CN111259588B - Method for acquiring optical surface error of reflector under coupling action of multiple physical fields - Google Patents
Method for acquiring optical surface error of reflector under coupling action of multiple physical fields Download PDFInfo
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Abstract
The invention provides a method for acquiring an error of an optical surface of a reflector under the coupling action of multiple physical fields, which comprises the steps of firstly, defining a rise reference point, utilizing the characteristic that an initial vector quantity at the center of the optical surface of the reflector is always kept unchanged under the loading constraint condition, and acquiring a real deformation quantity in the rise direction after any discrete point is deformed by the rise quantity before any discrete point is deformed and an equivalent vector quantity after any discrete point is deformed. And secondly, obtaining the coordinate values of all the discrete points of the corrected optical surface in finite element software, thereby improving the acquisition precision of the optical surface errors.
Description
Technical Field
The invention relates to a method for acquiring an error of an optical surface of a reflector, in particular to a method for acquiring an error of an optical surface of a reflector under the coupling action of multiple physical fields.
Background
For high performance optical systems (i.e., imaging systems and non-imaging systems), in order to obtain high quality imaging quality or precise pointing accuracy, it is necessary to ensure that the optical elements meet stringent surface error requirements. Surface errors are generally classified into surface profile errors and surface position errors. The surface type error is referenced by wavelength, and the variation of the surface type error under the action of various physical fields is generally strictly required to be a fraction of the wavelength; surface position errors are often reflected by rigid body displacements, and their magnitude is also required to be on the order of microns and micro radians.
Gravity field, temperature field, mechanical stress of assembly, adhesive curing shrinkage and the like can cause surface errors of the optical element. In engineering practice, the surface error of the optical element under a specific working condition is not measured and evaluated under the condition. The common method is to adopt a finite element analysis method to evaluate the influence of various external factors on the surface error. However, the optical surface error processing method commonly used at present is adopted to process the surface error of the multi-physical-field coupled reflector, and the following two problems mainly exist:
1. the data processing on the surface type error of the reflector in some of the prior published technical documents generally comprises the following processes: aiming at a reflector, defining the Z direction of an optical axis as a sagitta direction, introducing finite element discretization to obtain X, Y, Z coordinate values of a discrete point on the surface of the reflector, applying a physical field to obtain the deformation of the discrete point on the surface of the optical surface along the sagitta direction, solving an over-definite equation set consisting of the deformation in the sagitta direction, the coordinate values of the discrete point and a Zernike polynomial, and obtaining a Zernike coefficient and an optical surface shape error (PV & rms). However, under the action of a thermal force field, due to the fact that the reflector contracts or expands in the radial direction due to thermal stress, the vector deformation amount of the discrete points directly acquired by the method is not the true vector deformation of the reflector, and the accuracy of the calculation result is reduced or is wrong.
2. When the reflector is an aspheric reflector, the finite element method discretizes the established 3D model by means of UG, SolidWorks and other three-dimensional software to perform numerical simulation analysis, but because of the high-precision requirement (nm level) of optical surface error processing, the discretized initial optical surface in the finite element by means of the three-dimensional software model has larger errors, and the error analysis under the action of a subsequent multi-physical field cannot be met.
Disclosure of Invention
The method for acquiring the error of the optical surface of the reflector under the action of the multi-physical field coupling is provided for solving the problems that the accuracy of the acquired surface error result is reduced and even wrong due to the fact that the vector deformation of a discrete point acquired by the existing method of acquiring the error of the optical surface of the reflector under the action of a thermal force field is not the true vector deformation of the reflector, and when the error of the optical surface of the aspheric reflector is acquired by the existing method, the initial optical surface discretized in a finite element of a three-dimensional software model has a large error and cannot meet the problem of error analysis under the action of the following multi-physical field.
