CN112540422A - Curved surface-plane imaging conversion lens - Google Patents
Curved surface-plane imaging conversion lens Download PDFInfo
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- CN112540422A CN112540422A CN202011517928.9A CN202011517928A CN112540422A CN 112540422 A CN112540422 A CN 112540422A CN 202011517928 A CN202011517928 A CN 202011517928A CN 112540422 A CN112540422 A CN 112540422A
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B3/00—Simple or compound lenses
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B21/00—Microscopes
- G02B21/02—Objectives
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
Abstract
The invention relates to the technical field of curved surface imaging and curved surface imprinting, and discloses a curved surface-plane imaging conversion lens, which comprises N0The metal plates are stacked to form a three-dimensional columnar structure, channels with the thickness of the sub-wavelength magnitude are arranged between the metal plates, the first end faces of the metal plates are evenly distributed on the periphery of the curved surface, and the second end faces of the metal plates are evenly distributed on the same plane. The invention can directly convert the image distribution on the surface of the curved surface into a plane image in real time, and the imaging curved surface can be a closed curved surface with 360 degrees and any shape, so the invention can realize the image conversion from a full-angle curved surface to a plane. The problem that a traditional imaging instrument cannot directly image a full-angle curved surface object is solved.
Description
Technical Field
The invention relates to the technical field of curved surface imaging and curved surface imprinting, in particular to a curved surface-plane imaging conversion lens, which is used for a lens for directly converting an image on the whole curved surface into a plane image in a full angle manner in real time and can be reversely applied to realize the direct imaging of the plane image on a curved surface.
Background
The object plane and the image plane of the existing imaging system (such as a microscope) are generally flat, and the object with the curved surface cannot be directly imaged. For example, an optical microscope can only observe cells on a slide (plane surface), but cannot further observe fine structures on the entire cell surface (curved surface). For another example, the camera cannot directly obtain the pattern distribution on the whole surface (full-angle curved surface) of an automobile, and the original pattern distribution on the surface of the three-dimensional automobile can only be restored by the digital image processing technology through images or video information obtained by shooting at a plurality of different shooting angles. At present, the technology of imaging patterns on a curved surface mainly includes obtaining surface image distribution of a curved object from a plurality of shooting angles by a method of scanning spatial positions of a plurality of imaging instruments or one imaging instrument, converting obtained image information obtained from a plurality of viewing angles into electric signals, introducing the electric signals into a computer, and then performing digital image processing to obtain the whole image of the curved surface. This method requires the pre-design of image synthesis and restoration algorithms and will take a long time (it is not possible to image a curved surface directly); the process of acquiring full-angle information of an object becomes cumbersome, so that the real-time property of the image becomes poor (it is difficult to use for real-time panoramic imaging of patterns on a dynamically curved surface).
Disclosure of Invention
The novel lens capable of directly converting the full angle of the curved surface image into the plane image in real time is provided aiming at the problem that the existing imaging system can not directly image the full angle of the surface of the curved surface object in real time.
In order to solve the technical problems, the invention adopts the technical scheme that: a curved-plane imaging conversion lens comprises N0The metal plates with the thickness of the sub-wavelength magnitude are stacked and arranged to form a three-dimensional columnar structure, and the thick plates are arranged between the metal platesThe metal plate is provided with a channel with a sub-wavelength magnitude, the first end face of the metal plate is uniformly distributed on the periphery of the curved surface, and the second end face of the metal plate is uniformly distributed on the same plane.
The refractive index of the filling medium in the channel and the lengths of the two adjacent metal plates satisfy the following relationship:
wherein the content of the first and second substances,
is shown askThe refractive index of the medium filled in the stripe trench,
and
is shown askIs first and secondkThe section length of +1 metal plates in the cross section of the three-dimensional columnar structure, lambda represents the wavelength of the working electromagnetic wave,mis any positive integer.
The curved surface is a cylindrical curved surface, a sectional line of the metal plate in the cross section of the three-dimensional columnar structure is divided into a curve section and a straight line section, the end points of the curve sections of the metal plates are located on the same circular arc, and a curve cluster parameter equation of the shape of the curve section is as follows:
the length of the curve segment is:
the length of the straight line segment is:
wherein the content of the first and second substances,
curve cluster parameter equation representing curve segment of kth metal plate, N = (N)0-1)/2，r0The radius of the surface of the cylinder is shown,
representing any real constant taking on values between 0 and 1,
the length of the curved line segment is shown,
is composed of
The derivative of (a) of (b),
the radius of the cylinder is formed for the boundary contour of each channel curve part, d represents the image plane andcylindrical curved surfaceThe distance between the central axes of the two shafts,
represents a distance from the origin on the kth metal plate ofR 0The connecting line of the point and the coordinate origin and the figurexThe angle in the positive direction of the axis.
