Liquid crystal fresnel lens, eyeglasses, electronic products and driving method

By grouping electrode units in a liquid crystal Fresnel lens and adjusting their width, the light scattering problem caused by voltage discretization in the edge region is solved, achieving high-quality imaging and simplified voltage control, while reducing costs.

CN116482910BActive Publication Date: 2026-06-05CHENGDU YETA TECH CO LTD

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
CHENGDU YETA TECH CO LTD
Filing Date
2023-03-17
Publication Date
2026-06-05

AI Technical Summary

Technical Problem

Existing liquid crystal Fresnel lenses have low voltage discretization in the edge region, which leads to light scattering and affects image quality.

Method used

Multiple electrode units arranged along a first direction are used, and the electrode units are divided into a first electrode unit group and a second electrode unit group. The width of the electrode unit group is adjusted to increase the discreteness of the potential in the edge region. A smooth Fresnel lens is formed by controlling the potential distribution in the liquid crystal layer.

Benefits of technology

It effectively avoids light scattering, ensuring image quality, while simplifying drive voltage control and reducing costs.

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Abstract

The application belongs to the technical field of liquid crystal lens, and specifically relates to a liquid crystal Fresnel lens, glasses, electronic products and a driving method. The application comprises a first substrate, a first electrode layer, a liquid crystal layer, a second electrode layer and a second substrate which are sequentially stacked; the second electrode layer comprises a plurality of electrode units, the plurality of electrode units are sequentially divided into a first electrode unit group and a second electrode unit group along a first direction, each electrode unit comprises at least one conductive wire, the conductive wire extends from a position close to the center of the second electrode layer to a position away from the center of the second electrode layer, and the width change of each electrode unit in the second electrode unit group and the width of an adjacent electrode unit closer to the center of the second electrode layer is less than or equal to a first preset value. The application can effectively avoid the scattering of light caused by the low voltage discretization degree of the edge region of the liquid crystal Fresnel lens.
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Description

Technical Field

[0001] This invention belongs to the field of liquid crystal lens technology, specifically a liquid crystal Fresnel lens, eyeglasses, electronic products, and driving method. Background Technology

[0002] In certain applications, convenient adjustment of lens focal length is required. Liquid crystal lenses (LCDs) are suitable for these applications due to their electronically controlled focusing capabilities. Current LCD Fresnel lenses employ a concentric ring electrode structure, but this structure lacks sufficient precision in controlling the potential distribution, failing to achieve the desired Fresnel lens shape. In its patent publication CN114637155A, the applicant proposes using conductive wires to control the potential distribution in the Fresnel ring region. By applying a first driving voltage and a second driving voltage to the two ends of the conductive wire, different positions on the wire exhibit different potentials. Therefore, by adjusting the distribution of the conductive wire within the Fresnel ring region, the potential distribution can be precisely controlled. This approach offers advantages such as high precision in potential distribution control and simple driving voltage control.

[0003] After adopting the aforementioned scheme, the voltage distribution in most areas of the liquid crystal Fresnel lens is close to the ideal potential distribution. However, in the region near the edge of the liquid crystal Fresnel lens, the voltage discretization decreases, and the voltage distribution in the Fresnel ring region is not smooth enough, causing light scattering and resulting in reduced image quality. Summary of the Invention

[0004] In view of this, the present invention provides a liquid crystal Fresnel lens, eyeglasses, electronic products, and a liquid crystal lens driving method to solve the technical problem of light scattering caused by the low degree of voltage discretization in the edge region of the liquid crystal Fresnel lens in the prior art.

[0005] The technical solution adopted in this invention is:

[0006] In a first aspect, the present invention provides a liquid crystal lens.

[0007] In a second aspect, the present invention provides eyeglasses comprising the liquid crystal lens described in the first aspect.

[0008] Thirdly, the present invention provides an electronic product, including a control circuit and the liquid crystal lens described in the first aspect, wherein the control circuit is electrically connected to the liquid crystal lens.

[0009] Fourthly, the present invention provides a liquid crystal lens driving method for driving the liquid crystal lens described in the first aspect.

