CN109579739B - Off-axis catadioptric partial compensator system and design method - Google Patents
Off-axis catadioptric partial compensator system and design method Download PDFInfo
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Abstract
The invention relates to an off-axis catadioptric partial compensator system and a design method thereof, belonging to the technical field of photoelectric detection. The compensator system comprises two stages of compensators, the system design optimization method utilizes a three-stage aberration theory to establish a system full-aperture spherical aberration and astigmatism relational expression, combines a paraxial ray formula to establish an equation set related to the structural parameters of the compensator, then combines a genetic algorithm to solve initial structural parameters, builds a model in optical design software, sets an optimization target, optimizes operation numbers and optimization variables to optimize, and realizes the detection of the surface morphology of the non-rotationally symmetric aspheric surface. The system provided by the invention is simple in structure and easy to realize, can realize one-to-many surface shape detection, reduces the design difficulty and the processing cost of the compensator, and meanwhile, the compensator design method can effectively obtain the global optimum value of the initial structure, effectively avoids the self defects of the existing optical design software, and improves the detection precision of the non-rotationally symmetric aspheric surface.
Description
Technical Field
The invention relates to a compensator system for detecting a non-rotationally symmetric aspheric element and a design method thereof, belonging to the technical field of photoelectric detection.
Background
Aspheric surfaces are a widely used class of optical elements in modern optical systems. The aspheric surface, especially the non-rotational symmetric aspheric surface, can correct various aberrations simultaneously, can effectively improve the imaging quality of the system, increase the freedom degree of optical design, improve the flexibility of the system design and the like, and plays an important role in various fields. However, the detection of the non-rotationally symmetric aspheric surface is relatively difficult, so that the processing precision is difficult to guarantee, and therefore, the problem that needs to be solved urgently in the field of photoelectric detection at the present stage is to find a high-precision and simple-structure non-rotationally symmetric aspheric surface detection method.
In the existing non-rotational symmetry aspheric surface detection method, interferometry is a high-precision and high-sensitivity detection means, and is mainly divided into two types: zero compensation interferometry and partially compensated interferometry. The zero compensation interference method is to completely compensate the normal aberration of the measured surface when the compensator is designed, thereby realizing interference measurement. At present, common zero compensation interferometry methods mainly include: computational hologram compensation, Dall compensation, Offner compensation, and the like. However, the common features of these methods are: the compensator has higher design and processing difficulty, can only compensate the aspheric surface with a certain parameter, and has small measurement dynamic range and poor universality. The partial compensation interference method overcomes the problems of the zero compensation interference method, effectively improves the universality of the compensator, and relatively reduces the design and processing difficulty of the compensator. However, for the detection of the non-rotationally symmetric aspheric surface, the detected surface introduces non-rotationally symmetric aberrations such as astigmatism and coma aberration, and the aberrations to be compensated are relatively complex, which is very challenging for the calculation and design of the compensator structure.
In the existing partial compensation interference method for non-rotationally symmetric aspheric surfaces, chinese invention patent CN105352451B provides a quasi-universal compensation mirror based on a deformable mirror and a design method thereof. However, the design result of the method has great dependence on the design accuracy of the first-stage compensator, namely the lens or the lens group, the surface type design of the second-stage compensator, namely the deformable mirror completely depends on the optimization of optical design software, the optimization process easily falls into a local optimal value, so that the compensator meeting the design index cannot be obtained, and the deformable mirror has the defects of high control difficulty, high cost and the like.
The difficulty of the interference method detection of the non-rotationally symmetric aspheric surface lies in the calculation, design and processing of the compensator. In order to overcome the defects in the prior art, a compensator with a simple structure and high detection precision needs to be researched, the calculation method of the compensator is optimized, and the design result is prevented from falling into a local optimal value in the optimization process.
Disclosure of Invention
The invention aims to solve the problems of complex structure, high component cost, high possibility of leading an optimization result to fall into a local optimum value and the like of the existing compensator, and provides an off-axis catadioptric partial compensator system and a design method thereof.
The purpose of the invention is realized by the following technical scheme.
An off-axis catadioptric partial compensator system for a non-rotationally symmetric aspheric surface, comprising: the CCD detector, the imaging objective lens, the collimated laser, the spectroscope, the reference mirror, the first-stage compensator and the second-stage compensator jointly form an off-axis catadioptric partial compensator.
