CN116626891A - Construction, preparation and application method of hypersurface based on free-form surface substrate - Google Patents
Construction, preparation and application method of hypersurface based on free-form surface substrate Download PDFInfo
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Abstract
The invention discloses a construction, preparation and application method of a hypersurface based on a free-form surface substrate, wherein the hypersurface comprises a free-form surface and a hypersurface, the free-form surface is used as a substrate, and the construction method comprises the following steps of: obtaining an optical free-form surface base model capable of optimizing system aberration based on aberration theory; constructing a phase distribution diagram of the contribution required by the super surface according to aberration analysis of the free-form surface substrate model; obtaining a micro-structure and a super-surface of the super-surface unit by using a time domain finite difference method according to the obtained phase distribution diagram; verifying focusing and imaging performance of the super surface obtained by using a time domain finite difference method; and programming a hypersurface optical system design and evaluation algorithm to evaluate the hypersurface optical system. The hypersurface formed by the optical free-form surface and the hypersurface in the invention can realize the requirements of compact, light weight, multifunction and high image quality of an imaging optical system, and provides a new design theory and realization approach for the design and realization of the traditional optical system.
Description
Technical Field
The invention relates to the technical field of optical design, in particular to a method for constructing a hypersurface based on a freeform surface substrate and application thereof.
Background
A hypersurface is a hybrid optical surface structure comprising an optical freeform surface and a hypersurface, which has the dual imaging advantage of generating a new imaging mode and optical element, wherein: the optical free-form surface can pertinently correct various aberrations of the optical system, increases the depth of field, enlarges the field of view, improves the system performance, optimizes the system structure, and has important significance for the development of high performance, light weight and microminiaturization of the modern optical system; the super surface has excellent capability of regulating and controlling physical characteristics such as optical field phase, amplitude, polarization and the like in a sub-wavelength scale, and can realize regulation, transmission and focusing of light waves through a simple structural design. The appearance of hypersurface provides a new idea for the realization of the traditional optical design theory and technology.
At present, research on optical free-form surfaces and super-surfaces is very active in various universities, research institutions and the like in the world, so that the rapid development of theories and technologies is promoted, great achievements are obtained, and the research on the super-surfaces still belongs to a starting stage. The existing hypersurface structure is generally of a plane structure, cannot adapt to an irregular surface state in practical application, and is limited in application environment.
Disclosure of Invention
The invention aims to provide a construction, preparation and application method of a hypersurface based on a free-form surface substrate, aberration correction is realized through the cooperative design of the free-form surface and the hypersurface, high-resolution imaging is realized through compactness, shape retention and folding surface type, and better image quality is obtained.
In order to achieve the above object, the present invention provides a method for constructing a hypersurface based on a free-form surface substrate, wherein the hypersurface comprises a free-form surface and a hypersurface, and the free-form surface is used as a substrate, and the steps are as follows:
s1, obtaining an optical free-form surface type function capable of optimizing system aberration based on aberration theory;
s2, constructing a minimum distortion mapping and unit approximate plane design model from the curved surface super surface to the plane super surface reference surface, wherein the construction process needs to construct a phase distribution diagram of the contribution required by the super surface according to aberration analysis of the free curved surface base model; obtaining a micro-structure and a super-surface of the super-surface unit by using a time domain finite difference method according to the obtained phase distribution diagram; optimizing by using the super-surface compensation mechanism and the design method of the obtained free-form surface substrate after the initial model is constructed;
s3, verifying focusing and imaging performances of the super surface obtained by using a time domain finite difference method;
s4, designing a hypersurface optical system and evaluating the hypersurface optical system by an evaluation algorithm.
The super surface is composed of a series of tiny optical elements (such as nano-antenna, photonic crystal and the like), and the precise regulation and control of the phase, intensity and the like of light can be realized by changing the material, angle and the like of the nano-antenna. Because the size of the nanoantenna (pillar) is very small, typically in the scale range of tens to hundreds of nanometers, while the size of the hypersurface is typically on the order of millimeters or centimeters. Thus, at the scale of the hypersurface, the surface around the nanoantenna (post) appears smooth and can be considered as a continuous approximately planar optical element.
