CN110701998A - Nonlinear error correction method for optical fiber Michelson interferometer - Google Patents

Nonlinear error correction method for optical fiber Michelson interferometer Download PDF

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CN110701998A
CN110701998A CN201911036469.XA CN201911036469A CN110701998A CN 110701998 A CN110701998 A CN 110701998A CN 201911036469 A CN201911036469 A CN 201911036469A CN 110701998 A CN110701998 A CN 110701998A
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optical fiber
michelson interferometer
nonlinear error
interference
light source
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胡鹏程
董祎嗣
杨睿韬
乐志涛
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/0207—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer
    • G01B9/02072—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer by calibration or testing of interferometer

Abstract

A nonlinear error correction method of an optical fiber Michelson interferometer belongs to the technical field of optical fiber interferometry; according to the invention, on the premise of not changing the positions of the first reflector and the second reflector, wavelength pre-scanning is carried out on the laser wavelength modulatable light source, and the optical path difference between the reference beam and the measuring beam of the interferometer is continuously changed by utilizing the continuous change of the output laser wavelength, so that the interference signal obtained by the detector generates at least one period of phase change, the pre-extraction of the characteristic parameters of the interference signal is realized, the nonlinear error correction is realized in the measuring process by utilizing the pre-extracted characteristic parameters, and the high-precision displacement measurement is carried out; the method realizes the pre-extraction of the characteristic parameters of the interference signals of the optical fiber Michelson interferometer, can effectively solve the problem of correcting nonlinear errors in interference measurement, particularly in micro-displacement measurement, and has obvious technical advantages in the field of precision measurement.

Description

Nonlinear error correction method for optical fiber Michelson interferometer
Technical Field
The invention belongs to the technical field of optical fiber interferometry, and mainly relates to a nonlinear error correction method of an optical fiber Michelson interferometer.
Background
With the rapid development of scientific research and the rapid improvement of industrial production level, the scientific research and industrial fields also put forward higher requirements on displacement measurement, and the minimum variation of displacement measurement is developing towards the nanometer magnitude direction. The optical fiber Michelson interferometer is an instrument for measuring high-precision displacement by utilizing a laser interference principle, and has the advantages of non-contact, high precision and the like. An optical fiber Michelson interferometer comprises a laser wavelength modulatable light source; the laser wavelength can modulate the light source to perform sine modulation of the wavelength; a fiber coupler that splits the wavelength-modulatable light source into a reference beam and a measurement beam; a first mirror capable of reflecting the reference beam; a second mirror capable of reflecting the measuring beam, the second mirror being generally fixed to the object to be measured and moving with the object to be measured; a photodetector capable of detecting an interference signal formed by interference of a reference beam reflected by said first mirror and a measurement beam reflected by said second mirror; and the signal processing unit is coupled with the photoelectric detector and is suitable for collecting the interference signal output by the photoelectric detector. Compared with other laser interferometers, the laser interferometer has the advantages of simple structure, easiness in circuit processing, low requirement on environment and the like, so that the laser interferometer is more widely applied to the field of displacement measurement. However, in practical applications, the existence of the nonlinear error has been a key problem for realizing high-precision measurement by the optical fiber michelson interferometer.
