A high-precision laser interferometric distance measurement method based on multi-wavelength error decomposition

Abstract

The application belongs to the technical field of high-precision laser ranging, and provides a high-precision laser interferometric ranging method based on multi-wavelength error decomposition.The application aims at the contradiction between precision and range expansion caused by error amplification in multi-wavelength ranging, uses multi-wavelength interferometric measurement to obtain the phase of each wavelength, establishes a multi-dimensional phase coordinate system, decomposes the error vector into components parallel and perpendicular to the ideal linear relationship, separates and eliminates the perpendicular error component containing the amplification effect, reconstructs the wavelength combination, repeats the above process to construct multiple combined wavelengths, and realizes the combination of large-range low-precision and small-range high-precision ranging results.The application can significantly improve the ranging precision and is suitable for absolute distance measurement scenarios with long distance, high precision and high dynamic.

Description

Technical Field

[0001] This invention belongs to the field of high-precision laser ranging technology, specifically relating to a high-precision laser interferometric ranging method based on multi-wavelength error decomposition. Background Technology

[0002] Large-scale, high-precision laser absolute ranging technology holds significant value in cutting-edge scientific research and advanced industrial processing, such as applications like satellite formation flying and large-scale laser coordinate measurement. Compared to the relative displacement measurement of traditional interferometers, laser absolute ranging technology can directly obtain absolute distance information through a single measurement. Therefore, ranging methods urgently need to significantly extend the measurement range from hundreds of nanometers at the interferometer level to tens of meters or even thousands of kilometers to meet the needs of different scenarios.

[0003] Multi-wavelength interferometry (MWI) significantly expands the measurement range by synthesizing interferometric ranging results from multiple wavelengths. This method flexibly combines different wavelengths to generate composite wavelengths of various lengths. Long composite wavelengths are used for large-area coarse measurements, while short wavelengths are used for high-precision fine measurements, thus achieving a balance between range and accuracy. The current state of existing technology is as follows: 1. Due to the error amplification effect in multi-wavelength ranging, while extending the range to Λ / λ times, the measurement error is also amplified proportionally, making it difficult to break through the micrometer level in ranging accuracy, thus creating an inherent contradiction between measurement range and accuracy. Existing solutions mostly improve ranging accuracy by optimizing the light source design to reduce the synthesized wavelength Λ, thereby reducing the error amplification factor Λ / λ.

[0004] 2. Some existing technologies use Fabry-Perot (FP) cavities with a free spectral range of 0.75 GHz to achieve multi-wavelength frequency stabilization, obtaining a synthesized wavelength of approximately 4 mm (with an error amplification factor Λ / λ of approximately 5128). However, this approach relies on a complex feedback system to maintain FP cavity stability, making it extremely sensitive to external environmental conditions, which limits its practicality and stability.

[0005] 3. Existing technologies propose using two electro-optical combs as multi-wavelength light sources. The numerous teeth of the electro-optical combs simultaneously generate composite wavelengths for coarse and fine distance measurement. By coordinating different composite wavelengths, a balance between a large range and high accuracy is achieved. However, this approach still does not fundamentally solve the core problem of proportionally amplified ranging errors introduced by phase measurement after extending the range with a specific composite wavelength.

[0006] 4. In some existing technologies, long averaging times are used to improve ranging accuracy in order to reduce the impact of synthetic wavelength amplification on system accuracy. Although this method can effectively suppress random noise, excessively long averaging times can cause significant lag in the measurement of moving targets, thus severely limiting the system's ability to measure dynamic targets.

