A method for absolute distance measurement based on phase solution

Abstract

The application is an absolute distance measurement method based on phase solution, which constructs a theoretical model of spectral interferometry, calibrates data, realizes calibration matching of the theoretical model and spectral signals, reads spectral data in the measurement stage, uniformly resamples data in the wave number domain according to the pixel-wavelength relationship obtained by calibration, obtains the resampled signals in the wave number domain, then, pre-processes the data in the wave number domain, including frequency domain coarse measurement and sub-pixel peak searching based on fast Fourier transform (FFT), and acquires a coarse measurement distance, on this basis, interface inherent phase delay compensation is carried out, combined with complex spectral phase fine measurement and order locking, and finally, through an ultra-precision absolute distance synthesis method, a fine measurement distance is obtained. The method can realize micro-nano level precision ultra-precision absolute distance measurement, and is highly suitable for high-speed real-time online detection in fields such as semiconductor manufacturing, precision optical processing and micro-nano assembly.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and specifically to an absolute distance measurement method based on phase calculation. Background Technology

[0002] Currently, the demand for non-contact absolute ranging technology is increasingly urgent in fields such as semiconductor manufacturing, precision optical processing, and micro / nano assembly. Spectral-domain white-light interferometric ranging, with its advantages of being non-contact, highly accurate, and providing absolute ranging, has become one of the important technical approaches for precision distance measurement. These systems typically consist of core components such as a broadband light source, an interferometric probe, and a broadband spectrometer. Their stable operating principle and high measurement accuracy have led to their widespread application. However, with the ever-increasing demands for ranging resolution and anti-interference capabilities in ultra-precision machining, the limitations of traditional white-light interferometric solutions based on pure frequency extraction are becoming increasingly apparent, restricting their widespread application in harsh and complex industrial environments.

[0003] While spectral-domain white-light interferometric absolute ranging technology offers significant advantages in non-contact and absolute measurement, its application in high-precision real-time measurement still faces numerous challenges. Most existing mainstream methods rely excessively on direct frequency domain peak extraction. Due to the inherent limitations of the optical physical resolution of spectrometers and the discrete frequency resolution of Fast Fourier Transform (FFT) algorithms, the "pick-fence effect" and spectral leakage are easily introduced during signal processing. This algorithmic flaw generates substantial truncation errors during distance extraction, making it difficult to achieve micrometer-level precision and thus failing to meet the stringent nanometer-level resolution requirements of ultra-precision manufacturing.

[0004] To address the challenges of limited accuracy and poor environmental adaptability in spectral interferometry systems, a technique based on complex spectrum main lobe phase calculation and lightweight dynamic compensation has emerged. This technique, by combining frequency domain coarse measurement and complex spectrum phase extraction, achieves a breakthrough in ranging resolution, providing a new technical path for ultra-precise absolute ranging. Therefore, this invention proposes an absolute distance measurement method based on phase calculation. By highly integrating high-precision wavelength calibration, lightweight resampling, Gaussian sub-pixel peak finding, and complex spectrum phase inversion algorithms, it achieves nanometer-level measurement accuracy and strong resistance to temperature drift, effectively overcoming the discretization errors and environmental inaccuracies of traditional methods. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems existing in the prior art and provide an absolute distance measurement method based on phase calculation to achieve ultra-precise absolute distance measurement with micro-nano level accuracy.

