A zoom lens system based on an annular conical side mirror

By using a ring-shaped conical side mirror design and a rotation mechanism, the translation mechanism of the traditional lens system is simplified, achieving high-precision and stable zoom effect. This solves the problems of large size and mechanical complexity of traditional zoom lens systems, and improves the performance and imaging quality of the optical system.

CN119986993BActive Publication Date: 2025-12-12BEIJING UNIV OF TECH
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Patent Information

Application Number
CN202510242044.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-03-03
Publication Date
2025-12-12
Estimated Expiration
2045-03-03

AI Technical Summary

Technical Problem

Traditional optical zoom lens systems suffer from problems such as large size, limited adjustment precision, and high mechanical complexity, making it difficult to achieve high-precision and stable zoom effects.

Method used

It adopts a ring-shaped conical side mirror design, simplifies the translation mechanism through a rotation mechanism, and achieves continuous adjustment of focal length by utilizing the curvature change of the conical side. Combined with differential control and mirror layout, it optimizes the light propagation path and focusing position.

Benefits of technology

It achieves high-precision and stable zoom control, reduces mechanical errors, improves system flexibility and imaging quality, simplifies system structure, reduces distortion, and enhances the integration and response speed of the optical system.

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Abstract

The application relates to the technical field of optical zoom lens application, in particular to a zoom lens system based on a ring-shaped conical side mirror, which comprises two supports, two center frames and two groups of ring-shaped lenses, the ring-shaped lenses of the zoom lens system are curved from conical strip lenses, the continuous change of focal length is realized by utilizing the change of the curvature of the conical side surface, unlike a traditional lens system, the zoom lens system controls the propagation path of light by accurately adjusting the geometric shape and curvature of the conical side surface, so that a more smooth and continuous zooming effect is realized, the zoom lens system not only can reduce the complexity of mechanical components, but also can improve the flexibility and precision of the zoom system, and has great development potential.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical zoom lens application, in particular to a zoom lens system based on annular conical side mirror. BACKGROUND

[0002] With the rapid development of optical technology, zoom lenses are increasingly widely used in imaging, optical communication, laser scanning, projection technology and other fields.

[0003] However, traditional optical zoom systems usually rely on mechanical movement of lens groups or changing the shape of lenses to adjust the focal length. Although this design has been widely used, it has certain limitations, such as large volume, limited adjustment precision, high mechanical complexity and other problems. In order to overcome these limitations, zoom systems based on new lens designs have become an important direction of optical research. SUMMARY

[0004] In view of the problems in the prior art, the present application provides a zoom lens system based on annular conical side mirror, which solves the limitations of existing zoom lenses in precision, distortion control and structural complexity. By bending the traditional conical mirror into a ring shape, the original translation mechanism can be simplified through a rotation mechanism, thereby optimizing the design and improving the stability and accuracy of the system. The zoom lens system based on annular conical side mirror not only helps to improve the performance of optical systems, but also promotes the innovation of optical design and manufacturing technology, with high scientific research value and application prospect.