[0007] In summary, existing multi-wavelength interferometric ranging schemes are limited by error amplification effects, lacking a method to effectively reduce the error amplification effect of the synthesized wavelength. This prevents them from achieving micrometer-level or even higher precision absolute distance measurements over ranges of tens of meters or even longer. An innovative measurement method is urgently needed to fundamentally resolve the contradiction between measurement range and accuracy by separating and compensating for the error effects in the synthesized wavelength, thereby meeting the high-precision ranging requirements of fields such as precision measurement, space exploration, and advanced manufacturing. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a high-precision laser interferometric ranging method based on multi-wavelength error decomposition, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows: A high-precision laser interferometric ranging method based on multi-wavelength error decomposition includes the following steps: Step 1: Use lasers of multiple wavelengths to perform multi-wavelength interferometry on the same distance to be measured to obtain the corresponding phase results. The phase results include multiple phases corresponding to multiple wavelengths. Calculate the composite wavelength using two of the wavelengths, and calculate the composite wavelength phase using the phases of the two wavelengths to obtain the distance to be measured, including measurement error. Step 2: Determine the ideal distance measurement result when there is no measurement error, and obtain the ideal linear relationship when there is no measurement error; then calculate the actual measurement error when there is a phase measurement error. Step 3: Establish a multi-dimensional phase coordinate system, convert the phase measurement results into vectors, and use phase vector addition to represent the actual phase measurement results, ideal true phase value, and random phase measurement error of the distance measurement; determine the representation of the ideal linear relationship in the multi-dimensional phase coordinate system and the corresponding standardized direction vector; Step 4: Perform orthogonal analysis on the random phase measurement error to obtain the error components that are aligned with and perpendicular to the ideal linear relationship direction; Step 5: Separate and eliminate the vertical error component in the multidimensional phase coordinate system, and calculate the corrected phase vector through vector projection, retaining the component that does not include the amplification error. Step 6: Substitute the corrected phase into the formula for calculating the synthetic wavelength to obtain a measurement result that is closer to the true distance. Step 7: Select a new wavelength to construct a new synthetic wavelength. Repeat steps 1-6 to obtain new measurement results. Expand the measurement range by selecting an appropriate wavelength and synthesize the ranging results of a large range of low precision and a high precision range of small precision.

[0009] Furthermore, step 1 includes: utilizing multiple wavelengths l 1. l 2… l n The laser performs multi-wavelength interferometry measurements on the same distance to be measured, among which... l 1> l 2>…> l n Phases were obtained respectively. ,express l 1. l 2… l n After the distance to be measured L Introduced phase change; using two of the phases to calculate the composite wavelength, including the error, for the distance to be measured. L ij : ; Among them Λ ij The wavelength is the synthesized wavelength.

[0010] Furthermore, step 2 includes: when there is no error, the ideal ranging result is expressed as: ; in, l wavelength ， for phase ， That is to say l 1. l 2… l n The ideal error-free phase after the distance to be measured, and L t The ideal distance to be measured; To obtain the ideal linear relationship without error: ; Under the influence of various phase measurement errors, the actual measurement results will deviate from the ideal linear relationship; during the process of extending the measurement range, the measurement range is magnified by Λ. ij / l At the same time, the ranging error was also amplified Λ ij / l The measurement error is expressed as: times, ; in and δ represents the phase measurement error of the two phases respectively. L This indicates the ranging error in multi-wavelength measurements.

[0011] Furthermore, step 3 includes: establishing a multidimensional coordinate system. The ideal linear relationship in this space is characterized as: ; The phase measurement results are vectorized to obtain The actual phase measurement result, ideal true phase value, and random phase measurement error of any single distance measurement are respectively expressed as: P , P t and P e Their relationship can be expressed using phase vector addition as follows: ; Ideal linear relationships are represented by standardized direction vectors: ; in Represents a standardized vector. v 1. v 2… v n These represent the components of the standardized vector.

[0012] Furthermore, step 4 includes: addressing random phase measurement errors. P e Orthogonalization analysis is performed, and the components aligned with the ideal linear relationship direction are represented as follows: P e / / , P e / / The introduced ranging error δ L / / It can be represented as: ; There also exists a vector perpendicular to the direction of the ideal linear relationship. P e⊥ , P e⊥ The introduced ranging error δ L ⊥ Represented as: ; Error vector P e / / and P e⊥ The distance measurement error introduced by the two components is expressed as: ; in, and express P e⊥ In a multidimensional coordinate system The component perpendicular to the ideal linear relationship, express P e / / In a multidimensional coordinate system The parallel error component in.

[0013] Furthermore, step 5 includes: utilizing a multidimensional coordinate system For vertical error components P e⊥ Orthogonal separation and elimination are performed to obtain the measurement error component free from amplification error. P e / / Using vector projection, P e⊥ The corrected vector is obtained after removal. P c , represented as: ; In the formula, · represents the vector inner product, which is used to calculate the corrected phase. Represented as: .

[0014] Furthermore, step 6 includes: adjusting the phase corrected in step 5. By substituting the values ​​into the formula for calculating the synthetic wavelength, a distance closer to the actual distance can be obtained. L cij , represented as: .

[0015] Furthermore, step 7 includes: reselecting the wavelength. l g and l h Constructing a new synthetic wavelength Λ gh = l g l h / ( l g - l h Repeat steps 1 to 6 to obtain the new ranging result. L cgh When a suitable wavelength is selected... l g and l h To obtain a larger synthetic wavelength Λ ghThis expands the measurement range by using a synthesis formula to combine large-area, low-precision ranging results with high-precision, small-area ranging results. ; floor() is the floor function.

