A piezoelectric adaptive x-ray mirror surface shape control system and method based on wavefront feedback

Abstract

This application provides a piezoelectric adaptive X-ray mirror surface shape control system and method based on wavefront feedback. The system includes an X-ray mirror, a wavefront detector, a piezoelectric controller, and a piezoelectric actuator group. The piezoelectric actuator group includes an odd number of piezoelectric actuators arranged along the meridian of the mirror, wherein the middle piezoelectric actuator corresponds to the peak position of the surface shape deformation caused by thermal load. The piezoelectric controller determines the current residual wavefront error based on the reflected X-ray wavefront information and judges whether it meets the preset wavefront holding condition. If it does not meet the condition, it generates a piezoelectric actuator voltage based on the unit response relationship of each piezoelectric actuator and a preset voltage constraint to drive the piezoelectric actuator to adjust the mirror surface shape, and forms a closed-loop control by re-acquiring wavefront information. This application can improve the wavefront holding accuracy of X-ray mirrors under thermal load.

Description

Technical Field

[0001] This application relates to the field of X-ray mirror surface shape control technology, and in particular to a piezoelectric adaptive X-ray mirror surface shape control system and method based on wavefront feedback. Background Technology

[0002] High-repetition-rate hard X-ray free-electron lasers and fourth-generation synchrotron radiation sources can provide high-brightness, high-coherence X-ray beams. To obtain a stable focused spot and maintain wavefront quality at the experimental sample, the grazing-incidence X-ray mirrors in the beamline need to minimize wavefront distortion caused by surface shape errors during transmission.

[0003] Under high average power or high repetition rate operating conditions, X-ray mirrors are subjected to significant thermal loads. Even with active cooling structures, mirrors can still experience thermally induced surface deformation on the order of nanometers to tens of nanometers. Since X-ray mirrors typically operate at small grazing angles of incidence, even minute errors in mirror height can cause reflection wavefront distortion, further leading to downstream focusing spot broadening, sidelobe enhancement, or a decrease in Strell ratio.

[0004] Existing methods for reducing thermally induced surface shape errors mainly include cooling structure optimization, thermal compensation, and adaptive mirror compensation. Adaptive mirrors typically utilize piezoelectric actuators or bending mechanisms to actively adjust the mirror surface shape to compensate for surface deviations caused by thermal load, assembly errors, or other disturbances. However, existing adaptive mirrors and their control methods still have shortcomings in high-heat-load X-ray applications.

[0005] On the one hand, the arrangement of piezoelectric actuators often does not fully take into account the spatial distribution of thermo-induced deformation in the radial direction of the mirror. When the peak of thermo-induced deformation is located near the radial center of symmetry of the mirror, if the arrangement of the piezoelectric actuators places the central region at the interval between adjacent actuators, the local surface shape error in that region is difficult to be effectively compensated.

[0006] On the other hand, the surface response generated by piezoelectric actuators has spatial coupling characteristics. If compensation is based solely on the independent adjustment of a single actuator, it is difficult to achieve a stable overall surface correction effect while satisfying voltage amplitude constraints and adjacent voltage difference constraints.

[0007] Furthermore, during high-repetition-frequency operation, thermal load and surface shape errors may change with the operating conditions. Existing methods often lack a closed-loop correction mechanism based on actual X-ray wavefront feedback, making it difficult to continuously update the piezoelectric actuator voltage according to real-time or near-real-time residual wavefront errors.

[0008] Therefore, it is necessary to provide an adaptive piezoelectric X-ray mirror surface shape control system and method, which combines piezoelectric actuator arrangement, unit surface shape response relationship, preset voltage constraint and wavefront feedback closed-loop control to achieve effective compensation and wavefront maintenance of thermally induced surface shape error of X-ray mirror. Summary of the Invention

[0009] In view of the above-mentioned problems in the prior art, the purpose of this application is to provide a piezoelectric adaptive X-ray mirror surface shape control system and method based on wavefront feedback, so as to improve the surface shape control accuracy and wavefront holding capability of X-ray mirrors under high thermal load conditions.

[0010] To achieve the above objectives, a first aspect of this application provides a piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback. The system includes: an X-ray mirror, a wavefront detector, a piezoelectric controller, and a piezoelectric actuator assembly. The X-ray mirror includes an optical reflecting surface for reflecting incident X-rays. The piezoelectric actuator assembly is disposed opposite the optical reflecting surface of the X-ray mirror, and includes an odd number of piezoelectric actuators arranged sequentially along the meridional direction of the X-ray mirror. The center of the piezoelectric actuator located in the middle position coincides with the center of symmetry of the X-ray mirror in the meridional direction, the center of symmetry corresponding to the peak position of surface shape deformation caused by thermal load. The wavefront detector is disposed on the outgoing light path side of the X-ray mirror, and its output terminal is connected to the signal input terminal of the piezoelectric controller for acquiring X-ray wavefront information reflected by the X-ray mirror and sending the X-ray wavefront information to the piezoelectric controller. The piezoelectric controller is used to... The current residual wavefront error of the X-ray reflector is determined, and it is judged whether the current residual wavefront error meets the preset wavefront maintenance condition. When the current residual wavefront error meets the preset wavefront maintenance condition, the piezoelectric controller maintains the current piezoelectric actuator voltage applied to the piezoelectric actuator group and controls the wavefront detector to continue to collect the X-ray wavefront information. When the current residual wavefront error does not meet the preset wavefront maintenance condition, the piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the pre-obtained unit response relationship of each piezoelectric actuator and the equivalent residual surface shape converted from the current residual wavefront error. The controller applies voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector. Based on the X-ray wavefront information re-collected by the wavefront detector, the residual wavefront error is updated, and the judgment of the preset wavefront maintenance condition is continued according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector. In some embodiments, the process by which the piezoelectric controller determines the current residual wavefront error information based on the X-ray wavefront information includes: reconstructing the X-ray wavefront information to obtain the measured wavefront distribution after reflection by the X-ray mirror; spatially registering and aligning the measured wavefront distribution with a preset target wavefront distribution to obtain an initial wavefront error distribution; removing low-order terms from the initial wavefront error distribution to obtain a residual wavefront error distribution; calculating the root mean square value of the wavefront error based on the residual wavefront error distribution, and using the root mean square value of the wavefront error as an evaluation parameter characterizing the current residual wavefront error. The low-order term removal process includes removing piston terms, tilt terms, and defocus terms corresponding to the optimal sphere or optimal arc.