The first-stage compensator is composed of a lens or a lens group and is used for generating aberration (such as spherical aberration) with rotational symmetry to realize compensation of the rotational symmetry aberration of the surface to be measured, and meanwhile, the non-rotational symmetry aberration is generated by controlling the eccentricity and the inclination of the first-stage compensator and is used for compensating the low-order non-rotational symmetry aberration of the surface to be measured. The second-stage compensator is an off-axis spherical reflector, and the non-rotational symmetry high-order aberration compensation is realized by controlling the eccentricity and the inclination of the off-axis spherical reflector.
The optical path that above-mentioned component constitutes is: the collimated laser passes through the spectroscope, one beam of light is reflected to form reference light, the other beam of light is transmitted to form measuring light, the measuring light is reflected after passing through the reference mirror, the first-stage compensator, the second-stage compensator and the to-be-measured non-rotationally symmetric aspheric surface, passes through the second-stage compensator and the first-stage compensator again, penetrates through the reference mirror, forms interference fringes with the reference light, and is observed at the CCD detector through the imaging objective lens.
The invention also provides a design optimization method aiming at the system. Firstly, analyzing the whole system based on a three-level aberration theory, a paraxial ray theory and the like, establishing an equation, and deducing and calculating an initial structure. And then, setting system initial structure parameters by taking optical design software as a design platform, and carrying out initial optimization on an initial system according to actual requirements so as to meet the geometric relation requirement of the system structure. And finally, taking the initially optimized system as a new initial structure, and carrying out secondary optimization on the system to obtain the system meeting the surface shape error detection of the non-rotationally symmetric aspheric surface.
Advantageous effects
1. The invention has simple and easy realization of the structure, can realize the detection of the non-rotational symmetric aspheric surface only by the lens and the spherical reflector with relatively simple structures, has relatively simple system calibration and adjustment, can realize the one-to-many surface shape detection as part of the compensator, and effectively reduces the design difficulty and the processing cost of the compensator;
2. the design method of the compensator fully considers the characteristic of non-rotational symmetric aberration and combines a genetic algorithm to obtain the global optimum value of the initial structure parameter, thereby effectively avoiding the problem that the design result falls into the local optimum value and can not meet the design index due to the self defect of the optical design software.
Drawings
FIG. 1 is a schematic illustration of the use of a partial compensator of the present invention in a Fizeau interferometer;
FIG. 2 is a flow chart of a partial compensator detection method according to the present invention;
the system comprises a laser 1, a collimating laser 2, a spectroscope 3, a reference mirror 4, a first-stage compensator 5, a second-stage compensator 6, an imaging objective lens 7, a CCD detector 8 and a non-rotationally symmetric aspheric surface to be detected.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, an off-axis catadioptric partial compensator system for a non-rotationally symmetric aspheric surface includes: the device comprises a collimated laser 1, a spectroscope 2, a reference mirror 3, a first-stage compensator 4, a second-stage compensator 5, an imaging objective 6 and a CCD detector 7. The first stage compensator 4 and the second stage compensator 5 together form an off-axis catadioptric partial compensator.
The first-stage compensator 4 is composed of a lens or a lens group, and is used for generating aberration (such as spherical aberration) with rotational symmetry to compensate the rotational symmetry aberration of the non-rotationally symmetric aspheric surface 8 to be measured, and simultaneously, the eccentricity and the inclination of the first-stage compensator 4 are controlled to generate non-rotationally symmetric aberration for the low-order non-rotationally symmetric aberration of the non-rotationally symmetric aspheric surface 8 to be measured. The second stage compensator 5 is an off-axis spherical mirror, and compensates for non-rotationally symmetric higher order aberrations by controlling its eccentricity and tilt.
The optical path that above-mentioned component constitutes is: the collimated laser 1 passes through the spectroscope 2, one beam of light is reflected to form reference light, and the other beam of light is transmitted to form measuring light. The measuring light is reflected by the reference mirror 3, the first-stage compensator 4, the second-stage compensator 5 and the non-rotationally symmetric aspheric surface 8 to be measured, passes through the second-stage compensator 5 and the first-stage compensator 4 again, penetrates through the reference mirror 3, forms interference fringes with the reference light, and is observed at the CCD detector 7 through the imaging objective 6.
