and the piezoelectric stack positioning sleeve 41 is prevented from being rigidly connected with the embedded slot 203 in the radial direction, thereby protecting the piezoelectric stack 42 positioned in the piezoelectric stack positioning sleeve; meanwhile, through the matching of the toothed sheet protection ring 413 and the embedded groove hole 203, the assembly of the piezoelectric pile positioning sleeve 41 in the movable end plate 2 is facilitated, the rotation resistance after the assembly can be improved, and the relative movement between the piezoelectric pile positioning sleeve 41 and the movable end plate 2 is avoided. It is further preferable that the piezoelectric stack positioning sleeve 41 is provided with a wire groove 414 on an outer circumferential surface of the end where the socket hole 412 is located for restraining the wire of the piezoelectric stack 42.
As shown in fig. 14, the capacitive displacement sensor unit includes a capacitive displacement sensor probe 7, a target board, and a signal conditioning circuit, where a cable core layer of the capacitive displacement sensor probe 7 is connected to an input end of the signal conditioning circuit, an output end of the signal conditioning circuit is connected to an inner cable shielding layer of the capacitive displacement sensor probe 7 through an interface circuit, and the signal conditioning circuit uses a fully driven cable technology to make the cable core layer and the inner cable shielding layer of the capacitive displacement sensor probe 7 have the same potential through a 1:1 operational amplifier, and capacitive current between them is eliminated, and after the outer cable shielding layer is grounded, capacitance between the inner and outer shielding layers is shielded, so that only a sensor capacitance exists between the cable core layer of the probe and the ground. The full driving scheme can effectively eliminate the influence of the parallel capacitance on measurement and improve the measurement precision of the capacitance displacement sensor.
As shown in fig. 15 and 16, the capacitive displacement sensor probe 7 includes a first pole piece mounting seat 71 and a second pole piece mounting seat 72 which are arranged in parallel and opposite to each other up and down, the first pole piece mounting seat 71 and the second pole piece mounting seat 72 are made of aluminum alloy materials, a target pole plate 73 is fixedly embedded in the bottom surface of the first pole piece mounting seat 71, a fixed pole plate 74 is fixedly embedded in the top surface of the second pole piece mounting seat 72, and the target pole plate 73 is matched with the fixed pole plate 74 to perform capacitive measurement. A plurality of (e.g. 3) contacts 75 are uniformly arranged on the top surface of the first pole piece mounting seat 71 and the bottom surface of the second pole piece mounting seat 72, and the surfaces of the electric shock 75 on the same mounting seat are positioned in the same plane.
As shown in fig. 5 and 17, the outer side of the inner circular side wall 101 of the fixed end plate 1 is provided with a probe embedding groove 104 located below the outer circular hinge 9, the capacitance displacement sensor probe 7 is embedded in the groove and is close to the piezoelectric stack 42, the first pole piece mounting seat 71 located above is fixedly connected to the top wall of the probe embedding groove 104 through bolts, 3 contacts 75 on the first pole piece mounting seat are tightly attached to the top wall of the probe embedding groove 104, the second pole piece mounting seat 72 located below is fixedly connected to the bottom wall of the probe embedding groove 104 through bolts, 3 contacts 75 on the second pole piece mounting seat are tightly attached to the bottom wall of the probe embedding groove 104, and the gap between the two target pole plates 73 and the fixed pole plates 74 is measured in real time by negative feedback, so that the displacement of the circular hinge can be accurately obtained. The spacing between the target plate 73 and the fixed plate 74 is about 50um, so that the displacement output of the phase shifter is accurately converted into a change in capacitance of the capacitive displacement sensor probe 7. The capacitive displacement sensor probe 7 and the matched signal processing circuit are integrated and customized by adopting the existing circuit structure. The range of the sensor is about 200 microns and the static resolution is about 1nm.
Because the fixed polar plate 74 and the target polar plate 73 are connected through the mounting seat and the probe embedding groove 104 to enable the electric potential to be the same, the ground potential between the target polar plate 73 and the outside can be isolated, the leakage of charges is prevented, the electric field is uniform, and the edge effect is eliminated. The mounting seat can be used for shielding external noise interference. The target plate is made of a conductive metal sheet, and a metal layer can be plated on a glass substrate or a ceramic substrate with low expansion coefficient and high strength for better flatness.
