CN114924411A - Light beam transformation system design method for medium and long distance laser Doppler velocimeter - Google Patents
Light beam transformation system design method for medium and long distance laser Doppler velocimeter Download PDFInfo
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Abstract
The invention discloses a method for designing a light beam transformation system for a medium-distance and long-distance laser Doppler velocimeter, which comprises the following steps: establishing a process model of the Gaussian beam passing through the defocusing type beam transformation system, and sequentially obtaining a defocusing amount matrix of the optical system; establishing a diffraction transmission model of electromagnetic field distribution between an incident plane of an optical system and a designed target working distance based on an aberration theory; the light intensity distribution of a conversion system consisting of lenses with different spherical aberration characteristics at the target working distance is obtained based on a diffraction transmission model, then the light intensity distribution is converted into a corresponding light spot radius, and the light spot size at the working distance required by the design of a velocimeter system is used as a limiting condition to obtain a lens combination meeting the design requirement of an optical system. The method is applied to the technical field of laser Doppler velocity measurement, introduces an aberration term into a diffraction transmission model, can more accurately reflect the light intensity distribution of the Gaussian beam after passing through a beam transformation system, and provides a theoretical basis closer to the reality for the design of the system.
Description
Technical Field
The invention relates to the technical field of laser Doppler velocity measurement, in particular to a light beam transformation system design method for a medium-distance and long-distance laser Doppler velocimeter.
Background
Since birth, the laser doppler technology has the excellent characteristics of high measurement precision, large dynamic range, capability of realizing non-contact measurement and the like, is widely applied to scientific research and industrial production, and plays an important role in scenes such as vehicle-mounted combined navigation, strip speed measurement in steel production and the like.
To measure the speed of a long-distance object, a measuring beam of a medium-and-long-distance laser doppler velocimeter usually passes through collimation or beam expansion of a defocusing type beam transformation system and then is emitted to the object to be measured, the quality of a velocimeter signal is closely related to the imaging quality of the beam transformation system, the medium-and-long-distance laser doppler velocimeter usually adopts a coaxial transmission type optical system, wherein the influence of the spherical aberration of the optical system is particularly obvious, particularly, the working distance (the distance between the velocimeter and the object to be measured) of the current laser doppler velocimeter tends to be hundreds of meters or even kilometers, and the influence of the spherical aberration of the optical transformation system on the measurement result of the velocimeter is more obvious.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for designing a light beam transformation system for a medium-and-long-distance laser Doppler velocimeter, which can be used for designing the light beam transformation system which is more suitable for the measurement performance requirement for the medium-and-long-distance laser Doppler velocimeter.
In order to achieve the above object, the present invention provides a method for designing a light beam transformation system for a medium and long distance laser doppler velocimeter, comprising the following steps:
step 1, establishing a process model of a Gaussian beam passing through a defocused beam transformation system based on a transmission matrix theory of the Gaussian beam;
step 3, establishing a diffraction transmission model of electromagnetic field distribution between an incidence plane of the defocusing type optical system and a designed target working distance position based on a diffraction theory and an aberration theory;
step 4, obtaining lens matrix elements corresponding to the concave lens and the convex lens when the concave lens and the convex lens are combined at different focal lengths and the total spherical aberration coefficient of the defocusing optical system based on the defocusing amount matrix, the concave lens focal length value vector and the convex lens focal length value vector of the defocusing optical system;
step 5, substituting the lens matrix elements and the spherical aberration coefficients corresponding to each group into a diffraction transmission model respectively to obtain corresponding electromagnetic field distribution converted by the defocusing type optical system, and further obtain light intensity distribution of a conversion system consisting of lenses with different spherical aberration characteristics at a target working distance;
and 6, converting the light intensity distribution at the working distance into a corresponding light spot radius, and obtaining the lens combination meeting the design requirement of the optical system by taking the size of the light spot at the working distance required by the design of the velocimeter system as a limiting condition.
In one embodiment, in step 1, the process model of the gaussian beam passing through the defocused beam transformation system is:
wherein L is the working distance of the laser Doppler velocimeter in medium and long distance, f 1 And f 2 The focal lengths of the concave lens and the convex lens of the defocusing optical system, respectively, delta is the defocusing amount of the defocusing optical system (i.e. the distance between the focal points of the two lens groups), and omega 0 The radius of the gaussian beam of the incident defocused optical system,λ is the wavelength of the gaussian beam and T is the transpose of the matrix.