The specific technical scheme of the invention is as follows:
the invention provides a method for acquiring an optical surface error of a reflector under the coupling action of multiple physical fields, which is carried out according to the following steps when the reflector is an aspheric reflector:
step 1: establishing an aspheric reflector three-dimensional model in three-dimensional software according to a standard equation of the aspheric reflector, and defining the origin of coordinates of the three-dimensional model as the optical surface center point of the aspheric reflector three-dimensional model; the standard equation of the aspheric surface reflector specifically comprises:
2rz＝x2+y2+(1+k)·z2；
r is the curvature radius of the aspheric reflector, k is the aspheric coefficient, and x, y and z are the coordinate values of the discrete points of the optical surface;
step 2: reading the three-dimensional model of the aspheric reflector by finite element software, and discretizing the three-dimensional model of the aspheric reflector to obtain a coordinate value set of all discrete points after discretization of the optical surface of the three-dimensional model of the aspheric reflector
And step 3: extracting non-rise direction coordinate set in coordinate value set
Substituting the three-dimensional model into a standard equation of the aspheric reflector, and calculating to obtain a set of all coordinate values of the optical surface of the three-dimensional model of the aspheric reflector after correction
And 4, step 4: loading constraint conditions on the aspheric reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
And 5: defining a rise reference point in the aspheric reflector three-dimensional model, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the aspheric reflector optical surface center, which is marked as l;
step 6: according to the initial vector height l of the center of the optical surface of the aspheric reflector and the coordinate value of any discrete point of the optical surface of the three-dimensional model of the aspheric reflector in the vector height direction before deformation
And the coordinate value of any discrete point of the optical surface of the aspheric reflector three-dimensional model in the sagitta direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd equivalent vector quantity Sag 'after deformation of any discrete point'i(ii) a Equivalent vector quantity Sag 'after deformation of any discrete point'iComprises the following steps: projecting the position of any discrete point on the optical surface after deformation to the rise amount corresponding to the position on the optical surface of the aspheric surface reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
And 7: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating position errors in the optical surface errors of the aspheric mirror;
the surface shape accuracy of the Zernike coefficient fitting was evaluated to calculate PV and rms values representing the surface shape of the aspherical mirror optical surface.
The invention also provides a method for acquiring the optical surface error of the reflector under the coupling action of multiple physical fields, which is carried out according to the following steps when the reflector is a spherical reflector:
step 1: establishing a three-dimensional model of the spherical reflector in three-dimensional software according to a standard equation of the spherical reflector, and defining the origin of coordinates of the three-dimensional model as the central point of the optical surface of the three-dimensional model of the spherical reflector; the standard equation of the spherical reflector is specifically as follows:
2rz＝x2+y2；
r is the curvature radius of the spherical reflector, and x, y and z are the coordinate values of the discrete points on the optical surface;
step 2: reading the three-dimensional model of the spherical reflector through finite element software, and discretizing the three-dimensional model of the spherical reflector to obtain a coordinate value set of all discrete points after discretization of the optical surface of the three-dimensional model of the spherical reflector
And step 3: loading constraint conditions on the spherical reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
And 4, step 4: defining a rise reference point in a three-dimensional model of the spherical reflector, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the optical surface center of the spherical reflector, and recording the initial vector quantity as l;
and 5: according to the initial vector height l of the center of the optical surface of the spherical reflector and the coordinate point of any discrete point of the optical surface of the three-dimensional model of the spherical reflector in the vector height direction before deformation
And the coordinate point of any discrete point of the optical surface of the spherical reflector three-dimensional model in the sagittal height direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd the equivalent vector quantity Sag after any discrete point deformationi'; equivalent vector quantity Sag 'after deformation of any discrete point'iProjecting the position of any discrete point on the optical surface after deformation to the corresponding rise amount of the position on the optical surface of the spherical reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
Step 6: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating the position error in the optical surface error of the spherical reflector;
the surface shape accuracy of the Zernike coefficient fitting is evaluated to calculate PV and rms values representing the surface shape of the optical surface of the spherical reflector.
Further, the two constraints include a gravitational field, a temperature field, a mechanical stress, and a glue curing shrinkage.
The invention has the beneficial effects that:
1. according to the method, the rise reference point is defined, the characteristic that the initial vector quantity of the center of the optical surface of the reflector is always kept unchanged under the loading constraint condition is utilized, the real deformation quantity of any discrete point in the rise direction after being deformed is obtained through the rise quantity before being deformed and the equivalent vector quantity after being deformed, the accurate optical surface error of the reflector can be obtained through the real deformation quantity, the analysis and calculation precision of the optical surface error is improved, and the generation of an error or an unreliable result is avoided.
