阅读说明：本技术 一种自由曲面控制的方法及装置 (Method and device for controlling free-form surface ) 是由 王丽萍 吴越 张旭 金春水 于 2021-07-16 设计创作，主要内容包括：本发明涉及极紫外光刻技术领域,具体涉及一种自由曲面控制的方法及装置,方法包括：输入自定义曲面的面型,生成自由曲面；对所述自由曲面进行分析,判断所述自由曲面是否有形成凹凸面；若所述自由曲面没有凹凸面,则所述自由曲面满足制造条件,否则对所述自由曲面的二阶导数进行调控,避免所述自由曲面出现凹凸面。本发明通过对自由曲面多项式的二阶导数的符号进行控制,使得在自由曲面在设计阶段考虑设计的自由曲面元件加工检测的可行性,避免自由曲面设计过程中因元件变化剧烈,降低自由曲面的元件制造难度。(The invention relates to the technical field of extreme ultraviolet lithography, in particular to a method and a device for controlling a free-form surface, wherein the method comprises the following steps: inputting the surface type of the self-defined curved surface to generate a free curved surface; analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface; and if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided. The invention controls the sign of the second derivative of the free-form surface polynomial, so that the feasibility of processing and detecting the designed free-form surface element is considered in the design stage of the free-form surface, and the difficulty in manufacturing the free-form surface element due to severe element change in the free-form surface design process is avoided.)

1. A method of free form surface control, comprising the steps of:

inputting the surface type of the self-defined curved surface to generate a free curved surface;

analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface;

and if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided.

2. The method of free form surface control of claim 1, wherein generating a free form surface in the inputting the profile of the custom surface comprises:

selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

writing a macro file by using a CODE-V (CODE-variable) self-contained macro language grammar based on the gradient of the surface polynomial;

and selecting the corresponding macro file to complete the input of the surface type of the self-defined curved surface.

3. The method of free form surface control of claim 1, wherein generating a free form surface in the inputting the profile of the custom surface comprises:

selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

writing a C language file by using the syntax of a CODE-V and C language interface based on the gradient of the surface polynomial, and generating a DLL file;

and the input of the user-defined surface type can be completed by selecting the corresponding DLL file.

4. The method of free-form surface control of claim 2 or 3, wherein the custom surface profile is usable for ray tracing.

5. The method of claim 1, wherein analyzing the free-form surface to determine whether the free-form surface has a concave-convex surface comprises:

taking a range value [ a, b ] on the free-form surface, wherein a continuous function set in the [ a, b ] is f (x);

judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein if f (x) is a convex function, the convex surface is a convex surface, and if f (x) is a concave surface, the concave function is a concave surface.

6. The method for controlling a free-form surface according to claim 5, wherein the controlling the second derivative of the free-form surface to avoid the concave-convex surface of the free-form surface comprises:

determining the positive and negative signs of a second derivative of the free-form surface according to the concave-convex performance of the (f) (x) function;

and controlling second derivatives of all points of the polynomial of the free-form surface to be in the same sign, so that concave and convex surfaces are avoided.

7. The method of free-form surface control of claim 1, further comprising, prior to modulating the second derivative of the free-form surface:

the amount of deviation of the free-form surface is calculated to control the amount of deviation of the free-form surface.

8. An apparatus for free form surface control, comprising:

the free-form surface generation module is used for inputting the surface type of the self-defined surface to generate a free-form surface;

the free-form surface analysis module is used for analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface;

and the concave-convex surface regulating and controlling module is used for regulating and controlling the second derivative of the free-form surface to avoid the concave-convex surface of the free-form surface if the free-form surface has no concave-convex surface.

9. The free-form surface controlled apparatus of claim 8, wherein the free-form surface analysis module comprises:

a value taking unit, which is used for taking a range value [ a, b ] on the free curved surface, and a continuous function arranged in [ a, b ] is f (x);

the judging unit is used for judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein the function f (x) is a convex surface if the function f (x) is a convex surface, and the function f (x) is a concave surface if the function f (x) is a concave surface.

