CN109974576A - Nonlinear error correction method and device for single-frequency laser interferometer - Google Patents

Abstract

Single frequency laser interferometer nonlinearity erron modification method and device belong to laser measuring technique field；The present invention can be under the premise of having no need to change the first reflecting mirror and the second reflector position, continuous optical path difference variation is generated between measuring beam and reference beam using spiral phase plate, so that interference signal generates enough phase changes, realize the preextraction to interference signal characteristic parameter, to be modified using the characteristic parameter of preextraction to the nonlinearity erron during single frequency laser interferometer displacement measurement, high precision position shift measurement is realized；The amendment problem that the present invention realizes the preextraction to single frequency laser interferometer interference signal characteristic parameter, can effectively solve the problem that nonlinearity erron in interferometry especially micro-displacement measurement has significant technical advantage in field of precision measurement.

Description

Single-frequency laser interferometer nonlinear error correction method and device

technical field

The invention belongs to the technical field of laser measurement, and mainly relates to a nonlinear error correction method and device of a single-frequency laser interferometer.

Background technique

With the rapid development of scientific research and the rapid improvement of industrial production levels, scientific research and industrial fields have also put forward higher requirements for displacement measurement, and the minimum change of displacement measurement is also developing towards the nanometer level. Single-frequency laser interferometry is an instrument for high-precision displacement measurement using the principle of laser interferometry. It has the advantages of non-contact and high precision. A single-frequency laser interferometer includes at least one light source capable of providing a single-frequency laser; a beam splitter that divides the single-frequency light source into a reference beam and a measurement beam; a first reflector that can reflect the reference beam; a mirror that can reflect the measurement beam The second reflector, the second reflector is usually fixed on the object to be measured, and moves together with the object to be measured; at least one photodetector capable of detecting interference signals, and the interference signals pass through the first reflector The reflected reference beam is formed by interference with the measurement beam reflected by the second mirror; and a signal processing unit, coupled to the photodetector, is adapted to collect the interference signal output by the photodetector; the reference The light beam and the measurement beam have the same frequency. Compared with the dual-frequency laser interferometer, it is more widely used in the field of displacement measurement due to its simple structure, easy circuit processing, lower environmental requirements, and unlimited measurement speed in principle. However, in practical applications, the existence of nonlinear errors has always been a key problem that limits the high-precision measurement of single-frequency laser interferometers.

Figure 1 shows a typical single-frequency laser interferometer structure. The single-frequency laser emitted from laser 1 is split into a reference beam and a measurement beam by a polarization beam splitter 2; the reflected beam is reflected by a plane mirror A 4 as a reference beam, and is reflected twice After passing through the 1/4 wave plate A3, the transmitted beam is reflected by the plane mirror B6 as the measuring beam, and after passing through the 1/4 wave plate B5 twice, the reference beam and the measuring beam are respectively transmitted and reflected through the polarization beam splitter prism 2; After the light beam and the measurement beam pass through the 1/2 wave plate 7, their polarization direction is rotated by 45°, after being split by the non-polarizing beam splitter 8, the transmitted light is incident on the photodetector A through the 1/4 wave plate C 9 and the polarizing beam splitting prism B 10 11 and photodetector B 12, the two-way signal obtains the interference signal _Ix after subtraction operation through operator A 13; the reflected light through non-polarization beam splitter prism 8 is incident on photodetector C 15 and photoelectricity through polarization beam splitter C 14 Detector D 16, the two signals are subtracted by the arithmetic unit B 17 to obtain the interference signal I _y . Ideally, I _x and I _y can be expressed as: (P.Hu, J.Zhu, X.Guo, and J.Tan,"Compensation for the Variable Cyclic Error in Homodyne Laser Interferometers,"Sensors,2015,15(2 ):3090-3106.):

Among them, A is the AC amplitude of the interference signal, and φ is the phase difference between the reference beam and the measurement beam. It can be seen from this that I _x and I _y are sine and cosine functions with respect to φ, and in an ideal state, their amplitudes are equal, the DC offset is zero, and they are orthogonal to each other. However, in practice, due to the imperfections of optical devices, I _x and I _y can be expressed as:

Among them, A _x and A _y are the DC bias errors respectively, B _x and _By are the unequal amplitude errors, respectively, and δ is the non-orthogonal error. It can be seen from formula (2) that I _x and I _y actually represent the sine and cosine functions containing the above three differences. When the above-mentioned two interference signals with three differences are directly used for displacement calculation, periodic nonlinear errors will be generated, which will affect the measurement accuracy. Therefore, it is _necessary to correct I _x and I _y by obtaining the characteristic parameters A _x , A _y , B _x , By and δ of the interference signal to obtain ideal orthogonal interference signals cosφ and sinφ, thereby realizing the correction of nonlinear errors.

