CN117419660A - Mechanical phase shifting method for air-bearing heavy-load reference mirror - Google Patents
Mechanical phase shifting method for air-bearing heavy-load reference mirror Download PDFInfo
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Abstract
The invention discloses a mechanical phase shifting method for an air floatation supporting heavy-load reference mirror, and belongs to the technical field of optical precision measurement. The implementation method of the invention comprises the following steps: realizing zero-clearance micro-displacement of a mechanical phase shifting system of the heavy-duty reference mirror through elastic deformation of a spring; the piezoelectric ceramics and the spring are flexibly connected and combined to realize the spatial translation of the heavy-load reference mirror; the large-caliber mechanical phase shift driving system adopts two rows of flexible steering micro-displacement mechanisms with the same side edges to be uniformly arranged in the same form to realize space synchronous driving and realize the phase shift of the heavy-duty reference mirror in space nanometer level; the high-precision displacement sensor is combined with the piezoelectric ceramic to realize in-situ monitoring and PID closed-loop driving of three points in space; the air floatation support gravity unloading of the heavy-load reference mirror and the reference mirror space phase shift error calibration model are used for realizing the space translation of the heavy-load reference mirror in the nano-scale resolution, realizing the high-precision high-stability mechanical phase shift in the large-caliber interferometry and improving the large-caliber optical detection and processing precision.
Description
Technical Field
The invention relates to a mechanical phase shifting method for an air floatation supporting heavy-load reference mirror, and belongs to the technical field of optical precision measurement.
Background
The large-caliber (phi >450 mm) optical element is in the core position in the optical measurement fields of astronomical telescope, inertial confinement fusion device, semiconductor wafer detection and the like, and the quality of the surface morphology is one of key parameters for determining the overall performance index of a high-precision optical system. Therefore, the method has great significance in accurately measuring the surface morphology of the large-caliber optical element. The large-caliber interferometer is an important tool for realizing the surface shape detection of the large-caliber optical element, and the existing large-caliber interferometer adopts a phase-shifting interferometry (PSI) technology with strong background interference resistance and high precision. The basic principle of PSI is to introduce phase shift into the interferogram and calculate the phase and surface profile distribution by collecting multiple frames of phase shift interferograms. The phase shift is the most critical step in PSI, and the accuracy of the phase shift directly determines the measurement accuracy. The most classical and widely used phase shifting mode is the mechanical phase shifting of the reference mirror at present, namely, the reference mirror is driven to move step by extension of piezoelectric ceramics (PZT), so that the phase shifting is introduced into the reference light. The phase shifting mode has high precision, and can compensate the inclination phase shifting error caused by the cantilever type fixed structure of the reference mirror by independently controlling each PZT. Therefore, the method becomes the most commonly used phase shifting method for the middle-caliber and small-caliber interferometers at present by the advantages of simplicity, effectiveness, low cost and high precision. However, when the caliber of the reference mirror exceeds phi 600mm, the mass of the reference mirror is obviously increased, for example, the weight of the reference mirror with the caliber of phi 800mm reaches about 800KG, so that the traditional mechanical phase shifting mode cannot realize phase shifting measurement, namely the phase shifting is not movable. Therefore, the traditional reference mirror mechanical phase shifting mode is difficult to realize large-caliber high-precision phase shifting interferometry.
Currently, large-caliber phase-shifting interferometers with the diameter of more than 600mm such as 24 inches of ZYGO and 610mm caliber interferometers of Veeco technology all adopt a wavelength tuning phase-shifting mode, a tunable laser is used as an interferometer light source, and the phase shift is introduced by tuning the wavelength change of the laser. The advantage of wavelength tuning phase shifting is that both the reference mirror and the measured mirror remain stationary during the phase shifting measurement, which greatly increases the mechanical stability of the instrument system. However, the wavelength tuning phase shift method has the following problems in principle: 1) Chromatic aberration is introduced by wavelength change, lens parameters are difficult to design, and an optical system has large adjustment error, so that the system has large phase shift error; 2) The amount of phase shift introduced by wavelength tuning is related to the length of an interference cavity, the phase shift in the case of a long interference cavity needs wavelength tuning with high resolution, the phase shift in the case of a short interference cavity needs wavelength tuning in a large range, and the existing wavelength tuning laser cannot meet the requirements of high resolution and large range tuning at the same time; therefore, the application range of wavelength tuning phase shift is limited, and the phase shift precision needs to be improved. Wavelength tuning utilizes variable wavelength to realize phase shift, changes a reference, introduces principle errors, is difficult to realize high-precision measurement and tracing, and has the problem of inaccurate measurement.
