CN109115125B - Method for digitally representing surface topography of laser-damaged silicon-based or germanium-based optical element - Google Patents
Method for digitally representing surface topography of laser-damaged silicon-based or germanium-based optical element Download PDFInfo
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- CN109115125B CN109115125B CN201811092972.2A CN201811092972A CN109115125B CN 109115125 B CN109115125 B CN 109115125B CN 201811092972 A CN201811092972 A CN 201811092972A CN 109115125 B CN109115125 B CN 109115125B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
Abstract
The invention provides a digitalized characterization method for the surface topography of a laser-damaged silicon-based or germanium-based optical element, which aims to solve the problems that the existing method can only qualitatively describe the damaged topography, the characterization result is not enough to support the output characteristic analysis of a subsequent system, or the damaged surface information can be completely acquired but the data volume is overlarge. Firstly, carrying out three-dimensional topography test on a damaged surface of an optical element to obtain complete three-dimensional surface data, and then carrying out two-dimensional spatial filtering by utilizing a Gaussian function; fitting the curve in the space cross section of the damaged shape curved surface by utilizing the sinc-like function to obtain a fitting target function and a parameter solution set U1、U2、U3And U4(ii) a Then in parameter set U1、U2、U3、U4Intermediate random construction parameter vector [ A0，B0，C0，D0]And substituting the parameter vector into the fitting objective function to obtain a curve capable of representing the damage morphology. The invention only needs a small amount of parameters to approximate and completely characterize the complex three-dimensional damage appearance characteristics.
Description
Technical Field
The invention relates to a digitalized characterization method for the surface topography of a laser-damaged silicon-based or germanium-based optical element.
Background
For a high-energy laser system and a photoelectric system, optical elements in the system are easily damaged in the strong laser action process, and the performance of the system is further influenced. At present, in the aspect of analyzing and evaluating the surface topography characteristics of a laser-damaged silicon-based or germanium-based optical element, three methods are available: the first method is to measure by using a Normarski microscope or an atomic force microscope, qualitatively describe the damage morphology by using geometric morphology, and the common description types comprise miro-pits, shell-like cracks, crater and the like; the second method is characterized by using the damage diameter and the damage depth; and thirdly, the surface is measured in three dimensions by using a laser confocal microscope or a white light interferometer to obtain complete three-dimensional surface data.
The above methods all have certain disadvantages: the first method can only describe the damage morphology qualitatively, and the qualitative description result cannot be applied to the output characteristic analysis of a subsequent system; the second method only characterizes the damage morphology from two dimensions of the damage diameter and the damage depth, and the characterization result is not enough to support the output characteristic analysis of a subsequent system; the third method can completely acquire and characterize the surface topography of the damaged optical element, but the data size is too large, which causes inconvenience for subsequent analysis and utilization.
Disclosure of Invention
In order to solve the technical problems that the existing evaluation method for the surface topography characteristics of the laser-damaged silicon-based or germanium-based optical element can only qualitatively describe the damaged topography, the characterization result is not enough to support the subsequent system output characteristic analysis, or the data volume is too large although the damaged surface information can be completely acquired, the invention provides a digitalized characterization method for the surface topography of the laser-damaged silicon-based or germanium-based optical element, which can more completely characterize the complicated three-dimensional damaged topography characteristics by using a small number of parameters, and the characterization result can be used for the system output characteristic analysis after damage on one hand, and can also guide the damage repair topography design theoretically and guide the improvement and perfection of the repair process on the other hand.
The invention has the following inventive concept:
firstly, carrying out three-dimensional topography test on the damaged surface of an optical element to obtain complete three-dimensional surface data, and then carrying out two-dimensional spatial filtering by utilizing a Gaussian function; because the common laser spots are Gaussian spots and the two-dimensional distribution of the common laser spots in a far field is a Bessel function, a quasi-sinc function is used for fitting a curve in a space section of the damaged shape curved surface to obtain a fitting target function and a parameter solution set U1、U2、U3And U4(ii) a Parameter set U subsequently constructed1、U2、U3、 U4In the corresponding random generation of A0、B0、C0、D0Constructing a parameter vector [ A ]0，B0，C0，D0]The parameter vector [ A ] is set0，B0，C0，D0]And substituting the fitting objective function to construct a curve capable of representing the damage morphology.