Fig. 1 is a typical light source modulation type optical fiber michelson interferometer structure, a sinusoidal signal generating device 1 generates a sinusoidal signal to a wavelength-tunable laser 2, and performs sinusoidal modulation on the wavelength of the laser output by the wavelength-tunable laser 2, and the laser emitted by the wavelength-tunable laser 2 is split into a reference beam and a measuring beam by an optical fiber coupler 3; wherein the reference beam is collimated by the first collimator 4, reflected by the first reflector 5, the measuring beam is collimated by the second collimator 6, reflected by the second reflector 7, the reference beam and the measuring beam return to the optical fiber coupler 3 in the original path to interfere, and are output by the other end of the optical fiber coupler 3 and are merged into the photoelectric detector 8, and the ideal form of the output signal of the photoelectric detector 8 is as follows:
Figure BDA0002250130450000011
signal is phasedThe generated carrier demodulation unit 9 obtains Um1And Um2A signal; ideally, Um1And Um2Can be expressed as:
Figure BDA0002250130450000012
Figure BDA0002250130450000013
wherein B is the AC amplitude of the interference signal, C is the sum of the phase modulation depths, J1(C) And J2(C) In order to be a function of the Bessel function,
Figure BDA0002250130450000014
and
Figure BDA0002250130450000015
is a frequency-doubled and frequency-doubled carrier, and is expressed in the form of:
ideally, the amplitude of the phase carrier is adjusted so that J1(C)＝J2(C) Setting the carrier fundamental frequency signal and the frequency multiplication signal in the multiplier to have the same amplitude, i.e. K1＝K2，
Figure BDA0002250130450000023
Is the phase difference between the reference and measurement optical paths. It can be seen that Um1And Um2Appear to relate to
Figure BDA0002250130450000024
The sine and cosine functions of (1) are equal in amplitude and zero in direct current bias and are orthogonal to each other under an ideal state. However, in practical cases, light is emitted due to carrier phase delayStrong concomitant modulation cause to Um1And Um2Can be expressed as: (Kai Wang, Min Zhang, Fajie Duan, Shangan Xie, and Yanbiao Liao, "measurement of the phase shift between interactions and frequency modulations with in DFB-LDand its interactions on PGC modulation in a fiber-optical sensor system," applied. Opt,52(29),7194, 7199(2013).)
Figure BDA0002250130450000025
Figure BDA0002250130450000026
Where m is the light intensity modulation factor, P1、P2、θ1And theta2The expression is as follows:
Figure BDA0002250130450000027
Figure BDA0002250130450000028
Figure BDA0002250130450000029
Figure BDA00022501304500000210
the above formula can be simplified into:
Figure BDA00022501304500000211
Figure BDA00022501304500000212
wherein A isx、AyRespectively, a DC offset error, Bx、ByAre respectively unequal errorThe difference, δ, is the non-quadrature error. As can be seen from the formula, Um1And Um2Which in practice appears as a sine-cosine function containing the three differences mentioned above. When the two paths of interference signals containing the three differences are directly used for displacement calculation, periodic nonlinear errors can be generated, and the measurement precision is influenced. Therefore, the characteristic parameter A of the interference signal must be obtainedx、Ay、Bx、ByAnd delta to Um1And Um2And correcting to obtain an ideal orthogonal interference signal, thereby realizing nonlinear error correction.
A nonlinear error correction method is firstly proposed by Heydemann in 1981, and the method utilizes a least square method to carry out ellipse fitting on interference signals with more than one period so as to obtain characteristic parameters of the interference signals and further realize the correction of the nonlinear error (P.L.M.Heydemann, Determination and correction of the quadrature segmentation errors in interferometers. opt.1981,20:3382 and 3384), the method is a classic method for correcting the nonlinear error, researchers propose various improved methods according to the method and can be called as a Heydemann correction method; dai of German Federal physical research institute extracts nonlinear error parameters in real time by detecting maximum values and minimum values in one period of each path of interference signals, so as to realize real-time correction of nonlinear errors (G. -L.Dai, F.Pohlenz, H. -U.Danzebrink, K.Hasche, G.Wilkening, Improving the performance of interference meters in metallic scanning probes, meass.Sci.Techniol.2004, 15: 444-. Although the above two methods realize the correction of the nonlinear error, the precondition that the method can work normally is as follows: the phase of the interference signal varies by no less than one period.