10. The free-form surface controlled apparatus of claim 8, wherein the asperity conditioning module comprises:

a second derivative judging unit for determining the positive and negative signs of the second derivative of the free curved surface according to the concave-convex property of the f (x) function;

and the second derivative regulating and controlling unit is used for controlling the second derivatives of all points of the polynomial of the free-form surface to be of the same sign, so that the concave-convex surface is avoided.

Technical Field

The invention relates to the technical field of extreme ultraviolet lithography, in particular to a method and a device for controlling a free-form surface.

Background

With the development and progress of scientific technology, the requirements of people on an imaging optical system are gradually improved, and the imaging optical system is developed towards the directions of large view field, large aperture, wide band and the like while realizing high image quality so as to meet the requirements of different application scenes. Compared with a transmissive system, a reflective system has the following advantages: no chromatic aberration exists, and good image quality can be kept in a wide waveband range; the optical path in the optical system can be folded, the system has high transmittance and good thermal stability, and is not easily influenced by radiation. Furthermore, the curved surface of the reflective system can be made large relative to the transmissive system and weight reduction is easily achieved. However, conventional coaxial reflection systems typically have a central obscuration that limits the resolution, incident light energy, and field of view size of the system. Therefore, researchers have begun to use off-axis field of view, off-axis aperture, or tilted surfaces to eliminate the obscuration of the system, which also greatly increases the design difficulty of the system. Since the rotational symmetry of the system is broken, many unconventional aberrations with special field-of-view dependent properties are generated, which are difficult to correct by rotationally symmetric spherical or aspherical surfaces. Thus, when off-axis systems are required to achieve good image quality, the field of view or NA of the system is often limited, and the use of a free-form surface may be a good solution to this problem. The aberration form introduced by the free-form surface completely corresponds to the aberration form introduced by the decentering inclination of the surface with respect to the spherical surface or the aspherical surface. The free form surface is particularly suitable for the design of off-axis reflective systems.

Extreme Ultraviolet Lithography (EUVL) is a projection Lithography technique that uses Extreme Ultraviolet light with a wavelength of 13.5nm as a working wavelength, and has a natural advantage that the exposure wavelength is reduced by one order of magnitude, so that the limitation on the numerical aperture and the process factor of an objective lens can be well released, the objective lens becomes a next-generation Lithography technique, and the EUVL is a preferred technique for realizing the industrialization of a 7nm and below technology node integrated circuit. Since euv light has a very strong absorption for almost all optical materials, euv lithography uses reflective elements. The resolution formula is that in order to achieve higher resolution, the NA of the EUVL objective optical system needs to be continuously increased. For a High-NA (NA is more than or equal to 0.4) optical system, the 4x micro-scale ratio, the full view field and the 6inch mask are not feasible any more, the incident angle is increased suddenly due to the High NA, the shadow effect is increased and the contrast is reduced to an unacceptable range seriously, and the solution is to reduce the incident angle of the mask, increase the incident angle of the mask and increase the contrastAnd adding an objective lens micro-scaling. Weighing image plane full field of view 2633mm²The required reduction ratio is provided in a different direction using an anamorphic optical system than using a 6inch mask. The anamorphic objective lens with the XY direction micro-scale ratio of 4x/8x can use a 6inch mask to realize 2616.5mm²Half field exposure, providing optimal yield and resolution, has been difficult to achieve with conventional rotationally symmetric spherical or aspherical surfaces, requiring the use of free-form surfaces.

The extreme ultraviolet lithography High-NA projection objective has extremely High imaging quality requirements, depends on aberration balance, has extremely High requirements on a free-form surface, and therefore, the design of the High-NA projection deformable objective with enough design freedom to realize the super-diffraction limit resolution is required.

In the design process of the extreme ultraviolet lithography deformable objective lens, the problems of overlarge deviation of a free-form surface and multiple concave-convex surfaces exist, the existing design needs to realize the design of the extreme ultraviolet lithography objective lens with the super diffraction limit, an XY polynomial with a high polynomial term number needs to be adopted, the surface of a free-form surface element is more and more complex along with the continuous increase of the designed term number, and therefore a technical scheme capable of regulating and controlling the concave-convex surfaces of the free-form surface is needed to avoid the violent change in the design process of the free-form surface.

