Synthetic wavelength interference ranging method based on phase coordinate system characteristic rotation

Abstract

The invention belongs to the technical field of high-precision laser ranging, and provides a synthetic wavelength interferometric ranging method based on phase coordinate system characteristic rotation. Laser pairs with two wavelengths are used for measuring the same target, the distance to be measured is calculated according to the interferometric phase, the measurement range is expanded, and meanwhile, the method is used for suppressing the amplification effect of random phase measurement errors. Establishing a characteristic linear relation in a two-dimensional coordinate system, vectorizing a phase measurement result, constructing a coordinate system parallel to an ideal relation, rotating a measurement vector to a new coordinate system through a matrix, separating and eliminating a vertical error component, and obtaining a high-precision distance measurement result approaching a true value; the method does not need extra hardware system support, avoids long-time average calculation, can significantly improve the distance measurement precision in a long-distance range, maintains the dynamic measurement capability of the system, is suitable for high-precision absolute distance measurement scenes such as precision industrial measurement and space detection, and has a wide application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-precision laser ranging, and particularly relates to a synthetic wavelength interferometric ranging method based on phase coordinate system characteristic rotation. BACKGROUND

[0002] Large-range high-precision laser absolute ranging technology has important significance in the fields of cutting-edge science and advanced industrial processing, such as satellite formation flight and large-scale coordinate measurement based on laser. Compared with the relative displacement measurement technology of an interferometer, the laser absolute ranging technology can obtain absolute distance information through a single measurement. Therefore, it is necessary to greatly expand the measurement range from hundreds of nanometers of the interferometer to tens of meters or even thousands of kilometers through the ranging technology to meet the needs of different applications.

[0003] Multi-wavelength interferometry (MWI) expands the measurement range by synthesizing the ranging results of multiple wavelengths. This method can freely combine different wavelengths to generate synthetic wavelengths of different lengths, use a wavelength with a larger measurement range for coarse measurement, and use a wavelength with a smaller measurement range but higher precision for fine measurement, achieving the balance between large range and high precision.

[0004] The existing technology is restricted by the error amplification effect, which restricts the further improvement of the measurement precision of the synthetic wavelength. This characteristic is that when the measurement range of the synthetic wavelength is expanded by Λ / λ times, the measurement error is also amplified by the same multiple, making it difficult to break through the micron level in ranging precision. This error amplification effect directly leads to the contradiction between the measurement range and the measurement precision. Most of the existing methods reduce the synthetic wavelength Λ to reduce the error amplification multiple Λ λ , to improve the ranging precision. To solve this problem, some existing solutions use long-time averaging to improve the ranging precision in order to reduce the influence of the synthetic wavelength amplification effect on the system precision. Although this method can effectively suppress random noise, the long averaging time will cause significant lag in the measurement of moving targets, thereby severely limiting the measurement capability of the system for dynamic targets.

[0005] In summary, the existing synthetic wavelength interferometric ranging scheme is restricted by the error amplification effect, and there is a lack of a method that can effectively reduce the error amplification effect of the synthetic wavelength, so that micron-level or even higher precision absolute distance measurement cannot be achieved in a range of tens of meters or even further. An innovative measurement method is urgently needed to separate and compensate the error effect in the synthetic wavelength, to fundamentally solve the contradiction between the measurement range and the precision, to meet the high-precision ranging needs in the fields of precision measurement, space exploration and advanced manufacturing. SUMMARY

