Absolute and relative distance measurement method based on double-sideband frequency scanning interferometry system

Abstract

The application discloses an absolute and relative distance measurement method based on a double-sideband frequency scanning interference system, and mainly solves the problems of low precision and incapability of calculating relative distance when an existing method is used to solve absolute distance of an interference signal with slightly poor stationarity, and the scheme comprises the following steps: 1) generating a complex exponential signal by using two-way orthogonal digital electric signals output by the double-sideband frequency scanning interference system; 2) performing full-phase preprocessing on the generated complex exponential signal; 3) performing fast Fourier transform on the preprocessed complex exponential signal to obtain a full-phase spectrum thereof; 4) calculating instantaneous phases of upper sideband and lower sideband signals in the complex exponential signal according to the full-phase spectrum; and 5) solving the relative distance of a measured object at the moment by the instantaneous phases, and simultaneously solving the absolute distance of the measured object by combining a sliding window method. The application can effectively improve the measurement precision of the absolute distance, and simultaneously realizes the measurement of the relative distance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of distance measurement, further relates to an absolute distance and relative distance measurement method, in particular to an absolute and relative distance measurement method based on a double-sideband frequency scanning interference system, which can be used for distance measurement in a double-sideband frequency scanning interference distance measurement system. BACKGROUND

[0002] High-precision distance measurement technology is of great significance to both basic scientific research and advanced manufacturing. In particular, in the field of space science, the spacecraft formation flight technology represented by the European "Darwin Plan", "Gravitational Wave Plan" and "Music Plan" has put forward very high precision requirements for on-orbit measurement. The double-sideband frequency scanning interference distance measurement technology can realize high-precision distance measurement. This technology not only eliminates the error term introduced by Doppler shift, but also has good nonlinearity, greatly reducing the influence of sweep nonlinearity on distance measurement accuracy. It is one of the most promising and valuable distance measurement technologies at present.

[0003] In 2017, Di Mo published an article entitled "Double-sideband frequency scanning interferometry for long-range dynamic absolute measurement" in the journal of Applied Physics B: Lasers and Optics. The article proposes an absolute distance calculation method based on fast Fourier transform (FFT). This method transforms the interference signal into the frequency domain through FFT. There are two peak points in the frequency domain, and the positions of the two peak points in the frequency domain are the number of light fringes. Finally, the absolute distance is calculated by the number of light fringes. However, this method has the disadvantage that for scenes with low signal-to-noise ratio, the accuracy of absolute distance calculation is relatively low.

[0004] In 2018, Keshu Zhang published a paper titled "Double-sideband frequency scanning interferometry for outdoor environmental distance measurement" in the journal *Optical Communications*, proposing an absolute distance calculation method based on full-phase fast Fourier transform (APFFT). This method first extracts two signals, S1 and S2, of equal length from the beginning and end of the interference signal. Signal S1 is then transformed to the frequency domain using the APFFT algorithm. The transformed frequency domain contains two peak points, and the phases corresponding to these peak points are the instantaneous phases of the upper and lower sideband signals at the midpoint of signal S1. The same operation is performed on signal S2 to obtain the instantaneous phases of the upper and lower sideband signals at the midpoint of signal S2. Finally, the interference signal from the midpoint of signal S1 to the midpoint of signal S2 is transformed to the frequency domain using fast Fourier transform (FFT). The frequency domain also contains two peak points, and their positions in the frequency domain correspond to the integer fringe numbers of the upper and lower sideband signals in the interference signal. Finally, the absolute distance can be calculated based on the integer fringe count and instantaneous phase corresponding to the upper and lower sideband signals in the interference signal, respectively. This method improves the accuracy of absolute distance calculation for scenarios with low signal-to-noise ratios. However, it still has shortcomings: first, the accuracy is low, or even impossible, when calculating the absolute distance for interference signals with slightly poor stationarity; second, if the target is in a state of small-amplitude, high-frequency vibration, this method cannot measure its relative distance within one sweep cycle. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by proposing a method for measuring absolute and relative distances based on a double-sideband frequency scanning interferometer system, so as to achieve high-precision measurement of absolute and relative distances for interferometer signals with slightly poor stability.