The thickness of the metal plate is less than or equal to one fourth of the wavelength of the working electromagnetic wave.
The thickness of the channel between the metal plates is less than or equal to one quarter of the wavelength of the working electromagnetic wave.
And isotropic media are filled in the channel.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a curved surface-plane imaging conversion lens which can convert a full-angle image of a curved surface into a plane image so as to assist a plane imaging instrument with a limited visual angle and further realize the function of full-angle real-time imaging on the surface of a curved object. The invention does not need to increase the number of observation devices and other devices, does not need to convert the acquired optical image information into an electric signal, and also avoids the post image data processing. The lens of the invention can be used as a front structure of other traditional imaging instruments (such as a microscope) to directly realize full-angle optical curved surface imaging (as shown in figure 5). Meanwhile, the invention can also be used reversely (the curved surface is used as the image surface, and the plane is used as the object surface), and the pattern on the plane mask plate is stamped on the curved surface, so that the invention is used for the curved surface stamping technology. When observing the image distribution on the curved surface, the image distribution of the curved surface can be directly converted into a plane image in real time by means of the invention. The imaging curved surface of the lens is a closed curved surface with 360 degrees and any shape, and the image conversion from a full-angle curved surface to a plane can be realized. The problem that a traditional imaging instrument cannot directly image a full-angle curved surface object is solved. The lens obtained by the invention can be used as a front structure of a microscope (or other imaging instruments with plane image surfaces), and further can be used for directly observing the whole surface detail image of a micro curved surface object (such as a cell surface). The lens can also be applied reversely, namely, a plane image is directly converted into a curved surface image, and the lens is applied to the technologies of curved surface imprinting, curved surface photoetching and the like.
Drawings
Fig. 1 is a schematic structural diagram of a curved-plane imaging conversion lens according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a curved-plane imaging conversion lens according to a second embodiment of the present invention;
FIG. 3 is a simulation result of image distribution (variation of surface magnetic field with polar angle θ) of the cylindrical object plane of the lens in the second embodiment of the present invention;
FIG. 4 is a simulation result of image distribution (variation of surface magnetic field with polar angle θ) of the cylindrical image plane of the lens in the second embodiment of the present invention;
fig. 5 is a schematic view of a lens used for observing the surface topography of a micro curved surface by a microscope front-end system according to an embodiment of the invention.
In the figure: 1 is a metal plate, 2 is a channel, 3 is a curved surface, 4 is a plane, and 5 is an object to be measured.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, but 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.
Example one
As shown in fig. 1, a curved-plane imaging conversion lens according to an embodiment of the present invention is characterized by including N0 A metal plate 1 with a thickness of sub-wavelength order, wherein N0The structure is characterized in that the structure is a positive integer larger than zero, the metal plates 1 are stacked to form a three-dimensional columnar structure, channels 2 with the thickness of a sub-wavelength magnitude are arranged between the metal plates 1, the first end faces of the metal plates 1 are uniformly distributed on the periphery of the curved surface 3, and the second end faces of the metal plates 1 are uniformly distributed on the same plane 4. The curved surface 3 can be used as the object plane of the lens, the plane 4 can be used as the image plane of the lens, and a curved object to be imaged is placed on the object plane (any curved surface 3 corresponding to fig. 1) of the lens, so that a planar projection image with a curved surface pattern distribution can be directly obtained on the image plane (the plane 4 corresponding to fig. 1) of the lens, and the plane 4 can also be used as the object plane of the lens, and the curved surface 3 can be used as the image plane of the lens, so that the pattern on the plane is projected onto the curved surface.
In this embodiment, the lens is a three-dimensional column, and fig. 1 is a two-dimensional cross-sectional view of the lens. The lens consists of metal plates 1 spaced at a sub-wavelength interval and having a thickness of the order of a sub-wavelength (for example, equal to or less than a quarter of the wavelength of the operating electromagnetic waves). The channels between the metal plates are filled with an isotropic medium of a specific refractive index. The metal plate array connects the object plane and the image plane of the lens. The lens can directly image the image distribution on the curved object plane to the planar image plane to obtain the corresponding planar image distribution, thereby realizing the conversion function of the curved surface-planar image.
