CN113690719A - High-precision piston phase closed-loop control method and system - Google Patents

High-precision piston phase closed-loop control method and system Download PDF

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CN113690719A
CN113690719A CN202110947761.8A CN202110947761A CN113690719A CN 113690719 A CN113690719 A CN 113690719A CN 202110947761 A CN202110947761 A CN 202110947761A CN 113690719 A CN113690719 A CN 113690719A
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interference fringe
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CN113690719B (en
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马鹏飞
常琦
侯天悦
常洪祥
张雨秋
龙金虎
邓宇
粟荣涛
吴坚
李�灿
姜曼
马阎星
周朴
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National University of Defense Technology
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Abstract

The high-precision piston phase closed-loop control method and the system thereof comprise the steps of obtaining an interference fringe sub-image of each unit light beam in a laser array, carrying out two-dimensional Fourier transform on the interference fringe sub-image of each unit light beam, obtaining two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit light beam; in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array is found through a mode function, an amplitude value corresponding to the frequency spectrum parameter is found through an amplitude function, the amplitude value is a piston phase noise value of each unit light beam and is used for compensating the piston phase of each unit light beam, smaller phase-locked residual errors can be achieved, the synthesis efficiency of coherent synthesis is improved, and the brightness of synthesized laser is further improved.

Description

High-precision piston phase closed-loop control method and system
Technical Field
The invention relates to the technical field of strong laser, in particular to a high-precision piston phase closed-loop control method and system in a fiber laser coherent synthesis system.
Background
The optical fiber laser has the advantages of good beam quality, convenient thermal management and the like due to the strict optical field constraint of a compact waveguide structure, and has wide application in the fields of industrial processing, scientific research and the like in recent years. However, the single-path fiber laser is bound in the extremely small cross section of the fiber core, and the increase of the power density can more easily excite the phenomena of nonlinear effect, unstable mode and the like, so that the further improvement of the power of the fiber laser is restricted on the premise of keeping the beam quality. The laser coherent array adopting Master Oscillator Power Amplifier (MOPA) can expand the number of fiber laser arrays, reduce the Power density requirement of single-path laser, and disperse heat to different links, thereby breaking through the output Power limitation of the single-path laser, obtaining laser output with higher Power and higher brightness, and being a typical scheme for realizing a high-energy laser system.
However, if only the simple power superposition of the fiber laser array is performed, only the power superposition of the fiber laser array can be realized, and different fibers introduce different phase noises, so that the light spot form presents the light field distribution of a "similar high-order mode", and the brightness of the output laser cannot be ensured. In order to effectively realize the improvement of brightness, phase control must be performed on each path of fiber laser to compensate for phase noise between the paths, so that the paths of fiber laser are coherently superposed on a target plane.
For piston phase control, according to different control methods and different control logics, an indirect control method for realizing closed-loop control based on indirect measurement of phase noise amplitude and a direct control method for compensating based on direct measurement of phase noise amplitude value can be divided. The indirect control method is developed mainly based on an optimization algorithm, and is typically represented by a random parallel gradient descent algorithm and the like, however, the method has the problem of controlling bandwidth descent along with the expansion of the number of laser array elements. The direct control method can directly obtain a piston phase error value of each path of laser, and perform closed-loop control according to the calculated piston phase value of each path of laser, typically represented by an interference fringe extraction method, a dithering method and the like based on linear intensity signal calculation. For the dithering method, along with the expansion of the array elements, the time domain and frequency domain expansion of the dithering method is limited, thereby influencing the expansion of the number of synthesis paths. For the interference fringe extraction method based on linear intensity signal calculation, the fringe extreme value coordinates are calculated by relying on the linear intensity signals of the interference fringes. The accuracy of the calculation result of the method is severely limited by the sampling resolution of the interference fringe of each unit light beam, so that in a large array element synthesis system, the imaging area of each unit light beam is limited, the error between the calculation result and the piston phase noise is large, the piston phase noise cannot be strictly counteracted when the piston phase value obtained by the calculation of the interference fringe is corrected by a closed-loop phase control circuit, and the expansion of the synthesis path number and the reduction of the efficiency are finally influenced.
Disclosure of Invention
In order to improve the difficulty of accuracy of calculating the piston phase error through interference fringes, the invention provides a high-precision piston phase closed-loop control method and a high-precision piston phase closed-loop control system, which utilize all data of a two-dimensional image to carry out combined calculation to obtain accurate phase information, solve the problem of insufficient calculation precision caused by insufficient sampling rate when the traditional method only adopts linear intensity signal one-dimensional data operation, and realize high-precision piston phase closed-loop control in a large array element coherent synthesis system.