In one embodiment, in step 3, the diffraction transmission model of the electromagnetic field distribution between the incidence plane of the defocused optical system and the designed target working distance is as follows:
in the formula, E (r, L) defocusing optical system has electromagnetic field distribution at designed target working distance, i represents imaginary number unit, k represents wave number, E 0 (r 0 ) Representing the electromagnetic field distribution, r, of the Gaussian beam on the plane of incidence 0 Representing the radial variation of the incident plane of the gaussian beam, r represents the radial variation in polar coordinates at the working distance,
a Bessel function of zero order;
C 4 the spherical aberration coefficient of the defocusing optical system is specifically as follows:
in the formula, n 0 Is the refractive index of the lens material, f is the focal length of the lens, p is the incident factor of the beam (related to the way the beam is incident into the lens), q is the surface form factor of the lens, S is the image distance in this incident mode, R 1 And R 2 The radii of curvature of the front and rear surfaces of the lens, respectively;
A. b, C, D matrix elements in the defocused optical system matrix are specifically:
d＝f 2 +f 1 +Δ
where d is the distance from the rear surface of the concave lens to the front surface of the convex lens in the defocus optical system.
In one embodiment, in step 5, the light intensity distribution of the transformation system composed of the lenses with different spherical aberration characteristics at the target working distance is specifically:
I(r,L)＝E(r,L)·E * (r,L)
in the formula, E * (r, L) is the conjugate of the electromagnetic field distribution E (r, L) of the defocused optical system at the designed target working distance.
In one embodiment, in step 6, the step of obtaining the lens combination meeting the design requirement of the optical system by using the size of the light spot at the working distance required by the design of the velocimeter system as a limiting condition specifically includes:
and taking the focal lengths of the concave lens and the convex lens as independent variables, carrying out three-dimensional curved surface graphical expression on the relationship between the spot radius of the measuring beam at the working distance and the focal lengths of the concave lens and the convex lens, intersecting a plane omega (const) with the three-dimensional curved surface graph, and obtaining the focal length values of the concave lens and the convex lens corresponding to points on the intersection line of the plane omega and the three-dimensional curved surface graph, namely the focal length values of the concave lens and the convex lens which meet the design requirements of the optical system.
In one embodiment, the design method further comprises:
and 7, screening the lens group combinations meeting the requirements according to the actual conditions, and optimizing the surface type of the lens group by using ZMAX optical design software, thereby completing the design and selection of the parameters of the light beam transformation system.
Compared with the prior art, the light beam transformation system design method for the medium-and-long-distance laser Doppler velocimeter provided by the invention introduces the aberration item into the diffraction transmission model, can more accurately reflect the light intensity distribution of the Gaussian light beam after passing through the defocused light beam transformation system, and provides a theoretical basis closer to the reality for the design of the system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of a design method in an embodiment of the present invention;
fig. 2 is an internal structural view of a defocused beam conversion system in an embodiment of the present invention.
The implementation, functional features and advantages of the present invention will be further described with reference to the accompanying drawings.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that all the directional indicators (such as up, down, left, right, front, and rear … …) in the embodiment of the present invention are only used to explain the relative position relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indicator is changed accordingly.
In addition, the descriptions related to "first", "second", etc. in the present invention are only for descriptive purposes and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "connected," "secured," and the like are to be construed broadly, and for example, "secured" may be a fixed connection, a removable connection, or an integral part; the connection can be mechanical connection, electrical connection, physical connection or wireless communication connection; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of the technical solutions by those skilled in the art, and when the technical solutions are contradictory to each other or cannot be realized, such a combination of the technical solutions should not be considered to exist, and is not within the protection scope of the present invention.
The embodiment discloses a method for designing a light beam transformation system for a medium-and-long-distance laser Doppler velocimeter, which is used for designing the light beam transformation system which is more suitable for the measurement performance requirement for the medium-and-long-distance laser Doppler velocimeter. Referring to fig. 1, the method specifically includes the following steps 1-, 7.
Step 1, establishing a process model of passing the Gaussian beam through the defocused beam transformation system based on a transmission matrix theory of the Gaussian beam, namely, deducing the relationship between the defocused amount of the system and the focal length of a lens group in the defocused beam transformation system under the condition of a designed target working distance (namely, a certain distance between the beam waist of the Gaussian beam after system transformation and the emergent surface of the system) through the process model.
