CN113358272A - System and method for extracting laser plasma profile - Google Patents

System and method for extracting laser plasma profile Download PDF

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CN113358272A
CN113358272A CN202110569877.2A CN202110569877A CN113358272A CN 113358272 A CN113358272 A CN 113358272A CN 202110569877 A CN202110569877 A CN 202110569877A CN 113358272 A CN113358272 A CN 113358272A
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laser plasma
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CN113358272B (en
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袁欢
柯伟
王小华
杨爱军
刘定新
荣命哲
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Xian Jiaotong University
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    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L21/00—Vacuum gauges
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
    • H01J37/32—Gas-filled discharge tubes
    • H01J37/32917—Plasma diagnostics
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The present disclosure discloses a system for extracting a laser plasma profile, comprising: a plasma generating unit which generates plasma by transmitting laser pulses along a first optical path and irradiating a vacuum chamber; the imaging unit is used for capturing the plasma which returns along the first optical path and continues to be transmitted along the second optical path so as to obtain a first laser plasma image; and the image processing unit is used for processing the first laser plasma image to obtain a second laser plasma image and extracting the profile of the laser plasma from the second laser plasma image.

Description

System and method for extracting laser plasma profile
Technical Field
The disclosure belongs to the field of plasma image processing, and particularly relates to a system and a method for extracting a laser plasma profile.
Background
The Laser plasma technology is a technology for generating plasma by bombarding a target with high-energy pulse Laser, and is widely applied to the fields of Laser induced breakdown spectroscopy (Laser induced breakdown spectroscopy), pulse Laser deposition (Pulsed Laser deposition) and the like.
Compared with the traditional vacuum switch vacuum degree detection method, the vacuum degree detection technology of the vacuum switch based on the laser plasma technology has higher detection precision and lower detection lower limit, greatly reduces the influence of environmental conditions, and is expected to break through the technical bottleneck of vacuum degree detection of the vacuum switch for more than half a century. A large number of research results show that the laser plasma appearance characteristics, the laser plasma outline area, the laser plasma radiation intensity and the like have obvious differences under different air pressures. The method has important significance in researching the evolution characteristics of the laser plasma under the vacuum condition, obtains characteristic parameters of the laser plasma capable of representing the vacuum degree, and can provide theoretical basis and application basis for the vacuum degree detection method of the vacuum switch based on the laser plasma imaging technology. The laser plasma profile is a key parameter for representing vacuum, and the influence of the vacuum degree on the laser plasma can be most visually expressed. Laser plasma in vacuum expands rapidly, with lifetimes typically on the order of microseconds, and sizes also on the order of microns. The evolution process of the laser plasma under vacuum cannot be directly observed through human eyes, so that the acquisition difficulty of the laser plasma profile is increased. Therefore, with the aid of a highly sensitive imaging device ICCD camera, a laser plasma image is taken in the expansion phase in the nanosecond time scale, and the laser plasma profile is acquired by processing the laser plasma image. However, due to the quantum characteristics of photons and the influence of the background noise of the device, the laser plasma image has certain noise, the plasma imaging boundary is very fuzzy, and the laser plasma profile cannot be accurately defined and described.
Disclosure of Invention
In view of the deficiencies in the prior art, it is an object of the present disclosure to provide a method for extracting a laser plasma profile, which can extract a laser plasma profile quickly and accurately.
In order to achieve the above purpose, the present disclosure provides the following technical solutions:
a system for extracting a laser plasma profile, comprising:
a plasma generating unit which generates plasma by transmitting laser pulses along a first optical path and irradiating a vacuum chamber;
the imaging unit is used for capturing the plasma which returns along the first optical path and continues to be transmitted along the second optical path so as to obtain a first laser plasma image;
and the image processing unit is used for processing the first laser plasma image to obtain a second laser plasma image and extracting the profile of the laser plasma from the second laser plasma image.
