CN107490847B - Rotary zoom lens system and implementation method thereof - Google Patents

Rotary zoom lens system and implementation method thereof Download PDF

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CN107490847B
CN107490847B CN201710653218.0A CN201710653218A CN107490847B CN 107490847 B CN107490847 B CN 107490847B CN 201710653218 A CN201710653218 A CN 201710653218A CN 107490847 B CN107490847 B CN 107490847B
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lens
sided convex
focal length
lens group
convex lens
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CN107490847A (en
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滕少华
霍颖翔
滕璐瑶
张巍
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B15/00—Optical objectives with means for varying the magnification
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/02—Simple or compound lenses with non-spherical faces
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/02—Simple or compound lenses with non-spherical faces
    • G02B3/08—Simple or compound lenses with non-spherical faces with discontinuous faces, e.g. Fresnel lens
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G02F1/1313—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells specially adapted for a particular application

Abstract

The invention discloses a rotary zoom lens system and a realization method thereof, the rotary zoom lens system comprises a first lens group, a second lens group and a liquid crystal module, the optical axis of the first lens group and the optical axis of the second lens group are on the same straight line, the focal length of the superposed first lens group and second lens group is changed along with the change of the relative angle of the first lens group and the second lens group, and the liquid crystal module is arranged at one side of the first lens group or one side of the second lens group. The focal length of the superposed first lens group and second lens group of the invention changes along with the change of the relative angle of the two lens groups, and the invention can be matched with the liquid crystal module to ensure that the lens system can zoom by changing the relative angle between the lens groups without adjusting the distance between the lens groups, thereby saving space, ensuring that the system has small volume and simple manufacture. The invention can be widely applied to the field of optical instruments.

Description

Rotary zoom lens system and implementation method thereof
Technical Field
The invention relates to the field of optical instruments, in particular to a rotary zoom lens system and an implementation method thereof.
Background
The continuous zooming optical system is an optical system of which the focal length is continuously changed in a certain range, the position of an image plane is kept still in the zooming process, the relative aperture is basically unchanged, and the image quality is kept good in the zooming process. Typically, the relative aperture of the system is constant during the course of changing the focal length. The zoom system gives full play to the zooming capability, along with the practicability of the automatic focusing technology and the progress of the processing technology, on the basis of ensuring the imaging quality, the zoom optical lens introduces a plurality of new design ideas, and careful research is carried out on the use of a focusing mode and an aspheric surface, so that the subsequent miniaturization and microminiaturization become feasible, and the appearance of the zoom mobile phone lens is promoted.
At present, in cameras and projectors, a conventional design mode is to form a lens system by overlapping a plurality of lenses, and then achieve the purpose of changing a focal length by changing distances between the lenses in the lens system, but zooming is achieved by adjusting the distances between the lenses, which inevitably results in that more space needs to be reserved in the system, and the volume of the system is larger; when manufacturing such a lens system, it is necessary to ensure that the central optical axes of the respective lenses are always aligned before and after movement, which makes the manufacturing difficult.
Disclosure of Invention
In order to solve the above technical problems, the present invention aims to: a rotary zoom lens system which is small in size and simple to manufacture is provided.
Another object of the invention is: a method of implementing a rotary zoom lens system that is small and simple to manufacture is provided.
The technical scheme adopted by the invention is as follows:
a rotary zoom lens system comprises a first lens group, a second lens group and a liquid crystal module, wherein the optical axis of the first lens group and the optical axis of the second lens group are on the same straight line, the focal length of the first lens group and the second lens group after being overlapped changes along with the change of the relative angle of the first lens group and the second lens group, and the liquid crystal module is installed on one side of the first lens group or one side of the second lens group.
Further, the first lens group and the second lens group each include at least one lens, and a focal length of the lens varies with a radial angle.
Further, the first lens group comprises a first single-sided convex lens, the second lens group comprises a second single-sided convex lens, the first single-sided convex lens and the second single-sided convex lens are the same, the plane of the first single-sided convex lens is opposite to the plane of the second single-sided convex lens, and the liquid crystal module is installed between the first single-sided convex lens and the second single-sided convex lens.
Further, the cylindrical coordinate surface curved surface equation of the first single-sided convex lens is as follows:
Figure BDA0001368594450000021
wherein f is the focal length value, ω is the refractive index, m is the distance from the point on the curved surface to the center of the lens, and r is the distance from the point on the curved surface to the center of the circle.
Further, the first single-sided convex lens is a fresnel lens, and the cylindrical coordinate surface curved surface equation of the fresnel lens is as follows:
Figure BDA0001368594450000022
wherein tau is the Fresnel lens pitch,
Figure BDA0001368594450000023
the amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
Furthermore, the edge of the first single-sided convex lens is also provided with a tooth-shaped structure.