In order to achieve the above-mentioned precondition, it is necessary to make the phase of the interference signal vary by not less than one cycle (2 pi), that is, the optical path difference between the reference optical path and the measurement optical path varies by not less than the laser wavelength. In practice, the method usually adopted is to move the first mirror or the second mirror, and to change the optical path length of the measuring beam or the reference beam, so as to realize the phase change of the interference signal. Both of these approaches have certain drawbacks in practice. The method of moving the second mirror is generally to obtain an interference signal having a phase change larger than one cycle by controlling the movement of the object to be measured so that the second mirror generates a displacement larger than a half wavelength of the laser light. However, in actual circumstances, the displacement of the object to be measured that can move is smaller than the above-mentioned displacement, and even the object cannot move freely, so that the above-mentioned precondition cannot be satisfied. In contrast, the method of moving the first mirror is generally to add additional piezo-ceramic or other motion control element to drive the first mirror, which also generates a displacement larger than half the wavelength of the laser light, and the displacement is relatively controllable, so that the above-mentioned precondition can be usually satisfied. However, this method also has certain problems: the additional motion control elements increase the complexity of the system and control and inevitably affect the positional stability of the first mirror, thereby introducing measurement errors.
In 2015, Zhu et al proposed a method for nonlinear error correction using optical switches, which configured one optical switch on each of the reference and measurement optical paths, and by the combination of "on" and "off" of the two optical switches, could obtain some nonlinear error parameters in interference signals when the object to be measured is in a stationary state, (j.zhu, p.hu, j.tan, a modulation laser mapping of detection nanometer displacement acquisition by using optical filters. appl.opt.2015,54: 10196-. However, this method also has certain drawbacks: the method can only be matched with a specific single-frequency interferometer light path and is not suitable for the optical fiber Michelson interferometer, and the method can only obtain direct current offset errors and unequal amplitude error parameters in three differences of characteristic parameters of interference signals, but can not obtain non-orthogonal error parameters, so that the method has no universality.
Disclosure of Invention
Aiming at the problems of the nonlinear correction method, the invention provides and develops a nonlinear error correction method and a device of an optical fiber Michelson interferometer, the invention carries out wavelength prescan on the premise of not changing the positions of a first reflector and a second reflector by giving a laser wavelength modulatable light source, and the continuous change of output laser wavelength is utilized to enable the optical path difference between a reference beam and a measuring beam of the interferometer to generate continuous change, so that an interference signal obtained by a detector generates phase change of at least one period, the characteristic parameter of the interference signal is pre-extracted, and the aim of nonlinear error correction is realized in the measuring process by utilizing the pre-extracted characteristic parameter.
The purpose of the invention is realized by the following technical scheme:
1. the nonlinear error correction method of the optical fiber Michelson interferometer comprises the following steps:
a light source with a tunable laser wavelength;
an optical path structure, comprising: the laser beam splitting device is used for splitting laser emitted by the light source into a reference beam and a measuring beam, the first reflecting device is used for reflecting the reference beam, and the second reflecting device is used for reflecting the measuring beam;
a photodetector capable of detecting an interference signal formed by interference of a reference beam reflected by said first reflecting means and a measuring beam reflected by said second reflecting means;
characterized in that the method comprises:
the method comprises the following steps: turning on the optical fiber Michelson interferometer, continuously changing the output laser wavelength of the light source, and further changing the phase difference between the reference beam and the measuring beam, so that the phase difference generates at least one period of continuous change;
step two: extracting characteristic parameters of the interference signals;
step three: and correcting the nonlinear error in the displacement measurement process of the optical fiber Michelson interferometer by using the extracted characteristic parameters.
2. The method for correcting nonlinear error of the optical fiber Michelson interferometer according to claim 1, characterized in that: the beam splitting means may be: fiber coupler, non-polarizing beam splitter.
3. The method for correcting nonlinear error of the optical fiber Michelson interferometer according to claim 1, characterized in that: the first and second reflecting means may be: plane mirror, pyramid prism, Faraday rotator mirror.
