A method for estimating and compensating for angle cross-range bias in differential wavefront sensing

Abstract

The present application relates to the technical field of differential wavefront sensing angle, especially to a differential wavefront sensing angle lateral shift estimation and compensation method, comprising: independently performing sinusoidal intensity modulation on reference light and measurement light, so that the two light beams carry different frequency identifiers, realizing power decoupling in the interference signal; incident to a four-quadrant photodetector and interference occurs, collecting and processing the interference electric signal to obtain four digital signals to be measured; performing three independent signal processing branches on the four digital signals to be measured in parallel, respectively solving the lateral shift of the reference light and the measurement light, and the pitch angle and yaw angle observation values containing pseudo-differential phase errors; constructing a pseudo-differential phase component, and real-time deducting the pseudo-differential phase component from the pitch angle and yaw angle observation values to compensate for the suppression of lateral shift errors. The advantage is that the intensity modulation-based interference two-beam amplitude real-time extraction and lateral shift estimation are realized, the error is effectively suppressed, and the angle measurement accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of differential wavefront sensing angle technology, and in particular to a method for estimating and compensating for the lateral offset of differential wavefront sensing angle. Background Technology

[0002] Precision angle measurement is one of the core technologies in modern high-end equipment manufacturing and scientific instruments, widely used in fields such as lithography lens alignment, satellite laser communication pointing, inertial navigation platform leveling, and space gravitational wave detection. Its measurement accuracy directly determines the system's performance boundaries. Among numerous angle measurement technologies, Differential Wavefront Sensing (DWS) has become an important tool in the field of precision angle measurement due to its high measurement accuracy. DWS is a high-precision angle measurement technology based on the principle of laser interferometry. Its principle is to compare the phase differences of the signals in the four quadrants of a quadrant photodiode (QPD) to inversely deduce the beam angle between two interfering beams, thereby inverting the deflection of the verification quality. It has outstanding advantages such as non-contact operation, anti-interference, and compact structure. However, in practical applications, due to assembly and processing errors in the optomechanical components of the laser interferometry system, the alignment of the two interfering beams relative to the QPD center cannot be completely guaranteed at the zero position. This causes a lateral offset of the beams relative to the QPD center, introducing a pseudo-differential phase component coupled with the angle measurement phase, which restricts the accuracy and reliability of the angle measurement.

[0003] To address the aforementioned issues, existing technologies have proposed several solutions. For instance, some solutions, through theoretical analysis and experimental verification, have identified that the lateral offset of the beam relative to the center of the four-quadrant photodetector couples with the wavefront curvature and generates a pseudo-differential phase signal during propagation, leading to phenomena such as "false tilt" and "zero-point offset," ultimately resulting in nonlinear errors and residual angle deviations in differential wavefront sensing. Other solutions optimize the optical structure and assembly method, placing the QPD detector on the conjugate plane at the beam waist to reduce parasitic phase caused by wavefront curvature, thereby mitigating measurement deviations caused by zero-point offset. Still others employ a conjugate imaging system to suppress beam offset generated by the remote measurement beam and improve the overlap between the reference and measurement beams, thus reducing nonlinear errors in angle measurement. Finally, some solutions establish high-precision numerical models to analyze the overall noise sources of differential wavefront sensing technology, identifying lateral offset as a key error source, and employing post-processing methods to suppress noise and improve angle measurement accuracy.

[0004] However, the existing technology still has many shortcomings, including: (1) Some technical solutions only identify the measurement deviation phenomenon caused by lateral offset, without deeply analyzing its internal influence mechanism; some technical solutions simplify the measurement beam to a flat-top beam, ignoring the non-uniform energy distribution characteristics of the actual laser beam; some technical solutions use Gaussian beam models, but only analyze the influence of lateral offset on the measurement of a single yaw angle, without studying the comprehensive action mechanism under the dual-axis coupling state of pitch and yaw angles, and cannot fully reflect the error law in real measurement. (2) In terms of error suppression methods, the scheme of using optical structure optimization will significantly increase the optical complexity of the system, increase the requirements for optical path design and assembly accuracy, and the engineering implementation cost is high. (3) The scheme of using data post-processing regards the influence of lateral offset as a static error, does not have dynamic real-time processing capability, and is difficult to apply to high dynamic and strong disturbance measurement scenarios. (4) The pseudo-differential phase component introduced by the lateral offset is coupled with the real angle measurement signal, making it difficult to accurately model and quantitatively evaluate the angle measurement error. Existing methods mostly rely on optical structure modification or offline post-processing, and none of them have formed an online and quantitative compensation strategy based on an accurate Gaussian beam physical model.