[0006] To achieve the above objectives, the technical solution of the present invention includes the following:

[0007] (1) Using the two orthogonal digital electrical signals output by the double-sideband frequency scanning interferometer system, a complex exponential signal e(n) is obtained;

[0008] (2) Perform full-phase preprocessing on the complex exponential signal e(n) to obtain the preprocessed complex exponential signal e(i);

[0009] (3) Perform a fast Fourier transform on the preprocessed complex exponential signal e(i) to obtain its full-phase spectrum;

[0010] (4) Calculate the instantaneous phase of the upper sideband signal based on the full-phase spectrum of e(i). and the instantaneous phase of the lower sideband signal

[0011]

[0012]

[0013] wherein, and are the decimal instantaneous phases of the upper sideband signal and the lower sideband signal corresponding to the two peak points in the e(i) all-phase spectrum at the starting moment of e(i) respectively; N upper (i) and N lower (i) are the positions of the two peak points in the e(i) all-phase spectrum in the spectrum respectively; π is the circular constant, is the floor symbol, and mod is the remainder symbol;

[0014] (5) the relative distance of the object to be measured at the starting moment of e(i) is calculated according to the instantaneous phases and , and the absolute distance of the object to be measured is further calculated through the sliding window algorithm.

[0015] Compared with the prior art, the present application has the following advantages:

[0016] Firstly, since the present application extracts the instantaneous phases of the interference signal at multiple time points in one sweep cycle, compared with the traditional method of extracting the instantaneous phases of the interference signal at the beginning and the end, not only the absolute distance measurement can be performed, but also the relative displacement measurement in one sweep cycle can be realized.

[0017] Secondly, since the present application extracts the instantaneous phases of the interference signal at multiple time points and combines the sliding window method, high-precision absolute distance measurement can be realized in the case of poor stability of the interference signal, and the problem of low absolute distance measurement precision caused by poor stability of the interference signal is effectively solved. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a schematic diagram of the structure of the existing double-sideband frequency scanning interference ranging system;

[0019] Figure 2 is the implementation flowchart of the present application;

[0020] Figure 3 is a simulation result diagram of the absolute distance measurement using the traditional method;

[0021] Figure 4 is a simulation result diagram of the absolute distance measurement using the method of the present application;

[0022] Figure 5 is a simulation result diagram of the relative distance measurement using the method of the present application. DETAILED DESCRIPTION

[0023] The embodiments and effects of the present application are further described in detail below with reference to the accompanying drawings:

[0024] Embodiment one: refer to the attached Figure 2 The present application provides an absolute and relative distance measurement method based on a double-sideband frequency scanning interference system, comprising the following steps:

[0025] Step 1. Obtain a complex exponential signal e(n) from two-channel orthogonal digital signals output by the double-sideband frequency scanning interference system, and realize as follows:

[0026] e(n) = I(n) + jQ(n),

[0027] wherein I(n) and Q(n) represent two-channel orthogonal digital signals output by the double-sideband frequency scanning interference system, j represents the imaginary part of the complex number, n = 1, 2, …, TxFs, T is a frequency scanning period, and Fs is the sampling rate of the analog-to-digital converter.

[0028] Step 2. Perform all-phase preprocessing on the complex exponential signal e(n) to obtain a preprocessed complex exponential signal e(i), and obtain as follows:

[0029] (2.1) Construct a convolution window W c of length 2N-1, and perform weighting on the complex exponential signal composed of the (N-1)th sample point of the complex exponential signal e(n) and its previous N-1 sample points and subsequent N-1 sample points, i.e., a total of 2N-1 sample points, to obtain a weighted signal e w (i), which is represented as follows:

[0030] e w (i) = W c × [e((N-1)×(i-1)+1), …, e((N-1)×(i+1)+1)]

[0031] wherein N represents the sampling point number of the all-phase FFT algorithm, i = 1, 2, …, TxFs / (N-1), and Fs is the sampling rate of the analog-to-digital converter;

[0032] (2.2) In the weighted signal e w (i), add the sampling points with an interval of N two by two to obtain the preprocessed complex exponential signal e(i):

[0033] e(i) = e w (i) + e w (i+N).