The liquid crystal display device further comprises a main support, wherein the main support is provided with an opening, and the liquid crystal module is embedded into the opening.
Further, still include step motor, driving belt, power wheel and first pivot, step motor and first pivot all with main support fixed connection, the power wheel is installed in first pivot, the power wheel meshes with first single face lens, step motor and power wheel pass through driving belt transmission.
The support device further comprises a support wheel and a second rotating shaft, the second rotating shaft is fixedly connected with the main support, the support wheel is installed on the second rotating shaft, and the support wheel is meshed with the first single-face convex lens.
The other technical scheme adopted by the invention is as follows:
a method of implementing a rotary zoom lens system, comprising the steps of:
calculating surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group;
calculating the shielding area of the liquid crystal module according to the surface curved surface equation of the lens in the first lens group and the lens in the second lens group;
and obtaining the rotary zoom lens system according to the surface curved surface equation of the lens in the first lens group, the surface curved surface equation of the lens in the second lens group and the shielding area of the liquid crystal module.
Further, the lens in the first lens group is a first single-sided convex lens, the lens in the second lens group is a second single-sided convex lens, and the first single-sided convex lens and the second single-sided convex lens are the same.
Further, the calculating the surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group includes:
inputting the shortest focal length, the longest focal length, the light transmittance and the material refractive index of the rotary zoom lens system;
obtaining a synthetic focal length function of the first single-sided convex lens and the second single-sided convex lens in a rectangular coordinate system according to a focal length superposition theorem, wherein the expression of the synthetic focal length function is as follows:
Ω(f 1 ,f 2 )＝(f 1 *f 2 )/(f 1 +f 2 )；
wherein, f 1 Is the focal length of the first single-sided convex lens, f 2 Is a second single side convexThe focal length of the mirror;
performing distortion transformation on the synthesized focal length function in the rectangular coordinate system according to the shortest focal length, the longest focal length, the light transmittance and the material refractive index to obtain a focal length function after the distortion transformation of the first single-sided convex lens and the second single-sided convex lens, wherein the expression of the focal length function after the distortion transformation is as follows:
Figure BDA0001368594450000031
wherein, Z 0 ＝2Z c ，Z c Is the central focal length, Z 0 Is a function of twice the central focal length, the intermediate variable
Figure BDA0001368594450000032
The expression for the intermediate variable x is:
Figure BDA0001368594450000033
wherein v is H Is the maximum value of the intermediate variable x, v L Is the minimum value of an intermediate variable x, x ∈ (v) L ,v H )，
Figure BDA0001368594450000034
Is a radial angle;
obtaining a radial derivative function of the first single-sided convex lens and the second single-sided convex lens according to the focal length function after the distortion transformation, wherein the expression of the radial derivative function is as follows:
Figure BDA0001368594450000035
wherein f is a focal length value, omega is a refractive index, and r is a distance from a point on the curved surface to the center of a circle;
integrating the obtained radial derivative function to obtain surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens, wherein the expressions of the surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens are as follows:
Figure BDA0001368594450000036
where m is the distance from a point on the curved surface to the center of the lens.
Further, the step of calculating the surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group further includes: converting the first single-sided convex lens and the second single-sided convex lens into the Fresnel lens, wherein the surface curve equation after the first single-sided convex lens and the second single-sided convex lens are converted into the Fresnel lens is as follows:
Figure BDA0001368594450000037
wherein tau is the screw pitch of the Fresnel lens,
Figure BDA0001368594450000038
the amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
Further, the expression of the shielding area of the liquid crystal module in polar coordinates is as follows:
Figure BDA0001368594450000039
or
Figure BDA0001368594450000041
Wherein the content of the first and second substances,
Figure BDA0001368594450000042
is the radial angle of the lens, m is the distance from a point on the curved surface to the center of the lens, m 2 Is the radius of the second single-sided convex lens, tau is the pitch, phi () is a function of the radial angle, mu is a positive integer, iota is the extension length, epsilon is a count value for exhaustion related to iota, and theta isA first single-sided convex lens and a second single-sided convex lens
Figure BDA0001368594450000043
The included angle of (c).
The rotary zoom lens system of the invention has the beneficial effects that: the zoom lens comprises a first lens group, a second lens group and a liquid crystal module, wherein the focal length of the superposed first lens group and second lens group is changed along with the change of the relative angle of the two lens groups, and the zoom lens can be matched with the liquid crystal module to enable a lens system to zoom by changing the relative angle between the lens groups without zooming by adjusting the distance between the lens groups, so that the space is saved, the size of the system is small, and the manufacture is simple.