[0005] Therefore, there is an urgent need to develop a differential wavefront sensing angle method that does not rely on complex optical structures, can calculate the lateral deflection of the beam in real time, and can perform online biaxial compensation for the pseudo-differential phase, so as to achieve high-precision, high-dynamic, and high-stability angle measurement. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for estimating and compensating for the lateral offset of the differential wavefront sensing angle.

[0007] The purpose of this invention is to provide a method for estimating and compensating for the lateral offset of a differential wavefront sensing angle, which specifically includes the following steps: S1. The reference light and the measurement light are independently modulated with sinusoidal intensity so that the two lights carry different frequency markers, thereby achieving power decoupling in the interference signal; S2. The intensity-modulated reference light and the measurement light are incident on the four-quadrant photodetector and interfere with each other. The interference electrical signals are collected and processed to obtain four digital signals to be measured. S3. Perform three independent signal processing branches in parallel on the four digital signals under test to calculate the lateral offset between the reference light and the measurement light, as well as the pitch and yaw angle observations including pseudo-differential phase errors. S4. Based on the calculated lateral offset, construct pseudo-differential phase components. Subtract the pseudo-differential phase components from the pitch and yaw angle observations in real time to obtain the compensated true pitch and yaw angles, thereby suppressing the lateral offset error.

[0008] Preferably, in step S1, the same laser source is divided into two coherent beams, a reference beam and a measurement beam, and sinusoidally modulated using different modulation angular frequencies, so that the reference beam and the measurement beam can be independently separated in the signal domain.

[0009] Preferably, the interference electrical signal in step S2 can be expressed in integral form: ; In the formula: This represents the interference electrical signal within a single quadrant of a four-quadrant photodetector; I For interference light intensity; The initial intensity of the laser beam; , These are the complex amplitudes of the measurement light and the reference light, respectively. 1 / e 2 beam radius; w () represents the spot radius of the Gaussian beam at the propagation distance; , These represent the pitch angle rotation around the x-axis and the yaw angle rotation around the y-axis, respectively. This refers to the laser propagation distance. , These are the intensity modulation depths of the measurement light and the reference light, respectively; , These are the intensity modulation angular frequencies of the measuring light and the reference light, respectively. , The initial phases are modulated by the intensity of the measurement light and the reference light, respectively; , , , The integration limit parameter determines the position of each quadrant of the four-quadrant photodetector. to , to These are coefficients related to the Gaussian beam parameters, propagation distance, and deflection angle. , To measure the lateral offset of light on the detector; , The lateral offset of the reference light on the detector; , These are the DC and AC component coefficients of the interference electrical signal, respectively. x, y, z The coordinates are within the Gaussian beam.

[0010] Preferably, in the integral expression of the interference electrical signal: ; ; ; ; ; In the above formula: Rayleigh length, , λ Wavelength; The radius of the light spot on the four-quadrant photodetector. ; For the central light intensity, , P This represents the optical power of a Gaussian beam. A This represents the amplitude of the Gaussian beam; k For wave number, ; Let be the radius of curvature of the wavefront. ; The laser frequency.

[0011] Preferably, in step S3, the lateral offset of the reference light is: ; ; In the formula: , This indicates the lateral offset of the reference light on the detector; , The lateral offset of the reference light on the detector; This refers to the laser propagation distance. , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing algorithm. This indicates the propagation distance of the Gaussian beam. The radius of the light spot at that location; The lateral shift of the measured light is: ; ; In the formula, , These are the lateral offset components of the measured light on the detector; , To measure the lateral offset of light on the detector; , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing (DPS) algorithm. This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of the light spot at that location; The expressions for the pitch and yaw angle observations, including pseudo-differential phase errors, are as follows: ; In the formula: , These represent the pitch and yaw angle observations directly output by the differential wavefront sensing algorithm, respectively. , , , These represent the phases of the interference signals corresponding to the four quadrants A, B, C, and D of the four-quadrant photodetector; , This represents the phase term coefficients related to the detector geometry and Gaussian beam parameters. , These are coefficients related to the Gaussian beam parameters, propagation distance, and deflection angle. k For wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundary of the four-quadrant photodetector; This indicates the propagation distance of the Gaussian beam. The radius of curvature of the wavefront at that location; , To measure the lateral offset of light on the detector; , Let be the lateral offset of the reference light on the detector; where and It is a pseudo-differential phase component caused by lateral offset.