[0005] The technical scheme adopted by the present application to solve its technical problems is: a zoom lens system based on an annular conical side mirror, comprising two supports, two center frames and two sets of annular lenses, the two supports are arranged in parallel, the bottom end of each of the two supports is provided with a fixed base for mounting, a main shaft is horizontally connected between the two parallel supports, the two center frames are rotationally fitted on the main shaft, the two sets of annular lenses are fixed on the two center frames respectively, and the two sets of annular lenses are oppositely arranged, the annular lens of the zoom lens system is curved from a conical strip lens, the continuous change of the curvature of the conical side surface is used to realize the continuous change of the focal length, unlike the traditional lens system, it controls the propagation path of light by accurately adjusting the geometric shape and curvature of the conical side surface, so as to realize a more smooth and continuous zoom effect, the zoom lens system not only can reduce the complexity of mechanical parts, but also can improve the flexibility and precision of the zoom system, has great development potential, at the same time, it is also helpful to enrich and expand the research of optical zoom technology, by proposing a new zoom principle, the focusing position of light is controlled by the change of geometric curvature, which provides a new idea for the design of optical elements, and may lead to a new breakthrough in the field of optical zoom, the traditional conical lens is curved into an annular shape, and the zoom is realized by the rotational fitting of the center frame and the main shaft, the propagation direction and focusing position of light are controlled by dynamically adjusting the side curvature of the conical lens, which breaks through the limitation of fixed curvature in traditional lens design, this new optical system can realize high-precision zoom control without increasing the number of lenses, which significantly improves the integration and reliability of the optical system, compared with the traditional zoom lens system, not only can reduce mechanical moving parts and improve response speed, but also provides an innovative solution for the technical progress in the fields of optical sensors, imaging systems and other fields, which has strong technical foresight, in addition, this rotating mechanism is more stable than the translation mechanism, which can effectively reduce the accumulation of mechanical errors, the annular lens is fixed on the center frame and rotates through differential control, this structure makes the movement of the lens more stable during zooming, avoiding the imaging blur caused by the position deviation or shaking of the lens, by bending the traditional conical lens into an annular shape, the original translation mechanism can be simplified through the rotating mechanism, so as to optimize the design and improve the stability and precision of the system, the zoom lens system based on the annular conical side mirror not only helps to improve the performance of the optical system, but also promotes the innovation of optical design and manufacturing technology, which has high scientific research value and application prospect.

[0006] Each of the annular lenses is composed of two half-annular lenses, which are semicircular structures after the bending of the conical strip lens, and the annular lenses of the zoom lens system are bent from the conical strip lens. The unique structure makes the light more evenly distributed when passing through the lens, reducing the deflection and scattering of light, thereby effectively reducing the distortion. The two sets of annular lenses are oppositely arranged and form different total focal lengths through differential control. This design can achieve better optical compensation at different focal lengths, further optimizing the imaging quality.

[0007] Preferably, a fixed hoop is provided outside each of the two sets of annular lenses. The fixed hoop constrains the annular lenses on the central frame. By providing the fixed hoop, the annular lenses are fixed to ensure that they do not shift or shake during zoom adjustment, reducing imaging errors caused by loose lenses.

[0008] Preferably, the zoom lens system further comprises a front panel and a rear panel, which are arranged in parallel. The two supports are located between the front panel and the rear panel.

[0009] Preferably, the front panel is provided with an imaging hole and an imaging hole, and the rear panel is provided with a plurality of mounting holes. The mounting holes on the rear panel correspond to the installation of mirrors. Two of the mirrors are aligned with the imaging hole and the imaging hole, respectively. The imaging hole and the imaging hole on the front panel are used to receive and output light, respectively, providing a clear path for light transmission. The mounting holes on the rear panel are used to install mirrors, which are aligned with the imaging hole and the imaging hole to ensure that light can accurately enter and exit the system. The parallel arrangement of the front panel and the rear panel, as well as the precise alignment of the imaging hole and the imaging hole, allows light to be transmitted efficiently, reducing light loss during transmission. The reasonable layout of the mirrors further optimizes the optical path, ensuring that light can accurately enter and exit the system, improving the overall efficiency of the system.

[0010] Preferably, the mirror aligned with the imaging hole can receive the light entering the imaging hole, and the mirror aligned with the imaging hole can reflect the light entering the imaging hole.

[0011] Preferably, the mirror aligned with the imaging hole receives the image of the light, which is reflected by the remaining mirrors in turn, and the image is flipped by 90 degrees when it reaches the mirror aligned with the imaging hole. Through the reflection of the mirrors, the light can be flipped by 90 degrees after passing through the two sets of annular lenses. This design allows the image to adjust the angle after being processed once, and then processed again by the annular lenses, thereby processing the up-down and left-right directions of the image. Through the reflection and angle adjustment of the mirrors, the light can pass through the two sets of annular lenses twice. This double processing method can significantly improve the restoration of the image and reduce distortion.

[0012] Preferably, the front panel and the rear panel are both vertical disc-shaped structures, the front panel is provided with a first supporting leg at the bottom for supporting, and the rear panel is provided with a second supporting leg at the bottom for supporting.

[0013] Preferably, the total focal length formula of the two groups of annular lenses is:

[0014] Preferably, the two groups of annular lenses cooperate to correct the difference in magnification at both ends of the picture, and the change in magnification is symmetric about the center.

