CN116625649B - Parameter determination and inspection method for bifocal optical system - Google Patents
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Abstract
The invention provides a parameter measurement and inspection method for a bifocal optical system, and relates to the technical field of automatic detection. According to the invention, the quick construction of the measuring environment is realized by constructing the double-focus system, and a high-precision instrument is not needed, so that the measurement hardware requirement of radius parameters is reduced, the mathematical model of the light intensity distribution of the light intensity on the calculation shaft is obtained by carrying out mathematical modeling on the light intensity distribution of different light sources, and the theoretical numerical calculation of the light intensity on the shaft is realized; the availability of the bifocal system can be rapidly checked through the bifocal system checking step, the radius parameter is measured after the bifocal system is checked, so that the accurate and reliable radius parameter is obtained, and finally, the parameter is checked, so that the accurate radius parameter value is obtained. The method has low hardware requirement and simple operation, can rapidly determine the radius parameter of the Fresnel zone plate, and has practical and popularization values.
Description
Technical Field
The invention relates to the technical field of automatic detection, in particular to a parameter measurement and inspection method for a bifocal optical system.
Background
Along with the development of various lasers and the rapid development of various laser technologies, the application of lasers is also spread over a plurality of fields such as science and technology, economy, military and the like; therefore, more and more application scenes need to be used to the lens; the Fresnel zone plate and the lens are similar in nature, have the characteristic of converging light, have the advantages of large area, portability, foldability and the like, and are particularly suitable for optical ranging, remote optical communication and aerospace technology.
However, the existing method for measuring various parameters of the Fresnel zone plate is complex, and a complex and precise optical parameter measuring instrument is needed; at some time, we cannot quickly acquire the optical parameter measuring instruments, which clearly limits the popularization and use of the fresnel zone plate in daily life.
Therefore, it is necessary to provide a parameter measurement and inspection method for a bifocal optical system to solve the above-mentioned problems.
Disclosure of Invention
In order to solve the technical problems, the parameter determination and inspection method for the bifocal optical system is used for determining the radius parameter of the Fresnel zone plate, and the radius parameter of the Fresnel zone plate is obtained by constructing the bifocal optical system and collecting related parameters in the system, and the parameter inspection is carried out on the radius parameter to obtain the final radius parameter; the method comprises a bifocal system building step, a light intensity distribution modeling step, a bifocal system checking step, a radius parameter measuring step and a radius parameter checking step; the user inputs the related parameter data, the parameter and data calculation is automatically calculated by a computer preset program, and the radius parameter after the inspection is output.
As a further solution, a bifocal system building step: a bifocal optical system consisting of a Fresnel zone plate and a thin lens is built, and the bifocal optical system comprises a light source, a fixed track, a first lens frame, a second lens frame and a light screen; the light source is arranged through a plane wave light source or a basic mode Gaussian beam, the first lens frame is used for placing a Fresnel zone plate, a thin lens is placed behind the first lens frame, the distance between the first lens frame and the second lens frame is fixed through the second lens frame, the distance between the first lens frame and the second lens frame is kept to be a thin lens focal distance, the light screen is used for collecting light intensity distribution, and the fixed track is used for fixing and keeping the light source, the first lens frame and the second lens frame on the same center axis.
As a further solution, determining relevant parameters in the bifocal optical system, and building corresponding mathematical models of light intensity distribution for the plane wave light source and the fundamental mode Gaussian beam respectively; wherein the first mirror frame is used as an incident surfaceRP 1 The geometric focus on the shaft is set asFThe spot, the screen being the exit faceRP 2 Exit surfaceRP 2 The on-axis observation point at the position is set asPA dot; measuring plane of incidenceRP 1 And (3) withFFocal length between pointsfMeasurement ofFDots andPdistance between pointsz。
As a still further solution, a bifocal system checking step: obtaining a standard Fresnel zone plate, wherein the radius parameters of the standard Fresnel zone plate are known; after the standard fresnel zone plate is placed,
turning on a plane wave light source to irradiate, and collecting light intensity and plane wave data on a first standard axis through a light screen; substituting the plane wave data and the radius parameters of the standard Fresnel zone plate into a plane wave distribution model, and calculating to obtain a first light intensity theoretical value; comparing the light intensity on the first standard axis with a first theoretical light intensity value;
starting a fundamental mode Gaussian beam for irradiation, and collecting light intensity and fundamental mode Gaussian beam wave data on a second standard axis through a light screen; substituting the fundamental mode Gaussian beam wave data and the radius parameters of the standard Fresnel zone plate into a fundamental mode Gaussian beam distribution model, and calculating to obtain a second light intensity theoretical value; comparing the light intensity on the second standard axis with a second theoretical value of light intensity;
if both the two systems are matched, the two systems pass the standard test, otherwise, the two systems do not pass the standard test, analyzing the error and readjusting the bifocal system.
