CN114994913B - Low-sensitivity three-reflector design method based on multi-initial-point quasi-Newton optimization - Google Patents
Low-sensitivity three-reflector design method based on multi-initial-point quasi-Newton optimization Download PDFInfo
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Abstract
The invention relates to a design method of a low sensitivity three-telescope based on multi-initial-point quasi-Newton optimization, which comprises the steps of establishing an optical system manufacturing performance evaluation model comprising design wave aberration and offset wave aberration, representing the evaluation model by using a lens spacing to obtain an evaluation model formula taking the lens spacing as a variable, taking the evaluation model formula as an optimization index of the system, dividing each lens spacing into a plurality of grids at equal intervals to form a plurality of calculation units, optimizing the evaluation model formula by adopting a quasi-Newton method, taking the minimum value of the optical system manufacturing performance as a global optimal value, and finally obtaining the optimized three-telescope system with low offset sensitivity. The three-reflection telescope system has better manufacturing performance, improves the accuracy of system manufacturing performance evaluation, does not need a large amount of ray tracing, can be completed only by tracing paraxial edge rays and principal rays, and has the advantages of small calculated amount, short time and high optimization speed.
Description
Technical Field
The invention relates to the technical field of optical system design, in particular to a low-sensitivity three-reflector design method based on multi-initial-point quasi-Newton optimization.
Background
The three-reflector has a larger imaging field of view, and is widely applied to astronomical observation, remote sensing and other fields at present. The conventional design method of the three-telescope system generally corrects various primary aberrations based on aberration and optical structural parameters, and obtains an optical system with good quality. However, the tolerance is usually too tight, the manufacturing cost and the processing and assembling difficulties of the system are great, and the disturbance resistance of the system is weak.
Based on the above, consider designing a three-way system with low trim sensitivity. The existing desensitizing method of the optical system mainly comprises an analytical method and a numerical method. Numerical methods are commonly used, and generally rely on complex global optimization algorithms and extensive ray tracing processes to obtain design results, including overall optimization and ray angle optimization. The general procedure of the global optimization method is to construct multiple structures based on an initial structure to simulate the state of an optical system with quantitative errors. The set of multiple structures is optimized by a global optimization function to find an optimal design. The ray incidence angle optimization method optimizes the system by using the incidence angle of a representative ray (typically an edge ray) on the optical surface as an index for evaluating the sensitivity of the system, and also by using a global optimization function to achieve a low sensitivity design. The analysis method takes aberration theory as design guidance to optimally design the overall performance of the optical system. It is generally necessary to establish a quantitative analytical relationship between the tuning error and the wavefront difference caused thereby, thereby evaluating the manufacturing performance of the optical system, and to realize a design of low tuning sensitivity by optimizing the manufacturing performance.
The traditional optical design flow of the three-telescope isolates two steps of system performance optimization and tolerance distribution, and the optical design optimization process does not consider the influence of image quality degradation caused by manufacturing and adjustment errors, but only pursues the optimal design performance. After the design is completed, the tolerance analysis is typically tight. The strict tolerance leads to serious degradation of imaging quality and performance degradation caused by the adjustment error of the optical component during the adjustment process of the optical system. The good performance of an optical system after being put into service should be a more final goal pursued by the optical designer than the performance that software has designed.
Disclosure of Invention
Aiming at the problem that the traditional three-telescope optical design method does not consider the influence of system performance and adjustment errors at the same time, so that the adjustment sensitivity of the three-telescope optical system is high, the invention provides a low-sensitivity three-telescope design method based on multi-initial-point quasi-Newton optimization.