[0010] Beneficial Effects: The liquid crystal lens, eyeglasses, electronic product, and liquid crystal lens driving method of the present invention utilize multiple electrode units arranged along a first direction to control the potential distribution of each annular region in the liquid crystal layer, and divide these first units into a first electrode unit group and a second electrode unit group. The potential of the annular region controlled by the electrode units of the first electrode unit group deflects the liquid crystal in each annular region to form a liquid crystal Fresnel lens. The width of each electrode unit in the second electrode unit group is appropriately reduced compared to the width of the adjacent electrode unit closer to the center of the second electrode layer, so that the number of concentric arcs or curve segments of the conductive lines in the electrode units located at the edge of the liquid crystal Fresnel lens is maintained sufficiently. This increases the discreteness of the potential in these regions, making the potential distribution within the Fresnel annular region smoother, thereby effectively avoiding light scattering and ensuring image quality. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, and these are all within the protection scope of the present invention.

[0012] Figure 1 This is a three-dimensional structural schematic diagram of the liquid crystal Fresnel lens of the present invention;

[0013] Figure 2 This is a schematic diagram of the structure of the second electrode layer in this invention;

[0014] Figure 3 This is a schematic diagram illustrating the decomposition of the electrodes in the second electrode layer into individual electrode units according to the present invention.

[0015] Figure 4 This is a schematic diagram showing the width relationship of each unit of the liquid crystal Fresnel lens of the present invention;

[0016] Figure 5 This is a schematic diagram of the electrode unit of the present invention using concentric circular arcs;

[0017] Figure 6 This is a schematic diagram of one of the concentric arc structure electrode units of the present invention;

[0018] Figure 7 This is a schematic diagram of the structure of the electrode unit of the present invention using a spiral.

[0019] Figure 6 This is a schematic diagram of one of the spiral structure electrode units of the present invention;

[0020] Figure 9This is a schematic diagram of the structure of the second electrode layer when the lead assembly is used in this invention;

[0021] Figure 10 This is a structural illustration of an electrode unit when the present invention employs a lead assembly.

[0022] Figure 11 A schematic diagram of a structure in which a conductive element is placed at the junction of two adjacent electrode units;

[0023] Figure 12 A partially enlarged view showing the placement of a conductive element at the junction of two adjacent electrode units;

[0024] Figure 13 This is a schematic flowchart of the liquid crystal lens driving method used in this invention;

[0025] Explanation of reference numerals in the drawings: First substrate 10, first electrode layer 20, liquid crystal layer 30, second electrode layer 40.

[0026] First electrode unit 411, second electrode unit 412, third electrode unit 413, fourth electrode unit 414, fifth electrode unit 415, sixth electrode unit 416, first electrode unit group 41, second electrode unit group 42, conductive line 43, concentric arc 431, connecting segment 432, outermost curve segment 433, innermost curve segment 434, remaining curve segments 435, lead assembly 44, first lead 441, second lead 442, second substrate 50. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. It should be noted that, in this document, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. In the description of the present invention, it should be understood that the terms "center," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements, but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, the element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Where there is no conflict, embodiments of the present invention and the various features thereof can be combined with each other, all of which are within the scope of protection of the present invention.

[0028] Example 1

[0029] This embodiment provides a liquid crystal Fresnel lens. The Fresnel lens is based on the principle that the curvature of an optical surface determines its imaging characteristics. In the design of the optical lens, the surface curvature remains constant, but the thickness of the surface is reduced during manufacturing. This type of lens can still converge light, focusing incident light onto its surface to a focal point.

[0030] In practical lens manufacturing and applications, a spherical lens can be considered as several discontinuous components, with excess parts removed while maintaining its original surface curvature during manufacturing to ensure light deflection. The function of these discontinuous components is achieved by the central circle and a series of concentric rings on the Fresnel lens. This embodiment utilizes the regular deflection of the liquid crystal layer 30 under an electric field to achieve the function of the concentric rings of the Fresnel lens, thus achieving an optical effect equivalent to that of a Fresnel lens using a liquid crystal lens.

[0031] like Figure 1As shown, the liquid crystal Fresnel lens of this embodiment includes a first substrate 10, a first electrode layer 20, a liquid crystal layer 30, a second electrode layer 40, and a second substrate 50 stacked sequentially.