Disclosure of Invention

The embodiment of the invention provides a method and a device for controlling a free-form surface, which are used for controlling the free-form surface of an element, avoiding violent change in the design process of the free-form surface and reducing the manufacturing difficulty of the element of the free-form surface.

According to an embodiment of the present invention, there is provided a method of free-form surface control, including the steps of:

inputting the surface type of the self-defined curved surface to generate a free curved surface;

analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface;

and if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided.

Further, the inputting the surface type of the custom curved surface and generating the free curved surface includes:

selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

writing a macro file by using a CODE-V (CODE-variable) self-contained macro language grammar based on the gradient of the surface polynomial;

and selecting the corresponding macro file to complete the input of the surface type of the self-defined curved surface.

Further, the inputting the surface type of the custom curved surface and generating the free curved surface includes:

selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

writing a C language file by using the syntax of a CODE-V and C language interface based on the gradient of the surface polynomial, and generating a DLL file;

and the input of the user-defined surface type can be completed by selecting the corresponding DLL file.

Further, the surface shape of the self-defined curved surface can be used for ray tracing.

Further, analyzing the free-form surface to determine whether the free-form surface has a concave-convex surface includes:

taking a range value [ a, b ] on the free-form surface, wherein a continuous function set in the [ a, b ] is f (x);

judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein if f (x) is a convex function, the convex surface is a convex surface, and if f (x) is a concave surface, the concave function is a concave surface.

Further, the adjusting and controlling of the second derivative of the free-form surface to avoid the occurrence of concave-convex surfaces on the free-form surface comprises:

determining the positive and negative signs of a second derivative of the free-form surface according to the concave-convex performance of the (f) (x) function;

and controlling second derivatives of all points of the polynomial of the free-form surface to be in the same sign, so that concave and convex surfaces are avoided.

Further, before the second derivative of the free-form surface is regulated, the method further includes:

the amount of deviation of the free-form surface is calculated to control the amount of deviation of the free-form surface.

According to another embodiment of the present invention, there is provided an apparatus for free-form surface control, including:

the free-form surface generation module is used for inputting the surface type of the self-defined surface to generate a free-form surface;

the free-form surface analysis module is used for analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface;

and the concave-convex surface regulating and controlling module is used for regulating and controlling the second derivative of the free-form surface to avoid the concave-convex surface of the free-form surface if the free-form surface has no concave-convex surface.

Further, the free form surface analysis module includes:

a value taking unit, which is used for taking a range value [ a, b ] on the free curved surface, and a continuous function arranged in [ a, b ] is f (x);

the judging unit is used for judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein the function f (x) is a convex surface if the function f (x) is a convex surface, and the function f (x) is a concave surface if the function f (x) is a concave surface.

Further, the concave-convex surface regulation and control module comprises:

a second derivative judging unit for determining the positive and negative signs of the second derivative of the free curved surface according to the concave-convex property of the f (x) function;

and the second derivative regulating and controlling unit is used for controlling the second derivatives of all points of the polynomial of the free-form surface to be of the same sign, so that the concave-convex surface is avoided.

The method and the device for controlling the free-form surface input the surface type of the self-defined surface to generate the free-form surface; analyzing the free-form surface and judging whether the free-form surface has a concave surface or a convex surface; and if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided. According to the method, the feasibility of processing and detecting the designed free-form surface element is considered in the design stage of the free-form surface by controlling the second derivative of the free-form surface, so that the problem that the manufacturing difficulty of the free-form surface element is reduced due to severe element change in the design process of the free-form surface is avoided.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the drawings:

FIG. 1 is a flow chart of a method of free form surface control of the present invention;

FIG. 2 is a flow chart of inputting the profile of a custom surface according to the present invention;

FIG. 3 is another flow chart of inputting the profile of a custom surface according to the present invention;

fig. 4 is a block schematic diagram of the free form surface controlled apparatus of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the 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.

It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

Example 1

Referring to fig. 1 to 3, according to an embodiment of the present invention, there is provided a method of free form surface control, including the steps of:

s101: inputting the surface type of the self-defined curved surface to generate a free curved surface;

s102: analyzing the free-form surface, and judging whether the free-form surface has a concave surface or a convex surface;

s103: if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided.