Disclosure of Invention
Aiming at the problems of the conventional mechanical phase shift immobility and inaccurate wavelength tuning measurement in the large-caliber interferometry, the invention aims to provide the mechanical phase shift method for the air-floatation supporting heavy-load reference mirror, which realizes the phase shift of the heavy-load reference mirror in the space nanometer level by the three-point synchronous driving of the space flexibly combined by the piezoelectric ceramics and the springs at the two sides; the high-precision displacement sensor is combined with the piezoelectric ceramic to realize in-situ monitoring and PID closed-loop driving of three points in space; the air floatation support gravity unloading of the heavy-load reference mirror and the reference mirror space phase shift error calibration model are used for realizing the space translation of the heavy-load reference mirror in the nano-scale resolution, realizing the high-precision high-stability mechanical phase shift in the large-caliber interferometry and avoiding the principle defect of the conventional large-caliber wavelength tuning phase shift. The invention is beneficial to the construction of the large-caliber phase-shifting interferometer and improves the large-caliber optical detection and processing precision.
The aim of the invention is achieved by the following technical scheme.
The invention discloses a mechanical phase shifting method of an air floatation supporting heavy-load reference mirror, which comprises the following steps:
step one: root of Chinese characterAccording to the large-caliber interferometry phase shift measurement principle, the phase shift displacement p is obtained d Phase shift delta (t) from reference mirror in interferometry n ) The relation between the two is that the phase shift p of the reference mirror on the air floatation workbench is monitored in real time through a high-precision displacement sensor d And the spatial attitude of the reference mirror realizes real-time monitoring and high-precision compensation of phase shift errors, and ensures the accuracy of phase shift in the interferometry process.
Where λ is the laser source wavelength.
Step two: the spatial three-point synchronous driving method combining piezoelectric ceramics and spring soft connection is utilized to ensure that the reference mirror realizes spatial translation in the phase shifting process. The driving structure comprises an air floatation guide rail, piezoelectric ceramics, a spring flexible connecting mechanism and the like. Gravity unloading of the heavy-duty reference mirror is realized through the air floatation guide rail, zero-clearance micro-displacement of a mechanical phase shifting system of the heavy-duty reference mirror is realized by utilizing elastic deformation of a spring, and piezoelectric ceramics are used as phase shifting steps of the mechanical phase shifting mechanism.
Step three: and (5) performing initial calibration of the mechanical phase shifting system of the heavy-duty reference mirror. The problems of different phasors and inconsistent displacement in three directions exist in the mechanical phase shifting process, so that the phase shifting steps obtained by monitoring the three displacement sensors are inconsistent, linear, nonlinear and inclined phase shifting errors exist, and the phase shifting errors are large, so that the measured surface shape result cannot be calculated. Therefore, for the high-precision mechanical phase shifting system of the air-floatation supported heavy-duty reference mirror, the calibration is an important link. In the primary calibration process, the displacement data after phase shifting and the voltage-displacement curve of the three-way PZT are obtained, a least square fitting is carried out, a voltage-displacement quadratic polynomial is obtained, and the voltage-displacement relation of the piezoelectric ceramics calibrated by the quadratic polynomial is used as the basis of an input signal of a mechanical phase shifting system, so that the accurate phase shifting of the large-caliber mechanical phase shifting system is ensured. The high-precision displacement sensor monitors that the phase shift value is s and the ideal phase shift value is s in real time ideal The driving voltage is u,the least square fitting is adopted to calculate the required voltage as the input voltage of the piezoelectric ceramic, and the output voltage u of the piezoelectric ceramic after calibration is obtained out And (3) finishing mechanical phase shift primary calibration of the heavy-load reference mirror:
step four: and performing in-situ monitoring and PID closed-loop driving control on three points in space, constructing a mechanical phase shifting model of the heavy-duty reference mirror for realizing closed-loop driving of the mechanical phase shifting system of the heavy-duty reference mirror, and simplifying the mechanical phase shifting system into a mass-spring-damping second-order system. Based on mechanical and electronic parameters of the driving structure in the second step and rigidity and damping of the air floatation supporting mechanism, constructing a spatial translational motion model of the heavy-duty reference mirror, and obtaining an open-loop transfer function of the large-caliber mechanical phase shifting system, wherein the open-loop transfer function is expressed as follows:
wherein G is PSI G is the transfer function of the mechanical phase shift system of the heavy-duty reference mirror PZT As the transfer function of piezoelectric ceramics, G ac Is a transfer function of a direct current high voltage amplification power supply, and G ac ＝K v ，K t The rigidity of the mechanical phase shifting transmission mechanism comprises a driving component PZT and a spring linking mechanism. R in equivalent circuit of PZT i Is the internal resistance of the PZT driving power supply, R p Is the equivalent resistance of PZT, C p Is equivalent capacitance of PZT, alpha is voltage displacement conversion coefficient, omega n Is the undamped natural frequency of the system, and the damping ratio of the xi system.