2. The invention obtains the coordinate values of all discrete points of the corrected optical surface in finite element software, avoids the problem of insufficient dimensional precision of a parameterized model caused by the fact that conventional three-dimensional modeling software is used for analyzing errors of the optical surface, can correct a completely ideal spatial aspheric optical surface according to an aspheric equation, and provides conditions for subsequent data processing and error analysis.
3. The method can be used as an optimization method of a system-level optical system under complex working conditions, forms optical-mechanical closed-loop optimization and guides the design of a high-performance system.
Drawings
FIG. 1 is a schematic view of the optical surface of a reflector and its deformation under the coupling effect of multiple physical fields.
FIG. 2 is a flow chart of the present invention.
FIG. 3 is a flowchart of the correction of all discrete points on the optical surface of an aspherical mirror;
fig. 4 is a flowchart of calculating the true deformation of discrete points on the optical surface of the aspheric mirror.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Two core problems in the existing optical surface error acquisition method are respectively:
firstly, when the reflector is an aspheric reflector, all discrete point coordinate values of the optical surface have errors.
Let the standard equation of the aspherical mirror be:
2rz＝x2+y2+(1+k)·z2
in the above formula, r is a curvature radius, k is an aspheric coefficient, and x, y, and z are coordinates of discrete points on the optical surface. Theoretically, the discrete point coordinates obtained by discretizing the three-dimensional model of the imported finite element satisfy the relationship. In actual processing, due to the precision problem of the dimensional parameters of the three-dimensional modeling software, a certain discrete point S is obtained by assuming a finite element environmentiIs a coordinate value of
And
will appear
This means that when the optical surface is deformed by the action of the loaded physical field, this unequal error amount will be superimposed into the sagitta deformation, resulting in a reduction in the accuracy of the calculation result.
Secondly, the sagitta deformation of any discrete point on the optical surface of the reflector is not the real sagitta deformation (the problem exists in both the aspheric reflector and the spherical reflector).
When multi-physical-field is acted, the deformation of the optical surface of the reflector does not only generate rigid body displacement along the gravity field effect, but also contracts or expands along the radial direction due to the influence of linear expansion, so that S of finite element calculation is causediZ-direction deformation of point
True deflection in rise direction
Is not equal, i.e.
At this time, if continue with
Substituting Zernike polynomial to calculate error function, the obtained optical surface error value deviates from true value, and the data is not credible and needs to be calculated by
Substitution
And (6) performing calculation.
The method corrects coordinates of all discrete points arranged in the aspheric surface reflector, calculates the true vector height direction deformation amount as a key technical link, processes the optical surface error of the aspheric surface reflector under multi-physical field coupling to obtain high-precision surface error data, can judge the performance of an optical element and an optical system under various working conditions on one hand, and can be used as a criterion of closed-loop optimization design on the other hand to carry out overall design and optimization of the optical system.
As shown in fig. 1 to 4, the optical surface error obtaining method for the aspherical mirror using the method of the present invention includes the following steps:
step 1: establishing an aspheric reflector three-dimensional model in three-dimensional software according to a standard equation of the aspheric reflector, and defining the origin of coordinates of the three-dimensional model as the optical surface center point of the aspheric reflector three-dimensional model; the standard equation of the aspheric surface reflector specifically comprises:
2rz＝x2+y2+(1+k)·z2；
r is the curvature radius of the aspheric reflector, k is the aspheric coefficient, and x, y and z are the coordinate values of the discrete points of the optical surface;
step 2: reading the three-dimensional model of the aspheric reflector by finite element software, and discretizing the three-dimensional model of the aspheric reflector to obtain a coordinate value set of all discrete points after discretization of the optical surface of the three-dimensional model of the aspheric reflector
And step 3: extracting non-rise direction coordinate set in coordinate value set
Substituting the three-dimensional model into a standard equation of the aspheric reflector, and calculating to obtain a set of all coordinate values of the optical surface of the three-dimensional model of the aspheric reflector after correction
The specific calculation process is as follows:
note the book
For corrected discrete points SiInitial Z coordinate values, i.e.