The method and the device for controlling the free-form surface input the surface type of the self-defined surface to generate the free-form surface; analyzing the free-form surface, and judging whether the free-form surface has a concave surface or a convex surface; if the free-form surface has no concave-convex surface, the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled, and the concave-convex surface of the free-form surface is avoided. The invention controls the sign of the second derivative of the free-form surface polynomial, so that the feasibility of processing and detecting the designed free-form surface element is considered in the design stage of the free-form surface, and the difficulty in manufacturing the free-form surface element due to severe element change in the free-form surface design process is avoided.

In an embodiment, the inputting the surface type of the custom surface and the generating the free surface includes:

s201: selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

s202: writing a macro file by using a CODE-V self-contained macro language grammar based on the gradient of the surface type polynomial;

s203: and the input of the surface type of the user-defined curved surface can be finished by selecting the corresponding macro file.

The number of free-form surface items supported by current optical design business software such as CODE-V is limited, when the design freedom requirement is greater than the default number of items of software, an optical designer needs to select a self-defined surface type expression and the corresponding number of items according to personal requirements, a User defined surface type (User defined surface) option provided by CODE-V is used, and a designer realizes the input of a self-defined surface type by writing a macro file or a Dynamic Link Library (DLL) file.

The following describes the input of a custom profile by writing a macro file using CODE-V self-contained macro language syntax according to the present invention with specific embodiments:

the method comprises the following steps: firstly, a designer needs to select a self-defined surface type polynomial and calculate the gradient of the polynomial;

step two: writing a macro file based on CODE-V self-contained macro language grammar;

step three: and selecting the CODE-V custom surface type, and selecting the corresponding macro file to complete the input of the custom surface type.

In an embodiment, the inputting the surface type of the custom surface and the generating the free surface includes:

s301: selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

s302: writing a C language file by using the syntax of a CODE-V and C language interface based on the gradient of the surface type polynomial, and generating a DLL file;

s303: and the input of the user-defined surface type can be completed by selecting the corresponding DLL file.

The following explains the input of the custom face type by writing a C language file by using the syntax of the CODE-V and C language interfaces in the invention by a specific embodiment;

the method comprises the following steps: firstly, a designer needs to select a self-defined surface type polynomial and calculate the gradient of the polynomial;

step two: writing a C language file to generate a DLL file based on the syntax of a CODE V and C language interface;

step three: and selecting a CODE V custom surface type, and selecting a corresponding DLL file to finish the input of the custom surface type.

In an embodiment, a custom curved surface profile can be used for ray tracing. The input of the self-defined surface type is completed by using a mode that a CODE-V self-contained macro language grammar writes a macro file or a C language file is written by a grammar of a CODE V and C language interface to generate a DLL file, and the self-defined surface type input by the two modes is explicitly written by a polynomial expression and a gradient expression thereof, so that the self-defined surface can be used for ray tracing.

In an embodiment, analyzing the free-form surface to determine whether the free-form surface has a concave-convex surface includes:

taking a range value [ a, b ] on the free-form surface, and setting a continuous function in the [ a, b ] as f (x);

judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein if f (x) is a convex function, the convex surface is a convex surface, and if f (x) is a concave surface, the concave function is a concave surface.

The invention provides a free-form surface control method which controls a free-form surface element in a design stage. The method controls the free-form surface based on the relation between the sign of the second derivative of the free-form surface function and the concave-convex performance of the function, so that a plurality of concave-convex surfaces are avoided.

The functional relief of the free-form surface is defined as: when the f (x) function is a convex function, the second derivative of the f (x) function is less than 0, and when the f (x) function is a concave function, the second derivative of the f (x) function is greater than 0;

in particular, for one in [ a, b]The above successive functions f (x), if any₁And x₂∈[a,b]So thatIf the constant is true in (a, b), the function is called a convex function; if it isWhen (a, b) is always true, the function is called a concave function. When the function f (x) is a convex function, the second derivative of the function f (x) is less than 0; when the function is a concave function, the second derivative of the function f (x) is greater than 0.

In the embodiment, the adjusting and controlling the second derivative of the free-form surface to avoid the occurrence of concave-convex surfaces on the free-form surface comprises:

determining the sign of a second derivative of the free-form surface according to the concave-convex performance of the (f) (x) function;

and controlling second derivatives of all points of the polynomial of the free-form surface to be in the same sign, so that concave and convex surfaces are avoided.