In order to achieve the technical purpose, the invention adopts the following specific technical scheme:
the high-precision piston phase closed-loop control method comprises the following steps:
dividing seed laser into two parts, inputting one part into a laser array coherent synthesis unit for generating a laser array, and taking the other part as a reference beam;
acquiring an included angle between the optical axis of the reference beam and the optical axis of the laser array;
collecting a part of laser arrays generated by a laser array coherent synthesis unit, carrying out beam shrinking on the laser arrays, and detecting interference fringe images of the shrunk laser arrays and reference beams by using a high-speed camera;
dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array;
performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam;
in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, and finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is a piston phase noise value of each unit light beam;
and converting the piston phase noise value of each unit light beam into a voltage value of each unit light beam at two ends of the corresponding phase modulator in the laser array coherent combination unit, applying corresponding voltage to the corresponding phase modulator, and performing closed-loop control on the piston phase of each unit light beam in the laser array.
Further, the two-dimensional spectral information distribution of the interference fringe sub-image of each unit beam is as follows:
Figure BDA0003217334010000031
in the formula, (x, y) is the position coordinate of the pixel point in the interference fringe subimage, (u, v) is the frequency spectrum coordinate of the pixel point in the image obtained after the two-dimensional Fourier transform of the interference fringe subimage, and fi(x, y) represents the distribution relation of the interference light spot light intensity signal of the ith unit light beam along with the position, Fi(u, v) represents a spectrum distribution function after two-dimensional Fourier transform is carried out on the light intensity signal of the interference light spot of the ith unit light beam, e represents a natural constant, and j represents an imaginary number unit;
and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam as follows:
Figure BDA0003217334010000041
where, | | is a modulus function in complex operations, and arg () is an argument function in complex operations.
Further, the voltage value of each unit beam at two ends of the corresponding phase modulator in the laser array coherent combining unit is:
Figure BDA0003217334010000042
wherein the content of the first and second substances,
Figure BDA0003217334010000043
taking the value of piston phase noise of the ith unit beam, VπIs half-wave power of a phase modulatorAnd (6) pressing.
Further, the invention provides a method for calculating the position coordinate of the maximum value of the interference fringe with high precision, which is different from a method for calculating the extreme value coordinate of the fringe in the prior art, and comprises the following steps:
dividing seed laser into two parts, inputting one part into a laser array coherent synthesis unit for generating a laser array, and taking the other part as a reference beam;
acquiring an included angle between the optical axis of the reference beam and the optical axis of the laser array;
collecting a part of laser arrays generated by a laser array coherent synthesis unit, carrying out beam shrinking on the laser arrays, and detecting interference fringe images of the shrunk laser arrays and reference beams by using a high-speed camera;
dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array;
performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam;
in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is also a piston phase noise value of each unit light beam;
calculating the fringe interval of the interference fringe pattern according to the included angle between the optical axis of the reference beam and the optical axis of the laser array and the central wavelength of the seed laser;
and according to the ratio of the amplitude value to 2 pi, combining the fringe intervals of the interference fringe patterns to obtain the position coordinates of the maximum value of the interference fringes in each interference fringe sub-image.
Further, the fringe spacing of the interference fringe pattern of the present invention is:
Figure BDA0003217334010000051
wherein d represents the fringe spacing of the interference fringe pattern, theta represents the included angle between the optical axis of the reference beam and the optical axis of the laser array, and lambda represents the central wavelength of the seed laser.
Furthermore, the position coordinate x of the maximum value of the interference fringe in each interference fringe sub-image of the inventioni，maxThe following are:
Figure BDA0003217334010000052
wherein the content of the first and second substances,
Figure BDA0003217334010000053
taking the value of piston phase noise of the ith unit beam, xi,centerAnd the coordinate of the central position of the interference fringe sub-image corresponding to the ith unit beam.
Furthermore, the seed laser of the present invention is derived from a seed laser, the laser output by the seed laser is power-amplified by a preamplifier, and then is divided into two parts by a 1 × 2 fiber beam splitter, one part is input to a laser array coherent combining unit for generating a laser array, and the other part is used as a reference beam. Further, the seed laser is a narrow linewidth linearly polarized optical fiber seed laser.