Need to satisfy
Due to SiX, Y direction coordinates are accurate and reliable, then it can be recorded
Is composed of
Is obtained by the above formula
Substitution
As SiForm SiCorrected coordinate value set of (2)
And 4, step 4: loading constraint conditions on the aspheric reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
The constraint conditions comprise a gravity field, a temperature field, mechanical stress, adhesive curing shrinkage and the like;
and 5: defining a rise reference point in the aspheric reflector three-dimensional model, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the aspheric reflector optical surface center, which is marked as l;
step 6: according to the initial vector height l of the center of the optical surface of the aspheric reflector and the coordinate point of any discrete point of the optical surface of the aspheric reflector three-dimensional model in the vector height direction before deformation
And aspheric surfaceCoordinate value of any discrete point of optical surface of reflector three-dimensional model in sagittal height direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd equivalent vector quantity Sag 'after deformation of any discrete point'i(ii) a Equivalent vector quantity Sag 'after deformation of any discrete point'iProjecting the position of any discrete point on the optical surface after deformation to the corresponding rise amount of the position on the optical surface of the aspheric surface reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
And 7: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating position errors in the optical surface errors of the aspheric mirror;
the surface shape accuracy of the Zernike coefficient fitting was evaluated to calculate PV and rms values representing the surface shape of the aspherical mirror optical surface.
When the method is used for the spherical reflector, all coordinate values of the optical surface of the three-dimensional model of the spherical reflector do not need to be corrected, so the method comprises the following steps:
step 1: establishing a three-dimensional model of the spherical reflector in three-dimensional software according to a standard equation of the spherical reflector, and defining the origin of coordinates of the three-dimensional model as the central point of the optical surface of the three-dimensional model of the spherical reflector; the standard equation of the spherical reflector is specifically as follows:
2rz＝x2+y2；
r is the curvature radius of the spherical reflector, and x, y and z are the coordinate values of the discrete points on the optical surface;
step 2: reading the three-dimensional model of the spherical reflector through finite element software, and discretizing the three-dimensional model of the spherical reflector to obtain a coordinate value set of all discrete points after discretization of the optical surface of the three-dimensional model of the spherical reflector
And step 3: loading constraint conditions on the spherical reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
And 4, step 4: defining a rise reference point in a three-dimensional model of the spherical reflector, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the optical surface center of the spherical reflector, and recording the initial vector quantity as l;
and 5: according to the initial vector height l of the center of the optical surface of the spherical reflector and the coordinate point of any discrete point of the optical surface of the three-dimensional model of the spherical reflector in the vector height direction before deformation
And optical surface of three-dimensional model of spherical reflectorCoordinate point of discrete point in rise direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd equivalent vector quantity Sag 'after deformation of any discrete point'i(ii) a Equivalent vector quantity Sag 'after deformation of any discrete point'iProjecting the position of any discrete point on the optical surface after deformation to the corresponding rise amount of the position on the optical surface of the spherical reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
Step 6: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating the position error in the optical surface error of the spherical reflector;
the surface shape accuracy of the Zernike coefficient fitting is evaluated to calculate PV and rms values representing the surface shape of the optical surface of the spherical reflector.
Claims (4)
1. A method for acquiring the optical surface error of a reflector under the coupling action of multiple physical fields is characterized by comprising the following steps: when the reflector is an aspheric reflector, the method comprises the following steps:
step 1: establishing an aspheric reflector three-dimensional model in three-dimensional software according to a standard equation of the aspheric reflector, and defining the origin of coordinates of the three-dimensional model as the optical surface center point of the aspheric reflector three-dimensional model; the standard equation of the aspheric surface reflector specifically comprises:
2rz＝x2+y2+(1+k)·z2；
r is the curvature radius of the aspheric reflector, k is the aspheric coefficient, and x, y and z are the coordinate values of the discrete points of the optical surface;
step 2: reading the three-dimensional model of the aspheric reflector by finite element software, and discretizing the three-dimensional model of the aspheric reflector to obtain a coordinate value set of all discrete points after discretization of the optical surface of the three-dimensional model of the aspheric reflector
Wherein S isiIs an arbitrary discrete point of the optical surface;
and step 3: extracting non-rise direction coordinate set in coordinate value set
Substituting the three-dimensional model into a standard equation of the aspheric reflector, and calculating to obtain a set of all coordinate values of the optical surface of the three-dimensional model of the aspheric reflector after correction
And 4, step 4: loading constraint conditions on the aspheric reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
And 5: defining a rise reference point in the aspheric reflector three-dimensional model, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the aspheric reflector optical surface center, which is marked as l;
step 6: according to the initial vector height l of the center of the optical surface of the aspheric reflector and the coordinate value of any discrete point of the optical surface of the three-dimensional model of the aspheric reflector in the vector height direction before deformation
And the coordinate value of any discrete point of the optical surface of the aspheric reflector three-dimensional model in the sagitta direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd equivalent vector quantity Sag 'after deformation of any discrete point'i(ii) a Equivalent vector quantity Sag 'after deformation of any discrete point'iComprises the following steps: projecting the position of any discrete point on the optical surface after deformation to the rise amount corresponding to the position on the optical surface of the aspheric surface reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
And 7: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating position errors in the optical surface errors of the aspheric mirror;
the surface shape accuracy of the Zernike coefficient fitting was evaluated to calculate PV and rms values representing the surface shape of the aspherical mirror optical surface.