[0006] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution: An absolute distance measurement method based on phase calculation, the method comprising the following steps: Step S1: Construct a ranging model based on phase calculation: Construct a phase model in the total interference light intensity; Step S2: Spectral data calibration: Perform pixel-wavelength mapping, extract integer pixels of feature peaks, demodulate sub-pixel peak sequence by three-point parabolic interpolation, and then fit pixel-wavelength polynomial coefficients under the current environment using the least squares method. Step S3: Wavenumber Domain Uniform Resampling: Read the calibration polynomial coefficients from Step S2, calibrate the wavelength of the acquired signal and perform wavenumber domain conversion, and calculate the real-time limiting wavelength λ at the physical boundary pixel. max , λ min This refreshes the initial beam k start =1 / λ max k end =1 / λ min And the beam range ∆k, to perform resampling at the target wavenumber point; Step S4: Data preprocessing: DC removal processing is performed on the resampled interference signal to eliminate the DC background component in the interference spectrum; Step S5: Frequency Domain Coarse Measurement and Sub-pixel Peak Finding Based on FFT: After preprocessing, the interference signal undergoes Fast Fourier Transform (FFT). A sub-pixel interpolation method based on a Gaussian model is used to finely estimate the spectral peaks. After taking the natural logarithm of the amplitudes at three points, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset δ of the peak relative to the integer frequency points, thus obtaining the coarse measurement distance d. coarse ; Step S6: Interface inherent phase delay compensation: All reflection and transmission effects in each light path except for the distance propagation phase are respectively classified into equivalent complex amplitude coefficients. The transmission phase is canceled by sharing the transmission path between the two light paths. Based on the phase angle difference of the reflection coefficients of the measurement light path and the reference light path, a fixed interface inherent phase delay term is extracted for compensation. Step S7: Complex spectrum phase precision measurement and order locking: The wrapped phase is calculated point by point in the main lobe frequency range of the complex spectrum output by FFT. Then, one-dimensional phase expansion is performed on the wrapped phase sequence to eliminate the 2π jump. Linear interpolation is performed at the sub-pixel floating point peak obtained in step S5 to obtain continuous measurement phase. The integer interference order is locked by rounding the absolute coarse distance measurement. Step S8: Ultra-precise absolute distance synthesis: The determined integer order and the measured phase are inversely solved to obtain the precise distance.

[0007] Furthermore, in step S1, a two-beam interferometric measurement is used. When broadband low-coherence light enters the interferometric ranging probe, the measurement light reflected from the surface of the sample being measured coherently superimposes with the reference light reflected from the reference mirror inside the probe. The expression for the total spatial interference light intensity received by the spectrometer is: , In the formula, I0(λ) is the spectral intensity envelope of the broadband light source, A(λ) is the DC background term determined by the interface reflectivity, system transmittance, and detector response, B(λ) is the modulation amplitude term that determines the visibility of the interference fringes, where A(λ)≥B(λ)≥0 to ensure that the light intensity at any wavelength is physically achievable, n(λ) is the refractive index of the measured medium, d is the absolute geometric distance to be measured, Φ0(λ) is the initial phase term introduced by the interface reflection phase, system optical path, and other fixed phase factors; based on the distance-related term in the interference phase, the equivalent wavenumber is introduced. Therefore, the phase model in the total interference intensity simplifies to: .

[0008] Furthermore, in step S2, raw pixel-domain interferometric spectral data carrying distance modulation information is acquired through spectral detection. The relationship between the detector pixel coordinate x and the wavelength λ can be expressed by the spectrometer calibration parameters as follows: , In the formula, p0, p1, and p2 are pixel-wavelength mapping coefficients. By locking the integer pixels of the feature peak and combining the three-point parabolic difference, the sub-pixel peak sequence {X0, x1, ..., x} is demodulated. N-1 The polynomial coefficients under the current environment are obtained by least squares fitting. , , .

[0009] Furthermore, in step S3, the resampled light intensity at the target wavenumber point is obtained by weighting the four original pixels adjacent to the target pixel coordinates using a cubic B-spline interpolation kernel function.

[0010] Furthermore, in step S3, in [k start k end Within a certain range, N equally spaced sampling points are constructed to obtain the target equivalent wavenumber sequence: , The target pixel coordinates x of the resampled mapping are estimated by interpolation. i Light intensity at a location: First, pre-filtering is performed on the data. After pre-filtering, for each target pixel coordinate x... i Interpolation is performed by selecting the four nearest original pixels. Let the positions of the four nearest pixels be x. i.0 x i.1 x i.2 x i.3 The corresponding interpolation coefficients are c i.0 c i.1 c i.2 ci.3 Target wavenumber point k i The resampled light intensity at that point can be expressed as: , In the formula, I(x) i.j I represents the light intensity value at the location of neighboring pixels in the original pixel sequence after pre-filtering. r (k i () represents the wavenumber domain light intensity after resampling; The difference coefficient is determined by the normalized distance between the target location and the locations of its neighboring pixels: , In the formula, ∆x is the pixel sampling interval, and β 3 (·) represents the cubic B-spline kernel function.

