Characteristic analysis method of micropore inner wall dark field microscopic imaging system

Abstract

The invention provides a method for analyzing characteristics of a micropore inner wall dark field microscopic imaging system, belongs to the technical field of dark field microscopic measurement, and solves the problem that the characteristics of the dark field microscopic imaging system are changed due to the fact that the edge of a micropore shields illumination and detection light beams when the inner wall of the micropore is measured by adopting a dark field microscopic measurement technology. Comprising the following steps: step 1, analyzing a micropore inner wall dark field microscopic imaging process, and determining illumination apertures and detection aperture pupil functions of a micropore inner wall dark field microscopic imaging system under different micropore detection depths H; 2, determining the upper and lower limits of integration based on the obtained detection aperture pupil function, and constructing a shielding aperture point spread function suitable for the micropore inner wall dark field microscopic imaging system under different micropore detection depths H; and 3, performing Fourier transform on the calculated spread functions of the illumination aperture and the detection aperture of the micropore inner wall dark field microscopic imaging system to obtain a transfer function, and further analyzing the spatial domain and frequency domain imaging characteristics of the system.

Description

Technical Field

[0001] The invention relates to a method for analyzing characteristics of a dark-field microscopic imaging system of a micropore inner wall, and belongs to the technical field of dark-field microscopic measurement. Background Art

[0002] Fuel nozzles and turbine blades are key components of aircraft engines and gas turbines. Both fuel nozzle orifices and turbine blade air film holes are spatially distributed micropores. High-precision three-dimensional topography measurement of micropores is crucial for improving the performance of aircraft engines and gas turbines. Dark-field microscopy is an effective means of measuring the three-dimensional topography of micropore inner walls. When using dark-field microscopy to measure the inner walls of micropores, the occlusion of the illumination and detection beams by the edges of the micropores causes changes in the characteristics of the dark-field microscopy imaging system. Therefore, a method for analyzing the characteristics of dark-field microscopy imaging systems for micropore inner walls is needed to explore the limits of dark-field microscopy imaging capabilities and provide guidance for the design and further optimization of dark-field microscopy imaging systems for micropore inner walls. Summary of the Invention

[0003] The present invention aims to solve the problem that when measuring the inner wall of a micropore using dark-field microscopy measurement technology, the micropore edge blocks the illumination and detection beams, resulting in changes in the characteristics of the dark-field microscopy imaging system. A method for analyzing the characteristics of the dark-field microscopy imaging system of the inner wall of a micropore is proposed.

[0004] The technical solution adopted by the present invention to solve the above problems is: the present invention comprises the following steps:

[0005] Step 1: Analyze the dark field microscopy imaging process of the micropore inner wall and determine the illumination aperture and detection aperture pupil function of the dark field microscopy imaging system of the micropore inner wall at different micropore detection depths H;

[0006] Step 2: Determine the upper and lower limits of the integral based on the obtained detection aperture pupil function, and construct the occlusion aperture point spread function suitable for the dark field microscopy imaging system of the micropore inner wall at different micropore detection depths H;

[0007] Step 3: Perform Fourier transform on the calculated point spread functions of the illumination aperture and detection aperture of the dark-field microscopy imaging system of the micropore inner wall to obtain the transfer function, and then analyze the spatial and frequency domain imaging characteristics of the system.

[0008] Furthermore, in step 1, the optical axis of the dark field microscopic imaging system of the inner wall of the micropore is coaxial with the edge of one side of the micropore, the optical axis is perpendicular to the micropore, and the illumination is semi-aperture, and the diameter of the micropore is D.

[0009] Further, for the occlusion relationship between the other side edge of the micro-hole and the effective illumination and detection apertures in step 1, objective lenses are set at three positions of the micro-hole detection depths H1, H2, and H3. The micro-hole detection depth corresponding to position 1 is H1, and the other side edge of the micro-hole at this position does not occlude the effective illumination and detection apertures, that is, H1tanθ1 < D. The micro-hole detection depth corresponding to position 2 is H2, and the micro-hole detection depth corresponding to position 3 is H3. The other side edges of the micro-holes corresponding to positions 2 and 3 occlude the effective illumination and detection apertures, that is, H2tanθ2 = D, H3tanθ3 > D. The effective illumination and detection apertures are circular. Here, θ is the angle between the semi-aperture illumination path and one side edge of the micro-hole. At position 2, the detection aperture is inscribed in the effective illumination range.