[0016] One ranging method: A dual-electro-optical-comb laser generates two pairs of optical combs with different repetition frequencies for absolute distance measurement; one of the optical combs is a local oscillator optical comb, and the other is a signal optical comb; The local oscillator optical comb is converted into spatial light by the second beam expander and collimator, and the signal optical comb is converted into spatial light by the first beam expander and collimator. The local oscillator optical comb and the signal optical comb are then illuminated by the first, second, third, and fourth beam splitters, respectively, and reflected by the target. After reflection, they return along the original optical path and interfere with the local oscillator optical comb transmitted through the corresponding beam splitters at the third and fourth beam splitters. After interference, the local oscillator optical comb and the measurement optical comb form an interference signal in front of the first and second photodetectors. The phase of the interference signal includes the measurement information related to the distance of the measurement path. The two photodetectors convert the optical comb interference signal into an electrical signal, which is then acquired by the data acquisition module and processed by the phase error orthogonal separation and elimination multi-wavelength interference ranging module. When the phase measurement error orthogonal separation and elimination multi-wavelength interferometric ranging module performs data processing, it adopts the aforementioned high-precision laser interferometric ranging method based on multi-wavelength error decomposition.

[0017] The present invention has the following beneficial effects: (1) Balancing high precision and long distance measurement: This invention effectively separates and suppresses key error components that amplify synchronously with the range expansion in multi-wavelength ranging by multi-wavelength error decomposition and vector orthogonal processing. While achieving a large measurement range, it can still improve the absolute distance measurement accuracy from tens of micrometers to sub-micrometers or even tens of nanometers, significantly improving the overall performance and reliability of the ranging system. (2) Low cost and easy implementation: This invention relies only on multi-wavelength interferometric phase measurement and data processing algorithms to improve accuracy. It does not require expensive hardware such as high-stability frequency locking devices or optical frequency combs, which greatly reduces the difficulty and cost of system construction. It has excellent economy and integration, and is easy to deploy quickly in various application environments such as industrial inspection and space exploration. (3) High dynamic capability: Traditional multi-wavelength ranging often relies on long-term averaging to improve accuracy, which leads to a decrease in data update rate and thus limits the real-time measurement of moving targets. The accuracy improvement method proposed in this invention can achieve high-precision ranging without long-term averaging, which significantly improves the real-time response and dynamic measurement capability of the system. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention; Figure 2 This is the error distribution coordinate system of the present invention; Figure 3 This is the error vector decomposition scheme of the present invention; Figure 4 The diagram shows the device structure of the present invention; in the diagram: 1. Dual electro-optical comb laser, 2. First beam expander collimator, 3. Second beam expander collimator, 4. First beam splitter, 5. Second beam splitter, 6. Third beam splitter, 7. Fourth beam splitter, 8. Target to be measured, 9. First photodetector, 10. Second photodetector, 11. Data acquisition module, 12. Phase measurement error orthogonal separation and elimination multi-wavelength interference ranging module; Figure 5 The multi-wavelength light source spectrum and interference signal spectrum of this invention; Figure 6 Simulation of the error magnitude of the present invention; Figure 7 This invention provides a comparison of the ranging error after error correction with the error before correction. Detailed Implementation

[0019] The following will be based on embodiments of the present invention. Figure 1-Figure 4 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0020] like Figure 1 A high-precision laser interferometric ranging method based on multi-wavelength error decomposition includes the following steps: Step 1, using multiple wavelengths l 1. l 2… l n The laser performs multi-wavelength interferometry measurements on the same distance to be measured, among which... l 1> l 2>…> l n Phases were obtained respectively. That is to say l 1. l 2… l n After the distance to be measured L The introduced phase change can be used to calculate the composite wavelength using two of the phase measurements. The calculation is as described above; the distance to be measured, including errors, can be calculated using any two phase measurements. L ij : ; Among them Λ ij The synthesized wavelength is denoted as Λ. ij = l i l j / ( l i - l j ),in l i > l j When using synthetic wavelengths for distance measurement, the measurement range extends from... l i / 2 and l j / 2 increased to Λ ij / 2, which expands the measurement range.