The method of the invention has the beneficial effects that: the method comprises the steps of calculating surface curved surface equations of lenses in a first lens group and lenses in a second lens group, calculating a shielding area of a liquid crystal module according to the surface curved surface equations and the shielding area of the liquid crystal module to obtain the rotary zoom lens system.
Drawings
FIG. 1 is a schematic cross-sectional view of a rotary zoom lens system of the present invention;
FIG. 2 is an exploded view of a rotary zoom lens system of the present invention;
FIG. 3 is a first functional diagram of the superimposed focal lengths of the first lens group and the second lens group;
FIG. 4 is a second plot of the superimposed focal lengths of the first lens group and the second lens group;
FIG. 5 is a flowchart of a method of implementing a rotary zoom lens system according to a fourth embodiment of the present invention;
FIG. 6 is a schematic view of a radial bisection method of a Fresnel lens in an implementation of the rotary zoom lens system of the present invention;
FIG. 7 shows w in an implementation of a rotary zoom lens system according to the invention L 、w H 、v L 、v H And a value relation graph of k.
Detailed Description
Referring to fig. 1, a rotary zoom lens system includes a first lens group 1, a second lens group 2, and a liquid crystal module 3, wherein a center of the first lens group 1 and a center of the second lens group 2 are coaxial, a focal length of the first lens group 1 and the second lens group 2 after being stacked varies with a relative angle of the first lens group 1 and the second lens group 2, and the liquid crystal module 3 is mounted on one side of the first lens group 1 or one side of the second lens group 2.
Further preferably, the first lens group 1 and the second lens group 2 each include at least one lens, and a focal length of the lens varies with a radial angle.
Further, as a preferred embodiment, the first lens group 1 includes a first single-sided convex lens, the second lens group 2 includes a second single-sided convex lens, the first single-sided convex lens and the second single-sided convex lens are identical, a plane of the first single-sided convex lens and a plane of the second single-sided convex lens are opposite, and the liquid crystal module 3 is installed between the first single-sided convex lens and the second single-sided convex lens.
Further preferably, the cylindrical coordinate surface curved surface equation of the first single-sided convex lens is as follows:
Figure BDA0001368594450000051
wherein f is a focal length value, ω is a refractive index, m is a distance from a point on the curved surface to the center of the lens, and r is a distance from a point on the curved surface to the center of the circle.
Further as a preferred embodiment, the first single-sided convex lens is a fresnel lens, and the cylindrical coordinate surface curved surface equation of the fresnel lens is as follows:
Figure BDA0001368594450000052
wherein tau is the Fresnel lens pitch,
Figure BDA0001368594450000053
the amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
Further preferably, the edge of the first single-sided convex lens is further provided with a tooth-shaped structure.
Referring to fig. 2, further as a preferred embodiment, the liquid crystal display device further includes a main support 4, wherein an opening is formed on the main support 4, and the liquid crystal module 3 is inserted into the opening.
Referring to fig. 2, as a further preferred embodiment, the system further includes a stepping motor 5, a transmission belt 6, a power wheel 7 and a first rotating shaft 8, the stepping motor 5 and the first rotating shaft 8 are both fixedly connected to the main bracket 4, the power wheel 7 is mounted on the first rotating shaft 8, the power wheel 7 is engaged with the first single-sided lens, and the stepping motor 5 and the power wheel 7 are driven by the transmission belt 6.
Referring to fig. 2, further as a preferred embodiment, the device further includes a supporting wheel 9 and a second rotating shaft 10, the second rotating shaft 10 is fixedly connected with the main bracket 4, the supporting wheel 9 is mounted on the second rotating shaft 10, and the supporting wheel 9 is meshed with the first single-sided convex lens.
A method of implementing a rotary zoom lens system, comprising the steps of:
calculating surface curved surface equations of the lenses in the first lens group 1 group and the lenses in the second lens group 2 group;
calculating the shielding area of the liquid crystal module 3 according to the surface curved surface equation of the lenses in the first lens group 1 and the lenses in the second lens group 2;
and obtaining the rotary zoom lens system according to the surface curved surface equation of the lens in the first lens group 2, the surface curved surface equation of the lens in the second lens group 2 and the shielding area of the liquid crystal module 3.
In a further preferred embodiment, the lenses in the first lens group 1 group are first single-sided convex lenses, the lenses in the second lens group 2 group are second single-sided convex lenses, and the first single-sided convex lenses and the second single-sided convex lenses are the same.