Preferably, the plasma generation unit includes a pulse laser, a dichroic mirror, a first plano-convex lens, and a vacuum chamber, which are sequentially disposed along the first optical path.
Preferably, the imaging unit includes a second plano-convex lens and an ICCD camera sequentially arranged along the second optical path.
Preferably, the image processing unit includes:
the first processing subunit is used for removing background noise on the first laser plasma image to obtain a second laser plasma image;
the second processing subunit is used for performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
and the extraction unit is used for extracting and obtaining all contour points of the laser plasma by marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface.
The present disclosure also provides a method of extracting a laser plasma profile, comprising the steps of:
s100: shooting to obtain a first laser plasma image;
s200: removing background noise on the first laser plasma image to obtain a second laser plasma image;
s300: performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
s400: and marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface, wherein the marked pixel points are contour points of the laser plasma.
Preferably, step S300 includes the steps of:
s301: describing the distribution of the photosensitive intensity values of all pixel points on the second laser plasma image by using a two-dimensional normal distribution function;
s302: calculating a criterion function of the two-dimensional normal distribution function;
s303: and calculating parameter estimation of the criterion function, namely obtaining the two-dimensional Gaussian curved surface.
Preferably, the two-dimensional normal distribution function is represented as:
Figure BDA0003082287490000031
wherein x and y are position coordinates of pixel points, f (x and y) is the photosensitive intensity value of the pixel points of the de-noised laser plasma image (x and y), G is the amplitude of two-dimensional normal distribution, and x is the amplitude of the two-dimensional normal distribution0，y0Position parameter, σ, being two-dimensionally normally distributedx，σyIs a scale parameter of two-dimensional normal distribution.
Preferably, the criterion function is expressed as:
Figure BDA0003082287490000041
wherein, (x, y) (x, y is 1, 2, 3., N) is the coordinate of the pixel point, fxyDe-noising the intensity value of the sensitization for the point, G is the amplitude of the normal distribution, x0，y0As a position parameter, σx，σyIs a scale parameter of two-dimensional normal distribution.
Preferably, the parameter estimation of the two-dimensional normal distribution function is represented as:
Figure BDA0003082287490000042
Figure BDA0003082287490000043
Figure BDA0003082287490000044
Figure BDA0003082287490000045
Figure BDA0003082287490000046
wherein, c0Is a constant coefficient, c1Is the coefficient of x, c2Is a coefficient of y, c3Is x2Coefficient, c4Is y2Coefficient of performance
Preferably, in step S400, the set value is a peak value of a height value of the two-dimensional gaussian curved surface
Figure BDA0003082287490000051
And (4) doubling.
Compared with the prior art, the beneficial effect that this disclosure brought does:
1. the laser plasma profile representing the vacuum degree can be rapidly and accurately obtained, and a research method and an application basis can be provided for a vacuum switch vacuum detection technology based on a laser plasma imaging technology;
2. the laser plasma profile can be rapidly and accurately obtained no matter what environmental air pressure and radiation intensity the laser plasma is in;
3. the laser plasma profile can be extracted quickly and accurately no matter whether the laser plasma is at any stage of the life cycle.
Drawings
FIG. 1 is a schematic diagram of a system for extracting a laser plasma profile according to one embodiment of the present disclosure;
FIG. 2 is a schematic flow chart of a method for extracting a laser plasma profile according to another embodiment of the present disclosure;
FIG. 3(a) is a matrix of raw image values output by an ICCD camera; fig. 3(b) is a background noise removed image value matrix output by an ICCD camera according to another embodiment of the present disclosure;
FIG. 4(a) is an image of a denoised plasma; FIG. 4(b) is a graph of intensity of light intensity at each pixel in a plasma image; FIG. 4(c) is a two-dimensional Gaussian surface map obtained by fitting; FIG. 4(d) is an extracted plasma profile;
FIG. 5 is a graph of results of extracting laser plasma profiles at different lifetime stages provided by another embodiment of the present disclosure;
FIG. 6 is a graph of laser plasma profile results for different intensities of radiation extracted as provided by another embodiment of the present disclosure;
fig. 7 is a graph of the results of extracting laser plasma profiles at different pressures provided by another embodiment of the present disclosure.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 7 of the accompanying drawings. While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present disclosure is to be determined by the terms of the appended claims.