If the surface damage is caused by the super-Gaussian spots, the surface damage can be fitted by using a rectangular step function, and at the moment, only two corresponding parameters are needed to form a parameter set.
The technical solution of the invention is as follows:
the method for digitally characterizing the surface topography of the laser-damaged silicon-based or germanium-based optical element is characterized by comprising the following steps of:
1) obtaining three-dimensional topography data
Carrying out three-dimensional shape test on the optical element to be characterized damaged by laser irradiation to obtain complete three-dimensional shape data;
2) obtaining a damage shape curved surface:
performing two-dimensional Gaussian filtering on the three-dimensional shape data to obtain a damage shape curved surface;
3) obtaining transversal data
3.1) establishing a space coordinate system by taking the center of a damaged area of the optical element to be characterized as an origin O, taking a plane passing through the origin O and parallel to the bottom surface of the optical element to be characterized as an xOy plane, and taking a direction passing through the origin O and parallel to the thickness direction of the optical element to be characterized as a z-axis direction;
3.2) selecting a plane which passes through a z axis and is vertical to an xOy plane and has an included angle theta with the x axis direction, and intersecting the plane with the damage morphology curved surface obtained in the step 2) to obtain section line data corresponding to different theta angles;
4) fitting of parameters
According to different section line data, performing parameter fitting on the section line data by using a quasi-sinc function to obtain a fitting target function:
A. b, C, D is a damage characterization parameter caused by Gaussian spots;
5) constructing a real solution set of parameters
From the fitted objective function, an extremum (A) is selected therefrommin、Amax)、(Bmin、Bmax)、 (Cmin、Cmax) And (D)min、Dmax) Respectively constructing corresponding parameter real number solution sets U1、U2、 U3And U4：
U1＝{x|Amin≤x≤Amax,x∈R}；
U2＝{x|Bmin≤x≤Bmax,x∈R}；
U3＝{x|Cmin≤x≤Cmax,x∈R}；
U4＝{x|Dmin≤x≤Dmax,x∈R}；
6) Constructing a vector of parameters
Parameter real number solution set U constructed based on step 5)1、U2、U3And U4Randomly constructing any set of parameter vectors [ A ]0，B0，C0，D0]Wherein A is0∈U1,B0∈U2,C0∈U3,D0∈U4；
7) Obtaining a characterization curve y0
Using the parameter vector [ A ] constructed in the step 6)0，B0，C0，D0]Substituting the fitting objective function to obtain a characterization curve y capable of representing the surface damage morphology of the optical element to be characterized0：
Further, the three-dimensional shape test in the step 1) is realized by using a laser confocal microscope or a white light interferometer.
The invention also provides another method for digitally characterizing the surface topography of a laser-damaged silicon-based or germanium-based optical element, which is characterized by comprising the following steps of:
1) obtaining three-dimensional topography data
Carrying out three-dimensional shape test on the optical element to be characterized damaged by laser irradiation to obtain complete three-dimensional shape data;
2) obtaining a damage shape curved surface:
performing two-dimensional Gaussian filtering on the three-dimensional shape data to obtain a damage shape curved surface;
3) obtaining transversal data
3.1) establishing a space coordinate system by taking the center of a damaged area of the optical element to be characterized as an origin O, taking a plane passing through the origin O and parallel to the bottom surface of the optical element to be characterized as an xOy plane, and taking a direction passing through the origin O and parallel to the thickness direction of the optical element to be characterized as a z-axis direction;
3.2) selecting a plane which passes through a z axis and is vertical to an xOy plane and has an included angle theta with the x axis direction, and intersecting the plane with the damage morphology curved surface obtained in the step 2) to obtain section line data corresponding to different theta angles;
4) fitting of parameters
According to different section line data, performing parameter fitting on the section line data by using a rectangular step function to obtain a fitting target function:
m, N characterization parameter of damage caused by flat-topped light spot, R0Is the radius of the lesion area;
5) constructing a real solution set of parameters
Selecting extremum (M) from the fitted objective function obtained in step 4)min、Mmax)、 (Nmin、Nmax) Respectively constructing corresponding parameter real number solution sets Q1、Q2：
Q1＝{x|Mmin≤x≤Mmax,x∈R}；
Q2＝{x|Nmin≤x≤Nmax,x∈R}；
6) Constructing a vector of parameters
Parameter real number solution set Q constructed based on step 5)1、Q2Randomly constructing any set of parameter vectors [ M ]0，N0]Wherein M is0∈Q1,N0∈Q2；
7) Obtaining a characterization curve y0
Using the parameter vector [ M ] constructed in the step 6)0，N0]Substituting the fitting objective function to obtain a characterization curve y capable of representing the surface damage morphology of the optical element to be characterized0：
Further, the three-dimensional shape test in the step 1) is realized by using a laser confocal microscope or a white light interferometer.