Aiming at the three-telescope system, in order to solve the problems and realize the design of reducing the offset sensitivity, the invention adopts the following technical scheme:
a design method of a low-sensitivity three-reflection telescope based on multi-initial-point quasi-Newton optimization comprises the following steps:
step one: establishing an optical system manufacturing performance evaluation model, wherein the expression of the optical system manufacturing performance evaluation model is as follows:
wherein A is a three-telescope systemManufacturing performance;to design wave aberration, this is indicated in the field of view +.>The value of the root mean square wave aberration generated during the design of the medium optical system; />For detuning wave aberration, indicated by field of view +.>The value of the root mean square wave aberration caused by the tuning error;
step two: giving the eccentricity value and the inclination angle value in the optical system manufacturing performance evaluation model by estimating the tolerance range of the three-telescope system in the field of viewSelecting a view field point for calculating the designed wave aberration and the offset wave aberration;
step three: writing the optical system manufacturing performance evaluation model into Zemax software in the form of macro language function, and solving out offset wave aberration of the three-reflector system
Step four: the optical design software is utilized to directly obtain the design wave aberration of the three-reflector system
Step five: expressing the offset wave aberration expressionAnd the design wave aberration +.>Substituting the optical system manufacturing performance evaluation model;
step six: according to a corresponding formula among the mirror radius, the secondary coefficient and the mirror distance, the mirror radius and the secondary coefficient in the optical system manufacturing performance evaluation model obtained in the step five are expressed by the mirror distance, and an evaluation model formula which only takes the mirror distance as a variable is obtained;
step seven: dividing each mirror interval into a plurality of grids at equal intervals to form a plurality of calculation units;
step eight: and selecting an initial point in each calculation unit, calling fminunc function in Matlab to perform quasi-Newton optimization on the evaluation model formula, solving a global optimal value of the manufacturing performance A of the optical system in a set scope of change of the mirror spacing, solving the mirror spacing corresponding to the global optimal value, deducing other optical structure parameters of the three-telescope system according to the solved mirror spacing, and finally obtaining the three-telescope system with low offset sensitivity after optimization.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a low-sensitivity three-telescope design method based on multi-initial-point quasi-Newton optimization, which is characterized in that an optical system manufacturing performance evaluation model comprising system design residual errors and wave aberration generated by mirror surface imbalance is established, the evaluation model is expressed by mirror spacing to obtain an evaluation model formula taking the mirror spacing as a variable, the evaluation model formula is used as an optimization index of the system, each mirror spacing is equally divided into a plurality of grids to form a plurality of calculation units, the evaluation model formula is optimized by adopting a quasi-Newton method, and the minimum value of the optical system manufacturing performance is used as a global optimal value, so that the optimized three-telescope system with low imbalance sensitivity is finally obtained. The three-telescope system obtained after optimization has good quality and low offset sensitivity, and compared with the traditional optimization method, the three-telescope system has better manufacturing performance, and compared with the traditional rest desensitization methods, the three-telescope system improves the accuracy of system manufacturing performance evaluation, and the design method does not need a large amount of ray tracing, only needs to trace the paraxial marginal ray and the principal ray, and has the advantages of small calculated amount, short time and high optimization speed.
Drawings
FIG. 1 is a flow chart of a method of designing a low sensitivity three-reflector based on multi-initial-point quasi-Newton optimization according to the present invention;
FIG. 2 is a view field point selected by an optical system manufacturing performance evaluation model and wave aberration calculation;
FIG. 3 is a schematic diagram of a segmented computing unit of the present invention;
FIG. 4 is a schematic view of the initial optical configuration of a three-mirror telescope;
FIG. 5 is a schematic diagram of the optical structure of a three-mirror telescope (a) optimized by a conventional optimization method and a schematic diagram of the optical structure of a three-mirror telescope (b) optimized by a manufacturing performance multi-initial point quasi-Newton optimization method according to the present invention;
FIG. 6 is a graph (a) of results after optimization using a conventional optimization method and a graph (b) of results after optimization using a multi-initial point Newton's optimization method for manufacturing performance in the present invention.
Detailed Description
The technical scheme of the present invention will be described in detail with reference to the accompanying drawings and preferred embodiments.
As shown in FIG. 1, the invention provides a low-sensitivity three-reflector design method based on multi-initial-point quasi-Newton optimization, which comprises the following steps:
step one: and establishing an optical system manufacturing performance evaluation model.
In the step, wave aberration is selected as an evaluation index of design residual errors and adjustment errors, and an optical system manufacturing performance evaluation model is established and used for evaluating the manufacturing performance A of the three-reflector. The expression of the optical system manufacturing performance evaluation model is:
wherein A is the manufacturing performance of the three-telescope system;is indicated at the field of view +>The value of Root Mean Square (RMS) wave aberration generated when designing the mid-optical system is defined as the design wave aberration; />Representing the visual field +.>The value of RMS wave aberration caused by the tuning error in (a) is defined as offset wave aberration. Design wave aberration->In the system optimization process, the system can be directly called in the optical design software. Therefore, the key to establishing the optical system manufacturing performance evaluation model is to obtain the offset wave aberration +.>Is an expression of (2).