As a further solution, the radius parameter determination step: after the Fresnel zone plate to be tested is placed, a plane wave light source is started to irradiate, and light intensity and plane wave data on a first axis are collected through a light screen; inverse calculation is carried out through a light intensity distribution mathematical model of the plane wave light source to obtain a radius parameter association type; substituting the light intensity and plane wave data on the first axis into the radius parameter association type, and calculating to obtain the measured radius parameter.
As a further solution, the radius parameter checking step: after placing the Fresnel zone plate to be tested, starting a basic mode Gaussian beam for irradiation, and collecting light intensity on a second axis and basic mode Gaussian beam wave data through a light screen; acquiring the measured radius parameter and substituting the radius parameter into a mathematical model of the light intensity distribution of the Gaussian beam of the fundamental mode, and calculating to obtain the light intensity on a theoretical axis; and comparing the theoretical on-axis light intensity with the second on-axis light intensity, and if the error is within the confidence range, obtaining the final radius parameter.
As a still further solution, the on-axis light intensity distribution modeling includes a plane wave distribution model:
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,μis a non-dimensional parameter, and is a non-dimensional parameter,u=πN 1 [z/(f+z)]，N 1 fresnel number, which is any transparent band seen from the geometric focus.
As a still further solution, the on-axis light intensity distribution modeling includes a fundamental mode gaussian beam distribution model:
；
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,k =2π/λis the number of waves to be used,，/>，/>，fresnel number, which is the fundamental mode gaussian beam, ">Is the beam waist width of the fundamental mode Gaussian beam, < ->The radius parameter of the maximum half-wave band,E * (Z)is thatE(Z)The conjugate is taken out of the reaction kettle,E(Z)is the exit field distribution.
As a further solution, by combining，/>Substituting the mathematical model of the light intensity distribution of the plane wave light source;
and (4) back calculation to obtain a radius parameter association type:
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,I 1 for the light intensity on the first axis,is the maximum half-wave band radius parameter.
As a further solution, by the maximum half-wave band radius parameter, an arbitrary half-wave band radius parameter is calculated：
；
Wherein, as a parameter of the radius of the maximum half-wave band,mthe current half-wave band is correspondingly numbered.
Compared with the related art, the parameter determination and inspection method for the bifocal optical system provided by the invention has the following beneficial effects:
according to the invention, the quick construction of the measuring environment is realized by constructing the double-focus system, and a high-precision instrument is not needed, so that the measurement hardware requirement of radius parameters is reduced, the mathematical model of the light intensity distribution of the light intensity on the calculation shaft is obtained by carrying out mathematical modeling on the light intensity distribution of different light sources, and the theoretical numerical calculation of the light intensity on the shaft is realized; the availability of the bifocal system can be rapidly checked through the bifocal system checking step, the radius parameter is measured after the bifocal system is checked, so that the accurate and reliable radius parameter is obtained, and finally, the parameter is checked, so that the accurate radius parameter value is obtained. The method has low hardware requirement and simple operation, can rapidly determine the radius parameter of the Fresnel zone plate, and has practical and popularization values.
Drawings
FIG. 1 is a flow chart of a method for measuring and checking parameters of a bifocal optical system provided by the invention;
fig. 2 is a system schematic diagram of a parameter measurement and inspection method for a bifocal optical system according to an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and embodiments.
As shown in fig. 1, the parameter measurement and inspection method for a bifocal optical system provided in this embodiment is used for measuring radius parameters of a fresnel zone plate, and by constructing the bifocal optical system and collecting related parameters in the system, obtaining the radius parameters of the fresnel zone plate, and performing parameter inspection on the radius parameters to obtain final radius parameters; the method comprises a bifocal system building step, a light intensity distribution modeling step, a bifocal system checking step, a radius parameter measuring step and a radius parameter checking step; the user inputs the related parameter data, the parameter and data calculation is automatically calculated by a computer preset program, and the radius parameter after the inspection is output.
It should be noted that: the existing method for measuring various parameters of the Fresnel zone plate is complex, and a complex and precise optical parameter measuring instrument is needed; the most important parameter is the radius parameter of the fresnel zone plate.