The invention has the beneficial effects that:
1. the method is simple and reliable in principle, a three-dimensional measurement result of discrete points does not need to be constructed, only a few of characterization curves constructed by parameters are needed to approximate and completely characterize the complex three-dimensional damage morphology characteristics, and the characterization results can be used for calculating a downstream light field of a system and guiding the design of damage repairing morphology.
2. Compared with the method for qualitatively describing the damage morphology by using the geometric morphology and the method for representing the damage diameter and the damage depth, which is mentioned in the background technology, the method can represent the damage morphology by using a specific mathematical model, so that the subsequent usability of the damage morphology is improved, and compared with the method for obtaining the surface damage morphology by using the three-dimensional measurement, which is mentioned in the background technology, the method can greatly reduce the data volume in the subsequent analysis.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the spatial coordinates and constructed sectional lines constructed on the surface of a damaged optical element according to the present invention;
FIG. 3 shows the variation range of the fitting parameter A, B, C, D where θ is in the range of 0 to 180 degrees in the embodiment of the present invention, where a is the variation range of the parameter A, B is the variation range of the parameter B, C is the variation range of the parameter C, and D is the variation range of the parameter D;
FIG. 4 is a characterization curve y obtained in accordance with an embodiment of the present invention0；
FIG. 5 is a graph showing RMS (root mean square) values of randomly generated damage features and line-cutting errors of theta in the range of 0 to 180 degrees according to an embodiment of the present invention;
Detailed Description
The invention will be further explained with reference to the drawings.
Referring to fig. 1, the method for digitally characterizing the surface topography of a laser-damaged silicon-based or germanium-based optical element provided by the invention specifically comprises the following steps:
step 1: acquiring three-dimensional shape data:
under the condition of ensuring the stability of the testing environment (namely, non-vibration condition), a laser confocal microscope or a white light interferometer is utilized to carry out three-dimensional shape testing on an optical element (a silicon-based optical element or a germanium-based optical element) to be characterized, which is damaged by laser irradiation, so as to obtain complete three-dimensional shape data.
Step 2: obtaining a damage shape curved surface:
and (3) performing two-dimensional Gaussian filtering processing on the three-dimensional topography data acquired in the step (1) by using a Gaussian filter specified by the ISO11562 standard to obtain a damage topography curved surface, namely a damage area shown in FIG. 2.
And step 3: acquiring transversal data:
and 3.1, establishing a space coordinate system by taking the center of the damaged area of the optical element to be represented as an origin O, taking the plane passing through the origin O and parallel to the bottom surface of the optical element to be represented as an xOy plane, and taking the thickness direction of the optical element passing through the origin O and parallel to the thickness direction of the optical element to be represented as a z-axis direction.
And 3.2, selecting a plane which is perpendicular to the xOy plane through the z axis and has an included angle theta with the x axis direction, and intersecting the plane with the damage morphology curved surface obtained in the step 2) to obtain section line data corresponding to different theta angles.