Preferably, the optical freeform surface base model based on aberration theory and capable of optimizing system aberration according to S1 specifically includes:
s1.1, adopting ray tracing to trace and analyze rays transmitted through a preset optical system, and obtaining aberration required to be corrected by the optical system;
s1.2, a free-form surface base model capable of optimizing system aberration is obtained by adopting a node aberration theory, and the aberration can be simply understood that the deviation exists between the actual optical system imaging and the ideal optical imaging. The Sielder theory, hopkins theory, etc. can clearly describe the aberrations of rotationally symmetric systems
The wave aberration of a rotationally symmetric system can be written according to Hopkins wave aberration theory as:
k＝2p+m,l＝2n+m,
wherein W is the total wave aberration; (W) klm ) j Is the aberration coefficient; j is the sum of the aberration contributions of each facet; H. ρ is normalized field of view and aperture coordinates, respectively; phi is the polar angle of the aperture coordinate, and the view field coordinate and the aperture coordinate of the system are scalar quantities at the moment;
for aberrations of non-rotationally symmetric systems, the field of view coordinates are vectorized with the aperture coordinates, i.e. h=he iθ ，ρ＝ρe iφ The Hopkins wave aberration of a non-rotationally symmetric system can be described in terms of vectors as:
when the system is eccentrically inclined, the whole system does not introduce a new aberration type, but introduces a plurality of aberrations (such as constant coma, linear field asymmetric astigmatism, linear field conjugate astigmatism, and the like) with special field dependence characteristics of the original aberration type. The point in the full field aberration field where the aberration point for each aberration is zero may no longer be in the zero field. But rather a relative movement occurs, sometimes even more than one point where the aberration is zero.
Preferably, the phase distribution map of S2 is calculated as follows:
the hypersurface is a refractive hypersurface, the space and time coherent light is assumed to be incident on the hypersurface, the light interacts on the free surface and the hypersurface, the phase of the optical path difference is accumulated, A is a point on the incident light, B is a point on the refractive light, and the free surface is at a point [ x ] 0 ,y 0 ,z(x 0 ,y 0 )]The phases provided are:
wherein k is a wave vector;
light at the super surface point (x 0 ,y 0 ) Reflection ofThe phase contributed by the latter is noted as phi meta (x 0 ,y 0 ) So that after the light is reflected, the hypersurface is at point [ x ] 0 ,y 0 ；z(x 0 ,y 0 )]The total phase is provided:
thus, for a point on the hypersurface, the total phase provided is:
Φ metaform (x,y；z(x,y))＝Φ meta +Φ freeform (x,y；z(x,y))。
a preparation method of a hypersurface based on a free-form surface substrate comprises the following steps:
s1, obtaining a free-form surface substrate based on optical free-form surface modeling and aberration theory analysis;
s2, obtaining a phase distribution diagram of contribution required by construction of the super surface by using Zemax software, wherein the phase distribution diagram specifically comprises the following steps:
s2.1, replacing the super surface with a binary surface 2 in Zemax software for simulation, namely replacing and optimizing the refraction and diffraction system with the refraction and diffraction system to obtain the phase provided by the binary surface 2, namely the phase distribution provided by the corresponding super surface;
s2.2, optimizing and correcting aberration by adopting a damping least square method in Zemax software;
s2.3 the phase profile provided by the binary surface 2 after optimization is obtained in the Zemax software.
S3, obtaining a microstructure and a super surface of the super surface unit by using a finite difference method in a time domain through FDTD software, and observing effect graphs of different sections of the microstructure and the super surface, wherein the method specifically comprises the following steps:
s3.1 build-up with SiO in FDTD software 2 Si-SiO as substrate 2 A unit microstructure of the structure;
s3.2, obtaining a database of phases and transmittance under different parameters of the structure according to a time domain finite difference method;
s3.3, establishing a corresponding super surface by utilizing a phase and transmittance database of the unit structure according to the phase distribution diagram in the S2;
s3.4, observing effect graphs of different sections of the fiber reinforced plastic in FDTD software;
s4, preparing an optical free-form surface through precision die pressing or single-point diamond turning, obtaining a super-surface through nanoimprint or enhanced electron beam lithography, and then attaching the free-form surface to the super-surface;
the enhanced electron beam lithography (Enhanced Electron Beam Lithography) is a high resolution nano-processing technique that can be used to prepare nanostructures such as hypersurfaces. Has higher resolution and faster processing speed compared with the traditional electron beam lithography technology. The working principle is that electron beams are utilized to locally irradiate on the surface of a sample, so that the photoresist on the surface of the sample is chemically or physically changed, and the required nano structure is formed. Compared with the traditional electron beam lithography technology, the method adopts higher electron beam energy and shorter beam spot, thereby realizing higher resolution and faster processing speed. The application range is very wide, including fields of nanoelectronics, nano optics, nano machinery and the like. In the aspect of preparing the hypersurface and other nano structures, high-precision photoetching can be realized, so that high-resolution imaging is realized. Meanwhile, multi-level nano processing can be realized, so that a more complex nano structure is realized.