Furthermore, the laser array coherent combining unit of the present invention includes a collimator array composed of a 1 × N fiber beam splitter, N phase modulators, N main amplifiers, and N collimators, seed laser input to the laser array coherent combining unit is equally divided into N paths of unit beams by the 1 × N fiber beam splitter, each path of unit beam corresponds to one path of transmission path, each path of transmission path is sequentially provided with a phase modulator, a main amplifier, and a collimator, and each path of unit beam is subjected to phase modulation and power amplification by the phase modulator and the main amplifier in sequence and then collimated and output by the collimator in the collimator array.
Furthermore, the reference beam of the invention passes through an adjustable gain optical fiber amplifier, is collimated by a reference light collimator and then enters the semi-transparent semi-reflecting mirror, a small part of laser array obtained by sampling by a sampling mirror is contracted by an optical beam reducer and then enters the semi-transparent semi-reflecting mirror, the laser array is transmitted and reflected by the semi-transparent semi-reflecting mirror and then enters the high-speed camera, and the high-speed camera is used for detecting the interference fringe image of the contracted laser array and the reference beam.
Furthermore, the invention makes the interference fringe image clearly visible by adjusting the output angle of the reference light collimator and the inclination angle of the half-transmitting and half-reflecting mirror.
The invention also provides a high-precision piston phase closed-loop control system, which comprises:
the seed laser generating unit is used for generating seed laser and dividing the seed laser into two parts, one part is input into the laser array coherent combining unit and used for generating a laser array, and the other part is used as a reference beam;
the laser array coherent combination unit comprises a collimator array consisting of a 1 XN optical fiber beam splitter, N phase modulators, N main amplifiers and N collimators, wherein seed laser input into the laser array coherent combination unit is divided into N paths of unit beams through the 1 XN optical fiber beam splitter, each path of unit beam corresponds to one path of transmission path, the phase modulators, the main amplifiers and the collimators are arranged in each path of transmission path in sequence, and each path of unit beam is subjected to phase modulation and power amplification through the phase modulators and the main amplifiers in sequence and then is output by collimation through the collimators in the collimator array;
the laser array sampling unit comprises a sampling mirror and an optical beam reducer, and the sampling mirror collects the laser array to the optical beam reducer to obtain a laser array after beam reduction;
the image acquisition unit is used for detecting an interference fringe image of the shrunk laser array and the reference beam by using a high-speed camera;
the interference fringe resolving module is used for carrying out region division on the interference fringe image according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array; performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam; in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, and finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is a piston phase noise value of each unit light beam;
and the phase control unit is used for converting the piston phase noise value of each unit light beam into a voltage value at two ends of the corresponding phase modulator of each unit light beam in the laser array coherent synthesis unit, applying corresponding voltage to the corresponding phase modulator and performing closed-loop control on the piston phase of each unit light beam in the laser array.
Compared with the prior art, the invention has the beneficial effects that:
the invention utilizes the advantage of more sampling points of the high-speed camera, improves the accuracy of the stripe position to the level far exceeding the pixel size through two-dimensional Fourier transform in mathematics, and obtains the high-accuracy stripe position.
Compared with the existing phase control method, the magnitude improvement of the calculation precision in the phase calculation process is realized. Therefore, the invention has smaller control residual error and higher control precision.
The method provided by the invention has expansibility, and the calculation method for acquiring the position of the high-precision interference fringe by using the two-dimensional image also has important application in other fields related to fringe data processing, such as the field of optical fiber sensing.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a high-precision closed-loop control system for piston phase according to an embodiment of the present invention;
FIG. 2 is a diagram showing the result of obtaining the position coordinates of the maximum value of the interference fringes by the conventional method, i.e., calculating the maximum value of the interference fringes in the whole image and obtaining the position coordinates thereof, for the interference fringe sub-image of the unit beam with the piston phase noise of 0rad in one embodiment;
FIG. 3 is a schematic diagram of a two-dimensional pattern drawn by a modulo function proposed in the present invention for an interference fringe sub-image of a unit beam with a piston phase noise of 0rad, wherein the area shown by a rectangular frame represents a spectral parameter corresponding to an included angle between the optical axis of a reference beam and the optical axis of a laser array;