The bottom end surface of the fixed end plate 1 is internally and fixedly embedded with a lead wire switching PCB 8, and the piezoelectric driver unit 4 and the capacitance displacement sensor unit 7 are electrically connected with an external cable through the lead wire switching PCB 8. As shown in fig. 18, the lead switching PCB 8 is an annular plate structure, and a lead board caulking groove 105 (as shown in fig. 7) matching with the shape of the lead switching PCB 8 is formed on the bottom surface of the fixed end plate 1, so that the lead switching PCB 8 can be completely embedded in the lead board caulking groove 105 and placed on the inner side of the rear cover plate 3. The edge of the lead switching PCB 8 is fixedly provided with a plurality of connecting flanges, the inner side and the outer side of the lead plate caulking groove 105 are respectively provided with screw holes corresponding to the connecting flanges, and the lead switching PCB 8 is fixed in the lead plate caulking groove 105 through the cooperation of the connecting flanges and screws positioned in the screw holes.
As shown in fig. 6 and 7, a cable through hole 106 is formed in the side wall of the fixed end plate 1, and a wire-binding groove 107 is formed between the cable through hole 106 and the wire-guiding plate groove 105. The wire hooping device 11 is fixedly embedded in the wire hooping device embedding groove 107 through a screw and is used for fixing a cable; a cable protective sleeve 10 is disposed within the cable perforation 106 for cable protection and assisted positioning.
As shown in fig. 19, three capacitance displacement sensor probes 7 are integrated in the hinge of the phase shifter, and sensor voltage is collected by an AD chip to a singlechip system, and can be converted into real-time output displacement of the phase shifter through calculation; the target displacement can be given by an upper computer and updated to a singlechip system through serial communication; the target displacement and the three paths of measured displacement are calculated by a digital PID algorithm in the singlechip to obtain the control voltage of each path of piezoelectric stack, the three paths of DA chips are used for outputting analog voltage and amplifying and outputting the analog voltage through the power amplification board to drive the piezoelectric stack 42, and the stroke closed-loop control of the hinge output plane of the phase shifter is realized.
The process of implementing the phase shifter phase shift function by the piezoelectric stack 42 is: after the piezoelectric pile 42 is excited by the power supply, the piezoelectric pile 42 generates displacement and pushes the movable end plate 2 to move, so that the inner annular hinge 5 deforms under the action of tensile force, the outer annular hinge 9 also synchronously deforms, and the hinge structure is kept to have a parallelogram cross section with a parallelogram hollow shape; the capacitance displacement sensor unit detects the displacement of the outer annular hinge 9 in real time, compares the displacement with a preset displacement through the closed-loop control circuit, and compensates the error between the displacement and the preset displacement in real time until the movable end plate moves to a preset phase-shifting position.
In practical application, the phase shifter has two working modes, namely distributed discrete phase shifting and integral continuous phase shifting. Fig. 20 (a) shows an actual displacement curve of distributed discrete phase shift, which is shaped like a multi-stage step. In this mode of operation, the phase shifter will move forward in specific steps, waiting 1-2s for each step of movement, allowing the camera to acquire images. Fig. 20 (b) shows an actual displacement curve of the integral continuous phase shifter, which is shaped like a sawtooth wave. In this mode of operation, the phase shifter will be pushed forward rapidly and then retracted at a constant speed. The camera may acquire images at a fixed frame rate during the uniform rollback phase of the phase shifter. The actual displacement curve of the integral continuous phase shifter has shorter measurement time than the actual displacement curve of the distributed discrete phase shift, can effectively reduce the introduction of other environmental errors, can reduce the temperature drift and time drift of a camera and a light source to a certain extent, and has more advantages in the final measurement effect. The phase shifter displacements referred to herein all move in a continuous phase shifting mode of operation, unless specifically stated.
The core function of the phase shifter is to precisely push the reference mirror to produce a fixed amount of phase shift of the interference image over time (frames). The errors in these image phase shift amounts in principle determine the measurement errors of the PSI. Thus, in the case of stable camera frame rate, the error of the PSI phase measurement depends on the speed error of the phase shifter (its mounted reference mirror).