In an offset optical system, decentering and tilting of the mirror surface mainly introduce coma and astigmatism of asymmetric field of view, which are main aberrations causing degradation of image quality of the optical system after the completion of the adjustment process.
In the three-mirror telescope, tilt and decentration errors of the Secondary Mirror (SM) and the Tertiary Mirror (TM) are analyzed, usually with reference to the position of the Primary Mirror (PM). Here the coefficients Z of the four main low-order terms of the normalized Fringe wavefront Zernike polynomial are chosen 5 ，Z 6 ，Z 7 and Z8 To characterize coma and astigmatism resulting from the imbalance. In the case that each tuning error acts alone, each Zernike polynomial coefficient is calculated separately to obtain the contribution of the offset wave aberration and combinedOffset wave aberration becoming a systemDysregulated wave aberration->The specific formula of (2) is given by:
wherein ,Z5 、Z 6 、Z 7 、Z 8 As coefficients of zernike polynomials, Z 5 and Z6 Is third-order astigmatism, Z 7 and Z8 For third-order coma, the subscript T in the formula represents aberration introduced by the tilt error, and the subscript D represents aberration introduced by the decenter error.
Third-order astigmatism Z caused by maladjustment 5 and Z6 Coma of third order Z 7 and Z8 Both closely related to tilt and eccentricity errors. These Zernike polynomials can be expressed in terms of field of view (FOV) and optical structural parameters, i.e., offset wave aberrationIt can be represented by an optical structural parameter, which in turn is adjusted to control the wave aberration caused by the misalignment. The following will derive z 5,D ,z 5,T ,z 6,D ,z 6,T ,z 7,D ,z 7,T ,z 8,D and z8,T Is described.
When the optical element is deregulated, the centre of the aberration field will shift, and we introduce vector aberration theory (Nodal Aberration Theory, NAT). The vector aberration theory is mainly studied about the aberration of an optical system when there is a tilt and decentration of the optical system elements. In the detuned state, according to the relation between the Sedel coefficient and the normalized Zernike coefficient (considering the first nine items), the third-order coma based on NAT can be given by the following formula:
wherein , and />Coma vectors introduced for disorders, respectively +.>X-component and y-component of> and />The expression of (2) is as follows:
wherein ,W131,sph,SM Spherical component of the coefficient of coma aberration of secondary mirror, W 131,asph,SM Aspheric component of secondary mirror coma aberration coefficient, W 131,sph,TM Is the spherical component, W, of the coefficient of the three-mirror coma wave aberration 131,asph,TM Is the aspherical component of the three-mirror coma aberration coefficient,offset vector sphere X-axis component for the aberration field of the secondary mirror,>for the aberration field offset vector aspherical X-axis component of the secondary mirror,>offset vector sphere Y-axis component for the aberration field of the secondary mirror,>for the aberration field offset vector aspherical Y-axis component of the secondary mirror,>an aberration field for three mirrors is offset by the vector sphere X-axis component,>an aberration field offset vector aspherical X-axis component for a three mirror,>the aberration field for the three mirrors is offset by the vector sphere Y-axis component,the aberration field for the three mirrors is offset by the vector aspheric Y-axis component.
When the system aperture stop is located on the primary mirror, the secondary mirror image difference field offset vector and the tertiary mirror aberration field offset vector of the primary telescope system are shown in equations (5) and (6), respectively.
Sub-mirror difference field offset vector:
three-mirror aberration field offset vector:
wherein ,XDESM YDE for secondary mirror X-axis direction eccentric error SM ADE is the Y-axis direction eccentric error of the secondary mirror SM BDE for secondary mirror tilt error about the X-axis SM XDE for secondary mirror tilt error around Y-axis TM Is the eccentric error of X-axis direction of the three mirrors, YDE TM ADE is the eccentric error of the Y axis direction of the three mirrors TM For three-mirror tilt error about the X-axis, BDE TM Is three in threeThe mirror is tilted about the Y-axis by an error,is the incidence angle of the paraxial chief ray of the chief mirror, d 1 D is the distance between the primary mirror and the secondary mirror 2 R is the distance between the secondary mirror and the triple mirror 1 Radius of curvature r of primary mirror 2 Radius of curvature r for secondary mirror 3 Is the radius of curvature of the three mirrors. XDE described above SM 、YDE SM 、ADE SM 、BDE SM 、XDE TM 、YDE TM 、ADE TM 、BDE TM Is defined in accordance with Decenter andReturn in codev11.5.
