Nano-displacement real-time measurement system and method based on laser polarization interferometry

Abstract

The present invention discloses a nano-displacement real-time measurement system based on laser polarization interference, including an infrared laser, a first polarizer, a variable aperture, a first polarization beam splitter prism, a first 1 / 4 wave plate, a movable plane reflector, a second 1 / 4 wave plate, a fixed plane reflector, a third 1 / 4 wave plate, a depolarization beam splitter prism, a second polarizer, a second polarization beam splitter prism, a first photodetector, a second photodetector, a third photodetector, a data acquisition card and a host computer. The present invention also discloses a nano-displacement real-time measurement method based on laser polarization interference. The present invention uses a single-frequency laser to achieve a simple structure and low-cost nano-displacement real-time measurement, overcoming the problems of complex structure and high cost of a traditional dual-frequency laser interferometer. At the same time, the displacement direction is realized by judging the rotation direction of the polarization state, solving the dilemma that the traditional single-frequency laser interferometer cannot distinguish the back and forth vibration of the measured object.

Description

Technical Field

[0001] The present invention belongs to the technical field of laser interference displacement precision measurement, and in particular relates to a nanometer displacement real-time measurement system based on laser polarization interference, and also relates to a nanometer displacement real-time measurement method based on laser polarization interference. Background Art

[0002] At present, in my country's high-precision fields such as modern mechanical processing, bioengineering, nanoscience and technology, and advanced optical devices, the requirements for precision measurement are gradually transitioning from micrometer level to nanometer level and even sub-nanometer level. Laser interferometer has become an important means of precision measurement due to its inherent stability and smallness.

[0003] Based on the principle of laser interference, people invented single-frequency laser interferometers such as Michelson interferometer and Mach-Zehnder interferometer for high-precision micro-displacement measurement, which have been widely used in the field of precision measurement. However, due to the poor stability of single-frequency laser light sources, the difficulty in eliminating interference signal errors, and the problem of inability to distinguish the direction of measured displacement, the improvement of the resolution of laser interferometry technology has been greatly restricted. In 1970, HP invented the dual-frequency laser measurement system. The dual-frequency laser interferometer uses the Doppler effect and beat frequency phenomenon to calculate the displacement information of the object being measured. It has the advantages of stable measurement, strong anti-interference ability, and high resolution. However, the optical path of the dual-frequency laser measurement system is very complex and the cost is relatively high.

[0004] In addition to the above two types of interference, two beams of circularly polarized light of the same frequency can also interfere, but the interference result is different from the above two types of interference. It has neither interference pattern nor beat frequency signal, but is reflected in the polarization state. Through quantitative measurement of the polarization state, the phase relationship between the two beams of light can be obtained, and the resolution at the nanometer or even sub-nanometer level can be achieved. The displacement measurement system based on circularly polarized light interference can, on the one hand, solve the dilemma that a single-frequency interferometer cannot distinguish the back and forth vibration of the measured object, and has practical value; on the other hand, circularly polarized light interference can use a single-frequency laser, which greatly reduces the cost compared to the dual-frequency laser interference system. So far, there has been no report on the development of a complete system based on circular polarization interferometry technology in China. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a real-time measurement system for nano-displacement based on laser polarization interferometry, and also provides a real-time measurement method for nano-displacement based on laser polarization interferometry, aiming to solve the problems that single-frequency laser interferometers cannot distinguish directions and dual-frequency laser interferometers have complex optical paths and high costs, thereby improving measurement accuracy and practicability.

[0006] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0007] The nano-displacement real-time measurement system based on laser polarization interference includes an interference optical path system, wherein the interference optical path system includes an infrared laser, a first polarizer, a variable aperture, a first polarization beam splitter prism, a first 1 / 4 wave plate, a movable plane reflector, a second 1 / 4 wave plate, a fixed plane reflector, and a third 1 / 4 wave plate.

