CN111736335A - Design method of initial structure of off-axis multi-mirror free-form surface optical system - Google Patents
Design method of initial structure of off-axis multi-mirror free-form surface optical system Download PDFInfo
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Abstract
The invention relates to a method for designing an initial structure of an off-axis multi-inverse free-form surface optical system, which adopts a double seed curve expansion method to construct each free-form surface in the system, so that the construction precision of the free-form surface is greatly improved, an imaging optical system consisting of a plurality of free-form surfaces can be designed by introducing auxiliary virtual image points, in order to verify the reliability of the method, the initial structures of various different types of off-axis multi-inverse free-form surface imaging systems are designed by using the method, and the result is obtained by tracing light rays, so that the result shows that the off-axis multi-inverse free-form surface imaging optical system designed by using the method has high design speed, good stability, high efficiency and good imaging quality. The method also designs an optical system of the vehicle-mounted head-up display, and a good design effect is achieved.
Description
Technical Field
The invention relates to the technical field of off-axis optical system design, in particular to an optical system design containing a free-form surface in an off-axis system, and specifically relates to a design method of an initial structure of an off-axis multi-inverse free-form surface optical system.
Background
Compared with an on-axis optical system, the off-axis optical system can fold the optical path to make the system mechanism compact. Compared with a transmission system, the reflection system has no dispersion of light with different wavelengths, the free-form surface can increase the degree of freedom of design, reduce the number of optical elements and effectively correct the asymmetric aberration. Therefore, the off-axis free-form surface reflection imaging optical system has the advantages of compact structure, no chromatic aberration, no blocking and the like, and is widely applied to telescopes, ultra-short focus projection objectives, hyperspectral imaging spectrometers and the like. Designing or choosing a reasonable initial structure is the most critical step for designing an optical system, which determines the performance that can be achieved by the final system optimization, and if the initial structure is poor, the later optimization will not take a long time to achieve a better imaging quality. For an off-axis optical system, it is difficult to find a suitable initial structure for the off-axis optical system, and therefore, it is very important to develop a design method for the initial structure of the off-axis optical system.
The patent (application number: 201911259383.3) proposes a design method for a free-form surface in an off-axis free-form surface imaging optical system, which cannot solve the problem that the normal vector error of each sampling point is gradually increased in the expansion process of a seed curve; the single-seed dotted line expansion method needs a virtual surface when designing the free curved surface, and the virtual surface needs to be provided with sampling points, so that the processing is complex and tedious.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a design method for a free-form surface in an off-axis free-form surface imaging optical system, can design various off-axis imaging optical systems based on a double-seed curve expansion method and a plurality of virtual image points, and can improve the design precision, the design efficiency and the reliability.
According to the technical scheme provided by the invention,
a design method of an initial structure of an off-axis multi-reflector free-form surface optical system comprises the following steps:
firstly, on an initial plane S plane, uniformly sampling m × n data points in a matrix manner, taking each sampling point as an initial point of a ray, emitting a ray, and sampling the raysAre parallel to each other, and the first starting point on the light starting surface is set as S11And S11The light rays emitted from the same line are named as S1jThe first starting point of the second line is set as S21And S21The light rays emitted from the same line are named as S2jAnd so on in turn;
According to S in step 111A first emergent characteristic ray r is emitted11In the characteristic ray r11Selecting a point P on the path11First ray r11Is incident on P11After the point is reflected, a path is formed, and a point M is taken on the path11Light reaches M11After the point is reflected, a path is formed, and a point R is taken on the path11The light reaches R11After point reflection, the light is converged to an image point and is marked as I;
characteristic ray r emitted from S surface11Through P11Then directly forming a virtual imaging point I1The light emitted from the S surface passes through P11And M11Forming a virtual imaging point after reflection and recording as I2；
Wherein S11P11As vector of incident light, P11I1For the outgoing ray vector, P is determined from the vector form of the law of reflection11Normal vector N of points11；
Step 3, calculating a seed curve:
in step 2, when the per-P is obtained11Normal vector N of points11P can be calculated11Tangent plane of the point, a second characteristic ray r12And a passing point P11Point of intersection P of tangent planes12As a second sampling point on the free-form surface, the normal vector N of the second data point can be obtained by the law of reflection in the same way12And its tangent plane, using characteristic ray r13The intersection with the plane obtains the 3 rd sampling point, and so on, thereby obtaining the P on the free-form surface P11、P12… … to P1jForming a first curve, namely a seed curve;
and 4, obtaining all sampling points on the free curved surface according to the seed curve:
from the first row characteristic ray r11、r12……r1jThe emergent rays can obtain a seed curve, and the seed curve is calculated according to the method for calculating the seed curve in the step 3 and sequentially passes through the rays r21、r22……r2jThe emergent light is obtained from P21、P22… … to P2jThe formed second curve is analogized in turn, the process is continuously repeated to obtain all sampling points on the free-form surface P, and the sampling points on the free-form surface P obtained from the S plane are marked as forward calculation sampling points;
and 5, reversely calculating a second group of sampling points:
the surface data points are calculated in reverse to sample the last point P of the data points in forward directionmnAs a reference point, the light incident on the point is S on the light source surfacemnThe light emitted by a point, i.e. the sampled light rmnThis ray is also the last sampled ray in the forward calculation, so rmnIs incident on PmnThe corresponding unit direction vector and the unit emission vector are PmnUnit direction vector P to virtual image pointmnI1，
In the reverse calculation, all the ray starting points and direction vectors are consistent with those in the forward calculation, but the sequence of using the rays is reversed, and the surface starting point P of the reverse calculation is knownmnStarting points and direction vectors of all sampled rays, and virtual image point I1Then, according to the steps (1) and (2), the first row of characteristic data points, i.e. the first seed curve, is calculated, and then all the subsequent rows are obtained by expanding the first row of characteristic data points, and at this time, the second group of characteristic data points on the free-form surface can be all calculated. Finally, two groups of characteristic data points on the free-form surface are obtained, and the two groups of characteristic data points have a common point PmnThe first group of points are free-form surface sampling points calculated in the forward direction, the second group of points are free-form surface sampling points calculated in the reverse direction, and then the two groups of free-form surface sampling points are sampledThe points are fitted together to form a free-form surface.
And 6, calculating all sampling points of the plurality of free-form surfaces:
the above calculation process is only to calculate the sampling point on the first free-form surface P, and the above method is used to design a plurality of free-form surfaces, and then the secondary mirror M and the tertiary mirror R are designed by the above method: calculating the sampling point on M, wherein all the sampling light rays incident to the M mirror are the light rays reflected from the reflecting mirror P, so that the incident light ray vectors are known and are incident to the virtual image point I after being reflected by the M mirror1Initial reference point M on M11It is known that the previous steps can be used to derive from M11Starting to calculate all the sampling points on the positive M, and then calculating the last 1 point M from the positive directionmnAs an initial point, a sampling point is reversely calculated, so that a sampling point reversely calculated on the M reflector is obtained, and a sampling point of the M surface calculated in the forward direction and a sampling point on the M reflector calculated in the reverse direction can be obtained;
similarly, the sampling point on R is calculated, all the sampling light rays incident to the R mirror are the light rays reflected from the reflector M, so that the incident light ray vectors are known, the sampling light rays are incident to the point I after being reflected by the R mirror, and the initial reference point R on R is11It is known that the former procedure can be used to derive from R11All sampling points on R are calculated in the forward direction, and then R is calculated from the last 1 point in the forward directionmnAs an initial point, sampling points are reversely calculated, so that 2 groups of sampling points in the forward direction and the reverse direction on the R reflector are obtained;
and 7, polynomial fitting of the free-form surface shape:
discrete sampling points are obtained by the calculation of the method, in order to trace light, verify results and further optimize a designed system in optical design software, the sampling points need to be fitted into a continuous curved surface, an X-Y polynomial is adopted to fit the surface type of the free curved surface,
and 8, designing an off-axis multi-reflector (N >3) free-form surface, wherein the design method of the off-axis N-reflector free-form surface imaging optical system is the same as the design steps of the three-reflector free-form surface optical system, and the like, and N initial points are set in the step 6, and N-1 virtual image points are introduced.
