CN113155279A - Single-point measurement method for laser beam quality - Google Patents
Single-point measurement method for laser beam quality Download PDFInfo
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Abstract
The invention discloses a single-point measurement method for laser beam quality, which obtains x/y direction differential phase and light intensity information by transforming a four-wave transverse shearing interference pattern, reconstructs the phase information to be measured by adopting a differential zernike algorithm, reconstructs complex amplitude according to the phase information and the light intensity information, obtains the complex amplitude and the light spot size omega (z) of different axial positions by respectively adopting an angular spectrum algorithm and a second-order moment method, and further fits a laser transmission curve equation, thereby obtaining a far field divergence angle theta (theta) of a laser beam0Beam waist spot size omega0And a beam quality factor M2. The measuring method can realize real-time monitoring of the quality of the laser beam, is also suitable for measuring the quality of the pulse laser beam, and has the advantages of simplicity, high measuring efficiency and the like.
Description
Technical Field
The invention relates to a single-point measurement method for the beam quality of a laser, and belongs to the technical field of laser.
Background
The laser has been widely used in the fields of national economy, national defense safety and the like due to the characteristics of good monochromaticity, good coherence, good directivity, high brightness and the like. The quality of the laser beam has been a focus of attention of laser development, production and application workers. A multi-spot method beam quality measuring instrument represented by Spiricon, Thorlabs, etc., in the united states, which samples and measures spot sizes at 10 or more different positions in the laser beam axial direction mainly by moving an image detector (such as a CCD camera, a CMOS camera) in the beam axial direction, and requires that at least half or more of the positions are located in the rayleigh range, and then obtains the beam quality factor of the laser beam by hyperbolic fitting, has been widely used in practice. The more axial position samples, the higher the fitting accuracy, and the higher the measurement accuracy. Because the image detector needs to be moved along the axial direction of the light beam during each sampling, the light beam needs to be ensured to be vertically incident to the detection surface of the image detector all the time in the whole measuring process before measurement, the measuring period is long, the light path is difficult to adjust, and the introduced measuring error is large, so that the real-time monitoring of the quality of the laser beam cannot be met, and the method is not suitable for measuring the quality of the pulse laser beam.
Disclosure of Invention
Aiming at the problems of large measurement error, long measurement period and difficult light path adjustment of the quality of laser beams by a multipoint method and the problem that the real-time quality of the laser beams cannot be metThe invention aims to provide a single-point measurement method for measuring the beam quality of a laser, which is used for acquiring a far-field divergence angle theta by a four-wave transverse shear interference method0Beam waist spot omega0Beam quality factor M2And the like.
As shown in fig. 1, the present invention provides a single-point measurement method for laser beam quality, which comprises the following steps:
acquiring a four-wave transverse shearing interference image with pixel number width W and pixel number length H; the image has no background noise and saturated pixels;
the four-wave transverse shear interferogram in the first step is acquired by: splitting a light beam of a laser to be detected by adopting a two-dimensional phase grating, blocking light beams of other diffraction orders by using an aperture diaphragm, allowing only four sub-light beams of the (plus or minus 1) orders to pass through, and focusing the four sub-light beams on a detection surface of an image sensor through a lens, thereby obtaining a four-wave transverse shearing interference pattern on the image sensor;
performing Fourier transform on the four-wave transverse shearing interference graph to obtain a frequency spectrum, wherein the Fourier transform formula is as formula (1), the four-wave transverse shearing interference graph in the frequency domain comprises a central zero frequency and four pairs of fundamental frequencies, a midpoint O of the central zero frequency is taken as a coordinate origin, a horizontal right direction is taken as an x-axis positive direction, a vertical upward direction is taken as a y-axis positive direction, and a rectangular coordinate system xOy is established;
step three, respectively screening out a positive level frequency spectrum and a zero level frequency spectrum in the x direction and the y direction by adopting a frequency domain filtering method, and performing inverse Fourier transform by using a formula (2) to obtain phase distribution in the x direction and the y direction so as to obtain differential phase information delta phi in the x direction and the y directiontAnd light intensity information It；
