CN111679428A - Multi-optical-path optical system initial structure searching method based on paraxial aberration theory - Google Patents
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Abstract
A multi-light path optical system initial structure searching method based on paraxial aberration theory relates to the field of optical instruments. The invention solves the problems that the selected initial structure has great influence on the subsequent optimization result in the design and optimization process of the existing multi-light-path composite optical system, the existing method can only calculate the initial structure of a single system, and the focal length distribution and aberration correction of a plurality of light paths cannot be realized. The method comprises the steps of establishing a multi-light-path composite optical system objective function consisting of optical system structural layout constraint conditions, focal power distribution and paraxial aberration, and solving the problem of the optimal solution of the objective function. A fast search of the initial structure is achieved. The searching method has good on-axis aberration correction characteristic, has reasonable and compact optical machine structure parameters, and is suitable for establishing the initial structure of the multi-optical path multi-focal length composite optical system and optimizing the optics.
Description
Technical Field
The invention relates to the technical field of multi-light-path composite imaging and detection, in particular to a method for quickly searching an initial structure of a multi-light-path composite optical system based on a paraxial aberration theory.
Background
With the increasing demand for comprehensive measurement and detection of multiple spectral bands of targets, the multi-band composite optical system gradually becomes a development trend of a remote imaging detection optical system. The visible light system can provide a high-resolution target image and enrich target detail information. The infrared optical system has stronger penetrating power and better anti-interference capability, and can work all day long. The laser has good monochromaticity, strong directivity, strong anti-interference capability and large information capacity, and is a main means for optical communication and distance measurement. The multiband optical system can better reflect the optical characteristics of the target by measuring different optical characteristics of the target, so that the detection and measurement system has more accurate precision, and the comprehensive detection and identification capability of the optical system is improved.
The coaxial catadioptric optical system is widely applied to a multi-spectral-band multi-optical-path system due to compact structure and simple processing, detection and assembly. In the design and optimization process of the optical system, the selection of the initial structure has great influence on the subsequent optimization and design results of the system. The existing related method can only be used for calculating the initial structure of a single system, and cannot realize the focal length distribution and aberration correction of a plurality of optical paths. Because the detection requirements of different spectral bands are different, the parameters of optical systems such as focal length, field of view and the like are also different.
In order to solve the problems, an initial structure searching method based on optical-mechanical structure size parameters and paraxial aberration correction is provided, an optimization function and boundary conditions based on a conventional genetic optimization algorithm are established, and the quick search of the initial structure of the multi-light-path composite optical system with good on-axis aberration characteristics and optical-mechanical structure parameters can be realized.
Disclosure of Invention
The invention provides a method for searching an initial structure of a multi-optical-path optical system based on a paraxial aberration theory, aiming at solving the problems that the selected initial structure has a large influence on a subsequent optimization result in the design and optimization process of the existing multi-optical-path composite optical system, the existing method can only calculate the initial structure of a single system, and the focal length distribution and aberration correction of a plurality of optical paths cannot be realized.