[0021] Step 2, when there is no error, the ideal distance measurement result can be expressed by the formula: ; in That is to say l 1. l 2… l n The ideal error-free phase after the distance to be measured, and L t Let be the ideal distance to be measured. Furthermore, using the above relationship, the ideal linear relationship without error can be obtained: ; Under the influence of various phase measurement errors, the actual measurement results will deviate from the ideal linear relationship. This is because the measurement range is magnified Λ during the range extension process. ij / l At the same time, the ranging error was also amplified Λ ij / l The measurement error is expressed as: times, ; in and δ represents the phase measurement error of the two phases respectively. L This represents the ranging error in multi-wavelength measurements. Compared to single-frequency interferometry, the phase measurement error... The introduced ranging error is only Therefore, random errors are amplified Λ ij / l This multiple becomes the main component of distance measurement error.

[0022] Step 3: Establish a multidimensional coordinate system , Figure 2 The following example uses a three-dimensional coordinate system. An ideal linear relationship can be represented in this space as: ; This relationship is based on as independent variable n A straight line in 3D space. The phase measurement results are vectorized to obtain... This helps to better describe the relationships in the coordinate system. Let the actual phase measurement result, the ideal true phase value, and the random phase measurement error for any single distance measurement be expressed as follows: P , P t and P e Their relationship can be expressed using phase vector addition as follows: ; Meanwhile, the ideal linear relationship can be represented by a standardized direction vector, written as: ; in Represents a standardized vector. v 1. v 2… v n Let represent the components of the normalized vector, and for any term in the normalized vector, we have v m =λ1 / λ m (m=1, 2… n The ideal linear relationship direction vector will be utilized subsequently. v Vector of phase measurement results P Complete the ranging error assessment and error correction.

[0023] Step 4, follow as follows Figure 3 The direction shown indicates the error vector. P e Orthogonalization analysis is performed, and the components aligned with the ideal linear relationship direction are represented as follows: P e / / The ranging error δ introduced by this phase measurement error L / / It can be represented as: ; There also exists a vector perpendicular to the direction of the ideal linear relationship. P e⊥ The ranging error δ introduced by this phase measurement error L ⊥ It can be represented as: ; Error vector Pe / / and P e⊥ The distance measurement error introduced by the two components can be expressed as: ; in and express P e⊥ exist The component in the coordinate system perpendicular to the ideal linear relationship. express P e / / Parallelism error components in the same coordinate system. This formula is used to evaluate the errors introduced in different directions of distance measurement. Furthermore, it can be seen that the distance measurement error perpendicular to the ideal linear relationship... and By Λ ij / l Magnified many times.

[0024] Step 5, using Components of perpendicularity error of coordinate system P e⊥ Orthogonal separation and elimination are performed to obtain the measurement error component free from amplification error. P e / / Utilizing, for example Figure 3 The vector projection shown will P e⊥ The corrected vector is obtained after removal. P c , represented as: ; In the above formula, · represents the vector dot product, and the corrected phase can be calculated using this formula. Represented as: ; Step 6: Substitute the corrected vector into the synthetic wavelength calculation formula to obtain a distance that more closely approximates the true distance. L cij , represented as: ; Step 7, reselect wavelength l g and l h (in l g > l h and g - h <i-j ), constructing a new synthetic wavelength Λ gh = l g l h / ( l g - l h Repeat steps 1 through 6 to obtain the new ranging result. L cgh When choosing a suitable wavelength l g and l h This allows for obtaining a larger synthetic wavelength Λ gh This expands the measurement range, allowing for the synthesis of large-area, low-precision ranging results with high-precision, small-area ranging results using a synthesis formula. ; The `floor()` function performs a floor operation. This method requires no additional hardware support and can significantly improve ranging accuracy while maintaining the system's dynamic measurement capabilities. It is suitable for absolute distance measurement scenarios that require long distance, high accuracy, and high dynamic capabilities.

[0025] This invention utilizes multiple wavelengths l 1. l 2… l n ( l 1> l 2>…> l n A laser is used to perform interferometric measurements on the same target to obtain the corresponding phase. A synthetic wavelength Λ is constructed by using any two wavelengths. ij This enables the measurement range to expand from a single wavelength. l / 2 extends to Λ ij / 2. However, while extending the range, the ranging error introduced by phase measurement is also amplified Λ ij / l To suppress the amplification effect of random phase measurement errors, this invention... An ideal linear relationship is established in a multidimensional coordinate system, the phase measurement results are vectorized, and the perpendicular error component is eliminated through an orthogonal separation algorithm. Preserve parallel components Used for distance calculation, effectively removing Λ ij / lBy mitigating the amplified error, a high-precision ranging result approaching the true value is obtained. Furthermore, by reselecting the wavelength combination and repeating this decomposition and correction process, a larger composite wavelength can be obtained, achieving hierarchical synthesis of large-range low-precision results and small-range high-precision results, balancing range expansion and improved ranging accuracy. This method requires no additional hardware modules and does not rely on long-term averaging processing. While ensuring the system's rapid response to dynamic targets, it achieves a significant improvement in ranging accuracy. It can be widely applied in absolute distance measurement applications such as precision industrial measurement and space exploration, where high requirements are placed on measurement range, accuracy, and dynamic performance, and has significant potential for widespread adoption.