To facilitate an understanding of the embodiments of the present disclosure, the following detailed description is to be considered in conjunction with the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present disclosure.
In one embodiment, as shown in FIG. 1, a system for extracting a laser plasma profile, comprises:
a plasma generating unit which generates plasma by transmitting laser pulses along a first optical path and irradiating a vacuum chamber;
the imaging unit is used for capturing the plasma which returns along the first optical path and continues to be transmitted along the second optical path so as to obtain a first plasma image;
and the image processing unit is used for processing the first laser plasma image to obtain a second laser plasma image and extracting the profile of the laser plasma from the second laser plasma image.
In the prior art, because the size of the plasma profile can only be described qualitatively by human eyes, the identification of the plasma profile is not only time-consuming but also not high in accuracy, the scheme disclosed by the invention can quantitatively describe the plasma ground profile and the area size of the plasma profile, and the plasma profile can be extracted within one second and given by inputting the plasma image into a program internally provided with the method.
In another embodiment, the plasma generation unit includes a pulse laser, a dichroic mirror, a first plano-convex lens, and a vacuum chamber, which are sequentially disposed along the first optical path.
In another embodiment, the imaging unit includes a second plano-convex lens and an ICCD camera arranged in sequence along the second optical path.
In another embodiment, the image processing unit includes:
the first processing subunit is used for removing background noise on the first laser plasma image to obtain a second laser plasma image;
the second processing subunit is used for performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
and the extraction unit is used for extracting and obtaining all contour points of the laser plasma by marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface.
In another embodiment, as shown in fig. 2, the present disclosure also provides a method of extracting a laser plasma profile, comprising the steps of:
s100: shooting to obtain a first laser plasma image;
s200: removing background noise on the first laser plasma image to obtain a second laser plasma image;
in this step, the pixels of the light-sensitive surface of the ICCD camera are 1024 × 1024. The output result of the ICCD camera is a 1024 × 1024 matrix of values, as shown in fig. 3(a), each value in the matrix represents the intensity value of the laser plasma radiation detected by the pixel, and the magnitude of the value directly reflects the magnitude of the intensity of the laser plasma radiation detected by the pixel, so that it is defined as the photosensitive intensity value of the pixel of the laser plasma image in the present disclosure. Because of the inherent background noise of the ICCD camera, the background noise-removed photosensitive intensity value can be obtained by subtracting the inherent background noise of the ICCD camera from the result output by the ICCD, and the intensity of laser plasma radiation can be reflected better. Illustratively, in this embodiment, the maximum value of the background noise value of the ICCD camera is 150, and the light sensitivity intensity value of a certain pixel is 3881, then the background-free light sensitivity intensity value of the pixel is 3731; another point has a light sensitivity value of 109, which is smaller than the maximum value of the noise floor, and the background light sensitivity value of the point is 0, as shown in fig. 3 (b).
S300: performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
s400: and marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface, wherein the marked pixel points are contour points of the laser plasma.
In this embodiment, in a normal case, the lifetime of the laser plasma under a high vacuum condition is only several hundred nanoseconds to several microseconds, and the shortest exposure time of the ICCD camera can reach 2 ns; and connecting the ICCD camera with a computer, inputting a laser plasma image shot by the ICCD camera into a program for presetting the method for extracting the laser plasma profile, and outputting the laser plasma profile after the preset program processing. The method can quickly and accurately extract the laser plasma profile, provides a method for researching the dynamic evolution of the laser plasma under vacuum, and lays a foundation for developing a vacuum degree detection method of a vacuum switch based on a laser-induced plasma imaging technology.