[0015] Preferably, a differential control is matched on the two center frames, the rotation of the two annular lenses forms a differential through the differential control, and the two annular lenses can combine to form different total focal lengths F in the presence of the differential.

[0016] The beneficial effects of the present application are:

[0017] (1) In the present application, the annular lenses of the zoom lens system are curved from conical strip lenses, and the continuous change of the focal length is realized by using the change of the curvature of the conical side surface, which is different from the traditional lens system, which controls the propagation path of light by accurately adjusting the geometric shape and curvature of the conical side surface, thereby realizing a more smooth and continuous zoom effect, the zoom lens system not only can reduce the complexity of mechanical components, but also can improve the flexibility and precision of the zoom system, has great development potential, at the same time, it is also helpful to enrich and expand the research of optical zoom technology, by proposing a new zoom principle, the focusing position of light is controlled by the change of geometric curvature, which provides a new idea for the design of optical elements, and may lead to a new breakthrough in the field of optical zoom.

[0018] (2) In the present application, the zoom lens system bends the traditional conical lens into a ring shape, and realizes zooming through the rotation of the center frame and the main shaft. By dynamically adjusting the side curvature of the conical lens, the propagation direction and focusing position of the light rays are controlled, breaking the limitation of fixed curvature in traditional lens design. This new optical system can achieve high-precision zoom control without increasing the number of lenses, significantly improving the integration and reliability of the optical system. Compared with traditional zoom lens systems, it not only reduces mechanical moving parts and improves response speed, but also provides an innovative solution for the technical progress in the fields of optical sensors and imaging systems, with strong technical foresight. In addition, this rotating mechanism is more stable than the translation mechanism, which can effectively reduce the accumulation of mechanical errors. The ring-shaped lens is fixed on the center frame and rotates through differential control. This structure makes the lens movement more stable during zooming, avoiding image blur caused by lens position deviation or shaking. By bending the traditional conical lens into a ring shape, the original translation mechanism can be simplified through the rotating mechanism, thereby optimizing the design and improving the stability and accuracy of the system. The zoom lens system based on the ring-shaped conical side lens not only helps to improve the performance of the optical system, but also promotes the innovation of optical design and manufacturing technology, with high scientific research value and application prospect.

[0019] (3) In the present application, the ring-shaped lens of the zoom lens system is bent from a conical strip lens. This unique structure allows light to be more evenly distributed when passing through the lens, reducing light deflection and scattering, thereby effectively reducing distortion. Two sets of ring-shaped lenses are arranged oppositely and form different total focal lengths through differential control. This design can achieve better optical compensation at different focal lengths, further optimizing the imaging quality.

[0020] (4) In the present application, the zoom lens system adopts a ring-shaped conical side lens structure and realizes zooming through a rotating mechanism, eliminating the need for complex translation mechanisms and multiple lens groups, greatly simplifying the structure of the system. The two supports and the main shaft provide stable support for the entire system. The rotation of the center frame and the ring-shaped lens realizes the zoom function. This structural design makes the overall layout of the system more compact, significantly reducing the volume and weight. BRIEF DESCRIPTION OF DRAWINGS

[0021] The present application will be further described below in conjunction with the drawings and examples.

[0022] Figure 1 The present application is a schematic diagram of the overall structure.

[0023] Figure 2 The present application is a front view of the overall structure.

[0024] Figure 3 is Figure 1Detail view of area A.

[0025] Figure 4 Schematic diagram of front panel structure of the present application.

[0026] Figure 5 Schematic diagram of ring-shaped lens structure of the present application.

[0027] Figure 6 Sectional view of different focal lengths of semi-ring lens of the present application.

[0028] Figure 7 Schematic diagram of simulation of the present application.

[0029] Figure 8 Total focal length curve diagram of the present application.

[0030] Figure 9 Feasibility simulation diagram of focal length change of strip-shaped conical side mirror of the present application.

[0031] Figure 10 Simulation diagram of focal length change and distortion of ring-shaped conical side mirror of the present application.

[0032] Figure 11 Usability measurement diagram of simulation and simulation distortion of the present application.

[0033] Figure 12 Functional simulation diagram of focal length change of ring-shaped lens.