[0010] Further, determining the illumination aperture and detection aperture pupil functions of the dark-field microscopic imaging system of the micro-hole inner wall at different micro-hole detection depths H in step 1 specifically includes:

[0011] Calculating the radius r of the circle where the micro-hole is mapped to the pupil plane according to the geometric relationship between the micro-hole projected onto the pupil plane, and combining with the pupil plane radius a to calculate the pupil function P(ξ,η)1 at position 1 and the pupil function P(ξ,η)2 at positions 2 and 3;

[0012] The calculation formula for the radius r of the circle where the micro-hole is mapped to the pupil plane is:

[0013] r = dD / 2H (1);

[0014] In formula (1), d is the imaging distance of the microscopic system;

[0015] The calculation formula for the pupil function P(ξ,η)1 at position 1 is:

[0016]

[0017] The calculation formula for the pupil function P(ξ,η)2 at positions 2 and 3 is: <000**********8>

[0018]

[0019] Further, constructing the occlusion aperture point spread function for the dark-field microscopic imaging system of the micro-hole inner wall at position 1 in step 2 specifically includes:

[0020] The moon-shaped occlusion formed by the illumination beam in the detection aperture is divided into two bow-shaped integral sums to obtain the occlusion aperture point spread function h(x,y)1 for the dark field microscopy imaging system of the micropore inner wall at position 1. The boundary point x0 of the two bow-shaped areas is solved to obtain the upper and lower limits of the effective integral aperture area, and then substituted into formula (4) to obtain the point spread function calculation result when the edge of the other side of the micropore at position 1 does not form an occlusion on the illumination and detection apertures;

[0021] The calculation formula of the obstruction aperture point spread function h(x,y)1 for the dark field microscopy imaging system of the micropore inner wall at position 1 is:

[0022]

[0023] The calculation formula of the arcuate area dividing point x0 is:

[0024]

[0025] The upper and lower limits of the effective integral aperture area are calculated as follows:

[0026]

[0027] Furthermore, the obstruction aperture point spread function for the micropore inner wall dark field microscopy imaging system constructed at positions 2 and 3 in step 2 specifically includes:

[0028] According to the geometric relationship of the microhole projection to the pupil plane calculated by formula (1), the circle formed by the effective illumination is integrated to obtain the obstruction aperture point spread function h(x,y)2 for the microhole inner wall dark field microscopy imaging system at positions 2 and 3;

[0029] The calculation formula of the obstruction aperture point spread function h(x,y)2 for the dark field microscopy imaging system of the micropore inner wall at positions 2 and 3 is:

[0030]

[0031] The beneficial effects of the present invention are:

[0032] The present invention analyzes the influence of micropore edge occlusion on dark-field microscopy characteristics from the perspective of theoretical modeling. As the micropore detection depth increases, the illumination and detection aperture shapes change, and two occlusion situations will occur. The present invention fully analyzes the influence of micropore edge occlusion on dark-field microscopy characteristics in each case, explores the capacity limit of the dark-field microscopy system, and provides theoretical guidance for the design of dark-field microscopy system for micropore inner wall and the realization of three-dimensional morphology reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1Schematic flow chart of a method for analyzing the characteristics of a dark-field microscopic imaging system for the inner wall of a micro-hole provided by the present invention;

[0034] Figure 2 Schematic diagram of the dark-field microscopic imaging process of the inner wall of a micro-hole and the shape of the effective aperture provided by the present invention;

[0035] Figure 3 Schematic diagram of the mapping relationship of the effective aperture of the dark-field microscopic imaging of the inner wall of a micro-hole provided by the present invention, Figure 3 in which, (a) is the schematic diagram of the mapping relationship of the effective aperture of the dark-field microscopic imaging of the inner wall of a micro-hole at position 1, (b) is the schematic diagram of the mapping relationship of the effective aperture of the dark-field microscopic imaging of the inner wall of a micro-hole at position 2, and (c) is the schematic diagram of the mapping relationship of the effective aperture of the dark-field microscopic imaging of the inner wall of a micro-hole at position 3;