FIG. 4 is a schematic diagram of a two-dimensional pattern drawn by using the argument function proposed in the present invention for an interference fringe sub-image of a unit beam with piston phase noise of 0rad, in which the region shown by a rectangular frame represents the acquired piston phase value;
FIG. 5 is a diagram showing the result of obtaining the position coordinates of the maximum value of the interference fringe for an interference fringe sub-image of a unit beam with piston phase noise of 2.6202rad by the conventional method of calculating the maximum value of the interference fringe in the whole image and obtaining the position coordinates thereof;
FIG. 6 is a schematic diagram of a two-dimensional pattern drawn by a modulo function proposed in the present invention for an interference fringe sub-image of a unit beam with piston phase noise of 2.6202rad, where the area shown by the rectangular frame represents the spectral parameter corresponding to the included angle between the optical axis of the reference beam and the optical axis of the laser array;
FIG. 7 is a schematic diagram of a two-dimensional pattern using the argument function proposed in the present invention for an interference fringe sub-image of a unit beam with piston phase noise of 2.6202rad, where the region shown by the rectangular box represents the acquired piston phase value;
FIG. 8 is a diagram illustrating the effect of calculating the residual error of the piston phase for determining the fringe position by calculating the coordinate of the maximum value of the interference fringe according to the conventional method in one embodiment;
FIG. 9 is a graph illustrating the effect of calculating residual error using the method of the present invention, i.e., using two-dimensional Fourier transformed piston phases, in one embodiment;
reference numbers in fig. 1:
101. a seed laser; 102. a preamplifier; 103. a 1 × 2 fiber splitter; 104. a 1 XN fiber optic splitter; 105. a phase modulator; 106. a main amplifier; 107. an array of collimators; 201. an adjustable gain optical fiber amplifier; 202. a reference light collimator; 203. a sampling mirror; 204. an optical beam reducer; 205. a semi-transparent semi-reflective mirror; 301. a high-speed camera; 302. an interference fringe position resolving module; 303. a phase control unit.
Detailed Description
In order to make the technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a high-precision piston phase closed-loop control method and system based on two-dimensional image full-data combination resolving, which can more accurately calculate the accurate position of a fringe center through image data of a discretely sampled high-speed camera. Compared with the traditional method that the calculation precision of the stripe position depends on the size of the pixel point, the calculation method of the stripe position provided by the invention improves the precision by more than one magnitude. By a more accurate fringe position calculation method, when the piston phase of the unit light beam is compensated, a smaller phase-locked residual error can be realized, so that the synthesis efficiency of coherent synthesis is improved, and the brightness of the synthesized laser is further improved.
Specifically, an embodiment of the present invention provides a method for calculating a position of a high-precision interference fringe, including:
referring to fig. 1, an embodiment of the present invention provides a high-precision piston phase closed-loop control system, which includes a narrow-linewidth linearly polarized fiber seed laser 101, a preamplifier 102, a 1 × 2 fiber splitter 103, a 1 × N fiber splitter 104, a phase modulator 105, a main amplifier 106, a fiber collimator 107, an adjustable gain fiber amplifier 201, a reference light collimator 202, a sampling mirror 203, an optical beam reducer 204, a half mirror 205, a high-speed camera 301, an interference fringe position resolving module 302, and a phase control unit 303. Wherein the seed laser 101 is a narrow linewidth linearly polarized fiber seed laser.
The laser output from the seed laser 101 is first power amplified by a low power preamplifier 102, and then split by a 1 × 2 fiber splitter, wherein a part of the laser is input to the laser array coherent combining unit for generating a laser array, and a part of the laser is used as a reference beam.
The seed laser input into the coherent combining unit of the laser array is firstly divided equally into N paths of unit beams by the 1 × N fiber beam splitter 104, each path of unit beam corresponds to one path of transmission path, a phase modulator 105, a main amplifier 106 and a fiber collimator 107 are sequentially arranged in each path of transmission path, and each path of unit beam is subjected to phase modulation and power amplification by the phase modulator 105 and the main amplifier 106 in sequence and then is output in a collimated manner by the fiber collimator 107 in the collimator array.
The reference beam passes through an adjustable gain fiber amplifier 201, is collimated by a reference beam collimator 202, and then enters a half mirror 205. The laser array output by the collimator array in the laser array coherent combination unit passes through the sampling mirror 203, the sampling mirror 203 is a high-reflection mirror, most energy laser arrays are reflected and output, and the laser array with a small part of energy is transmitted by the high-reflection mirror, then is contracted by the optical beam reducer, and then enters the semi-transmitting semi-reflection mirror to be used as probe light for phase control. The reference beam incident to the half mirror and the contracted laser array are transmitted and reflected by the half mirror and then incident to the high-speed camera, and the interference fringe image of the contracted laser array and the reference beam is detected by the high-speed camera.