The method for searching the initial structure of the multi-optical-path optical system based on the paraxial aberration theory is realized by the following steps:
step one, establishing a multi-optical path optical power distribution optimization function clause based on an optical power distribution method of a multi-optical path composite optical system; the specific process is as follows:
the multi-light path composite optical system is divided into a catadioptric light path at the front end and a reflective light path at the rear end, and the focal powers of the catadioptric light path and the reflective light path are reasonably distributed; obtaining a combined focal length of the reflection light path and a combined focal length of the refraction and reflection light path;
secondly, on the basis of a paraxial aberration theory, the secondary mirror is equivalent to a combination of a single thin lens and a parallel flat plate, and paraxial aberration optimization function components of a reflection light path and a refraction and reflection light path are obtained; the specific process is as follows:
the light of the refraction and reflection light path is reflected by the primary mirror and then passes through the secondary mirror to be converged and imaged, and the spherical aberration of the single thin lens is as follows:
wherein α is the primary mirror obscuration ratio caused by the secondary mirror, β is the magnification of the secondary mirror, A is the spherical aberration coefficient, n is the refractive index of the substrate material of the secondary mirror, e2Is the aspheric coefficient of the secondary mirror, r1、r2The radii of curvature of the right and left surfaces of the secondary mirror, respectively;
a ═ a (α, β), represented by the following formula:
in the formula, R1And R2The radii of curvature of the reflecting surfaces of the primary and secondary mirrors respectively,
the spherical aberration formula of the parallel flat plate is as follows:
in the formula, h1、h2The height of the edge ray in the primary and secondary mirrors, i1、i2Is the incident angle of light on both sides of the parallel plate, i'1、i'2The light rays are emitted from two surfaces of the parallel flat plate; d0Thickness of the parallel plate at focal length normalization, u1、u2Is the angle between the incident ray and the optical axis of the parallel plate i1＝i2′＝-u1，i1′＝i2＝-u2，f1Is the focal length of the reflected light path;
then the total paraxial first-order spherical aberration of the catadioptric light path is:
in the formula, SI_Catadioptric_PMIs the primary spherical aberration, S, of the primary mirror in the catadioptric pathI_Catadioptric_SM_thin lensIs the spherical aberration of a single thin lens, SI_Catadioptric_SM_Parallel plateSpherical aberration of parallel plates;
thirdly, establishing an optical-mechanical structure parameter optimization function clause of the multi-optical-path system according to the optical-mechanical structure parameter requirement of the composite optical system on the rear intercept behind the primary mirror;
constraint condition C ═ l 'of system structure layout'2-k2d is back intercept of reflected light path l'2Is the distance from the secondary mirror to the image plane, k2D is the primary and secondary mirror spacing;
step four, establishing an integral optimization objective function F;
obtaining α, e according to the primary spherical aberration of the reflection optical path composed of the primary and secondary mirrors and the total paraxial primary spherical aberration of the refraction and reflection optical path obtained in the third step1,e2,d0Is hiddenExpression:
in the formula, SI_ReflectionIs the primary spherical aberration of the reflected light path;
the objective function is then expressed as:
in the formula, ωi(i is 1,2,3,4) is corresponding weight, and phi is constraint condition of system focal length;
and step five, optimizing the objective function F to obtain the initial structure parameter of the optical system corresponding to the minimum objective function, and completing the search of the initial structure of the multi-optical-path composite optical system.
The invention has the beneficial effects that: the searching method adopts a paraxial aberration correction method, light rays of a catadioptric light path are reflected by a main mirror and then pass through a secondary mirror to be converged and imaged, the secondary mirror can be regarded as a plano-convex lens in a transmission light path, the secondary mirror of a catadioptric system is equivalently a combined lens group consisting of an ideal thin lens and a parallel flat plate with a certain thickness, and a paraxial aberration formula of the catadioptric light path is deduced by utilizing the relevant aberration theory of the main mirror, the thin lens and the parallel flat plate and is used as one of optimization function clauses in an initial structure searching method.
The invention considers the focal power distribution, the structure layout problem and the aberration problem of the system, establishes a multi-optical-path composite optical system objective function consisting of the optical system structure layout constraint condition, the focal power distribution and the paraxial aberration through the optimization variable parameters including the optical structure profile parameter, the primary and secondary reflector aspheric surface coefficient and the focal power distribution coefficients of the two reflection and refraction optical paths, and converts the parameter problem of the initial structure of the optical system into the problem of solving the optimal solution of the objective function.
The method can simply, conveniently and quickly search the initial structure of the multi-light-path composite optical system by using the conventional genetic algorithm on the premise of not increasing the complexity of the algorithm by using the given method for searching and solving the initial structure of the focal length distribution and paraxial aberration.
In the invention, the structural layout constraint conditions of the optical-mechanical system are as follows: and the secondary mirror obscuration and the back intercept of the two reflection light paths are restrained by using the obscuration ratio and the secondary mirror magnification caused by the secondary mirror, so that a reasonable optical-mechanical structural layout is obtained.
According to the initial structure searching method, the weight proportion among the related optimization function items is properly adjusted through the optimization functions, the parameter problem of the initial structure of the optical system is converted into the problem of solving the optimal solution of the target function F, and a group of initial structure system parameters which meet the requirements that the focal length distribution of two optical paths is reasonable, the system focus shift amount can meet the requirement of the subsequent optical system design and the paraxial aberration is small are solved.