2. The method for obtaining the errors of the optical surface of the reflecting mirror under the coupling action of the multiple physical fields as claimed in claim 1, wherein: the constraint conditions in the step 4 comprise a gravity field, a temperature field, a mechanical stress and adhesive curing shrinkage.
3. A method for acquiring the optical surface error of a reflector under the coupling action of multiple physical fields is characterized by comprising the following steps: when the reflector is a spherical reflector, the method comprises the following steps:
step 1: establishing a three-dimensional model of the spherical reflector in three-dimensional software according to a standard equation of the spherical reflector, and defining the origin of coordinates of the three-dimensional model as the central point of the optical surface of the three-dimensional model of the spherical reflector; the standard equation of the spherical reflector is specifically as follows:
2rz＝x2+y2；
r is the curvature radius of the spherical reflector, and x, y and z are the coordinate values of the discrete points on the optical surface;
step 2: reading the three-dimensional model of the spherical reflector through finite element software, and discretizing the three-dimensional model of the spherical reflector to obtain the three-dimensional model of the spherical reflectorSet of coordinate values of all discrete points after discretization of model optical surface
Wherein S isiIs an arbitrary discrete point of the optical surface;
and step 3: loading constraint conditions on the spherical reflector three-dimensional model in finite element software, and performing numerical simulation calculation to obtain each discrete point deformation set
And 4, step 4: defining a rise reference point in a three-dimensional model of the spherical reflector, and defining a connecting line between the rise reference point and the coordinate origin of the three-dimensional model in the step 1 as an initial vector quantity of the optical surface center of the spherical reflector, and recording the initial vector quantity as l;
and 5: according to the initial vector height l of the center of the optical surface of the spherical reflector and the coordinate point of any discrete point of the optical surface of the three-dimensional model of the spherical reflector in the vector height direction before deformation
And the coordinate point of any discrete point of the optical surface of the spherical reflector three-dimensional model in the sagittal height direction after deformation
Calculating high vector quantity Sag before deformation of any discrete pointiAnd equivalent vector quantity Sag 'after deformation of any discrete point'i(ii) a Equivalent vector quantity Sag 'after deformation of any discrete point'iProjecting the position of any discrete point on the optical surface after deformation to the corresponding rise amount of the position on the optical surface of the spherical reflector three-dimensional model before deformation along the rise direction;
the specific calculation formula is as follows:
then the true deformation of any discrete point along the rise direction is:
so as to obtain the true deformation set of any discrete point
Step 6: defining the least square error function of the rise deformation obtained by the finite element and the rise deformation described by the Zernike polynomial as follows:
in the formula: wtiA weighting factor of the optical surface represented by the discrete points to the overall optical surface;
Osidiscrete point edge rise deformation represented by Zernike polynomial;
calculating Zernike coefficients by zero derivation, thereby calculating the position error in the optical surface error of the spherical reflector;
the surface shape accuracy of the Zernike coefficient fitting is evaluated to calculate PV and rms values representing the surface shape of the optical surface of the spherical reflector.
4. The method for obtaining the errors of the optical surface of the reflecting mirror under the coupling action of the multiple physical fields as claimed in claim 3, wherein: the constraint conditions in the step 3 comprise a gravity field, a temperature field, a mechanical stress and adhesive curing shrinkage.
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