In another embodiment, step S300 includes the steps of:
s301: describing the distribution of the photosensitive intensity values of all pixel points on the second laser plasma image by using a two-dimensional normal distribution function;
in this step, since the gaussian mode pulse laser is used in this embodiment, the laser energy is gaussian distributed (i.e., two-dimensionally normally distributed) in the cross section of the laser propagation direction, and thus the generated laser plasma radiation is also gaussian distributed in the cross section of the laser propagation direction, i.e., exponentially decays from the center of the radiation to both sides. Therefore, when the laser plasma is imaged from the laser incidence direction, the obtained de-noising photosensitive intensity value is also in gaussian distribution (namely, two-dimensional normal distribution), and can be described by using a two-dimensional normal distribution function, wherein the two-dimensional normal distribution function is expressed as:
Figure BDA0003082287490000091
wherein x and y are position coordinates of pixel points, f (x and y) is the photosensitive intensity value of the pixel points of the de-noised laser plasma image (x and y), G is the amplitude of two-dimensional normal distribution, and x is the amplitude of the two-dimensional normal distribution0，y0Position parameter, σ, being two-dimensionally normally distributedx，σyIs a scale parameter of two-dimensional normal distribution.
S302: calculating a criterion function of the two-dimensional normal distribution function;
in this step, the number of pixels of the ICCD photosurface used in this embodiment is 1024 × 1024, and the background-removed photosensing intensity value f (x, y) (x, y is 1, 2, 3.. multidot.1024) conforms to the two-dimensional normal distribution, and a criterion function is given as follows:
Figure BDA0003082287490000101
wherein, (x, y) (x, y is 1, 2, 3., N) is the coordinate of the pixel point, fxyDe-noising the intensity value of the sensitization for the point, G is the amplitude of the normal distribution, x0，y0As a position parameter, σx，σyIs a scale parameter of two-dimensional normal distribution.
At this time, only { x, y, lin (f) needs to be obtainedxy) Binary quadratic minimization fitting of (f) }, so that the fitting error is minimized, with x, y as arguments, lin (f)xy) As a dependent variable, the criterion function can also be expressed as:
linfxy＝c0+c1x+c2y+c3x2+c4y2
wherein, c0Is a constant coefficient, c1Is the coefficient of x, c2Is a coefficient of y, c3Is x2Coefficient, c4Is y2And (4) the coefficient.
S303: and calculating parameter estimation of the criterion function, namely obtaining the two-dimensional Gaussian curved surface.
In this step, the parameter estimation of the criterion function is expressed as:
Figure BDA0003082287490000102
Figure BDA0003082287490000103
Figure BDA0003082287490000111
Figure BDA0003082287490000112
Figure BDA0003082287490000113
wherein, c0Is a constant coefficient, c1Is the coefficient of x, c2Is a coefficient of y, c3Is x2Coefficient, c4Is y2Coefficient of performance
In another embodiment, in step S400, the set value is a peak value of the height value of the two-dimensional gaussian surface
Figure BDA0003082287490000114
And (4) doubling.
In this embodiment, the pulsed laser used is a Gaussian pulsed laser, and the boundary of the cross section of the Gaussian pulsed laser in the propagation direction is generally selected to be at peak intensity
Figure BDA0003082287490000115
The boundary of the laser plasma is also taken as the peak intensity of the fitted surface in this disclosure
Figure BDA0003082287490000116
And (4) doubling.