[0036] Figure 4 Schematic diagram of the results of the lateral intensity distribution of the illumination point spread function at three positions provided by the present invention, Figure 4 in which, (a) is the schematic diagram of the calculation results of the imaging characteristics in the spatial domain and frequency domain of the system at position 1, (b) is the schematic diagram of the calculation results of the imaging characteristics in the spatial domain and frequency domain of the system at position 2, and (c) is the schematic diagram of the calculation results of the imaging characteristics in the spatial domain and frequency domain of the system at position 3. Detailed implementation manners

[0037] Detailed implementation manner 1: In combination with Figure 1-4 to illustrate this implementation manner. As Figure 1 shown, the steps of a method for analyzing the characteristics of a dark-field microscopic imaging system for the inner wall of a micro-hole described in this implementation manner include:

[0038] S1: Analyze the dark-field microscopic imaging process of the inner wall of a micro-hole, and determine the illumination aperture and the detection aperture pupil function of the dark-field microscopic imaging system for the inner wall of a micro-hole at the micro-hole detection depth H1;

[0039] As Figure 2 shown, the analysis in this implementation manner corresponds to position 1. The optical axis of the dark-field microscopic imaging system for the inner wall of a micro-hole is coaxial with one side edge of the micro-hole, the optical axis is perpendicular to the micro-hole, and it is semi-aperture illumination. The diameter of the micro-hole is D. The micro-hole detection depth corresponding to position 1 is H1, and the other side edge of the micro-hole does not block the effective illumination and detection apertures, that is, H1tanθ1 < D. The included angle between the semi-aperture illumination path and one side edge of the micro-hole is θ1;

[0040] According to the geometric relationship between the micro-hole projected onto the pupil plane, calculate the radius r of the circle of the micro-hole mapped onto the pupil plane, and combine it with the radius a of the pupil plane to calculate the pupil function P(ξ,η)1 at position 1;

[0041] The calculation formula for the radius r of the circle of the micro-hole mapped onto the pupil plane is:

[0042] r=dD / 2H (1);

[0043] In formula (1), d is the imaging distance of the microscope system;

[0044] The calculation formula of pupil function P(ξ,η)1 at position 1 is:

[0045]

[0046] S2: Determine the upper and lower limits of the integral based on the obtained detection aperture pupil function, and construct the occlusion aperture point spread function suitable for the dark field microscopy imaging system of the micropore inner wall at different micropore detection depths H;

[0047] Depend on Figure 3 (a) It can be seen that the effective illumination and detection aperture is a moon shape, which is an irregular area. In this case, the obstruction aperture point spread function of the micropore inner wall dark field microscopy imaging system needs to be obtained by dividing the moon shape into two bow-shaped integral sums. Based on the pupil function, the upper and lower limits of the two bow-shaped integrals are determined respectively, and the obstruction aperture point spread function suitable for the micropore inner wall dark field microscopy imaging system is constructed, see formula (3), where x0 is the dividing point of the two bow-shaped areas, see formula (4), and the upper and lower limits of the effective integral aperture area are obtained, see formula (5), which can be solved according to the objective lens parameters, micropore size and the relative position relationship between the two, and then brought into formula (3) to obtain the point spread function calculation result when the edge of the other side of the micropore does not obstruct the illumination and detection aperture when it is in position 1;

[0048] The calculation formula of the obstruction aperture point spread function h(x,y)1 for the dark field microscopy imaging system of the micropore inner wall at position 1 is:

[0049]

[0050] The calculation formula of the arcuate area dividing point x0 is:

[0051]

[0052] The upper and lower limits of the effective integral aperture area are calculated as follows:

[0053]

[0054] S3: Perform Fourier transform on the calculated diffusion functions of the illumination aperture and detection aperture of the dark field microscopy imaging system on the inner wall of the micropore to obtain the transfer function, and then analyze the spatial and frequency domain imaging characteristics of the system. The calculation results are as follows: Figure 4 As shown in (a).