In addition, the coma aberration coefficient (W 131,sph,SM ,W 131,asph,SM ,W 131,sph,TM and W131,asph,TM ) Can be calculated by the seidel formula, the calculation formula is as follows:
wherein ,y1 B is the incidence height of the light at the edge of the main mirror s2 B is the secondary coefficient of the secondary mirror s3 Is the secondary coefficient of the three mirrors.
By taking equations (4) - (7) into equation (3), the Zernike coefficient z can be obtained 7 and z8 Let ADE in formulas (5) and (6) SM 、ADE TM and BDESM 、BDE TM At 0, the coma aberration, z, can be obtained when there is only decentering 7,D and z8,D XDE (X-ray diffraction) order SM 、XDE TM and YDESM 、YDE TM At 0, the coma aberration, z, can be obtained when only tilt disorder exists 7,T and z8,T 。
Similarly, in the detuned state, the NAT-based third order astigmatism can be given by:
wherein , and />Coma vectors introduced for disorders, respectively +.>X-component and y-component of> and />The expression of (2) is as follows:
wherein ,W222,sph,SM Spherical component of the coefficient of the sub-mirror scattered wave aberration, W 222,asph,SM Aspheric component of the sub-mirror scattered wave aberration coefficient, W 222,sph,TM Is the spherical component of the three-mirror scattered wave aberration coefficient, W 222,asph,TM Is a three-mirror image scattered wave aberration coefficient aspheric component.
In addition, the astigmatic aberration coefficient (W) 222,sph,SM ,W 222,asph,SM ,W 222,sph,TM and W222,asph,TM ) Can be calculated by the seidel formula, the calculation formula is as follows:
substituting equations (5), (6), (9) and (10) into equation (8) can yield the Zernike coefficient z 5 and z6 The term is used to obtain the third-order astigmatism Z 5 and Z6 . ADE is given in equations (5) and (6) SM 、ADE TM and BDESM 、BDE TM At 0, it can be obtained that only eccentricity existsAstigmatism at detuning, i.e. z 5,D and z6,D . XDE order SM 、XDE TM and YDESM 、YDE TM At 0, astigmatism in the presence of tilt disorder alone, i.e. z, can be obtained 5,T and z6,T . So far, a specific expression of offset wave aberration has been derived and expressed as a form concerning optical structural parameters.
Step two: and giving the eccentric value and the inclination angle value in the optical system manufacturing performance evaluation model through estimating the tolerance range of the three-telescope system. Preferably, the eccentricity value may be set to 0.1mm and the inclination value may be set to 1.5'. And, in the field of viewIs selected for calculating the design wave aberration +.>And dysregulated wave aberration->The selected view field point is shown in fig. 2, wherein black points are used for representing view field points, which are (-1, 1), (0, 1), (-1, 0), (0, 0), (-1, -1) and (0. -1), respectively.
Step three: writing the optical system manufacturing performance evaluation model into Zemax software in the form of macro language function according to offset wave aberrationSolving the offset wave aberration of the three-telescope system in Zemax software according to the calculation formula (2)
Step four: the optical design software is utilized to directly obtain the design wave aberration of the three-reflector system
Step five: and step three, obtaining the detuned waveAberration ofAnd the design wave aberration obtained in the step four +.>Substituting the model into the optical system manufacturing performance evaluation model to obtain the manufacturing performance A of the three-reflector system.
Step six: and (3) according to a corresponding formula among the mirror radius, the secondary coefficient and the mirror distance, the mirror radius and the secondary coefficient in the optical system manufacturing performance evaluation model obtained in the step five are expressed by the mirror distance, so that an evaluation model formula taking the mirror distance as a variable is obtained. In this step, the corresponding formulas between the mirror radius, the secondary coefficient and the mirror pitch are disclosed in detail in the paper "z.gu, y.wang, and c.yan," Analytical design method of three-mirror anastigmatic telescope with mirror spacings as free design arameters, "j.astron.telesc.instron.syst.6 (04), 044007 (2020)", and will not be described in detail here.
Step seven: dividing each mirror interval into a plurality of grids at equal intervals to form a plurality of calculation units. For example, each mirror pitch may be equally divided into 10 grids, as shown in FIG. 3, where d 1 、d 2 、d 3 The distance between the primary mirror and the secondary mirror, the distance between the secondary mirror and the triple mirror, and the distance between the triple mirror and the plane mirror are respectively represented.