Step four, utilizing the differential phase information delta phi in the x direction and the y direction obtained in the step threetPerforming least square fitting to calculate zernike coefficient, and reconstructing phase information phi of the measured laser beam by using the zernike coefficient and zernike polynomialt；
Step five, according to the obtained light intensity information ItAnd phase information
Respectively reconstructing the complex amplitude E of the laser beam at the position z of 0 by using the formula (3) to the formula (5)0(x, y) complex amplitude conjugate E0(x, y) and intensity distribution I0(x，y)；
I(x,y)＝E(x,y)*E*(x,y) (5)
Sixthly, complex amplitude information E of the axial coordinates z at different positions of the laser beam is obtained according to a formula (3) and an angular spectrum algorithm formula (6)z(x,y)；
Where λ is the wavelength of the laser, fxAnd fyIs a fourier transform pair in the frequency domain;
step seven, solving the light intensity distribution I of more than 10 different axial positions in the Rayleigh range according to the formulas (4) to (6)z(x,y)；
Step eight, solving the spot size omega of the different axial positions of the light beams according to the formula (7)x(z) and ωy(z)；
Step nine, the size omega of the light spotx(z)、ωy(z) substituting the axial position coordinate z into equation (8) and fitting the coefficients A, B and C by means of the least square method to obtain a spatial transmission curve equation of the X/Y-direction laser beam;
ωx(z)2＝AxZ2+BxZ+Cx，ωy(z)2＝AyZ2+ByZ+Cy (8)
step ten, respectively obtaining the far field divergence angle theta of the laser beam in the X/Y direction according to the formulas (9) to (11)0Beam waist spot size omega0And a beam quality factor M2。
Has the advantages that: according to the laser beam quality single-point measurement method provided by the invention, a laser transmission characteristic curve equation can be fitted by detecting the vertical axis light spot at any position of the measured laser beam along the axial direction, so that the beam waist light spot size, the far field divergence angle and the light beam quality factor of the measured laser beam are solved, the real-time monitoring of the laser beam quality can be realized, the method is also suitable for measuring the pulse laser beam quality, and the method has the advantages of simplicity in measurement method, high measurement efficiency and the like.
Drawings
FIG. 1 is a flow chart of a single point measurement method for laser beam quality.
Detailed Description
Embodiment 1 a laser beam quality single point measurement method.
As shown in fig. 1, the present invention provides a single-point measurement method for laser beam quality, which comprises the following steps:
acquiring a four-wave transverse shearing interference image with pixel number width W and pixel number length H; the image has no background noise and saturated pixels;
the four-wave transverse shear interferogram in the first step is acquired by: splitting a light beam of a laser to be detected by adopting a two-dimensional phase grating, blocking light beams of other diffraction orders by using an aperture diaphragm, allowing only four sub-light beams of the (plus or minus 1) orders to pass through, and focusing the four sub-light beams on a detection surface of an image sensor through a lens, thereby obtaining a four-wave transverse shearing interference pattern on the image sensor;
performing Fourier transform on the four-wave transverse shearing interference graph to obtain a frequency spectrum, wherein the Fourier transform formula is as formula (1), the four-wave transverse shearing interference graph in the frequency domain comprises a central zero frequency and four pairs of fundamental frequencies, a midpoint O of the central zero frequency is taken as a coordinate origin, a horizontal right direction is taken as an x-axis positive direction, a vertical upward direction is taken as a y-axis positive direction, and a rectangular coordinate system xOy is established;
step three, respectively screening out a positive level frequency spectrum and a zero level frequency spectrum in the x direction and the y direction by adopting a frequency domain filtering method, and performing inverse Fourier transform by using a formula (2) to obtain phase distribution in the x direction and the y direction so as to obtain differential phase information delta phi in the x direction and the y directiontAnd light intensity information It；
Step four, utilizing the differential phase information delta phi in the x direction and the y direction obtained in the step threetPerforming least square fitting to calculate Zernike coefficient, and reconstructing phase information phi of the measured laser beam by using the Zernike coefficient and Zernike polynomialt；
Step five, according to the obtained light intensity information ItAnd phase information
Respectively reconstructing the complex amplitude E of the laser beam at the position z of 0 by using the formula (3) to the formula (5)0(x, y) complex amplitude conjugate E0(x, y) and intensity distribution I0(x，y)；