In the optical design process, the concavity and the convexity of the free-form surface element are judged according to the focal power of the free-form surface element, the second derivative symbol of the free-form surface element is determined according to the concavity and the convexity, the symbol is written into optical design software in a macro text form in the design process, and the second derivatives of all points of the free-form surface polynomial are controlled to be the same number, so that the concave and the convex surfaces are avoided; the same sign means that if the second derivative has positive or negative, the second derivative is made to be positive or negative so as to avoid the concave-convex surface.

In an embodiment, before the adjusting and controlling the second derivative of the free-form surface, the method further includes:

the amount of deviation of the free-form surface is calculated to control the amount of deviation of the free-form surface.

Since many free-form surfaces are obtained by superimposing non-rotationally symmetric terms on the basis of the base spherical surface or the base quadratic surface, the deviation of the free-form surfaces from the base function along the Z direction is calculated to describe the deviation of the free-form surfaces based on the polynomial of a given free-form surface type. Taking xy polynomial as an example, the surface expression is:

wherein the basis function isThe deviation of the two formulas is the deviation of the free curved surface; in the design of a free-form surface, similarly to an aspheric element, the aspheric degree and the steepness of the aspheric degree of the element determine whether processing and detection can be realized, and the deviation amount also needs to be controlled in the design of the free-form surface. After the system is added with the self-defined surface types and respectively added with the free-form surface control, if the conditions are not met, the optimization design scheme is changed to ensure that the optimization is smoother and more optimal, so that the final optimization is realizedThe result is satisfactory free-form surface control.

Example 2

Referring to fig. 1 to 4, according to another embodiment of the present invention, there is provided an apparatus for free-form surface control, including:

a free-form surface generating module 100, configured to input a surface type of a custom-defined surface to generate a free-form surface;

the free-form surface analysis module 200 is configured to analyze a free-form surface and determine whether the free-form surface has a concave surface or a convex surface;

the concave-convex surface regulating and controlling module 300 is used for regulating and controlling the second derivative of the free-form surface to avoid the occurrence of the concave-convex surface if the free-form surface does not have the concave-convex surface, wherein the free-form surface meets the manufacturing condition, otherwise, the second derivative of the free-form surface is regulated and controlled.

In the method and the device for controlling the free-form surface, the sign of the second derivative of the polynomial of the free-form surface is controlled by the concave-convex surface regulation and control module 300, so that the feasibility of processing and detection of the designed free-form surface element is considered in the design stage of the free-form surface, and the difficulty in manufacturing the free-form surface element due to severe element change in the design process of the free-form surface is avoided.

Further, the step of inputting the surface type of the custom surface and generating the free-form surface comprises:

s201: selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

s202: writing a macro file by using a CODE-V self-contained macro language grammar based on the gradient of the surface type polynomial;

s203: and the input of the surface type of the user-defined curved surface can be finished by selecting the corresponding macro file.

The number of free-form surface items supported by current optical design business software such as CODE-V is limited, when the design freedom requirement is greater than the default number of items of software, an optical designer needs to select a self-defined surface type expression and the corresponding number of items according to personal requirements, a User defined surface type (User defined surface) option provided by CODE-V is used, and a designer realizes the input of a self-defined surface type by writing a macro file or a Dynamic Link Library (DLL) file.

The following describes the input of a custom profile by writing a macro file using CODE-V self-contained macro language syntax according to the present invention with specific embodiments:

the method comprises the following steps: firstly, a designer needs to select a self-defined surface type polynomial and calculate the gradient of the polynomial;

step two: writing a macro file based on CODE-V self-contained macro language grammar;

step three: and selecting the CODE-V custom surface type, and selecting the corresponding macro file to complete the input of the custom surface type.

Further, the step of inputting the surface type of the custom surface and generating the free-form surface comprises:

selecting a surface type polynomial of a self-defined curved surface, and calculating the gradient of the surface type polynomial;

writing a C language file by using the syntax of a CODE-V and C language interface based on the gradient of the surface type polynomial, and generating a DLL file;

and the input of the user-defined surface type can be completed by selecting the corresponding DLL file.