Further, the construction of each free-form surface mirror in the system uses a double-seed curve expansion method.
Further, the double-seed curve expansion algorithm is to calculate a seed curve from an initial point, then expand forward to obtain all sampling points on the free-form surface called forward sampling points, use the last point of the forward sampling points as the initial point, calculate the seed curve, and then expand backward to obtain all sampling points on the free-form surface called backward sampling points.
Further, by using virtual image points, a plurality of free-form surface mirrors can be designed, using N free-form surface mirrors requires N-1 virtual image points.
Further, in step 5, the polynomial of the free-form surface is obtained by fitting the two sets of sampling points in forward and reverse directions together.
Compared with the prior art, the invention has the following advantages:
the off-axis imaging optical system with the plurality of free-form surfaces can be designed based on the double-seed curve expansion method and the plurality of virtual image points, the design precision, the design efficiency and the reliability can be improved, the imaging performance of the system can be effectively improved, all free-form surface sampling points can be directly calculated in the design process, and the process of feedback correction is not needed, so the calculation speed is high, the design method is simple and effective, and the method can be applied in a very wide field.
Drawings
FIG. 1 is a schematic diagram of a free-form surface off-axis three-reflection system.
FIG. 2 is a schematic diagram of characteristic data points on a free-form surface.
FIG. 3a shows the calculation of points on the seed curve.
FIG. 3b is a schematic diagram of forward computation of a first set of characteristic data point calculations for a free-form surface.
FIG. 3c is a schematic representation of the inverse free-form surface computation of a second set of characteristic data points.
FIG. 3d is a schematic diagram comparing two sets of characteristic data points on a free-form surface.
Fig. 4 shows two sets of sampling points calculated in forward and reverse directions, respectively.
FIG. 5 is a schematic diagram of normal vector deviations.
Fig. 6a is a schematic view of a single free-form surface mirror.
FIG. 6b is the MTF curve for a single free-form surface designed by the single seed curve expansion method.
FIG. 6c is the MTF curve of the free-form surface designed by the method of double-seed curve expansion.
FIG. 7a shows an initial structure of a free-form off-axis dual-reflection system.
FIG. 7b is a dual inverse free-form MTF curve designed using a single seed curve expansion method.
Fig. 7c is a free-form MTF curve designed by using the method of double-seed curve expansion.
FIG. 8 is a schematic view of a Z-shaped off-axis three-mirror free-form surface optical system.
FIG. 9 is a schematic diagram of a compact off-axis three-mirror free-form surface optical system.
Detailed Description
The invention will be further described with reference to examples in the drawings to which:
the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A design method of an initial structure of an off-axis multi-reflector free-form surface optical system comprises the following steps:
firstly, uniformly sampling m × n data points in a matrix form on an initial plane S plane, wherein the number of the data points is determined according to the spatial range of the plane, generally taking 100 parts of the data points in equal parts, taking each sampling point as the initial point of a light ray, emitting the light ray, enabling the sampling light rays to be parallel to each other, and enabling the light ray to be on the initial planeThe first starting point is set as S11And S11The light rays emitted from the same line are named as S1jThe first starting point of the second line is set as S21And S21The light rays emitted from the same line are named as S2jAnd so on in turn;
According to S in step 111A first emergent characteristic ray r is emitted11In the characteristic ray r11Selecting a point P on the path11First ray r11Is incident on P11After the point is reflected, a path is formed, and a point M is taken on the path11Light reaches M11After the point is reflected, a path is formed, and a point R is taken on the path11The light reaches R11After point reflection, the light is converged to an image point and is marked as I;
characteristic ray r emitted from S surface11Through P11Then directly forming a virtual imaging point I1The light emitted from the S surface passes through P11And M11Forming a virtual imaging point after reflection and recording as I2；