[0012] Preferably, in step S4, the compensated true pitch angle and yaw angle are expressed as follows: ; ; In the formula, , These are the actual pitch and yaw angles obtained after compensation; k For wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundary of the four-quadrant photodetector; , These are the lateral offset components of the measured light on the detector; , These are the lateral offset components of the reference light on the detector; This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of curvature of the wavefront at that location; , These are the pitch and yaw angle observations, including pseudo-differential phase errors.

[0013] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) This invention realizes real-time extraction of amplitude and lateral offset estimation of two interferometric beams based on intensity modulation, providing a low-cost error suppression method for achieving high-precision angle measurement without complex optomechanical structure modulation. (2) The present invention uses signal processing methods to estimate and compensate for lateral offset in real time, which not only significantly improves the system’s real-time response capability to dynamic disturbances, but also effectively avoids the time delay and measurement information loss of traditional post-processing methods. (3) The present invention provides an active compensation strategy for lateral offset based on intensity modulation, which can flexibly adjust the weights of demodulation parameters such as modulation depth and modulation frequency according to the signal-to-noise ratio requirements and dynamic range requirements of the measurement scenario, so as to achieve high-precision adaptive suppression of lateral offset error under different conditions. Attached Figure Description

[0014] Figure 1 This is a flowchart of a differential wavefront sensing angle lateral offset estimation and compensation method provided in an embodiment of the present invention.

[0015] Figure 2 This is a coordinate system and quadrant distribution diagram of a four-quadrant photodetector (QPD) provided according to an embodiment of the present invention.

[0016] Figure 3 The results are simulation results of four-quadrant electrical signals provided according to embodiments of the present invention.

[0017] Figure 4 The cross-term signal is generated by the interference of the measurement light and the reference light on a four-quadrant photodetector after being modulated by sinusoidal intensity at different frequencies, according to an embodiment of the present invention.

[0018] Figure 5 This is a curve comparing the angle measurement error of the method according to the present invention with that of the traditional differential wavefront sensing angle method. Detailed Implementation

[0019] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0021] This invention provides a method for estimating and compensating for the lateral offset of the differential wavefront sensing angle. See the flowchart below. Figure 1 Specifically, it includes the following steps: S1. Independent sinusoidal intensity modulation of the reference beam and the measurement beam: The laser output from the same laser source is divided into two coherent beams, a reference beam and a measurement beam. During the laser source preparation stage, the reference beam and the measurement beam are independently sinusoidally modulated, and the modulation frequencies used for the two beams are different. This allows both the reference beam and the measurement beam to carry frequency identifiers that can be distinguished from each other in the signal domain. This enables power decoupling of the two beams in the subsequent interference signal, laying the foundation for extracting the light intensity information of the reference beam and the measurement beam separately and independently calculating the lateral offset of the two beams.

[0022] S2. Acquisition and Obtaining Four-Quadrant Interference Digital Electrical Signals: The reference light and measurement light, after independent intensity modulation, are Gaussian beams, and the pitch and yaw angles deflect simultaneously during the measurement process; the two beams interfere on the photosensitive surface of the four-quadrant photodetector (QPD), and the interference electrical signal formed by the intensity-modulated reference signal and the measurement signal (monochromatic signal) captured by the QPD can be expressed in integral form: ; in: ; ; ; ; ; In the above formula: This represents the interference electrical signal within a single quadrant of a four-quadrant photodetector; I For interference light intensity; , These are the complex amplitudes of the measurement light and the reference light, respectively. The initial intensity of the laser beam; 1 / e 2 Beam radius (beam waist radius); w () represents the spot radius of the Gaussian beam at the propagation distance; , These are the pitch angle rotation around the x-axis (vertical tilt) and the yaw angle rotation around the y-axis (horizontal tilt). This refers to the laser propagation distance. , These are the intensity modulation depths of the measurement light and the reference light, respectively; , These are the intensity modulation angular frequencies of the measuring light and the reference light, respectively. , The initial phases are modulated by the intensity of the measurement light and the reference light, respectively; , , , The integration limit parameter determines the position of each quadrant of the four-quadrant photodetector. to , to These are coefficients related to the Gaussian beam parameters, propagation distance, and deflection angle. , To measure the lateral offset of light on the detector; , The lateral offset of the reference light on the detector; , These are the DC and AC component coefficients of the interference electrical signal, respectively. x, y, z The coordinates are within the Gaussian beam. Rayleigh length, , λ Wavelength; The radius of the light spot on the QPD. ; For the central light intensity, , P This represents the optical power of a Gaussian beam. A This represents the amplitude of the Gaussian beam; k For wave number, ; Let be the radius of curvature of the wavefront. ; The laser frequency; Integral limit parameter , , , The value of determines the position of the four quadrants of the QPD. The coordinate system and quadrant distribution on the QPD are as follows: Figure 2 As shown in Table 1, the correspondence between the integration limit parameters and the four quadrants of QPD is as follows. Table 1. Correspondence between integration limit parameters and the four quadrants of QPD