[0032] In this embodiment, the liquid crystal Fresnel lens may employ a layered structure. The aforementioned first substrate 10, first electrode layer 20, liquid crystal layer 30, second electrode layer 40, and second substrate 50 are located in different layers, and the aforementioned layers are stacked and arranged along the light transmission direction of the liquid crystal lens, i.e., the normal direction of each layer.

[0033] like Figure 2 and Figure 3 As shown, the second electrode layer 40 includes a plurality of electrode units, which are arranged sequentially from a position close to the center of the second electrode layer 40 to a position away from the center of the second electrode layer 40. Figure 3 This is a schematic diagram showing the disassembly of the second electrode layer into individual electrode units from the inside out.

[0034] The plurality of electrode units are divided into a first electrode unit group 41 and a second electrode unit group 42 along a first direction, wherein the first direction is from the center of the second electrode layer 40 to the edge of the second electrode layer 40.

[0035] The electrode units of the first electrode unit group 41, driven by the first voltage and the second voltage, deflect the liquid crystal in the liquid crystal layer 30 to form a liquid crystal Fresnel lens. Figure 2 The Fresnel liquid crystal lens includes six electrode units, of which the first electrode unit 411, the second electrode unit 412, and the third electrode unit 413 belong to the first electrode unit group 41, and the fourth electrode unit 414, the fifth electrode unit 415, and the sixth electrode unit 416 belong to the second electrode unit group 42.

[0036] This embodiment utilizes electrode units to control the electric field distribution acting on the liquid crystal layer 30. One electrode unit can control the electric field distribution of a ring region in the liquid crystal layer 30, causing the liquid crystal molecules in that ring region to deflect according to a certain pattern, thereby realizing the optical function of a concentric ring in a Fresnel lens. In this way, multiple electrode units can be used to control the electric field distribution of different ring regions, and cause the liquid crystal molecules in these ring regions to deflect, thereby realizing the optical function of each concentric ring in the Fresnel lens, so that the phase delay of light after passing through the ring region of the liquid crystal layer 30 is the same as the phase delay of light after passing through the concentric ring of the Fresnel lens.

[0037] Since the concentric rings of the Fresnel lens are arranged in concentric rings from the inside out, the electrode units in this embodiment are also arranged sequentially from the position closest to the center of the second electrode layer 40 to the position furthest from the center of the second electrode layer 40. This results in the ring regions controlled by these electrode units also being arranged in concentric rings from the inside out, so that these ring regions together form a complete liquid crystal Fresnel lens.

[0038] To improve the accuracy of the electric field distribution in the central circular region and the annular region controlled by the electrode unit, in this embodiment, each electrode unit includes at least one conductive line 43. The conductive line 43 extends from a position near the center of the second electrode layer 40 towards a position away from the center of the second electrode layer 40. Figure 5 As shown, the spacing between adjacent conductive lines 43 ( Figure 5 The distance d in the middle is less than or equal to 100 μm;

[0039] In this embodiment, the electrodes of the first electrode layer 20 provide a common voltage to the liquid crystal lens after a voltage is applied. In a specific implementation, one end of the conductive line 43 of each electrode unit can be connected to a power supply providing the first driving voltage through an electrode lead, so that the first driving voltage provided by the power supply is applied to one end of the conductive line 43 through the electrode lead. Then, the other end of the conductive line 43 is connected to a power supply providing the second driving voltage through an electrode lead, so that the second driving voltage provided by the power supply is applied to the other end of the conductive line 43 through the electrode lead. In this way, one end of the conductive line 43 is given the first voltage, while the other end is given the second voltage.

