High-stability synthetic wavelength phase demodulation method

Abstract

The invention belongs to the technical field of optical measurement, and particularly relates to a high-stability synthetic wavelength phase demodulation method. The method comprises the following steps: based on three-wavelength synthesis phase preprocessing and branch correction, expanding an unambiguous range to a millimeter level by calculating a secondary synthesis wavelength; in the staged processing strategy, a rough measurement height contour is generated by using a corrected synthetic phase, and then efficient candidate height screening is realized by combining integer period traversal and local microentry error function optimization; and finally, abnormal solutions are eliminated through multi-wavelength consistency inspection, and the noise immunity is ensured. The method does not need to depend on complex hardware, large-range (dozens of microns) high-precision (sub-nano-scale) measurement is achieved through pure-method design, the surface contour detection requirement of a large-size workpiece is met, the single-pixel processing time is shortened to the microsecond level, real-time measurement is supported, and the method is suitable for large-size surface appearance detection in the fields of aerospace, precision manufacturing and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of optical measurement, and in particular relates to a synthetic wavelength phase demodulation method. Background Art

[0002] In fields such as large-scale equipment manufacturing, precision machinery installation, and aerospace, there is a growing demand for high-precision, large-range, and real-time distance and height measurement. While traditional laser interferometry (LII) is widely used in precision engineering due to its nanometer-level accuracy, its core reliance on integer counting and segmentation of interference fringes results in an unambiguous measurement range of only half the laser wavelength (i.e., [0, λ / 2]). This makes it impossible to achieve unambiguous measurement when faced with height differences or surface undulations on large workpieces, severely limiting its application.

[0003] In order to break through the range limitation of single-wavelength measurement, multi-wavelength interferometry technology based on absolute ranging mode has become a key direction. This technology expands the unambiguous measurement range to the synthetic wavelength level by synthesizing interference signals of multiple wavelengths, significantly improving the large-scale measurement capability. However, the current multi-wavelength interferometry technology still faces multiple challenges: (1) Inherent limitations of single wavelength: Single-wavelength phase measurement is limited by the physical wavelength and can only obtain height information of [0,λ / 2]. For millimeter-level height differences of aerospace components or surface profile measurements of large-scale equipment, frequent phase unpacking is required, which is easily affected by noise interference and leads to solution errors. (2) Phase ambiguity in multi-wavelength synthesis: Traditional multi-wavelength synthesis technology relies on the phase difference of two or three wavelengths to calculate the synthesized wavelength. However, in actual applications, the frequency stability of the multi-wavelength light source (such as wavelength drift caused by temperature and vibration) and the strict matching requirements of the wavelength spanning the range lead to "phase ambiguity" in the synthesized phase - that is, different heights may correspond to the same wrapped phase. A complex branch selection algorithm is required to identify the true phase branch. The algorithm is highly complex and easily affected by noise, especially in the step-type height change area (such as the joint surface of mechanical components). Unwrapping errors are prone to occur. (3) Efficiency and accuracy bottleneck of the coarse-fine combination strategy: Existing methods lack an efficient integer cycle search strategy when combining coarse measurement (based on synthetic wavelength to expand the range) with fine measurement (based on single wavelength to improve accuracy). For example, blindly traversing all possible integer cycles within the synthetic wavelength period causes the amount of calculation to increase exponentially with the increase of the range; at the same time, there is a lack of a multi-wavelength consistency verification mechanism. When a wavelength is contaminated by noise, it is impossible to effectively eliminate abnormal solutions, which ultimately leads to the accumulation of height solution errors. Traditional technologies face the contradiction of "range-accuracy-efficiency" when measuring over a large range. There is an urgent need for a multi-wavelength phase solution algorithm that does not rely on ultra-high-precision light sources and has both efficient search strategies and robustness tests to meet the measurement needs of modern precision engineering.

[0004] Currently, most technologies achieve phase measurement by building optical systems (such as polarization interferometers and multi-laser hardware). However, there is still room for optimization in high-precision solutions at the purely algorithmic level, especially in synthetic phase correction, coarse-fine combination strategies, and error robustness. Summary of the Invention

[0005] The purpose of the present invention is to propose a highly stable synthetic wavelength phase demodulation method that does not rely on special hardware, so as to achieve large-scale, noise-resistant and unambiguous height measurement, and meet the high-precision real-time measurement needs of large-scale equipment manufacturing, aerospace and other fields.