The invention has the following characteristics and good effects:
compared with a Heydemann or extremum correction method, the method can perform wavelength prescan on the premise of not changing the positions of the first reflector and the second reflector by the wavelength-modulatable light source, and the optical path difference between the reference beam and the measuring beam of the interferometer generates continuous change by using the continuous change of the output laser wavelength, so that the interference signal obtained by the detector generates phase change of at least one period, thereby realizing the pre-extraction of the characteristic parameters of the interference signal, realizing the purpose of nonlinear error correction in the measuring process by using the pre-extracted characteristic parameters, and providing the measuring precision. Compared with the two methods, the technical scheme of the invention particularly solves the problem that the nonlinear error of the measured displacement smaller than the half wavelength of the laser cannot be effectively compensated, and improves the precision of displacement measurement. Compared with the method for correcting the nonlinear error by using the optical switch, the method does not need to increase the complexity of an optical path, only adds a signal generating device for wavelength prescan in the wavelength-tunable laser, and is suitable for the optical fiber Michelson interferometer.
Drawings
FIG. 1 is a schematic diagram of a typical light source modulation type optical fiber Michelson interferometer structure formed by an optical fiber coupler;
FIG. 2 is a schematic diagram of the general configuration of the present invention as applied to the exemplary light source-modulated fiber Michelson interferometer of FIG. 1;
FIG. 3 is a schematic diagram of a compact optical source modulation fiber Michelson interferometer constructed by non-polarizing beam splitters;
FIG. 4 is a schematic diagram of the overall configuration of the present invention as applied to the compact light source modulated fiber Michelson interferometer of FIG. 3;
description of part numbers in fig. 1: the device comprises a sinusoidal signal generating device 1, a laser wavelength modulatable light source 2, an optical fiber coupler 3, a first collimator 4, a second collimator 5, a first reflector 6, a second reflector 7, a photoelectric detector 8, a phase generation carrier demodulation unit 9 and an upper computer 10.
Part number in fig. 2 illustrates: the device comprises a sinusoidal signal generating device 11, a pre-scanning signal generating device 12, a laser wavelength modulatable light source 13, an optical fiber coupler 14, a first collimator 15, a second collimator 16, a first reflector 17, a second reflector 18, a photoelectric detector 19, a phase generation carrier demodulating unit 20, a nonlinear correcting unit 21 and an upper computer 22.
Part number in fig. 3 illustrates: the device comprises a sinusoidal signal generating device 1, a laser wavelength modulatable light source 2, an optical fiber circulator 3, a collimator 4, a non-polarizing spectroscope 5, a first reflector 6, a second reflector 7, a photoelectric detector 8, a phase generation carrier demodulation unit 9 and an upper computer 10.
Part number in fig. 4 illustrates: the device comprises a sinusoidal signal generating device 11, a pre-scanning signal generating device 12, a laser wavelength modulatable light source 13, a fiber circulator 14, a collimator 15, a non-polarizing beam splitter 16, a first reflector 17, a second reflector 18, a photodetector 19, a phase generation carrier demodulating unit 20, a nonlinear correcting unit 21 and an upper computer 22.
Detailed Description
Since the optical fiber michelson interferometer itself has different forms of optical path structures, the following description will be made in detail by taking a typical optical fiber michelson interferometer composed of an optical fiber coupler shown in fig. 2 as an example.
A laser wavelength pre-scanning-based nonlinear error correction device for a Michelson fiber interferometer comprises a sinusoidal signal generation device 11, a pre-scanning signal generation device 12, a laser wavelength modulatable light source 13, a fiber coupler 14, a first collimator 15, a second collimator 16, a first reflector 17, a second reflector 18, a photoelectric detector 19, a phase generation carrier demodulation unit 20, a nonlinear correction unit 21 and an upper computer 22; the output end of the sine signal generating device 11 is provided with a laser wavelength modulatable light source 13, the output end of the pre-scanning signal generating device 12 is provided with a laser wavelength modulatable light source 13, the output end of the wavelength modulatable single-frequency laser 13 is provided with an optical fiber coupler 14, the output end of the optical fiber coupler 14 is respectively provided with a first collimator 15 and a second collimator 16, the output end of the first collimator 15 is provided with a first reflecting mirror 17, the output end of the second collimator 16 is provided with a second reflecting mirror 18, the input end of the optical fiber coupler 14 is provided with a photoelectric detector 19, the output end of the photoelectric detector 19 is provided with a phase generation carrier demodulation unit 20, the output end of the phase generation carrier demodulation unit 20 is provided with a nonlinear correction unit 21, and the output end of the.