In this embodiment, the process model of the gaussian beam passing through the defocused beam transformation system is as follows:
wherein L is the working distance of the laser Doppler velocimeter in medium and long distance, f 1 And f 2 The focal lengths of the concave lens and the convex lens of the defocusing optical system respectively, delta is the defocusing amount of the defocusing optical system (namely the distance between the focal points of the two lenses), and omega 0 The radius of the Gaussian beam of the incident defocusing optical system is lambda, the wavelength of the Gaussian beam is lambda, and T is the transpose of the matrix.
And 2, substituting the target working distance designed by the laser Doppler velocimeter system, the concave lens focal length value vector and the convex lens focal length value vector of the defocusing optical system into the process model to obtain a defocusing amount matrix of the defocusing optical system.
And 3, under the paraxial approximation condition, establishing a diffraction transmission model of the electromagnetic field distribution between the defocusing type optical system incident plane and the designed target working distance on the basis of a diffraction theory, an aberration theory and a matrix expression of the lens system. Wherein, the matrix elements of the lens system are expressed as the functions of the focal length of the lens, the distance between the lenses, the working distance and the defocusing amount, and the spherical aberration of the lens is expressed as the functions of the refractive index and the focal length of the material.
In this embodiment, the diffraction transmission model of electromagnetic field distribution between the incidence plane of the defocused optical system and the designed target working distance is:
in the formula, E (r, L) defocusing optical system has electromagnetic field distribution at designed target working distance, i represents imaginary number unit, k represents wave number, E 0 (r 0 ) Representing the electromagnetic field distribution, r, of the Gaussian beam on the plane of incidence 0 Representing the radial variation of the incident plane of the gaussian beam, r represents the radial variation in polar coordinates at the working distance,
a Bessel function of zero order;
C 4 is the spherical aberration coefficient of the defocused optical system, particularlyComprises the following steps:
in the formula, n 0 Is the refractive index of the lens material, f is the focal length of the lens, p is the incidence factor of the beam (related to the way the beam enters the lens), q is the surface form factor of the lens, S is the image distance in this incidence mode, R 1 And R 2 The radii of curvature of the front and rear surfaces of the lens, respectively;
A. b, C, D matrix elements in the defocusing optical system matrix are specifically:
d＝f 2 +f 1 +Δ (7)
where d is the distance from the rear surface of the concave lens to the front surface of the convex lens in the defocus optical system.
And 4, obtaining a corresponding lens matrix element and a total spherical aberration coefficient of the defocusing optical system when the concave lens and the convex lens are combined at different focal lengths based on the defocusing amount matrix, the concave lens focal length value vector and the convex lens focal length value vector of the defocusing optical system.
And 5, substituting the lens matrix elements and the spherical aberration coefficients corresponding to each group into the diffraction transmission model respectively to obtain corresponding electromagnetic field distribution after being converted by the defocused optical system, and further obtain the light intensity distribution of a conversion system consisting of lenses with different spherical aberration characteristics at the target working distance, wherein the light intensity distribution is as follows:
I(r,L)＝E(r,L)·E * (r,L) (8)
in the formula, E * (r, L) is the conjugate of the electromagnetic field distribution E (r, L) of the defocused optical system at the designed target working distance, at which the measuring beam spot radius r at the working distance L Corresponding to a light field intensity of I (r) L ,L)＝e -2 The distance from the position of I (0, L) to the spot center.
And 6, converting the light intensity distribution at the working distance into a corresponding light spot radius, and obtaining the lens combination meeting the design requirement of the optical system by taking the size of the light spot at the working distance required by the design of a velocimeter system as a limiting condition.
In the specific implementation process, the same Gaussian beam output by the medium-distance and long-distance laser Doppler velocimeter is converted by a defocusing optical system consisting of concave lenses and convex lenses with different spherical aberration characteristics to obtain corresponding r L The value is obtained. Under the premise that the respective materials of the concave lens and the convex lens are consistent, the focal lengths of the concave lens and the convex lens are used as independent variables, and the radius r of the measuring beam spot at the working distance L The relation between the two can be three-dimensional curved surface r L ＝F(f 1 ,f 2 ) And graphically representing, and then taking the size of a light spot at a working distance required by the design of a velocimeter system as a limiting condition, namely, a plane omega (const) is intersected with the three-dimensional curved surface, and focal length values of the concave lens and the convex lens corresponding to points on the intersection line of the plane omega (const) and the three-dimensional curved surface are the lens combination meeting the design requirement of the optical system.