The method has good on-axis aberration correction characteristic, reasonable and compact optical machine structure parameters, can realize full-field high imaging quality through subsequent optical optimization, and is suitable for establishing the initial structure of the multi-light path multi-focal length composite optical system and optimizing the optics.
The searching method establishes a target optimization function and boundary conditions, and can realize the quick search of the initial structure of the multi-light-path composite optical system with good on-axis aberration characteristics and optical-mechanical structure parameters by using a conventional simple optimization algorithm. The method can quickly search the initial structure of the multi-light-path composite optical system with better paraxial imaging quality under the composite optical structure parameters, is simple and quick, can effectively reduce the manual experience influence and the initial structure design difficulty of an optical designer, improves the initial structure establishing efficiency, and shortens the initial structure searching and optimizing time.
Drawings
FIG. 1 is a schematic diagram of an optical path structure of a multi-optical path compound optical system in the method for searching an initial structure of a multi-optical path optical system based on paraxial aberration theory according to the present invention;
FIG. 2 is a flowchart of a method for searching an initial structure of a multi-optical path optical system based on paraxial aberration theory according to the present invention;
FIG. 3 is a schematic diagram illustrating parameters required for aberration modeling and ray tracing of a catadioptric and two-mirror optical path based on paraxial aberration theory for a multi-optical path optical system initial structure search method based on paraxial aberration theory according to the present invention;
FIG. 4 is a convergence curve of an objective function F of an initial structure of a multi-optical path compound optical system;
FIG. 5 is a schematic diagram of an initial configuration of an optical system before searching;
FIG. 6 is a schematic diagram of an initial structure of an optical system searched based on paraxial aberration theory and an optical-mechanical structure parameter method;
FIG. 7 is a corresponding MTF curve of the optical transfer function of the initial structure;
fig. 8 is an optical transfer function MTF curve of the optimized visible light path.
Detailed Description
In a first embodiment, the method for searching an initial structure of a multi-optical path optical system based on paraxial aberration theory according to the present embodiment is described with reference to fig. 1 to 8, and includes a multi-optical path composite optical system, where the multi-optical path composite optical system is a common-aperture three-channel multi-spectral-band optical system, and an optical structure layout of the multi-optical path composite optical system is shown in fig. 1. The functions of visible light imaging, long-wave infrared imaging and laser radar detection can be simultaneously completed. The optical system is established based on a Ritchey-Chretien type main optical system consisting of a main mirror 1 and a secondary mirror 2, and is divided into a catadioptric optical path at the front end and a reflecting optical path at the rear end in order to ensure the compactness of the system and finish the optical function with high quality; the refraction and reflection light path at the front end is a laser radar light path, and target light rays are reflected by the primary mirror 1 and then reach a laser path image surface 4 through the secondary mirror 2 and the laser path correcting mirror group 3. The secondary mirror 2 is made of optical glass material, has high transmittance in a near infrared region while having good thermal stability, and is coated with a selective transmission light splitting optical film on the surface thereof, so that visible light and long-wavelength infrared light are reflected on the surface of the secondary mirror and enter a rear end reflection light path, and laser light in a narrow spectrum band is transmitted on the right surface of the secondary mirror to form a front end reflection light path, as shown in fig. 1. And then, the left end lens of the secondary mirror is utilized to further correct residual aberration of the primary mirror and the transmission secondary mirror, so that the design of a laser radar receiving system is realized.
The reflecting light path at the rear end is a visible light path and an infrared light path of the imaging system, the target light is reflected by the primary mirror 1 and the secondary mirror 2, and then is imaged at a visible light path image surface 8 and an infrared path image surface 9 respectively through the beam splitter prism 5, the rear-end visible light path correcting mirror 6 and the infrared path correcting mirror 7. The light splitting cubic prism 5 is formed by splicing two triangular prisms, the light transmission spectrum section of the material extends from visible light to long-wave infrared, and the inclined plane of the light splitting cubic prism 5 is plated with a selective transmission optical film to reflect the visible light and transmit the infrared.