[0008] The light beam emitted by the infrared laser becomes linearly polarized light after passing through the first polarizer, and then the beam diameter is adjusted by the variable aperture to enter the first polarization beam splitter prism, and then decomposed into two beams of linearly polarized light P light and S light with equal energy by the first polarization beam splitter prism. The S light reflected by the first polarization beam splitter prism becomes left-handed circularly polarized light after passing through the first 1 / 4 wave plate, and then becomes right-handed circularly polarized light after being reflected by the movable plane reflector, and then passes through the first 1 / 4 wave plate again to become P light and returns to the first polarization beam splitter prism and transmits the first polarization beam splitter prism. After the beam splitter prism, the P light is incident on the third 1 / 4 wave plate as the measuring light; after being transmitted by the first polarization beam splitter prism, the P light passes through the second 1 / 4 wave plate and becomes right-handed circularly polarized light and enters the fixed plane reflector, and is reflected by the fixed plane reflector and becomes right-handed circularly polarized light, and then passes through the second 1 / 4 wave plate again to become S light and returns to the first polarization beam splitter prism, and then is reflected by the first polarization beam splitter prism as the reference light and enters the third 1 / 4 wave plate, and the reference light and the measuring light are combined by the third 1 / 4 wave plate and interfere to obtain linearly polarized light.

[0009] As mentioned above, the angles between the first quarter wave plate, the second quarter wave plate, the third quarter wave plate and their respective principal optical axes are all 45°.

[0010] The nano-displacement real-time measurement system based on laser polarization interference also includes a signal acquisition and processing system, which includes a depolarization beam splitter prism, a second polarizer, a second polarization beam splitter prism, a first photodetector, a second photodetector, a third photodetector, a data acquisition card, and a host computer.

[0011] The linearly polarized light obtained by the interference after beam combination by the third 1 / 4 wave plate is divided into two beams of equal energy by the depolarizing beam splitter prism. One beam passes through the second polarizer which forms an angle of 45° with the polarization direction of the incident light and enters the first photodetector. The other beam passes through the second polarizing beam splitter prism and is divided into reflected S light and transmitted P light. The reflected S light and the transmitted P light are incident on the second photodetector and the third photodetector respectively. The first photodetector, the second photodetector and the third photodetector input the collected electrical signals into the data acquisition card, which collects the signals, performs analog-to-digital conversion and transmits them to the host computer.

[0012] The real-time measurement method of nano-displacement based on laser polarization interference includes the following steps:

[0013] Step 1: The host computer performs differential analysis on the signals detected by the first photodetector and the second photodetector to obtain a signal I y , the signals detected by the second photodetector and the third photodetector are differentiated to obtain I x , I x =h+a cosφ

[0014] I y =k+b sin(φ+σ)

[0015] Among them, a and b are the amplitudes of the AC components, and σ is the signal I y and signal I x The phase difference between them, h and k are the magnitudes of the DC components,

[0016] Step 2: Use the least squares elliptic error correction algorithm to correct the signal I y and signal I x Correction is performed, and the corrected signal I x and signal I y Denoted as I′ x and I′ y ,

[0017] I′ x =cosφ

[0018] I′ y = sinφ

[0019] Step 3: Based on the error-corrected orthogonal signal I′ x and I′ y Generate a Lissajous circle and subdivide it into N parts. The number of subdivisions corresponding to the phase φ to be measured is S N Indicates that The displacement Δx of the plane reflector (6) is obtained based on the following formula:

[0020] As mentioned above, step 2 includes the following steps:

[0021] Step 2.1: Eliminate signal I y and signal I x The common term φ is obtained as follows:

[0022]

[0023] Step 2.2: Define the general formula of the ellipse equation x 2 +Bxy+Cy 2 +Dx+Ey+F=0, calculate the expression of error correction parameters h, k, a, b, σ,

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Parameters B, C, D, E, and F are obtained by solving the following linear equations:

[0031]

[0032] Among them, x i and i Signal I x and signal I y For the data corresponding to the i-th sampling time point, substitute the obtained parameters B, C, D, E, and F into the expressions of the error correction parameters h, k, a, b, and σ to obtain the measurement results of the error correction parameters h, k, a, b, and σ.

[0033] According to the error correction parameters h, k, a, b, σ, the signal I x and signal I y Error correction is performed, and the corrected signal I x and signal I y Denoted as I′ x and I′ y .

[0034] The number of subdivisions S in step 3 as described above N Obtained by the following steps:

[0035] According to the error-corrected signal I′ x and signal I′ y Generate a Lissajous circle, subdivide the Lissajous circle into N parts, and divide the four quadrants of the Lissajous figure into 8 intervals, namely the first interval Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 and Section 8 According to the error-corrected signal I′ x and I′ yThe positive or negative value determines the quadrant m where the phase φ to be measured is located, m = 1, 2, 3, 4 are the quadrant values. If the phase φ to be measured is not in the first quadrant, the phase φ to be measured is converted to φ′ in the first quadrant, where Then, according to the error-corrected signal I′ x and signal I′ y The absolute value of the value determines the interval of the quadrant where the phase φ to be measured is located: for the 1st to 8th interval, the subdivision number S N The calculation formula is S N1 , NS N1 ,in