For a particle, its displacement process is expected to be uniform and accurate. Thus, the speed error may be further subdivided into a non-linear error and an average speed error. Nonlinear error is used to describe the uniformity of displacement and measures the inconsistency between a particle's actual displacement versus time curve and its first-order fit. The first order fitted curve generally represents the desired linear motion, while the nonlinear error represents the deviation between the actual motion and the linear motion. The average velocity error represents the difference between the average velocity of the particles and the desired velocity. However, the measurement target of the Fizeau laser interferometer is a plane on which the phase shift amount of each point is expected to be uniform. The motion profile of each point on the reference mirror should therefore also be uniform, the so-called translational motion. Spatial consistency is used herein to describe the error between points in translational motion.
In summary, the speed error for the phase shifter can be refined to three parameters: nonlinear errors, average speed errors, spatial consistency errors. To this end, the present invention provides a multi-stage correction method for a closed-loop piezoelectric driven phase shifter to calibrate these three error indicators.
A multistage correction method for a closed-loop piezoelectric driven phase shifter, applied to the aforementioned piezoelectric driven mechanical phase shifter, as shown in fig. 21, comprising the steps of:
Step 1, correcting nonlinear errors by using a capacitance displacement sensor, specifically: setting up a platform test, testing the displacement of the output point position of the phase shifter by using a laser interferometer, applying 0V voltage and 150V maximum driving voltage to each piezoelectric driving unit, recording the displacement range of each point by using the laser interferometer, recording the corresponding indication range of each capacitance displacement sensor, and realizing head-tail calibration; applying a voltage difference from 0V to each piezoelectric driver unit Each voltage value duration is/>The step-shaped excitation voltage of the phase shifter is obtained by recording an output displacement curve by using a laser interferometer, recording corresponding readings of a capacitance displacement sensor, calculating nonlinear errors of the phase shifter, performing linear interpolation correction, and circularly correcting three-way locus output of the phase shifter until the nonlinearity of the phase shifter meets the requirement.
Fig. 22 shows a schematic diagram of the shifter displacement output, where (a) in fig. 22 is in a non-energized state and (b) in fig. 22 is in a driven state. The piezoelectric driver unit 4, when excited by a voltage, elongates L 0 due to the inverse piezoelectric effect, pushing the movable part of the phase shifter (the movable end plate 2) forward by L 1. The capacitive displacement sensor probe 7 can measure in real time the gap distance value L between the moving part and the fixed part (fixed end plate 1) of the phase shifter, which varies by an amount very close to the actual displacement output of the phase shifter. At very small ranges, the capacitive displacement sensor has very good linearity (0.003%) between input displacement and output voltage. In other words, the movement of the movable part of the phase shifter is constant during operation as long as the voltage detected by the sensor is kept increasing at a constant speed. Theoretically, the time consistency error of the phase shifter speed can be reduced to the level of the nonlinear error of the capacitive displacement sensor by using the capacitive displacement sensor to perform closed-loop control on the piezoelectric stack. Meanwhile, the mass (5 kg-20 kg) of the reference mirror carried by the phase shifter has huge inertia, and certain filtering is carried out on the motion process of the phase shifter, so that the time consistency error is further reduced.
And 2, correcting the space consistency error and the average speed error by utilizing the interference image.
The method for obtaining the actual speed of a specific point is as follows:
The light intensity expression at any position on the interference image is:
（1）
Wherein, 、/>For two beams of coherent light at the point/>Light intensity at the spot; /(I)The initial optical path difference between the reference mirror and the measured mirror comprises the surface morphology information of the measured mirror; /(I)Is a specific phase amount that varies with time; taking an eight-step phase shifter method as an example, every time/>Value increase/>The Fizeau interferometer will take an interference image once as shown in FIG. 23.
If ideal phase change between two adjacent frames of images is takenFor/>The ideal displacement between the corresponding two adjacent frames of images is:
（2）
Ideal displacement between two adjacent frames of images Generated by the displacement of the output of the phase shifter, the ideal speed of the phase shifterThe method comprises the following steps:
（3）
Wherein, Is the wavelength of the light source,/>For image capture frame rate value,/>Is the time interval between two adjacent frames; when the phase shifter is operating at ideal speed, the/>, of the first frame0, Ninth frame/>For/>Then their corresponding intensities I 1 and I 9 will be identical, which is true for any point on the image. That is, the first image and the ninth image will be identical.