Therefore, the embodiment provides a simple and efficient method for measuring and checking radius parameters, the quick construction of a measurement environment is realized by constructing a double-focus system, and a high-precision instrument is not needed, so that the requirement of measurement hardware of the radius parameters is reduced, mathematical modeling is performed on light intensity distribution of different light sources to obtain a light intensity distribution mathematical model for calculating light intensity on an axis, and theoretical numerical calculation of the light intensity on the axis is realized; the availability of the bifocal system can be rapidly checked through the bifocal system checking step, the radius parameter is measured after the bifocal system is checked, so that the accurate and reliable radius parameter is obtained, and finally, the parameter is checked, so that the accurate radius parameter value is obtained. The method has low hardware requirement and simple operation, can rapidly determine the radius parameter of the Fresnel zone plate, and has practical and popularization values.
As a further solution, a bifocal system building step: a bifocal optical system consisting of a Fresnel zone plate and a thin lens is built, and the bifocal optical system comprises a light source, a fixed track, a first lens frame, a second lens frame and a light screen; the light source is arranged through a plane wave light source or a basic mode Gaussian beam, the first lens frame is used for placing a Fresnel zone plate, a thin lens is placed behind the first lens frame, the distance between the first lens frame and the second lens frame is fixed through the second lens frame, the distance between the first lens frame and the second lens frame is kept to be a thin lens focal distance, the light screen is used for collecting light intensity distribution, and the fixed track is used for fixing and keeping the light source, the first lens frame and the second lens frame on the same center axis.
It should be noted that: as shown in fig. 2, in this embodiment, the relevant parameters are fixed and the light intensity distribution is collected by a bifocal system, so as to implement subsequent mathematical modeling and radius parameter reasoning calculation, and the bifocal system is formed by a simpler fresnel zone plate and a thin lens structure, and the light intensity distribution is collected by using a light screen; the light screen does not need to collect complete light intensity distribution, only needs to collect the light intensity distribution value on the shaft, and can be realized through the related sensor. Wherein, Ois the incident planeRP 1 A center point.
As a further solution, the light intensity distribution modeling step: double-focus optical system for measurementRespectively aiming at the plane wave light source and the basic mode Gaussian beam, and constructing a corresponding light intensity distribution mathematical model; wherein the first mirror frame is used as an incident surfaceRP 1 The geometric focus on the shaft is set asFThe spot, the screen being the exit faceRP 2 Exit surfaceRP 2 The on-axis observation point at the position is set asPA dot; measuring plane of incidenceRP 1 And (3) withFFocal length between pointsfMeasurement ofFDots andPdistance between pointsz。
It should be noted that: as shown in fig. 2, after the bifocal optical system is built, the relevant parameters are cured, and the light intensity distribution mathematical model for the bifocal optical system can be built by collecting the relevant parameters and combining the light source parameters.
As a still further solution, a bifocal system checking step: obtaining a standard Fresnel zone plate, wherein the radius parameters of the standard Fresnel zone plate are known; after the standard fresnel zone plate is placed,
turning on a plane wave light source to irradiate, and collecting light intensity and plane wave data on a first standard axis through a light screen; substituting the plane wave data and the radius parameters of the standard Fresnel zone plate into a plane wave distribution model, and calculating to obtain a first light intensity theoretical value; comparing the light intensity on the first standard axis with a first theoretical light intensity value;
starting a fundamental mode Gaussian beam for irradiation, and collecting light intensity and fundamental mode Gaussian beam wave data on a second standard axis through a light screen; substituting the fundamental mode Gaussian beam wave data and the radius parameters of the standard Fresnel zone plate into a fundamental mode Gaussian beam distribution model, and calculating to obtain a second light intensity theoretical value; comparing the light intensity on the second standard axis with a second theoretical value of light intensity;
if both the two systems are matched, the two systems pass the standard test, otherwise, the two systems do not pass the standard test, analyzing the error and readjusting the bifocal system.
It should be noted that: the radius parameters of the standard Fresnel zone plate are known, so that the calculation accuracy of the mathematical model of the light intensity distribution of the plane wave light source and the basic mode Gaussian beam can be verified through the standard Fresnel zone plate, and when the mismatch condition occurs, the mathematical model of the light intensity distribution and the bifocal optical system are obtained by readjusting aiming at the mismatch cause.
As a further solution, the radius parameter determination step: after the Fresnel zone plate to be tested is placed, a plane wave light source is started to irradiate, and light intensity and plane wave data on a first axis are collected through a light screen; inverse calculation is carried out through a light intensity distribution mathematical model of the plane wave light source to obtain a radius parameter association type; substituting the light intensity and plane wave data on the first axis into the radius parameter association type, and calculating to obtain the measured radius parameter.