The transmitted light transmitted from the high-reflection mirror is reduced by the optical beam reducer to be equivalent to the reference beam and the target surface size of the high-speed camera, and the construction of a Mach-Zehnder interferometer optical path system is realized through the semi-transparent semi-reflection mirror. And the high-speed camera is used as an image acquisition unit and is used for detecting interference fringe images of the shrunk laser array and the reference beam. And the interference fringe resolving module extracts piston phase information hidden in the interference fringe image. Specifically, the interference fringe resolving module divides the interference fringe image into regions according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array; performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam; in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, and finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is a piston phase noise value of each unit light beam. And the phase control unit is used for converting the piston phase noise value of each unit light beam into a voltage value at two ends of the corresponding phase modulator of each unit light beam in the laser array coherent synthesis unit, applying corresponding voltage to the corresponding phase modulator and performing closed-loop control on the piston phase of each unit light beam in the laser array.
An embodiment of the present invention provides a high-precision piston phase closed-loop control method, including:
the seed laser is divided into two parts, one part is input into the laser array coherent combination unit to be used for generating the laser array, and the other part is used as a reference beam.
And acquiring an included angle theta between the optical axis of the reference beam and the optical axis of the laser array.
And collecting a part of laser arrays generated by the laser array coherent synthesis unit, shrinking the laser arrays, and detecting interference fringe images of the shrunk laser arrays and the reference beams by using a high-speed camera.
And dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array.
And performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, wherein the two-dimensional frequency spectrum information distribution comprises the following steps:
Figure BDA0003217334010000121
in the formula, (x, y) is the position coordinate of the pixel point in the interference fringe subimage, (u, v) is the frequency spectrum coordinate of the pixel point in the image obtained after the two-dimensional Fourier transform of the interference fringe subimage, and fi(x, y) represents the distribution relation of the interference light spot light intensity signal of the ith unit light beam along with the position, Fi(u, v) represents a spectrum distribution function after two-dimensional Fourier transform is carried out on the light intensity signal of the interference light spot of the ith unit light beam, e represents a natural constant, and j represents an imaginary number unit;
and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam as follows:
Figure BDA0003217334010000122
where, | | is a modulus function in complex operations, and arg () is an argument function in complex operations.
In the two-dimensional spectral information distribution of the interference fringe sub-image of each unit beam, passing through the modulus function Mi(u, v) finding out the frequency spectrum parameter corresponding to the included angle theta between the optical axis of the reference beam and the optical axis of the laser array, and obtaining the frequency spectrum parameter through the amplitude function Ai(u, v) finding out amplitude values corresponding to the frequency spectrum parameters, wherein the amplitude values are values of piston phase noise of each unit light beam
Figure BDA0003217334010000131
Converting the piston phase noise value of each unit light beam into a voltage value of each unit light beam at two ends of a corresponding phase modulator in a laser array coherent combination unit, and the method comprises the following steps:
Figure BDA0003217334010000132
wherein the content of the first and second substances,
Figure BDA0003217334010000133
taking the value of piston phase noise of the ith unit beam, VπIs the half-wave voltage of the phase modulator.
And finally, applying corresponding voltage to the corresponding phase modulator to perform closed-loop control on the piston phase of each unit beam in the laser array.
An embodiment of the present invention provides a method for calculating a position coordinate of a maximum value of an interference fringe with high precision, including:
the seed laser is divided into two parts, one part is input into the laser array coherent combination unit to be used for generating the laser array, and the other part is used as a reference beam.
And acquiring an included angle theta between the optical axis of the reference beam and the optical axis of the laser array.
And collecting a part of laser arrays generated by the laser array coherent synthesis unit, shrinking the laser arrays, and detecting interference fringe images of the shrunk laser arrays and the reference beams by using a high-speed camera.
And dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array.
And performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, wherein the two-dimensional frequency spectrum information distribution comprises the following steps:
Figure BDA0003217334010000141
in the formula, (x, y) is the position coordinate of the pixel point in the interference fringe subimage, (u, v) is the frequency spectrum coordinate of the pixel point in the image obtained after the two-dimensional Fourier transform of the interference fringe subimage, and fi(x, y) represents the distribution relation of the interference light spot light intensity signal of the ith unit light beam along with the position, Fi(u, v) represents the intensity signal of the interference spot for the i-th unit beamPerforming a two-dimensional Fourier transformed spectrum distribution function, wherein e represents a natural constant, and j represents an imaginary number unit;
and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam as follows:
Figure BDA0003217334010000142
where, | | is a modulus function in complex operations, and arg () is an argument function in complex operations.