Based on a transfer function of a mechanical phase shift system of a heavy-duty reference mirror, a feedback model of the mechanical phase shift control system is constructed, the spatial attitude of the reference mirror TF on the air floatation workbench is monitored in real time by utilizing a high-precision displacement sensor, the transfer function is brought into the phase shift control system, a fuzzy PID control mechanism is adopted, the phase shift amount of each step of the reference mirror TF is ensured to be the same, the angle swing error and the rotation error are reduced, and the in-situ monitoring and PID closed-loop driving control of three points in space are realized.
Step five: and performing phase unwrapping, unwrapping and Zernike polynomial fitting to remove the translation and inclination based on the obtained phase shift of the steps to obtain the RF surface shape parameters of the standard measured mirror, namely, monitoring data through a high-precision displacement sensor to realize the measurement of the RF surface shape parameters of the standard measured mirror.
According to the mechanical phase shifting method of the air-bearing heavy-duty reference mirror, in the large-caliber interference phase shifting measurement, the zero-clearance micro displacement of a mechanical phase shifting system of the heavy-duty reference mirror is realized through the elastic deformation of the spring, the displacement output by the piezoelectric ceramic driver is ensured to be transmitted to the output end of the whole large-caliber mechanical phase shifting device, and the mechanical phase shifting output precision is ensured. The piezoelectric ceramic and the spring are flexibly connected and combined to realize the spatial translation of the heavy-load reference mirror. The large-caliber mechanical phase-shifting driving system realizes space synchronous driving by adopting a flexible regulation and control micro-displacement driving mode through two rows of identical spring queues at the side edge. The driving structure comprises an air floatation guide rail, piezoelectric ceramics, a spring flexible connecting mechanism and the like.
The invention discloses a mechanical phase shift method of an air floatation supporting heavy-duty reference mirror, which is based on a transfer function of a mechanical phase shift system of the heavy-duty reference mirror, constructs a feedback model of a mechanical phase shift control system, monitors the spatial posture of a reference mirror TF on an air floatation workbench in real time by utilizing a high-precision displacement sensor, brings transfer function parameters into the phase shift control system, adopts a fuzzy PID control mechanism, takes an error e and the change ec of the error as input, and corrects PID parameters on line by utilizing the fuzzy rule so as to meet the self-setting requirements of e and ec of the PID parameters at different moments. Proportion of deviation K P Integral K I Differential K D The control quantity is formed by linear combination, and in the fuzzy control process, the output of the controller is calculated by combining the position given difference value with the position feedback, namely the position error, with 3 parameters of proportion, integral and derivative. Namely, the position deviation e and the change rate ec of the position deviation are input, and the change amount delta K of 3 parameters of PID is output P 、ΔK I 、ΔK D . Thus, by controlling the controlled object, the simulation is performedHuman thinking is not dependent on an object model, and the parameter setting of the large-caliber mechanical phase shifting system is performed by utilizing the dynamic information of a controlled process and reasoning a proper control quantity according to rule knowledge. And optimizing the controller parameters in real time. The phase shift amount of each step of the reference mirror TF is guaranteed to be the same, the angle swing error and the rotation error are reduced, and the in-situ monitoring and PID closed-loop driving control of three points in space are realized.