It should be noted that: since other parameters are fixed and known, the radius parameter correlation can be obtained by back calculation through a mathematical model of the light intensity distribution of the plane wave light source, and through the light intensity and plane wave data (mainly wavelength on the first axisEqual parameters) can be calculated to obtain the radius parameters.
As a further solution, the radius parameter checking step: after placing the Fresnel zone plate to be tested, starting a basic mode Gaussian beam for irradiation, and collecting light intensity on a second axis and basic mode Gaussian beam wave data through a light screen; acquiring the measured radius parameter and substituting the radius parameter into a mathematical model of the light intensity distribution of the Gaussian beam of the fundamental mode, and calculating to obtain the light intensity on a theoretical axis; and comparing the theoretical on-axis light intensity with the second on-axis light intensity, and if the error is within the confidence range, obtaining the final radius parameter.
It should be noted that: the step mainly comprises the steps of realizing rapid verification of parameters through mathematical models of different light sources, and if the measured radius parameters are accurate, the calculation results of the parameters are all established in the mathematical models of different light sources, so that the rapid verification of the radius parameters is realized.
As a still further solution, the on-axis light intensity distribution modeling includes a plane wave distribution model:
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,μis a non-dimensional parameter, and is a non-dimensional parameter,u=πN 1 [z/(f+z)]，N 1 fresnel number, which is any transparent band seen from the geometric focus.
It should be noted that: in this embodiment, a dual-focusing optical system is formed by using the focal point of the thin lens and the main focal point of the fresnel zone plate, and plane waves without converging effect are passed through the system, and the light intensity distribution formula thereof is deduced based on the Collins formula.
As a still further solution, the on-axis light intensity distribution modeling includes a fundamental mode gaussian beam distribution model:
；
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,k =2π/λis the number of waves to be used,，/>，/>，fresnel number, which is the fundamental mode gaussian beam, ">Is the beam waist width of the fundamental mode Gaussian beam, < ->The radius parameter of the maximum half-wave band,E * (Z)is thatE(Z)The conjugate is taken out of the reaction kettle,E(Z)is the exit field distribution.
It should be noted that: in this embodiment, an on-axis light intensity distribution formula of the fundamental mode gaussian beam after passing through the bifocal optical system is derived from the Collins formula.
As a further solution, by combining，/>Substituting the mathematical model of the light intensity distribution of the plane wave light source;
and (4) back calculation to obtain a radius parameter association type:
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,I 1 for the light intensity on the first axis,is the maximum half-wave band radius parameter.
It should be noted that: the embodiment adopts the inverse-push radius parameter association type of the light intensity distribution mathematical model of the plane wave light source, mainly the light intensity distribution mathematical model of the plane wave light source is simpler, the inverse-push radius parameter association type of the inverse-push is also simpler, and the rapid calculation and the derivation are convenient.
Transforming the plane wave distribution model can obtain the followingμIs defined by the relation:
；
will beSubstitution intoμWe can get the relation of (2)N 1 Is defined by the relation:
；
will beSubstitution intoN 1 By simplifying and transforming the relation of (C) we can get +.>Is defined by the relation:
；
from this formula we can substitute each parameter to calculate the corresponding maximum half-wave band radius parameter.
As a further solution, by the maximum half-wave band radius parameter, an arbitrary half-wave band radius parameter is calculated：
；
Wherein, as a parameter of the radius of the maximum half-wave band,mthe current half-wave band is correspondingly numbered.
It should be noted that: the radius parameters of each half-wave band can be calculated by the radius parameters of the maximum half-wave band，FIG. 2 shows FresnelNumber of half-wave bandsM=2Is an optical system of (a)，r 1 As a first half-band radius parameter,r 2 is the second half-wave band radius parameter, and is also the maximum half-wave band radius parameter of the systemThe method comprises the steps of carrying out a first treatment on the surface of the At this time, the liquid crystal display device,r 2 can be calculated by combining the formulasr 1 。
The foregoing is only illustrative of the present invention and is not to be construed as limiting the scope of the invention, and all equivalent structures or equivalent flow modifications which may be made by the teachings of the present invention and the accompanying drawings or which may be directly or indirectly employed in other related art are within the scope of the invention.