[0036] The real-time measurement method of nano-displacement based on laser polarization interference also includes a step of judging the forward and reverse movement of the movable plane reflector (6):

[0037] Assume that the Lissajous figure changes continuously for z intervals, z≤8. From the zth interval forward, the interval number of the next interval is subtracted from the interval number of the previous interval to obtain △z. The forward and reverse movements of the movable plane reflector (6) are determined based on the following formula:

[0038]

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. The use of single-frequency laser realizes the real-time measurement of nano-displacement with simple structure and low cost, overcoming the problems of complex structure and high cost of traditional dual-frequency laser interferometer;

[0041] 2. The displacement direction is determined by judging the rotation direction of the polarization state, which solves the problem that the traditional single-frequency laser interferometer cannot distinguish the back-and-forth vibration of the measured object;

[0042] 3. Integrate polarization interference technology, virtual instrument technology and signal processing technology, use the least square method for error correction, reduce data acquisition errors, and achieve high-precision displacement resolution through data subdivision algorithm, theoretically increasing the displacement resolution to 0.63nm. The entire system can operate stably and has reliability;

[0043] 4. It realizes fully automated control and real-time display of signal acquisition and data processing, and increases the visualization and practicality of the laser polarization interferometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a system schematic diagram of the present invention;

[0045] Figure 2 It is a dynamic trend diagram of the error correction parameters during the use of the present invention;

[0046] Figure 3 This is a flow chart of displacement direction identification during the use of the present invention;

[0047] Figure 4 This is the main interface diagram of the host computer LabVIEW platform used in the present invention;

[0048] Figure 5 is a displacement resolution diagram during use of the present invention;

[0049] Figure 6 It is a static stability test diagram during the use of the present invention;

[0050] In the figure: 1. 650nm wavelength semiconductor infrared laser, 2. first polarizer, 3. adjustable aperture, 4. first polarization beam splitter prism, 5. first 1 / 4 wave plate, 6. movable plane reflector, 7. second 1 / 4 wave plate, 8. fixed plane reflector, 9. third 1 / 4 wave plate, 10. depolarizing beam splitter prism, 11. second polarizer, 12. first photodetector, 13. second polarization beam splitter prism, 14. second photodetector, 15. third photodetector, 16. data acquisition card, 17. commercial polarimeter, 18. host computer. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0052] Example

[0053] like Figure 1 As shown, the nano-displacement real-time measurement system based on laser polarization interference includes an interference optical path system and a signal acquisition and processing system. The interference optical path system includes an infrared laser 1, a first polarizer 2, a variable aperture 3, a first polarization beam splitter prism 4, a first 1 / 4 wave plate 5, a movable plane reflector 6, a second 1 / 4 wave plate 7, a fixed plane reflector 8, and a third 1 / 4 wave plate 9. The signal acquisition and processing system includes a depolarization beam splitter prism 10, a second polarizer 11, a first photodetector 12, a second polarization beam splitter prism 13, a second photodetector 14, a third silicon photocell 15, a data acquisition card 16, and a host computer 18.

[0054] During operation, the light beam emitted by the infrared laser 1 becomes linearly polarized light after passing through the first polarizer 2, and the polarization direction of the linearly polarized light forms an angle of 45° with the horizontal direction. The linearly polarized light passes through the variable aperture 3 to adjust the beam diameter, and is incident on the first polarization beam splitter prism 4, where it is decomposed into two linearly polarized lights P and S with equal energy and perpendicular directions. The S light reflected by the first polarization beam splitter prism 4 becomes left-handed circularly polarized light after passing through the first 1 / 4 wave plate 5, and then becomes right-handed circularly polarized light after being reflected by the movable plane reflector 6, and then becomes P light after passing through the first 1 / 4 wave plate 5 again, and returns to the first polarization beam splitter prism 4. The transmitted P light becomes right-handed circularly polarized light after passing through the second 1 / 4 wave plate 7, and then becomes right-handed circularly polarized light after being reflected by the fixed plane reflector 8, and then becomes S light after passing through the second 1 / 4 wave plate 7 again, and returns to the first polarization beam splitter prism 4. The S light that returns to the first polarization splitter prism 4 and is reflected and the P light that returns to the first polarization splitter prism 4 and is transmitted pass through the third 1 / 4 wave plate 9 to generate right-handed circularly polarized light and left-handed circularly polarized light again and interfere to generate linearly polarized light.