[0011] In some embodiments of the first aspect of this application, the piezoelectric controller is used to determine the current residual wavefront error of the X-ray reflector based on the X-ray wavefront information. The specific process includes: reconstructing the X-ray wavefront information to obtain a measured wavefront distribution after reflection by the X-ray reflector; spatially registering and aligning the measured wavefront distribution with a preset target wavefront distribution using a phase reference, and calculating the difference between the measured wavefront distribution and the preset target wavefront distribution to obtain an initial wavefront error distribution; performing low-order aberration removal processing on the initial wavefront error distribution, wherein the low-order aberration removal processing includes removing piston terms, tilt terms, and defocus terms corresponding to the optimal spherical surface from the initial wavefront error distribution to obtain a residual wavefront error distribution; calculating the root mean square value of the wavefront error based on the residual wavefront error distribution, and using the root mean square value of the wavefront error as the current residual wavefront error.

[0012] In some embodiments of the first aspect of this application, the preset wavefront preservation condition includes: the root mean square value of the wavefront error characterizing the current residual wavefront error is less than or equal to a preset residual wavefront error threshold; wherein the preset residual wavefront error threshold is determined based on the target Strell ratio and the wavelength of the incident X-ray.

[0013] In some embodiments of the first aspect of this application, the preset residual wavefront error threshold satisfies:

[0014] ;

[0015] in, The preset residual wavefront error threshold is... The wavelength of the X-rays reflected by the X-ray mirror is [wavelength]. The target is Strømby.

[0016] In some embodiments of the first aspect of this application, the piezoelectric controller pre-obtains the unit response relationship corresponding to each piezoelectric actuator. The specific process is as follows: a unit reference voltage is applied to any piezoelectric actuator individually, while the remaining piezoelectric actuators are in a non-actuating state; the actuation surface shape of the X-ray mirror generated by the piezoelectric actuator under the unit reference voltage applied to it individually is obtained, and the unit response relationship corresponding to the piezoelectric actuator is determined according to the following formula:

[0017] ;

[0018] in, Preset reference surface shape; The actuation surface shape corresponding to the i-th piezoelectric actuator after applying a unit reference voltage; Unit reference voltage; Let represent the unit response relationship of the i-th piezoelectric actuator.

[0019] In some embodiments of the first aspect of this application, the specific process of calculating the piezoelectric actuator voltage corresponding to each of the piezoelectric actuators includes: combining the unit response relationships corresponding to each piezoelectric actuator according to the arrangement order of the piezoelectric actuators in the meridional direction to construct a response matrix; using the piezoelectric actuator voltage vector to be determined as a variable, establishing a predictive compensation surface shape expression generated by the piezoelectric actuator group under the action of the piezoelectric actuator voltage vector to be determined based on the response matrix; performing the same low-order term removal process on the predictive compensation surface shape expression and the equivalent residual surface shape; wherein, the low-order term removal process includes removing the overall bias term, tilt term, and defocus term corresponding to the optimal sphere or optimal arc; under a preset voltage constraint, solving for the piezoelectric actuator voltage vector that minimizes the residual amount after superimposing the predictive compensation surface shape after the low-order term removal process and the equivalent residual surface shape after the low-order term removal process, and taking each voltage component in the piezoelectric actuator voltage vector as the piezoelectric actuator voltage of the corresponding piezoelectric actuator.

[0020] In some embodiments of the first aspect of this application, the preset voltage constraint includes: the voltage of each piezoelectric actuator is less than or equal to a preset first voltage threshold; the piezoelectric actuator voltages corresponding to two adjacent piezoelectric actuators satisfy a preset amplitude constraint, specifically as follows:

[0021] ;

[0022] in, Indicates the first The piezoelectric actuator voltage corresponding to each piezoelectric actuator. Indicates the first +1 piezoelectric actuator voltage This is a preset second voltage threshold.

[0023] In some embodiments of the first aspect of this application, when the updated residual wavefront error does not meet the preset wavefront hold condition, the piezoelectric controller calculates the incremental piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the updated equivalent residual surface shape corresponding to the updated residual wavefront error and the unit response relationship of each piezoelectric actuator; the piezoelectric controller is further configured to superimpose the incremental piezoelectric actuator voltage with the currently applied piezoelectric actuator voltage, and drive the corresponding piezoelectric actuator according to the superimposed piezoelectric actuator voltage until the updated residual wavefront error meets the preset wavefront hold condition.

[0024] In some embodiments of the first aspect of this application, each piezoelectric actuator in the piezoelectric actuator group is arranged at equal pitch along the meridional direction of the X-ray reflector, a non-actuating gap is formed between two adjacent piezoelectric actuators, and the X-ray reflector has end margins at both ends in the meridional direction where no piezoelectric actuators are provided.

[0025] A second aspect of this application also provides a piezoelectric adaptive X-ray mirror surface shape control method based on wavefront feedback. The method includes: acquiring X-ray wavefront information reflected by the X-ray mirror based on a wavefront detector; determining the current residual wavefront error of the X-ray mirror based on the X-ray wavefront information, and determining whether the current residual wavefront error meets a preset wavefront maintenance condition; if the current residual wavefront error meets the preset wavefront maintenance condition, maintaining the current piezoelectric actuator voltage applied to the piezoelectric actuator assembly, and continuing to acquire the X-ray wavefront information based on the wavefront detector. If the current residual wavefront error does not meet the preset wavefront holding condition, the piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the pre-obtained unit response relationship of each piezoelectric actuator; and applies voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector, and determines the updated residual wavefront error based on the X-ray wavefront information re-acquired by the wavefront detector, and continues to execute the judgment of the preset wavefront holding condition according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector.