The correction method of nonlinear error was first proposed by Heydemann in 1981. He used the least square method to perform ellipse fitting on the interference signal greater than one period, so as to obtain the characteristic parameters of the interference signal, so as to realize the correction of nonlinear error (P.L.M. Heydemann,Determination and correction of quadrature fringemeasurement errors in interferometers.Appl.Opt.1981,20:3382-3384), this method is a classic method of nonlinear error correction, researchers have proposed a variety of improved methods based on this method, all of which can be It is called the Heydemann correction method; Dai of the German Federal Institute of Physics detects the maximum value and minimum value of each interference signal within one cycle, extracts the nonlinear error parameters in real time, and realizes the real-time correction of the nonlinear error (G .-L. Dai, F. Pohlenz, H.-U. Danzebrink, K. Hasche, G. Wilkening, Improving the performance of interferometers in metrological scanning probe microscopes. Meas. Sci. Technol. 2004, 15:444-450), It is called the extremum correction method. Although the above two methods can correct the nonlinear error, the prerequisite for their normal operation is that the phase change of the interference signal is not less than one cycle.

In order to realize the above preconditions, it is necessary to make the phase of the interference signal change not less than one cycle (2π), that is, the change of the optical path difference between the reference beam and the measuring beam is not less than the laser wavelength. The method usually adopted in practice is to move the second reflector or the first reflector, and realize the phase change of the interference signal by changing the optical path of the measuring beam or the reference beam. However, these two methods have certain defects in practice. The method of moving the second mirror is generally to control the movement of the measured object so that the second mirror produces a displacement greater than half the wavelength of the laser, so as to obtain the interference signal with a phase change greater than one period. However, in actual situations, sometimes the displacement that the measured object can move is smaller than the above-mentioned displacement and even cannot move freely, so the above precondition cannot be satisfied. In contrast, the method of moving the first reflector is generally to drive the first reflector by adding additional piezoelectric ceramics or other motion control elements, and also make it produce a displacement greater than half the wavelength of the laser, because the displacement is relatively controllable , so the above preconditions can usually be satisfied. However, this method also has certain problems: additional motion control components increase the complexity of the system and control, and inevitably affect the position stability of the first mirror, thereby introducing measurement errors.

In 2015, Zhu et al. proposed a method for nonlinear error correction using an optical switch. This method configures an optical switch in each of the reference and measurement beams. Part of the nonlinear error parameters in the interference signal obtained when the object is at rest, (J.Zhu,P.Hu,J.Tan,Homodyne laservibrometer capable of detecting nanometer displacements accurately by usingoptical shutters.Appl.Opt.2015,54:10196 –10199). The method cooperates with a specific optical path, and can realize the correction of nonlinear errors in the measurement whose displacement is less than λ/2. However, this method also has certain defects: first, this method can only obtain the DC bias error and unequal amplitude error parameters in the three differences of the characteristic parameters of the interference signal, but cannot obtain the non-orthogonal error parameters, so it needs to The measurement can only be performed with a specific interference optical path structure, which is not universal; secondly, this method requires two optical switches, which leads to an increase in the size of the device, and requires multiple operations on the two optical switches, and the steps are complicated.

SUMMARY OF THE INVENTION

In view of the problems existing in the above nonlinear correction method, the present invention proposes and develops a method and device for nonlinear error correction of a single-frequency laser interferometer based on a spiral phase plate. The present invention does not need to change the first reflection mirror and the second reflection On the premise of the position of the mirror, a spiral phase plate is added to the position of the reference beam of the single-frequency laser interferometer or the common optical path of the measurement beam, and the phase delay characteristic of the spiral phase plate is used to make the optical path difference between the reference beam and the measurement beam of the interferometer. A continuous change is generated, so that the interference signal obtained by the detector produces sufficient phase change, and the pre-extraction of the characteristic parameters of the interference signal is realized, and the purpose of nonlinear error correction is realized in the measurement process by using the pre-extracted characteristic parameters.