[0055] The linearly polarized light generated by interference is split into two light beams with equal energy by a depolarizing beam splitter prism 10. One beam passes through a second polarizer 11 which forms an angle of 45° with its polarization direction and enters a first photodetector 12. The other beam passes through a second polarizing beam splitter prism 13 and is split into two beams, namely, reflected S light and transmitted P light. The reflected S light and the transmitted P light are incident on a second photodetector 14 and a third photodetector 15, respectively.

[0056] The signal I of the first photodetector 12 is obtained D1 , the signal I of the second photodetector 14 D2 , the signal I of the third photodetector 15 D3 It can be expressed as:

[0057]

[0058]

[0059]

[0060] In formulas (1)-(3), E is the total light intensity amplitude of the interference between the right-handed circularly polarized light and the left-handed circularly polarized light generated after passing through the third quarter wave plate 9, is the phase difference between right-handed circularly polarized light and left-handed circularly polarized light. D1 ,I D2 ,I D3 After being transmitted to the host computer 18 through the data acquisition card 16, a two-to-two differential operation can be performed to obtain a sinusoidal signal I D1-D2 and cosine signal I D2-D3 :

[0061]

[0062]

[0063] Where φ is the phase to be measured, and Sinusoidal signal I D1-D2 and cosine signal I D2-D3 The Lissajous figure is obtained in the host computer 18. In the experiment, due to the interference of environmental vibration noise, circuit noise, unstable laser light source and optical component manufacturing process, the actual sine signal I D1-D2 and cosine signal I D2-D3 There will be three errors: unequal amplitude error, non-orthogonal error and DC level drift error, which will cause the actual output sinusoidal signal I D1-D2 and cosine signal I D2-D3 It is not an orthogonal signal. D1-D2 and I D2-D3 The corresponding actual sine signal and cosine signal are represented by I y and I x It is expressed as: Where a and b are the amplitudes of the AC components, a≠b is the unequal amplitude error; σ is the sinusoidal signal I y and cosine signal I x The phase difference between them, when σ≠90°, it represents the existence of non-orthogonal error; h and k are the magnitudes of the DC components, that is, the DC level drift error.

[0064] In order to obtain the information of the phase φ to be measured, the present invention first uses the least squares elliptic error correction algorithm to correct the error, and converts the actual signal I x and signal I y Simplifying and eliminating the common term φ yields: and the general form of the ellipse equation x 2 +Bxy+Cy 2 +Dx+Ey+F=0, we can get the expressions of error correction parameters h, k, a, b, σ:

[0065]

[0066] The optimal ellipse parameters B, C, D, E, and F are obtained by solving the following linear equations:

[0067]

[0068] Among them, x i and i Signal I x and signal I yAt the data corresponding to the i-th sampling time point, the obtained ellipse optimal parameters B, C, D, E, F are substituted into formula (6) to obtain the error correction parameters h, k, a, b, σ, as follows: Figure 2 Shown are the dynamic measurement results of the error correction parameters h, k, a, b, σ, where N is the number of subdivisions of the Lissajous circle.

[0069] According to the measured error correction parameters h, k, a, b, σ, the actual signal I x and signal I y After error correction, the two signals obtained are orthogonal to each other, and I′ x and I′ y express: Taking the wavelength λ of the laser used as the scale, when the signal changes a complete Lissajous circle, the change △x of the displacement of the movable plane reflector 6 is a complete wavelength λ=650nm. In order to further improve the accuracy of the instrument, the present invention further uses the tangent lookup table subdivision algorithm to subdivide the phase, and according to the error-corrected signal I′ x and I′ y Generate a Lissajous circle and subdivide it into N = 1024 parts. The subdivision number corresponding to the phase φ to be measured is S N Indicates that To solve the subdivision number S corresponding to the phase φ to be measured N , divide the four quadrants of the Lissajous circle into 8 equal intervals, namely the first interval Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 and Section 8 According to the error-corrected signal I′ x and I′ y The positive or negative value determines the quadrant m where the phase φ to be measured is located, and m = 1, 2, 3, 4 are the quadrant values. If the phase φ to be measured is not in the first quadrant, the phase φ to be measured is converted to φ′ in the first quadrant, where Then, according to the error-corrected orthogonal signal I′ x and I′ y The absolute value of the value determines the interval of the quadrant where the phase φ to be measured is located: for the 1st to 8th interval, the subdivision number S N The calculation formula is S N1 , in according to The phase φ to be measured is calculated, and the displacement △x of the movable plane reflector 6 is obtained based on the following formula: The theoretical displacement resolution of this method is 0.63nm.