[0023] After photoelectric conversion, signal amplification, anti-aliasing filtering, and analog-to-digital conversion, the four interferometric electrical signals are processed to obtain four digital test signals corresponding to the four quadrants of the QPD, which are used for subsequent lateral offset and angle calculations; the four digital test signals ADC A / B / C / D are as follows: Figure 1 As shown, its pattern of behavior is as follows: I integralSimilarly, simulations of four-quadrant electrical signals using Matlab are as follows: Figure 3 As shown, it mainly consists of four parts; E DC The portion consists of DC components, which will not be analyzed; the focus will be on the remaining components: For Extraction of key angle measurement information in some parts: using Matlab Simulation, making m m = m r =0.3; f m =10kHz; f r =20kHz; φ m = φ r =0; this indicates that it contains a DC component with an amplitude of approximately 0.9881, such as Figure 4 As shown.

[0024] S3. Solving the lateral offset of the two beams based on mixing filtering and differential power sensing (DPS) algorithm: For the four digital signals under test obtained in step S2, three independent signal processing branches are executed in parallel to solve the lateral offset of the reference beam and the measurement beam on the QPD and the angle observation value containing pseudo-differential phase, as follows: (1) Reference light lateral offset calculation branch: The four digital signals under test are respectively compared with the local oscillator of the reference light modulation angular frequency. Digital mixing is performed, and then the DC component, i.e., the power of the reference light distributed in each quadrant of the QPD, is obtained through low-pass filtering. Then, by combining the Differential Power Sensing (DPS) algorithm, we can obtain: ; Therefore, the lateral offset of the reference light is: ; ; In the above formula: , The lateral offset of the reference light on the detector; This refers to the laser propagation distance. , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing (DPS) algorithm. This indicates the propagation distance of the Gaussian beam. The radius of the light spot at that location.

[0025] (2) Measurement of the transverse offset of the light: The four digital signals to be measured are respectively compared with the local oscillator of the modulation angular frequency of the light. Digital mixing is performed, and low-pass filtering is used to extract the intensity distribution of the measurement light in the four quadrants of the QPD, i.e., the power of the measurement light in each quadrant. The measurement light power in each quadrant is then input into a differential power sensing (DPS) algorithm to calculate the lateral offset of the measurement light on the detector plane; specifically as follows: combined with the integral expression... The lateral shift of the measured light can be obtained as follows: ; ; In the formula, , These are the lateral offset components of the measured light on the detector; , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing (DPS) algorithm. This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of the light spot at that location; , These are the pitch angle rotation around the x-axis (vertical tilt) and the yaw angle rotation around the y-axis (horizontal tilt). This refers to the laser propagation distance. , , , This is the integration limit parameter; (3) Angle observation value calculation branch: Input the four digital signals to be measured into the digital phase-locked loop (DPLL) to extract the phase of the four quadrants. , , , Substituting these values ​​into the differential wavefront sensing (DWS) algorithm, we obtain the pitch and yaw angle observations, which include pseudo-differential phase errors. , The expression is as follows: ; In the formula: , These represent the pitch and yaw angle observations directly output by the differential wavefront sensing algorithm, respectively. , , , These represent the phases of the interference signals corresponding to the four quadrants A, B, C, and D of the four-quadrant photodetector; , This represents the phase term coefficients related to the detector geometry and Gaussian beam parameters. kFor wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundaries of a four-quadrant photodetector (QPD); This indicates the propagation distance of the Gaussian beam. The radius of curvature of the wavefront at that location; , To measure the lateral offset of light on the detector; , Let be the lateral offset of the reference light on the detector; where and It is the pseudo-differential phase component caused by lateral offset, which can be clearly seen due to and The existence of this means that the pseudo-differential phase component is a time-varying variable.