The object of the present invention is achieved through the following technical solutions:

A single-frequency laser interferometer nonlinear error correction method, the single-frequency laser interferometer includes: at least one light source capable of providing a single-frequency laser; an optical path, the optical path includes: a beam splitter, a first reflector and a second reflector mirror, wherein the beam splitter is adapted to split the single-frequency light source into a reference beam and a measurement beam, the first reflector is adapted to reflect the reference beam, and the second reflector is adapted to reflect the measurement light beam; at least one photodetector capable of detecting an interference signal, the interference signal is formed by the interference of the reference beam reflected by the first mirror and the measurement beam reflected by the second mirror.

The helical phase plate is a phase retardation element composed of a helical structure, and the phase retardation of the incident beam at each position along its circumferential direction changes linearly and regularly. Therefore, by adding at least one helical phase plate in the optical path of the single-frequency laser interferometer, the helical phase plate is suitable for changing the phase difference between the reference beam and the measurement beam; by rotating at least one of the at least one The spiral phase plate, changes the position of the reference beam and/or the measurement beam incident on the spiral phase plate, so that the phase difference between the reference beam and the measurement beam produces a continuous change; the corresponding interference signal produces a corresponding In the process of single-frequency laser interferometer displacement measurement, the nonlinear error correction of the measured displacement can be realized by using the pre-extracted nonlinear error parameters. During this process, the positions of the reference beam and the measurement beam incident on the helical phase plate should remain unchanged.

The position of the spiral phase plate is selected from between the beam splitter and the first reflector and between the beam splitter and the second reflector.

The position where the reference beam or measuring beam is incident on the spiral phase plate deviates from the center of the spiral phase plate, that is, the reference beam or measuring beam will not coincide with the center of the spiral phase plate, and the center of the spiral phase plate The diameter is at least twice the diameter of the measurement beam or reference beam incident on the helical phase plate, so that the phase delay of the helical phase plate to each point within the diameter of the reference beam or measurement beam at a certain moment is approximately equal, the approximation The effect meets the requirements of those skilled in the art.

A single-frequency laser interferometer nonlinear error correction device, the device includes at least one light source capable of providing single-frequency laser light; an optical path, the optical path includes: a beam splitter, a first reflection mirror and a second reflection mirror, wherein, The beam splitter is adapted to divide the single-frequency light source into a reference beam and a measurement beam, the first reflection mirror is adapted to reflect the reference beam, and the second reflection mirror is adapted to reflect the measurement beam; at least one a photodetector capable of detecting an interference signal, the interference signal is formed by the interference of a reference beam reflected by the first mirror and a measurement beam reflected by the second mirror; and at least one helical phase plate, each One of the helical phase plates is placed in the optical path, the helical phase plate is adapted to vary the phase difference between the reference beam and the measurement beam. The device further includes: a signal processing unit, coupled to the photodetector, adapted to collect an interference signal output by the photodetector, and the characteristic parameter of the interference signal indicates that the single-frequency laser interferometer is in the displacement measurement process. nonlinear error.

The position of the spiral phase plate is selected from between the beam splitter and the first reflector and between the beam splitter and the second reflector.

The position where the reference beam or the measuring beam is incident on the helical phase plate deviates from the center of the helical phase plate, that is, the reference beam or the measuring beam does not coincide with the center of the helical phase plate, and the The diameter is at least twice the diameter of the measuring beam or the reference beam incident on the helical phase plate, so that the phase delays of the helical phase plate to each point in the reference beam or the measuring beam diameter at a certain moment are approximately equal. The effect meets the requirements of those skilled in the art.

The present invention has following characteristics and good effect:

(1) Compared with the Heydemann or extremum correction method, this method can use the spiral phase plate to generate a continuous flow between the measurement beam and the reference beam without changing the positions of the first and second mirrors. The change of the optical path difference can realize the pre-extraction of the characteristic parameters of the interference signal, so as to correct the nonlinear error in the interferometric measurement process, and realize the high-precision displacement measurement. Compared with the above two methods, the present invention especially solves the problem that the nonlinear error cannot be effectively compensated when the measured displacement is less than the half wavelength of the laser, and improves the measurement accuracy.