[0040] Because the conductive line 43 of the electrode unit has a certain resistance, the potential at different lengths of the conductive line 43 differs after a first voltage and a second voltage are applied to its two ends. Thus, the potential on the conductive line 43 changes gradually and continuously along its length. Since the conductive line 43 extends from a position near the center of the second electrode layer 40 in the annular region to a position away from the center of the second electrode layer 40 in the annular region, it gradually passes through various positions in the annular region from the inside out during its extension. Therefore, as the conductive line 43 extends from the inside out in the annular region, the potential near the area traversed by the conductive line 43 changes gradient accordingly. The electric field intensity in the corresponding annular region of the liquid crystal layer 30 controlled by this electrode unit also changes gradient in the radial direction. By controlling the magnitudes of the first and second voltages, the potential of the liquid crystal layer 30 in the annular region controlled by the electrode unit can be controlled to gradually increase from the inside out along the radial direction of the liquid crystal Fresnel lens, reaching its maximum at the outer edge of the annular region. Alternatively, the potential of the liquid crystal layer 30 within the annular region controlled by the single control electrode can gradually increase from the inside to the outside along the radial direction of the liquid crystal Fresnel lens, reaching its maximum at the inner edge of the annular region. In this embodiment, the length of the conductive line 43 is greater than its width and thickness, therefore the conductive line 43 is linear. The number of conductive lines 43 can be one or more.

[0041] Since the alignment of the liquid crystal director can be electrically controlled and exhibits different refractive index gradient distributions in a non-uniform electric field, applying a potential with a certain gradient distribution to the liquid crystal layer 30 can induce the liquid crystal director in the liquid crystal layer 30 to form a non-uniform distribution, thereby causing the emitted light passing through the liquid crystal layer 30 to produce a specific phase delay distribution.

[0042] Therefore, in this embodiment, the potential distribution of the annular region controlled by each electrode unit can be determined based on the corresponding delay distribution of light in each annular region of an ideal Fresnel lens, and the shape of the conductive line 43 of each electrode unit and the width of each electrode unit can be set according to the aforementioned potential distribution. With the first driving voltage and the second driving voltage set, the width of each electrode unit along the first direction also affects the potential distribution of the liquid crystal lens.

[0043] To achieve the ideal optical effect of a Fresnel lens, the width of the annular region must satisfy:

[0044] w i =r0(i 1 / 2 - (i-1) 1 / 2 )

[0045] Where wi is the width of the i-th ring, r0 is the width of the 1-th ring, and i is a positive integer greater than or equal to 1. The larger the value of i, the closer the ring is to the edge of the lens. In the art, it is generally believed that the width of each ring region of a Fresnel lens must be set according to the aforementioned requirements to achieve the ideal optical effect of a Fresnel lens. However, in liquid crystal Fresnel lenses designed according to the aforementioned requirements, the voltage discretization is reduced, and the voltage distribution within the Fresnel ring region is not smooth enough, causing light scattering and resulting in a decrease in image quality.

[0046] like Figure 4 As shown, this application employs a method of grouping and setting the width of the electrode units of the liquid crystal Fresnel lens. Specifically, all electrode units are divided into two groups: one group consists of electrode units located at the lens edge, and the other group consists of the remaining electrode units. For the electrode units belonging to the first electrode unit group 41, the width of each electrode unit is still set according to the requirement of forming a Fresnel lens by liquid crystal deviation. Let there be m electrode units in the first electrode unit group 41, that is, the width of each electrode unit in the first electrode unit group 41 satisfies: w i =r0(i 1 / 2 - (i-1) 1 / 2 Where 1 ≤ i ≤ m, and i and m are both positive integers. The larger the value of i, the closer the ring is to the edge of the lens. For example... Figure 4 In the liquid crystal cylindrical lens, among the 10 electrode units from the inside out, the widths of the first 4 electrode units are w1, w2, w3, and w4, respectively. The widths of these 4 electrode units satisfy w i =r0(i 1 / 2 - (i-1) 1 / 2 ).

[0047] For the electrode units belonging to the second electrode unit group 42, the width of these electrode units is not set exactly to meet the requirement of forming a Fresnel lens for liquid crystal deviation. Instead, the width of each electrode unit in the second electrode unit group 42 is less than or equal to the width of the adjacent electrode unit closer to the center of the second electrode layer 40. For example... Figure 4 In the 10 electrode units of the liquid crystal cylindrical lens from the inside out, the widths of the last 6 electrode units are w5, w6, w7, w8, w9, and w10 respectively. The widths of these 4 electrode units satisfy the condition that the change in width between each electrode unit in the second electrode unit group 42 and the width of the adjacent electrode unit closer to the center of the second electrode layer 40 is less than or equal to a first preset value.