Further as a preferred embodiment, the calculating the surface curved surface equations of the lenses in the first lens group 1 group and the lenses in the second lens group 2 group includes:
inputting the shortest focal length, the longest focal length, the light transmittance and the material refractive index of the rotary zoom lens system;
according to the focal length superposition theorem, a synthetic focal length function of the first single-sided convex lens and the second single-sided convex lens in a rectangular coordinate system is obtained, and the expression of the synthetic focal length function is as follows:
Ω(f 1 ,f 2 )＝(f 1 *f 2 )/(f 1 +f 2 )；
wherein f is 1 Is the focal length of the first single-sided convex lens, f 2 The focal length of the second single-sided convex lens;
performing distortion transformation on the synthesized focal length function in the rectangular coordinate system according to the shortest focal length, the longest focal length, the light transmittance and the material refractive index to obtain a focal length function after the distortion transformation of the first single-sided convex lens and the second single-sided convex lens, wherein the expression of the focal length function after the distortion transformation is as follows:
Figure BDA0001368594450000061
wherein Z is 0 ＝2Z c ，Z c Is the central focal length, Z 0 Is a function of twice the center focal length, an intermediate variable
Figure BDA0001368594450000062
The expression for the intermediate variable x is:
Figure BDA0001368594450000063
wherein v is H Is the maximum value of the intermediate variable x，v L Is the minimum value of the intermediate variable x, x ∈ (v) L ,v H )，
Figure BDA0001368594450000064
Is a radial angle;
obtaining a radial derivative function of the first single-sided convex lens and the second single-sided convex lens according to the focal length function after the distortion transformation, wherein the expression of the radial derivative function is as follows:
Figure BDA0001368594450000065
wherein f is a focal length value, omega is a refractive index, and r is a distance from a point on the curved surface to the center of a circle;
integrating the obtained radial derivative function to obtain surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens, wherein the expressions of the surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens are as follows:
Figure BDA0001368594450000066
where m is the distance from a point on the curved surface to the center of the lens.
Further as a preferred embodiment, the step of calculating the surface curved surface equations of the lenses in the first lens group 1 and the lenses in the second lens group 2 further comprises: converting the first single-sided convex lens and the second single-sided convex lens into the Fresnel lens, wherein the surface curve equation after the first single-sided convex lens and the second single-sided convex lens are converted into the Fresnel lens is as follows:
Figure BDA0001368594450000071
wherein tau is the screw pitch of the Fresnel lens,
Figure BDA0001368594450000072
for Fresnel lensing instituteResulting in a lens thickness cut that varies with pole diameter.
Further as a preferred embodiment, the expression of the shielding area of the liquid crystal module 3 in polar coordinates is:
Figure BDA0001368594450000073
or
Figure BDA0001368594450000074
Wherein the content of the first and second substances,
Figure BDA0001368594450000075
is the radial angle of the lens, m is the distance from a point on the curved surface to the center of the lens, m 2 Is the radius of the second single-sided convex lens, tau is the thread pitch, phi () is a function of the value of the radial angle, mu is a positive integer, iota is the run-out length, epsilon is a count value for exhaustion related to iota, theta is the first single-sided convex lens and the second single-sided convex lens
Figure BDA0001368594450000076
The included angle of (c).
A first embodiment of the invention is given in connection with fig. 1:
the lens system of the present embodiment mainly includes a first lens group 1, a second lens group 2, and a liquid crystal module 3.
The central optical axes of the first lens group 1 and the second lens group 2 are aligned, the first lens group 1 and the second lens group 2 can rotate relative to each other with the central axis as a rotating shaft, and the superposed focal length of the first lens group 1 and the second lens group 2 changes with the relative angle change of the first lens group 1 and the second lens group 2.
The liquid crystal module 3 can be installed between the first lens set 1 and the second lens set 2, the second is installed at one side of the first lens set 1 and is not adjacent to the second lens set 2, the third is installed at one side of the second lens set 2 and is not adjacent to the first lens set 1, and the liquid crystal module 3, the first lens set 1 and the second lens set 2 are installed closely without a gap in the middle.
The first lens group 1 and the second lens group 2 adopt a structure of overlapping a plurality of lenses (which may be fresnel lenses), so that the focal length parameters of the lens groups can be closer to ideal lenses, as long as the requirement that the overlapped focal length of the first lens group 1 and the second lens group 2 changes along with the change of the relative angle of the first lens group 1 and the second lens group 2 is met, and the number of the lenses and the lens parameters can be flexibly adjusted according to the actual situation.
A second embodiment of the invention is given in connection with fig. 2:
the lens system of the present embodiment mainly includes a first lens group 1, a second lens group 2, and a liquid crystal module 3. The first lens group 1 is a first single-sided convex lens, and the second lens group 2 is a second single-sided convex lens.