Based on the foregoing, the correction flow designed in the present invention specifically includes:
Step 2.1, inputting a motion planning curve with a preset period of T, performing closed-loop control on displacement output of each piezoelectric driver unit, obtaining m x N interference images in m periods of T by utilizing a Sophie interferometer at a fixed frame rate of T/N, obtaining an actual average speed of a specific point corresponding to each piezoelectric driver unit by analyzing the interference images, thereby obtaining a motion gesture corresponding to the phase shifter, wherein N is the frame number of the images shot by the Sophie interferometer in a single period of T, and m and N are positive integers, and ；
Respectively taking gray values of specific points corresponding to each piezoelectric driver unit on the interference image as ordinate, taking the sequence number of a shooting frame as abscissa, and drawing to obtain a discrete graph after subtracting the respective average value;
As shown in fig. 24, the gray value points are interpolated by a cubic spline curve to simulate the intersection point of the continuous gray value change curve and the horizontal axis as Then dot/>The average time period of the dark change at is/>：
（4）
The average time interval between two adjacent frames of images is：
（5）
The actual average speed of the phase shifter at this point is available in combination with (2)The method comprises the following steps:
（6）。
Step 2.2, if the difference value between the actual speed and the ideal speed of any specific point is larger than a preset tolerance, scaling the previous motion planning curve based on the ratio of the ideal speed to the actual speed to obtain a new motion planning curve;
And 2.3, replacing the previous motion planning curve with a new motion planning curve, and repeating the steps 2.1 and 2.2 in the same way until the difference value between the actual speed and the ideal speed of each specific point is not greater than a preset tolerance, thereby completing the correction of the spatial consistency and the average speed error of the displacement speed of the phase shifter.
The invention builds two different experimental platforms to test each index of the phase shifter. The experimental platform for measuring nonlinear errors, repeated positioning errors, resolution is named: a displacement performance measurement Platform (DISPLACEMENT PERFORMANCE MEASUREMENT PLATFORM, abbreviated as DPM Platform); the experimental platform for measuring spatial consistency error, average speed error is named: dynamic characteristics assessment Platform (DYNAMIC CHARACTERISTICS ASSESSMENT Platform, DCA Platform for short).
A schematic of the 3d model of DPM Platform is shown in fig. 25. The phase shifter 121 is bolted to a large bracket 122 made of stainless steel. A steel plate 123 weighing 5kg is mounted on the front face of the phase shifter. Screw holes are arranged on two sides of the steel flat plate and used for fixing the mass bar, and the mass of the steel flat plate after weight increase can reach 20kg at most. The front face of the steel plate has three sets of threaded interfaces for securing the mirror 124. The threaded joints are symmetrically distributed circumferentially and have an included angle of 120 degrees. The geometric centers of these screw joints are defined as a measured point T, a measured position R, and a measured position L, respectively, in the clockwise direction from the uppermost position.
Directly in front of the mirror are beam splitter 125, ranshao XL-80 laser 126, which form a Michelson interferometer. The reflecting mirror and the spectroscope form an interference arm, the reference mirror and the spectroscope form a reference arm, and the XL-80 laser is used as a laser light source and a measuring device. These three positions are measured in each experiment of the phase shifter to evaluate the displacement accuracy of one plane. Thus, the mirror will be fixed in turn to the three measured positions of the steel plate, while the other parts of the interferometer will be adjusted to the corresponding optical paths.
The test platform for spatial consistency and average speed is equivalent to a normal working Fizeau laser interferometer as shown in FIG. 26. The two-dimensional adjusting frame 131 is fixed to the front surface of the phase shifter. A reference mirror 132 is mounted on the two-dimensional adjustment frame. A measured mirror 133 is placed right in front of the reference mirror.
After all experimental platforms are built, a transparent wind shield made of acrylic materials is added, so that rapid temperature change caused by wind is prevented. The ambient temperature throughout the experiment was 20 to 20.2 degrees and the humidity was 51% rh.
Testing of open loop phase shifter nonlinearity:
The open loop output characteristics of the phase shifter were tested with the help of the DPM Platform. The test content includes nonlinear errors and repeated positioning errors. "nonlinear error" refers to the degree of deviation of the linear relationship between the input (commanded) position and the actual position of the displacement stage. The term "repeatability of the phase shifter" means that the phase shifter can be returned to the same position with high accuracy when the command is received a plurality of times under the same condition.