[0011] Furthermore, in step S4, before performing the FFT, the resampled interference signal is first deDC-processed, i.e., the signal mean is subtracted to eliminate the DC background component in the interference spectrum; after deDC-processing, a window function is applied to the signal to reduce sidelobe leakage caused by finite-length truncation; let the resampled signal after deDC-processing be I. r Given ω(n) and the window function ω(n), the windowed signal is represented as: , In the formula, N is the mean of the resampled signal. resample This represents the number of resampling points. The windowed signal is padded with zeros to the nearest N. FFT =M·N resample M is the zero-padding factor, which refines the discrete frequency grid without changing the physical frequency resolution of the signal itself, so that the main peak of the spectrum can be more finely discretely represented on the frequency axis, thereby reducing the peak position quantization error caused by the picket fence effect.

[0012] Furthermore, in step S5, let q represent the FFT frequency point index, and let the frequency domain amplitude spectrum be denoted as P[q]. Let the integer peak index in the amplitude spectrum be q. max Its amplitude is b=P[q max The magnitudes of the two adjacent points are a=P[q] max -1] and c=P[q max +1], after taking the natural logarithm of the three-point amplitude, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset of the peak relative to the integer frequency point: , This yields the floating-point peak index: , Since the frequency of the interference signal in the equivalent wavenumber domain corresponds to the round-trip optical path term 2d of the measured distance, the coarse distance measurement is expressed as: , In the formula N FFT N is the number of FFT points after zero padding. FFT .

[0013] Furthermore, in step S6, a Mirau-type interferometer probe is used for both the reference optical path and the measurement optical path, and the equivalent complex amplitude coefficient of the reference optical path is set to C. ref (λ), the equivalent complex amplitude coefficient of the measurement optical path is C meas (λ), the two returning light fields are represented as follows: , , In the formula, E0(λ) is the incident light field, d is the measured distance, and n gap (λ) is the refractive index of the medium between the probe and the surface being measured. After the two optical fields re-merge, the interference term changes from... The decision is made, where * represents its conjugate complex number. Ignoring the common amplitude factor and utilizing the condition that the transmission phases of the two beams share a transmission path and thus cancel each other out, the total interference phase is written as: , Therefore, the inherent phase delay of the interface is defined as: .

[0014] Furthermore, in step S7, within the main lobe range, the complex spectral phase Φ(q) is expressed as: , The phase within the main lobe neighborhood of the FFT changes strictly linearly with the frequency index q. Based on this described linear relationship of the main lobe phase, the wrap-around phase is calculated point-by-point within the main lobe frequency range of the complex spectrum output by the FFT: , Perform a one-dimensional phase unrolling on the phase sequence in the neighborhood of the main lobe to obtain a continuous phase sequence, and then perform a phase unrolling at the sub-pixel peak q. float Linear interpolation is performed at the point to obtain the measured phase Φ. measured The n=0th sampling point of the equivalent wavenumber uniform resampling sequence corresponds to the initial equivalent wavenumber k. start Therefore, the initial phase of the analytic signal at this point is: , At the subpixel true peak q float At this point, the discrete frequency is exactly equal to the true frequency of the signal, and the frequency deviation is 0. Substituting this value, we can strictly obtain Φ(q). floatBased on this correspondence, and according to the phase model of beam splitting interference, at the initial equivalent wavenumber k = θ0, start At that point, the absolute total phase of the interference signal satisfies: , In the formula, m is the integer interference order, and d is the true absolute distance to be determined. A combined solution strategy of coarsely determining the order and finely measuring the phase compensation is adopted. First, the distance d obtained from the coarse frequency domain measurement is used... coarse Predicted Interference Level: .

[0015] Furthermore, in step S8, the determined integer order m is compared with the measured phase Φ. measured The inverse solution yields the precise distance: .

[0016] The beneficial effects of this invention are: 1. Completely eliminate the risk of failure of the "fence effect" and "skipping order" algorithm: This invention suppresses sidelobe leakage through data preprocessing (DC removal, windowing, and zero padding), and innovatively uses Gaussian logarithmic subpixel peak finding to strictly compress the frequency truncation error of the discrete Fourier transform; the coarse measurement error is only distributed on the order of hundreds of nanometers, which is much smaller than half of the distance between adjacent interference orders, providing an absolutely reliable theoretical guarantee for subsequent interference order locking.