[0048] The magnitude of the first preset value can be set empirically. This preset value should be such that, when the change is less than or equal to this preset value, the edge of the Fresnel liquid crystal lens does not significantly cause light scattering. The change in width refers to the absolute value of the difference between the width of the electrode unit and the width of its adjacent electrode unit closer to the lens center. For example, the width of the j-th electrode unit is w. j Then the electrode unit adjacent to it and closer to the center of the lens is the (j-1)th electrode unit, and let the width of the (j-1)th electrode unit be w. j-1 Then the absolute value of the difference between the width of the j-th electrode unit and its adjacent electrode unit closer to the center of the lens, |w j - w j-1 |, where |w j - w j-1 |That is, the change in width of the j-th electrode unit compared to the width of the adjacent electrode unit that is closer to the center of the second electrode layer 40.

[0049] In this embodiment, after setting the width of the electrode units in the second electrode unit group 42 according to the aforementioned requirements, the liquid crystal Fresnel lens can maintain a sufficient number of concentric arcs 431 or curve segments of the conductive lines 43 in the electrode units located in the edge region of the liquid crystal Fresnel lens. This increases the discreteness of the potential in these regions, making the potential distribution within the Fresnel ring region smoother, thereby effectively avoiding light scattering and ensuring image quality. Since the human eye's field of vision is relatively small, this embodiment controls the variation of the electrode unit width in the edge region of the liquid crystal Fresnel lens, while still setting the electrode unit width according to the Fresnel lens ring width requirements in other regions. This allows these regions to form an ideal Fresnel lens, and the edge regions also avoid light scattering, thus ensuring image quality while meeting user needs.

[0050] As an optional but advantageous implementation, in this embodiment, the outer boundary radius of the first electrode unit is set to r0, and the outer boundary radius of the i-th electrode unit arranged from the center of the second electrode layer 40 to the edge of the second electrode layer 40 is set to r. i If the i-th electrode unit belongs to the second electrode unit group 42, then r satisfies i =r0i x , where i is an integer greater than or equal to 1, and 0.5 < x ≤ 1. At this time, the first preset value is the maximum value of the change in width between each electrode unit in the second electrode unit group that satisfies the aforementioned conditions and the width of the adjacent electrode unit that is closer to the center of the second electrode layer.

[0051] Since each electrode unit has two boundaries, one closer to the center of the second electrode layer 40 and the other closer to the edge of the second electrode layer 40, in this embodiment, the outer boundary of the electrode unit is the boundary of the electrode unit closer to the edge of the second electrode layer 40. In the aforementioned scheme, the width of the second electrode in the second electrode unit group 42 is adjusted based on the width of the Fresnel annular region. This ensures that the electrode units in the second electrode unit group 42 have a sufficient number of concentric arcs 431 or curve segments, and also allows the portion near the center of the lens to approach the width of the Fresnel lens annular region, thereby achieving a better overall user experience.

[0052] As one optional implementation, in this embodiment, the width of each electrode unit in the second electrode unit group 42 is equal to the width of the adjacent electrode unit closer to the center of the second electrode layer 40, with no change in width. In this case, the width of each electrode unit in the second electrode unit group 42 remains consistent. This arrangement can better reduce light scattering in the lens edge region.

[0053] Because the liquid crystal director arrangement is electrically adjustable, it exhibits different refractive index gradient distributions in a non-uniform electric field. Therefore, applying a potential with a certain gradient distribution can induce the liquid crystal director to form a non-uniform distribution. Thus, in this embodiment, the potential distribution of the annular region corresponding to each electrode unit can be adjusted by adjusting the first and second voltages applied across the conductive lines 43, thereby adjusting the overall potential distribution of the liquid crystal Fresnel lens and thus the focal length of the liquid crystal Fresnel lens. Although this embodiment has multiple conductive lines 43, only two voltages are needed to drive the liquid crystal lens and enable its operation. Furthermore, only one or both of these voltages need to be adjusted simultaneously to control the optical power of the liquid crystal Fresnel lens; independent control of each conductive line 43 is not required. Therefore, the control method is very simple, requires fewer electrode leads, and has lower cost.