[0055] Specific implementation method 2: Combination Figure 1-4 This embodiment is described as follows. Figure 1As shown, the steps of a micropore inner wall dark field microscopy system characteristic analysis method described in this embodiment include:

[0056] S1: Analyze the dark field microscopy imaging process of the micropore inner wall and determine the illumination aperture and detection aperture pupil function of the dark field microscopy imaging system of the micropore inner wall at the micropore detection depths H2 and H3;

[0057] like Figure 2 As shown, the analysis of this embodiment corresponds to positions 2 and 3. The optical axis of the dark-field microscopy imaging system on the inner wall of the micropore is coaxial with the edge of one side of the micropore, the optical axis is perpendicular to the micropore, and the illumination is semi-aperture. The diameter of the micropore is D. The micropore detection depth corresponding to position 2 is H2, and the micropore detection depth corresponding to position 3 is H3. The edge of the other side of the micropore blocks the effective illumination and detection aperture, that is, H1tanθ2<D,H3tanθ3> D, the angles between the semi-aperture illumination path and the edge of one side of the microhole are θ2 and θ3 respectively. At position 2, the detection aperture is inscribed in the effective illumination range.

[0058] The radius r of the circle of the microhole mapped to the pupil surface is calculated based on the geometric relationship between the microhole and the pupil surface, and the pupil function P(ξ,η)2 at positions 2 and 3 is calculated in combination with the pupil surface radius a.

[0059] The calculation formula of pupil function P(ξ,η)2 at position 2 and position 3 is:

[0060]

[0061] S2: Determine the upper and lower limits of the integral based on the obtained detection aperture pupil function, and construct the occlusion aperture point spread function suitable for the dark field microscopy imaging system of the micropore inner wall at the micropore detection depths H2 and H3;

[0062] like Figure 3 (b) and Figure 3 As shown in (c), the effective illumination and detection apertures at positions 2 and 3 are both circular. The circle formed by the effective illumination is integrated according to the geometric relationship of the microhole projection to the pupil plane calculated by formula (1), and the obstruction aperture point spread function h(x, y)2 for the microhole inner wall dark field microscopy imaging system at positions 2 and 3 is obtained;

[0063] The calculation formula of the obstruction aperture point spread function h(x,y)2 for the dark field microscopy imaging system of the micropore inner wall at positions 2 and 3 is:

[0064]

[0065] S3: Perform Fourier transform on the calculated diffusion functions of the illumination aperture and detection aperture of the dark field microscopy imaging system on the inner wall of the micropore to obtain the transfer function, and then analyze the spatial and frequency domain imaging characteristics of the system. The calculation results are as follows: Figure 4 (b) and Figure 4 (c) shown.

[0066] In summary, the present invention analyzes the influence of micropore edge occlusion on dark-field microscopy characteristics from the perspective of theoretical modeling. As the micropore detection depth increases, the shapes of the illumination and detection apertures change, and two occlusion situations will occur. The present invention fully analyzes the influence of micropore edge occlusion on dark-field microscopy characteristics in each case, explores the capacity limit of the dark-field microscopy system, and provides theoretical guidance for the design of the dark-field microscopy system for the inner wall of the micropore and the realization of three-dimensional morphology reconstruction.

[0067] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for analyzing characteristics of a micropore inner wall dark field microscopy imaging system, characterized in that: The steps of the method for analyzing the characteristics of a dark-field microscopic imaging system for the inner wall of a micro-hole include: Step 1: Analyze the dark-field microscopic imaging process of the inner wall of the micro-hole, and determine the illumination aperture and the detection aperture pupil function of the dark-field microscopic imaging system for the inner wall of the micro-hole at different micro-hole detection depths H. Step 2: Based on the obtained detection aperture pupil function, determine the upper and lower limits of the integral, and construct the occlusion aperture point spread function applicable to the dark-field microscopic imaging system for the inner wall of the micro-hole at different micro-hole detection depths H. Step 3: Perform Fourier transform on the calculated point spread functions of the illumination aperture and the detection aperture of the dark-field microscopic imaging system for the inner wall of the micro-hole to obtain the transfer function, and further analyze the imaging characteristics of the system in the spatial domain and the frequency domain.