The invention discloses a mechanical phase shifting method of an air floatation supporting heavy-load reference mirror, which comprises the steps of firstly carrying out system calibration before large-caliber interferometry, calculating nonlinear coefficients and phase shifting quantities of each channel in a mechanical phase shifting system according to displacement data acquired by a high-precision displacement sensor, and carrying out correction of piezoelectric ceramic feeding parameters according to a calibration algorithm of the large-caliber phase shifting system, thereby effectively inhibiting phase shifting errors of the large-caliber interferometry phase shifting system. When large-caliber mechanical phase shifting calibration is carried out, linear voltage is output according to a PZT control board card, the voltage is increased by 25mV in each step, the time of each step is 10ms, the indication of a displacement sensor is recorded once every moving step, the test is repeated for ten times, and the average is obtained, so that the voltage-displacement characteristic curve of each path of piezoelectric ceramics is obtained. Thus, the nonlinear coefficient and the phase shift amount of each channel in the mechanical phase shift system are obtained. Then evaluating the phase shift calibration result, and performing linear fitting on a voltage-displacement curve of the phase shifter by adopting a least square method to obtain a first-order linear equation:
D s ＝p 0 +p 1 d r +γ
wherein p is 0 、p 1 And (3) linear fitting polynomial coefficients, and gamma is fitting residual error. |gamma| max Maximum value of residual absolute value, D s For the maximum displacement of PZT, the PZT nonlinear coefficient τ can be expressed as:
the degree of deviation of the actual voltage-displacement of the PZT from the theoretical voltage-displacement is characterized by a nonlinear coefficient. The greater τ indicates a greater degree of deviation, and thus greater phase shift error for the mechanical phase shift system. And carrying out least square method quadratic fitting according to the PZT output curve in the calibration of the mechanical phase shifting system to solve the voltage required by each step when the PZT moves by 1000 nm. The obtained voltage value is used as a PZT input signal. And the accuracy of the phase shift quantity of each phase shift is represented by the phase shift step accuracy.
The invention discloses a mechanical phase shifting method of an air floatation supporting heavy-load reference mirror, which adopts calibration before phase shifting and PID real-time monitoring control in the process of carrying out large-caliber mechanical phase shifting, and can select to carry out the calibration before phase shifting and the PID real-time monitoring calibration simultaneously or select to carry out the phase shifting calibration only or carry out the PID real-time monitoring control only to carry out phase shifting error suppression according to different conditions of a large-caliber mechanical phase shifting system.
The invention discloses a mechanical phase shifting method of an air-bearing heavy-load reference mirror, which adopts a high-precision displacement sensor to monitor, wherein the displacement sensor comprises a high-precision grating sensor and a capacitance sensor, and comprises other high-precision displacement monitoring sensors.
The beneficial effects are that:
1. the invention discloses a mechanical phase shifting method of an air-bearing heavy-load reference mirror, which realizes the phase shifting of the heavy-load reference mirror in space nanometer level by the synchronous driving of three points in space combined by piezoelectric ceramics and springs; the spring flexible connection mechanism can ensure that the displacement output by the piezoelectric ceramic driver is transmitted to the output end of the whole phase shifting mechanism without gaps, and provides a novel phase shifting method and means for the construction of the large-caliber phase shifting interferometer.
2. According to the mechanical phase shifting method of the air-bearing heavy-duty reference mirror, in the mechanical phase shifting system of the heavy-duty reference mirror, the air-bearing is used for supporting, the spring soft connection is combined with the piezoelectric ceramics, the heavy-duty reference mirror TF is driven to realize phase shifting, and in order to ensure the phase shifting precision, the control mode of combining primary calibration with PID real-time feedback is adopted to realize high-precision phase shifting measurement. The invention solves the problem that the traditional mechanical phase shift can not realize the phase shift of large-caliber interferometry, and improves the mechanical phase shift precision.
3. According to the mechanical phase shifting method for the air-bearing heavy-duty reference mirror, through the air-bearing gravity unloading of the heavy-duty reference mirror and the reference mirror space phase shifting error calibration model, the space translation of the heavy-duty reference mirror in the nano-scale resolution is realized, the high-precision high-stability mechanical phase shifting in the large-caliber interferometry is realized, and the principle defect of the existing large-caliber wavelength tuning phase shifting is avoided. The invention provides a novel phase shifting method and means for the construction of a large-caliber phase shifting interferometer.
Drawings
FIG. 1 is a schematic diagram of a mechanical phase shifting method of an air bearing heavy load reference mirror according to the present invention;
FIG. 2 is a schematic diagram of a spatial translational motion model of an air bearing heavy-duty reference mirror according to the invention;
FIG. 3 is a schematic diagram of the mechanical phase shift calibration and PID control of the reloaded reference mirror of the present invention;
FIG. 4 is a schematic diagram of a mechanical phase shift calibration of an air bearing heavy duty reference mirror according to the present invention;
FIG. 5 is a graph of the high-precision phase shift result of an air bearing heavy-duty reference mirror according to the invention;
wherein: 1-large caliber interferometer host machine support frame, 2-large caliber interferometer host machine, 3-small caliber beam expanding lens group, 4-large caliber collimating lens, precision adjusting frame of 5-reference lens, 6-reference lens TF, 7-high precision displacement monitoring sensor, 8-spring mechanism, 9-piezoelectric ceramic PZT, 10-air floatation guide rail, 11-standard measured lens RF, precision adjusting frame of 12-standard measured lens, 13-phase displacement stepping, rigidity K of 14-mechanical phase shifting transmission mechanism t 15-weight M of the large-caliber mechanical phase shifting mechanism, 16-rigidity K of the mechanical phase shifting guide rail and 17-damping coefficient mu.