[0070] Displacement direction identification is realized on the basis of the above demodulation subdivision. The above process converts the error-corrected signal I′ x and signal I′ y Divided into 8 intervals. When the movable plane reflector 6 moves forward, the interval corresponding to the Lissajous circle of the signal changes according to the rule of 1-2-3-4-5-6-7-8-1, mainly in ascending order; when the movable plane reflector 6 moves backward, the interval corresponding to the Lissajous figure of the signal changes according to the rule of 4-3-2-1-8-7-6-5-4, mainly in descending order. Assume that the Lissajous figure of the signal changes continuously for z (z≤8) intervals, starting from the zth interval forward, subtract the interval number of the previous interval from the interval number of the next interval to obtain △z, and judge the displacement direction according to the positive or negative value of △z: However, there are two exceptions: (1) the z intervals of change include the change from the first interval to the eighth interval; (2) the z intervals of change include the change from the eighth interval to the first interval. The improved judgment method is: According to the above conditions, the displacement is determined to be forward or reverse. Figure 3 Shown is a complete flow chart of detailed decomposition and displacement orientation identification.

[0071] like Figure 4 The figure shows the LabVIEW front panel of the host computer. In the above measurement system, the drawing of Lissajous figures before and after correction, the error correction algorithm based on the least squares method, the demodulation subdivision algorithm based on the tangent lookup table algorithm, the displacement calculation, direction identification and real-time display are all completed based on the LabVIEW virtual instrument platform.

[0072] like Figure 5 It is shown that the minimum displacement in the environmental noise detected by the present invention. In the actual measurement process, the minimum displacement resolution caused by the present invention in the presence of environmental interference is 15.869nm, which proves that the experimental resolution of the present invention should be better than 15.869nm.

[0073] like Figure 6 The figure shows the static stability test of the system of the present invention. The displacement change of the above-mentioned measurement system over a period of time is in a stable state, which can prove the stability and reliability of the present invention.

[0074] The signal acquisition and processing system (10-16, 18) is replaced by a commercial polarimeter 17, and the change in the azimuth angle △α of the linear polarized light formed by the interference of the right-handed circularly polarized light and the left-handed circularly polarized light is directly measured by the polarimeter 17. The relationship between △α and the displacement change △x of the movable reflector 6 is: The results show that in the process of measuring random noise, the minimum displacement resolution obtained by the commercial polarimeter is 10.219 nm. The comparison proves that the minimum resolution of the present invention is comparable to that of the commercial polarization analyzer, and has the advantages of high stability and low cost.