The present embodiment is described with reference to fig. 2, and the method for searching the initial structure of the multi-optical path optical system of the present embodiment is specifically realized by the following steps:
establishing a multi-optical path focal power distribution optimization function clause based on a focal power distribution method of a multi-optical path composite optical system; the overall length of the system is not too long, and the layout is reasonable as much as possible, so that the focal power of the front and rear end optical paths of the optical system needs to be reasonably distributed. For a two-mirror system, the focal power of the primary and secondary mirrors has a certain relationship with the structural parameters, and the calculation of the initial structure can be realized through the distribution of the focal power. The front end of the optical system is a laser receiving unit, the focal length of a laser light path is smaller than that of an imaging unit, a proper optical focal length value is selected under the condition that the aberration condition is met, and the two paths of optical focal lengths are reasonably distributed. The imaging system needs to split light of two wave bands, the field angle is large, off-axis aberration and on-axis aberration can be corrected, and when the beam splitter prism and the correction lens group are reasonably added, the focal extension amount is not too short.
In the existing multi-light path composite optical system, the focal length calculation formula for a single thick lens is as follows:
wherein r is1' and r2' radius of curvature of both sides of Single Thick lens, N0Refractive index of external medium at incident end of thick lens, N1Is the refractive index of the thick lens material itself, N2Is an external medium of the exit end of the thick lensThe refractive index of the material, t, is the axial center thickness of the thick lens.
Since the refractive indexes of the incident end and the emergent end of the reflector are consistent, and the refractive index of the reflector is-1, according to the formula (1), the focal length calculation formula of the reflector can be simplified as follows:
wherein R is the curvature radius of the reflector. In the case of an ideal thin lens, t is 0, and for a plano-convex thin lens, its focal length can be simplified as:
wherein r is the curvature radius of the plane convex lens curved surface. The power distribution formula of the two-lens system is as follows:
φ＝φ1+φ2-tφ1φ2(4)
wherein phi is1Is the focal power of the primary mirror, phi2Is the focal power of the secondary mirror (reflective or transmissive optical path), phi is the combined focal power of the two mirror system, the focal power being the reciprocal of the focal length.
In this embodiment, d is the primary-secondary mirror pitch, which is described with reference to fig. 3. The reflected light path is that the light is reflected by the primary mirror and the secondary mirror to reach the focus of F1 at the right end of the primary mirror. The refraction and reflection light path is that light rays are reflected by the primary mirror and then refracted by the secondary mirror to reach the focus of F2 at the left end of the secondary mirror. The combined focal length of the reflected light path is:
the combined focal length of the refraction and reflection optical path is as follows:
wherein n is1Is the refractive index of the external medium at the incident end of the primary mirror, n'1Refractive index of external medium at exit end of primary mirror，n2Is the refractive index, n ', of the external medium of the incident end at the right side surface of the secondary mirror thin lens'2Is the refractive index of the internal medium of the refractive end at the right surface of the thin secondary lens, n3Is the refractive index, n ', of the refractive-end internal medium at the left side surface of the secondary mirror thin lens'3Is the refractive index of the exit end external medium at the left side surface of the thin secondary lens. R1And R2The radii of curvature of the reflecting surfaces of the primary and secondary mirrors, respectively.
Secondly, on the basis of a paraxial aberration theory, the secondary mirror is equivalent to a combination of a thin lens and a parallel flat plate, and paraxial aberration optimization function components of a reflection light path and a refraction and reflection light path are deduced;
according to the structural design requirement of imaging quality, an initial structure including the structure size and the barrier is reasonably selected.
Setting the focal length of the primary mirror to f1' the object distance of the main mirror is l2The image distance of the secondary mirror is l2'。h1、h2The heights of the edge rays of the primary mirror 1 and the secondary mirror 2 are the half apertures v of the primary mirror and the secondary mirror2、v2' the object-side aperture angle and the image-side aperture angle of the primary mirror, α the blocking ratio of the primary mirror caused by the secondary mirror, β the magnification of the secondary mirror, which can represent the original profile and the coefficient of third-order aberration, etc., related parameters:
the normalized profile parameters (system focal length normalization) of the initial structure can be expressed based on paraxial optical theory: d is the distance between the primary mirror and the secondary mirror:
according to the theory of third-order aberration, the primary spherical aberration of two reflecting light paths consisting of the primary mirror and the secondary mirror is as follows:
wherein S isI_Reflection_PMPrincipal spherical aberration of a two-mirror system, SI_Reflection_SMSecondary spherical aberration of two-mirror system, e1Is the aspheric coefficient of the primary mirror, e2The aspheric coefficients of the secondary mirror.