The first single-sided convex lens and the second single-sided convex lens are identical single-sided convex lenses (provided with a plane and a curved surface), and the two single-sided convex lenses are single-sided convex lenses of which the focal lengths change along with the change of radial angles; the first single-sided convex lens and the second single-sided convex lens are opposite in plane, the central optical axes are on the same axis, the liquid crystal module 3 is clamped between the first single-sided convex lens and the second single-sided convex lens, the first single-sided convex lens, the second single-sided convex lens and the liquid crystal module 3 are tightly installed, no gap is reserved in the middle, and the first single-sided convex lens and the second single-sided convex lens can rotate around the axis relatively.
The first single-sided convex lens and the second single-sided convex lens can be realized by adopting a special circular single-sided convex lens, and the cylindrical coordinate surface curved surface equation of the special circular single-sided convex lens is as follows:
Figure BDA0001368594450000081
wherein f is a focal length value, ω is a refractive index, m is a distance from a point on the curved surface to the center of the lens, and r is a distance from a point on the curved surface to the center of the circle.
F may be represented by F (x, Z) 0 ) Expressed as:
Figure BDA0001368594450000082
Figure BDA0001368594450000083
Z c is the central focal length, Z 0 ＝2Z c (ii) a The expression of x is:
Figure BDA0001368594450000084
Figure BDA0001368594450000085
denotes the radial angle of the lens, x ∈ (v) L ,v H )。
The edge of the first single-sided convex lens is also provided with a tooth-shaped structure which is used for being meshed with a transmission mechanism.
Referring to fig. 2, the lens system of the present invention further includes a main support 4, a stepping motor 5, a driving belt 6, a power wheel 7, a first rotating shaft 8, a support wheel 9, and a second rotating shaft 10.
Wherein, the main support 4 has an opening with the same shape and size as the liquid crystal module 3, the liquid crystal module 3 is embedded into the opening of the main support 4, and the main support 4 is used for supporting all parts.
Step motor 5, first pivot 8, second pivot 10 are all fixed on main support 4, power wheel 7 is installed in first pivot 8, the first half of power wheel 7 is first belt pulley, and the latter half is the gear, first belt pulley and the meshing of first single face lens, the last second belt pulley of installing of step motor 5, driving belt 6 is installed on first belt pulley and second belt pulley, supporting wheel 9 is installed and is constituteed supporting component and with the meshing of first single face convex lens in second pivot 10, supporting wheel 9 can realize with ordinary gear, supporting component is used for supporting first single face convex lens, guarantees that its rotation is smooth and its center does not take place the skew. The support assemblies are provided with three groups which are meshed with the first single-sided convex lens, and the three groups of support assemblies and the power wheel 7 form four supporting points of the first single-sided convex lens. The stepping motor 5 is used for driving a power wheel 7 through a transmission belt 6 to enable the first single-sided convex lens to rotate.
Third embodiment of the invention:
the first single-sided convex lens and the second single-sided convex lens in the second embodiment may also be implemented by using a circular fresnel lens, and a cylindrical coordinate surface curved surface equation of the circular fresnel lens is as follows:
Figure BDA0001368594450000091
wherein the expression of S (f, ω, m) is:
Figure BDA0001368594450000092
tau is the Fresnel lens pitch, f is the focal length, omega is the material refractive index, and m is the distance from a point on the curved surface to the center of the lens
Figure BDA0001368594450000093
Substituting S (f, omega, m) to obtain
Figure BDA0001368594450000094
The amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
The working principle of the rotary zoom lens system of the present invention is illustrated below:
taking the first lens group 1 and the second lens group 2 as an example of a lens group whose focal length changes with a change in radial angle, let f 1 ,f 2 The focal lengths of the two lens groups, and the focal length function omega (f) superposed by the two lens groups 1 ,f 2 ) The expression is as follows:
Figure BDA0001368594450000095
since the two lens groups are identical (i.e. the focal parameters are identical) and the mounting directions are opposite, i.e. the focal lengths of the two lens groups are opposite when rotating, at any time, if
Figure BDA0001368594450000096
Then it must have
Figure BDA0001368594450000097
Wherein
Figure BDA0001368594450000098
As a function of the focal length of the lens assembly,
Figure BDA0001368594450000099
is the radial angle of the lens group. In the present invention, the focal lengths of the two lens groups vary with the radial angle, so that the focal length function of the lens groups
Figure BDA00013685944500000910
Is a curve, so that the focal length function omega (f) of the two lens groups after being superposed 1 ,f 2 ) As shown in fig. 3. As can be seen from FIG. 3, the focal length variation of the lens assembly of the present invention can make the superposition result of the two lens assemblies equivalent to a common lens with the same focal length in the radial direction.