And 4, step 4: parameter fitting:
the following two cases are divided:
situation one, the laser spot is a Gaussian spot
According to the section line data corresponding to different theta angles, parameter fitting is respectively carried out on the section line data by utilizing a quasi-sinc function to obtain a fitting objective function:
wherein A, B, C, D is a lesion characterization parameter;
case two, the laser spot is a flat-top spot (i.e. super-Gaussian spot)
According to different section line data, performing parameter fitting on the section line data by using a rectangular step function to obtain a fitting target function:
m, N characterization parameter of damage caused by flat-topped light spot, R0Is the radius of the lesion area;
and 5: constructing a parameter real number solution set:
situation one, the laser spot is a Gaussian spot
Selecting extremum (A) from the fitted objective function obtained in step 4min、Amax)、 (Bmin、Bmax)、(Cmin、Cmax) And (D)min、Dmax) Respectively constructing corresponding parameter sets U1、U2、U3And U4：
U1＝{x|Amin≤x≤Amax,x∈R}；
U2＝{x|Bmin≤x≤Bmax,x∈R}；
U3＝{x|Cmin≤x≤Cmax,x∈R}；
U4＝{x|Dmin≤x≤Dmax,x∈R}；
Case two, the laser spot is a flat-top spot
Selecting extremum (M) from the fitted objective function obtained in step 4min、Mmax)、 (Nmin、Nmax) Respectively constructing corresponding parameter real number solution sets Q1、Q2：
Q1＝{x|Mmin≤x≤Mmax,x∈R}；
Q2＝{x|Nmin≤x≤Nmax,x∈R}；
Step 6: constructing a vector of parameters
Situation one, the laser spot is a Gaussian spot
Parameter real number solution set U constructed based on step 51、U2、U3And U4Randomly constructing a set of parameter vectors [ A ]0，B0，C0，D0]Wherein A is0∈U1,B0∈U2,C0∈U3,D0∈ U4；
Case two, the laser spot is a flat-top spot
Parameter real number solution set Q constructed based on step 5)1、Q2Randomly constructing any set of parameter vectors [ M ]0，N0]Wherein M is0∈Q1,N0∈Q2；
And 7: obtaining a characterization curve y0
Situation one, the laser spot is a Gaussian spot
The parameter vector [ A ]0，B0，C0，D0]Substituting the fitting objective function to obtain a characterization curve y of the surface damage morphology characteristics of the optical element to be characterized0：
Case two, the laser spot is a flat-top spot
Using the parameter vector [ M ] constructed in the step 6)0，N0]Substituting the fitting objective function to obtain a characterization curve y capable of representing the surface damage morphology of the optical element to be characterized0：
The following experiments were carried out by way of specific examples, with reference to FIGS. 3-5:
for the Gaussian spots, the method is adopted to carry out digital characterization on the damaged surface morphology of the silicon-based optical element, and the result is as follows:
according to the method, the original three-dimensional surface data are obtained in the step 1, then the original three-dimensional surface data are processed in the steps 2-4, the fitting parameters of theta in the range of 0-180 degrees are obtained, and extreme values are selected, wherein the extreme values are shown in the table 1 specifically:
TABLE 1
| A | B | C | D | |
| Maximum value | 2.14×10-5 | 2.4×10-5 | 34974.62 | 94118.05 |
| Minimum value | 2.04×10-5 | 4.17×10-6 | 26748.10 | 12312.22 |
Respectively constructing parameter real number solution set U by using parameters in Table 11、U2、U3And U4：：
U1＝{x|2.04×10-5≤x≤2.14×10-5,x∈R}；
U2＝{x|4.17×10-6≤x≤2.4×10-5,x∈R}；
U3＝{x|26748.10≤x≤34974.62,x∈R}；
U4＝{x|12312.22≤x≤94118.05,x∈R}；
By means of U1、U2、U3、U4Constructing a random parameter vector [ 2.125X 10 ]-5，9.9944 ×10-5，26940.36，67424.62]。
Substituting the parameter vector into the sine function-like expression to obtain a damage morphology characteristic curve y0Calculating to obtain y0RMS value of error between any of the different angle sections, as shown in figure 5. From FIG. 5, it can be seen that the characterization curve y obtained by the present invention0Deviation from actual damage transversal is basically 10-5And the magnitude can approximate and completely represent the damage appearance.