The technical solution proposed by the present disclosure will be described below with reference to fig. 4(a) to 4 (d). FIG. 4(a) shows the result of an ICCD camera; fig. 4(b) is a three-dimensional intensity graph of a laser plasma image, wherein x and y axes represent the serial numbers of pixel points, and z axis represents the denoising photosensitive intensity value of each pixel point, so that it can be seen that the denoising photosensitive intensity value of each pixel point conforms to two-dimensional normal distribution; FIG. 4(c) shows the noise reduction effectThe light intensity value three-dimensional intensity graph is subjected to Gaussian surface fitting to obtain a two-dimensional Gaussian surface, namely the denoising photosensitive intensity value is subjected to two-dimensional normal distribution fitting, and the two-dimensional normal distribution surface is drawn according to the fitting result, namely the two-dimensional Gaussian surface; selecting the height value (i.e. z-axis value) of the Gaussian curve as the peak value of the height value
Figure BDA0003082287490000121
The multiplied points are laser plasma contour boundaries, and coordinates (x, y) are extracted; as in the present example, the peak height value of the Gaussian surface obtained by fitting is 483.28141
Figure BDA0003082287490000122
65.40503, selecting a point with background photosensitive intensity value of 65.40503 as a boundary point and extracting coordinates (x, y) according to a row or a column, and selecting the most similar point as the boundary point if the row or the column has no accurate value of 65.40503, wherein the selection results are as follows: (373, 276), (353, 340), etc.; the laser plasma profile boundary points are marked on the laser plasma image, resulting in fig. 4 (d).
In the following, it is verified that the technical scheme of the present disclosure can extract the laser plasma profile under different conditions by combining with specific embodiments.
The PIMAX3 ICCD camera manufactured by Princeton Instruments is used, the minimum time resolution is 2ns, namely the minimum exposure gate width is 2ns, and the maximum gate width can reach the second level. The laser is preferably a Brilliant Eazy Nd: YAG pulse laser, can compress the pulse width of laser pulse to 5ns through the mode of adjusting Q, the maximum laser energy is 150 mJ. Pulsed laser generated by a laser penetrates through the dichroic mirror and is focused on a target material in the vacuum chamber through a BK7 plano-convex lens with the focal length of 150mm, the target material generates laser-induced plasma under the bombardment of high-energy pulsed laser, and the laser plasma is collimated by the BK7 plano-convex lens and then reflected by the dichroic mirror to be imaged on the ICCD camera. The gate width of the ICCD camera is set to be 100ns, and the gain is 100; the energy of the laser is 10mJ, the pulse width is 5ns, the ICCD is triggered by a Q-switch out signal of the laser to be exposed, the exposure starting time is controlled by adjusting the delay of the ICCD camera relative to an internal clock T0, and then the ICCD camera is controlled to shoot laser plasmas at different service life stages. The pulse laser bombards a preset target material in the vacuum cavity to generate laser-induced plasma, and the laser plasma is collimated by a BK7 plano-convex lens with the focal length of 150mm and then reflected by a dichroic mirror to be imaged on an ICCD camera.
In order to verify that the technical scheme of the present disclosure can extract the laser plasma profiles at different lifetime stages, the present embodiment extracts laser plasma profiles at four lifetime stages of 50ns, 150ns, 350ns, and 450 ns. The results of the laser plasma profiles extracted in the four life stages in this embodiment are shown in fig. 5, and the gray circles are the laser plasma profiles extracted in this embodiment, and it is obvious that the technical scheme provided by the present disclosure can well extract the laser plasma profiles in different life stages.
In order to verify that the technical scheme of the present disclosure can extract the profiles of the laser plasmas with different radiation intensities, the present disclosure extracts the profiles of the laser plasmas under the three intensity conditions of weak plasma radiation, medium plasma radiation and strong plasma radiation, the result of the extracted profiles of the laser plasmas with different radiation intensities is shown in fig. 6, and the gray circles are the extracted profiles of the laser plasmas, so that it is obvious that the technical scheme of the present disclosure can well extract the profiles of the laser plasmas with different radiation intensities.