In this embodiment, the lens is composed of N0Block metal plate and N0-1 channel, each channel being filled with an isotropic homogeneous dielectric material. The shape of the subwavelength metal plate may be arbitrary, and may be other distribution such as a curved distribution, instead of a straight distribution as shown in the figure). Wherein, the firstkThe refractive index of the medium filled in the strip channel and the lengths of the two adjacent metal plates satisfy the following relation:
wherein the content of the first and second substances,
is shown askThe refractive index of the medium filled in the stripe trench,
and
is shown askIs first and secondkThe section length of +1 metal plates in the cross section of the three-dimensional columnar structure, lambda represents the wavelength of the working electromagnetic wave irradiating the sample,mis any positive integer.
Example two
In the second embodiment of the invention, the object plane (curved surface 3) of the lens is taken as a cylindrical surface as an example, and a specific lens design example is given. The lens is a three-dimensional column, and the two-dimensional cross-sectional view thereof is shown in fig. 2. The lens is composed of (2N + 1) metal plates 1 with sub-wavelength spacing and 2N channels 2 positioned between the metal plates, wherein N is a positive integer larger than zero, isotropic media with specific refractive indexes are filled in the channels 2, and the thickness of the metal plates is of sub-wavelength magnitude (for example, less than or equal to one quarter of the wavelength of working electromagnetic waves). The metal plate array connects the object plane (cylindrical curved surface 3 in fig. 2) and the image plane (flat surface 4 in fig. 2) of the lens. The space inside the cylindrical curved surface 3 in fig. 2 is air, which can be used for placing an object 5 to be observed. The surface of the object to be observed and the object plane of the lens have the same shape, and the surface of the object to be observed is required to be attached to the object plane of the lens when the lens is used. The lens can directly image the image on the cylindrical object plane to the plane image plane to obtain a plane image, and further realize the function of cylindrical-plane image conversion.
Specifically, in this embodiment, a sectional line of the metal plate 1 in the cross section of the three-dimensional columnar structure is divided into a curved line segment and a straight line segment, and the endpoints of the curved line segments of the metal plates are located on the same arc.
Regarding the design of the curve segments: the shape of the curved surface section of the kth metal plate is defined by the parameter equation of a curve cluster
Determining that the curve cluster parameter equation of the curve segment shape is as follows:
regarding the design of the straight line segment: one end point of the straight line segment of the kth metal plate is coincided with the end point of the curve segment of the kth metal plate, and the other end point is positioned on the image plane. The straight sections of all the metal plates are parallel to the x-axis.
The length of the curve segment is:
the length of the straight line segment is:
wherein the content of the first and second substances,
a curve cluster parametric equation representing the curve segment of the kth metal plate,kis a positive integer, k =1,2,3, …,2N, N = (N)0-1)/2，r0The radius of the surface of the cylinder is shown,
representing any real constant taking on values between 0 and 1,
the length of the curved line segment is shown,
is composed of
The derivative of (a) of (b),
the radius of the cylindrical surface is formed for the boundary contour of each channel curve part, d represents the distance between the image plane and the central axis of the cylindrical curved surface,θis a line connecting points on a curve cluster and an origin pointxThe included angle of the axes is set by the angle,
represents a distance from the origin on the kth metal plate ofR 0Is connected with the coordinate origin of the point (namely the intersection point of straight line segments of the curve segment) of (A) and the figurexThe angle in the positive direction of the axis. Point is located atxThe value above the axis is positive and the point is locatedxThe value below the axis is negative.
In addition, in this embodiment, 2NThe refractive index of the isotropic medium filled with the stripe trenches is:
where n iskIs shown askThe refractive index of the medium filled in the stripe trench,l kis shown askThe length of the inner sectional line (including the curve section and the straight section) of the block metal plate on the two-dimensional cylindrical surface,l k+1is shown in (A)k+ 1) the length of the inner sectional line (including curve segment and straight segment) of the metal plate on the two-dimensional cylindrical surface, λ is the wavelength of the working electromagnetic wave,mis any positive integer.