Step eight: a mid-scale fminunc function is called in Matlab to achieve multi-initial point-quasi-newton optimization of manufacturing performance. Specifically, an initial point is selected in each calculation unit, an fminunc function is called in Matlab to perform quasi-Newton optimization on the evaluation model formula obtained in the step six, all results of the manufacturing performance A of the optical system are solved in a set scope of variation of the mirror distance (for example, the scope of variation of the mirror distance is +/-10% of the distance of each mirror distance), the minimum value of the results is taken as a global optimal value in all the results, then the mirror distance corresponding to the global optimal value is solved, then the rest optical structure parameters (including the mirror radius and the secondary coefficient) of the three-mirror system are deduced according to the solved mirror distance, and the three-mirror system with low offset sensitivity is finally obtained after optimization.
Further, the design method of the low-sensitivity three-mirror telescope based on the multi-initial-point quasi-Newton optimization further comprises the following steps:
step nine: and analyzing the adjustment performance of the optimized three-telescope system based on the Monte Carlo method to predict the adjustment performance of the optimized three-telescope system.
The invention provides a low-sensitivity three-telescope design method based on multi-initial-point quasi-Newton optimization, which is characterized in that an optical system manufacturing performance evaluation model comprising system design residual errors and wave aberration generated by mirror surface imbalance is established, the evaluation model is expressed by mirror spacing to obtain an evaluation model formula taking the mirror spacing as a variable, the evaluation model formula is used as an optimization index of the system, each mirror spacing is equally divided into a plurality of grids to form a plurality of calculation units, the evaluation model formula is optimized by adopting a quasi-Newton method, and the minimum value of the optical system manufacturing performance is used as a global optimal value, so that the optimized three-telescope system with low imbalance sensitivity is finally obtained. The three-telescope system obtained after optimization has good quality and low offset sensitivity, and compared with the traditional optimization method, the three-telescope system has better manufacturing performance, and compared with the traditional rest desensitization methods, the three-telescope system improves the accuracy of system manufacturing performance evaluation, and the design method does not need a large amount of ray tracing, only needs to trace the paraxial marginal ray and the principal ray, and has the advantages of small calculated amount, short time and high optimization speed.
The effects of the present invention will be described in detail with reference to specific examples of design of the three-telescope system
An F/20 off-axis three-mirror telescope with a light-transmitting aperture of 6.6m is used as a reference system. The system parameters are shown in table 1, the initial optical structure is shown in fig. 4, the three-mirror system comprises a main mirror 1, a secondary mirror 2, a three-mirror 3 and a plane mirror 4, the parallel light reaches the main mirror 1 after being incident, reaches the secondary mirror 2 after being reflected by the main mirror 1, reaches the three-mirror 3 after being reflected by the secondary mirror 2, reaches the plane mirror 4 after being reflected by the three-mirror 3, and reaches the image plane 5 after being reflected by the plane mirror 4. The full field of view is 0.3 deg. x 0.15 deg., and the offset angle of the field of view is 0.2 deg.. The aperture diaphragm of the telescope is positioned on the primary mirror 1, and the rotation symmetry axes of the primary mirror 1, the secondary mirror 2 and the three mirrors 3 are coincident. A plane reflector 4 is additionally arranged between the three mirrors 3 and the optical path of the image plane 5 and is used for turning the optical path.
Table 1 initial lens parameters
| Surface of the body | Radius of curvature (millimeter) | Thickness (millimeter) | Secondary coefficient |
| Main mirror | -16287.757 | -7170 | -0.995 |
| Secondary mirror | -2318.335 | 7965 | -1.836 |
| Three mirrors | -2702.046 | -1845 | -0.720 |
| Plane reflecting mirror | Infinity | 3006.431 |
The initial structure of the three-telescope system is optimized by using the traditional optimization method and the manufacturing performance multi-initial-point quasi-Newton optimization method in the invention respectively so as to compare the reducing effect of different optimization modes on the offset sensitivity and the optimization efficiency. Finally, monte carlo tolerance analysis is used to evaluate and compare the optimization results.