(2) Compared with the method of using an optical switch for nonlinear error correction, only one optical element with a small volume is used, which replaces two optical switches with complex mechanical structures, reducing the system volume and complexity, and The operation steps are simplified; since all the characteristic parameters of the interference signal can be extracted without depending on the specific interference optical path structure, the correction accuracy of the nonlinear error is improved, and the applicability of the correction method is improved.

Description of drawings

Fig. 1 is the configuration structure schematic diagram of the two-division optical path single-frequency laser interferometer composed of the existing polarization beam splitting prism and plane reflector;

Fig. 2 is a schematic diagram of the overall configuration when the present invention is applied to the single-frequency laser interferometer in Fig. 1 as an example;

Fig. 3 is a schematic diagram of the relative position of the spiral phase plate and the beam of the present invention;

Part number description in Figure 1: 1 single-frequency laser, 2 polarization beam splitter prism A, 3 1/4 wave plate A, 4 first reflector, 5 1/4 wave plate B, 6 second reflector, 7 1/2 Wave plate, 8 beam splitters, 9 1/4 wave plate C, 10 polarization beam splitter B, 11 photodetector A, 12 photodetector B, 13 subtractor A, 14 polarization beam splitter C, 15 photodetector C, 16 photodetector D, 17 subtractor B, 18 signal processing unit.

Part number description in Figure 2: 21 single-frequency laser, 22 polarization beam splitter prism A, 23 spiral phase plate, 24 rotation axis, 251/4 wave plate A, 26 first mirror, 27 1/4 wave plate B, 28th Two mirrors, 29 1/2 wave plate, 30 non-polarizing beam splitter, 311/4 wave plate C, 32 polarizing beam splitting prism B, 33 photodetector A, 34 photodetector B, 35 subtractor A, 36 polarizing beam splitter Prism C, 37 photodetector C, 38 photodetector D, 39 subtractor B, 40 signal processing unit, 41 position A.

Part number description in Figure 3: 23 helical phase plates, 42 beam positions.

Detailed ways

Since the single-frequency laser interferometer itself has different forms of optical path structures, the embodiment of the present invention will be described in detail below by taking the two-subdivided optical path single-frequency interferometer composed of the polarization beam splitter prism and the plane reflector shown in Figure 2 as an example. .