[0034] Step 3. Perform fast Fourier transform on the preprocessed complex exponential signal e(i) to obtain its all-phase spectrum;

[0035] Step 4. Calculate the upper sideband signal instantaneous phase and the lower sideband signal instantaneous phase of e(i) respectively according to the full-phase spectrum of e(i) and

[0036]

[0037]

[0038] wherein, and are the decimal instantaneous phases of the upper sideband signal and the lower sideband signal of the two peak points in the full-phase spectrum of e(i) at the starting time of e(i) respectively; N upper (i) and N lower (i) are the positions of the two peak points in the full-phase spectrum of e(i) in the spectrum respectively; π is the circular constant, is the floor symbol, and mod is the remainder symbol.

[0039] Step 5. Calculate the relative distance of the object to be measured at the starting time of e(i) according to the instantaneous phases and and further solve it through the sliding window algorithm to obtain the absolute distance of the object to be measured.

[0040] The relative distance of the object to be measured at the starting time of e(i) is obtained according to the following formula:

[0041]

[0042] wherein λ = 1550 nm is the wavelength of the laser emitted by the narrow linewidth laser, and π is the circular constant.

[0043] The absolute distance of the object to be measured is obtained according to the following steps:

[0044] (5.1) Subtract the two instantaneous phases with an interval of T×Fs / (N-1)-windowsize from the upper sideband signal instantaneous phase and the lower sideband signal instantaneous phase obtained in step 4 to obtain the first phase difference and the second phase difference as follows:

[0045]

[0046]

[0047] wherein windowsize is the number of sliding window points set, k = 1, 2, …, windowsize, and N represents the sampling point number of the full-phase FFT algorithm.

[0048] (5.2) by phase difference and and the relative displacement L obtained in step (5) relative (i) calculate the absolute distance L(k) of the kth point in the sliding window of the object to be measured:

[0049]

[0050] where c is the propagation speed of light, π is the circular constant, f L is the center frequency of the laser emitted by the narrow linewidth laser, K is the sweep speed of the sweep signal source, T is one sweep period, and Fs is the sampling rate of the analog-to-digital converter;

[0051] (5.3) take k = 1, 2, …, windowsize, obtain the absolute distance of all points in the sliding window of the object to be measured according to step (5.2), and take the average to obtain the final absolute distance L.

[0052] Example 2: The overall implementation steps of the distance measurement method proposed in this example are the same as those in Example 1. Now refer to Figure 1 The specific structure and parameter settings of the double-sideband frequency scanning interferometric distance measurement system are further described as follows:

[0053] The double-sideband frequency scanning interferometric distance measurement system used in this example includes a narrow linewidth laser with a wavelength of 1550 nm, a sweep signal source, a Mach-Zehnder MZM modulator, a driver, a fiber beam splitter, an erbium-doped fiber amplifier EDFA, a circulator, an optical antenna, a corner cube prism, a 90° optical mixer, a balanced photodetector BPD1, a balanced photodetector BPD2, an analog-to-digital converter AD, and a programmable logic gate array FPGA, wherein:

[0054] The narrow linewidth laser is connected with the Mach-Zehnder MZM modulator and is used to generate a light signal E with a wavelength of 1550 nm.

[0055] The sweep signal source is connected with the driver and is used to generate a sweep electrical signal with a frequency range of 5 GHz to 10 GHz.

[0056] The driver is connected with the sweep signal source and is used to amplify the power of the sweep electrical signal generated by the sweep signal source by a certain multiple.

[0057] The Mach-Zehnder MZM modulator is connected with the narrow linewidth laser and is used to modulate the sweep signal generated by the sweep signal source with the light signal E as the optical carrier base frequency signal to obtain a modulated light signal.

[0058] The fiber beam splitter is connected with the Mach-Zehnder MZM modulator and is used to divide the obtained modulated light signal into reference end signals and measurement end signals;

[0059] EDFA connected with the optical fiber beam splitter, for amplifying the measured optical signal power by a certain multiple;

[0060] The circulator is connected with the EDFA, for changing the polarization direction of the two reflected back polarization beam splitter PBS light beams, so that the interference occurs;

[0061] The optical antenna is connected with the circulator, for transmitting the light signal output by the circulator;

[0062] The corner cube prism is located on the right side of the optical antenna, for reflecting the light signal emitted by the optical antenna back;

[0063] The 90° optical mixer is connected with the circulator, for interfering the measured optical signal and the reference optical signal, and generating four optical signals with 90° phase difference in sequence;