A design method of an off-axis catadioptric partial compensator system specifically comprises the following steps:
step 1: basic parameters of the system are determined.
Basic parameters are set based on the system architecture, including the entrance pupil diameter D and the wavelength λ.
Step 2: and establishing an equation system related to the system structure parameters.
Firstly, an aberration coefficient relational expression of the whole system is established by a three-level aberration theory. To simplify the design, consider the spherical aberration S that does not vary with off-axis amountⅠAnd non-rotationally symmetric aberration astigmatism SⅢTo achieve compensation of non-rotationally symmetric aspheric aberrations. Spherical aberration SⅠAnd astigmatism SⅢAre respectively:
SI＝∑hP+∑hΔP (1)
wherein:
J＝n(uhz-uzh) (7)
in the formula, h is the incident height of the first auxiliary ray, i.e. the edge ray, hzIs the incident height of the second auxiliary light ray, i is the incident angle, i ' is the emergent angle, u is the object-side aperture angle, u ' is the image-side aperture angle, n and n ' respectively represent the incident-side refractive index and the transmission-or reflection-side refractive index, k is the quadratic aspheric coefficient, R0Is the vertex radius of curvature, u, of the surface to be measuredzIs the second assist ray angle of incidence.
Secondly, because the light passes through the off-axis catadioptric partial compensator twice and is only reflected once on the non-rotationally symmetric aspheric surface to be measured, an aberration relation equation between the system and the surface to be measured is established as follows:
2Si supplement+SI is not＝0 (8)
2SIII supplement+SIII non＝0 (9)
Wherein S isI supplementIs the spherical aberration, S, of the off-axis catadioptric partial compensatorI is notIs the spherical aberration generated by the non-rotationally symmetric aspheric surface to be measured. SIII supplementAstigmatism, S, of an off-axis catadioptric partial compensatorIII supplementIs the astigmatism generated by the non-rotationally symmetric aspheric surface to be measured. When the aberration relation is established, the aberration relation between the off-axis catadioptric partial compensator and the full aperture of the surface to be measured is considered, so that the aberration introduced by the non-rotational symmetry of the system is fully considered.
Thirdly, establishing an equation of the object image square aperture angle of each refraction and reflection surface relative to the curvature radius by using a paraxial ray expression:
where r is the radius of curvature for each refractive and reflective surface. In summary, equations (8), (9) and (10) establish a system of equations for the structural parameters of the off-axis catadioptric partial compensator.
And step 3: and solving the equation set by using a mathematical solving tool to obtain the initial structure parameters of the off-axis catadioptric partial compensator.
Setting the distance d between the vertex of the lens (group) and the vertex of the spherical reflector according to the prior knowledge and the design requirement of the practical system1And the distance d from the vertex of the spherical reflector to the vertex of the non-rotationally symmetric aspheric surface to be measured2. Solving the initial structure parameters of the off-axis catadioptric partial compensator based on a genetic algorithm to obtain the global optimal values of the initial structure parameters of the off-axis catadioptric partial compensator, and performing iterative computation on the basis to obtain the initial structure parameters of the off-axis catadioptric partial compensator finally used for modeling.
And 4, step 4: and modeling and optimizing the system structure by using optical design software.
Firstly, modeling is carried out on the system according to the initial structure parameters obtained in the step 3 in the optical design software, so that the problem that the design result falls into a local optimal value due to the defects of the optical design software is solved.
Secondly, setting the obtained initial structure parameters and the eccentricity and the inclination of the off-axis catadioptric partial compensator as optimization variables, and initially optimizing the system by taking the wave front PV as an optimization target so as to solve the problem that edge light rays cannot enter the system due to paraxial approximation. If the system has the problem of light shielding, the light position is controlled by combining the ZPL instruction, and the initially optimized system is used as a new initial system.
The system after the initial optimization is completed can ensure that edge light rays enter the system and have no light ray shielding problem. On the basis, the system is optimized secondarily, optimization variables and optimization targets of the system are the same as those of the initial optimization, so that a result that interference fringes are relatively sparse at an image surface is obtained, and residual wave fronts at the moment are recorded.