2. The method for analyzing characteristics of a micropore inner wall dark field microscopy system according to claim 1, characterized in that: In Step 1, the optical axis of the dark-field microscopic imaging system for the inner wall of the micro-hole is coaxial with one edge of the micro-hole, the optical axis is perpendicular to the micro-hole, and it is semi-aperture illumination. The diameter of the micro-hole is D.

3. The method for analyzing characteristics of a micropore inner wall dark field microscopy system according to claim 1, characterized in that: In Step 1, according to the occlusion relationship of the effective illumination and detection apertures by the other edge of the micro-hole, objectives are set at three positions with micro-hole detection depths H1, H2, and H3. The micro-hole detection depth corresponding to Position 1 is H1, and the other edge of the micro-hole at this position does not form an occlusion for the effective illumination and detection apertures, that is, H1tanθ1 < D. The micro-hole detection depth corresponding to Position 2 is H2, and the micro-hole detection depth corresponding to Position 3 is H3. The other edges of the micro-holes corresponding to Position 2 and Position 3 form an occlusion for the effective illumination and detection apertures, that is, H2tanθ2 = D, H3tanθ3 > D. The effective illumination and detection apertures are circular. Here, θ is the included angle between the semi-aperture illumination path and one edge of the micro-hole. At Position 2, the detection aperture is inscribed in the effective illumination range.

4. The method for analyzing characteristics of a micropore inner wall dark field microscopy system according to claim 1, characterized in that: In Step 1, determining the illumination aperture and the detection aperture pupil function of the dark-field microscopic imaging system for the inner wall of the micro-hole at different micro-hole detection depths H specifically includes: Calculate the radius r of the circle mapped by the micro-hole to the pupil plane according to the geometric relationship of the micro-hole projected onto the pupil plane, and combine it with the radius a of the pupil plane to calculate the pupil function P(ξ,η)1 at Position 1 and the pupil function P(ξ,η)2 at Positions 2 and 3. The calculation formula for the radius r of the circle mapped by the micro-hole to the pupil plane is: r = dD / 2H (1); In formula (1), d is the imaging distance of the microscopic system. The calculation formula for the pupil function P(ξ,η)1 at Position 1 is: The calculation formula for the pupil function P(ξ,η)2 at Positions 2 and 3 is:

5. The method for analyzing characteristics of a micropore inner wall dark field microscopy system according to claim 1, characterized in that: In Step 2, constructing the occlusion aperture point spread function for the dark-field microscopic imaging system at Position 1 specifically includes: Divide the crescent occlusion formed by the illumination beam in the detection aperture into the integral summation of two bow-shaped regions, obtain the occlusion aperture point spread function h(x,y)1 for the dark-field microscopic imaging system at Position 1, solve the demarcation point x0 of the two bow-shaped regions, obtain the upper and lower limits of the effective integral aperture region, and substitute them into formula (4) to obtain the calculation result of the point spread function when the other edge of the micro-hole at Position 1 does not form an occlusion for the illumination and detection apertures. The calculation formula for the occlusion aperture point spread function h(x,y)1 for the dark-field microscopic imaging system at Position 1 is: The calculation formula of the arcuate area dividing point x0 is: The upper and lower limits of the effective integral aperture area are calculated as follows:

6. The method for analyzing characteristics of a micropore inner wall dark field microscopy system according to claim 1, characterized in that: The obstruction aperture point spread function for the micropore inner wall dark field microscopy imaging system constructed at positions 2 and 3 in step 2 specifically includes: According to the geometric relationship of the microhole projection to the pupil plane calculated by formula (1), the circle formed by the effective illumination is integrated to obtain the obstruction aperture point spread function h(x,y)2 for the microhole inner wall dark field microscopy imaging system at positions 2 and 3; The calculation formula of the obstruction aperture point spread function h(x,y)2 for the dark field microscopy imaging system of the micropore inner wall at positions 2 and 3 is:

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