In the test process, no built-in capacitance displacement sensor participates, and the phase shifter is directly driven by applying quantitative voltage to the piezoelectric stack. As shown in fig. 27 (a), the excitation voltage curve is stepped, and the abscissa indicates time and the ordinate indicates voltage. There are 11 step-excitation voltage segments, starting from 0V up to 150V, the voltage difference between each voltage is 15V, and the duration of each step-excitation voltage segment is about 2s. Sequentially marking the serial number of each step excitation voltage section from low to high as；
While driving the phase shifter, the actual displacement curves of the 3 measured positions were recorded at a sampling rate of 100Hz, respectively, and the test was repeated 10 times. Taking the first test of measurement position No. 1 as an example, the displacement-time curve of the single point of the phase shifter is shown in fig. 27 (b). The average value of the displacement of the time length of 0.5s after the excitation voltage of each step is stabilized is taken as a measured value. In the first placeThe average measurement value obtained by each step excitation voltage segment is/>：
（7）
Wherein,In the phase shifterThe/>, obtained by the step-excited voltage sectionSecondary measurement,/>For the number of measurements, here/>；
The specific point is at the firstRepeated positioning accuracy of each step excitation voltage section is/>：
（8）
Taking outThe maximum value of (2) is the repeated positioning precision of the phase shifter;
average measured value of corresponding step excitation voltage segment with serial number of step excitation voltage segment as abscissa For the ordinate, 11 data points are obtained, and least square fitting is carried out on the data points to obtain a fitting curve, so that the predicted output value/> of the fitting curve can be obtained for each data pointThe nonlinear error S is:
（9）
Tables 1 and 2 show the results of testing the open loop output characteristics of the phase shifters having a mass of 5kg and a mass of 20kg, respectively.
TABLE 1 open loop control parameters for phase shifter under 5kg load
| Measured position | Maximum displacement (μm) | Repeated positioning accuracy (nm) | Nonlinear error |
| T | 11.51 | 5.3 | 4.496% |
| R | 13.24 | 1.9 | 4.549% |
| L | 11.11 | 3.3 | 3.001% |
TABLE 2 open loop control parameters for phase shifters under 20kg load
| Measured position | Maximum displacement (μm) | Repeated positioning accuracy (nm) | Nonlinear error |
| T | 11.52 | 3.7 | 4.501% |
| R | 13.40 | 2.2 | 4.554% |
| L | 11.00 | 1.5 | 3.039% |
Testing of closed loop phase shifter nonlinearity:
The closed loop output characteristics of the phase shifter were tested with the help of DPM Platform. In the testing process, the output voltages of the corresponding internal capacitance displacement sensors under different actually measured displacements are recorded simultaneously, and the sensing characteristic curve of the capacitance displacement sensor is calculated by interpolation based on the output voltages. Using the sensing characteristic curve, an analog diagram of fig. 27 (a) is made as shown in fig. 28 (a). The motion planning curve is also a stepwise curve, the abscissa is also time, but the ordinate is displacement. There are 11 step displacement segments in the figure, and the step displacement segments are sequentially increased from 0um to 1um to 10um. Similarly, the maintenance time of the step displacement sections is 2s, and the step displacement sections are respectively named as step displacement sections 0-10 from low to high.
Referring to the open loop test process, the phase shifter is tested by adopting the identical means, and the acquired data is subjected to the identical data processing. Taking the first test of measurement position No. 1 as an example, the displacement-time curve of the single point of the phase shifter is shown in fig. 28 (b). Tables 3 and 4 show the results of closed loop output characteristic test of the phase shifters having a mass of 5kg and a mass of 20kg, respectively.
TABLE 3 closed loop control parameters of phase shifter under 5kg load
| Measured position | Maximum displacement (μm) | Repeated positioning accuracy (nm) | Nonlinear error |
| T | 9.99 | 1.4 | 0.032% |
| R | 9.99 | 1.9 | 0.042% |
| L | 10.1 | 2.3 | 0.046% |
TABLE 4 closed loop control parameters for phase shifters under 20kg load
| Measured position | Maximum displacement (μm) | Repeated positioning accuracy (nm) | Nonlinear error |
| T | 9.99 | 2.3 | 0.026% |
| R | 9.98 | 1.8 | 0.049% |
| L | 10.02 | 2.5 | 0.046% |
Resolution testing
The closed loop resolution of the phase shifter was tested with the help of DPM Platform. Fig. 29 (a) is a motion planning curve for test resolution, and the abscissa is time and the ordinate is target displacement. Fig. 29 (b), fig. 29 (c) and fig. 29 (d) are phase shifter displacement versus time curves measured by the interferometer at three test points, respectively. The step noise peak-to-peak value in the figure is about 1nm, and the displacement resolution of the phase shifter is about 0.15nm. In practice the theoretical displacement resolution of the phase shifter should be smaller, but the resolution cannot be measured due to environmental factors and limitations of interferometer resolution.