Designed through the figure 2The simulation results of the mirror are given by fig. 3 and 4. The parameters used in the simulation were: n =30, λ =2.1414m, τ =1/6, r0=0.3m，R0=1m，d=1.1m，mAnd = 1. The image distribution on the object plane (object surface magnetic field distribution) function is: hz0=sin4θ。
FIG. 3 is the image distribution on the object plane of the lens: polar angle theta is horizontal axis, z component H of magnetic field at each point of object planez1Is the vertical axis. FIG. 4 is the image distribution on the image plane of the lens: in FIG. 4, the y-axis is the horizontal axis, and the z-component H of the magnetic field at each point on the image planez2Is the vertical axis. The image plane image distribution in fig. 4 is consistent with the object plane image distribution in fig. 3 in shape, and the curved-plane image conversion function that the lens can directly convert the image distribution on the cylindrical object plane into the planar image plane at all angles is verified.
The lens parameters of the present invention can be pre-designed and adjusted for different application scenarios (e.g., different frequencies of electromagnetic waves illuminating a sample or different sizes of desired imaging planes). The lens has the capability of performing curved image-plane image conversion on a curved object surface and performing full-angle imaging on an object, and has better real-time performance than the combination of multiple devices and digital image processing. If the size of the image plane is required, the size of the image plane can be adjusted and controlled by adjusting the shape of the channel. The design case can be widely applied to various fields which need to carry out wide-angle observation on curved surface objects and have high requirements on real-time performance.
The invention provides a method for converting a full-angle image of a curved surface into a planar image, which is used for assisting a planar imaging instrument with a limited visual angle so as to realize the function of full-angle real-time imaging on the surface of a curved object. The invention does not need to increase the number of observation devices and other devices, does not need to convert the acquired optical image information into an electric signal, and also avoids the post image data processing. The lens of the invention can be used as a front structure of other traditional imaging instruments (such as a microscope) to directly realize full-angle optical curved surface imaging (as shown in figure 5). Meanwhile, the invention can also be used reversely (the curved surface is used as the image surface, and the plane is used as the object surface), and the pattern on the plane mask plate is stamped on the curved surface, so that the invention is used for the curved surface stamping technology.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A curved-plane imaging conversion lens is characterized by comprising N0The metal plate structure is characterized in that the metal plates (1) are of sub-wavelength magnitude thickness, the metal plates (1) are arranged in a stacked mode to form a three-dimensional columnar structure, channels (2) are arranged between the metal plates (1) and are of sub-wavelength magnitude thickness, the first end faces of the metal plates (1) are evenly distributed on the periphery of the curved face (3), and the second end faces of the metal plates are evenly distributed on the same plane (4).
2. A curved-plane image conversion lens as claimed in claim 1, wherein the refractive index of the filling medium in the trench (2) and the length of two adjacent metal plates (1) satisfy the following relationship:
wherein the content of the first and second substances,
is shown askThe refractive index of the medium filled in the stripe trench,
and
is shown askIs first and secondk+1 metal plateThe stub length, λ, within the cross section of the three-dimensional columnar structure represents the wavelength of the operating electromagnetic wave,mis any positive integer.
3. A curved-planar imaging conversion lens as claimed in claim 2, wherein the curved surface (3) is a cylindrical curved surface, the sectional line of the metal plate in the cross section of the three-dimensional cylindrical structure is divided into a curved line segment and a straight line segment, the end points of the curved line segment of each metal plate are located on the same circular arc, and the parametric equation of the curved cluster of the curved line segment shape is as follows:
the length of the curve segment is:
the length of the straight line segment is:
wherein the content of the first and second substances,
curve cluster parameter equation representing curve segment of kth metal plate, N = (N)0-1)/2，r0The radius of the surface of the cylinder is shown,
representing any real constant taking on values between 0 and 1,
the length of the curved line segment is shown,
is composed of
The derivative of (a) of (b),
the radius of the cylinder is formed for the boundary contour of each channel curve part, d represents the image plane andcylindrical curved surfaceThe distance between the central axes of the two shafts,
represents a distance from the origin on the kth metal plate ofR 0The connecting line of the point and the coordinate origin and the figurexThe angle in the positive direction of the axis.
4. A curved-planar imaging conversion lens as claimed in claim 1, wherein said metal plate has a thickness equal to or less than one quarter of the wavelength of the working electromagnetic wave.
5. A curved-planar image conversion lens according to claim 1, characterized in that the thickness of the channels (2) between the metal plates (1) is less than or equal to a quarter of the wavelength of the working electromagnetic wave.
6. A curved-planar image conversion lens according to claim 1, wherein said channel (2) is filled with an isotropic medium.
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