Let theta be two lens groups
Figure BDA00013685944500000911
The included angle of (c). If the first lens group 1 is rotated by pi/2 radians, i.e. θ = pi/2, still using the lens groups having the focal length parameter characteristics shown in fig. 3, the superimposed focal lengths of the two lens groups will change, and the changed effect is shown in fig. 4, and the superimposed focal lengths of the two lens groups will have two steps, which shows that by changing the relative angles of the two lens groups, the portions of the lens system in different radial directions can be made to have two different focal lengths. The liquid crystal module 3 is used for shielding the radial sector of the lens group corresponding to the right half high step shown in figure 4, or shielding the sector of the left step, and the lens system becomes oneA rotary zoom lens system close to a single focal length.
Fourth embodiment of the invention:
a realization method of the rotary zoom lens system mainly comprises the following steps:
s1, calculating surface curved surface equations of the lenses in the first lens group 1 and the lenses in the second lens group 2;
s2, calculating a shielding area of the liquid crystal module 3 according to surface curved surface equations of the lenses in the first lens group 1 and the lenses in the second lens group 2;
and S3, obtaining the rotary zoom lens system according to the surface curved surface equation of the lenses in the first lens group 1, the surface curved surface equation of the lenses in the second lens group 2 and the shielding area of the liquid crystal module 3.
Referring to fig. 5, steps S1 to S2 will be described in detail by taking an example in which the first lens group 1 is a first single-sided convex lens, the second lens group 2 is a second single-sided convex lens, and the first single-sided convex lens and the second single-sided convex lens are the same.
The step S1 includes:
s101, inputting the shortest focal length, the longest focal length, the light transmittance and the material refractive index of the rotary zoom lens system;
the longest focal length Z max And the shortest focal length Z min The following relationship should be satisfied:
Z min ≤Z 0 ，Z max ≥Z 0 ；
Figure BDA0001368594450000101
Z 0 ＝2Z c ；
wherein T () is the inverse of the focal function F (), Z c Is the central focal length (the combined focal length of the lens system when the relative angle theta of the first single-sided convex lens and the second single-sided convex lens is = 0), F is the focal length, and F is substituted into F -1 (x,Z 0 ) To obtain F -1 (f,Z 0 )。
Referring to fig. 7, the value range of the transmittance k should satisfy the following relationship:
Figure BDA0001368594450000102
Figure BDA0001368594450000103
wherein v is H For the maximum value of the focal length, v, of the lens system in the domain of the function T () that is obtained for satisfying the minimum light transmission L For the lens system corresponding to the minimum value of the focal length, w, in the domain of the function T () that satisfies the minimum light transmittance available L Is the shortest focal length Z of the single-sided convex lens min Corresponding value, w, in the field of the function T () H Is the longest focal length Z of a single-sided convex lens max Corresponding value, w, in the field of the function T () L ＝T(Z min ,Z 0 )；w H ＝T(Z max ,Z 0 ) T () is the inverse of the focus function F ().
S102, calculating system errors by using an error formula to determine the reasonability of values of the current shortest focal length, the current longest focal length, the current light transmittance and the current material refractive index, and if the errors are small, the values are reasonable, wherein the expression of the error formula is as follows:
Figure BDA0001368594450000104
wherein m is the focal length.
S103, in an original direct coordinate system, obtaining a synthetic focal length function of the first single-sided convex lens and the second convex lens according to a focal length superposition theorem, wherein the expression of the synthetic focal length function is as follows:
Ω(f 1 ,f 2 )＝(f 1 *f 2 )/(f 1 +f 2 )；
wherein f is 1 Is the focal length of the first single-sided convex lens, f 2 The focal length of the second single-sided convex lens;
s104, synthesizing the focal length function and Z in the original rectangular coordinate system 0 Can be obtained as equation (1))：
Figure BDA0001368594450000111
Wherein x is 1 And x 2 The variable, C is an ordinary number, F (x) 1 )＝f 1 ，F(x 2 )＝f 2 。
And (3) performing distortion transformation on the equation (1) according to the shortest focal length, the longest focal length, the light transmittance and the material refractive index to obtain an expression of the focal length function of the first single-sided convex lens and the second single-sided convex lens, wherein the expression is as follows:
Figure BDA0001368594450000112
wherein, Z c Is the central focal length, Z 0 Is a function of twice the central focal length, the intermediate variable
Figure BDA0001368594450000113
Z 0 ＝2Z c The expression for the variable x is:
Figure BDA0001368594450000114
wherein v is H Is the maximum value, v, of the intermediate variable x L Is the minimum value of an intermediate variable x, x ∈ (v) L ,v H )，
Figure BDA0001368594450000115
Is the radial angle of the lens;
s105, deriving according to the focal length function structure after the distortion transformation to obtain a radial derivative function of the first single-sided convex lens and the second single-sided convex lens, wherein the expression of the radial derivative function is as follows:
Figure BDA0001368594450000116
after simplification, the following is obtained:
Figure BDA0001368594450000117
wherein F is a focal length value, namely a focal length function F (), omega is a refractive index, and r is a distance from a point on the curved surface to the center of a circle;
s106, integrating the radial guide numerical function to obtain surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens;
Figure BDA0001368594450000118
wherein F is a focal length value, i.e. a focal length function F (), ω is a refractive index, m is a distance from a point on the curved surface to the center of the lens, and r is a distance from a point on the curved surface to the center of the circle.