[0026] As described above, this application has the following beneficial effects:

[0027] This application improves the piezoelectric actuator assembly's ability to compensate for local thermally induced surface shape errors by corresponding the piezoelectric actuator assembly to the spatial distribution of surface shape deformation caused by thermal load. Wavefront information reflected by the X-ray mirror is acquired through a wavefront detector, and the piezoelectric controller determines the residual wavefront error, calculates the piezoelectric actuator voltage, and drives the piezoelectric actuators to adjust the mirror surface shape, gradually satisfying the preset wavefront holding conditions after reflection. A response matrix is ​​constructed based on the unit surface shape response relationship of each piezoelectric actuator, and the piezoelectric actuator voltage is calculated in conjunction with preset voltage constraints, improving the accuracy and stability of piezoelectric actuator voltage calculation. By re-acquiring wavefront information, updating the residual wavefront error, and performing incremental voltage correction, a closed-loop control based on wavefront feedback is formed, achieving adaptive adjustment of the mirror surface shape. This reduces the impact of piezoelectric actuator response coupling, thermal load changes, and model errors on surface shape compensation accuracy, thereby improving the surface shape control effect and wavefront holding capability of the X-ray mirror under high thermal load conditions. Attached Figure Description

[0028] Figure 1 The diagram shown is a schematic representation of a piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback in one embodiment of this application.

[0029] Figure 2 The diagram shown is a schematic diagram of the control flow of a piezoelectric actuator assembly in one embodiment of this application.

[0030] Figure 3 The diagram shown is a schematic representation of the unit response relationship of each piezoelectric actuator in one embodiment of this application.

[0031] Figure 4 The diagram shown is a flowchart illustrating a piezoelectric adaptive X-ray mirror surface shape control method based on wavefront feedback in one embodiment of this application. Detailed Implementation

[0032] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0033] In the embodiments of this application, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" do not necessarily imply that they are different.

[0034] It should be noted that, in the embodiments of this application, the words "exemplary" or "for example" indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0035] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0036] Before providing a further detailed description of the present invention, the nouns and terms used in the embodiments of the present invention are explained, and the nouns and terms used in the embodiments of the present invention are subject to the following interpretations:

[0037] <1> X-ray reflector: An optical element used in X-ray free-electron laser or synchrotron radiation beamlines, having an optical reflective surface for reflecting incident X-ray pulses in a grazing incidence manner.

[0038] <2> Piezoelectric actuator: A ceramic element that uses the inverse piezoelectric effect to convert electrical signals into mechanical deformation. It is bonded to the back of a reflector and is used to generate in-plane strain when a voltage is applied to drive the reflector to bend and deform.

[0039] To facilitate understanding of the embodiments of this application, firstly, in conjunction with Figure 1 Detailed explanation. Figure 1 A schematic diagram of a wavefront feedback-based piezoelectric adaptive X-ray mirror surface shape control system 100 is shown in this embodiment of the invention. The wavefront feedback-based piezoelectric adaptive X-ray mirror surface shape control system 100 in this embodiment includes: an X-ray mirror 101, a wavefront detector 102, a piezoelectric controller 103, and a piezoelectric actuator assembly 104.

[0040] The X-ray mirror 101 includes an optical reflecting surface for reflecting incident X-rays. In this embodiment, the X-ray mirror 101 is preferably made of single-crystal silicon material, with dimensions of 1000 mm (meridian direction, i.e., length direction) × 60 mm (sagittal direction, i.e., width direction) × 60 mm (thickness direction). Single-crystal silicon has high thermal conductivity (approximately 148 W / (m·K)) and low coefficient of thermal expansion (approximately 2.6 × 10⁻⁻⁻⁶). 6 / K), which can maintain good surface stability under high repetition rate heat load. However, even with single-crystal silicon, non-negligible thermal bulges will still occur under hundreds of watts of heat load, which is why piezoelectric active compensation is introduced in this embodiment. The optical reflecting surface is machined with ultra-precision, and its initial surface accuracy is better than 1 nm (RMS, root mean square value) to meet the wavefront quality requirements under grazing incidence even without heat load.

[0041] The back side of the optical reflecting surface (i.e., the side opposite to the optical reflecting surface) is used to bond the piezoelectric actuator assembly 104. Since the reflector is a long, thin plate structure, its stiffness is much greater in the meridional direction than in the sagittal direction, and the spatial distribution of the thermal load varies significantly along the meridional direction but is approximately uniform along the sagittal direction. Therefore, in this embodiment, the surface shape control only requires one-dimensional bending control along the meridional direction to meet the wavefront holding requirement, without the need to arrange piezoelectric actuators in the sagittal direction. The piezoelectric actuator assembly 104 is located on the opposite side of the optical reflecting surface of the X-ray reflector 101, and includes an odd number of piezoelectric actuators (e.g., 21) arranged sequentially along the meridional direction of the X-ray reflector 101. The center of the piezoelectric actuator located in the middle position corresponds to the peak region of the thermally induced deformation of the X-ray reflector 101 in the meridional direction, i.e., the geometric symmetry center.

[0042] In one embodiment of this application, each piezoelectric actuator in the piezoelectric actuator group is arranged at equal pitch along the meridional direction of the X-ray reflector, a non-actuating gap is formed between two adjacent piezoelectric actuators, and the X-ray reflector has end margins at both ends in the meridional direction where no piezoelectric actuators are provided.

[0043] In one specific embodiment, the X-ray reflector 101 is a single-crystal silicon plane mirror with dimensions of 1000 mm × 60 mm × 60 mm, and the front side is an optical reflective surface. Twenty-one piezoelectric actuators are bonded to the back of the X-ray reflector at equal pitches along the meridional direction, wherein each piezoelectric actuator is 40 mm long, the non-actuating gap is 5 mm, and a 30 mm end allowance is left at each end of the X-ray reflector.