In order to verify that the technical scheme of the disclosure can extract laser plasma profiles under different air pressures, the disclosure also extracts 10-3Pa，10-2Pa，10-1Pa，100Pa，101Pa，102Pa，103Pa，104Pa，105Pa laser plasma profile at nine gas pressures. The extracted laser plasma profiles under different air pressures are shown in fig. 7, and the gray circles are the laser plasma profiles extracted in this embodiment, so that it is obvious that the technical scheme of the present disclosure can well extract the laser plasma profiles under different air pressures.

Claims (10)

1. A system for extracting a laser plasma profile, comprising:
a plasma generating unit which generates plasma by transmitting laser pulses along a first optical path and irradiating a vacuum chamber;
the imaging unit is used for capturing the plasma which returns along the first optical path and continues to be transmitted along the second optical path so as to obtain a first laser plasma image;
and the image processing unit is used for processing the first laser plasma image to obtain a second laser plasma image and extracting the profile of the laser plasma from the second laser plasma image.
2. The system of claim 1, wherein preferably, the plasma generating unit comprises a pulse laser, a dichroic mirror, a first plano-convex lens and a vacuum chamber arranged in sequence along the first optical path.
3. The system of claim 1, wherein the imaging unit comprises a second plano-convex lens and an ICCD camera arranged in sequence along a second optical path.
4. The system of claim 1, wherein the image processing unit comprises:
the first processing subunit is used for removing background noise on the first laser plasma image to obtain a second laser plasma image;
the second processing subunit is used for performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
and the extraction unit is used for extracting and obtaining all contour points of the laser plasma by marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface.
5. A method of extracting a laser plasma profile, comprising the steps of:
s100: shooting to obtain a first laser plasma image;
s200: removing background noise on the first laser plasma image to obtain a second laser plasma image;
s300: performing Gaussian surface fitting on the photosensitive intensity value of each pixel point on the second laser plasma image to obtain a two-dimensional Gaussian surface;
s400: and marking all pixel points with Z-axis coordinate values as set values on the two-dimensional Gaussian curved surface, wherein the marked pixel points are contour points of the laser plasma.
6. The method of claim 1, wherein step S300 comprises the steps of:
s301: describing the radiation intensity value distribution of each pixel point on the second laser plasma image by using a two-dimensional normal distribution function;
s302: calculating a criterion function of the two-dimensional normal distribution function;
s303: and calculating parameter estimation of the criterion function, namely obtaining the two-dimensional Gaussian curved surface.
7. The method of claim 6, wherein the two-dimensional normal distribution function is represented as:
Figure DEST_PATH_BDA0003082287490000031
wherein x and y are position coordinates of pixel points, f (x and y) is the photosensitive intensity value of the pixel points of the de-noised laser plasma image (x and y), G is the amplitude of two-dimensional normal distribution, and x is the amplitude of the two-dimensional normal distribution0，y0Position parameter, σ, being two-dimensionally normally distributedx，σyIs a scale parameter of two-dimensional normal distribution.
8. The method of claim 6, wherein the criterion function is represented as:
Figure FDA0003082287480000022
wherein, (x, y) (x, y is 1, 2, 3., N) is the coordinate of the pixel point, fxyDe-noising the intensity value of the sensitization for the point, G is the amplitude of the normal distribution, x0，y0As a position parameter, σx，σyIs a scale parameter of two-dimensional normal distribution.
9. The method of claim 6, wherein the two-dimensional Gaussian surface parameter estimate is expressed as:
Figure FDA0003082287480000031
Figure FDA0003082287480000032
Figure FDA0003082287480000033
Figure FDA0003082287480000034
Figure DEST_PATH_BDA0003082287490000113
wherein, c0Is a constant coefficient, c1Is the coefficient of x, c2Is a coefficient of y, c3Is x2Coefficient, c4Is y2And (4) the coefficient.
10. The method according to claim 5, wherein the set value is the peak value of the height value of the two-dimensional Gaussian surface in step S400
Figure FDA0003082287480000036
And (4) doubling.
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