Wherein S11P11As vector of incident light, P11I1For the outgoing ray vector, P is determined from the vector form of the law of reflection11Normal vector N of points11；
Step 3, calculating a seed curve:
in step 2, when the per-P is obtained11Normal vector N of points11P can be calculated11Tangent plane of the point, a second characteristic ray r12And a passing point P11Point of intersection P of tangent planes12As a second sampling point on the free-form surface, the normal vector N of the second data point can be obtained by the law of reflection in the same way12And its tangent plane, using characteristic ray r13The intersection with the plane obtains the 3 rd sampling point, and so on, thereby obtaining the P on the free-form surface P11、P12… … to P1jForm a firstOne curve, called the seed curve;
wherein S11P11As vector of incident light, P11I1For the outgoing ray vector, P is determined from the vector form of the law of reflection11Normal vector N of points11The vector form formula of the reflection law is:
Inij×Nij＝Outij×Nij(1)
and 4, obtaining all sampling points on the free curved surface according to the seed curve:
from the first row characteristic ray r11、r12……r1jThe emergent rays can obtain a seed curve, and the seed curve is calculated according to the method for calculating the seed curve in the step 3 and sequentially passes through the rays r21、r22……r2jThe emergent light is obtained from P21、P22… … to P2jThe formed second curve is analogized in turn, the process is continuously repeated to obtain all sampling points on the free-form surface P, and the sampling points on the free-form surface P obtained from the S plane are marked as forward calculation sampling points;
in the process of calculating the normal vector, as shown in fig. 5, the passing point P is calculated by the above-described stepsi,jThe normal vector is N, but actually passes through point Pi,jShould be N ', the actual normal vector N' may be represented by Pi,jAdjacent point Pi+1,jAnd Pi,j+1Two vectors of v are formed1＝Pi+1,j-Pi,jAnd v2＝Pi,j+1-Pi,jThus passing through point Pi,jThe normal vector N' of (a) is:
calculating the deviation angle theta between the normal vector and the actual normal vectorN:
In the step, in the process of calculating all sampling points on the free-form surface through seed curve expansion, the deviation of the angle is larger and larger along with the continuous expansion of the seed curve, the sampling point on the second curve is calculated from the seed curve, the deviation angle is smaller, and when the point on the last curve is calculated, the error is larger. This deviation of the normal vector is then compensated by a double seed curve, extending from both ends, respectively.
And 5, reversely calculating a second group of sampling points:
the surface data points are calculated in reverse to sample the last point P of the data points in forward directionmnAs a reference point, the light incident on the point is S on the light source surfacemnThe light emitted by a point, i.e. the sampled light rmnThis ray is also the last sampled ray in the forward calculation, so rmnIs incident on PmnThe corresponding unit direction vector and the unit emission vector are PmnUnit direction vector P to virtual image pointmnI1，
In the reverse calculation, all the ray starting points and direction vectors are consistent with those in the forward calculation, but the sequence of using the rays is reversed, and the surface starting point P of the reverse calculation is knownmnStarting points and direction vectors of all sampled rays, and virtual image point I1Then, according to the steps (1) and (2), the first row of characteristic data points, i.e. the first seed curve, is calculated, and then all the subsequent rows are obtained by expanding the first row of characteristic data points, and at this time, the second group of characteristic data points on the free-form surface can be all calculated. Finally, two groups of characteristic data points on the free-form surface are obtained, and the two groups of characteristic data points have a common point PmnThe first group of points are free-form surface sampling points calculated in the forward direction, the second group of points are free-form surface sampling points calculated in the reverse direction, and then the two groups of free-form surface sampling points are combined together to be fitted into a free-form surface. In this step, the polynomial of the free-form surface is formed by a forward sumAnd fitting the two groups of sampling points in reverse direction together.