Detailed Description
The invention is further described below with reference to the drawings and examples.
As shown in figure 1, in the mechanical phase shifting method of the air floatation supporting heavy-duty reference mirror, parallel beams emitted by an interferometer host 2 positioned on a large-caliber interferometer host support frame 1 pass through a small-caliber beam expanding system 3, and are collimated by a large-caliber collimating mirror 4 to form parallel beams with caliber of 820mm, and enter the large-caliber mechanical phase shifting system to be reflected by the surfaces of a reference mirror 6 and a standard measured mirror 11 in sequence, so that reference light and measuring light are formed. The reference light and the measuring light return along the original path of the optical axis of the large-caliber interferometer system, and enter the large-caliber interferometer host 2 after the two beams of the reference light and the measuring light are coherently interfered, so that interference fringes are formed to process and obtain the surface shape result of the measured mirror. In the large-caliber mechanical phase shifting system, as shown in fig. 2, a reference mirror 6 is fixed on a heavy carrier gas floating guide rail 10, a spring mechanism 8 interacts with piezoelectric ceramics 9, a precise adjusting mechanism 5 for driving the reference mirror on the air floating guide rail and the reference mirror 7 move in a stepping manner along a linear guide rail with high precision and no friction, a high-precision displacement monitoring sensor 7 monitors in the phase shifting process to obtain a phase shifting displacement step 13, and further real-time monitoring and high-precision compensation of phase shifting errors are realized.
In order to ensure the phase shifting precision of the large-caliber mechanical phase shifting system, a mechanical phase shifting system calibration and PID feedback control scheme shown in figure 3 is adopted, and the spatial attitude of a reference mirror TF on the air floatation workbench is monitored in real time by utilizing a high-precision displacement sensor. In the mechanical phase shifting system of the heavy-duty reference mirror, the spring is combined with the PZT through the air floatation support, the heavy-duty reference mirror TF is driven to realize phase shifting, and in order to ensure the phase shifting precision, the control mode of combining primary calibration with PID real-time feedback is adopted to realize high-precision phase shifting measurement. In the primary calibration process, the displacement data after phase shifting and the voltage-displacement curve of the three paths of PZT are obtained, a least square fitting is carried out, a voltage-displacement quadratic polynomial is obtained, and according to the relationship of PZT voltage-displacement calibrated by the quadratic polynomial, the voltage-displacement quadratic polynomial is used as the basis of an input signal of a mechanical phase shifting system, so that the accurate phase shifting of the large-caliber mechanical phase shifting system is ensured. In the process of large-caliber interferometry, a transfer function is brought into a phase-shifting control system, PID closed-loop driving is adopted, angular pendulum errors and rotation errors are reduced in the phase-shifting process, in-situ monitoring of three points in space is realized, phase-shifting errors are corrected, and spatial translation of a reference mirror TF is ensured as shown in FIG. 4.
By the monitoring of the high-precision displacement sensor, the primary calibration and PID closed-loop control are realized, and the phase shift error existing in the large-caliber mechanical system is effectively restrained. FIG. 5 shows the actual output displacement curve of the mechanical phase shift system of the heavy-duty reference mirror after the initial calibration is completed, the single-step phase shift time is 40ms, the curves obtained by monitoring the upper and lower high-precision displacement sensors of the reference mirror TF are basically coincident, and the difference value of the three phase shift displacement curves is smaller than 10nm. It can be seen that the up-and-down moving distance of the TF reference mirror is basically the same, the angle pendulum error and the rotation error in the phase shifting process are small, the nano-scale resolution space translation of the heavy-duty reference mirror is realized, the initial calibration of the mechanical phase shifting system lays a good foundation for the improvement of the resolving precision of the phase shifting interference fringes, and the measuring precision of the large-caliber interference system is ensured.
The mechanical phase shift method for the air-bearing heavy-load reference mirror comprises the following measuring steps:
step one: according to the large-caliber interference phase shift measurement principle, the phase shift displacement p is obtained d Phase shift delta (t) from reference mirror in interferometry n ) The relation between the two is that the phase shift p of the reference mirror on the air floatation workbench is monitored in real time through a high-precision displacement sensor d And the spatial attitude of the reference mirror realizes real-time monitoring and high-precision compensation of phase shift errors, and ensures the accuracy of phase shift in the interferometry process.