[0017] 2. Eliminates the dual principle errors of discrete interpolation and probe parasitism: The algorithm reveals the strict linear phase relationship of the main lobe of the FFT complex spectrum. The measured phase extracted at the sub-pixel peak position physically corresponds precisely to the initial interference phase angle at the initial wavenumber, realizing phase extraction without truncation error. At the same time, an interface-inherent phase delay model is established to compensate for the micron-level parasitic bias caused by the absorption of the optical thin film material, successfully approximating the final ranging error to the nanometer level.

[0018] 3. Extremely high algorithm robustness and hardware affinity: Each measurement only refreshes the limiting wavelength and endpoint wavenumber, while the huge cubic B-spline interpolation mapping table remains fixed, completely avoiding wavenumber axis distortion caused by spectrometer temperature drift, and greatly reducing the system's edge computing power overhead, making it highly compatible with high-speed real-time online detection of embedded hardware. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention. Figure 2 This is a schematic diagram illustrating the dual-beam measurement principle of the present invention. Figure 3 This is a comparison diagram of the interference signals before and after uniform resampling in the wavenumber domain according to the present invention; Figure 4This is a schematic diagram of the reference optical path and measurement optical path of the Mirau-type interferometer probe of the present invention; Figure 5 This is a comparison diagram of the interference signals before and after uniform resampling in the wavenumber domain according to the present invention; Figure 6 This is a comparison chart of the error distribution between coarse and fine measurements across the entire measurement range of this invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] like Figure 1 As shown, an absolute distance measurement method based on phase calculation is described, which includes the following steps: Step S1: Construct a ranging model based on phase calculation: Construct a phase model in the total interference light intensity; Step S2: Spectral data calibration: Perform pixel-wavelength mapping, extract integer pixels of feature peaks, demodulate sub-pixel peak sequence by three-point parabolic interpolation, and then fit pixel-wavelength polynomial coefficients under the current environment using the least squares method. Step S3: Wavenumber Domain Uniform Resampling: Read the calibration polynomial coefficients from Step S2, calibrate the wavelength of the acquired signal and perform wavenumber domain conversion, and calculate the real-time limiting wavelength λ at the physical boundary pixel. max , λ min This refreshes the initial beam k start =1 / λ max k end =1 / λ min And the beam range ∆k, to perform resampling at the target wavenumber point; Step S4: Data preprocessing: DC removal processing is performed on the resampled interference signal to eliminate the DC background component in the interference spectrum; Step S5: Frequency Domain Coarse Measurement and Sub-pixel Peak Finding Based on FFT: After preprocessing, the interference signal undergoes Fast Fourier Transform (FFT). A sub-pixel interpolation method based on a Gaussian model is used to finely estimate the spectral peaks. After taking the natural logarithm of the amplitudes at three points, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset δ of the peak relative to the integer frequency points, thus obtaining the coarse measurement distance d. coarse ; Step S6: Interface inherent phase delay compensation: The needle summarizes all reflection and transmission effects in each light path except for the distance propagation phase into equivalent complex amplitude coefficients, and takes advantage of the condition that the transmission phases of the two light paths are canceled by sharing the transmission path. Based on the difference in the amplitude angle of the reflection coefficients of the measurement light path and the reference light path, a fixed interface inherent phase delay term is extracted for compensation. Step S7: Complex spectrum phase precision measurement and order locking: The wrapped phase of the complex spectrum output by FFT is calculated point by point in the main lobe frequency range. Then, one-dimensional phase expansion is performed on the wrapped phase sequence to eliminate the 2π jump. Linear interpolation is performed at the sub-pixel floating point peak obtained in step S5 to obtain continuous measurement phase. The integer interference order is locked by rounding the absolute coarse measurement distance. Step S8: Ultra-precise absolute distance synthesis: The determined integer order and the measured phase are inversely solved to obtain the precise distance.

[0022] In step S1, a two-beam interferometry measurement is used, such as... Figure 2 The diagram shows the principle of two-beam interferometry. When broadband low-coherence light enters the interferometric ranging probe, the measurement light reflected from the surface of the sample being measured coherently superimposes with the reference light reflected from the reference mirror inside the probe. The expression for the total spatial interference light intensity received by the spectrometer is: , In the formula, I0(λ) is the spectral intensity envelope of the broadband light source, A(λ) is the DC background term determined by the interface reflectivity, system transmittance and detector response, B(λ) is the modulation amplitude term that determines the visibility of interference fringes, where A(λ)≥B(λ)≥0 to ensure that the light intensity at any wavelength is physically achievable, n(λ) is the refractive index of the measured medium, d is the absolute geometric distance to be measured, and Φ0(λ) is the initial phase term introduced by the interface reflection phase, system optical path and other fixed phase factors. Based on the distance correlation term in the interferometric phase, an equivalent wavenumber is introduced. Therefore, the phase model in the total interference intensity simplifies to: .