I(x,y)＝E(x,y)*E*(x,y) (5)
Sixthly, complex amplitude information E of the axial coordinates z at different positions of the laser beam is obtained according to a formula (3) and an angular spectrum algorithm formula (6)z(x,y)；
Where λ is the wavelength of the laser, fxAnd fyIs a fourier transform pair in the frequency domain;
step seven, solving the light intensity distribution I of more than 10 different axial positions in the Rayleigh range according to the formulas (4) to (6)z(x,y)；
Step eight, solving the spot size omega of the different axial positions of the light beams according to the formula (7)x(z) and ωy(z)；
Step nine, the size omega of the light spotx(z)、ωy(z) substituting the axial position coordinate z into equation (8) and fitting the coefficients A, B and C by means of the least square method to obtain a spatial transmission curve equation of the X/Y-direction laser beam;
ωx(z)2＝AxZ2+BxZ+Cx，ωy(z)2＝AyZ2+ByZ+Cy (8)
step ten, respectively obtaining the far field divergence angle theta of the laser beam in the X/Y direction according to the formulas (9) to (11)0Beam waist spot size omega0And a beam quality factor M2。
Claims (1)
1. A single-point measurement method for the quality of a laser beam is characterized by comprising the following steps:
acquiring a four-wave transverse shearing interference image with pixel number width W and pixel number length H; the image has no background noise and saturated pixels;
the four-wave transverse shear interferogram in the first step is acquired by: splitting a light beam of a laser to be detected by adopting a two-dimensional phase grating, blocking light beams of other diffraction orders by using an aperture diaphragm, allowing only four sub-light beams of the (plus or minus 1) orders to pass through, and focusing the four sub-light beams on a detection surface of an image sensor through a lens, thereby obtaining a four-wave transverse shearing interference pattern on the image sensor;
performing Fourier transform on the four-wave transverse shearing interference graph to obtain a frequency spectrum, wherein the Fourier transform formula is as formula (1), the four-wave transverse shearing interference graph in the frequency domain comprises a central zero frequency and four pairs of fundamental frequencies, a midpoint O of the central zero frequency is taken as a coordinate origin, a horizontal right direction is taken as an x-axis positive direction, a vertical upward direction is taken as a y-axis positive direction, and a rectangular coordinate system xOy is established;
step three, respectively screening out a positive level frequency spectrum and a zero level frequency spectrum in the x direction and the y direction by adopting a frequency domain filtering method, and performing inverse Fourier transform by using a formula (2) to obtain phase distribution in the x direction and the y direction so as to obtain differential phase information in the x direction and the y direction
And light intensity information It；
Step four, utilizing the differential phase information in the x direction and the y direction obtained in the step three
Performing least square fitting to calculate zernike coefficient, and reconstructing phase information of the measured laser beam by using the zernike coefficient and zernike polynomial
Step five, according to the obtained light intensity information ItAnd phase information
Respectively reconstructing the complex amplitude E of the laser beam at the position z of 0 by using the formula (3) to the formula (5)0(x, y) complex amplitude conjugate E0(x, y) and intensity distribution I0(x，y)；
I(x,y)＝E(x,y)*E*(x,y) (5)
Sixthly, complex amplitude information E of the axial coordinates z at different positions of the laser beam is obtained according to a formula (3) and an angular spectrum algorithm formula (6)z(x,y)；
Where λ is the wavelength of the laser, fxAnd fyIs a fourier transform pair in the frequency domain;
step seven, solving the light intensity distribution I of more than 10 different axial positions in the Rayleigh range according to the formulas (4) to (6)z(x,y)；
Step eight, solving the spot size omega of the different axial positions of the light beams according to the formula (7)x(z) and ωy(z)；
Step nine, the size omega of the light spotx(z)、ωy(z) substituting the axial position coordinate z into equation (8) and fitting the coefficients A, B and C by means of the least square method to obtain a spatial transmission curve equation of the X/Y-direction laser beam;
step ten, respectively obtaining the far field divergence angle theta of the laser beam in the X/Y direction according to the formulas (9) to (11)0Beam waist spot size omega0And a beam quality factor M2。
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| CN113639967A (en) * | 2021-08-09 | 2021-11-12 | 南京理工大学 | Laser beam quality real-time measuring method based on special-shaped prism |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113639967A (en) * | 2021-08-09 | 2021-11-12 | 南京理工大学 | Laser beam quality real-time measuring method based on special-shaped prism |
| CN113639967B (en) * | 2021-08-09 | 2024-06-07 | 南京理工大学 | Laser beam quality real-time measurement method based on special prism |
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