[0006] The high-stability synthetic wavelength phase demodulation method proposed in the present invention includes: based on three-wavelength synthetic phase preprocessing and branch correction, the unambiguous range is expanded to the millimeter level by calculating the secondary synthetic wavelength; a staged processing strategy is adopted to first generate a rough height profile using the corrected synthetic phase, and then an integer cycle traversal and local micro-advance are combined with error function optimization to achieve efficient candidate height screening; finally, a multi-wavelength consistency test is performed to eliminate abnormal solutions and ensure noise resistance. The specific steps are as follows:

[0007] Step 1. Calculation of synthetic wavelength and synthetic phase: For the three-way wrapped phase data, the corresponding wavelengths are linearly combined to construct a three-wave synthetic phase. The three-way wrapped phase data refers to a set of wrapped phase data generated by three light sources with different wavelengths. In optical phase measurement, phase wrapping is an inherent phenomenon caused by the detector's periodic response to the phase (2π truncation). The true phase φ is truncated to φ = φ mod 2π, just like folding the continuous "time axis" into a "clock scale."

[0008] At a single wavelength, a wrapping is triggered every λ / 2 increase in height. At a composite wavelength, the wrapping trigger height is Λ / 2. This composite phase eliminates the 2π wrapping effect of a single wavelength, extending the unambiguous measurement range to half the secondary composite wavelength. Here, λ is the wavelength and Λ is the composite wavelength.

[0009] Step 2: Adaptive Branch Correction: To ensure that the phase jump reflects the actual step height difference on the surface of the object, the synthesized phase should be moved to the correct branch so that the height corresponding to the step position jump spans a full cycle. Because when the phase jumps by 2π, the mathematical properties of the wrapped phase may cause the same wrapped phase value to correspond to the actual phase change in two directions (for example, +2π or -2π), making it impossible to uniquely determine the true phase during unwrapping, resulting in ambiguity. Therefore, this correction accurately reflects the change in height across the synthesized wavelength period, avoiding unwrapping ambiguity caused by bidirectional ambiguity.

[0010] Step 3: Calculate the rough altitude: Use the corrected three-wave composite phase to obtain the rough altitude. The rough value can correctly reflect the large jump within half the composite wavelength, providing an unambiguous preliminary altitude profile.

[0011] Step 4: Integer cycle traversal and candidate height generation: Generate a candidate height set with the coarse-measured height as the center and the synthetic wavelength length as the period, covering the possible integer cycle ambiguity interval and reducing the computational complexity of blind search.

[0012] Step 5: Local inching and error function optimization: Optimize the local inching and error function by taking a step size of δh = 1 × 10 -9 Dense sampling is performed to generate a high-precision candidate set. For each candidate height, the three-way fringe integer order is calculated. This is accelerated and parallelized using a Just-In-Time Compilation Algorithm (JIT). An error function, Err, is defined to minimize Err and select the optimal candidate height, suppressing the interference of single-wavelength noise on the fringe order.

[0013] Step 6: Single-wavelength height restoration and consistency judgment: Restore the three single-wave heights based on the optimal number of whole cycles. If the difference between the three is less than the preset tolerance, the average of the three is taken as the final height. Otherwise, it is marked as a mismatch and the noise anomaly solution is eliminated.

[0014] Furthermore, the specific synthetic wavelength and synthetic phase calculation of step 1 includes:

[0015] Secondary composite wavelength and composite phase calculation, pairwise composite wavelength calculation, composite wavelength calculation of any two wavelengths:

[0016]

[0017] Specifically:

[0018] Then, referring to the dual-wavelength synthesis principle, it is extended to three wavelengths, and the secondary synthetic wavelength is further synthesized through two groups of primary synthetic wavelengths:

[0019]

[0020] According to the maximum measurement range, the secondary synthetic wavelength is selected, and its unambiguous measurement range is [0, Λ 123 / 2], where unambiguity means that there is a unique and definite mapping relationship between the measurement result and the measured physical quantity (such as height, distance), which can cover height differences from microns to millimeters.

[0021] The phase difference between any two wavelengths produced by the composite wavelength is,

[0022] φ ij =φi -φ j ,(i,j=1,2,3)

[0023] Therefore, we know that φ 123 =((φ1-φ2)-(φ2-φ3)),

[0024] Then generate the three-wavelength composite phase, perform a linear combination of the three-way wrapped phase and take the phase principal value:

[0025]

[0026] Among them, mod2π represents the three-wavelength phase wrapped in 2π, and the three-way wrapped phase diagrams φ1, φ2, and φ3 correspond to the three wavelengths λ1, λ2, and λ3 respectively. Referring to the dual-wavelength phase difference calculation logic, it is extended to the three-wavelength linear combination.