Spatial consistency correction test based on interference image analysis:
The on-line correction of the phase shifter was tested using DCA Platform. To simulate systematic errors caused by environmental factors, the motion planning curves of the three-way stack are scaled differently. After the phase shifter is started, an optical system of the Fizeau interferometer is used for recording interference images, and the total number of the interference images is 80 frames. By using the method, the gray values of the three points of the interference image are extracted and fixed, and the speeds of the three points are obtained. The motion planning curve is scaled based on the three-point velocity. And the above process is repeated until the three-point speed approaches the ideal speed value.
Fig. 30 is an interference image before the phase shifter speed correction, and (a) in fig. 30, (b) in fig. 30, and (c) in fig. 30 are difference images of the 1 st frame, the 25 th frame, and the two frames, respectively. Fig. 31 is an interference image after the phase shifter speed correction, and (a) in fig. 31, (b) in fig. 31, and (c) in fig. 31 are difference images of the 1 st frame, the 25 th frame, and the two frames, respectively. The phase shifter shifts about 1.5 times the wavelength between the 1 st and 25 th images, the more similar the two images, the more accurate the shift. After the correction is calculated, the two-dimensional correlation coefficient of the image is improved from 0.6658 to 0.999.
The invention provides a set of phase shifter precision guarantee scheme, which effectively reduces the error of phase shift. In the system design, the nonlinear error of the phase shifter is reduced by performing closed-loop control on the phase shifter with three built-in high-precision capacitance displacement sensors. In parameter calibration, the displacement output of the phase shifter is corrected by shooting interference images through an optical system of the interferometer, and the scheme is adopted for reducing the average speed error and the space consistency error of the phase shifter. Systematic errors caused by environmental changes and hysteresis nonlinearities of conventional open loop platform phase shifters are eliminated in principle. The experimental results show that: the range of the phase shifter is 10um, the carrying capacity is 20kg, the nonlinear error is 0.05%, the repeated positioning precision is 3nm, and the resolution is 1nm. After correction, the matrix correlation coefficient of the interference picture generated before and after the phase shifter is shifted by 1.5 times of wavelength is increased from 0.66 to 0.99. The phase shifter is excellent in nonlinear error and repeated positioning accuracy, and exceeds all devices in the current consultable documents.
Experimental results show that the method significantly reduces the errors of the phase shifter, including nonlinear errors, average speed errors, and spatial uniformity errors. Furthermore, the method theoretically avoids hysteresis nonlinearity and creep characteristics of the piezoelectric driver unit, while also automatically correcting for systematic errors caused by environmental changes (e.g., temperature drift and lens replacement). When applied to a Fizeau laser interferometer, the method enhances the function of the interferometer, providing higher surface profile measurement accuracy, long-term stability, measurement result repeatability, improved interference immunity, and wider application possibilities.
The foregoing description is only illustrative of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes or direct or indirect application in other related technical fields are included in the scope of the present invention.