In the two-dimensional spectral information distribution of the interference fringe sub-image of each unit beam, passing through the modulus function Mi(u, v) finding out the frequency spectrum parameter corresponding to the included angle theta between the optical axis of the reference beam and the optical axis of the laser array, and obtaining the frequency spectrum parameter through the amplitude function Ai(u, v) finding out amplitude values corresponding to the frequency spectrum parameters, wherein the amplitude values are values of piston phase noise of each unit light beam
Figure BDA0003217334010000143
Calculating the fringe interval of the interference fringe pattern according to the included angle between the optical axis of the reference beam and the optical axis of the laser array and the central wavelength of the seed laser, wherein the fringe interval is as follows:
Figure BDA0003217334010000144
wherein d represents the fringe spacing of the interference fringe pattern, theta represents the included angle between the optical axis of the reference beam and the optical axis of the laser array, and lambda represents the central wavelength of the seed laser.
According to the ratio of the amplitude value to 2 pi, combining the fringe intervals of the interference fringe patterns to obtain the position coordinate x of the maximum value of the interference fringe in each interference fringe sub-imagei，maxThe following are:
Figure BDA0003217334010000151
wherein the content of the first and second substances,
Figure BDA0003217334010000152
taking the value of piston phase noise of the ith unit beam, xi,centerAnd the coordinate of the central position of the interference fringe sub-image corresponding to the ith unit beam.
In order to show the superiority of the present invention compared with the conventional method, the conventional method calculates the maximum value of interference fringes in the whole image, acquires the position coordinates of the maximum value, and calculates the piston phase value by combining the fringe distance. The invention carries out a comparative experiment, which comprises the following steps:
FIG. 2 is a diagram illustrating the result of obtaining the position coordinates of the maximum value of the interference fringes by the conventional method for the interference fringe sub-image of the unit beam with the piston phase noise of 0rad in one embodiment. For the same interference fringe sub-image of the unit beam with the piston phase noise of 0rad aimed at in fig. 2, fig. 3 is a schematic diagram of a two-dimensional pattern drawn by using the modulus function proposed in the present invention, wherein the region shown by the rectangular frame represents the spectral parameter corresponding to the included angle between the optical axis of the reference beam and the optical axis of the laser array; fig. 4 is a schematic diagram of a two-dimensional pattern drawn by using the argument function proposed in the present invention, wherein the area shown by the rectangular box represents the acquired piston phase value. Because the interference fringe sub-image of the unit light beam with the piston phase noise of 0rad is aimed at, the position of the maximum value of the fringe is strictly in the central position (the coordinates are (82,83)) of the image, the position coordinates of the maximum value of the interference fringe and the accurate value of the piston phase value can be obtained by the traditional method and the method.
FIG. 5 is a diagram showing the result of obtaining the position coordinates of the maximum value of the interference fringe by the conventional method for the interference fringe sub-image of the unit beam with piston phase noise of 2.6202rad in one embodiment. For the same interference fringe sub-image of unit beam with piston phase noise of 2.6202rad in fig. 5, fig. 6 is a schematic diagram of a two-dimensional pattern drawn by using the modulo function proposed in the present invention, wherein the region shown by the rectangular frame represents the spectral parameter corresponding to the included angle between the optical axis of the reference beam and the optical axis of the laser array; fig. 7 is a schematic diagram of a two-dimensional pattern using the argument function proposed in the present invention, wherein the area indicated by the rectangular box represents the acquired piston phase value. In fig. 5, the value of the maximum coordinate of the fringe calculated by the conventional method on the y-axis is 65, and the corresponding piston phase is 2.4721 rad. The value of the maximum value coordinate of the stripe calculated by the method on the y axis and the piston phase are 63.9732 (wherein 63.9732 is 83-19.0268) and 2.6131rad respectively, so that the precision is obviously improved.
To further illustrate the advantages of the new method, without loss of generality, a set of differentiated piston phase errors was constructed by monte carlo simulation, comparing the piston phase calculation accuracy of the present invention with the conventional method, and the results are shown in fig. 8 and 9. FIG. 8 is a diagram showing the calculation of the residual error of the piston phase for determining the position of the interference fringe by calculating the coordinate of the maximum value of the interference fringe according to the conventional method; fig. 9 shows the calculation of the residual error using the method of the invention, i.e. using the piston phase of the two-dimensional fourier transform. It is evident that the root mean square error value of the calculated residuals is reduced from 0.0713rad in FIG. 8 to 0.0034rad in FIG. 9, increased by a factor of 20. Likewise, the accuracy of determining the position of the interference fringe maximum by the method proposed by the present invention is also improved by 20 times from the original pixel level. Therefore, the method can realize the calculation and compensation of the piston phase with smaller residual error and higher precision, and realize the laser synthesis with higher efficiency generated by a coherent synthesis system.