[0027] In step 2, the synthetic phase branch is corrected. Due to the multiple solution branches caused by phase periodicity, the jump ambiguity of the synthetic phase at the step position is corrected to the real branch using sign judgment:

[0028]

[0029] Ensure high uniqueness across cycle changes.

[0030] The rough height is quickly estimated in step 3, and the rough height is calculated based on the corrected synthetic phase to provide an unambiguous initial profile:

[0031]

[0032] At this time, the rough measurement value can be within ±Λ 123 The range of 1 / 2 correctly reflects large jumps, providing an unambiguous initial height profile.

[0033] In step 4, taking the rough measured height as the center, a candidate height set is generated according to the three-level synthetic wavelength period.

[0034]

[0035] Covering possible integer-week fuzzy intervals (such as n = -2, -1, 0, 1, 2) reduces the blind search range. The advantage of this is that a large range of altitudes can be searched up and down to increase the possibility of finding the final altitude, and the range can be manually controlled to improve efficiency.

[0036] In step 5, the step size is δh=1×10 -9Dense sampling is performed to generate a high-precision candidate set. The value of δh is related to the required speed. The JIT algorithm optimizes the algorithm execution efficiency through real-time compilation technology to meet real-time or quasi-real-time measurement requirements. It is mainly used to accelerate the intensive calculations in the fine search phase. The error function is set as:

[0037]

[0038] Its function is to traverse and search to find a high-resolution solution.

[0039] The present invention provides unambiguous measurement over a wide range: The unambiguous measurement range is determined by the secondary synthesized wavelengths. Selecting a wavelength combination enables unambiguous height measurement, meeting the requirements for surface profile inspection of large workpieces. Furthermore, through JIT algorithm acceleration and parallel traversal, single-pixel processing time is reduced to microseconds, enabling real-time measurement.

[0040] This method does not rely on complex hardware and can achieve large-scale (tens of micrometers) high-precision (sub-nanometer) measurement with pure method design. It is suitable for large-scale surface morphology detection in aerospace, precision manufacturing and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flowchart of the synthetic wavelength phase demodulation method of the present invention.

[0042] Figure 2 This is a comparison diagram of the step height simulation reconstruction of the present invention. DETAILED DESCRIPTION

[0043] The following is combined with Figure 1 、 2 The present invention is further described.

[0044] A highly stable synthetic wavelength phase demodulation method is proposed. A 50μm height step is generated by Python code for simulation. The generated step surface is compared with the recovered height. In order to verify the feasibility of the algorithm, the wavelengths are selected as λ1=448.3nm, λ2=531.8nm, and λ3=656.5nm.

[0045] In the simulation analysis, the secondary synthetic wavelength is 144.2μm. Reflection interferometry is simulated. The simulated specimen is a structure with 50μm height steps superimposed on a plane, such as Figure 2 As shown. The noise condition is simulated by adding Gaussian noise to the generated step surface. The mean and standard deviation of Gaussian noise are 0 and 10nm respectively. Then, the formula is:

[0046]

[0047] The phase wrapped by the corresponding wavelength is obtained to verify the feasibility of the algorithm.

[0048] See the algorithm flow Figure 1 , the specific steps are:

[0049] Step 1: Calculate the secondary synthetic wavelength and synthetic phase, calculate the pairwise synthetic wavelength, and calculate the synthetic wavelength of any two wavelengths.

[0050]

[0051] For example:

[0052] Then, referring to the dual-wavelength synthesis principle, it is expanded to three wavelengths, and the secondary synthetic wavelength is further synthesized through two sets of primary synthetic wavelengths.

[0053]

[0054] The secondary synthetic wavelength is selected according to the maximum measurement range required, and its unambiguous measurement range is [0, Λ 123 / 2], where unambiguity means that there is a unique mapping relationship between the measurement result and the measured physical quantity (such as height, distance), which can cover height differences from microns to millimeters. The phase difference produced by the composite wavelength between any two wavelengths is,

[0055] φ ij =φ i -φ j ,(i,j=1,2,3),

[0056] Therefore, we know that φ 123 =((φ1-φ2)-(φ2-φ3)), then generate the three-wavelength composite phase, perform linear combination of the three-way wrapped phase and take the phase principal value,

[0057]

[0058] Among them, mod2π represents the three-wavelength phase wrapped in 2π, and the three-way wrapped phase diagrams φ1, φ2, and φ3 correspond to the three wavelengths λ1, λ2, and λ3 respectively. Referring to the dual-wavelength phase difference calculation logic, it is extended to the three-wavelength linear combination.