Claims (4)
1. The method for digitally characterizing the surface topography of a laser-damaged silicon-based or germanium-based optical element is characterized by comprising the following steps of:
1) obtaining three-dimensional topography data
Carrying out three-dimensional shape test on the optical element to be characterized damaged by laser irradiation to obtain complete three-dimensional shape data;
2) obtaining a damage shape curved surface:
performing two-dimensional Gaussian filtering on the three-dimensional shape data to obtain a damage shape curved surface;
3) obtaining transversal data
3.1) establishing a space coordinate system by taking the center of a damaged area of the optical element to be characterized as an origin O, taking a plane passing through the origin O and parallel to the bottom surface of the optical element to be characterized as an xOy plane, and taking a direction passing through the origin O and parallel to the thickness direction of the optical element to be characterized as a z-axis direction;
3.2) selecting a plane which passes through a z axis and is vertical to an xOy plane and has an included angle theta with the x axis direction, and intersecting the plane with the damage morphology curved surface obtained in the step 2) to obtain section line data corresponding to different theta angles;
4) fitting of parameters
According to different section line data, performing parameter fitting on the section line data by using a quasi-sinc function to obtain a fitting target function:
A. b, C, D is a damage characterization parameter caused by Gaussian spots;
5) constructing a real solution set of parameters
From the fitted objective function, an extremum (A) is selected therefrommin、Amax)、(Bmin、Bmax)、(Cmin、Cmax) And (D)min、Dmax) Respectively constructing corresponding parameter real number solution sets U1、U2、U3And U4：
U1＝{x|Amin≤x≤Amax,x∈R}；
U2＝{x|Bmin≤x≤Bmax,x∈R}；
U3＝{x|Cmin≤x≤Cmax,x∈R}；
U4＝{x|Dmin≤x≤Dmax,x∈R}；
6) Constructing a vector of parameters
Parameter real number solution set U constructed based on step 5)1、U2、U3And U4Randomly constructing any set of parameter vectors [ A ]0，B0，C0，D0]Wherein A is0∈U1,B0∈U2,C0∈U3,D0∈U4；
7) Obtaining a characterization curve y0
Using the parameter vector [ A ] constructed in the step 6)0，B0，C0，D0]Substituting the fitting objective function to obtain a characterization curve y capable of representing the surface damage morphology of the optical element to be characterized0：
2. The method for digitally characterizing the surface topography of a laser-damaged silicon-based or germanium-based optical element according to claim 1, wherein: the three-dimensional shape test in the step 1) is realized by using a laser confocal microscope or a white light interferometer.
3. The method for digitally characterizing the surface topography of a laser-damaged silicon-based or germanium-based optical element is characterized by comprising the following steps of:
1) obtaining three-dimensional topography data
Carrying out three-dimensional shape test on the optical element to be characterized damaged by laser irradiation to obtain complete three-dimensional shape data;
2) obtaining a damage shape curved surface:
performing two-dimensional Gaussian filtering on the three-dimensional shape data to obtain a damage shape curved surface;
3) obtaining transversal data
3.1) establishing a space coordinate system by taking the center of a damaged area of the optical element to be characterized as an origin O, taking a plane passing through the origin O and parallel to the bottom surface of the optical element to be characterized as an xOy plane, and taking a direction passing through the origin O and parallel to the thickness direction of the optical element to be characterized as a z-axis direction;
3.2) selecting a plane which passes through a z axis and is vertical to an xOy plane and has an included angle theta with the x axis direction, and intersecting the plane with the damage morphology curved surface obtained in the step 2) to obtain section line data corresponding to different theta angles;
4) fitting of parameters
According to different section line data, performing parameter fitting on the section line data by using a rectangular step function to obtain a fitting target function:
m, N characterization parameter of damage caused by flat-topped light spot, R0Is the radius of the lesion area;
5) constructing a real solution set of parameters
Selecting extremum (M) from the fitted objective function obtained in step 4)min、Mmax)、(Nmin、Nmax) Respectively constructing corresponding parameter real number solution sets Q1、Q2：
Q1＝{x|Mmin≤x≤Mmax,x∈R}；
Q2＝{x|Nmin≤x≤Nmax,x∈R}；
6) Constructing a vector of parameters
Parameter real number solution set Q constructed based on step 5)1、Q2Randomly constructing any set of parameter vectors [ M ]0，N0]Wherein M is0∈Q1,N0∈Q2；
7) Obtaining a characterization curve y0
Using the parameter vector [ M ] constructed in the step 6)0，N0]Substituting the fitting objective function to obtain a characterization curve y capable of representing the surface damage morphology of the optical element to be characterized0：
4. The method for digitally characterizing the surface topography of a laser damaged silicon-based or germanium-based optical element according to claim 3, wherein: the three-dimensional shape test in the step 1) is realized by using a laser confocal microscope or a white light interferometer.
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