The following describes the input of the custom face type by writing a C language file by using the syntax of the CODE-V and C language interfaces in the invention with a specific embodiment;

the method comprises the following steps: firstly, a designer needs to select a self-defined surface type polynomial and calculate the gradient of the polynomial;

step two: writing a C language file to generate a DLL file based on the syntax of a CODE V and C language interface;

step three: and selecting a CODE V custom surface type, and selecting a corresponding DLL file to finish the input of the custom surface type.

Further, the profile of the custom curved surface can be used for ray tracing. The input of the self-defined surface type is completed by using a mode that a CODE V self-contained macro language grammar writes a macro file or a mode that a CODE V and C language interface grammar writes a C language file to generate a DLL file, and the self-defined surface type input by the two modes is explicitly written due to a polynomial expression and a gradient expression thereof, so the self-defined surface can be used for ray tracing.

In an embodiment, the free form surface analysis module comprises:

the value taking unit is used for taking a range value [ a, b ] on the free curved surface, and a continuous function arranged in the [ a, b ] is f (x);

the judging unit is used for judging the concave-convex performance of the function f (x) to determine whether the free curved surface has a concave-convex surface, wherein the function f (x) is a convex surface if the function f (x) is a convex surface, and the function f (x) is a concave surface if the function f (x) is a concave surface.

The invention provides a free-form surface control method which controls a free-form surface element in a design stage. The method controls the free-form surface based on the relation between the sign of the second derivative of the free-form surface function and the concave-convex performance of the function, so that a plurality of concave-convex surfaces are avoided.

The functional relief of the free-form surface is defined as: when the f (x) function is a convex function, the second derivative of the f (x) function is less than 0, and when the f (x) function is a concave function, the second derivative of the f (x) function is greater than 0;

specifically, for a function f (x) which is continuous in [ a, b ], if the sum epsilon [ a, b ] is constant in (a, b), the function is called a convex function; if (a, b) is always true, the function is called a concave function. When the function f (x) is a convex function, the second derivative of the function f (x) is less than 0; when the function is a concave function, the second derivative of the function f (x) is greater than 0.

In an embodiment, the concave-convex surface conditioning module comprises:

a second derivative judging unit for determining the second derivative sign of the free curved surface according to the concave-convex property of the f (x) function;

and the second derivative regulating and controlling unit is used for controlling the second derivatives of all points of the polynomial of the free-form surface to be of the same sign, so that the concave-convex surface is avoided.

In the optical design process, the concavity and the convexity of the free-form surface element are judged according to the focal power of the free-form surface element, the second derivative symbol of the free-form surface element is determined according to the concavity and the convexity, the second derivative symbol is written into optical design software in a macro text mode in the design process, and the second derivatives of all points of the free-form surface polynomial are controlled to be identical in number, so that the concave and the convex surfaces are avoided.

Further, before the second derivative of the free-form surface is regulated, the method further comprises:

the amount of deviation of the free-form surface is calculated to control the amount of deviation of the free-form surface.

Since many free-form surfaces are obtained by superimposing non-rotationally symmetric terms on the basis of the base spherical surface or the base quadratic surface, the deviation of the free-form surfaces from the base function along the Z direction is calculated to describe the deviation of the free-form surfaces based on the polynomial of a given free-form surface type. Taking xy polynomial as an example, the surface expression is:

wherein the basis function isThe deviation of the two formulas is the deviation of the free curved surface; in the design of a free-form surface, similarly to an aspheric element, the aspheric degree and the steepness of the aspheric degree of the element determine whether processing and detection can be realized, and the deviation amount also needs to be controlled in the design of the free-form surface. After the user-defined surface types are added to the system, after the free-form surface control is added respectively, if the conditions are not met, the optimization design scheme is changed to enable the optimization scheme to be smoother and more optimized, and the final optimization result meets the free-form surface control.

The invention provides a free-form surface control method which controls a free-form surface element in a design stage, and controls the sign of a second derivative of a free-form surface polynomial and the deviation control of the free-form surface polynomial and a basis function, so that the feasibility of processing and detection of the designed free-form surface element is considered in the free-form surface design stage, the violent change of the element in the free-form surface design process is avoided, and the difficulty of manufacturing the free-form surface element is reduced.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.