[0044] like Figure 1 As shown, the wavefront detector 102 is disposed on the outgoing light path side of the X-ray reflector 101 and is used to collect X-ray wavefront information reflected by the X-ray reflector 101. The output terminal of the wavefront detector 102 is connected to the signal input terminal of the piezoelectric controller 103 to transmit the collected wavefront information to the piezoelectric controller 103 in real time.

[0045] The piezoelectric controller 103 is used to receive the X-ray wavefront information sent by the wavefront detector 102 and determine the current residual wavefront error of the X-ray reflector 101 based on the wavefront information. The control signal output terminal of the piezoelectric controller 103 is connected to the voltage input terminal of each piezoelectric actuator in the piezoelectric actuator group 104 to form a real-time closed-loop feedback loop.

[0046] Furthermore, the piezoelectric controller 103 is used to determine the current residual wavefront error of the X-ray reflector based on the X-ray wavefront information, and to determine whether the current residual wavefront error meets the preset wavefront holding condition.

[0047] In one embodiment of this application, the piezoelectric controller is used to determine the current residual wavefront error of the X-ray reflector based on the X-ray wavefront information. The specific process includes: reconstructing the X-ray wavefront information to obtain a measured wavefront distribution after reflection by the X-ray reflector; spatially registering and aligning the measured wavefront distribution with a preset target wavefront distribution using a phase reference, and calculating the difference between the measured wavefront distribution and the preset target wavefront distribution to obtain an initial wavefront error distribution; performing low-order aberration removal processing on the initial wavefront error distribution, wherein the low-order aberration removal processing includes removing piston terms, tilt terms, and defocus terms corresponding to the optimal spherical surface from the initial wavefront error distribution to obtain a residual wavefront error distribution; calculating the root mean square value of the wavefront error based on the residual wavefront error distribution, and using the root mean square value of the wavefront error as the current residual wavefront error.

[0048] Specifically, in this embodiment, the wavefront detector 102 preferably employs a Hartmann wavefront sensor, which divides the reflected X-ray beam into multiple sub-apertures using a microlens array and records the positional offset of the light spot in each sub-aperture using a high-sensitivity X-ray camera. Since this positional offset is proportional to the local slope of the reflected wavefront, the piezoelectric controller 103 can obtain the measured wavefront distribution of the reflected wavefront by reconstructing the slope data of all sub-apertures. The measured wavefront distribution is phase data stored in the form of a two-dimensional matrix, and its physical meaning is the deviation of the reflected wavefront from an ideal plane wave (or an ideal spherical wave).

[0049] Further, the piezoelectric controller 103 spatially aligns and subtracts the measured wavefront distribution from the preset target wavefront distribution to obtain an initial wavefront error distribution. It should be noted that the preset target wavefront distribution in this embodiment is an ideal plane wavefront, meaning that under diffraction-limited focusing conditions, the emitted wavefront after reflection by the mirror should remain a plane wave. Before calculating the initial wavefront error distribution, the piezoelectric controller 103 first performs least-squares alignment on the measured wavefront distribution and the preset target wavefront distribution to remove translation and tilt, i.e., to eliminate constant and first-order term deviations introduced by detector installation errors or overall rigid body displacement of the mirror. After the least-squares alignment is completed, the point-by-point difference between the two is calculated to obtain the initial wavefront error distribution. The initial wavefront error distribution includes wavefront distortion introduced from all sources, including mirror surface processing errors, thermal deformation, piezoelectric actuator output deviations, and environmental disturbances.

[0050] Furthermore, the piezoelectric controller 103 also performs low-order aberration removal processing on the initial wavefront error distribution to obtain a residual wavefront error distribution. In a specific embodiment, the low-order aberration removal removes the optimal spherical surface, i.e., the defocus term, but retains the remaining higher-order aberration components. It should be noted that in grazing-incident reflective beamlines, the defocus component accounts for the majority of the error energy in the surface shape error generated after the mirror is heated. However, this defocus component is physically equivalent to changing the equivalent radius of curvature of the mirror, and this curvature change can be completely absorbed and compensated by the downstream focusing optics by readjusting the focusing distance, without needing to be handled by the piezoelectric actuator group 104 in this embodiment. Forcing the piezoelectric actuator group 104 to compensate for the defocus term will not only occupy the limited voltage stroke and adjacent voltage difference margin of the piezoelectric actuator, but may also introduce additional higher-order fitting errors. Therefore, in this embodiment, before optimizing the initial wavefront error distribution, the piezoelectric controller 103 first removes the defocus component from the optimization target, so that the limited control capability of the piezoelectric actuator group 104 is concentrated on compensating for the high-order spatial frequency components in thermal deformation, thereby obtaining a better wavefront holding effect under the same voltage constraint.

[0051] Furthermore, the piezoelectric controller calculates the root mean square value of the wavefront error based on the residual wavefront error distribution, and uses the root mean square value of the wavefront error as the current residual wavefront error.

[0052] In one embodiment of this application, the preset wavefront preservation condition includes: the current residual wavefront error is less than or equal to a preset residual wavefront error threshold; wherein, the preset residual wavefront error threshold is determined based on the target Strell ratio, as shown below:

[0053] ;(Formula 1)

[0054] in, The preset residual wavefront error threshold is... The wavelength of the X-rays reflected by the X-ray mirror is [wavelength]. The target is Strømby.

[0055] In one specific embodiment, the X-ray wavelength λ is approximately 0.1771 nm, and the target Strell ratio is 0.8. Then, according to Formula 1, the preset residual wavefront error threshold is approximately 13.3 pm. When the current residual wavefront error calculated by the piezoelectric controller is not greater than 13.3 pm, it is determined that the reflected wavefront meets the wavefront preservation condition. When the current residual wavefront error is greater than 13.3 pm, it is determined that piezoelectric surface shape compensation is required.