(1) Traditional optimization method
In order to verify the optimization effect of the evaluation model, the optical system is directly optimized without considering the influence of offset aberration. The radius of curvature, the secondary coefficient and the mirror spacing of the three mirrors are set as variables, wherein the distance from the plane mirror to the image surface is kept unchanged, and the distance from the three mirrors to the image surface is optimized by changing the distance from the three mirrors to the plane mirror. And selecting a default wavefront RMS evaluation function in Zemax software, and controlling the focus to be unchanged in the optimization process. The variation range of the mirror pitch d is set to ±10% of the respective distances. In order to avoid trapping local minima, hammer-shaped optimization function call Depth Limited Search (DLS) is used for optimization, and the optimization process can be completed in 20-30 minutes. The CPU used in the optimization was AMD Ryzen7 4800H@2.90GHz, memory model DDR4@2666MHz. The optimized optical system parameters are shown in table 2, and the structure is shown in fig. 5 (a).
TABLE 2 lens parameters after traditional optimization
| Surface of the body | Radius of curvature (millimeter) | Thickness (millimeter) | Secondary coefficient |
| Main mirror | -17903.491 | -7853.997 | -0.994 |
| Secondary mirror | -2634.344 | 8760.399 | -1.877 |
| Three mirrors | -3085.537 | -2326.482 | -0.702 |
| Plane reflecting mirror | Infinity | 3006.262 |
(2) Multi-initial point quasi-Newton optimization method for manufacturing performance
The initial structure of the same three-telescope system is optimized by using the multi-initial-point quasi-Newton optimization method of the manufacturing performance in the invention. The mirror pitch is equally divided into 10 grids, as shown in fig. 3, yielding 1000 computing units. The range of the lens spacing change is kept unchanged, the minimum value of the manufacturing performance A of the optical system and the corresponding lens spacing are solved by using the fminunc function, so that the parameters of the rest optical system are solved, and the calculation process can be completed within 10 seconds. The CPU used in the optimization was AMD Ryzen7 4800H@2.90GHz, memory model DDR4@2666MHz. The parameters of the optical system obtained after optimization are shown in table 3, and the structure is shown in fig. 5 (b).
TABLE 3 Multi-initial Point pseudo-Newton optimization of manufacturing Performance post-optimization lens parameters
| Surface of the body | Radius of curvature (millimeter) | Thickness (millimeter) | Secondary coefficient |
| Main mirror | -17592.442 | -7887.000 | -0.995 |
| Secondary mirror | -2179.653 | 7168.500 | -1.884 |
| Three mirrors | -2488.025 | -1360.000 | -0.709 |
| Plane reflecting mirror | Infinity | 3006.131 |
In order to evaluate and compare the imbalance sensitivity of different optimization results, the adjustment performance of the obtained three-telescope system after optimization is analyzed based on the Monte Carlo method. A monte carlo tolerance analysis method of 2000 samples was used to predict the tuning performance. Taking the eccentric and inclined amounts of the secondary mirror and the three mirrors as the system adjustment tolerance, the tolerance is uniformly distributed. In the tolerance analysis, the maximum value of the eccentricity tolerance in the X and Y directions of each surface was set to 0.1mm, the maximum value of the inclination tolerance in the X and Y axes was set to 1.5', and the calculated wavelength was 587.6nm. And the image plane position is used as a compensator. Statistical analysis was performed on the full field average wave aberration of 2000 monte carlo samples, and the analysis results are shown in table 4 and fig. 6.