S5, evaluating the obtained hypersurface by adopting an image quality evaluation algorithm.
For an image quality evaluation algorithm, the hypersurface modeling simulation, geometric optics, fluctuation optics, finite elements and other methods are fused, and a set of hypersurface optical system design and evaluation method based on deep learning is established by combining the programmable functions of the existing optical design software, so that the whole structure of the hypersurface optical system can be designed and evaluated, and the realizability of the hypersurface can be independently evaluated. Based on the design, the corresponding super-curved ultra-thin compact optical system design and image quality evaluation are completed; and finally, adopting an interferometer to finish wave-front aberration measurement, calculating a corresponding point spread function, an optical transfer function and the like through phase reconstruction and the like, comparing and analyzing theoretical calculation of optical design software with experimental test results, evaluating actual imaging quality and aberration correction effect, and verifying feasibility of a scheme and theoretical research results.
An application of hypersurface based on a free-form surface substrate comprises an optical system based on a hypersurface design.
Therefore, the construction and evaluation method and application of the hypersurface optical surface type of the seed curved surface substrate have the following beneficial effects:
(1) The single hypersurface structure is adopted to realize functions of aberration correction and the like of the traditional optical system, and the problems of complex structure and the like of the traditional optical system are solved;
(2) The ultra-surface structure is easy to process, has good imaging effect, is suitable for the design and the use requirements of special requirements of optical systems such as light and small size, compact type and the like, and helps to realize the development of lighter, more compact and more effective optical equipment;
(3) The image quality evaluation algorithm is combined with the methods of hypersurface modeling simulation, ray tracing, fluctuation optics, finite elements and the like, so that complicated steps of independent design, evaluation and the like in the traditional design are improved, and the integrated development trend of special optical system design and image quality evaluation can be realized.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a diagram of a hypersurface diagram of an application example 1 and a method for constructing a hypersurface based on a freeform surface substrate according to the present invention;
FIG. 2 is a modeling diagram of the microstructure of the hypersurface unit in FDTD software according to embodiment 1 of the present invention;
FIG. 3 is a diagram showing the phase and transmittance of the hypersurface unit microstructure according to example 1, (a) is a phase diagram, and (b) is a transmittance diagram;
FIG. 4 is a schematic diagram of generating a corresponding subsurface according to a scan parameter database according to embodiment 1 of the present invention;
FIG. 5 is a schematic diagram of the imaging principle of the ultra-compact optical system according to embodiment 2 of the present invention;
FIG. 6 is a diagram showing the construction of a four-mirror system according to embodiment 2 of the present invention;
FIG. 7 is a schematic view of an ultra-compact optical system according to embodiment 2 of the present invention;
FIG. 8 is an MTF diagram of an ultra-compact optical system according to embodiment 2 of the present invention;
FIG. 9 is a diagram showing the focusing effect of the super surface XOY plane at 20um focal length of the ultra-compact optical system of example 2 of the present invention;
FIG. 10 is a diagram showing the focusing effect of the super surface XOZ plane at 20um focal length for the ultra-compact optical system of example 2 of the present invention;
FIG. 11 is a diagram of the design of the hypersurface optical system and the programming implementation of the image quality evaluation algorithm of the present invention.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Example 1
Hypersurface has many applications in real life and production scenarios, for example, an X-toroidal ring-shaped substrate with an ergonomically more conforming face of a user may be used to make VR, AR devices. The construction process is as follows:
for an X toroidal surface, the surface expression of the optical free-form surface base model is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
wherein c is the radius of curvature on the curved axis, k x Is a conic coefficient, c x And c y Representing the curvature in the x and y directions, respectively.
Example 2
Taking the Zernike polynomial surface form as an example, the surface form expression is:
wherein c is a curved surfaceOn-axis curvature radius, k is a conical coefficient, r is half-caliber size, r 2 ＝x 2 +y 2 ，For polynomial, ai is a coefficient, which can be expanded as:
the term number of Zeinike polynomials is
When the free-form surface represented by the Zernike polynomial is used for designing the optical system, the advantages are that the general optical system has a circular aperture, the Zernike polynomial has the characteristic of orthogonality in a unit circle, the orthogonality enables coefficients of the Zernike polynomial to be independent of each other, the coefficients of the Zernike polynomial do not interfere with each other in optimization, each term in the Zernike polynomial can represent aberration characteristics, and the Zernike polynomial has a corresponding relation between the terms, so that aberration elimination can be controlled.