[0056] Furthermore, such as Figure 2 As shown, when the current residual wavefront error is less than or equal to a preset residual wavefront error threshold, the piezoelectric controller determines that the current residual wavefront error meets the preset wavefront holding condition and maintains the piezoelectric actuator voltage currently applied to the piezoelectric actuator group, while controlling the wavefront detector to continue acquiring X-ray wavefront information; when the current residual wavefront error is greater than the preset residual wavefront error threshold, the piezoelectric controller determines that the current residual wavefront error does not meet the preset wavefront holding condition and enters the piezoelectric actuator voltage calculation process to perform surface shape compensation on the X-ray reflector through the piezoelectric actuator group.

[0057] Specifically, when the current residual wavefront error does not meet the preset wavefront preservation condition, it indicates that the deviation of the actual wavefront after reflection by the X-ray mirror from the target wavefront has exceeded the allowable range, and surface shape compensation of the X-ray mirror needs to be performed by the piezoelectric actuator group. The piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the pre-obtained unit response relationship of each piezoelectric actuator and the equivalent residual surface shape obtained by converting the current residual wavefront error.

[0058] In one embodiment of this application, the piezoelectric controller pre-stores the unit response relationships corresponding to each piezoelectric actuator; wherein, the unit response relationship corresponding to any piezoelectric actuator is obtained by: applying a unit reference voltage to any piezoelectric actuator individually, while keeping the other piezoelectric actuators in a non-actuated state; obtaining the actuation surface shape of the X-ray mirror produced by the piezoelectric actuator under the unit reference voltage applied individually, and determining the unit response relationship corresponding to the piezoelectric actuator according to the following formula:

[0059] ;(Formula 2)

[0060] in, Preset reference surface shape; The actuation surface shape corresponding to the i-th piezoelectric actuator after applying a unit reference voltage; Unit reference voltage; Let represent the unit response relationship of the i-th piezoelectric actuator.

[0061] For any piezoelectric actuator in the piezoelectric actuator group, the piezoelectric controller applies a unit reference voltage to that actuator individually, while keeping the other piezoelectric actuators in a non-actuated state to avoid interference from other piezoelectric actuators with the surface response result of that actuator. Subsequently, the surface response of the X-ray mirror under the individual operation of that piezoelectric actuator is obtained through finite element simulation, actual measurement with surface shape detection equipment, or indirect measurement with a wavefront detector, and the surface response is used as the unit response relationship corresponding to that piezoelectric actuator.

[0062] In one specific embodiment, such as Figure 3 As shown, the unit reference voltage is 1V, and the number of piezoelectric actuators (PZTs) is 21. The horizontal axis represents the position of the X-ray mirror, and the vertical axis represents the influence on the surface shape of the X-ray mirror. The unit reference voltage can also be set to other calibration voltages according to the driving range of the piezoelectric actuators. Since the surface shape response of the piezoelectric actuators within their operating range approximately satisfies a linear relationship, when the actual applied voltage of the piezoelectric actuator is several times the unit reference voltage, the surface shape response generated by the piezoelectric actuator can be proportionally calculated according to the unit response relationship.

[0063] In one embodiment of this application, the specific process of calculating the piezoelectric actuator voltage corresponding to each of the piezoelectric actuators includes: combining the unit response relationships corresponding to each piezoelectric actuator according to the arrangement order of the piezoelectric actuators in the meridional direction to construct a response matrix; using the piezoelectric actuator voltage vector to be determined as a variable, establishing a predictive compensation surface shape expression generated by the piezoelectric actuator group under the action of the piezoelectric actuator voltage vector to be determined based on the response matrix; determining the corresponding equivalent residual surface shape based on the current residual wavefront error; and applying the... The predicted compensation surface shape expression and the equivalent residual surface shape are subjected to the same low-order term removal process; wherein, the low-order term removal process includes removing the overall bias term, tilt term, and defocus term corresponding to the optimal sphere or optimal arc; under the preset voltage constraint, the piezoelectric actuator voltage vector that minimizes the residual amount after superimposing the predicted compensation surface shape after the low-order term removal process and the equivalent residual surface shape after the low-order term removal process is solved, and each voltage component in the piezoelectric actuator voltage vector is taken as the piezoelectric actuator voltage of the corresponding piezoelectric actuator.

[0064] First, the piezoelectric controller acquires the unit response relationship for each piezoelectric actuator. This unit response relationship characterizes the ability of a single piezoelectric actuator to adjust the surface shape of the X-ray mirror under a unit reference voltage. Let the unit response relationship for the i-th piezoelectric actuator be... Where x represents the position of the X-ray mirror in the meridional direction, then This represents the change in mirror height at position x in the meridional direction caused by the i-th piezoelectric actuator under a unit reference voltage.

[0065] Furthermore, the piezoelectric controller, according to the arrangement order of each piezoelectric actuator in the meridional direction of the X-ray reflector, combines the unit response relationships corresponding to each piezoelectric actuator to form a response matrix M. Specifically, when the X-ray reflector selects m sampling positions in the meridional direction... And when the piezoelectric actuator group includes n piezoelectric actuators, the unit response vector corresponding to the i-th piezoelectric actuator can be expressed as:

[0066] ;(Formula 3)

[0067] The response matrix M can be represented as:

[0068] ;(Formula 4)

[0069] Where M is an m×n dimensional response matrix, Let represent the unit response vector corresponding to the i-th piezoelectric actuator, n represent the number of piezoelectric actuators, and m represent the number of sampling points.

[0070] Furthermore, the piezoelectric controller uses the voltage vector V of the piezoelectric actuator to be determined as a variable to establish a predictive compensation surface shape expression generated by the piezoelectric actuator group under the action of the voltage vector V of the piezoelectric actuator to be determined. The voltage vector V of the piezoelectric actuator to be determined can be expressed as:

[0071] ;(Formula 5)

[0072] Where Vi represents the voltage of the piezoelectric actuator to be determined corresponding to the i-th piezoelectric actuator. Based on the response matrix M, the predicted compensation surface shape It can be represented as:

[0073] ;(Formula 6)

[0074] in, This refers to the predicted compensation surface shape generated by the piezoelectric actuator assembly under the action of the voltage vector V of the piezoelectric actuator to be determined. It should be noted that V here is the variable to be determined. =MV represents the compensation surface shape that can be predicted under any candidate voltage vector V, but does not mean that V has been predetermined.