[0034] Figure 13 Laser test diagram of ring-shaped lens capability of the present application.

[0035] Figure 14 Schematic diagram of light converging structure of lens group of the present application.

[0036] Figure 15 Experimental diagram of light converging of lens group of the present application.

[0037] Figure 16 Experimental diagram of double-ring group of the present application.

[0038] In the figure: 1, support; 101, base; 2, main shaft; 3, center frame; 4, ring-shaped lens; 401, semi-ring lens; 5, fixed hoop; 6, front panel; 601, first support leg; 602, imaging hole; 603, imaging hole; 7, rear panel; 701, second support leg; 702, mounting hole; 8, reflecting mirror. DETAILED DESCRIPTION

[0039] In order to make the technical means, creative features, purposes and effects realized by the present application easy to understand, the present application is further described below in combination with specific embodiments.

[0040] As Figures 1-16As shown, the zoom lens system based on the annular conical side mirror of the application includes two supports 1, two center frames 3 and two sets of annular lenses 4. The two supports 1 are arranged in parallel, and the bottom end of each support 1 is provided with a fixed base 101 for installation. The two parallel supports 1 are horizontally connected with a main shaft 2, and the two center frames 3 are rotationally fitted on the main shaft 2. The two sets of annular lenses 4 are fixed on the two center frames 3 respectively, and the two sets of annular lenses 4 are arranged in opposite directions. When the annular lenses 4 are compressed, a special distortion will occur. A piece of annular lens placed in the opposite direction can correct it. The simulation image obtained from the simulation diagram can explain the principle. The original image is symmetrical on the left and right. After passing through a piece of annular lens 4, the left and right are not symmetrical, and the distortion of the central area appears. After passing through two pieces of annular lens 4, the image can be corrected to be symmetrical on the left and right, the central area distortion is small, and the imaging is available. The annular lens 4 of the zoom lens system is curved from a conical strip lens. The continuous change of the curvature of the conical side surface is used to realize the continuous change of the focal length. Unlike traditional lens systems, it controls the propagation path of light by accurately adjusting the geometric shape and curvature of the conical side surface, so as to realize a more smooth and continuous zoom effect. The zoom lens system not only can reduce the complexity of mechanical components, but also can improve the flexibility and precision of the zoom system, has great development potential, and at the same time, helps to enrich and expand the research of optical zoom technology. By proposing a new zoom principle, the focusing position of light is controlled by changing the geometric curvature, which provides a new idea for the design of optical elements, and may lead to a new breakthrough in the field of optical zoom. The zoom lens system bends the traditional conical lens into an annular shape, and realizes zooming through the rotational cooperation of the center frame 3 and the main shaft 2. The propagation direction and focusing position of light are controlled by dynamically adjusting the side curvature of the conical lens, which breaks through the limitation of fixed curvature in traditional lens design. This new optical system can realize high-precision zoom control without increasing the number of lenses, which significantly improves the integration and reliability of the optical system. Compared with traditional zoom lens systems, it not only reduces mechanical moving parts and improves response speed, but also provides an innovative solution for the technological progress in the fields of optical sensors, imaging systems and other fields, which has strong technical foresight. In addition, this rotating mechanism is more stable than the translation mechanism, which can effectively reduce the accumulation of mechanical errors. The annular lens 4 is fixed on the center frame 3 and rotates through differential control. This structure makes the lens movement more stable during zooming, avoiding image blur caused by lens position deviation or shaking. By bending the traditional conical lens into an annular shape, the original translation mechanism can be simplified through the rotating mechanism, thereby optimizing the design and improving the stability and accuracy of the system. The zoom lens system based on the annular conical side mirror not only helps to improve the performance of the optical system, but also promotes the innovation of optical design and manufacturing technology, which has high scientific research value and application prospect.

[0041] Each group of annular lenses 4 is composed of two half-ring lenses 401, which are half-ring structures after the bending of conical strip lenses. The annular lenses 4 of the zoom lens system are bent from conical strip lenses. This unique structure enables more uniform distribution of light when passing through the lenses, reduces light deflection and scattering, and effectively reduces distortion. The two groups of annular lenses 4 are oppositely arranged and form different total focal lengths through differential control. This design can achieve better optical compensation at different focal lengths, further optimizing the imaging quality.