[0064] The balanced photodetector BPD1 is connected with the 90° optical mixer, for converting the optical signal into an electrical analog signal, and eliminating the direct current component in the optical signal;

[0065] The balanced photodetector BPD2 is connected with the 90° optical mixer, for converting the optical signal into an electrical analog signal, and eliminating the direct current component in the optical signal;

[0066] The analog-to-digital converter AD is connected with the balanced photodetector BPD1 and BPD2, for converting the electrical analog signal into an electrical digital signal;

[0067] The programmable logic gate array FPGA is connected with the analog-to-digital converter AD, for operating the electrical signal after analog-to-digital conversion in the FPGA, and calculating the absolute distance and the relative distance of the object to be measured.

[0068] Embodiment three: reference Figure 2 The implementation steps of the embodiment are the same as those of embodiment one. Based on the system described in embodiment two, the specific examples of measuring the absolute distance and the relative distance are given to further describe the implementation process of the present application, and the steps are as follows:

[0069] Step a, generating a reference optical signal.

[0070] a1) generating a fixed frequency optical signal E(t) by a narrow line width laser with a wavelength of 1550nm:

[0071] E(t) = cos(2πf L t)

[0072] Wherein, t∈[0,T], T is the time of frequency scanning, f Lis the frequency of the narrow-linewidth laser, and π is the circular constant.

[0073] a2) The fixed frequency optical signal E is used as the optical carrier base frequency signal to modulate the swept frequency signal from the swept frequency signal source through the Mach-Zehnder modulator MZM to obtain the modulated optical signal E1(t):

[0074] E1(t) = cos [2π(f L +f0)t + πKt 2 ] + cos [2π(f L -f0)t - πKt 2 ];

[0075] where f0 is the initial frequency of the swept frequency signal source, and K is the frequency scanning rate.

[0076] a3) The modulated optical signal E1(t) is divided into reference end signal and measurement end signal through the optical fiber beam splitter, and the reference end signal is used as the reference optical signal S t (t):

[0077] S t (t) = cos [2π(f L +f0)t + πKt 2 ] + cos [2π(f L -f0)t - πKt 2 ]

[0078] Step b, generating a measurement optical signal.

[0079] b1) The measurement end signal passes through the erbium-doped fiber amplifier EDFA to amplify the power and then input to the circulator;

[0080] b2) The optical signal output by the circulator is transmitted by the optical antenna, reflected on the corner cube prism of the target to be measured, and then received by the optical antenna to obtain the measurement optical signal S r (t):

[0081]

[0082] where s r,upper (t) represents the upper sideband of the echo signal, and s r,lower (t) represents the lower sideband of the echo signal, c is the speed of light, v is the movement speed of the target, L is the initial optical path, t ∈ [0, T], and T is the time of one frequency scanning.

[0083] Step c, obtaining two orthogonal analog electrical signals I(t) and Q(t).

[0084] c1) inputting the reference light signal and the measurement light signal into a 90° optical mixer to occur dry interference, obtaining four light signals S1(t), S2(t), S3(t) and S4(t) with phase difference of 90°:

[0085] S1(t) = offset + cos(2πw1t) + cos(2πw2t)

[0086]

[0087] S3(t) = offset + cos(2πw1t + π) + cos(2πw2t + π)

[0088]

[0089] wherein w1 is the angular frequency of the upper sideband signal in the interference signal, w2 is the angular frequency of the lower sideband signal in the interference signal, π is the circular constant, and offset is the direct current component;

[0090] c2) passing the light signal S1(t) and the light signal S3(t) through a balanced photodetector BPD1 to eliminate the direct current component offset and convert into an analog electrical signal I(t):

[0091]

[0092] wherein c is the speed of light, v is the movement speed of the target, π is the circular constant, f L is the center frequency of the laser emitted by the narrow line width laser, f0 is the starting frequency of the sweep source, K is the sweep speed of the sweep source, and L is the starting optical path

[0093] c3) passing the light signal S2(t) and the light signal S4(t) through a balanced photodetector BPD2 to eliminate the direct current component offset and convert into an analog electrical signal Q(t):

[0094]

[0095] Step d, generating a complex exponential signal e(n).