[0023] In step S2, raw pixel-domain interferometric spectral data carrying distance modulation information is acquired through spectral detection. The relationship between the detector pixel coordinate x and the wavelength λ can be expressed by the spectrometer calibration parameters as follows: , In the formula, p0, p1, and p2 are pixel-wavelength mapping coefficients. By locking the integer pixels of the feature peak and combining the three-point parabolic difference, the sub-pixel peak sequence {X0, x1, ..., x} is demodulated. N-1 The polynomial coefficients under the current environment are obtained by least squares fitting. , , .

[0024] In step S3, the resampled light intensity at the target wavenumber point is obtained by weighting the four original pixels adjacent to the target pixel coordinates using a cubic B-spline interpolation kernel function.

[0025] In step S3, in [kstart k end Within a certain range, N equally spaced sampling points are constructed to obtain the target equivalent wavenumber sequence: , Due to the resampling mapping target pixel coordinates x i Since the light intensity is usually non-integer, it cannot be directly read from the original pixel spectrum. Therefore, it is necessary to estimate the light intensity at this location through interpolation, and then estimate the x-coordinate of the target pixel in the resampled mapping through interpolation. i Light intensity at a location: First, pre-filtering is performed on the data. After pre-filtering, for each target pixel coordinate x... i Interpolation is performed by selecting the four nearest original pixels. Let the positions of the four nearest pixels be x. i.0 x i.1 x i.2 x i.3 The corresponding interpolation coefficients are c i.0 c i.1 c i.2 c i.3 Target wavenumber point k i The resampled light intensity at that point can be expressed as: , In the formula, I(x) i.j I represents the light intensity value at the location of neighboring pixels in the original pixel sequence after pre-filtering. r (k i () represents the wavenumber domain light intensity after resampling; The difference coefficient is determined by the normalized distance between the target location and the locations of its neighboring pixels: , In the formula, ∆x is the pixel sampling interval, and β 3 (·) represents the cubic B-spline kernel function, and the comparison of the interference signals before and after uniform resampling in the wavenumber domain is as follows: Figure 3 As shown.

[0026] In step S4, before performing the FFT, the resampled interference signal is first deDC-processed, i.e., the signal mean is subtracted to eliminate the DC background component in the interference spectrum; after deDC-processing, a window function is applied to the signal to reduce sidelobe leakage caused by finite length truncation; let the resampled signal after deDC-processing be I. r Given ω(n) and the window function ω(n), the windowed signal is represented as: , In the formula, N is the mean of the resampled signal. resample This represents the number of resampling points. The windowed signal is padded with zeros to the nearest N.FFT =M·N resample , where M is the zero-padding factor. Zero-padding does not change the physical frequency resolution of the signal itself, but it can refine the discrete frequency grid, so that the main peak of the spectrum can be more finely discretely represented on the frequency axis, thereby reducing the peak position quantization error caused by the picket fence effect.

[0027] In step S5, as Figure 4 The diagram shows a Gaussian subpixel peak finding algorithm. After preprocessing, the interference signal undergoes a Fast Fourier Transform (FFT) to obtain its frequency domain amplitude spectrum. Let q denote the FFT frequency point index, and the frequency domain amplitude spectrum be denoted as P[q]. Let q be the index of the integer peak values ​​in the amplitude spectrum. max Its amplitude is b=P[q max The magnitudes of the two adjacent points are a=P[q] max -1] and c=P[q max +1], after taking the natural logarithm of the three-point amplitude, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset of the peak relative to the integer frequency point: , This yields the floating-point peak index: , Since the frequency of the interference signal in the equivalent wavenumber domain corresponds to the round-trip optical path term 2d of the measured distance, the coarse distance measurement is expressed as: , In the formula N FFT N is the number of FFT points after zero padding. FFT .