A single-frequency laser interferometer nonlinear error correction device based on a spiral phase plate, the device includes a single-frequency laser 21, a polarization beam splitting prism A 22, a spiral phase plate 23, a quarter wave plate A 25, a first reflector 26 , 1/4 wave plate B 27, second mirror 28, 1/2 wave plate 29, non-polarized beam splitter prism 30, 1/4 wave plate C 31, polarized beam splitter prism B 32, photodetector A 33, photodetection B 34, subtractor A 35, polarization beam splitter prism C 36, photodetector C 37, photodetector D38, subtractor B 39; on the outgoing optical path of the single-frequency laser 21, the polarization beam splitter prism A 22, 1/ 4 wave plates B 27 and the second reflecting mirror 28, the 1/4 wave plate B 27 is located in the x, y plane, and is coaxial with the polarizing beam splitter prism A 22, and the fast axis direction of the 1/4 wave plate B 27 is the same as the y The axis is 45° counterclockwise, and the second reflecting mirror 28 is parallel to the 1/4 wave plate B 27; the 1/4 wave plate A 25 and the first reflecting mirror 26 are sequentially arranged on the reflected light path of the polarizing beam splitter prism A 22, The 1/4 wave plate A 25 is located in the y and z planes, and is coaxial with the polarizing beam splitter prism A 22, and the direction of the fast axis of the 1/4 wave plate A 25 is 45° clockwise from the y axis, and the first reflection The mirror 26 is parallel to the 1/4 wave plate A 25; the 1/2 wave plate 29, the non-polarized beam splitting prism 30, and the 1/4 wave are sequentially arranged on the opposite side of the polarizing beam splitting prism A 22 on the opposite side of the first reflecting mirror 26 Plate C 31, polarization beam splitter prism B 32, photodetector A 33, the 1/2 wave plate 29 is located in the y, z plane, and is coaxial with the polarization beam splitter prism A 22, and the 1/2 wave plate 29 is in the fast axis direction It is 22.5° counterclockwise with the z-axis, the 1/4 wave plate C 31 is located in the y and z planes, and is coaxial with the polarizing beam splitter prism A 22, and the fast axis direction of the 1/4 wave plate C 31 is counterclockwise with the z-axis A photodetector B 34 is arranged on the reflected light path of the polarizing beam splitting prism B 32; a polarizing beam splitting prism C 36 and a photodetector C 37 are sequentially arranged on the reflected light path of the non-polarizing beam splitting prism 30; A photodetector D 38 is configured on the reflected light path of the polarizing beam splitting prism C 36; the interference signals detected by the photo detector A 33 and the photo detector B 34 are input to the subtractor A 35 for subtraction to obtain the interference signal I _x ; The interference signal detected by the photodetector C37 and the photodetector D 38 is input to the subtractor B39 for subtraction to obtain the interference signal _Iy ; it is configured between the polarizing beam splitter prism A 22 and the 1/4 wave plate A 25 The spiral phase plate 23, the spiral phase plate 23 is located in the y and z planes, and its rotation axis 24 is located in the center of the spiral phase plate 23 and has a certain distance from the optical axis; the spiral phase plate 23 can also be arranged at the position A 41. , that is, the polarizing beam splitter prism A 22 and the 1/4 wave plate are arranged in parallel and coaxially with the 1/4 wave plate B 27 Between B 27.

The following also takes the two-subdivided optical path single-frequency interferometer composed of the polarization beam splitter prism and the plane reflector shown in Figure 2 as an example, and the steps of the method are described as follows:

(1) Turn on the single-frequency laser interferometric vibrometer, and the single-frequency laser emits a single-frequency laser beam, which is first vertically incident through the helical phase plate, and then the horizontal and vertical polarization components in the laser are separated into measurement beams by a polarization beam splitter prism and the reference beam; the reference beam passes through the 1/4 wave plate, and then returns to the original path after being reflected by the mirror; at the same time, after the measurement beam passes through the 1/4 wave plate, it is irradiated to the object to be measured (such as flat mirror, corner prism, The surface of the measured object) is reflected and returned along the original path; both the reference beam and the measurement beam pass through the 1/4 wave plate twice, and the polarization state is rotated by 90° and then enters the polarization beam splitter prism again; because the reference beam passes through the helical phase twice successively board, thus introducing a size of The phase change of the beam splitting prism; the reference beam and the measuring beam of orthogonal horizontal and vertical polarization states emitted from the polarizing beam splitter prism pass through the beam splitter prism and other devices, and finally pass through the detector and the subtractor to obtain two paths as shown in formula (2). Interference signals I _x and I _y containing three differences;

(2) When the spiral phase plate is rotated around its center, the position of the reference beam incident on the spiral phase plate also changes accordingly. According to the working characteristics of the spiral phase plate, the phase delay of the spiral phase plate to the reference beam also varies with the reason change to The amount of change is At this time, the phase of the measurement beam does not change; therefore, in this process, the variation of the optical path difference between the reference beam and the measurement beam is The corresponding phase changes of the two interference signals I _x and I _y are also Store the two-way interference signals I _x and I _y in the changing process; when That is, when the variation of the optical path difference is greater than the laser wavelength λ, the phase variation of the two interference signals I _x and I _y exceeds one period, and the Lissajous figure is a complete elliptical pattern;

(3) According to the two-way interference signals I _x and I _y stored in step (2), and using three-difference parameter extraction methods, such as ellipse fitting method and extremum detection method, two-way interference signals I _x and I _y can be obtained The triple difference parameters of , that is, the characteristic parameters of the interference signal: A _x , B _x , A _y , B _y and δ;

(4) During the displacement measurement of the single-frequency laser interferometer, keep the position of the reference beam incident on the helical phase plate unchanged, and use the characteristic parameters of the interference signal obtained in step (3) to perform the following operations:

The triple difference in the interference signal can be eliminated, that is, the ideal orthogonal interference signal sin(φ) and cos(φ) can be obtained, so as to realize the correction of the nonlinear error in the interferometric measurement process and improve the measurement accuracy.