[0096] d1) sampling the two analog electrical signals I(t) and Q(t) after passing through an analog-to-digital converter AD to obtain two digital electrical signals I(n) and Q(n):

[0097] d2) taking the digital electrical signal I(n) as the real part and the digital electrical signal Q(n) as the imaginary part to form a complex exponential signal e(n):

[0098] e(n) = I(n) + jQ(n)

[0099] Wherein, j represents the imaginary part of the complex number, n = 1, 2…, T x Fs, T is a sweep cycle, Fs is the sampling rate of the analog-to-digital converter AD;

[0100] Step e, full-phase preprocessing is performed on the complex exponential signal e(n) to obtain a complex exponential signal e(i).

[0101] e1) a convolution window W c The (N-1) x i+1 sample point of the complex exponential signal e(n) and the complex exponential signal composed of the previous N-1 sample points and the subsequent N-1 sample points, a total of 2N-1 sample points, are weighted to obtain a weighted signal e w (i):

[0102] e w (i) = W c x [e((N-1) x (i-1)+1),…,e((N-1) x (i+1)+1)]

[0103] Wherein, N represents the sampling point number of the full-phase FFT algorithm, i = 1, 2,…, T x Fs / (N-1), Fs is the sampling rate of the analog-to-digital converter;

[0104] e2) the weighted signal e w (i) is added to obtain a full-phase preprocessed complex exponential signal e(i):

[0105] e(i) = e w (i) + e w (i+N)

[0106] Step f, the instantaneous phase of the upper and lower sideband signals in the complex exponential signal e(i) is calculated And

[0107] f1) the complex exponential signal e(i) is subjected to fast Fourier transform to obtain the full-phase spectrum of the complex exponential signal e(i);

[0108] f2) two peak points will appear in the full-phase spectrum of the complex exponential signal e(i), corresponding to the two frequency component signals in the interference signal, i.e. the upper sideband signal and the lower sideband signal, the phases corresponding to the two peak points are the decimal instantaneous phases of the upper sideband signal and the lower sideband signal at the starting time of the complex exponential signal e(i) And

[0109] f3) the positions of the two peak points in the spectrum represent the integer cycle number N of the instantaneous phases of the upper sideband signal and the lower sideband signal upper (i) and N lower (i);

[0110] f4) the fractional instantaneous phase from the upper sideband signal and the lower sideband signal and and the number of integer periods of the instantaneous phase N upper (i) and N lower (i), the instantaneous phase at the start of the complex exponential signal e(i) is calculated and

[0111] Step g, the relative distance and the absolute distance are calculated, which is the same as step 5 of example one.

[0112] The effect of the present application can be further illustrated by the following simulation results.

[0113] I. Simulation conditions

[0114] Using matlab simulation software, the wavelength of the laser is set to 1550nm, the sweep signal source sweep range is 5GHZ to 10GHZ, the sweep signal source one time scanning period is 1ms, the sampling rate of analog-to-digital converter AD is 100MHZ, the signal-to-noise ratio is 30dB, the sampling point number of full phase FFT algorithm is set to 32, the slip window number is 20, the absolute distance of the object to be measured is 500m, and the sine rule vibration with amplitude of 100 microns and frequency of 2000HZ is used, the sampling resolution is 10bit, and the simulation time is 1ms.

[0115] II. Simulation content

[0116] Simulation one, under the above simulation conditions, the absolute distance measurement precision graph is realized by using the existing method, and the result is as follows Figure 3 , wherein the abscissa represents the simulation time, and the ordinate represents the ranging accuracy. From Figure 3 it can be seen that the absolute distance measurement accuracy of the existing method is 30.23 microns.

[0117] Simulation two, under the above simulation conditions, the absolute distance measurement precision graph is realized by using the method of the present application, and the result is as follows Figure 4 , wherein the abscissa represents the simulation time, and the ordinate represents the ranging accuracy. From Figure 4 it can be seen that the standard deviation of the absolute distance measurement of the present application is 3.12 microns.

[0118] Simulation three, under the above simulation conditions, the relative distance measurement precision graph is realized by using the method of the present application, and the result is as follows Figure 5 , wherein the abscissa represents the simulation time, and the ordinate represents the ranging accuracy. From Figure 5 it can be seen that the relative distance measurement accuracy of the present application is 0.58 nanometers.