[0075] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A nano-displacement real-time measurement method based on laser polarization interference, using a nano-displacement real-time measurement system based on laser polarization interference, the system comprising an interference optical path system, the interference optical path system comprising an infrared laser (1), a first polarizer (2), a variable aperture (3), a first polarization beam splitter prism (4), a first 1 / 4 wave plate (5), a movable plane reflector (6), a second 1 / 4 wave plate (7), a fixed plane reflector (8), and a third 1 / 4 wave plate (9), The light beam emitted by the infrared laser (1) is converted into linear polarized light after passing through the first polarizing plate (2), and then is incident on the first polarizing beam splitting prism (4) after adjusting the beam diameter through the variable iris (3), and then is decomposed into two linear polarized light beams P and S with equal energy through the first polarizing beam splitting prism (4). The S light reflected by the first polarizing beam splitting prism (4) is converted into left-handed circular polarized light after passing through the first quarter wave plate (5), and then is converted into right-handed circular polarized light after being reflected by the movable plane reflecting mirror (6), and then is converted into P light again after passing through the first quarter wave plate (5), and returns to the first polarizing beam splitting prism (4) and transmits the first polarizing beam splitting prism (4). After passing through the optical prism (4), the light is incident on a third quarter wave plate (9) as measuring light; after being transmitted through the first polarization beam splitter prism (4), the P light passes through the second quarter wave plate (7) and becomes right-handed circularly polarized light, which is incident on a fixed plane reflector (8); after being reflected by the fixed plane reflector (8), the light becomes right-handed circularly polarized light, which passes through the second quarter wave plate (7) again and becomes S light, which returns to the first polarization beam splitter prism (4); after being reflected by the first polarization beam splitter prism (4), the light is incident on a third quarter wave plate (9) as reference light; after the reference light and the measuring light are combined through the third quarter wave plate (9), the linearly polarized light is obtained by interference. The angles between the first quarter wave plate (5), the second quarter wave plate (7), and the third quarter wave plate (9) and their respective principal optical axes are all 45°. The invention also includes a signal acquisition and processing system, which includes a depolarization beam splitter prism (10), a second polarizer (11), a second polarization beam splitter prism (13), a first photodetector (12), a second photodetector (14), a third photodetector (15), a data acquisition card (16), and a host computer (18). The linearly polarized light obtained by the third 1 / 4 wave plate (9) after beam combination is interfered and is split into two beams of equal energy by a depolarizing beam splitter prism (10). One beam passes through a second polarizing plate (11) which forms an angle of 45° with the polarization direction of the incident light and enters a first photodetector (12). The other beam passes through a second polarizing beam splitter prism (13) and is split into reflected S light and transmitted P light. The reflected S light and the transmitted P light are incident on a second photodetector (14) and a third photodetector (15) respectively. The first photodetector (12), the second photodetector (14) and the third photodetector (15) input the collected electrical signals into a data acquisition card (16). The data acquisition card (16) collects the signals, performs analog-to-digital conversion and transmits the signals to a host computer (18). It is characterized in that The above method comprises the following steps: Step 1: The host computer (18) performs differential analysis on the signals detected by the first photodetector (12) and the second photodetector (14) to obtain a signal I y , the signals detected by the second photodetector (14) and the third photodetector (15) are differentiated to obtain I x , I x =h+acosφ AND y =k+bsin(φ+σ) Among them, a and b are the amplitudes of the AC components, and σ is the signal I y and signal I x The phase difference between them, h and k are the magnitudes of the DC components, Step 2: Use the least squares elliptic error correction algorithm to correct the signal I y and signal I x Correction is performed, and the corrected signal I x and signal I y Denoted as I′ x and I′ y , I' x =cosφ I′ y =sinφ Step 3: Based on the error-corrected orthogonal signal I′ x and I′ y Generate a Lissajous circle and subdivide it into N parts. The number of subdivisions corresponding to the phase φ to be measured is S N Indicates that The displacement Δx of the plane reflector (6) is obtained based on the following formula:

2. The method for real-time measurement of nano-displacement based on laser polarization interferometry according to claim 1, characterized in that: The step 2 comprises the following steps: Step 2.1: Eliminate signal I y and signal I x The common term φ is obtained as follows: Step 2.2: Define the general formula of the ellipse equation x 2 +Bxy+Cy 2 +Dx+Ey+F=0, calculate the expression of error correction parameters h, k, a, b, σ, Parameters B, C, D, E, and F are obtained by solving the following linear equations: Among them, x i and i Signal I x and signal I y For the data corresponding to the i-th sampling time point, substitute the obtained parameters B, C, D, E, and F into the expressions of the error correction parameters h, k, a, b, and σ to obtain the measurement results of the error correction parameters h, k, a, b, and σ. According to the error correction parameters h, k, a, b, σ, the signal I x and signal I y After error correction, the corrected signal I x and signal I y Denoted as I′ x and I′ y .

3. The real-time measurement method of nano-displacement based on laser polarization interferometry according to claim 2 is characterized in that: The number of subdivisions S in step 3 N Obtained by the following steps: According to the error-corrected signal I′ x and I′ y Generate a Lissajous circle, subdivide the Lissajous circle into N parts, and divide the four quadrants of the Lissajous figure into 8 intervals, namely the first interval Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 and Section 8 According to the error-corrected signal I′ x and I′ y The positive or negative value determines the quadrant m where the phase φ to be measured is located, m = 1, 2, 3, 4 are the quadrant values. If the phase φ to be measured is not in the first quadrant, the phase φ to be measured is converted to φ′ in the first quadrant, where Then, according to the error-corrected orthogonal signal I′ x and I′ y The absolute value of the value determines the interval of the quadrant where the phase φ to be measured is located: for the 1st to 8th interval, the subdivision number S N The calculation formula is NS N1 ,in 4. The method for real-time measurement of nano-displacement based on laser polarization interferometry according to claim 3 is characterized in that: The method also includes a step of determining the forward and reverse movement of the movable plane reflector (6): Assume that the Lissajous figure changes continuously for z intervals, z≤8. From the zth interval forward, the interval number of the next interval is subtracted from the interval number of the previous interval to obtain Δz. The forward and reverse movements of the movable plane reflector (6) are determined based on the following formula:

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