[0026] S4. Pseudo-differential phase component compensation and true angle output: A pseudo-differential phase component is constructed based on the lateral offset of the reference light and the measurement light, and is subtracted from the angle observation value in real time to obtain the true measured angle after eliminating the offset error, thereby achieving the purpose of suppressing lateral offset. ; ; In the formula, , These are the actual pitch and yaw angles obtained after compensation; k For wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundaries of a four-quadrant photodetector (QPD); , These are the lateral offset components of the measured light on the detector; , These are the lateral offset components of the reference light on the detector; This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of curvature of the wavefront at that location; , These are the pitch and yaw angle observations, which include pseudo-differential phase errors. Through the above compensation, the time-varying pseudo-differential phase error is eliminated, and the final output is a high-precision angle measurement result without offset interference. This completes the lateral offset estimation and compensation of the differential wavefront sensing angle, greatly improving the angle measurement accuracy, stability and dynamic adaptability.

[0027] To verify the feasibility of this invention, it was validated using Matlab. The angle measurement errors of the traditional DWS angle measurement method and the differential wavefront sensing angle lateral offset estimation and compensation method proposed in this paper were compared. The following comparative measurements were conducted for verification: Set the deflection angle range of the object to be measured to -1 to 1 mrad for fixed-point measurement. The lateral offset of the reference beam is (0.03, 0.015) mm, and the lateral offset of the measurement beam is (0.02, 0.01) mm. Figure 5 As shown, the maximum error of the method of the present invention is approximately 3 μrad, while the maximum error of the traditional DWS angle measurement method is approximately 10 μrad. Simulation results show that the method of the present invention, by handling lateral offset and its related errors, significantly improves the angle measurement accuracy compared to the traditional DWS angle measurement method.

[0028] The key technical points of this invention are: (1) a laser source preparation system with independent sinusoidal intensity modulation of dual beams is adopted, and intensity modulation of different frequencies is applied to the reference light and the measurement light to effectively separate them, realize the independent decoupling extraction of the power of the reference light and the measurement light, and provide a signal basis for the online calculation of lateral offset; (2) considering the multi-physics coupling effect of beam lateral offset, pitch angle, yaw angle, wavefront curvature and spot energy distribution, a complete interference model with dual-axis angle and lateral offset that is more in line with the actual optical path is constructed to improve the accuracy of error characterization and compensation. (3) Real-time estimation of beam lateral offset is achieved based on mixing filter and differential power sensing (DPS), online calculation of the offset of reference light and measurement light on the detector surface, and synchronous identification of offset-related homogeneous errors without modification of hardware structure; (4) Angle observation values ​​are obtained based on digital phase-locked loop (DPLL) and differential wavefront sensing (DWS), and pseudo-differential phase components are constructed and deducted in real time to achieve dynamic, quantitative, and dual-axis synchronous compensation of lateral offset error, suppressing angle measurement error from the algorithm level, and significantly improving the system measurement accuracy and robustness. The advantages are: The differential wavefront sensing angle lateral offset estimation and compensation method provided by this invention is applicable to conventional differential wavefront sensing angle platforms including laser output, intensity modulation, interferometric reception and four-quadrant detection, without modification of existing hardware structure, and is achieved only through digital signal processing.

[0029] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0030] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for estimating and compensating for the lateral offset of a differential wavefront sensing angle, characterized in that: Specifically, the steps include the following: S1. The reference light and the measurement light are independently modulated with sinusoidal intensity so that the two lights carry different frequency markers, thereby achieving power decoupling in the interference signal; S2. The intensity-modulated reference light and the measurement light are incident on the four-quadrant photodetector and interfere with each other. The interference electrical signals are collected and processed to obtain four digital signals to be measured. S3. Perform three independent signal processing branches in parallel for the four digital signals under test: the reference light lateral offset calculation branch, the measurement light lateral offset calculation branch, and the angle observation calculation branch. The reference light lateral offset calculation branch and the measurement light lateral offset calculation branch calculate the lateral offset of the reference light and the measurement light, respectively. The angle observation calculation branch calculates the pitch angle and yaw angle observations, including pseudo-differential phase error. S4. Based on the lateral offset of the reference light and the measurement light obtained from the solution, construct pseudo-differential phase components. Subtract the pseudo-differential phase components from the pitch angle and yaw angle observations in real time to obtain the compensated true pitch angle and yaw angle to be measured, thereby suppressing the lateral offset error.