And 7, as an optional implementation mode, after a plurality of groups of lens combinations meeting the design requirements of the optical system are obtained, screening the lens group combinations meeting the requirements according to the actual conditions, and optimizing the surface type of the lens group by using ZMAX optical design software, thereby completing the design and selection of the parameters of the light beam transformation system.
The following describes a method for designing a beam transformation system in this embodiment with reference to specific examples.
Referring to fig. 2, the defocused beam transformation system is generally composed of a concave lens and a convex lens. Passing the Gaussian beam according to the formula (1) through a process model of a defocused beam transformation systemTarget working distance L and concave and convex lens focal length value vector f designed by laser Doppler velocimeter system 1 n ＝[f 11 f 12 … f 1n ] T 、f 2 m ＝[f 21 f 22 … f 2m ] T Substituting into (1), the corresponding defocus quantity matrix Delta can be obtained n×m The method comprises the following steps:
wherein m is the total number of concave lens groups participating in the screening, n is the total number of convex lens groups participating in the screening, Δ n×m Is the defocus amount of the combination of the mth concave lens and the nth convex lens.
Defocus matrix delta n×m And a vector f of focal length values of the two lenses 1 n And f 2 m When the matrix expression (6) and the spherical aberration coefficients (3), (4) and (5) of the defocusing system are substituted to obtain different focal length combinations of the two lenses, the corresponding lens matrix element A nm 、B nm 、C nm And D nm Spherical aberration coefficient C of each of the concave and convex lens groups 4_1n And C 4_2m And the total spherical aberration coefficient C of the system 4_nm The method comprises the following steps:
C 4_nm ＝C 4_1n +C 4_2m
then the lens matrix element A with the corresponding relation is added nm 、B nm 、D nm Spherical aberration coefficient C with the total system 4_nm The corresponding electromagnetic field distribution E converted by the optical system can be obtained in the formula (2) nm (r, L) is:
distribution of electromagnetic field E nm (r, L) is substituted for formula (8) to obtain the light intensity distribution I at the working distance nm (r, L) is:
I nm (r,L)＝E nm (r,L)·E nm * (r,L)
according to the light spot radius corresponding to the light field intensity I nm (r nm ,L)＝e -2 ·I nm R at (0, L) nm The light intensity distribution can be converted into corresponding spot radius so as to construct a spot radius matrix r corresponding to different lens combinations one by one n×m The method comprises the following steps:
further, each element in the spot radius matrix can be regarded as a function r of the focal length of the concave and convex lenses in the defocused optical system nm ＝F(f 1n ,f 2m ). Therefore, the function r can be obtained by using the focal lengths of the two lenses as independent variables nm ＝F(f 1n ,f 2m ) The relationship of (2) is visually expressed in a three-dimensional curved surface graphical form.
In the specific application process, the signal-to-noise ratio SNR of the remote laser Doppler velocimeter in the continuous optical system is as follows:
where eta is the optical efficiency of the system and B isEquivalent noise bandwidth of the system, F h The method is characterized in that the method is a noise coefficient, P is emergent measuring light power, L is a working distance, alpha is an attenuation coefficient of measuring light in the atmosphere, rho is a reflection coefficient of the surface of an object to be measured, omega is a facula radius of measuring light beams on the surface of the object to be measured, nu and lambda are frequency and wavelength of the measuring light respectively, and h is a Planck constant.
From the signal-to-noise ratio calculation formula, it can be seen that the signal-to-noise ratio of the remote laser Doppler velocimeter in the same continuous optical system at the same working distance is mainly influenced by the size of the spot radius of the measuring beam on the surface of the object to be measured, so that the spot radius omega of the measuring beam at the working distance can be designed according to the system performance target, and then r is used for designing nm A graphical representation of ω, with function r nm ＝F(f 1n ,f 2m ) The three-dimensional surfaces of the representations intersect, a point (f) on the line of intersection of the two 1n ,f 2m ,r nm ) The focal length value of the lens of the defocusing type light beam conversion system is a combination which meets the requirement of a velocimeter system on measuring signal to noise ratio.