[0026] This invention also proposes a high-precision multi-wavelength ranging device based on multi-wavelength error decomposition, comprising: a dual electro-optical comb laser 1, a first beam expander / collimator 2, a second beam expander / collimator 3, a first beam splitter 4, a second beam splitter 5, a third beam splitter 6, a fourth beam splitter 7, a first photodetector 9, a second photodetector 10, a data acquisition module 11, and a phase measurement error orthogonal separation and elimination multi-wavelength interference ranging module 12. The ranging method of this device is as follows: A dual-electric optical comb laser 1 generates two pairs of optical combs with different repetition frequencies for absolute distance measurement; one of the optical combs is a local oscillator optical comb, and the other is a signal optical comb. The signal light comb is collimated into spatial light by the first beam expander collimator 2, and then enters the measurement optical path via the first beam splitter 4 and the second beam splitter 5. The measurement light is then irradiated onto the target 8 by the third beam splitter 6 and the fourth beam splitter 7, and after being reflected by the target, it returns along the original optical path, interfering with the local oscillator light comb at the third beam splitter 6 and the fourth beam splitter 7. On the other hand, the local oscillator light comb is collimated into spatial light by the second beam expander collimator 3, and then enters the reference optical path via the first beam splitter 4 and the second beam splitter 5, interfering with the returning measurement light in front of the first photodetector 9 and the second photodetector 10, respectively. The two photodetectors convert the light comb interference signal into an electrical signal, which is then sent to the data acquisition module 11 for acquisition and processing. Subsequently, the phase measurement error is eliminated by orthogonal separation and the data is processed by the multi-wavelength interferometric ranging module 12. When the phase measurement error orthogonal separation and elimination multi-wavelength interferometric ranging module 12 performs data processing, it adopts the high-precision laser interferometric ranging method based on multi-wavelength error decomposition.

[0027] The target under test, 8, enters through the measurement path, and the spectrum of the dual electro-optical comb laser is as follows: Figure 5 As shown in (a), the signal optical comb repetition frequency is 60 MHz, and the local oscillator optical comb repetition frequency is 60.001 MHz. Their interference signal is as follows: Figure 5 As shown in (b), the spectrum of its interference signal exhibits a comb-like structure with equal intervals at 1 kHz. The phase on each spectrum is the same as the phase change introduced by the signal optical comb after passing through the distance to be measured.

[0028] The present invention provides a specific embodiment as follows: Step 1: Apply the lock-in amplification algorithm to all interference signals to calculate the distance to be measured, including the error. The phase values ​​are then obtained. That is to say l 1. l 2。。。 l n After the distance to be measured L The introduced phase change is used to calculate the measured distance, including errors, by synthesizing the wavelength using the phase measurement results. L ij : ; Among them Λ ij The synthesized wavelength is denoted as Λ. ij = l i l j / ( l i - l j ),in l i > l j When using synthetic wavelengths for distance measurement, the measurement range extends from... l i / 2 and l j / 2 increased to Λ ij / 2, thus extending the measurement range. In an electro-optical comb-based ranging system, the synthesized wavelength can be further expressed as Λ ij =c / ( i - j )Δ f , where Δ f The repetition frequency of the signal optical comb (i.e., 60MHz) was selected. i and j The larger the difference, the smaller the synthesized wavelength, and the higher the ranging accuracy. Under the parameters of this system, when i - j When the wavelength is 50, the synthesized wavelength is approximately 50 mm. When using the synthesized wavelength for distance measurement, the measurement range is from... l The range was increased from Λ / 2 (775nm) to Λ / 2 (25mm), thus expanding the measurement range.

[0029] Step 2, when there is no error, the ideal distance measurement result can be expressed by the formula: ; in That is to say l 1. l 2… l n The ideal error-free phase after the distance to be measured, and L t Let be the ideal distance to be measured. Furthermore, using the above relationship, the ideal linear relationship without error can be obtained: ; Under the influence of various phase measurement errors, the actual measurement results will deviate from the ideal linear relationship. This is because the measurement range is magnified Λ during the range extension process. ij / λ At the same time, the ranging error was also amplified Λ ij / l Times. This can be calculated using system parameters when... i - j When =50, the system Λ ij / l It is approximately 32258.