Claims (10)

1. a kind of single frequency laser interferometer nonlinearity erron modification method, include in single frequency laser interferometer:

At least one is capable of providing the light source of single-frequency laser；

Optical path includes: spectroscope, the first reflecting mirror and the second reflecting mirror in the optical path, wherein the spectroscope is suitable for institute It states monochromatic sources and is divided into reference beam and measuring beam, first reflecting mirror is suitable for reflecting the reference beam, and described second Reflecting mirror is suitable for reflecting the measuring beam；

At least one is able to detect the photodetector of interference signal, and the interference signal is reflected by first reflecting mirror Measuring beam that obtained reference beam and second reflecting mirror reflect, which is interfered, to be formed；

It is characterized in that, which comprises

Step 1: at least one spiral phase plate is placed in the optical path of single frequency laser interferometer, and the spiral phase plate is suitable Phase difference between the change reference beam and the measuring beam；

Step 2: by rotating at least one described spiral phase plate at least once, so that the reference beam and measuring beam Between phase difference generate continuous variation；

Step 3: the characteristic parameter of the interference signal is extracted；

Step 4: utilizing extracted characteristic parameter, to the nonlinearity erron during single frequency laser interferometer displacement measurement It is modified.

2. single frequency laser interferometer nonlinearity erron modification method according to claim 1, it is characterised in that: the step In one implementation process, the position of the spiral phase plate is selected between the spectroscope and the first reflecting mirror and the light splitting Between mirror and the second reflecting mirror.

3. single frequency laser interferometer nonlinearity erron modification method according to claim 1, it is characterised in that: the step In one implementation process, spiral phase plate is deviateed in the position that the reference beam or measuring beam are incident on the spiral phase plate Center.

4. single frequency laser interferometer nonlinearity erron modification method according to claim 1, it is characterised in that: the step In four implementation process, the reference beam and measuring beam should be made to be incident on the position on the spiral phase plate and kept not Become.

5. single frequency laser interferometer nonlinearity erron modification method according to claim 1, it is characterised in that: the spiral The diameter of phase-plate is at least two times of the measuring beam or reference beam diameter that are incident on the spiral phase plate.

6. a kind of single frequency laser interferometer nonlinearity erron correcting device, include in the device:

At least one is capable of providing the light source of single-frequency laser；

Optical path includes: spectroscope, the first reflecting mirror and the second reflecting mirror in the optical path, wherein the spectroscope is suitable for institute It states monochromatic sources and is divided into reference beam and measuring beam, first reflecting mirror is suitable for reflecting the reference beam, and described second Reflecting mirror is suitable for reflecting the measuring beam；

At least one is able to detect the photodetector of interference signal, and the interference signal is reflected by first reflecting mirror Measuring beam that obtained reference beam and second reflecting mirror reflect, which is interfered, to be formed；

It is characterized by: the device also includes at least one spiral phase plate, each described spiral phase plate is placed in described In optical path, the spiral phase plate is suitable for changing the phase difference between the reference beam and the measuring beam.

7. single frequency laser interferometer nonlinearity erron correcting device according to claim 6, it is characterised in that: described device Further include: signal processing unit couples the photodetector, suitable for acquiring the interference signal of the photodetector output, The characteristic parameter of the interference signal indicates the nonlinearity erron during the single frequency laser interferometer displacement measurement.

8. single frequency laser interferometer nonlinearity erron correcting device according to claim 6, it is characterised in that: the spiral The position of phase-plate is selected between the spectroscope and the first reflecting mirror and between the spectroscope and the second reflecting mirror.

9. single frequency laser interferometer nonlinearity erron correcting device according to claim 6, it is characterised in that: the reference Deviate the center of spiral phase plate in the position that light beam or measuring beam are incident on the spiral phase plate.

10. single frequency laser interferometer nonlinearity erron correcting device according to claim 6, it is characterised in that: the spiral shell The diameter of rotation phase-plate is at least two times of the measuring beam or reference beam diameter that are incident on the spiral phase plate.