And 6, calculating all sampling points of the plurality of free-form surfaces:
the above calculation process is only to calculate the sampling point on the first free-form surface P, and the above method is used to design a plurality of free-form surfaces, and then the secondary mirror M and the tertiary mirror R are designed by the above method: calculating the sampling point on M, wherein all the sampling light rays incident to the M mirror are the light rays reflected from the reflecting mirror P, so that the incident light ray vectors are known and are incident to the virtual image point I after being reflected by the M mirror1Initial reference point M on M11It is known that the previous steps can be used to derive from M11Starting to calculate all the sampling points on the positive M, and then calculating the last 1 point M from the positive directionmnAs an initial point, a sampling point is reversely calculated, so that a sampling point reversely calculated on the M reflector is obtained, and a sampling point of the M surface calculated in the forward direction and a sampling point on the M reflector calculated in the reverse direction can be obtained;
similarly, the sampling point on R is calculated, all the sampling light rays incident to the R mirror are the light rays reflected from the reflector M, so that the incident light ray vectors are known, the sampling light rays are incident to the point I after being reflected by the R mirror, and the initial reference point R on R is11It is known that the former procedure can be used to derive from R11All sampling points on R are calculated in the forward direction, and then R is calculated from the last 1 point in the forward directionmnAs an initial point, sampling points are reversely calculated, so that 2 groups of sampling points in the forward direction and the reverse direction on the R reflector are obtained;
and 7, polynomial fitting of the free-form surface shape:
the discrete sampling points are obtained by calculation in the method, in order to trace light rays, verify results and further optimize a designed system in optical design software, the sampling points are fitted into a continuous curved surface, an X-Y polynomial is adopted to fit the surface type of a free curved surface, such as a Zernike polynomial, a Chebyshev polynomial and an XY expansion polynomial, and because the optical system is symmetrical about a YOZ plane, only an X even-order term in the X-Y polynomial is used, the polynomial adopts a 5-order polynomial, and the expression is as follows:
wherein c is the curvature of the free-form surface, k is the conic coefficient, AiIs the coefficient of the XY polynomial.
And 8, designing an off-axis multi-reflector (N >3) free-form surface, wherein the design method of the off-axis N-reflector free-form surface imaging optical system is the same as the design steps of the three-reflector free-form surface optical system, and the like, and N initial points are set in the step 6, and N-1 virtual image points are introduced. By using virtual image points, a plurality of free-form surface mirrors can be designed, using N free-form surface mirrors requires N-1 virtual image points.
The construction of each free-form surface mirror in the system uses a double-seed curve expansion method. The double-seed curve expansion algorithm is characterized in that a seed curve is calculated from an initial point, then all sampling points on a free-form surface are obtained through forward expansion and are called forward sampling points, the last point of the forward sampling points is used as the initial point, the seed curve is calculated, and then all the sampling points on the free-form surface are obtained through reverse expansion and are called reverse sampling points.
The design method is used for designing an off-axis single free-form surface optical system, an off-axis double free-form surface optical system, a free-form surface off-axis three-mirror system and a compact free-form surface off-axis three-mirror system.
The method is used for a vehicle-mounted head-up display, an off-axis reflecting free-form surface hyperspectral imager, an off-axis reflecting free-form surface ultrashort focal projection objective lens and an off-axis reflecting free-form surface laser shaping system.
As shown in fig. 6a-6c, the present method is used in the case of off-axis single-free-form surface optical system designs,
an off-axis single-free-form-surface reflector is designed by using an algorithm of double-seed curve expansion, as shown in fig. 6, a key standard for evaluating the imaging quality of an optical system is a modulation transfer function curve MTF, a horizontal axis is a spatial frequency, the imaging quality is better when the MTF is larger at the same spatial frequency, free-form surfaces are respectively designed by using a single-seed curve expansion method and a double-seed curve expansion method, the corresponding MTF curves are shown in fig. 6(b) and (c), and it can be obviously seen that the MTF of a double-seed curve is superior to that of a single-seed curve, i.e., the imaging quality is obviously higher than that of a single-seed curve.
7a-7c are the designs of the present method for off-axis dual-free-form surface optical system
Fig. 7(a) is an off-axis double-inverse free-form surface system, free-form surfaces designed by using a single seed curve expansion method and a double-seed curve expansion method respectively have corresponding MTF curves of fig. 7(b) and (c), and it can be clearly seen that the MTF of the double-seed curve is superior to that of the free-form surface designed by the single seed curve, i.e. the imaging quality is significantly higher than that of the single seed curve. MTF curves of initial structures of two kinds of free-form surface reflection systems without subsequent optimization.