Where λ is the laser source wavelength.
Step two: the spatial three-point synchronous driving method combining piezoelectric ceramics and spring soft connection is utilized to ensure that the reference mirror realizes spatial translation in the phase shifting process. The driving structure comprises an air floatation guide rail, piezoelectric ceramics, a spring flexible connecting mechanism and the like. The gravity unloading of the heavy-duty reference mirror is realized through the air floatation guide rail, the zero-clearance micro-displacement of the mechanical phase shifting system of the heavy-duty reference mirror is realized through the elastic deformation of the spring, and the piezoelectric ceramics are used as the phase shifting steps of the mechanical phase shifting mechanism.
Step three: and (5) performing primary calibration of the large-caliber interference phase shifting system. In the primary calibration process, displacement data after five steps of phase shifting and a voltage-displacement curve of three paths of PZT are obtained, a least square fitting is carried out, a voltage-displacement quadratic polynomial is obtained, and according to the relationship of PZT voltage-displacement calibrated by the quadratic polynomial, the voltage-displacement quadratic polynomial is used as a basis of an input signal of a mechanical phase shifting system, so that accurate phase shifting of the large-caliber mechanical phase shifting system is ensured. High precisionThe displacement sensor monitors that the displacement value is s in real time, and the ideal value of the displacement is s ideal The driving voltage is u, the least square fitting is adopted, the required voltage is calculated and is used as the input voltage of the PZT, and the output voltage u of the piezoelectric ceramic after calibration is obtained out And (3) finishing mechanical phase shift primary calibration of the heavy-load reference mirror:
step four: and performing in-situ monitoring and PID closed-loop driving control on three points in space, constructing a mechanical phase shifting model of the heavy-load reference mirror, and simplifying the mechanical phase shifting system into a mass-spring-damping second-order system. And (3) constructing a spatial translational motion model of the heavy-duty reference mirror based on the mechanical and electronic parameters of the driving structure in the step two, the rigidity, the damping and other parameters of the air floatation supporting mechanism, and obtaining an open-loop transfer function of the large-caliber mechanical phase shifting system. Based on a transfer function of a mechanical phase shift system of a heavy-load reference mirror, and a high-precision displacement sensor, the spatial attitude of the reference mirror TF on an air floatation workbench is monitored in real time, the transfer function is brought into a phase shift control system, a fuzzy PID control mechanism is adopted, the phase shift amount of each step of the reference mirror TF is ensured to be the same, the angle swing error and the rotation error are reduced, and the in-situ monitoring and PID closed-loop driving control of three points in space are realized.
Step five: and after the mechanical phase shift calibration of the heavy-duty reference mirror is completed, carrying out the cavity precision test of the heavy-caliber interferometer, and carrying out algorithm processing such as phase expansion, unwrapping, zernike polynomial fitting elimination translation amount and inclination amount based on the obtained phase shift of the steps to obtain the RF surface shape parameters of the standard measured mirror. The experiment shows that the accuracy of the PV cavity reaches 0.06591 lambda, the average RMS value is 0.00912 lambda, and the simple repeatability of the RMS reaches 0.0004 lambda. In order to verify the accuracy of the test result, the cavity accuracy test is carried out on a ZYGO 32-inch interferometer by using the same TF and RF, and the experimental result shows that the test result obtained by using the air bearing heavy load reference mirror mechanical phase shifting method provided by the invention is identical to the test result of the ZYGO 32-inch interferometer, so that the accuracy and the reliability of the mechanical phase shifting method provided by the invention are verified.
The above description of the embodiments of the invention has been presented in connection with the drawings but these descriptions should not be construed as limiting the scope of the invention, which is defined by the appended claims, and any changes based on the claims are intended to be covered by the invention.