The following steps of the method are also illustrated, using as an example a typical fiber michelson interferometer constructed from a fiber coupler as shown in fig. 2:
(1) the method comprises the following steps that an optical fiber Michelson interferometer is turned on, a sine signal generating device generates sine waves to a laser wavelength modulatable light source, the output wavelength of the light source is subjected to sine modulation, the light source emits a laser beam, the laser beam firstly enters an optical fiber coupler, and then the laser beam is separated into a measuring beam and a reference beam through the optical fiber coupler; the reference beam passes through the collimator and then returns to the original path after being reflected by the reflector; meanwhile, the measuring beam irradiates a measured object (such as a plane reflector, a pyramid prism and the surface of the measured object) through a collimator, then is reflected and returns along the original path; the reference beam and the measuring beam return to the optical fiber coupler to interfere, the reference beam and the measuring beam are emitted by the optical fiber coupler and enter the photoelectric detector to be converted into electric signals, and the electric signals are input into the phase generation carrier unit to be processed to obtain two paths of interference signals U containing the three differencesm1And Um2；
(2) The pre-scanning signal generator is started to generate scanning signal to the wavelength-modulated single-frequency laser to make the laser output continuous scanning change, so that the variation of optical path difference between the reference optical path and the measuring optical path isTwo corresponding interference signals Um1And Um2The amount of phase change is also
Figure BDA0002250130450000052
Storing two paths of interference signals U in the change processm1And Um2(ii) a When in use
Figure BDA0002250130450000053
That is, when the variation of optical path difference is greater than laser wavelength lambda, two interference signals Um1And Um2The phase of (a) is changed by more than one period, and the Lissajous figure of the phase is a complete elliptical pattern;
(3) according to the two interference signals U stored in the step (2)m1And Um2Two interference signals U can be obtained by utilizing a three-difference parameter extraction method, such as an ellipse fitting method and an extreme value detection methodm1And Um2The three difference parameters of (2), i.e. the characteristic parameters of the interference signal: a. thex、Bx、Ay、ByAnd δ;
(4) keeping a signal given to a laser by a pre-scanning signal generating device unchanged in the displacement measurement process of the Michelson fiber interferometer, and using the characteristic parameters of the interference signal acquired in the step (3), performing the following operations:
Figure BDA0002250130450000061
the three differences in interference signals can be eliminated, and ideal orthogonal interference signals sin (phi) and cos (phi) can be obtained, so that the correction of nonlinear errors in the interference measurement process is realized, and the measurement accuracy is improved.

Claims (3)

1. The nonlinear error correction method of the optical fiber Michelson interferometer comprises the following steps:
a light source with a tunable laser wavelength;
an optical path structure, comprising: the laser beam splitting device is used for splitting laser emitted by the light source into a reference beam and a measuring beam, the first reflecting device is used for reflecting the reference beam, and the second reflecting device is used for reflecting the measuring beam;
a photodetector capable of detecting an interference signal formed by interference of a reference beam reflected by said first reflecting means and a measuring beam reflected by said second reflecting means;
characterized in that the method comprises:
the method comprises the following steps: turning on the optical fiber Michelson interferometer, continuously changing the output laser wavelength of the light source, and further changing the phase difference between the reference beam and the measuring beam, so that the phase difference generates at least one period of continuous change;
step two: extracting characteristic parameters of the interference signals;
step three: and correcting the nonlinear error in the displacement measurement process of the optical fiber Michelson interferometer by using the extracted characteristic parameters.
2. The method for correcting nonlinear error of the optical fiber Michelson interferometer according to claim 1, characterized in that: the beam splitting means may be: fiber coupler, non-polarizing beam splitter.
3. The method for correcting nonlinear error of the optical fiber Michelson interferometer according to claim 1, characterized in that: the first and second reflecting means may be: plane mirror, pyramid prism, Faraday rotator mirror.
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