For the catadioptric path, the primary spherical aberration generated by the primary mirror is:
the light rays of the refraction and reflection light path are reflected by the primary mirror and then pass through the secondary mirror to be converged and imaged, and at the moment, the secondary mirror can be regarded as a plano-convex lens in the transmission light path and is equivalent to a combined lens group of a thin lens and a parallel flat plate.
The primary spherical aberration for a single thin lens is:
SI＝h2 4A (14)
the expression of the primary spherical aberration coefficient A is as follows:
in a reflective system, let n be after a reflection2＝n3′＝-n0，n2′＝n3Where n is the refractive index of the secondary mirror substrate material (the material of the thin lens and the parallel plate are identical, the material refractive index is the same). When the thin lens is placed in air, then n 01. Is provided with
Wherein r is1、r2Radius of curvature of right and left surfaces of the thin secondary lens, /)1＝L2Then a can be expressed as:
wherein
The focal power of the single thin lens of the secondary mirror.
As can be seen from FIG. 3, according to the ray tracing sequence, the first surface on the right side of the thin secondary mirror lens in the refraction and reflection light path is the same as the reflection surface of the secondary mirror in the reflection light path, and the curvature radius r of the right surface of the thin secondary mirror lens1＝R2When the secondary mirror is approximated by a plano-convex thin lens equivalent, r2 is infinite, and the thickness t is 0, then
Then one can deduce that a ═ a (α, β) is expressed as
The right surface of the thin secondary lens is aspheric, and the aspheric aberration increment of the surface is as follows:
wherein the incident height h of the light on the secondary mirror2Half aperture of secondary mirror(primary mirror obscuration ratio due to secondary mirror) is the same.
h2＝α (22)
Therefore, the refractive-reflective optical path thin lens has spherical aberration:
for the parallel plate at the left end of the thin lens, the primary spherical aberration coefficient is:
SI_Catadioptric_SM_Parallel plate＝h1n1i1(i1-i1′)(i1′-u1)+h2n2i2(i2-i2′)(i2′-u2) (25)
wherein: i.e. i1、i2Is the incident angle of light on both sides of the parallel plate, i'1、i'2The exit angle of the light ray on the two sides of the parallel flat plate, u1、u2Is the angle between the incident ray and the optical axis of the parallel plate i1＝i2′＝-u1，i1′＝i2＝-u2Then the spherical aberration expression of the parallel plate can be deduced as
Wherein f is1For reflecting the focal length of the optical path, the parallel plate material is identical to the lens material, d0Is the thickness of the parallel plate when normalized by the focal length. The combined focal length of the catadioptric optical path can be obtained by equation (6).
Then the total paraxial first-order spherical aberration of the catadioptric light path is:
and thirdly, restraining the secondary mirror obscuration and the rear intercept of the two reflection light paths by using the obscuration ratio and the secondary mirror magnification caused by the secondary mirror to obtain a reasonable optical-mechanical structure layout.
As can be seen from equations (12) and (27), the spherical aberration of the two-way optical system can be written as AND α, e1,e2,d0The implicit expression concerned is:
considering the system power distribution, the structure layout problem and the aberration problem at the same time, the objective function can be expressed as:
wherein, ω isi(i ═ 1,2,3,4) is the corresponding weight, Φ is the system focal length assignment constraint, l'2D is the distance from the secondary mirror to the image plane, d is the primary and secondary mirror spacing, and C is the system structure layout constraint condition C ═ l'2-k2d is the back intercept of the two-inverse system, k2For adjusting the coefficient of the rear intercept, a beam splitter prism is required to be added in a reflection light path to split visible light and long-wave infrared light, a longer focus extension is required, optimization can be carried out according to the actual structural size, and generally k is2Taking 1.3-1.7.