[0006] To solve the above technical problems, the application provides a synthetic wavelength interferometric ranging method based on characteristic rotation of a phase coordinate system, to solve the problems in the prior art, and the technical scheme adopted by the application is as follows: A synthetic wavelength interferometric ranging method based on characteristic rotation of a phase coordinate system, comprising the following steps: Step 1, using two-wavelength λ 1 and λ 2 laser interferometers to measure the same distance to be measured, wherein λ 1> λ 2; phase and are obtained respectively; a synthetic wavelength is calculated to obtain the distance to be measured L including errors; Step 2, constructing an ideal ranging result without phase measurement errors L t and obtaining a characteristic linear relationship, and then calculating the measurement error through the distance to be measured L and the ideal ranging result L t ; Step 3, establishing a coordinate system, wherein the horizontal coordinate represents the phase measurement result of , the vertical coordinate represents the phase measurement result of , and the characteristic linear relationship is represented as a straight line with a slope of = k 1 / λ 2 in the λ coordinate system; the phase measurement result is vectorized, and the relationship among the actual phase measurement result, the ideal true phase value and the random phase measurement error is represented by vector addition; Step 4, establishing a new coordinate system with the characteristic linear relationship as the horizontal coordinate, determining the characteristic angle between the coordinate system and the original coordinate system, and then performing coordinate conversion by using a rotation matrix to map any point in the coordinate system to the new coordinate system; Step 5, obtaining the vector of the new coordinate system through the rotation matrix, separating and eliminating the vertical error component with an error amplification effect to obtain the corrected phase measurement result P c ; Step 6, synthesizing the corrected phase measurement result P c代入 with the synthetic wavelength calculation formula to obtain the ranging result L c .

[0007] Further, in step 1, the distance to be measured L is calculated by the following formula: ; where Λ is the synthetic wavelength, expressed as Λ = λ1- λ2. λ 1 λ 2 / ( λ 1- λ 2).

[0008] Further, in step 2: the ideal ranging result L t is expressed as: ; where and , i.e. the ideal error-free phase of λ 1 and λ 2 through the distance to be measured L ; the characteristic linear relationship is expressed as: ; the measurement error is expressed as: ; where and respectively represent the phase measurement errors of the two phases, and δ L represents the ranging error measured by the synthetic wavelength.

[0009] Further, in step 3, the phase measurement result is vectorized to obtain ; for the actual phase measurement result of any single distance measurement P , the ideal true phase value P t and the random phase measurement error P e are expressed as: .

[0010] Further, in step 4, the new coordinate system and the characteristic angle between the original θ coordinate system are expressed as: ; The coordinate conversion is performed by using a rotation matrix, and the rotation angle is the angle between the characteristic linear relationship and the original coordinate system. The rotation matrix is expressed as: .

[0011] Furthermore, step 5 includes: obtaining using a rotation matrix. Vectors in coordinate system P ′: ; In the above formula The term is set to zero to separate and eliminate the vertical error component that has an error amplification effect, thus obtaining the corrected phase measurement result. P c : ; in, and This is the corrected phase.

[0012] Furthermore, in step 6, the ranging results... L c Calculated using the following formula:

[0013] The present invention has the following beneficial effects: (1) Balancing high precision and long distance measurement: This invention effectively separates the key components in MWI caused by error amplification through a synthetic wavelength ranging method based on error decomposition, thereby avoiding the accuracy loss caused by the extended range of MWI measurement, achieving micron-level or even submicron-level absolute ranging accuracy in the range of tens of meters and above, and significantly improving the overall performance of the ranging system.

[0014] (2) Low cost and easy implementation: The present invention uses the synthetic wavelength phase measurement results combined with data processing algorithms to achieve high-precision ranging through pure algorithm error decomposition. It does not rely on high-cost hardware such as frequency stabilization devices or complex optical frequency comb systems, which reduces system complexity and implementation cost. It has excellent economy and integration, and is easy to promote and apply in industrial scenarios.

[0015] (3) High dynamic capability: Traditional synthetic wavelength ranging relies on long-term averaging to improve accuracy, which reduces the data update rate and thus limits the ability to measure dynamic targets. The ranging accuracy improvement method proposed in this invention can improve ranging accuracy without relying on long-term averaging, thus greatly improving the dynamic capability of the system. Attached Figure Description

[0016] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is the error distribution coordinate system of the present invention; Figure 3 This is a schematic diagram of the coordinate system rotation path of the present invention; Figure 4 This is a simplified structural diagram of an embodiment of the present invention; Figure 4 In the middle: First laser 1, second laser 2, fiber optic combiner 3, fiber optic collimator 4, first beam splitter 5, second beam splitter 6, reference mirror 7, target reflector 8, first photodetector 9, second photodetector 10, data processing module 11, two-dimensional phase coordinate system characteristic rotation ranging module 12; Figure 5 This invention provides a comparison of the ranging error after error correction with the error before correction. Detailed Implementation

[0017] The following will be based on embodiments of the present invention. Figures 1-5 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.