In the two cases, the imaging quality of the free-form surface off-axis multi-mirror system initial structure constructed by the double-seed curve expansion method is obviously superior to that of the single-seed curve expansion method.
By using the method, the initial structures of more complex off-axis multi-free-form surface optical systems, such as a Z-shaped off-axis three-mirror free-form surface imaging system and the initial structures of a compact off-axis three-mirror free-form surface system, can be calculated, and the initial structures have good optical performance, which once again explains that the double-seed curve expansion method has advantages for designing a multi-free-form surface off-axis reflection type optical system with a good initial structure.
The method is used for optically designing the vehicle-mounted head-up display (HUD), the vehicle-mounted head-up display is arranged on a vehicle, various information such as navigation pictures can be directly projected onto a windshield, and a driver can change the situation that the driver does not need to look down at various information such as information of an instrument panel and the like and navigation information and the like. In order to make the structure of the head-up display more compact, the head-up display is usually designed to be a structure of a folded light path, information output from an image source, such as navigation information or instrument panel information, is reflected by two free-form surface reflectors and then hits the windshield, and the information is reflected by the windshield and then enters the eyes of a driver, and meanwhile, the information outside the window can also enter the eyes of the driver through the windshield. The two off-axis free-form surface reflectors are designed into initial structures through the double seed curves introduced above, and then are further optimized through optical software.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by the present specification, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (5)
1. A design method of an initial structure of an off-axis multi-reflector free-form surface optical system comprises the following steps:
step 1, determining a sampling light:
firstly, on an initial plane S plane, uniformly sampling m × n data points in a matrix manner, taking each sampling point as an initial point of a ray, emitting a ray, enabling the sampled rays to be parallel to each other, and setting a first initial point on a ray initial plane as S11And S11The light rays emitted from the same line are named as S1jThe first starting point of the second line is set as S21And S21The light rays emitted from the same line are named as S2jAnd so on in turn;
step 2, determining the position P of the initial reference point11，M11，R11Determining a virtual image point I1，I2，I：
According to S in step 111A first emergent characteristic ray r is emitted11In the characteristic ray r11Selecting a point P on the path11First ray r11Is incident on P11After the point is reflected, a path is formed, and a point M is taken on the path11Light reaches M11After the point is reflected, a path is formed, and a point R is taken on the path11The light reaches R11After point reflection, the light is converged to an image point and is marked as I;
characteristic ray r emitted from S surface11Through P11Then directly forming a virtual imaging point I1The light emitted from the S surface passes through P11And M11After reflection form a virtualThe image point is marked as I2；
Wherein S11P11As vector of incident light, P11I1For the outgoing ray vector, P is determined from the vector form of the law of reflection11Normal vector N of points11；
Step 3, calculating a seed curve:
in step 2, when the per-P is obtained11Normal vector N of points11P can be calculated11Tangent plane of the point, a second characteristic ray r12And a passing point P11Point of intersection P of tangent planes12As a second sampling point on the free-form surface, the normal vector N of the second data point can be obtained by the law of reflection in the same way12And its tangent plane, using characteristic ray r13The intersection with the plane obtains the 3 rd sampling point, and so on, thereby obtaining the P on the free-form surface P11、P12… … to P1jForming a first curve, namely a seed curve;
and 4, obtaining all sampling points on the free curved surface according to the seed curve:
from the first row characteristic ray r11、r12……r1jThe emergent rays can obtain a seed curve, and the seed curve is calculated according to the method for calculating the seed curve in the step 3 and sequentially passes through the rays r21、r22……r2jThe emergent light is obtained from P21、P22… … to P2jThe formed second curve is analogized in turn, the process is continuously repeated to obtain all sampling points on the free-form surface P, and the sampling points on the free-form surface P obtained from the S plane are marked as forward calculation sampling points;
and 5, reversely calculating a second group of sampling points:
the surface data points are calculated in reverse to sample the last point P of the data points in forward directionmnAs a reference point, the light incident on the point is S on the light source surfacemnThe light emitted by a point, i.e. the sampled light rmnThis ray is also the last sampled ray in the forward calculation, so rmnIs incident on PmnPoint to point listBit direction vector, unit exit vector is PmnUnit direction vector P to virtual image pointmnI1，
In the reverse calculation, all the ray starting points and direction vectors are consistent with those in the forward calculation, but the sequence of using the rays is reversed, and the surface starting point P of the reverse calculation is knownmnStarting points and direction vectors of all sampled rays, and virtual image point I1Then, according to the steps (1) and (2), the first row of characteristic data points, i.e. the first seed curve, is calculated, and then all the subsequent rows are obtained by expanding the first row of characteristic data points, and at this time, the second group of characteristic data points on the free-form surface can be all calculated. Finally, two groups of characteristic data points on the free-form surface are obtained, and the two groups of characteristic data points have a common point PmnThe first group of points are free-form surface sampling points calculated in the forward direction, the second group of points are free-form surface sampling points calculated in the reverse direction, and then the two groups of free-form surface sampling points are fitted together to form a free-form surface;
and 6, calculating all sampling points of the plurality of free-form surfaces:
the above calculation process is only to calculate the sampling point on the first free-form surface P, and the above method is used to design a plurality of free-form surfaces, and then the secondary mirror M and the tertiary mirror R are designed by the above method: calculating the sampling point on M, wherein all the sampling light rays incident to the M mirror are the light rays reflected from the reflecting mirror P, so that the incident light ray vectors are known and are incident to the virtual image point I after being reflected by the M mirror1Initial reference point M on M11It is known that the previous steps can be used to derive from M11Starting to calculate all the sampling points on the positive M, and then calculating the last 1 point M from the positive directionmnAs an initial point, a sampling point is reversely calculated, so that a sampling point reversely calculated on the M reflector is obtained, and a sampling point of the M surface calculated in the forward direction and a sampling point on the M reflector calculated in the reverse direction can be obtained;
similarly, the sampling point on R is calculated, all the sampling light rays incident to the R mirror are the light rays reflected from the reflector M, so that the incident light ray vectors are known, the sampling light rays are incident to the point I after being reflected by the R mirror, and the initial reference point R on R is11It is known that the former procedure can be used to derive from R11All sampling points on R are calculated in the forward direction, and then R is calculated from the last 1 point in the forward directionmnAs an initial point, sampling points are reversely calculated, so that 2 groups of sampling points in the forward direction and the reverse direction on the R reflector are obtained;
and 7, polynomial fitting of the free-form surface shape:
discrete sampling points are obtained through calculation by the method, in order to trace light, verify results and further optimize a designed system in optical design software, the sampling points need to be fitted into a continuous curved surface, and the surface type of the free curved surface is fitted by adopting an X-Y polynomial;
and 8, designing an off-axis multi-reflector (N >3) free-form surface, wherein the design method of the off-axis N-reflector free-form surface imaging optical system is the same as the design steps of the three-reflector free-form surface optical system, and the like, and N initial points are set in the step 6, and N-1 virtual image points are introduced.
2. The method as claimed in claim 1, wherein the construction of each free-form surface reflector in the system uses a dual seed curve expansion method.
3. The design method of the initial structure of the off-axis multi-reflector free-form surface optical system as claimed in claim 2, wherein the dual-seed curve expansion algorithm is to calculate a seed curve from an initial point, then expand forward to obtain all sampling points on the free-form surface as forward sampling points, and calculate the seed curve and then expand backward to obtain all sampling points on the free-form surface as backward sampling points with the last point of the forward sampling points as the initial point.
4. The method of claim 1, wherein a plurality of free-form surface mirrors can be designed by using the virtual image points, and the use of N free-form surface mirrors requires N-1 virtual image points.
5. An off-axis multi-mirror free-form surface optical system initial structure design method as claimed in claim 1, wherein in step 5, the polynomial of the free-form surface is obtained by fitting two sets of forward and backward sampling points together.
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