Fifthly, converting the optical initial structure design into a target function optimization problem; optimizing the target function by using a genetic algorithm, and if the target function does not meet the requirements, performing iterative optimization on the item weight; and obtaining the initial structure parameters of the optical system corresponding to the minimum objective function, and completing the search of the initial structure of the multi-light-path composite optical system.
And C, converting the parameter problem of the initial structure of the optical system into a problem of solving the optimal solution of the objective function F through the objective function F established in the step four. The optimization is mainly to solve a group of initial structural system structural parameters which meet the requirements of reasonable focal length distribution of two optical paths, meet the requirements of subsequent optical system design and have small paraxial aberration by adopting a Genetic Algorithm (GA for short).
In this embodiment, the genetic algorithm is a relatively common algorithm, and the initial structure of the multi-optical path composite optical system can be simply, conveniently and quickly searched by using the above-mentioned focal length allocation and paraxial aberration solving method without increasing the complexity of the algorithm.
Second embodiment, the present embodiment will be described with reference to fig. 4 to 8, and the present embodiment is an example of the method for searching for an initial structure of a multi-optical path optical system based on paraxial aberration theory according to the first embodiment:
the solution of the initial structure is realized through MATLAB, and the main working parameters of GA are as follows: the number of individuals, nind (number of individuals), is 100, the maximum number of generations, maxgen (maximum number of generations) is 300, the number of binary digits, preci (precision of variables), of variables is 20, and the groove (Generation gap) GGAP is 0.9. The reflecting light path is an imaging system, the refraction and reflection light path is a laser receiving system, and in the aspect of aberration correction, the weight of the reflecting light path is slightly larger than that of the refraction and reflection light path. The specific variable parameter ranges are shown in the table:
TABLE 1 optimized variable value Range
And solving parameters of the multiband common R-C optical initial structure by adopting a genetic algorithm according to the objective function and the parameter range. Fig. 4 is a convergence curve of the objective function F of the initial structure of the multi-optical path composite optical system, and it can be seen from the graph that the value of F is gradually reduced, the convergence of the objective function is faster, which illustrates that the initial structure is more quickly searched. It can be seen from the objective function graph 4 that when the algorithm is optimized to 30 generations, the initial structure of the optical system has already reached a better condition, and the 100 th generation solution of the final solution of the system optimization is taken as the initial structure of the optical system. FIG. 5 is a diagram of an initial structure of the optical system before searching, corresponding to the 0 th generation of the objective function in FIG. 4. Fig. 6 is a schematic diagram of an initial structure of an optical system searched based on paraxial aberration theory and an optical-mechanical structure parameter method, which corresponds to the 100 th generation of the objective function in fig. 4. An optical transfer function MTF curve corresponding to the initial structure of the system is shown in FIG. 7, the initial structure of the system is optimized and solved under the condition of a single waveband and zero field of view, so that the on-axis imaging quality is high, but the off-axis aberration is reduced to some extent.
As can be seen from fig. 7, the MTF curve of the off-axis field tends to increase, and can be used as an initial structure for off-axis aberration optimization. When a subsequent optical system is designed, the correction lens group is required to further correct off-axis aberrations such as spherical aberration, coma, astigmatism and chromatic aberration, and the transmission correction lens at the rear end of the reflecting mirror is optimized by using optical design software, so that the off-axis aberrations can be corrected, and an optical transfer function (MTF) curve of a visible light path is shown in fig. 8, wherein the transfer function is greater than 0.4 within a cut-off frequency and is close to a diffraction limit. The result shows that the initial structure obtained by the searching method has better on-axis aberration characteristic, and the optical design result of the optical system which gives consideration to high imaging quality and reasonable optical machine structure parameters can be obtained through simple subsequent optimization.