In summary, although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.

Claims (10)

1. The high-precision piston phase closed-loop control method is characterized by comprising the following steps:
dividing seed laser into two parts, inputting one part into a laser array coherent synthesis unit for generating a laser array, and taking the other part as a reference beam;
acquiring an included angle between the optical axis of the reference beam and the optical axis of the laser array;
collecting a part of laser arrays generated by a laser array coherent synthesis unit, carrying out beam shrinking on the laser arrays, and detecting interference fringe images of the shrunk laser arrays and reference beams by using a high-speed camera;
dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array;
performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam;
in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, and finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is a piston phase noise value of each unit light beam;
and converting the piston phase noise value of each unit light beam into a voltage value of each unit light beam at two ends of the corresponding phase modulator in the laser array coherent combination unit, applying corresponding voltage to the corresponding phase modulator, and performing closed-loop control on the piston phase of each unit light beam in the laser array.
2. The method according to claim 1, wherein the two-dimensional spectrum information distribution of the interference fringe sub-image of each unit beam is as follows:
Figure FDA0003217334000000011
in the formula, (x, y) is the position coordinate of the pixel point in the interference fringe subimage, (u, v) is the frequency spectrum coordinate of the pixel point in the image obtained after the two-dimensional Fourier transform of the interference fringe subimage, and fi(x, y) represents the component of the interference light spot intensity signal of the ith unit light beam according to the positionCloth relation, Fi(u, v) represents a spectrum distribution function after two-dimensional Fourier transform is carried out on the light intensity signal of the interference light spot of the ith unit light beam, e represents a natural constant, and j represents an imaginary number unit;
and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam as follows:
Figure FDA0003217334000000021
where, | | is a modulus function in complex operations, and arg () is an argument function in complex operations.
3. The method for controlling the phase of the piston with high precision in the closed loop according to claim 1, wherein the voltage value of each unit beam at the two ends of the corresponding phase modulator in the laser array coherent combining unit is as follows:
Figure FDA0003217334000000022
wherein the content of the first and second substances,
Figure FDA0003217334000000023
taking the value of piston phase noise of the ith unit beam, VπIs the half-wave voltage of the phase modulator.
4. The high-precision piston phase closed-loop control method according to claim 1, 2 or 3, characterized in that the seed laser is derived from a seed laser, the laser output by the seed laser is power-amplified by a preamplifier, and then is divided into two parts by a 1 x 2 fiber beam splitter, one part is input to a laser array coherent combining unit for generating a laser array, and the other part is used as a reference beam;
the laser array coherent combination unit comprises a collimator array consisting of a 1 xN optical fiber beam splitter, N phase modulators, N main amplifiers and N collimators, seed laser input into the laser array coherent combination unit is divided into N paths of unit beams through the 1 xN optical fiber beam splitter, each path of unit beam corresponds to one path of transmission path, the phase modulators, the main amplifiers and the collimators are arranged in each path of transmission path in sequence, and each path of unit beam is subjected to phase modulation and power amplification through the phase modulators and the main amplifiers in sequence and then is output in a collimating mode through the collimators in the collimator array;
after passing through an adjustable gain optical fiber amplifier, a reference beam is collimated by a reference light collimator and then enters a semi-transparent semi-reflecting mirror, a small part of laser array obtained by sampling by a sampling mirror is contracted by an optical beam reducer and then enters the semi-transparent semi-reflecting mirror, the laser array is transmitted and reflected by the semi-transparent semi-reflecting mirror and then enters a high-speed camera, and the high-speed camera is used for detecting an interference fringe image of the contracted laser array and the reference beam.
5. The method as claimed in claim 4, wherein the output angle of the reference light collimator and the tilt angle of the half mirror are adjusted to make the interference fringe image clearly visible.