Example 3
To construct a hypersurface structure of a rotationally symmetric system as shown in fig. 1, the steps are as follows:
s1, obtaining an optical free-form surface base model capable of optimizing system aberration based on aberration theory;
s1.1, adopting ray tracing to trace and analyze the rays transmitted through a preset optical system, and obtaining the aberrations such as spherical aberration, coma aberration and the like required to be corrected by the optical system.
S1.2, finding out points with zero spherical aberration by adopting a node aberration theory, fitting the points, and finally fitting to obtain the surface shape of the free-form surface substrate capable of optimizing the system aberration.
S2.1, because no super-surface type exists in Zemax software, a binary surface 2 (diffraction surface) is used for replacing the super-surface, namely a refraction and diffraction system is used for replacing a refraction and diffraction system to optimize, so that phases provided by the binary surface 2, namely phase distribution provided by the corresponding super-surface, are obtained;
s2.2, optimizing the refraction and diffraction system in Zemax software, and correcting monochromatic aberration and chromatic aberration such as spherical aberration, coma aberration and the like by using related aberration operands;
s2.3 the phase map provided by this binary surface 2 is obtained in the Zemax software.
After obtaining the phase provided by the binary surface 2, i.e. the phase of the corresponding hypersurface, it is then necessary to build the microstructure of the hypersurface unit and its corresponding database. The present invention is exemplified by visible light, and is not intended to be limited to visible light, infrared light, and near infrared light.
S3.1 modeling in FDTD software as shown in FIG. 2, most optical glasses today use SiO 2 Is made of material, so that the unit microstructure of the super surface is made of SiO 2 Si is a microstructure material and is used as a substrate, and the formed Si microstructure cuboid column is positioned on SiO 2 The length and the width of the rectangular column of the Si microstructure are equal above the substrate;
s3.2, carrying out the scanning of the cuboid width and height from 50nm to 400nm according to a time domain finite difference method, and obtaining a scanning parameter database of the phase and the transmittance of the cuboid width and height, as shown in figure 3.
S3.2, generating a corresponding hypersurface by using a corresponding script according to the phase and sweep parameter database provided by the binary surface 2, as shown in fig. 4.
Example 4
According to the method, a set of optical system based on the ultra-compact ultra-surface is designed.
The ultra-compact optical system designed by the invention is an annular aperture ultra-thin system, the working principle of the ultra-compact optical system is shown in fig. 5, the lens is improved based on the traditional Grignard telescope structure, the whole optical system is only composed of a single piece of optical material, and the required optical surfaces are designed on the front surface and the rear surface of the optical system, and the optical system is usually called a flat plate structure or an annular aperture system. The light enters the optical system through the outermost annular aperture, then is reflected back and forth to form an image by the mirrors on the front and rear surfaces, and the light proceeds along a zigzag path and finally reaches the detector at the image plane.
Based on the design of the two-mirror system of the plan modern applied optics, the four-mirror system shown in fig. 6 is obtained after optimization.
However, four mirrors of the ultra-compact system are all positioned on the same substrate, so the material is set to be calcium fluoride, and the relationship between the thickness of the annular aperture system and the reflection times of the material is utilizedOptimizing the structure results in a circular aperture system as shown in fig. 7 with MTF as shown in fig. 8. Where T is the total thickness, EFL is the effective focal length, nc is the refractive index of the substrate material, and N is the number of refractive times. And observing the tangent plane of the obtained annular aperture system through software to obtain a super-surface XOY plane focusing effect diagram at the focal length of 20um shown in figure 9 and a super-surface XOZ plane focusing effect diagram at the focal length of 20um shown in figure 10.
According to the design thought of the hypersurface, the hypersurface capable of optimizing the annular aperture system can be designed in the same way.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (5)
1. A method for constructing a hypersurface based on a free-form surface substrate is characterized by comprising the following steps of: the hypersurface comprises a free-form surface and a hypersurface, and the free-form surface is used as a substrate and comprises the following steps:
s1, obtaining an optical free-form surface type function capable of optimizing system aberration based on aberration theory;
s2, constructing a minimum distortion mapping and unit approximate plane design model from the curved surface super surface to the plane super surface reference surface, wherein the construction process needs to construct a phase distribution diagram of the contribution required by the super surface according to aberration analysis of the free curved surface base model; obtaining a micro-structure and a super-surface of the super-surface unit by using a time domain finite difference method according to the obtained phase distribution diagram; optimizing by using the super-surface compensation mechanism and the design method of the obtained free-form surface substrate after the initial model is constructed;
s3, verifying focusing and imaging performances of the super surface obtained by using a time domain finite difference method;
s4, designing a hypersurface optical system and evaluating the hypersurface optical system by an evaluation algorithm.