Claims (3)
1. The method for searching the initial structure of the multi-light-path optical system based on the paraxial aberration theory is characterized by comprising the following steps of: the method is realized by the following steps:
step one, establishing a multi-optical path optical power distribution optimization function clause based on an optical power distribution method of a multi-optical path composite optical system; the specific process is as follows:
the multi-light path composite optical system is divided into a catadioptric light path at the front end and a reflective light path at the rear end, and the focal powers of the catadioptric light path and the reflective light path are reasonably distributed; obtaining a combined focal length of the reflection light path and a combined focal length of the refraction and reflection light path;
secondly, on the basis of a paraxial aberration theory, the secondary mirror is equivalent to a combination of a single thin lens and a parallel flat plate, and paraxial aberration optimization function components of a reflection light path and a refraction and reflection light path are obtained; the specific process is as follows:
the light of the refraction and reflection light path is reflected by the primary mirror and then passes through the secondary mirror to be converged and imaged, and the spherical aberration of the single thin lens is as follows:
wherein α is the primary mirror obscuration ratio caused by the secondary mirror, β is the magnification of the secondary mirror, A is the spherical aberration coefficient, n is the refractive index of the substrate material of the secondary mirror, e2Is the aspheric coefficient of the secondary mirror, r1、r2The radii of curvature of the right and left surfaces of the secondary mirror, respectively;
a ═ a (α, β), represented by the following formula:
in the formula, R1And R2The radii of curvature of the reflecting surfaces of the primary and secondary mirrors respectively,
the spherical aberration formula of the parallel flat plate is as follows:
in the formula, h1、h2The height of the edge ray in the primary and secondary mirrors, i1、i2Is the incident angle of light on both sides of the parallel plate, i'1、i'2The light rays are emitted from two surfaces of the parallel flat plate; d0Thickness of the parallel plate at focal length normalization, u1、u2Is the angle between the incident ray and the optical axis of the parallel plate i1＝i2′＝-u1，i1′＝i2＝-u2，f1Is the focal length of the reflected light path;
then the total paraxial first-order spherical aberration of the catadioptric light path is:
in the formula, SI_Catadioptric_PMIs the primary spherical aberration, S, of the primary mirror in the catadioptric pathI_Catadioptric_SM_thinlensIs the spherical aberration of a single thin lens, SI_Catadioptric_SM_ParallelplateSpherical aberration of parallel plates;
thirdly, establishing an optical-mechanical structure parameter optimization function clause of the multi-optical-path system according to the optical-mechanical structure parameter requirement of the composite optical system on the rear intercept behind the primary mirror;
constraint condition C ═ l 'of system structure layout'2-k2d is back intercept of reflected light path l'2Is the distance from the secondary mirror to the image plane, k2D is the primary and secondary mirror spacing;
step four, establishing an integral optimization objective function F;
obtaining α, e according to the primary spherical aberration of the reflection optical path composed of the primary and secondary mirrors and the total paraxial primary spherical aberration of the refraction and reflection optical path obtained in the third step1,e2,d0Implicit expression of (c):
in the formula, SI_ReflectionIs the primary spherical aberration of the reflected light path;
the objective function is then expressed as:
in the formula, ωi(i is 1,2,3,4) is corresponding weight, and phi is constraint condition of system focal length;
and step five, optimizing the objective function F to obtain the initial structure parameter of the optical system corresponding to the minimum objective function, and completing the search of the initial structure of the multi-optical-path composite optical system.
2. The method for searching for an initial structure of a multi-optical path optical system based on paraxial aberration theory according to claim 1, wherein: in the first step, the combined focal length of the reflection light path is:
in the formula, n1Is the refractive index of the external medium at the incident end of the primary mirror, n'1Is the refractive index of the external medium at the exit end of the primary mirror, n2Is the refractive index, n ', of the external medium of the incident end at the right side surface of the secondary mirror thin lens'2The refractive index of the internal medium of the refraction end at the right side surface of the thin secondary lens; r1And R2The radii of curvature of the reflecting surfaces of the primary and secondary mirrors, respectively.
The combined focal length of the refraction and reflection optical path is as follows:
in the formula, n3Is the refractive index of the refraction end internal medium at the left side surface of the thin secondary lens.
3. The method for searching for an initial structure of a multi-optical path optical system based on paraxial aberration theory according to claim 1, wherein: in the fourth step, the primary spherical aberration of the reflection light path composed of the primary and secondary mirrors is:
in the formula, SI_Reflection_PMIs the spherical aberration of the primary mirror in the reflected light path, SI_Reflection_SMIs the secondary spherical aberration in the reflected light path, e1Is the aspheric coefficient of the primary mirror.
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