[0059] Step 2: Correction of the synthetic phase branch, due to the multiple solution branches caused by phase periodicity,

[0060] Aiming at the ambiguity of the jump of the synthetic phase at the step position, the sign judgment is used to correct it to the real branch:

[0061]

[0062] Ensure high uniqueness across cycle changes.

[0063] Step 3: Rapid estimation of coarse height, based on the corrected synthetic phase, to calculate the coarse height and provide an unambiguous initial profile.

[0064]

[0065] At this time, the rough measurement value can be within ±Λ 123 The range of 1 / 2 correctly reflects large jumps, providing an unambiguous initial height profile.

[0066] Step 4: Integer cycle traversal and candidate height generation. With the coarse-measured height as the center, a set of candidate heights is generated according to the three-level synthetic wavelength period:

[0067]

[0068] Covering possible integer-week fuzzy intervals (such as n = -2, -1, 0, 1, 2) reduces the blind search range. The advantage of this is that a large range of altitudes can be searched up and down to increase the possibility of finding the final altitude, and the range can be manually controlled to improve efficiency.

[0069] Step 5: Local inching and error function optimization, dense sampling with a step size δh near each candidate height, such as δh = 1×10 -9 ,generate:

[0070]

[0071] Since the height can be uniquely determined for each single wavelength, the uniqueness of the integer i in the following formula cannot be accurately determined:

[0072]

[0073] Therefore, the error function is designed to obtain the unique k corresponding to the three wavelengths i , according to the above formula h cand k can be deduced in reverse i , for each obtained h cand , calculate the three-way integer fringe order:

[0074]

[0075] Then define the error function:

[0076]

[0077] where round(k i ) is a rounding function, the core of which is the calculated k i With rounded k i Make the difference until the three wavelength k i and round(k i) has the smallest absolute value, it can be considered that the only integer solution k has been found i , ending the search algorithm.

[0078] Step 6: Multi-wavelength consistency test and result output. First, restore the height of each single wavelength separately, and calculate the three-way unpacked height based on the optimal candidate height:

[0079]

[0080] Then make a consistency judgment, if the three wavelengths meet the

[0081]

[0082] In the above formula, ε = 1 × 10 -6 , then take the average as the final height

[0083]

[0084] Otherwise, it is marked as an invalid point, and the noise abnormal solution is eliminated.

[0085] According to the above algorithm steps, code simulation is carried out. In an environment with a Gaussian noise standard deviation of 10nm, a high-stability height recovery result can be obtained, and it is verified to be consistent with the initial height. The results are as follows Figure 2 As described above, the precise measurement results of the 50 μm step were verified, showing the comparison between the precise measurement height and the true value; the wavelengths selected for simulation were λ1 = 448.3 nm, λ2 = 531.8 nm, and λ3 = 656.5 nm.

[0086] Through the above implementation, unambiguous measurement can be achieved over a large range. The unambiguous measurement range is determined by the secondary synthetic wavelength. By selecting the wavelength combination, unambiguous height measurement can be achieved to meet the surface profile detection requirements of large-scale workpieces.