[0042] In an optional embodiment of the present embodiment, the outer side of each group of annular lenses 4 is provided with a fixing hoop 5, which constrains the annular lenses 4 on the center frame 3. By fixing the annular lenses 4 through the fixing hoop 5, it is ensured that the annular lenses 4 will not shift or shake during the zoom adjustment process, reducing the imaging errors caused by loose lenses.

[0043] In an optional embodiment of the present embodiment, the zoom lens system further includes a front panel 6 and a rear panel 7, which are arranged in parallel. The two supports 1 are located between the front panel 6 and the rear panel 7.

[0044] In an optional embodiment of the present embodiment, the front panel 6 is provided with an imaging hole 602 and an imaging hole 603, and the rear panel 7 is provided with a plurality of mounting holes 702. The mounting holes 702 on the rear panel 7 correspondingly mount mirrors 8, two of which are aligned with the imaging hole 602 and the imaging hole 603, respectively. The imaging hole 602 and the imaging hole 603 on the front panel 6 are used for receiving and outputting light, respectively, providing a clear path for light transmission. The mounting holes 702 on the rear panel 7 are used for mounting the mirrors 8, which are aligned with the imaging hole 602 and the imaging hole 603, ensuring that light can accurately enter and exit the system. The parallel arrangement of the front panel 6 and the rear panel 7, as well as the precise alignment of the imaging hole 602 and the imaging hole 603, enable efficient transmission of light, reducing light loss during transmission. The reasonable layout of the mirrors 8 further optimizes the optical path, ensuring that light can accurately enter and exit the system, improving the overall efficiency of the system.

[0045] In an optional embodiment of the present embodiment, the mirror 8 aligned with the imaging hole 602 can receive light entering the imaging hole 602, and the mirror 8 aligned with the imaging hole 603 can reflect light entering the imaging hole 603.

[0046] In an optional embodiment of the present embodiment, the mirror 8 aligned with the imaging hole 602 receives the image of the light, which is reflected by the remaining mirrors 8 in sequence, and after reaching the mirror 8 aligned with the imaging hole 603, the image can be flipped by 90 degrees. Through the reflection of the mirror 8, the light can be flipped by 90 degrees after being processed by the two sets of annular lenses 4. This design enables the image to be adjusted in angle after being processed once, and then processed by the annular lenses 4 again, so as to process the image in up-down and left-right directions. Through the reflection and angle adjustment of the mirror 8, the light can be processed twice by the two sets of annular lenses 4 in sequence. This double processing mode can significantly improve the restoration degree of the image and reduce distortion.

[0047] In an optional embodiment of the present embodiment, the front panel 6 and the rear panel 7 are both vertically disc-shaped structures, the front panel 6 is provided with a first supporting leg 601 at the bottom for supporting, and the rear panel 7 is provided with a second supporting leg 701 at the bottom for supporting.

[0048] In an optional embodiment of the present embodiment, the total focal length formula of the two sets of annular lenses 4 is:

[0049]

[0050] In an optional embodiment of the present embodiment, the two sets of annular lenses 4 cooperate to correct the difference in magnification at both ends of the image, and the change in magnification is symmetric about the center.

[0051] In an optional embodiment of the present embodiment, the two central frames 3 are matched with differential control, and the rotation of the two annular lenses 4 forms differential through differential control. The two annular lenses 4 can combine to form different total focal lengths F in the presence of differential. In the total focal length curve graph, the straight line is the change of focal length (f1 f2) of the symmetrically placed conical lens, and the curve is the change of total focal length (F) generated with the movement of the conical mirror. Each curve represents the F change symmetrically distributed about the center, and the multiple curves represent the curves of different f1 f2 positions.

[0052] Experimental conditions

[0053] 1. The feasibility simulation experiment of the focal length change of the bar-shaped conical side mirror is carried out, and different line segment lengths are formed after the equal length line segments pass through the measured sample, and the result is successful.

[0054] 2. The focal length change and distortion simulation experiment of the annular conical side mirror is carried out, and different height circular spots are formed after the equal large circular spots pass through the measured sample, and the result is successful.