[0030] Measurement error is expressed as: ; in and δ represents the phase measurement error of the two phases respectively. L This represents the ranging error in multi-wavelength measurements. Compared to single-frequency interferometry, the phase measurement error... The introduced ranging error is only Therefore, random errors are amplified Λ ij / l This multiple becomes the main component of distance measurement error.

[0031] Step 3: Establish a multidimensional coordinate system , Figure 2 The following example uses a three-dimensional coordinate system. An ideal linear relationship can be represented in this space as: ; This relationship is based on as independent variable n A straight line in 3D space. The phase measurement results are vectorized to obtain... This helps to better describe the relationships in the coordinate system. Let the actual phase measurement result, the ideal true phase value, and the random phase measurement error for any single distance measurement be expressed as follows: P , P t and P e Their relationship can be expressed using phase vector addition as follows: ; Meanwhile, the ideal linear relationship can be represented by a standardized direction vector, written as: ; The direction vector of the ideal linear relationship will be used subsequently. v Vector of phase measurement results P Complete the ranging error assessment and error correction.

[0032] Step 4, follow as follows Figure 3 The direction shown indicates the error vector. P e Orthogonalization analysis is performed, and the components aligned with the ideal linear relationship direction are represented as follows: P e / / The ranging error δ introduced by this phase measurement error L / / It can be represented as: ; There also exists a vector perpendicular to the direction of the ideal linear relationship. P e⊥ The ranging error δ introduced by this phase measurement error L ⊥ It can be represented as: ; Error vector P e / / and P e⊥ The distance measurement error introduced by the two components can be expressed as: ; in and express P e⊥ exist The component in the coordinate system perpendicular to the ideal linear relationship. express P e / / Parallelism error components in the same coordinate system. This formula is used to evaluate the errors introduced in different directions of distance measurement. Furthermore, it can be seen that the distance measurement error perpendicular to the ideal linear relationship... and By Λ ij / l Magnified many times.

[0033] To clearly illustrate the relationship between the two errors, simulation results obtained using system parameters are as follows: Figure 6 As shown, the horizontal axis represents the phase measurement error in the horizontal and vertical directions, and the vertical axis represents the two phase measurement errors. and The introduced distance measurement error. It can be seen that the distance measurement error in the parallel and perpendicular directions caused by random phase noise increases linearly, but the significant difference in the linear slope indicates that the distance measurement error is mainly caused by… lead to.

[0034] Step 5, using Components of perpendicularity error of coordinate system P e⊥ Orthogonal separation and elimination are performed to obtain the measurement error component free from amplification error. P e / / Utilizing, for example Figure 3 The vector projection shown will P e⊥ The corrected vector is obtained after removal. P c , represented as: ; In the above formula, · represents the vector dot product, and the corrected phase can be calculated using this formula. Represented as: ; Step 6: Substitute the corrected vector into the synthetic wavelength calculation formula to obtain a distance that more closely approximates the true distance. L cij , represented as: ; Step 7, reselect wavelength l g and l h (in l g > l h and g - h =1), constructing a new synthetic wavelength Λ gh = l g l h / ( l g - l h Repeat steps one through six to obtain the new ranging results. L cgh The error amplification factor Λ under this parameter gh / l g Approximately 3.226 × 10 6 The synthesis formula is used to combine large-area, low-precision ranging results with high-precision, small-area ranging results: ; The `floor()` function performs a floor function. Figure 7 As shown, the ranging error has been optimized from ±30μm to less than 40nm. This method requires no additional hardware support and does not increase system complexity. Furthermore, it does not involve data averaging, enabling the system to achieve dynamic measurement capabilities above 100kHz. Under these two conditions, ranging accuracy is significantly improved, making it suitable for absolute distance measurement scenarios requiring long distances, high accuracy, and high dynamic capabilities.

[0035] This invention relates to a multi-wavelength ranging method based on an ideal linear relationship. It generates a composite wavelength Λ= using multi-wavelength lasers. l i l j / ( l i - l j Expand the measurement range by using a phase detection module to acquire the phase of the interference signal. The method is to establish A coordinate system is used to establish an ideal linear relationship between phase measurement errors and other parameters. k = l i / l j Decompose into parallel ( P e / / ) and vertical ( P e⊥ The components of ) were used to separate the Λ that exist in the vertical direction. ij / l The component that amplifies the error by a factor of 1.