[0075] Further, the piezoelectric controller determines the corresponding equivalent residual surface shape based on the current residual wavefront error. Specifically, the piezoelectric controller can convert the residual wavefront error distribution corresponding to the current residual wavefront error into the equivalent residual surface shape of the X-ray mirror in the meridional direction based on a preset conversion relationship between wavefront error and mirror height error. The equivalent residual surface shape... It can be represented as:

[0076] ;(Formula 7)

[0077] in, Represents the equivalent residual surface vector. Indicates the j-th sampling point The equivalent residual surface height at the location, This indicates the j-th sampling position in the east-west direction of the X-ray reflecting mirror, and m represents the number of sampling points.

[0078] Furthermore, in order to compare the predicted compensated surface shape and the equivalent residual surface shape within the same surface shape component space, the piezoelectric controller performs a comparison of the predicted compensated surface shape. and the equivalent residual surface shape The same low-order term removal process is performed. This low-order term removal process can be represented by the low-order term removal operator P. The low-order term removal process includes removing the overall bias term, tilt term, and defocus term corresponding to the optimal sphere or optimal arc. By applying the same low-order term removal process to both, the influence of reference height, overall tilt, or defocus components that can be refocused and absorbed by downstream optical elements on the piezoelectric actuator voltage solution can be avoided, allowing the piezoelectric actuator group to be mainly used to compensate for the higher-order residual surface components that require active adjustment.

[0079] After completing the above processing, the piezoelectric controller solves for the piezoelectric actuator voltage vector under a preset voltage constraint. Specifically, the piezoelectric controller uses the predicted compensation surface shape P(MV) after low-order term removal processing and the equivalent residual surface shape P(MV) after low-order term removal processing as the basis for the calculation. The objective is to minimize the compensation residual obtained after superposition, and then solve for the piezoelectric actuator voltage vector V. The objective can be expressed as:

[0080] ;(Formula 8)

[0081] in, Let V represent the piezoelectric actuator voltage vector obtained from the solution, M represent the response matrix, and V represent the piezoelectric actuator voltage vector to be determined. Let P represent the equivalent residual surface shape, and let P represent the low-order term removal operator. This represents the square of the L2 norm.

[0082] The above formula uses P(MV) + P( The reason why this is used as the optimization objective is because MV represents the existing equivalent residual surface shape, while MV represents the predicted compensation surface shape generated by the piezoelectric actuator assembly. By solving for the piezoelectric actuator voltage vector that minimizes the residual amount after the two are superimposed, the predicted compensation surface shape can be made to be opposite in direction to the current equivalent residual surface shape, thereby canceling or reducing the current residual surface shape.

[0083] In one embodiment of this application, the preset voltage constraint includes a voltage constraint for a single piezoelectric actuator and a voltage difference constraint between adjacent piezoelectric actuators. For example, the preset voltage constraint may include:

[0084] |V i |≤Vmax; (Formula 9)

[0085] |V i -V i+1 |≤ΔVmax; (Formula 10)

[0086] Among them, V i V represents the piezoelectric actuator voltage corresponding to the i-th piezoelectric actuator. i+1 Vmax represents the voltage of the (i+1)th piezoelectric actuator, Vmax represents the upper limit of the allowable voltage for a single piezoelectric actuator, and ΔVmax represents the upper limit of the allowable voltage difference between two adjacent piezoelectric actuators. By setting the above preset voltage constraints, it is possible to avoid overvoltage operation of a single piezoelectric actuator and reduce the local surface shape changes caused by voltage jumps between adjacent piezoelectric actuators.

[0087] The piezoelectric controller obtains the voltage vector of the piezoelectric actuator by solving the problem. Afterwards, Each voltage component in the equation is used as the piezoelectric actuator voltage for the corresponding piezoelectric actuator, and the corresponding piezoelectric actuator is driven according to the voltage of each piezoelectric actuator, so that the piezoelectric actuator applies a surface shape adjustment effect to the X-ray mirror.

[0088] Furthermore, the piezoelectric controller is also used to apply voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector, and determine the updated residual wavefront error based on the X-ray wavefront information re-acquired by the wavefront detector, and continue to execute the judgment of the preset wavefront holding condition according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector.

[0089] In one embodiment of this application, when the updated residual wavefront error does not meet the preset wavefront hold condition, the piezoelectric controller calculates the incremental piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the updated equivalent residual surface shape corresponding to the updated residual wavefront error and the unit response relationship of each piezoelectric actuator; the piezoelectric controller is further configured to superimpose the incremental piezoelectric actuator voltage with the currently applied piezoelectric actuator voltage, and drive the corresponding piezoelectric actuator according to the superimposed piezoelectric actuator voltage until the updated residual wavefront error meets the preset wavefront hold condition.

[0090] Specifically, after completing one surface shape adjustment, the piezoelectric controller does not directly end the control process. Instead, it controls the wavefront detector to re-acquire the X-ray wavefront information reflected by the X-ray reflector, and determines the updated residual wavefront error based on the re-acquired X-ray wavefront information. The updated residual wavefront error is used to characterize the remaining deviation between the actual reflected wavefront and the target wavefront after the current piezoelectric actuator voltage is applied.

[0091] The piezoelectric controller compares the updated residual wavefront error with the preset wavefront holding condition. If the updated residual wavefront error meets the preset wavefront holding condition, it means that the current surface compensation result has met the preset wavefront holding requirement. The piezoelectric controller maintains the piezoelectric actuator voltage currently applied to the piezoelectric actuator group and continues to control the wavefront detector to perform wavefront monitoring.