[0028] In step S6, before the two beams re-merge, they undergo reflection and transmission through interfaces such as the probe's internal film, the reference reflecting surface, the beam splitter, and the surface under test. These processes introduce additional phase changes through the Fresnel coefficient, which are directly superimposed on the final interference phase, causing a nonlinear phase abrupt change in the optical field. To avoid unfolding the optical field propagation at each interface one by one, all reflection and transmission effects in each beam, except for the distance propagation phase, can be summarized into an equivalent complex amplitude coefficient, such as... Figure 5 The diagram shows the reference and measurement optical paths of a Mirau-type interferometer probe. Let C be the equivalent complex amplitude coefficient of the reference optical path. ref (λ), the equivalent complex amplitude coefficient of the measurement optical path is C meas (λ), the two returning light fields are represented as follows: , , In the formula, E0(λ) is the incident light field, d is the measured distance, and n gap(λ) is the refractive index of the medium between the probe and the surface being measured. After the two optical fields re-merge, the interference term changes from... The decision is made, where * represents its conjugate complex number. Ignoring the common amplitude factor and utilizing the condition that the transmission phases of the two beams share a transmission path and thus cancel each other out, the total interference phase is written as: , Therefore, the inherent phase delay of the interface is defined as: .

[0029] In step S7, within the main lobe range, the complex spectral phase Φ(q) is expressed as: , The phase within the main lobe neighborhood of the FFT changes strictly linearly with the frequency index q. Based on this described linear relationship of the main lobe phase, the wrap-around phase is calculated point-by-point within the main lobe frequency range of the complex spectrum output by the FFT: , Since the arctangent function has a limited output range, Φ is obtained directly. wrap (q) represents the wrapper phase, which may have a 2π jump. Therefore, a one-dimensional phase unfolding is needed to perform on the phase sequence in the neighborhood of the main lobe to obtain a continuous phase sequence. Subsequently, at the sub-pixel peak position q... float Linear interpolation is performed at the point to obtain the measured phase Φ. measured The n=0th sampling point of the equivalent wavenumber uniform resampling sequence corresponds to the initial equivalent wavenumber k. start Therefore, the initial phase of the analytic signal at this point is: , At the subpixel true peak q float At this point, the discrete frequency is exactly equal to the true frequency of the signal, and the frequency deviation is 0. Substituting this value, we can strictly obtain Φ(q). float Therefore, the extracted measurement phase Φ = θ0. measured That is, the initial wavenumber k of the resampled sequence. start The interference phase at the point is theoretically exactly equal to that at the point of intersection, eliminating the interpolation error caused by discrete sampling. Based on this correspondence, and according to the phase model of beam splitting interference, at the initial equivalent wavenumber k... start At that point, the absolute total phase of the interference signal satisfies: , In the formula, m is the integer interference order, and d is the true absolute distance to be determined. Since the formula contains both the integer order m and the distance d, the unique absolute distance cannot be directly obtained by relying solely on the phase within the period. Therefore, this invention adopts a combined solution strategy of coarsely determining the order and finely measuring the phase compensation. First, the distance d obtained by coarse measurement in the frequency domain is used. coarsePredicted Interference Level: .

[0030] In step S8, the determined integer order m is compared with the measured phase Φ. measured The inverse solution yields the precise distance: Comparison of error distribution between full-range coarse and fine measurements, for example Figure 6 As shown, the coarse measurement error is mainly distributed on the order of hundreds of nanometers, and the error amplitude is much smaller than half of the distance between adjacent interference orders, which can provide reliable initial values ​​for subsequent phase fine measurement. After complex spectrum phase extraction, interference order locking, and fine distance synthesis, the ranging error is further compressed to the nanometer level.