[0018] This invention utilizes two wavelengths λ 1 and λ 2 ( λ 1> λ 2) Using a laser to measure the same target, the distance to be measured is calculated based on the interference phase, thus expanding the measurement range from a single wavelength. λ / 2 is extended to Λ / 2, but the ranging error introduced by phase measurement is also amplified simultaneously. To suppress random phase measurement errors, Λ / λ The invention has a magnification effect of 100 times. A characteristic linear relationship is established in a two-dimensional coordinate system, the phase measurement results are vectorized, and a relationship parallel to the ideal relationship is constructed. Axis and vertical direction The axis, thus separating the Λ / λ Error amplification characteristics The measurement vector is rotated to a new coordinate system using a matrix, separating and eliminating the vertical error component. Preserve parallel components Used for distance calculation, thus effectively avoiding Λ / λ This method amplifies the error by a factor of several, resulting in high-precision ranging results that closely approximate the true value. It requires no additional hardware system support and avoids lengthy averaging calculations, significantly improving ranging accuracy over long distances while maintaining the system's dynamic measurement capabilities. It is suitable for high-precision absolute distance measurement scenarios such as precision industrial measurement and space exploration, and has broad application prospects.

[0019] like Figure 1 A synthetic wavelength interferometric ranging method based on characteristic rotation of the phase coordinate system includes: Step 1, using two wavelengths λ 1 and λTwo lasers are used to perform interferometric measurements on the same distance to be measured, where λ 1> λ 2. Obtain the phase respectively and That is to say λ 1 and λ 2. 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 : ; Where Λ is the synthesized wavelength, expressed as Λ= λ 1 λ 2 / ( λ 1- λ 2) When using synthetic wavelengths for distance measurement, the measurement range is from... λ 1 / 2 and λ The range was increased from 2 / 2 to Λ / 2, thus expanding the measurement range.

[0020] Step 2, when there is no phase measurement error, the ideal distance measurement result can be expressed by the formula: ; in and That is to say λ 1 and λ 2. 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 characteristic linear relationship under error-free conditions can be obtained: ; Under the influence of various phase measurement errors, the actual measurement results will deviate from this characteristic linear relationship. This is because the measurement range is magnified by Λ / during the range extension process. λ At the same time, the ranging error was also amplified by Λ / λ 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 synthetic wavelength measurement. Compared to single-frequency interferometry, this represents the phase measurement error. The introduced ranging error is only Therefore, random errors are amplified by Λ / λ This multiple becomes the main component of distance measurement error.

[0021] Step 3, establish as follows Figure 2 As shown coordinate system, the horizontal coordinate represents the measured phase result, and the vertical coordinate represents the measured phase result, the characteristic linear relationship can be characterized as a straight line with a slope of k = λ 1 / λ 2. The phase measurement result is vectorized to obtain . For any single distance measurement, the actual phase measurement result, the ideal true phase value and the random phase measurement error can be represented by a coordinate system, respectively as P , P t and P e , and the relationship can be represented by phase vector addition as: ; Step 4, the method of coordinate system rotation is used to improve the ranging accuracy. A new coordinate axis Figure 3 is established with the characteristic linear relationship as the horizontal coordinate, and the characteristic angle between the new coordinate axis and the original coordinate axis can be represented as: θ ; The coordinate rotation matrix is used for coordinate conversion, and the rotation angle is the angle between the characteristic linear relationship and the original coordinate system. The rotation matrix can be represented as: ; The rotation of the coordinate system can map any point in the coordinate system to the new coordinate system.

[0022] Step 5, the vector P ′ in the new coordinate system can be obtained by using the rotation matrix: ; In the calculation result, is the main part causing the ranging error amplification Λ / λ times, and the phase component is not affected by the Λ / λ times error amplification effect. Therefore, the characteristic coordinate rotation can separate the two phase components in the measured phase result P . By setting the term of the above formula to zero, the error amplification effect of the synthesized wavelength interference ranging can be effectively eliminated, and the corrected measured phase result P c is represented as: ; wherein, and ​The corrected phase.