Claims

1. A highly stable synthetic wavelength phase demodulation method, characterized in that: include: Based on three-wavelength synthetic phase preprocessing and branch correction, the unambiguous range is extended to the millimeter level by calculating the secondary synthetic wavelength. A staged processing strategy is adopted, first using the corrected synthetic phase to generate a rough height profile, then combining integer cycle traversal with local micro-advancement to optimize the error function to achieve efficient candidate height screening. Finally, a multi-wavelength consistency test is performed to eliminate abnormal solutions and ensure noise resistance. The specific steps are as follows: Step 1. Calculate the synthetic wavelength and synthetic phase: For the three-way wrapped phase data, the corresponding wavelengths are linearly combined to construct a three-wave synthetic phase. The three-way wrapped phase data refers to a set of wrapped phase data generated by three light sources with different wavelengths. Since phase wrapping is an inherent phenomenon in optical phase measurement caused by the periodic response of the detector to the phase, the true phase Φ is truncated to φ = Φ mod 2π. At a single wavelength, a wrapping is triggered every λ / 2 increase in height. At a composite wavelength, the wrapping trigger height is Λ / 2. This composite phase extends the unambiguous measurement range to half the secondary composite wavelength by eliminating the 2π wrapping effect of a single wavelength. Here, is the wavelength and Λ is the composite wavelength. Step 2: Adaptive branch correction: To ensure that the phase jump reflects the actual step-like height difference on the surface of the object, the synthesized phase is moved to the correct branch, so that the height corresponding to the step position jump spans a full cycle. Because when the phase jumps by 2π, the mathematical properties of the wrapped phase mean that the same wrapped phase value corresponds to the actual phase change in two directions, making it impossible to uniquely determine the true phase during unwrapping, resulting in ambiguity. Therefore, this correction accurately reflects the change in height across the synthesized wavelength period, avoiding unwrapping ambiguity caused by bidirectional ambiguity. Step 3: Calculate the rough altitude: Use the corrected three-wave composite phase to obtain the rough altitude. The rough value now correctly reflects the large jump within half the composite wavelength, providing an unambiguous preliminary altitude profile. Step 4: Integer cycle traversal and candidate height generation: Generate a candidate height set with the rough-measured height as the center and the synthetic wavelength length as the period, covering the possible integer cycle ambiguity interval and reducing the computational complexity of blind search; Step 5: Local inching and error function optimization: Optimize the local inching and error function by taking a step size of δh = 1 × 10 -9 Dense sampling is performed to generate a high-precision candidate set. For each candidate height, the three-way fringe integer order is calculated, and the Just-In-Time Compilation Algorithm (JIT) is used to accelerate and parallelize the traversal. An error function, Err, is defined to minimize Err and select the optimal candidate height, suppressing the interference of single-wavelength noise on the fringe order. Step 6: Single-wavelength height restoration and consistency judgment: Restore the three single-wave heights based on the optimal number of whole cycles. If the difference between the three is less than the preset tolerance, the average of the three is taken as the final height. Otherwise, it is marked as a mismatch and the noise anomaly solution is eliminated.

2. The synthetic wavelength phase demodulation method according to claim 1, characterized in that: The specific synthetic wavelength and synthetic phase calculation described in step 1 includes: Secondary composite wavelength and composite phase calculation, pairwise composite wavelength calculation, composite wavelength calculation of any two wavelengths: specifically: Then, based on the dual-wavelength synthesis principle, it is expanded to three wavelengths. Specifically, two sets of primary synthesized wavelengths are further synthesized into secondary synthesized wavelengths: According to the maximum measurement range, the secondary synthetic wavelength is selected, and its unambiguous measurement range is [0, Λ 1223 / 2], where unambiguity means that there is a unique mapping relationship between the measurement result and the measured physical quantity, which can cover height differences from micrometers to millimeters; The phase difference between any two wavelengths produced by the composite wavelength is, f ij =φ i -f j ,(i,j=1,2,3) Therefore, we know that φ 123 =((φ1-φ2)-(φ2-φ3)), Then generate the three-wavelength composite phase, perform a linear combination of the three-way wrapped phase and take the phase principal value: Among them, mod2π represents the three-wavelength phase wrapped in 2π, and the three-way wrapped phase diagrams φ1, φ2, and φ3 correspond to the three wavelengths λ1, λ2, and λ3 respectively. Referring to the dual-wavelength phase difference calculation logic, it is extended to the three-wavelength linear combination.

3. The synthetic wavelength phase demodulation method according to claim 2, characterized in that: The synthetic phase branch correction described in step 2 is to correct the multiple solution branches caused by phase periodicity, making the jump of the synthetic phase at the step position blurred, and correct it to the real branch using sign judgment. The specific method is: Ensure high uniqueness across cycle changes.

4. The synthetic wavelength phase demodulation method according to claim 3, characterized in that: The rough height fast estimate described in step 3 is calculated based on the corrected synthetic phase to provide an unambiguous initial profile: At this time, the rough measured value is within ±Λ 123 The range of 1 / 2 correctly reflects large jumps, providing an unambiguous initial height profile.

5. The synthetic wavelength phase demodulation method according to claim 4, characterized in that: In step 4, the candidate height set is generated based on the three-level synthetic wavelength period with the coarse-measured height as the center, which is specifically expressed as follows: Cover possible integer week fuzzy intervals to reduce the blind search range.

6. The synthetic wavelength phase demodulation method according to claim 5, characterized in that: In step 5, the step size is δh = 1 × 10 -9 Dense sampling is performed to generate a high-precision candidate set. The value of δh is related to the required speed. The JIT algorithm is used to optimize the algorithm execution efficiency to meet the real-time or quasi-real-time measurement requirements and to accelerate the intensive calculations in the fine search phase. The error function is set as: Its function is to traverse and search to find a high-resolution solution.

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