And finally, screening the lens group combinations meeting the requirements according to the actual conditions, and optimizing the surface type and the like of the lens by using ZMAX optical design software, thereby completing the design and selection of the parameters of the light beam transformation system. The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (6)
1. A light beam transformation system design method for a medium and long distance laser Doppler velocimeter is characterized by comprising the following steps:
step 1, establishing a process model of a Gaussian beam passing through a defocused beam transformation system based on a transmission matrix theory of the Gaussian beam;
step 2, substituting the target working distance designed by the laser Doppler velocimeter system, the concave lens focal length value vector and the convex lens focal length value vector of the defocusing optical system into the process model to obtain a defocusing amount matrix of the defocusing optical system;
step 3, establishing a diffraction transmission model of electromagnetic field distribution between an incidence plane of the defocusing type optical system and a designed target working distance position based on a diffraction theory and an aberration theory;
step 4, based on the defocusing amount matrix, the focal length value vector of the concave lens and the focal length value vector of the convex lens of the defocusing optical system, obtaining a corresponding lens matrix element and a total spherical aberration coefficient of the defocusing optical system when the concave lens and the convex lens are combined at different focal lengths;
step 5, substituting the lens matrix elements and the spherical aberration coefficients corresponding to each group into a diffraction transmission model respectively to obtain corresponding electromagnetic field distribution converted by the defocusing type optical system, and further obtain light intensity distribution of a conversion system consisting of lenses with different spherical aberration characteristics at a target working distance;
and 6, converting the light intensity distribution at the working distance into a corresponding light spot radius, and obtaining the lens combination meeting the design requirement of the optical system by taking the size of the light spot at the working distance required by the design of the velocimeter system as a limiting condition.
2. The method for designing a beam transformation system for a long-distance laser doppler velocimeter according to claim 1, wherein in step 1, the process model of passing the gaussian beam through the defocused beam transformation system is as follows:
wherein L is the working distance of the laser Doppler velocimeter in medium and long distance, f 1 And f 2 Respectively the focal lengths of the concave lens and the convex lens of the defocusing optical system, delta is the defocusing amount of the defocusing optical system, and omega 0 The radius of the Gaussian beam of the incident defocusing optical system is shown, and lambda is the wavelength of the Gaussian beam.
3. The method for designing a beam transformation system for a long-distance laser doppler velocimeter according to claim 1, wherein in step 3, the diffraction transmission model of the electromagnetic field distribution between the defocusing optical system incidence plane and the designed target working distance is:
in the formula, E (r, L) defocusing optical system distributes electromagnetic field at designed target working distance, i represents an imaginary number unit, k represents wave number, E 0 (r 0 ) Representing the electromagnetic field distribution, r, of the Gaussian beam on the plane of incidence 0 Representing the radial variation of the incident plane of the gaussian beam, r represents the radial variation in polar coordinates at the working distance,
a Bessel function of zero order;
C 4 the spherical aberration coefficient of the defocusing optical system is specifically as follows:
in the formula, n 0 Is the refractive index of the lens material, f is the focal length of the lens, p is the incident factor of the beam (related to the way the beam is incident into the lens), q is the surface form factor of the lens, S is the image distance in this incident mode, R 1 And R 2 The radii of curvature of the front and rear surfaces of the lens, respectively;
A. b, C, D matrix elements in the defocused optical system matrix are specifically:
d＝f 2 +f 1 +Δ
where d is the distance from the rear surface of the concave lens to the front surface of the convex lens in the defocus optical system.
4. The method as claimed in claim 1, wherein in step 5, the light intensity distribution of the conversion system composed of the lenses with different spherical aberration characteristics at the target working distance is as follows:
I(r,L)＝E(r,L)·E * (r,L)
in the formula, E * (r, L) is the conjugate of the electromagnetic field distribution E (r, L) at the designed target working distance for the defocused optical system.
5. The method for designing a light beam transformation system for a long-distance laser Doppler velocimeter according to claim 1, wherein in step 6,
the method is characterized in that the size of a light spot at a working distance required by the design of a velocimeter system is used as a limiting condition to obtain a lens combination meeting the design requirements of an optical system, and the method specifically comprises the following steps:
and taking the focal lengths of the concave lens and the convex lens as independent variables, carrying out three-dimensional curved surface graphical expression on the relation between the spot radius of the measuring beam at the working distance and the focal lengths of the concave lens and the convex lens, intersecting a plane omega const with the three-dimensional curved surface graph, and obtaining the focal length values of the concave lens and the convex lens corresponding to points on the intersection line of the plane omega const and the three-dimensional curved surface graph, namely the lens combination meeting the design requirements of the optical system.
6. The method for designing a beam transformation system for a long-distance laser doppler velocimeter according to any one of claims 1-5, further comprising:
and 7, screening the lens group combinations meeting the requirements according to the actual conditions, and optimizing the surface type of the lens group by using ZMAX optical design software, thereby completing the design and selection of the parameters of the light beam transformation system.
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