2. The differential wavefront sensing angle lateral offset estimation and compensation method according to claim 1, characterized in that: In step S1, the same laser source is divided into two coherent beams: a reference beam and a measurement beam. The reference beam and the measurement beam are sinusoidally modulated using different modulation angular frequencies, so that they can be independently separated in the signal domain.

3. The differential wavefront sensing angle lateral offset estimation and compensation method according to claim 1, characterized in that: The interference electrical signal in step S2 can be expressed in integral form: ； In the formula: This represents the interference electrical signal within a single quadrant of a four-quadrant photodetector; I For interference light intensity; The initial intensity of the laser beam; , These are the complex amplitudes of the measurement light and the reference light, respectively. 1 / e 2 beam radius; w () represents the spot radius of the Gaussian beam at the propagation distance; , These represent the pitch angle rotation around the x-axis and the yaw angle rotation around the y-axis, respectively. This refers to the laser propagation distance. , These are the intensity modulation depths of the measurement light and the reference light, respectively; , These are the intensity modulation angular frequencies of the measuring light and the reference light, respectively. , The initial phases are modulated by the intensity of the measurement light and the reference light, respectively; , , , The integration limit parameter determines the position of each quadrant of the four-quadrant photodetector. to , to These are coefficients related to the Gaussian beam parameters, propagation distance, and deflection angle. , To measure the lateral offset of light on the detector; , The lateral offset of the reference light on the detector; , These are the DC and AC component coefficients of the interference electrical signal, respectively. x, y, z The coordinates are within the Gaussian beam.

4. The differential wavefront sensing angle lateral offset estimation and compensation method according to claim 3, characterized in that: In the integral expression of the interference electrical signal: ； ； ； ； ； In the above formula: Rayleigh length, , λ Wavelength; The radius of the light spot on the four-quadrant photodetector. ; For the central light intensity, , P This represents the optical power of a Gaussian beam. A This represents the amplitude of the Gaussian beam; k For wave number, ; Let be the radius of curvature of the wavefront. ; The laser frequency.

5. The differential wavefront sensing angle lateral offset estimation and compensation method according to claim 1, characterized in that: In step S3, the lateral offset of the reference light is: ; ; In the formula: , This indicates the lateral offset of the reference light on the detector; , The lateral offset of the reference light on the detector; This refers to the laser propagation distance. , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing algorithm. This indicates the propagation distance of the Gaussian beam. The radius of the light spot at that location; The lateral shift of the measured light is: ； ； In the formula, , These are the lateral offset components of the measured light on the detector; , To measure the lateral offset of light on the detector; , These represent the normalized power difference signals related to the lateral offset of the reference light, calculated by the differential power sensing (DPS) algorithm. This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of the light spot at that location; The expressions for the pitch and yaw angle observations, including pseudo-differential phase errors, are as follows: ； In the formula: , These represent the pitch and yaw angle observations directly output by the differential wavefront sensing algorithm, respectively. , , , These represent the phases of the interference signals corresponding to the four quadrants A, B, C, and D of the four-quadrant photodetector; , This represents the phase term coefficients related to the detector geometry and Gaussian beam parameters. , These are coefficients related to the Gaussian beam parameters, propagation distance, and deflection angle. k For wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundary of the four-quadrant photodetector; This indicates the propagation distance of the Gaussian beam. The radius of curvature of the wavefront at that location; , To measure the lateral offset of light on the detector; , Let be the lateral offset of the reference light on the detector; where and It is a pseudo-differential phase component caused by lateral offset.

6. The differential wavefront sensing angle lateral offset estimation and compensation method according to claim 1, characterized in that: In step S4, the compensated true pitch and yaw angles are expressed as follows: ； ； In the formula, , These are the actual pitch and yaw angles obtained after compensation; k For wave number, , λ The wavelength of the laser; L , h These are the geometric dimensional parameters related to the quadrant center-to-center distance and quadrant boundary of the four-quadrant photodetector; , These are the lateral offset components of the measured light on the detector; , These are the lateral offset components of the reference light on the detector; This indicates the distance the Gaussian beam travels in the laser propagation process. The radius of curvature of the wavefront at that location; , These are the pitch and yaw angle observations, including pseudo-differential phase errors.

Images