[0023] Step 6, the corrected phase vector calculated above is P c代入 The synthetic wavelength calculation formula can obtain the distance L c , which is expressed as: ; The method does not require additional hardware support, can significantly improve the ranging accuracy on the premise of maintaining the dynamic measurement capability of the system, and is suitable for absolute distance measurement scenes requiring long distance, high precision and high dynamic capability.

[0024] The specific implementation of the application is as follows: Use the dual-wavelength light source as shown in Figure 4 The output is performed using two 1550nm waveband lasers, which are a first laser 1 and a second laser 2, and the outputs of the two lasers are between λ 1 and λ 2 wavelengths, λ 1 and λ 2 there is a frequency difference of 10GHz. The output light of the two lasers is combined into one path by using a fiber combiner 3, and is converted into spatial light by a fiber collimating mirror 4. After the laser is emitted, it is split by a first beam splitter 5, one of which is used as a reference path and the other of which is used as a measurement path. The λ 1 and λ 2 interference is collected by the first photodetector 9 to obtain the interference signal of the reference path. The measurement path is split by the second beam splitter 6, and the two paths are respectively reflected by the reference mirror 7 and the target mirror 8 and then detected by the second photodetector 10 to obtain the interference signal of the measurement path. The two interference signals are sent to the data processing module 11, and then subsequent calculation is performed through the two-dimensional phase coordinate system feature rotation ranging module 12.

[0025] Further, the interference signals of λ 1 and λ 2 collected by the measurement path and the reference path respectively use a phase-locked amplification algorithm, and a phase measurement result containing errors can be calculated. The phases and are obtained, that is, the phase changes introduced by λ 1 and λ 2 through the distance to be measured L The measured distance L containing errors is calculated by using the phase measurement result to calculate the synthetic wavelength, which is expressed as: ; Λ is the synthetic wavelength, which is expressed as Λ= λ 1 λ 2 / (λ 1- λ 2)=c / Δ f , where Δ f is the frequency difference between the two lasers (i.e. 10 GHz). With the system parameters, the synthetic wavelength is about 30 mm. When the synthetic wavelength is used for distance measurement, the measurement range is increased from λ / 2 (775 nm) to Λ / 2 (15 mm), realizing the extension of the measurement range.

[0026] Further, when there is no phase measurement error, the ideal distance measurement result can be expressed by the following equation: ; where and are the ideal error-free phases of λ 1 and λ 2 passing through the distance to be measured, and L t is the ideal distance to be measured. Further, the characteristic linear relationship when there is no error can be obtained by using the above relationship: ; Under the influence of various phase measurement errors, the actual measurement result will deviate from the characteristic linear relationship. Since in the process of extending the measurement range, the measurement range is enlarged by Λ / λ , at the same time, the distance measurement error is also enlarged by Λ / λ times (in this method, the magnification is about 19355), and the measurement error is expressed as: ; where and represent the phase measurement errors of L 1 and 2 respectively, and δ represents the distance measurement error of the synthetic wavelength measurement. Compared with the single-frequency interference measurement scene, the distance measurement error introduced by the phase measurement error is only λ , so the random error is enlarged by Λ / times and becomes the main part of the distance measurement error.

[0027] Figure 2 Further, a coordinate system as shown in is established, the horizontal coordinate represents the phase measurement result of , and the vertical coordinate represents the phase measurement result of , and the characteristic linear relationship can be characterized as a straight line with a slope of k = λ 1 / λ 2 in the coordinate system. The phase measurement result is vectorized to obtain The actual phase measurement result, the ideal real phase value and the random phase measurement error of any single distance measurement can be represented by coordinate system, respectively P 、 P t and P e The relationship can be represented by phase vector addition as follows: ; Further, the distance measurement precision is improved by using the method of coordinate system rotation. The characteristic linear relationship is taken as the horizontal coordinate, and a new coordinate axis Figure 3 is established as shown in the figure , and the characteristic angle θ between the new coordinate axis and the original coordinate axis can be represented as: ; The coordinate rotation matrix is used for coordinate conversion, and the rotation angle is the angle between the characteristic linear relationship and the original coordinate system. The rotation matrix can be represented as: ; The rotation of the coordinate system can map any point in the coordinate system to the new coordinate system.