Claims (6)
1. A mechanical phase shifting method of an air-bearing heavy-load reference mirror is characterized by comprising the following steps of: the method comprises the following steps of,
step one: according to the large-caliber interference phase shift measurement principle, the phase shift displacement p is obtained d Phase shift delta (t) from reference mirror in interferometry n ) The relation between the two is that the phase shift p of the reference mirror on the air floatation workbench is monitored in real time through a high-precision displacement sensor d The real-time monitoring and high-precision compensation of the phase shift error are realized by the spatial gesture of the reference mirror, and the accuracy of the phase shift in the interferometry process is ensured;
wherein lambda is the wavelength of the laser light source;
step two: the spatial three-point synchronous driving method combining the piezoelectric ceramic and the spring soft connection is utilized to ensure that the reference mirror realizes spatial translation in the phase shifting process; the driving structure comprises an air floatation guide rail, piezoelectric ceramics, a spring flexible connecting mechanism and the like; gravity unloading of the heavy-duty reference mirror is realized through the air floatation guide rail, zero-clearance micro-displacement of a mechanical phase shifting system of the heavy-duty reference mirror is realized by utilizing elastic deformation of a spring, and piezoelectric ceramics are used as phase shifting steps of a mechanical phase shifting mechanism;
step three: performing primary calibration of a mechanical phase shifting system of the heavy-duty reference mirror; the phase shift steps obtained by monitoring the three displacement sensors are inconsistent due to the problems of different phase shift quantities and inconsistent displacement in three directions in the mechanical phase shift process, linear, nonlinear and inclined phase shift errors exist, and the measured surface shape result cannot be calculated due to the large phase shift error;therefore, for the high-precision mechanical phase shifting system of the air-float supported heavy-duty reference mirror, the calibration is an important link; in the primary calibration process, the obtained phase-shifted displacement data and the voltage-displacement curve of the three-way PZT are subjected to least square fitting to obtain a voltage-displacement quadratic polynomial, and the voltage-displacement relation of the piezoelectric ceramics calibrated by the quadratic polynomial is used as the basis of an input signal of a mechanical phase shifting system to ensure the accurate phase shifting of the large-caliber mechanical phase shifting system; the high-precision displacement sensor monitors that the phase shift value is s and the ideal phase shift value is s in real time ideal The driving voltage is u, the least square fitting is adopted, the required voltage is calculated and is used as the input voltage of the piezoelectric ceramic, and the output voltage u of the piezoelectric ceramic after calibration is obtained out And (3) finishing mechanical phase shift primary calibration of the heavy-load reference mirror:
step four: performing in-situ monitoring and PID closed-loop driving control on three points in space, constructing a mechanical phase shifting model of the heavy-duty reference mirror for realizing closed-loop driving of the mechanical phase shifting system of the heavy-duty reference mirror, and simplifying the mechanical phase shifting system into a mass-spring-damping second-order system; based on mechanical and electronic parameters of the driving structure in the second step and rigidity and damping of the air floatation supporting mechanism, constructing a spatial translational motion model of the heavy-duty reference mirror, and obtaining an open-loop transfer function of the large-caliber mechanical phase shifting system, wherein the open-loop transfer function is expressed as follows:
wherein G is PSI G is the transfer function of the mechanical phase shift system of the heavy-duty reference mirror PZT As the transfer function of piezoelectric ceramics, G ac Is a transfer function of a direct current high voltage amplification power supply, and G ac ＝K v ，K t The rigidity of the mechanical phase shifting transmission mechanism comprises a driving component PZT and a spring linking mechanism; r in equivalent circuit of PZT i Is the internal resistance of the PZT driving power supply, R p Is the equivalent resistance of PZT, C p Is equivalent capacitance of PZT, alpha is voltage displacement conversion coefficient, omega n Damping ratio of the xi system is the undamped natural frequency of the system;
based on a transfer function of a mechanical phase shift system of a heavy-duty reference mirror, a feedback model of the mechanical phase shift control system is constructed, the spatial attitude of the reference mirror TF on the air floatation workbench is monitored in real time by utilizing a high-precision displacement sensor, the transfer function is brought into the phase shift control system, a fuzzy PID control mechanism is adopted, the phase shift amount of each step of the reference mirror TF is ensured to be the same, the angle swing error and the rotation error are reduced, and the in-situ monitoring and PID closed-loop driving control of three points in space are realized;
step five: and performing phase unwrapping, unwrapping and Zernike polynomial fitting to remove the translation and inclination based on the obtained phase shift of the steps to obtain the RF surface shape parameters of the standard measured mirror, namely, monitoring data through a high-precision displacement sensor to realize the measurement of the RF surface shape parameters of the standard measured mirror.
2. The mechanical phase shifting method of the air floatation supporting heavy-load reference mirror is characterized in that: in the large-caliber interference phase shift measurement, the zero-clearance micro displacement of a heavy-duty reference mirror mechanical phase shift system is realized through the elastic deformation of a spring, so that the displacement output by a piezoelectric ceramic driver is transmitted to the output end of the whole large-caliber mechanical phase shift device, and the mechanical phase shift output precision is ensured; the piezoelectric ceramics and the spring are flexibly connected and combined to realize the spatial translation of the heavy-load reference mirror; the large-caliber mechanical phase-shifting driving system realizes space synchronous driving by adopting a flexible regulation and control micro-displacement driving mode through two rows of identical spring queues at the side edge; the driving structure comprises an air floatation guide rail, piezoelectric ceramics and a spring flexible connecting mechanism.