[0092] If the updated residual wavefront error does not meet the preset wavefront preservation condition, it indicates that there is still an equivalent residual surface shape that has not been fully offset after the previous piezoelectric actuator voltage compensation. In this case, the piezoelectric controller calculates the incremental piezoelectric actuator voltage for each piezoelectric actuator based on the updated equivalent residual surface shape corresponding to the updated residual wavefront error and the unit response relationship of each piezoelectric actuator. The incremental piezoelectric actuator voltage is used to further correct the surface shape of the X-ray mirror based on the currently applied piezoelectric actuator voltage, rather than completely replacing the current piezoelectric actuator voltage.

[0093] Specifically, the piezoelectric controller superimposes the incremental piezoelectric actuator voltage with the currently applied piezoelectric actuator voltage to obtain a superimposed piezoelectric actuator voltage, and drives the corresponding piezoelectric actuator according to the superimposed piezoelectric actuator voltage. Subsequently, the piezoelectric controller again controls the wavefront detector to acquire X-ray wavefront information and redetermines and updates the residual wavefront error until the updated residual wavefront error meets the preset wavefront hold condition.

[0094] Through the above-mentioned closed-loop control process of re-acquisition, error judgment, incremental voltage calculation, and superposition application, the electrode crosstalk between piezoelectric actuators, the deviation between the unit response relationship and the actual response, and the surface shape error caused by thermal load changes can be continuously corrected, thereby improving the accuracy and stability of X-ray mirror surface shape control.

[0095] Figure 4 This is a schematic flowchart of the piezoelectric adaptive X-ray mirror surface shape control method based on wavefront feedback provided in an embodiment of this application. Figure 4 As shown, the method includes:

[0096] Step S41: Acquire X-ray wavefront information after reflection by the X-ray mirror based on the wavefront detector;

[0097] Step S42: Determine the current residual wavefront error of the X-ray mirror based on the X-ray wavefront information, and determine whether the current residual wavefront error meets the preset wavefront preservation condition.

[0098] Step S43: If the current residual wavefront error satisfies the preset wavefront holding condition, then maintain the current piezoelectric actuator voltage applied to the piezoelectric actuator group, and continue to collect the X-ray wavefront information based on the wavefront detector;

[0099] Step S44: If the current residual wavefront error does not meet the preset wavefront hold condition, the piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator according to the pre-obtained unit response relationship of each piezoelectric actuator; and applies voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector; and determines the updated residual wavefront error based on the X-ray wavefront information re-acquired by the wavefront detector; and continues to execute the judgment of the preset wavefront hold condition according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector.

[0100] It should be understood that the specific process of the above-mentioned corresponding steps has been described in detail in the above system embodiments, and will not be repeated here for the sake of brevity.

[0101] It should also be understood that the module division in the embodiments of this application is illustrative and only represents a logical functional division; in actual implementation, there may be other division methods. Furthermore, the functional modules in the various embodiments of this application can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0102] As used in this specification, the terms "component," "module," "system," etc., are used to refer to computer-related entities, hardware, firmware, combinations of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, an execution thread, a program, and / or a computer. As illustrated, applications running on computing devices and computing devices can both be components. One or more components may reside in a process and / or an execution thread, and components may be located on a single computer and / or distributed among two or more computers. Furthermore, these components can be executed from various computer-readable media on which various data structures are stored. Components can communicate, for example, via local and / or remote processes based on signals having one or more data packets (e.g., data from two components interacting with another component between a local system, a distributed system, and / or a network, such as the Internet interacting with other systems via signals).

[0103] In summary, this application provides a piezoelectric adaptive X-ray mirror surface shape control system and method based on wavefront feedback. The system includes an X-ray mirror, a wavefront detector, a piezoelectric controller, and a piezoelectric actuator group. The piezoelectric actuator group includes an odd number of piezoelectric actuators arranged along the meridian of the mirror, wherein the middle piezoelectric actuator corresponds to the peak position of the surface shape deformation caused by thermal load. The piezoelectric controller determines the current residual wavefront error based on the reflected X-ray wavefront information and judges whether it meets the preset wavefront holding condition. If not, it generates a piezoelectric actuator voltage based on the unit response relationship of each piezoelectric actuator and a preset voltage constraint to drive the piezoelectric actuator to adjust the mirror surface shape, and forms a closed-loop control by re-acquiring wavefront information. This application can improve the wavefront holding accuracy of X-ray mirrors under thermal load. Therefore, this application effectively overcomes the various shortcomings of the prior art and has high industrial application value.

[0104] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.

Claims

1. A piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback, characterized in that, The system includes: an X-ray reflector, a wavefront detector, a piezoelectric controller, and a piezoelectric actuator assembly; The X-ray mirror includes an optical reflecting surface for reflecting incident X-rays; The piezoelectric actuator group is disposed on the opposite side of the optical reflecting surface of the X-ray mirror. The piezoelectric actuator group includes an odd number of piezoelectric actuators arranged sequentially along the meridional direction of the X-ray mirror. The center of the piezoelectric actuator located in the middle position coincides with the center of symmetry of the X-ray mirror in the meridional direction. The center of symmetry corresponds to the peak position of the surface deformation caused by thermal load. The wavefront detector is located on the outgoing light path side of the X-ray reflector, and its output end is connected to the signal input end of the piezoelectric controller. It is used to collect X-ray wavefront information reflected by the X-ray reflector and send the X-ray wavefront information to the piezoelectric controller. The piezoelectric controller is used to determine the current residual wavefront error of the X-ray reflector based on the X-ray wavefront information, and to determine whether the current residual wavefront error meets the preset wavefront maintenance condition. When the current residual wavefront error meets the preset wavefront holding condition, the piezoelectric controller maintains the piezoelectric actuator voltage currently applied to the piezoelectric actuator group and controls the wavefront detector to continue acquiring the X-ray wavefront information; When the current residual wavefront error does not meet the preset wavefront hold condition, the piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the pre-obtained unit response relationship of each piezoelectric actuator and the equivalent residual surface shape obtained by converting the current residual wavefront error; and applies voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector, and determines the updated residual wavefront error based on the X-ray wavefront information re-acquired by the wavefront detector, and continues to execute the judgment of the preset wavefront hold condition according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector.

2. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, The piezoelectric controller is used to determine the current residual wavefront error of the X-ray reflector based on the X-ray wavefront information. The specific process includes: The X-ray wavefront information is reconstructed to obtain the measured wavefront distribution after reflection by the X-ray mirror. Spatial registration and phase reference alignment are performed between the measured wavefront distribution and the preset target wavefront distribution, and the difference between the measured wavefront distribution and the preset target wavefront distribution is calculated to obtain the initial wavefront error distribution. The initial wavefront error distribution is subjected to low-order aberration removal processing, wherein the low-order aberration removal processing includes removing the piston term, tilt term and defocus term corresponding to the optimal sphere from the initial wavefront error distribution to obtain the residual wavefront error distribution. The root mean square value of the wavefront error is calculated based on the residual wavefront error distribution, and the root mean square value of the wavefront error is used as the current residual wavefront error.

3. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, The preset wavefront preservation condition includes: the root mean square value of the current residual wavefront error is less than or equal to a preset residual wavefront error threshold; wherein, the preset residual wavefront error threshold is determined based on the target Strell ratio and the wavelength of the incident X-ray.

4. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 3, characterized in that, The preset residual wavefront error threshold satisfies: ； in, The preset residual wavefront error threshold is... The wavelength of the X-rays reflected by the X-ray mirror is [wavelength]. The target is Strømby.

5. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, The piezoelectric controller pre-obtains the unit response relationship corresponding to each piezoelectric actuator, and the specific process is as follows: Apply a unit reference voltage to any one piezoelectric actuator individually, while keeping the other piezoelectric actuators in a non-actuating state; The actuation surface shape of the X-ray reflector produced by the piezoelectric actuator under a single applied unit reference voltage is obtained, and the unit response relationship of the piezoelectric actuator is determined according to the following formula: ； in, Preset reference surface shape; The actuation surface shape corresponding to the i-th piezoelectric actuator after applying a unit reference voltage; Unit reference voltage; Let represent the unit response relationship of the i-th piezoelectric actuator.

6. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, The specific process of calculating the piezoelectric actuator voltage corresponding to each of the piezoelectric actuators includes: The unit response relationships of each piezoelectric actuator are combined according to the arrangement order of the piezoelectric actuators in the meridional direction to construct a response matrix; Using the voltage vector of the piezoelectric actuator to be determined as a variable, a predictive compensation surface shape expression for the piezoelectric actuator group generated under the action of the voltage vector of the piezoelectric actuator to be determined is established based on the response matrix. The same low-order term removal process is performed on the predicted compensation surface shape expression and the equivalent residual surface shape; wherein, the low-order term removal process includes removing the overall bias term, tilt term, and defocus term corresponding to the best sphere or best arc; Under a preset voltage constraint, the piezoelectric actuator voltage vector that minimizes the residual amount after superimposing the predicted compensation surface shape after the lower-order term removal process with the equivalent residual surface shape after the lower-order term removal process is solved, and each voltage component in the piezoelectric actuator voltage vector is taken as the piezoelectric actuator voltage of the corresponding piezoelectric actuator.

7. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, The preset voltage constraint includes: The voltage of each piezoelectric actuator is less than or equal to a preset first voltage threshold; The difference in piezoelectric actuator voltage between two adjacent piezoelectric actuators is less than or equal to a preset second voltage threshold. ； in, Indicates the first The piezoelectric actuator voltage corresponding to each piezoelectric actuator. Indicates the first +1 piezoelectric actuator voltage This is a preset second voltage threshold.

8. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, When the updated residual wavefront error does not meet the preset wavefront holding condition, the piezoelectric controller calculates the incremental piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the updated equivalent residual surface shape corresponding to the updated residual wavefront error and the unit response relationship of each piezoelectric actuator. The piezoelectric controller is also used to superimpose the incremental piezoelectric actuator voltage with the currently applied piezoelectric actuator voltage, and drive the corresponding piezoelectric actuator according to the superimposed piezoelectric actuator voltage until the updated residual wavefront error meets the preset wavefront holding condition.

9. The piezoelectric adaptive X-ray mirror surface shape control system based on wavefront feedback according to claim 1, characterized in that, Each piezoelectric actuator in the piezoelectric actuator group is arranged at equal pitch along the meridional direction of the X-ray reflector, and a non-actuating gap is formed between two adjacent piezoelectric actuators. Furthermore, the X-ray reflector has end margins at both ends in the meridional direction where no piezoelectric actuators are installed.

10. A piezoelectric adaptive X-ray mirror surface shape control method based on wavefront feedback, characterized in that, include: X-ray wavefront information after reflection by the X-ray mirror is acquired based on the wavefront detector; The current residual wavefront error of the X-ray reflector is determined based on the X-ray wavefront information, and it is determined whether the current residual wavefront error meets the preset wavefront preservation condition. If the current residual wavefront error satisfies the preset wavefront holding condition, the piezoelectric actuator voltage currently applied to the piezoelectric actuator group is maintained, and the X-ray wavefront information continues to be acquired based on the wavefront detector. If the current residual wavefront error does not meet the preset wavefront hold condition, the piezoelectric controller calculates the piezoelectric actuator voltage corresponding to each piezoelectric actuator based on the pre-obtained unit response relationship of each piezoelectric actuator; and applies voltage to the piezoelectric actuator according to the piezoelectric actuator voltage, so that it applies a surface shape adjustment effect to the X-ray reflector; and determines the updated residual wavefront error based on the X-ray wavefront information re-acquired by the wavefront detector; and continues to execute the judgment of the preset wavefront hold condition according to the updated residual wavefront error, so as to form a closed-loop control of the surface shape of the X-ray reflector.

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