S107, converting the first single-sided convex lens and the second single-sided convex lens into a Fresnel lens, taking the center of the first single-sided convex lens as the center of a circle to make a concentric circle, dividing the curved surface of the first single-sided convex lens into more than two circular ring areas, taking the center of the second single-sided convex lens as the center of a circle to make a concentric circle, dividing the curved surface of the second single-sided convex lens into more than two circular ring areas, wherein the circular ring areas divided by the first single-sided convex lens and the second single-sided convex lens are the same, and obtaining a surface curved surface equation after the first single-sided convex lens and the second single-sided convex lens are converted into the Fresnel lens, wherein the expression is as follows:
Figure BDA0001368594450000121
wherein tau is the Fresnel lens pitch, f is the focal length, omega is the refractive index, m is the distance from the point on the curved surface to the center of the lens, r is the distance from the point on the curved surface to the center of the circle, will
Figure BDA0001368594450000122
Substituting S (f, omega, m) to obtain
Figure BDA0001368594450000123
The amount of lens thickness cut produced for fresnel lensing varies with the polar diameter, which is a related concept of polar coordinates, and the distance from a point in the plane of the polar coordinates to the pole is the polar diameter.
When the first single-sided convex lens and the second single-sided convex lens are converted into the fresnel lens, the method adopted by the invention is a radial equal-division cutting method to ensure that the cut boundary lines are concentric circles, so that when a plurality of lenses rotate relatively, the circular ring areas of the lenses are always opposite, and the schematic diagram of the cutting method can refer to fig. 6. The first single-sided convex lens and the second single-sided convex lens are converted into the Fresnel lens, so that the lens can be thinner, the lens system has better optical performance, and the miniaturization of the lens system is facilitated.
And S108, rotationally staggering each annular region of the first single-sided convex lens, rotationally staggering each annular region of the second single-sided convex lens, and ensuring that the first single-sided convex lens and the second single-sided convex lens are identical after rotation. The respective circular ring areas of the first single-sided convex lens and the second single-sided convex lens are staggered in a rotating mode, so that the incident light uniformity can be improved.
S109, carrying out optical path checking calculation on the designed first single-sided convex lens, wherein the specific checking calculation step is as follows:
substituting zeta and r with different values into a light path verification formula, verifying whether a calculation result is within a set error range, wherein the expression of the light path verification formula is as follows:
Figure BDA0001368594450000124
wherein, x is the x-axis coordinate of the point, F is the focal length value, i.e. focal length function F (), ω is the refractive index, r is the distance from the point on the curved surface to the center of the circle, ζ is the included angle between the incident ray and the y-axis, a certain radial direction of the lens is the x-axis, and the main optical axis of the lens is the y-axis.
The step S2 includes:
s201, taking the center of the first single-sided convex lens as a pole point, and obtaining an ideal shielding area of the liquid crystal module 3 in the cylindrical coordinate as follows:
Figure BDA0001368594450000125
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0001368594450000126
theta is the radial angle of the lens and theta is the first and second single-sided convex lenses
Figure BDA0001368594450000127
The angle of the lens is m is the distance from the point on the curved surface to the center of the lens 2 Is the radius of the second single-sided convex lens, tau is the screw pitch, mu is a positive integer, and phi is a radial angle value function.
The specific blocking position of the blocking area is related to the relative rotation angle theta of the first single-sided convex lens and the second single-sided convex lens.
S202, if the occlusion region is enlarged by extending the edge to iota, the ideal occlusion region (any element belonging to the set is included in the occlusion region) in the cylindrical coordinates of the liquid crystal module 3 after enlarging the region is:
Figure BDA0001368594450000131
wherein iota is an extension length, and theta is a first single-sided convex lens and a second single-sided convex lens
Figure BDA0001368594450000132
The angle epsilon is the count value used to exhaust the correlation with iota.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. A rotary zoom lens system characterized by: the zoom lens comprises a first lens group, a second lens group and a liquid crystal module, wherein the optical axis of the first lens group and the optical axis of the second lens group are on the same straight line, the focal length of the superposed first lens group and second lens group changes along with the change of the relative angle of the first lens group and the second lens group, and the liquid crystal module is arranged on one side of the first lens group or one side of the second lens group;
the first lens group and the second lens group respectively comprise at least one lens, and the focal length of the lens is changed along with the change of the radial angle;
the first lens group comprises a first single-sided convex lens, the second lens group comprises a second single-sided convex lens, the first single-sided convex lens and the second single-sided convex lens are the same, the plane of the first single-sided convex lens is opposite to the plane of the second single-sided convex lens, and the liquid crystal module is arranged between the first single-sided convex lens and the second single-sided convex lens;
the cylindrical coordinate surface curved surface equation of the first single-sided convex lens is as follows:
Figure FDA0003875702960000011
wherein f is the focal length value, ω is the refractive index, m is the distance from the point on the curved surface to the center of the lens, and r is the distance from the point on the curved surface to the center of the circle.