[0031] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An absolute distance measurement method based on phase calculation, characterized in that, The method includes the following steps: Step S1: Construct a ranging model based on phase calculation: Construct a phase model in the total interference light intensity; Step S2: Spectral data calibration: Perform pixel-wavelength mapping, extract integer pixels of feature peaks, demodulate sub-pixel peak sequence by three-point parabolic interpolation, and then fit pixel-wavelength polynomial coefficients under the current environment using the least squares method. Step S3: uniform resampling in wave number domain: read the calibration polynomial coefficients in step S2, calibrate the wavelength of the collected signal and perform wave number domain conversion, calculate the real-time limit wavelength λ max , λ min at the physical boundary pixels, and then refresh the starting beam k start =1 / λ max , k end =1 / λ min and the beam range Δk, and perform resampling at the target wave number point; Step S4: Data preprocessing: DC removal processing is performed on the resampled interference signal to eliminate the DC background component in the interference spectrum; Step S5: Frequency Domain Coarse Measurement and Sub-pixel Peak Finding Based on FFT: After preprocessing, the interference signal undergoes Fast Fourier Transform (FFT). A sub-pixel interpolation method based on a Gaussian model is used to finely estimate the spectral peaks. After taking the natural logarithm of the amplitudes at three points, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset δ of the peak relative to the integer frequency points, thus obtaining the coarse measurement distance d. coarse ; Step S6: Interface inherent phase delay compensation: The needle summarizes all reflection and transmission effects in each light path except for the distance propagation phase into equivalent complex amplitude coefficients, and takes advantage of the condition that the transmission phases of the two light paths are canceled by sharing the transmission path. Based on the difference in the amplitude angle of the reflection coefficients of the measurement light path and the reference light path, a fixed interface inherent phase delay term is extracted for compensation. Step S7: Complex spectrum phase precision measurement and order locking: The wrapped phase of the complex spectrum output by FFT is calculated point by point in the main lobe frequency range. Then, one-dimensional phase expansion is performed on the wrapped phase sequence to eliminate the 2π jump. Linear interpolation is performed at the sub-pixel floating point peak obtained in step S5 to obtain continuous measurement phase. The integer interference order is locked by rounding the absolute coarse measurement distance. Step S8: Ultra-precise absolute distance synthesis: The determined integer order and the measured phase are inversely solved to obtain the precise distance.

2. The absolute distance measurement method based on phase calculation according to claim 1, characterized in that, In step S1, a dual-beam interferometry measurement is used. When broadband low-coherence light enters the interferometric ranging probe, the measurement light reflected from the surface of the sample being measured coherently superimposes with the reference light reflected from the reference mirror inside the probe. The expression for the total spatial interference light intensity received by the spectrometer is: ， In the formula, I0(λ) is the spectral intensity envelope of the broadband light source, A(λ) is the DC background term determined by the interface reflectivity, system transmittance and detector response, B(λ) is the modulation amplitude term that determines the visibility of interference fringes, where A(λ)≥B(λ)≥0 to ensure that the light intensity at any wavelength is physically achievable, n(λ) is the refractive index of the measured medium, d is the absolute geometric distance to be measured, and Φ0(λ) is the initial phase term introduced by the interface reflection phase, system optical path and other fixed phase factors. Based on the distance correlation term in the interferometric phase, an equivalent wavenumber is introduced. Therefore, the phase model in the total interference intensity simplifies to: .

3. The absolute distance measurement method based on phase calculation according to claim 2, characterized in that, In step S2, raw pixel-domain interferometric spectral data carrying distance modulation information is acquired through spectral detection. The relationship between the detector pixel coordinate x and the wavelength λ can be expressed by the spectrometer calibration parameters as follows: ， In the formula, p0, p1, and p2 are pixel-wavelength mapping coefficients. By locking the integer pixels of the feature peak and combining the three-point parabolic difference, the sub-pixel peak sequence {X0, x1, ..., x} is demodulated. N-1 The polynomial coefficients under the current environment are obtained by least squares fitting. , , .

4. The absolute distance measurement method based on phase calculation according to claim 3, characterized in that, In step S3, the resampled light intensity at the target wavenumber point is obtained by weighting the four original pixels adjacent to the target pixel coordinates using a cubic B-spline interpolation kernel function.

5. The absolute distance measurement method based on phase calculation according to claim 4, characterized in that, In step S3, in [k start k end Within a certain range, N equally spaced sampling points are constructed to obtain the target equivalent wavenumber sequence: ， The target pixel coordinates x of the resampled mapping are estimated by interpolation. i Light intensity at a location: First, pre-filtering is performed on the data. After pre-filtering, for each target pixel coordinate x... i Interpolation is performed by selecting the four nearest original pixels. Let the positions of the four nearest pixels be x. i.0 x i.1 x i.2 x i.3 The corresponding interpolation coefficients are c i.0 c i.1 c i.2 c i.3 Target wavenumber point k i The resampled light intensity at that point can be expressed as: ， In the formula, I(x) i.j I represents the light intensity value at the location of neighboring pixels in the original pixel sequence after pre-filtering. r (k i () represents the wavenumber domain light intensity after resampling; The difference coefficient is determined by the normalized distance between the target location and the locations of its neighboring pixels: ， In the formula, ∆x is the pixel sampling interval, and β 3 (·) represents the cubic B-spline kernel function.