Table 4 comparison of optimized results
| Traditional optimization (wave) | Manufacturing performance multi-initial point quasi-Newton optimization method (wave) | |
| Nominal value | 0.026 | 0.042 |
| Mean value of | 0.870 | 0.754 |
| Median of | 0.838 | 0.738 |
| Maximum value | 2.047 | 1.905 |
| Root mean square error | 0.934 | 0.793 |
As can be seen from fig. 6 and table 4, the adjustment performance of the optical system optimized by the conventional method is severely degraded. Under the condition that the range of variation of the lens spacing is 10%, the nominal value of the wavefront error of the optimization method result of the optical system manufacturing performance evaluation model is 1.6 times of that of the traditional optimization method, the Root Mean Square Error (RMSE) of the wavefront error is 84% of that of the traditional optimization method, and the median is 88% of that of the traditional optimization method. The comparison analysis result shows that the manufacturing performance multi-initial-point quasi-Newton optimization method has lower offset sensitivity than the traditional optimization method, and the imaging quality and the tuning sensitivity of the three-mirror telescope based on the manufacturing performance multi-initial-point quasi-Newton optimization are better.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (10)
1. The design method of the low-sensitivity three-reflector based on the multi-initial-point quasi-Newton optimization is characterized by comprising the following steps of:
step one: establishing an optical system manufacturing performance evaluation model, wherein the expression of the optical system manufacturing performance evaluation model is as follows:
wherein A is the manufacturing performance of the three-telescope system;to design wave aberration, this is indicated in the field of view +.>The value of the root mean square wave aberration generated during the design of the medium optical system; />For detuning wave aberration, indicated by field of view +.>The value of the root mean square wave aberration caused by the tuning error;
step two: giving the eccentricity value and the inclination angle value in the optical system manufacturing performance evaluation model by estimating the tolerance range of the three-telescope system in the field of viewSelecting a view field point for calculating offset wave aberration;
step three: writing the optical system manufacturing performance evaluation model into Zemax software in the form of macro language function, and solving out offset wave aberration of the three-reflector system
Step four: direct tuning acquisition using optical design softwareDesign wave aberration to a three-mirror telescope system
Step five: subjecting the detuned wave aberration toAnd the design wave aberration +.>Substituting the optical system manufacturing performance evaluation model;
step six: according to a corresponding formula among the mirror radius, the secondary coefficient and the mirror distance, the mirror radius and the secondary coefficient in the optical system manufacturing performance evaluation model obtained in the step five are expressed by the mirror distance, and an evaluation model formula which only takes the mirror distance as a variable is obtained;
step seven: dividing each mirror interval into a plurality of grids at equal intervals to form a plurality of calculation units;
step eight: and selecting an initial point in each calculation unit, calling fminunc function in Matlab to perform quasi-Newton optimization on the evaluation model formula, solving a global optimal value of the manufacturing performance A of the optical system in a set scope of change of the mirror spacing, solving the mirror spacing corresponding to the global optimal value, deducing other optical structure parameters of the three-telescope system according to the solved mirror spacing, and finally obtaining the three-telescope system with low offset sensitivity after optimization.
2. The method of claim 1, wherein the offset wave aberration is a low sensitivity three-mirror telescope design method based on multiple initial point quasi-newton optimizationThe formula of (2) is:
wherein ,Z5 、Z 6 、Z 7 、Z 8 As coefficients of zernike polynomials, Z 5 and Z6 Is third-order astigmatism, Z 7 and Z8 For third-order coma, the subscript T in the formula represents aberration introduced by the tilt error, and the subscript D represents aberration introduced by the decenter error.
3. The method for designing a low-sensitivity three-mirror telescope based on multi-initial-point quasi-Newton optimization according to claim 2, wherein the third-order coma Z 7 and Z8 The expression of (2) is as follows:
wherein , and />Coma vectors introduced for disorders, respectively +.>X-component and y-component of> and />The expression of (2) is as follows:
wherein ,W131,sph,SM Spherical component of the coefficient of coma aberration of secondary mirror, W 131,asph,SM Aspheric component of secondary mirror coma aberration coefficient, W 131,sph,TM Is the spherical component, W, of the coefficient of the three-mirror coma wave aberration 131,asph,TM Is the aspherical component of the three-mirror coma aberration coefficient,offset vector sphere X-axis component for the aberration field of the secondary mirror,>for the aberration field offset vector aspherical X-axis component of the secondary mirror,>offset vector sphere Y-axis component for the aberration field of the secondary mirror,>for the aberration field offset vector aspherical Y-axis component of the secondary mirror,>an aberration field for three mirrors is offset by the vector sphere X-axis component,>an aberration field offset vector aspherical X-axis component for a three mirror,>the aberration field for the three mirrors is offset by the vector sphere Y-axis component,an aberration field offset vector aspherical Y-axis component for a three mirror;