[0055] 3. Conduct simulation distortion usability tests to test the overall and central region distortion usability. Due to the influence of the image structure itself, the structural similarity SSIM fluctuates and increases with the cropping ratio, proving that the central image quality is better. All structural similarities are higher than 69%, indicating that the overall distortion characteristics are not serious.

[0056] 4. Perform a function-based simulation of the focal length change of the ring lens. A flatter central section of the blue line indicates a smaller focal length change on both sides, resulting in a more uniform overall focal length, which is better. The vertical distribution of the blue line represents the change of the total focal length F when the angle difference changes uniformly, and the sparser and more average the better.

[0057] 5. The test of the ring lens 4 under laser showed that the ring lens 4 has a high resistance to laser damage.

[0058] 6. An experiment was conducted to converge the light using the lens group. The experimental results showed that the light spot in the image was clear, there was no distortion, and the light intensity was evenly distributed.

[0059] 7. Conduct a double-ring combination experiment. By combining the thin segments, the middle segments, and the thick segments of the ring lens, different magnifications are formed, and the total focal length F is different.

[0060] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A zoom lens system based on an annular conical side mirror, comprising two holders (1), two center holders (3) and two sets of annular lenses (4), characterized in that: The two supports (1) are arranged in parallel, the bottom ends of the two supports (1) are provided with bases (101) for fixing installation, a main shaft (2) is horizontally connected between the two supports (1), the two center supports (3) are rotationally fitted on the main shaft (2), and the two groups of annular lenses (4) are fixed on the two center supports (3) respectively, and the two groups of annular lenses (4) are oppositely arranged. Each group of annular lenses (4) is composed of two half-ring lenses (401), and the half-ring lens (401) is a half-ring structure curved from a conical strip lens.

2. A zoom lens system based on an annular conical side mirror according to claim 1, characterized in that: The outer sides of the two groups of annular lenses (4) are clamped with fixing hoops (5), and the fixing hoops (5) constrain the annular lenses (4) on the center supports (3).

3. The zoom lens system based on an annular conical side mirror according to claim 1, characterized in that: The zoom lens system further comprises a front panel (6) and a rear panel (7), the front panel (6) and the rear panel (7) are arranged in parallel, and the two supports (1) are located between the front panel (6) and the rear panel (7).

4. A zoom lens system based on an annular conical side mirror according to claim 3, characterized in that: The front panel (6) is provided with an imaging hole (602) and an imaging hole (603), and the rear panel (7) is provided with a plurality of mounting holes (702), the mounting holes (702) on the rear panel (7) are correspondingly provided with reflecting mirrors (8), and two reflecting mirrors (8) are respectively aligned with the imaging hole (602) and the imaging hole (603).

5. A zoom lens system based on an annular conical side mirror according to claim 4, characterized in that: The reflecting mirror (8) aligned with the imaging hole (602) can receive light entering the imaging hole (602), and the reflecting mirror (8) aligned with the imaging hole (603) can reflect light entering the imaging hole (603).

6. A zoom lens system based on an annular conical side mirror according to claim 5, characterized in that: The image received by the reflecting mirror (8) aligned with the imaging hole (602) is reflected by the remaining reflecting mirrors (8) in turn, and after reaching the reflecting mirror (8) aligned with the imaging hole (603), the image can be flipped by 90 degrees.

7. The zoom lens system based on an annular conical side mirror according to claim 3, characterized in that: The front panel (6) and the rear panel (7) are both vertical disc-shaped structures, the front panel (6) is provided with a first supporting leg (601) at the bottom for supporting, and the rear panel (7) is provided with a second supporting leg (701) at the bottom for supporting.

8. The zoom lens system based on an annular conical side mirror according to claim 1, characterized in that: The formula for the total focal length of the two annular lenses (4) is:

9. The zoom lens system based on an annular conical facet mirror according to claim 8, characterized in that: The two groups of annular lenses (4) cooperate to correct the difference in magnification at both ends of the picture, and the change in magnification is symmetric about the center.

10. The zoom lens system based on an annular conical side mirror according to claim 9, characterized in that: The two center supports (3) are provided with differential control, the rotation of the two annular lenses (4) forms differential through differential control, and the two annular lenses (4) can combine to form different total focal lengths F in the presence of differential.

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