And 5: and judging whether the design result is feasible or not.
And calculating the maximum wavefront slope K of the residual wavefront, and judging whether the interference fringes at the moment can be detected. Usually, the number of pixels of the selected CCD detector is 1024 pixels × 1024 pixels, the maximum spatial frequency of the corresponding detectable interference fringes is about 0.45 λ/pixel, that is, K is less than or equal to 0.45 λ/pixel, the interference fringes can be detected, otherwise, the interference fringes cannot be detected, the structural parameters of the system do not meet the design indexes, the step 4 is required to return to perform the system parameter setting again, and the optimization is performed until the design indexes are met.
Examples
The non-rotationally symmetric aspheric surface measured in this example is an off-axis paraboloid of relatively simple structure with an aperture of 76.2mm, a vertex radius of curvature of 889mm, an aspheric coefficient of-1 and an off-axis amount of 10 mm. The specific process of designing the off-axis catadioptric partial compensator detection system for realizing the detection of the surface shape error of the non-rotationally symmetric aspheric surface is shown in fig. 2.
Step 1: and determining basic system parameters.
Based on the system configuration, the entrance pupil diameter D of the system was set to 81mm, and the wavelength λ was set to 532 nm.
Step 2: and establishing an equation system related to the system structure parameters.
And establishing an equation set of system initial structure parameters according to a three-level aberration theory and a paraxial ray formula, wherein the astigmatism and spherical aberration relational expression needs to consider the full aperture so as to fully consider the influence of aberration introduced by the non-rotationally symmetrical surface to be measured.
And step 3: and solving the equation set by using a mathematical solving tool, and solving the initial structure parameters of the off-axis catadioptric partial compensator.
Setting the distance d between the vertex of the lens (group) and the vertex of the spherical reflector according to the prior knowledge and the design requirement of the practical system1100mm and the distance d between the vertex of the spherical reflector and the vertex of the non-rotationally symmetrical aspheric surface to be measured2-500 mm. Solving the global optimal value of the initial structure of the off-axis catadioptric partial compensator based on a genetic algorithm, taking the global optimal value as an iterative initial value, and solving to obtain initial structure parameters for system modeling, namely the curvature radius r of two optical surfaces of the lens1＝-8.5787mm，r2Radius of curvature r of spherical mirror-8.2617 mm3＝-323.0668mm
And 4, step 4: and modeling and optimizing the system structure by using optical design software.
In the present embodiment, ZEMAX is selected as the optical design software. In thatIn the ZEMAX, modeling is carried out on the system according to the initial structure parameters obtained in the step 3, and an optimization variable, an optimization target and an optimization operand are set, so that the system is initially optimized, and the condition that light rays can enter the system and are shielded by no light rays is ensured. On the basis, the system is optimized secondarily, and the finally obtained optical parameter of the system is r1＝168.217619mm，r2＝-1030.439322mm，r3Spherical mirror aperture D of-89.718106 mm3＝9.375m3m3，2d1＝291.980398mm，d2-843.885967mm, decentration and tilt of lens and spherical mirror respectively being L1decenter＝1.173455mm，L1tilt＝0.005740054°，M1decenter＝-0.038789mm，M1tilt＝-10°。
And 5: and judging whether the design result is feasible or not.
And reading the optimized system residual wave front, and calculating the maximum wave front slope K of the residual wave front to be 0.373 lambda 8 pixel/pixel, wherein the maximum wave front slope K of the interference fringes detectable by the detector is 0.45 lambda/pixel, so that the interference fringes in the embodiment can be judged to be detected, and the designed off-axis catadioptric partial compensator is suitable.