[0036] This invention employs a pure algorithmic error decomposition method, balancing high accuracy with low cost. Based on an orthogonal error decomposition algorithm, the phase measurement results are processed and calculated in real time by a data processor, eliminating the need for expensive optical frequency combs or frequency stabilization modules. This method significantly improves accuracy while maintaining a wide range of measurements, and reduces system implementation costs and complexity.

[0037] This invention relates to an error decomposition method based on a coordinate system. Utilizing... Coordinate system analysis of phase error characteristics in multi-wavelength interferometry decomposes the error vector into a linear relationship parallel to the ideal ( P e / / ) and perpendicular to the ideal linear relationship ( P e⊥ The components of ) are separated using data processing algorithms to contain Λ ij / l amplification effect P e⊥ Components, based onP e / / A specific method for calculating high-precision absolute distance.

[0038] This invention presents a MWI error processing flow based on coordinate system analysis. The complete error analysis and processing workflow for the coordinate system includes: acquiring dual-wavelength data (… l i and l j Phase of the interference signal and Establish a coordinate system to represent the ideal linear relationship (slope). k = l i / l j The phase measurement results are decomposed into vectorized values ​​through vectorization analysis. P = P t + P e Separate vertical error P e⊥ The algorithm is implemented by suppressing the amplification effect through numerical calculation and finally outputting a high-precision absolute distance.

[0039] This invention provides a complete process from phase measurement, coordinate system establishment, error decomposition to final high-precision distance output. It includes a phase detection module obtaining the phase and a collaborative working method for coordinate establishment and error decomposition in a data processor. Furthermore, it incorporates a reconfigurable wavelength combination strategy, dynamically selecting different wavelengths ( l g , l h ) for constructing multiple combinations of wavelengths Λ gh By repeating the coordinate system analysis and error decomposition process, a hierarchical synthesis of large-scale low-precision ranging results and small-scale high-precision ranging results is achieved, which takes into account both range expansion and ranging accuracy improvement while maintaining the system's dynamic measurement capability.

[0040] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A high-precision laser interferometric ranging method based on multi-wavelength error decomposition, characterized in that, Includes the following steps: Step 1: Use lasers of multiple wavelengths to perform multi-wavelength interferometry on the same distance to be measured to obtain the corresponding phase results. The phase results include multiple phases corresponding to multiple wavelengths. Calculate the composite wavelength using two of the wavelengths, and calculate the composite wavelength phase using the phases of the two wavelengths to obtain the distance to be measured, including measurement error. Step 2: Determine the ideal distance measurement result when there is no measurement error, and obtain the ideal linear relationship when there is no measurement error; then calculate the actual measurement error when there is a phase measurement error. Step 3: Establish a multi-dimensional phase coordinate system, convert the phase measurement results into vectors, and use phase vector addition to represent the actual phase measurement results, ideal true phase value, and random phase measurement error of the distance measurement; determine the representation of the ideal linear relationship in the multi-dimensional phase coordinate system and the corresponding standardized direction vector; Step 4: Perform orthogonal analysis on the random phase measurement error to obtain the error components that are aligned with and perpendicular to the ideal linear relationship direction; Step 5: Separate and eliminate the vertical error component in the multidimensional phase coordinate system, and calculate the corrected phase vector through vector projection, retaining the component that does not include the amplification error. Step 6: Substitute the corrected phase into the formula for calculating the synthetic wavelength to obtain a measurement result that is closer to the true distance. Step 7: Select a new wavelength to construct a new synthetic wavelength, repeat steps 1-6 to obtain new measurement results, expand the measurement range by selecting a suitable wavelength, and synthesize the ranging results of large-range low precision and high precision small range. Step 3 includes: establishing a multidimensional coordinate system φ 1O φ 2…O φ n The ideal linear relationship in this space is characterized as: The phase measurement results are vectorized to obtain P =[ φ 1, φ 2,…, φ n The actual phase measurement result, ideal true phase value, and random phase measurement error of any single distance measurement are respectively expressed as: P , P t and P e Their relationship can be expressed using phase vector addition as follows: Ideal linear relationships are represented by standardized direction vectors: in Represents a standardized vector. v 1. v 2… v n The components representing the standardized vector; Step 4 includes: [addressing] random phase measurement errors. P e Orthogonalization analysis is performed, and the components aligned with the ideal linear relationship direction are represented as follows: P e / / , P e / / The introduced ranging error δ L / / It can be represented as: There also exists a vector perpendicular to the direction of the ideal linear relationship. P e⊥ , P e⊥ The introduced ranging error δ L ⊥ Represented as: Error vector P e / / and P e⊥ The distance measurement error introduced by the two components is expressed as: Where, δ φ i⊥ and δ φ j⊥ express P e⊥ In a multidimensional coordinate system φ 1O φ 2…O φ n The component perpendicular to the ideal linear relationship, δ φ 1 / / …δ φ n / / express P e / / In a multidimensional coordinate system φ 1O φ 2…O φ n Parallel error components in; Step 5 includes: utilizing a multidimensional coordinate system φ 1O φ 2…O φ n φ 1O φ 2…O φ n For vertical error components P e⊥ Orthogonal separation and elimination are performed to obtain the measurement error component free from amplification error. P e / / Using vector projection, P e⊥ The corrected vector is obtained after removal. P c , represented as: In the formula, · represents the vector inner product, which is used to calculate the corrected phase. φ 1c , φ 2c … φ nc Represented as: ； Step 7 includes: reselecting the wavelength λ g and λ h Constructing a new synthetic wavelength Λ gh = λ g λ h / ( λ g - λ h Repeat steps 1 through 6 to obtain the new ranging result. L cgh When a suitable wavelength is selected... λ g and λ h To obtain a larger synthetic wavelength Λ gh This expands the measurement range, allowing for the synthesis of large-area, low-precision ranging results with high-precision, small-area ranging results using a synthesis formula. floor() is the floor function.