Claims (4)
1. The parameter determination and inspection method for the bifocal optical system is used for determining the radius parameter of the Fresnel zone plate and is characterized in that the bifocal optical system is built, related parameters in the system are collected, the radius parameter of the Fresnel zone plate is obtained, and parameter inspection is carried out on the radius parameter to obtain a final radius parameter; the method comprises a bifocal system building step, a light intensity distribution modeling step, a bifocal system checking step, a radius parameter measuring step and a radius parameter checking step; the user carries out automatic calculation through a computer preset program by inputting related parameter data, parameter and data calculation, and outputs the radius parameter after the inspection;
the construction step of the double-focus system comprises the following steps: a bifocal optical system consisting of a Fresnel zone plate and a thin lens is built, and the bifocal optical system comprises a light source, a fixed track, a first lens frame, a second lens frame and a light screen; the light source is arranged through a plane wave light source or a basic mode Gaussian beam, the first lens frame is used for placing a Fresnel zone plate, a thin lens is closely placed behind the first lens frame, and the thin lens is fixed on the second lens frame and has a focal length offThe light screen is used for collecting light intensity distribution, and the fixed track is used for fixing and keeping the light source, the first mirror frame and the second mirror frame on the same center shaft;
a light intensity distribution modeling step: measuring relevant parameters in a bifocal optical system, and building a corresponding light intensity distribution mathematical model aiming at a plane wave light source and a fundamental mode Gaussian beam respectively; wherein the first mirror frame is used as an incident surfaceRP 1 The geometric focus on the shaft is set asFThe spot, the screen being the exit faceRP 2 Exit surfaceRP 2 The on-axis observation point at the position is set asPA dot; measuring plane of incidenceRP 1 And (3) withFFocal length between pointsfMeasurement ofFDots andPdistance between pointsz；
And (3) checking a bifocal system: obtaining a standard Fresnel zone plate, wherein the radius parameters of the standard Fresnel zone plate are known; after the standard fresnel zone plate is placed,
turning on a plane wave light source to irradiate, and collecting light intensity and plane wave data on a first standard axis through a light screen; substituting the plane wave data and the radius parameters of the standard Fresnel zone plate into a plane wave distribution model, and calculating to obtain a first light intensity theoretical value; comparing the light intensity on the first standard axis with a first theoretical light intensity value;
starting a fundamental mode Gaussian beam for irradiation, and collecting light intensity and fundamental mode Gaussian beam wave data on a second standard axis through a light screen; substituting the fundamental mode Gaussian beam wave data and the radius parameters of the standard Fresnel zone plate into a fundamental mode Gaussian beam distribution model, and calculating to obtain a second light intensity theoretical value; comparing the light intensity on the second standard axis with a second theoretical value of light intensity;
if both the two systems are matched, the two systems pass the standard test, otherwise, the two systems do not pass the standard test, analyzing errors and readjusting the bifocal system;
and a radius parameter measurement step: after the Fresnel zone plate to be tested is placed, a plane wave light source is started to irradiate, and light intensity and plane wave data on a first axis are collected through a light screen; inverse calculation is carried out through a light intensity distribution mathematical model of the plane wave light source to obtain a radius parameter association type; substituting the light intensity and plane wave data on the first axis into the radius parameter association type, and calculating to obtain a measured radius parameter;
radius parameter checking: after placing the Fresnel zone plate to be tested, starting a basic mode Gaussian beam for irradiation, and collecting light intensity on a second axis and basic mode Gaussian beam wave data through a light screen; acquiring the measured radius parameter and substituting the radius parameter into a mathematical model of the light intensity distribution of the Gaussian beam of the fundamental mode, and calculating to obtain the light intensity on a theoretical axis; and comparing the theoretical on-axis light intensity with the second on-axis light intensity, and if the error is within the confidence range, obtaining the final radius parameter.
2. The method for determining and verifying parameters of a bifocal optical system according to claim 1, wherein the on-axis light intensity distribution modeling comprises a plane wave distribution model:
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,u=πN 1 [z/(f+z)]，N 1 fresnel number, which is any transparent band seen from the geometric focus;，/>maximum half-wave band radius parameter.
3. The method for determining and verifying parameters of a bifocal optical system according to claim 1, wherein the on-axis light intensity distribution modeling comprises a fundamental mode gaussian beam distribution model:
；
；
wherein, A 0 as a complex constant, the phase difference is,fas the focal length of the lens is,Mfor the number of fresnel half-wave bands,zfor determination ofFDots andPthe distance between the points is such that,k=2π/λis the number of waves to be used,，/>，/>，/>，fresnel number, which is the fundamental mode gaussian beam, ">Is the beam waist width of the fundamental mode Gaussian beam, < ->The radius parameter of the maximum half-wave band,E * (Z)is thatE(Z)The conjugate is taken out of the reaction kettle,E(Z)is the exit field distribution.
4. The method for measuring and checking parameters of a bifocal optical system according to claim 2, wherein the radius parameter of any half-band is calculated by the maximum half-band radius parameter：
；
Wherein, as a parameter of the radius of the maximum half-wave band,mthe current half-wave band is correspondingly numbered.
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