3. The mechanical phase shifting method of the air floatation supporting heavy-load reference mirror is characterized in that: based on transfer function of mechanical phase shift system of heavy-duty reference mirror, a feedback model of mechanical phase shift control system is constructed, and high-precision displacement sensor is utilized to monitor air floatation in real timeThe spatial gesture of a reference mirror TF on a workbench is brought into a phase shift control system, a fuzzy PID control mechanism is adopted, an error e and a change ec of the error are taken as input, and PID parameters are corrected on line by using a fuzzy rule so as to meet the requirements of e and ec at different moments on PID parameter self-tuning; proportion of deviation K P Integral K I Differential K D The control quantity is formed by linear combination, and in the fuzzy control process, the output of the controller is calculated by the difference value between position setting and position feedback, namely the position error combines 3 parameters of proportion, integral and derivative; namely, the position deviation e and the change rate ec of the position deviation are input, and the change amount delta K of 3 parameters of PID is output P 、ΔK I 、ΔK D The method comprises the steps of carrying out a first treatment on the surface of the Therefore, by controlling the controlled object, the parameter setting of the large-caliber mechanical phase shifting system is performed by utilizing the dynamic information of the controlled process and reasoning the proper control quantity according to the rule knowledge without depending on the object model; and optimizing the parameters of the controller in real time; the phase shift amount of each step of the reference mirror TF is guaranteed to be the same, the angle swing error and the rotation error are reduced, and the in-situ monitoring and PID closed-loop driving control of three points in space are realized.
4. The mechanical phase shifting method of the air floatation supporting heavy-load reference mirror is characterized in that: before large-caliber interferometry, firstly, carrying out system calibration, calculating nonlinear coefficients and phase shifting quantities of each channel in a mechanical phase shifting system according to displacement data acquired by a high-precision displacement sensor, and carrying out correction of piezoelectric ceramic feeding parameters according to a large-caliber phase shifting system calibration algorithm to effectively inhibit phase shifting errors of the large-caliber interferometry phase shifting system; when large-caliber mechanical phase shifting calibration is carried out, linear voltage is output according to a PZT control board card, the voltage is increased by 25mV in each step, the total time is 200 steps, the time of each step is 10ms, the indication of a displacement sensor is recorded once every moving step, the test is repeated for ten times, and the average is taken, so that the voltage-displacement characteristic curve of each path of piezoelectric ceramics is obtained; thus, nonlinear coefficients and phase shift amounts of each channel in the mechanical phase shift system are obtained; then evaluating the phase shift calibration result, and performing linear fitting on a voltage-displacement curve of the phase shifter by adopting a least square method to obtain a first-order linear equation:
D s ＝p 0 +p 1 d r +γ
wherein p is 0 、p 1 The linear fitting polynomial coefficient is adopted, and gamma is the fitting residual error; |gamma| max Maximum value of residual absolute value, D s For the maximum displacement of PZT, the PZT nonlinear coefficient τ can be expressed as:
representing the deviation degree of actual voltage-displacement and theoretical voltage-displacement of the PZT by using a nonlinear coefficient; when τ is larger, the deviation degree is larger, and the phase shift error of the mechanical phase shift system is larger; performing least square quadratic fitting according to the PZT output curve in the calibration of the mechanical phase shifting system to solve the voltage required by each step when the PZT moves by 1000 nm; taking the obtained voltage value as a PZT input signal; and the accuracy of the phase shift quantity of each phase shift is represented by the phase shift step accuracy.
5. The mechanical phase shifting method of the air floatation supporting heavy-load reference mirror is characterized in that: in the process of carrying out large-caliber mechanical phase shifting, adopting calibration before phase shifting and PID real-time monitoring control, selecting the method for carrying out system calibration before large-caliber interferometry according to different conditions of a large-caliber mechanical phase shifting system; or the in-situ monitoring through three points of space as claimed in claim 3 is used simultaneously with a real-time PID closed-loop driving control method; or selecting only the method as claimed in claim 4 or selecting only the method as claimed in claim 3 for phase shift error suppression.
6. The mechanical phase shifting method of the air floatation supporting heavy-load reference mirror is characterized in that: the high-precision displacement sensor is used for monitoring, and comprises a high-precision grating sensor and a capacitance sensor, and comprises other high-precision displacement monitoring sensors.
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