[0028] Further, the vector P in the new coordinate system can be obtained by using the rotation matrix: ; In the calculation result, is the main part causing the distance measurement error amplification λ times, and the phase component is not affected by the error amplification effect λ times. Therefore, the separation of the two phase components in the phase measurement result P can be realized by using the characteristic coordinate rotation. By setting the term of the above formula to zero, the error amplification effect of the synthetic wavelength interference distance measurement can be effectively eliminated, and the corrected phase measurement result P c is obtained. ; Further, the corrected phase vector P c代入 obtained by the above calculation is substituted into the synthetic wavelength calculation formula, and the distance L c approaching the real value is obtained, and is represented as:

[0029] The simulation of the corrected result after using the method is as shown in the figure Figure 5As shown, the ranging error is optimized from originally ±13μm to less than 100nm. This method does not require additional hardware and does not increase the complexity of the system. At the same time, long-term data averaging is avoided, and the system has a dynamic measurement capability of several tens of kHz or more while improving the ranging accuracy. Therefore, it is very suitable for absolute distance measurement scenarios that require long distance, high accuracy, and high dynamic capability.

[0030] The above embodiments only describe the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications, variations, modifications, and replacements of the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A synthetic wavelength interferometry method based on phase coordinate system characteristic rotation, characterized in that, Comprising the steps of: Step 1, interferometric measurement of the same distance to be measured with two lasers of wavelengths λ 1 and λ 2, where λ 1> λ 2; obtaining phases and respectively; performing a synthetic wavelength calculation to obtain the distance to be measured L including the error; Step 2, constructing ideal ranging results in the absence of phase error L t and get the characteristic linear relationship, and then through the distance to be measured L and ideal ranging results L t measurement error; Step 3, establishment Coordinate system, the horizontal coordinate represents Phase measurement result of the vertical coordinate represents Phase measurement result, the characteristic linear relationship is characterized in the coordinate system as a straight line with a slope of k = λ 1 / λ 2; vectorize the phase measurement result, and express the relationship between the actual phase measurement result, the ideal true phase value and the random phase measurement error by vector addition.​ Step 4: Establish a new [structure / system] with the characteristic linear relationship as the x-axis. Coordinate system, determined Coordinate system and original The characteristic angles of the coordinate system are then used to perform coordinate transformation using a rotation matrix, in order to... Mapping any point in the coordinate system to the new Coordinate system; Step 5, obtain the new [matrix] through the rotation matrix. The vectors in the coordinate system are used to separate and eliminate the vertical error component, which has an error amplification effect, to obtain the corrected phase measurement result. P c ; Step 6, correct the phase measurement results P c代入 Synthetic wavelength calculation formula, get the ranging result L c .

2. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 1, wherein, In step 1, the distance to be measured L This is calculated by the formula: ； where Λ is the synthesis wavelength, expressed as Λ = 2n / d, where n is the refractive index of the material and d is the period of the structure. λ 1 λ 2 / ( λ 1- λ 2)。 3. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 2, wherein, In step 2: Ideal ranging result L t is expressed as: ； in and That is to say λ 1 and λ 2. Distance to be measured L The ideal error-free phase; the characteristic linear relationship is expressed as: ； Measurement error is expressed as: ； wherein and respectively represent the phase measurement errors of the two phases, δ L represents the ranging error of the combined wavelength measurement.

4. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 1, wherein, In step 3, the phase measurements are vectorized to obtain ; for any single distance measurement actual phase measurement P , ideal real phase value P t and random phase measurement error P e is expressed as a vector addition of phases 。 5. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 1, wherein, In step 4, the new The coordinate system is the same as the original The characteristic angle of the coordinate system is θ Is expressed as: ； Coordinate transformation is performed using a rotation matrix, with the angle between the characteristic linear relationship and the original coordinate system as the rotation angle, and the rotation matrix is expressed as: 。 6. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 5, wherein, Step 5 comprises obtaining the vector in the coordinate system using the rotation matrix the vector in the coordinate system P ′: ； In the above formula The term is set to zero to separate and eliminate the vertical error component that has an error amplification effect, thus obtaining the corrected phase measurement result. P c : ； wherein and is the corrected phase.

7. The synthetic wavelength interferometer range finding method based on phase reference frame characteristic rotation of claim 6, wherein, In step 6, the ranging result L c is calculated by the following formula:

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