2. A rotary zoom lens system according to claim 1, wherein: the first single-sided convex lens is a Fresnel lens, and a cylindrical coordinate surface curved surface equation of the Fresnel lens is as follows:
Figure FDA0003875702960000012
wherein tau is the Fresnel lens pitch,
Figure FDA0003875702960000013
the amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
3. A method of implementing a rotary zoom lens system of any of claims 1-2, wherein: the method comprises the following steps:
calculating surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group;
calculating the shielding area of the liquid crystal module according to the surface curved surface equation of the lens in the first lens group and the lens in the second lens group;
and obtaining the rotary zoom lens system according to the surface curved surface equation of the lens in the first lens group, the surface curved surface equation of the lens in the second lens group and the shielding area of the liquid crystal module.
4. A method of implementing a rotary zoom lens system according to claim 3, wherein: the calculating of the surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group includes:
inputting the shortest focal length, the longest focal length, the light transmittance and the material refractive index of the rotary zoom lens system;
obtaining a synthetic focal length function of the first single-sided convex lens and the second single-sided convex lens in a rectangular coordinate system according to a focal length superposition theorem, wherein the expression of the synthetic focal length function is as follows:
Ω(f 1 ,f 2 )＝(f 1 *f 2 )/(f 1 +f 2 )；
wherein, f 1 Is the focal length of the first single-sided convex lens, f 2 The focal length of the second single-sided convex lens;
performing distortion transformation on the synthesized focal length function in the rectangular coordinate system according to the shortest focal length, the longest focal length, the light transmittance and the material refractive index to obtain a focal length function after the distortion transformation of the first single-sided convex lens and the second single-sided convex lens, wherein the expression of the focal length function after the distortion transformation is as follows:
Figure FDA0003875702960000021
wherein Z is 0 ＝2Z c ，Z c Is the central focal length, Z 0 Is a function of twice the central focal length, the intermediate variable
Figure FDA0003875702960000022
The expression for the intermediate variable x is:
Figure FDA0003875702960000023
wherein v is H Is the maximum value of the intermediate variable x, v L Is the minimum value of an intermediate variable x, x ∈ (v) L ,v H )，
Figure FDA0003875702960000024
Is a radial angle;
obtaining a radial derivative function of the first single-sided convex lens and the second single-sided convex lens according to the focal length function after the distortion transformation, wherein the expression of the radial derivative function is as follows:
Figure FDA0003875702960000025
wherein f is a focal length value, omega is a refractive index, and r is a distance from a point on the curved surface to the center of a circle;
integrating the obtained radial derivative function to obtain surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens, wherein the expression of the surface curved surface equations of the first single-sided convex lens and the second single-sided convex lens is as follows:
Figure FDA0003875702960000026
where m is the distance from a point on the curved surface to the center of the lens.
5. A method of implementing a rotary zoom lens system of claim 4, wherein: the step of calculating the surface curved surface equations of the lenses in the first lens group and the lenses in the second lens group further comprises: converting the first single-sided convex lens and the second single-sided convex lens into the Fresnel lens, wherein the surface curve equation after the first single-sided convex lens and the second single-sided convex lens are converted into the Fresnel lens is as follows:
Figure FDA0003875702960000027
wherein tau is the screw pitch of the Fresnel lens,
Figure FDA0003875702960000028
the amount of lens thickness cut produced for fresnel lensing as a function of pole diameter.
6. A method of implementing a rotary zoom lens system according to claim 5, wherein: the expression of the shielding area of the liquid crystal module in the polar coordinate is as follows:
Figure FDA0003875702960000031
or
Figure FDA0003875702960000032
Wherein the content of the first and second substances,
Figure FDA0003875702960000033
is the radial angle of the lens, m is the distance from a point on the curved surface to the center of the lens, m 2 Is the radius of the second single-sided convex lens, and tau isPitch phi () is a value function of the radial angle, mu is a positive integer, iota is an extension length, epsilon is a count value for exhaustion associated with iota, and theta is a first and second single-sided convex lens
Figure FDA0003875702960000034
The included angle of (c).
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