6. A high accuracy piston phase closed loop control system, comprising:
the seed laser generating unit is used for generating seed laser and dividing the seed laser into two parts, one part is input into the laser array coherent combining unit and used for generating a laser array, and the other part is used as a reference beam;
the laser array coherent combination unit comprises a collimator array consisting of a 1 XN optical fiber beam splitter, N phase modulators, N main amplifiers and N collimators, wherein seed laser input into the laser array coherent combination unit is divided into N paths of unit beams through the 1 XN optical fiber beam splitter, each path of unit beam corresponds to one path of transmission path, the phase modulators, the main amplifiers and the collimators are arranged in each path of transmission path in sequence, and each path of unit beam is subjected to phase modulation and power amplification through the phase modulators and the main amplifiers in sequence and then is output by collimation through the collimators in the collimator array;
the laser array sampling unit comprises a sampling mirror and an optical beam reducer, and the sampling mirror collects the laser array to the optical beam reducer to obtain a laser array after beam reduction;
the image acquisition unit is used for detecting an interference fringe image of the shrunk laser array and the reference beam by using a high-speed camera;
the interference fringe resolving module is used for carrying out region division on the interference fringe image according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array; performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam; in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, and finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is a piston phase noise value of each unit light beam;
and the phase control unit is used for converting the piston phase noise value of each unit light beam into a voltage value at two ends of the corresponding phase modulator of each unit light beam in the laser array coherent synthesis unit, applying corresponding voltage to the corresponding phase modulator and performing closed-loop control on the piston phase of each unit light beam in the laser array.
7. A method for calculating a position coordinate of a maximum value of an interference fringe with high precision, comprising:
dividing seed laser into two parts, inputting one part into a laser array coherent synthesis unit for generating a laser array, and taking the other part as a reference beam;
acquiring an included angle between the optical axis of the reference beam and the optical axis of the laser array;
collecting a part of laser arrays generated by a laser array coherent synthesis unit, carrying out beam shrinking on the laser arrays, and detecting interference fringe images of the shrunk laser arrays and reference beams by using a high-speed camera;
dividing the interference fringe image into areas according to the arrangement mode of the laser array to obtain an interference fringe sub-image of each unit beam in the laser array;
performing two-dimensional Fourier transform on the interference fringe sub-image of each unit beam to obtain two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit beam, and further obtaining a modulus function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam;
in the two-dimensional frequency spectrum information distribution of the interference fringe sub-image of each unit light beam, finding a frequency spectrum parameter corresponding to an included angle between the optical axis of the reference light beam and the optical axis of the laser array through a mode function, finding an amplitude value corresponding to the frequency spectrum parameter through an amplitude function, wherein the amplitude value is also a piston phase noise value of each unit light beam;
calculating the fringe interval of the interference fringe pattern according to the included angle between the optical axis of the reference beam and the optical axis of the laser array and the central wavelength of the seed laser;
and according to the ratio of the amplitude value to 2 pi, combining the fringe intervals of the interference fringe patterns to obtain the position coordinates of the maximum value of the interference fringes in each interference fringe sub-image.
8. The method for calculating the position coordinates of the maximum value of interference fringes according to claim 7, characterized in that the two-dimensional spectrum information distribution of the interference fringe sub-image of each unit beam is as follows:
Figure FDA0003217334000000051
in the formula, (x, y) is the position coordinate of the pixel point in the interference fringe subimage, (u, v) is the frequency spectrum coordinate of the pixel point in the image obtained after the two-dimensional Fourier transform of the interference fringe subimage, and fi(x, y) represents the distribution relation of the interference light spot light intensity signal of the ith unit light beam along with the position, Fi(u, v) represents the two-dimensional Fourier operation of the interference light spot intensity signal of the ith unit light beamThe spectrum distribution function after the inner leaf transformation, e represents a natural constant, and j represents an imaginary number unit;
and further obtaining a mode function and an amplitude function of the two-dimensional frequency spectrum information of the interference fringe sub-image of each unit beam as follows:
Figure FDA0003217334000000052
where, | | is a modulus function in complex operations, and arg () is an argument function in complex operations.
9. The method according to claim 7, wherein the fringe spacing of the fringe pattern is:
Figure FDA0003217334000000053
wherein d represents the fringe spacing of the interference fringe pattern, theta represents the included angle between the optical axis of the reference beam and the optical axis of the laser array, and lambda represents the central wavelength of the seed laser.
10. The method according to claim 9, wherein the position coordinate x of the maximum value of the interference fringe in each of the interference fringe sub-images is the position coordinate x of the maximum value of the interference fringei，maxThe following are:
Figure FDA0003217334000000061
wherein the content of the first and second substances,
Figure FDA0003217334000000062
taking the value of piston phase noise of the ith unit beam, xi,centerAnd the coordinate of the central position of the interference fringe sub-image corresponding to the ith unit beam.
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