2. The high-precision laser interferometric ranging method based on multi-wavelength error decomposition according to claim 1, characterized in that, Step 1 includes: utilizing multiple wavelengths λ 1. λ 2… λ n The laser performs multi-wavelength interferometry measurements on the same distance to be measured, among which... λ 1> λ 2>…> λ n Phases were obtained respectively. φ 1. φ 2… φ n ,express λ 1. λ 2… λ n After the distance to be measured L Introduced phase change; using two of the phases to calculate the composite wavelength, including the error, for the distance to be measured. L ij : Among them Λ ij The wavelength is the synthesized wavelength.

3. The high-precision laser interferometric ranging method based on multi-wavelength error decomposition according to claim 1, characterized in that, Step 2 includes: When there is no error, the ideal distance measurement result is expressed as: in, λ wavelength φ is phase φ 1t , φ 2t … φ nt That is to say λ 1. λ 2… λ n The ideal error-free phase after the distance to be measured, and L t The ideal distance to be measured; To obtain the ideal linear relationship without error: Under the influence of various phase measurement errors, the actual measurement results will deviate from the ideal linear relationship; during the process of extending the measurement range, the measurement range is magnified by Λ. ij / λ At the same time, the ranging error was also amplified Λ ij / λ The measurement error is expressed as: times, Where δ φ i and δ φ j δ represents the phase measurement error of the two phases respectively. L This indicates the ranging error in multi-wavelength measurements.

4. The high-precision laser interferometric ranging method based on multi-wavelength error decomposition according to claim 1, characterized in that, Step 6 includes: adjusting the phase corrected in step 5. φ 1c , φ 2c … φ nc By substituting the values ​​into the formula for calculating the synthetic wavelength, a distance closer to the actual distance can be obtained. L cij , represented as: 。 5. A distance measurement method, characterized in that: A dual-electric optical comb laser (1) generates two pairs of optical combs with different repetition frequencies for absolute distance measurement; one of the optical combs is a local oscillator optical comb, and the other is a signal optical comb; The local oscillator light comb is converted into spatial light by the second beam expander collimator (3), and the signal light comb is converted into spatial light by the first beam expander collimator (2). The local oscillator light comb and the signal light comb are respectively illuminated to the target (8) after passing through the first beam splitter (4), the second beam splitter (5), the third beam splitter (6), and the fourth beam splitter (7). After being reflected by the target, they return along the original optical path and interfere with the local oscillator light comb transmitted through the corresponding beam splitter at the third beam splitter (6) and the fourth beam splitter (7). After interference, the local oscillator light comb and the measurement light comb form an interference signal in front of the first photodetector (9) and the second photodetector (10). The phase of the interference signal includes the measurement information related to the distance of the measurement path. Two photodetectors convert optical comb interference signals into electrical signals, which are then acquired by the data acquisition module (11) and processed by the phase error orthogonal separation and elimination multi-wavelength interference ranging module (12). When the phase error orthogonal separation and elimination multi-wavelength interferometric ranging module (12) performs data processing, it adopts a high-precision laser interferometric ranging method based on multi-wavelength error decomposition as described in any one of claims 1-4.

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