6. The absolute distance measurement method based on phase calculation according to claim 5, characterized in that, In step S4, before performing the FFT, the resampled interference signal is first deDC-processed, i.e., the signal mean is subtracted to eliminate the DC background component in the interference spectrum; after deDC-processing, a window function is applied to the signal to reduce sidelobe leakage caused by finite length truncation; let the resampled signal after deDC-processing be I. r Given ω(n) and the window function ω(n), the windowed signal is represented as: ， In the formula, N is the mean of the resampled signal. resample This represents the number of resampling points. The windowed signal is padded with zeros to the nearest N. FFT =M·N resample M is the zero-padding factor, which refines the discrete frequency grid without changing the physical frequency resolution of the signal itself, so that the main peak of the spectrum can be more finely discretely represented on the frequency axis, thereby reducing the peak position quantization error caused by the picket fence effect.

7. The absolute distance measurement method based on phase calculation according to claim 6, characterized in that, In step S5, let q represent the FFT frequency point index, and let the frequency domain amplitude spectrum be denoted as P[q]. Let the integer peak index in the amplitude spectrum be q. max Its amplitude is b=P[q max The magnitudes of the two adjacent points are a=P[q] max -1] and c=P[q max +1], after taking the natural logarithm of the three-point amplitude, a quadratic curve fitting is performed in the logarithmic domain to obtain the sub-pixel offset of the peak relative to the integer frequency point: ， This yields the floating-point peak index: ， Since the frequency of the interference signal in the equivalent wavenumber domain corresponds to the round-trip optical path term 2d of the measured distance, the coarse distance measurement is expressed as: ， In the formula N FFT N is the number of FFT points after zero padding. FFT .

8. The absolute distance measurement method based on phase calculation according to claim 7, characterized in that, In step S6, a Mirau-type interferometer probe is used for both the reference optical path and the measurement optical path. The equivalent complex amplitude coefficient of the reference optical path is set to C. ref (λ), the equivalent complex amplitude coefficient of the measurement optical path is C meas (λ), the two returning light fields are represented as follows: ， ， In the formula, E0(λ) is the incident light field, d is the measured distance, and n gap (λ) is the refractive index of the medium between the probe and the surface being measured. After the two optical fields re-merge, the interference term changes from... The decision is made, where * represents its conjugate complex number. Ignoring the common amplitude factor and utilizing the condition that the transmission phases of the two beams share a transmission path and thus cancel each other out, the total interference phase is written as: ， Therefore, the inherent phase delay of the interface is defined as: 。 9. The absolute distance measurement method based on phase calculation according to claim 8, characterized in that, In step S7, within the main lobe range, the complex spectral phase Φ(q) is expressed as: ， The phase within the main lobe neighborhood of the FFT changes strictly linearly with the frequency index q. Based on this described linear relationship of the main lobe phase, the wrap-around phase is calculated point-by-point within the main lobe frequency range of the complex spectrum output by the FFT: One-dimensional phase expansion is performed on the phase sequence in the neighborhood of the main lobe to obtain a continuous phase sequence, which is then analyzed at the sub-pixel peak position q. float Linear interpolation is performed at the point to obtain the measured phase Φ. measured The n=0th sampling point of the equivalent wavenumber uniform resampling sequence corresponds to the initial equivalent wavenumber k. start Therefore, the initial phase of the analytic signal at this point is: ， At the subpixel true peak q float At this point, the discrete frequency is exactly equal to the true frequency of the signal, and the frequency deviation is 0. Substituting this value, we can strictly obtain Φ(q). float Based on this correspondence, and according to the phase model of beam splitting interference, at the initial equivalent wavenumber k = θ0, start At that point, the absolute total phase of the interference signal satisfies: ， In the formula, m is the integer interference order, and d is the true absolute distance to be determined. A combined solution strategy of coarsely determining the order and finely measuring the phase compensation is adopted. First, the distance d obtained from the coarse frequency domain measurement is used... coarse Predicted Interference Level: 。 10. The absolute distance measurement method based on phase calculation according to claim 9, characterized in that, In step S8, the determined integer order m is compared with the measured phase Φ. measured The inverse solution yields the precise distance: 。

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