Claims (2)
1. A multi-stage correction method for a closed-loop piezoelectric driven phase shifter, characterized by: the piezoelectric driving mechanical phase shifter applying the multistage correction method comprises a fixed end plate and a movable end plate connected to the top end surface of the fixed end plate, wherein coaxial through holes with the same diameter are formed in the centers of the fixed end plate and the movable end plate, an inner annular hinge capable of being flexibly deformed is integrally arranged on the inner wall of an annular hole of the movable end plate, an outer annular hinge capable of being flexibly deformed is integrally arranged on the outer wall of an inner annular side wall of the fixed end plate, the top surface of the outer annular hinge is fixedly connected with the bottom surface of the inner annular hinge, and a plurality of groups of piezoelectric driver units and capacitance displacement sensor units which are uniformly distributed around the axis of the through hole are embedded in the bottom end surface of the fixed end plate;
The piezoelectric driver unit comprises a piezoelectric pile positioning sleeve fixedly embedded in the bottom end face of the movable end plate, a piezoelectric pile movably sleeved in the top of the piezoelectric pile positioning sleeve, a piezoelectric pile jacking column movably sleeved in the piezoelectric pile positioning sleeve and propped against the bottom end of the piezoelectric pile, and an expansion sleeve movably sleeved outside the bottom end of the piezoelectric pile jacking column, wherein the expansion sleeve is embedded in the bottom end face of the fixed end plate, and after the expansion bolt is screwed, the outer circumference of the expansion sleeve expands and deforms to be fixed in the fixed end plate;
the process for realizing the phase shifting function of the phase shifter through the piezoelectric stack comprises the following steps: after the piezoelectric pile is excited by a power supply, the piezoelectric pile generates displacement and pushes the movable end plate to move, so that the inner annular hinge deforms under the action of tensile force, and the outer annular hinge synchronously deforms, so that the hinge structure is kept to be a parallelogram section with a parallelogram hollow shape; the capacitive displacement sensor unit detects the displacement of the outer annular hinge in real time, compares the displacement with a preset displacement through the closed-loop control circuit, and compensates the error between the displacement and the preset displacement in real time until the movable end plate moves to a preset phase-shifting position;
The multistage correction method comprises the following steps:
step 1, correcting nonlinear errors by using a capacitance displacement sensor, specifically:
Step 1.1, a platform test is built, displacement of an output point position of a phase shifter is tested by using a laser interferometer, 0V voltage and 150V maximum driving voltage are applied to each piezoelectric driving unit, displacement range of each point position is recorded by using the laser interferometer, corresponding indication range of each capacitance displacement sensor is recorded, and head-tail calibration is realized;
step 1.2 applying a voltage difference starting from 0V to each piezoelectric driver cell Each voltage value has a duration ofRecording an output displacement curve by using a laser interferometer, recording corresponding readings of a capacitance displacement sensor, calculating nonlinear errors of the phase shifter, performing linear interpolation correction, and circularly correcting three-way locus output of the phase shifter until the nonlinearity of the phase shifter meets the requirement;
Step 2, correcting a space consistency error and an average speed error by utilizing an interference image, wherein the method specifically comprises the following steps:
Step 2.1, inputting a motion planning curve with a preset period of T, performing closed-loop control on displacement output of each piezoelectric driver unit, obtaining m x N interference images in m periods of T by using a Fizeau interferometer at a fixed frame rate of T/N, obtaining an actual average speed of a specific point corresponding to each piezoelectric driver unit by analyzing the interference images, thereby obtaining a motion gesture corresponding to the phase shifter, wherein N is the frame number of the Fizeau interferometer for shooting images in a single period of T, and m and N are positive integers, and ；
Step 2.2, if the difference value between the actual average speed and the ideal speed of any specific point is larger than a preset tolerance, scaling the previous motion planning curve based on the ratio of the ideal speed to the actual average speed to obtain a new motion planning curve;
and 2.3, replacing the previous motion planning curve with a new motion planning curve, and repeating the steps 2.1 and 2.2 in the same way until the difference value between the actual average speed and the ideal speed of each specific point is not greater than a preset tolerance, thereby completing the correction of the spatial consistency and the average speed error of the displacement speed of the phase shifter.
2. A multi-stage correction method for a closed-loop piezoelectric driven phase shifter according to claim 1, wherein: in step 2.1, the method for obtaining the actual average speed of a specific point is as follows:
The light intensity expression at any position on the interference image is:
（1）
Wherein, 、/>For two beams of coherent light at the point/>Light intensity at the spot; /(I)The initial optical path difference between the reference mirror and the measured mirror comprises the surface morphology information of the measured mirror; /(I)Is a specific phase amount that varies with time;
If ideal phase change between two adjacent frames of images is taken For/>The ideal displacement between the corresponding two adjacent frames of images is:
（2）
Ideal displacement between two adjacent frames of images Generated by the output displacement of the phase shifter, the ideal speed of the phase shifter/>The method comprises the following steps:
（3）
Wherein, Is the wavelength of the light source,/>For image capture frame rate value,/>Is the time interval between two adjacent frames;
respectively taking gray values of specific points corresponding to each piezoelectric driver unit on the interference image as ordinate, taking the sequence number of a shooting frame as abscissa, and drawing to obtain a discrete graph after subtracting the respective average value;
performing cubic spline curve interpolation on the gray value points to simulate that the intersection point of the continuous gray value change curve and the horizontal axis is Then dot/>The average time period of the dark change at is/>：
（4）
The average time interval between two adjacent frames of images is：
（5）
The actual average speed of the phase shifter at this point is available in combination with (2)The method comprises the following steps:
（6）。
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