2. The method for constructing a hypersurface based on a freeform surface substrate as claimed in claim 1, wherein the method comprises the steps of: s1, obtaining an optical free-form surface substrate model capable of optimizing system aberration based on aberration theory, wherein the optical free-form surface substrate model comprises the following specific steps:
s1.1, adopting ray tracing to trace and analyze rays transmitted through a preset optical system, and obtaining aberration required to be corrected by the optical system;
s1.2, a free-form surface base model capable of optimizing system aberration is obtained by adopting a node aberration theory, wherein the node aberration theory specifically comprises the following steps:
the wave aberration of a rotationally symmetric system can be written according to Hopkins wave aberration theory as:
k＝2p+m,l＝2n+m,
wherein W is the total wave aberration; (W) klm ) j Is the aberration coefficient; j is the sum of the aberration contributions of each facet; H. ρ is normalized field of view and aperture coordinates, respectively; phi is the polar angle of the aperture coordinate, and the view field coordinate and the aperture coordinate of the system are scalar quantities at the moment;
for aberrations of non-rotationally symmetric systems, the field of view coordinates are vectorized with the aperture coordinates, i.e. h=he iθ ，ρ＝ρe iφ The Hopkins wave aberration of a non-rotationally symmetric system can be described in terms of vectors as:
3. the method for constructing a hypersurface based on a freeform surface substrate as claimed in claim 1, wherein the method comprises the steps of: the phase distribution map described in S2 is calculated as follows:
the hypersurface is a refractive hypersurface, the space and time coherent light is assumed to be incident on the hypersurface, the light interacts on the free surface and the hypersurface, the phase of the optical path difference is accumulated, A is a point on the incident light, B is a point on the refractive light, and the free surface is at a point [ x ] 0 ,y 0 ,z(x 0 ,y 0 )]The phases provided are:
wherein k is a wave vector;
light at the super surface point (x 0 ,y 0 ) The phase contributed after reflection is denoted as phi meta (x 0 ,y 0 ) So that after the light is reflected, the hypersurface is at point [ x ] 0 ,y 0 ；z(x 0 ,y 0 )]The total phase is provided:
thus, for a point on the hypersurface, the total phase provided is:
Φ metaform (x,y；z(x,y))＝Φ meta +Φ freeform (x,y；z(x,y))。
4. a method of preparing a hypersurface based on a freeform substrate as claimed in any one of claims 1 to 3 which comprises the steps of:
s1, obtaining a free-form surface substrate based on optical free-form surface modeling and aberration theory analysis;
s2, obtaining a phase distribution diagram of contribution required by construction of the super surface by using Zemax software, wherein the phase distribution diagram specifically comprises the following steps:
s2.1, replacing the super surface with a binary surface 2 in Zemax software for simulation, namely replacing and optimizing the refraction and diffraction system with the refraction and diffraction system to obtain the phase provided by the binary surface 2, namely the phase distribution provided by the corresponding super surface;
s2.2, optimizing and correcting aberration by adopting a damping least square method in Zemax software;
s2.3 the phase profile provided by the binary surface 2 after optimization is obtained in the Zemax software.
S3, obtaining a microstructure and a super surface of the super surface unit by using a finite difference method in a time domain through FDTD software, and observing effect graphs of different sections of the microstructure and the super surface, wherein the method specifically comprises the following steps:
s3.1 build-up with SiO in FDTD software 2 Si-SiO as substrate 2 A unit microstructure of the structure;
s3.2, obtaining a database of phases and transmittance under different parameters of the structure according to a time domain finite difference method;
s3.3, establishing a corresponding super surface by utilizing a phase and transmittance database of the unit structure according to the phase distribution diagram in the S2;
s3.4, observing effect graphs of different sections of the fiber reinforced plastic in FDTD software;
s4, preparing an optical free-form surface through precision die pressing or single-point diamond turning, obtaining a super-surface through nanoimprint or enhanced electron beam lithography, and then attaching the free-form surface to the super-surface;
s5, evaluating the obtained hypersurface by adopting an image quality evaluation algorithm.
5. The use of a hypersurface based on a freeform base as claimed in any one of claims 1 to 4 including an optical system based on a hypersurface design which is ultra-compact.
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