when the system aperture diaphragm is positioned on the primary mirror, the secondary mirror image difference field offset vector and the three-mirror aberration field offset vector of the three-mirror telescope system are respectively:
wherein ,XDESM YDE for secondary mirror X-axis direction eccentric error SM ADE is the Y-axis direction eccentric error of the secondary mirror SM BDE for secondary mirror tilt error about the X-axis SM XDE for secondary mirror tilt error around Y-axis TM Is the eccentric error of X-axis direction of the three mirrors, YDE TM ADE is the eccentric error of the Y axis direction of the three mirrors TM For three-mirror tilt error about the X-axis, BDE TM Is a three mirror tilt error about the Y-axis,is the incidence angle of the paraxial chief ray of the chief mirror, d 1 D is the distance between the primary mirror and the secondary mirror 2 R is the distance between the secondary mirror and the triple mirror 1 Radius of curvature r of primary mirror 2 Radius of curvature r for secondary mirror 3 Radius of curvature for three mirrors;
the coma aberration coefficient of the three-telescope system can be calculated by a seidel formula, and the calculation formula is as follows:
wherein ,y1 B is the incidence height of the light at the edge of the main mirror s2 B is the secondary coefficient of the secondary mirror s3 Is the secondary coefficient of the three mirrors;
substituting equations (4) - (7) into equation (3) can result in third order coma Z 7 and Z8 ADE is given in formulas (5) and (6) SM 、ADE TM and BDESM 、BDE TM At 0, the coma aberration, z, can be obtained when there is only decentering 7,D and z8,D XDE (X-ray diffraction) order SM 、XDE TM and YDESM 、YDE TM At 0, the coma aberration, z, can be obtained when only tilt disorder exists 7,T and z8,T 。
4. A hyposensitization based on multiple initial point quasi-newtonian optimization according to claim 3The design method of the sensitivity three-reflector is characterized in that the three-order astigmatism Z 5 and Z6 The expression of (2) is as follows:
wherein , and />Coma vectors introduced for disorders, respectively +.>X-component and y-component of> and />The expression of (2) is as follows:
wherein ,W222,sph,SM Spherical component of the coefficient of the sub-mirror scattered wave aberration, W 222,asph,SM Aspheric component of the sub-mirror scattered wave aberration coefficient, W 222,sph,TM Is the spherical component of the three-mirror scattered wave aberration coefficient, W 222,asph,TM Aspheric components with three mirror images scattered wave aberration coefficients;
the astigmatic aberration coefficient of the three-telescope system can be calculated by the seidel formula, and the calculation formula is as follows:
substitution of formulas (5), (6), (9) and (10) into formula (8) can be achievedObtaining third-order astigmatism Z 5 and Z6 ADE is given in formulas (5) and (6) SM 、ADE TM and BDESM 、BDE TM At 0, the astigmatism z when there is only decentration can be obtained 5,D and z6,D XDE (X-ray diffraction) order SM 、XDE TM and YDESM 、YDE TM At 0, the astigmatism z when only tilt disorder exists can be obtained 5,T and z6,T 。
5. The low sensitivity three-mirror telescope design method based on multi-initial point quasi-newton optimization according to claim 1, characterized in that the three-mirror telescope system comprises a primary mirror (1), a secondary mirror (2), a three mirror (3) and a plane mirror (4), and the rotational symmetry axes of the primary mirror (1), the secondary mirror (2) and the three mirror (3) coincide;
the parallel light reaches the main mirror (1) after being incident, reaches the secondary mirror (2) after being reflected by the main mirror (1), reaches the three mirrors (3) after being reflected by the secondary mirror (2), reaches the plane mirror (4) after being reflected by the three mirrors (3), and reaches the image plane (5) after being reflected by the plane mirror (4).
6. The method of claim 1, wherein the eccentricity is set to 0.1mm and the tilt is set to 1.5'.
7. The method for designing the low-sensitivity three-mirror telescope based on the multi-initial-point quasi-Newton optimization according to claim 1, wherein each mirror pitch is equally divided into 10 grids, and the variation range of the mirror pitch is +/-10% of the mirror pitch.
8. The method for designing a low sensitivity three-mirror telescope based on multi-initial-point quasi-newton optimization of claim 1, further comprising the steps of:
step nine: and analyzing the adjustment performance of the optimized three-reflector system based on the Monte Carlo method.
9. The method of claim 8, wherein the sub-mirrors and the eccentric and tilt amounts of the three mirrors are used as system adjustment tolerances, the tolerances are uniformly distributed, the maximum value of the eccentric tolerances in the X and Y directions of each surface is set to 0.1mm, the maximum value of the tilt tolerances in the X and Y axes is set to 1.5', the calculated wavelength is 587.6nm, and the image plane position is used as a compensator for statistical analysis of the full field average wave aberration of the monte carlo sample.
10. The method of claim 9, wherein the total number of monte carlo samples is 2000.
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