Claims (2)
1. An off-axis catadioptric partial compensator system design method, comprising the steps of:
step 1: determining basic parameters of the system;
setting basic parameters including an entrance pupil diameter D and a wavelength lambda based on a system structure;
step 2: establishing an equation set related to system structure parameters;
firstly, establishing an aberration coefficient relational expression of the whole system by a three-level aberration theory; taking into account the spherical aberration S which does not vary with the off-axis quantityⅠAnd non-rotationally symmetric aberration astigmatism SⅢTo realize the compensation of non-rotational symmetric aspheric aberration, spherical aberration SⅠAnd astigmatism SⅢAre respectively:
SI＝∑hP+∑hΔP (1)
wherein:
J＝n(uhz-uzh) (7)
in the formula, h is the incident height of the first auxiliary ray, i.e. the edge ray, hzIs the incident height of the second auxiliary light ray, i is the incident angle, i ' is the emergent angle, u is the object-side aperture angle, u ' is the image-side aperture angle, n and n ' respectively represent the incident-side refractive index and the transmission-or reflection-side refractive index, k is the quadratic aspheric coefficient, R0Is the vertex radius of curvature, u, of the surface to be measuredzIs the second assist ray angle of incidence;
secondly, an aberration relation equation between the system and the surface to be measured is established as follows:
2Si supplement+SI is not＝0 (8)
2SIII supplement+SIII non＝0 (9)
Wherein S isI supplementIs the spherical aberration, S, of the off-axis catadioptric partial compensatorI is notIs the spherical aberration generated by the non-rotationally symmetric aspheric surface to be measured; sIII supplementAstigmatism, S, of an off-axis catadioptric partial compensatorIII supplementAstigmatism generated by the non-rotationally symmetric aspheric surface to be measured; when establishing the aberration relation, the aberration relation between the off-axis catadioptric partial compensator and the full aperture of the surface to be measured is considered, so as toFully considering the aberration introduced by the non-rotational symmetry of the system;
thirdly, establishing an equation of the object image square aperture angle of each refraction and reflection surface relative to the curvature radius by using a paraxial ray expression:
wherein r is the curvature radius corresponding to each refracting and reflecting surface; in conclusion, the equations of the structural parameters of the off-axis catadioptric partial compensator are established by the equations (8), (9) and (10);
and step 3: solving the equation set by using a mathematical solving tool to obtain initial structure parameters of the off-axis catadioptric partial compensator;
setting the distance d between the vertex of the lens and the vertex of the spherical reflector according to the prior knowledge and the design requirement of an actual system1And the distance d from the vertex of the spherical reflector to the vertex of the non-rotationally symmetric aspheric surface to be measured2(ii) a Solving the initial structure parameters of the off-axis catadioptric partial compensator based on a genetic algorithm to obtain the global optimal values of the initial structure parameters of the off-axis catadioptric partial compensator, and performing iterative computation on the basis to obtain the initial structure parameters of the off-axis catadioptric partial compensator finally used for modeling;
and 4, step 4: modeling and optimizing the system structure by using optical design software;
firstly, modeling a system in optical design software according to the initial structure parameters obtained in the step 3, and avoiding the problem that the design result falls into a local optimal value due to the defects of the optical design software;
secondly, setting the obtained initial structure parameters and the eccentricity and the inclination of the off-axis catadioptric partial compensator as optimization variables, and initially optimizing the system by taking the wave front PV as an optimization target so as to solve the problem that edge light rays cannot enter the system due to paraxial approximation; if the system has the problem of light shielding, the light position is controlled by combining a ZPL instruction, and the initially optimized system is used as a new initial system;
the system after the initial optimization is completed can ensure that edge light rays enter the system and have no light ray shielding problem; on the basis, carrying out secondary optimization on the system, wherein the optimization variables and the optimization targets of the secondary optimization are the same as those of the initial optimization, so as to obtain a result that interference fringes at an image surface are relatively sparse, and recording the residual wavefront at the moment;
and 5: judging whether the design result is feasible or not;
calculating the maximum wavefront slope K of the residual wavefront, and judging whether the interference fringes at the moment can be detected or not; if the interference fringes can not be detected, the structural parameters of the system do not accord with the design indexes, the step 4 is required to be returned to set the system parameters again, and optimization is carried out until the design indexes are met.
2. The method of claim 1, wherein the step 5 of determining whether the interference fringes are detectable comprises:
the number of pixels of the selected CCD detector is 1024 pixels multiplied by 1024 pixels, the maximum spatial frequency of the corresponding detectable interference fringes is about 0.45 lambda/pixel, namely when the maximum wavefront slope K of the residual wavefront is less than or equal to 0.45 lambda/pixel, the interference fringes can be detected, otherwise, the interference fringes can not be detected.
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