[0119] Comparison Figure 3 andFigure 4 The method can improve the absolute distance measurement precision of the traditional method from 30.23 microns to 3.12 microns, and the relative distance measurement precision from 0.3 microns to 0.03 microns. Figure 5 It can be seen that the method can realize the measurement of the relative distance in one sweep cycle, and indicates that the method can realize the high-precision absolute distance and relative distance measurement in the case that the stability of the interference signal is extremely poor.

[0120] The simulation analysis proves the correctness and effectiveness of the method.

[0121] The part not described in detail in the present application belongs to the common knowledge of the person skilled in the art.

[0122] The above only describes the preferred embodiments of the present application and does not limit the present application. Obviously, for those skilled in the art, after understanding the content and principles of the present application, various modifications and changes in form and details can be made without departing from the principles and structures of the present application. However, these modifications and changes based on the idea of the present application are still within the protection scope of the claims of the present application.

Claims

1. An absolute distance and relative distance measurement method based on a double sideband frequency scanning interferometry system, characterized in that, The instantaneous phase of the two-channel quadrature digital electrical signal output by the double-sideband frequency scanning interferometry system at multiple time points in a frequency scanning cycle is calculated by a full-phase algorithm, and the absolute distance and relative distance are further calculated according to all the instantaneous phases, including the following steps: (1) Using two-way orthogonal digital electrical signals outputted by the double sideband frequency scanning interference system, a complex exponential signal is obtained ; (2) performing all-phase preprocessing on the complex exponential signal to obtain a preprocessed complex exponential signal ;​ (3) The preprocessed complex exponential signal Perform a fast Fourier transform to obtain its full-phase spectrum; (4) According to the full-phase spectrum of , the upper sideband signal instantaneous phase and the lower sideband signal instantaneous phase are calculated respectively: ， wherein, and are respectively the fractional instantaneous phase of the upper sideband signal and the lower sideband signal at the start time instant of the two peak points in the full-phase spectrum; are respectively and are respectively the positions of the two peak points in the full-phase spectrum; is the ratio of the circumference to the diameter, is the floor symbol, is the modulo symbol; (5) Based on the instantaneous phase and Calculate the object under test in The relative distance at the starting moment is calculated, and then the absolute distance of the object to be measured is obtained by using the sliding window algorithm.

2. The method of claim 1, wherein, The complex exponential signal obtained in step (1) is implemented as follows: ， wherein and denotes the two quadrature digital electrical signals output by the double sideband frequency scanning interferometry system, denotes the imaginary part of a complex number, , is a sweep period, is the sampling rate of the analog-to-digital converter.

3. The method of claim 1, wherein, The pre-processed complex exponential signal obtained in step (2) is obtained according to the following steps: (2.1) a convolution window of length is applied to the complex exponential signal consisting of the first samples of the complex exponential signal and the preceding samples and the following samples, in total , to obtain a weighted signal , which is represented as follows: ， wherein represents all phase the number of sampling points of the algorithm, , is the sampling rate of the analog-to-digital converter; (2.2) In the weighted signal , the sampling points with interval are added two by two to obtain the preprocessed complex exponential signal : 。 4. The method of claim 1, wherein, In step (5), the object to be tested is in The relative distance at the starting time is obtained according to the following formula: ， wherein is the wavelength of the laser light emitted by the narrow linewidth laser, is the ratio of the circumference of a circle to its diameter.

5. The method of claim 4, wherein: The absolute distance of the object to be measured is obtained in step (5) and is realized as follows: (5.1) the upper sideband signal instantaneous phase and the lower sideband signal instantaneous phase wherein the two instantaneous phases separated by an interval are subtracted from each other, respectively, to obtain a first phase difference and a second phase difference as follows: ， wherein, is the number of set sliding window points, , denotes the number of sampling points of the full phase algorithm; (5.2) the relative distance obtained in step (5) by phase difference and the absolute distance of the i-th point in the sliding window of the object to be measured is calculated th point in the sliding window of the object to be measured : ， wherein, is the propagation speed of light, is the mathematical constant pi, is the center frequency of the laser light emitted by the narrow linewidth laser, is the sweep speed of the swept source, is one sweep period, is the sampling rate of the analog-to-digital converter; (5.3) Take , according to step (5.2), the absolute distance of all points in the slip window of the object to be measured is obtained, and the final absolute distance is obtained by averaging .

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