[0054] In this embodiment, the first substrate 10 and the second substrate 50 can be made of transparent materials with certain strength and rigidity, such as glass substrates, plastic substrates, etc. The first substrate 10 serves to support the liquid crystal lens. The first substrate 10 can also serve as a carrier for the first electrode layer 20, which can be deposited on the first substrate 10. The second substrate 50 also provides support and can also serve as a carrier for the second electrode layer 40, which can be deposited on the second substrate 50.

[0055] In this embodiment, the conductive lines 43 of each electrode unit can be made of a transparent conductive material, including but not limited to ITO electrodes, IZO electrodes, FTO electrodes, AZO electrodes, and IGZO electrodes. As an optional but advantageous implementation, the spacing between adjacent conductive lines 43 is the same in this embodiment. As an optional but advantageous implementation, the width of the conductive lines 43 is the same at all points in this embodiment.

[0056] To more precisely control the potential distribution in the annular region corresponding to the electrode unit and eliminate potential steps between adjacent conductive lines 43, the art typically employs filling the conductive lines 43 with a high-resistivity film or a high-dielectric-constant material. However, high-resistivity films and high-dielectric-constant materials suffer from unstable properties, which change significantly over time. Therefore, while using high-resistivity films or high-dielectric-constant materials can improve the precision of potential distribution control and eliminate potential steps between adjacent conductive lines 43, it cannot guarantee performance stability. This embodiment addresses this by setting the spacing between conductive lines 43 to within 100 μm to achieve a high-precision potential distribution and eliminate potential steps between adjacent conductive lines 43. This allows for an ideal potential distribution in the corresponding annular region without using a high-resistivity film, successfully avoiding the negative impact of the poor stability of high-resistivity films or high-dielectric-constant materials on the liquid crystal lens effect.

[0057] This embodiment can also change the polarity of the liquid crystal lens by altering the relationship between the first and second voltages applied to each electrode unit, thereby changing the liquid crystal lens from a negative lens to a positive lens or vice versa. For example, when the first voltage applied to the conductive line 43 near the center of the second electrode layer 40 is less than the second voltage applied to the conductive line 43 near the edge of the second electrode layer 40, the optical power of the liquid crystal Fresnel lens is positive, and the liquid crystal Fresnel lens exhibits the characteristics of a convex lens. In this case, glasses made using the liquid crystal lens of this embodiment can be used as reading glasses. When the relationship between the first and second voltages is changed so that the first driving voltage applied to the conductive line 43 near the center of the second electrode layer 40 is greater than the second voltage applied to the conductive line 43 near the edge of the second electrode layer 40, the optical power of the liquid crystal Fresnel lens is negative, and the liquid crystal lens exhibits the characteristics of a concave lens. In this case, glasses made using the liquid crystal lens of this embodiment can be used as nearsighted glasses.

[0058] The number of conductive lines 43 in an electrode unit can be one or more. As one optional implementation, when the number of conductive lines 43 in an electrode unit is greater than one, the conductive lines 43 belonging to that electrode unit can be rotationally symmetrical about a point in the second electrode layer 40. Rotational symmetry means that the image formed by simultaneously rotating all the conductive lines 43 around a point on the second electrode layer 40 by a certain angle completely overlaps with the previous image. When the conductive lines 43 are distributed in a rotationally symmetrical manner, the potential will also be distributed in a rotationally symmetrical manner.

[0059] like Figure 5 As shown, as an optional but advantageous implementation, the conductive wire 43 in this embodiment includes a plurality of concentric arcs 431 arranged along a first direction, and adjacent concentric arcs 431 are connected by connecting segments 432.

[0060] For ease of understanding, Figure 5 Different cross-sectional lines are used to represent different electrode units. Figure 5 The image shows three electrode units of a liquid crystal Fresnel lens. (For example...) Figure 6 As shown, for any one of the electrode units, the conductive line 43 of that electrode unit is composed of concentric arcs 431 connected end to end. These concentric arcs 431 fill the electrode unit from a position near the center of the second electrode layer 40 to a position away from the center of the second electrode layer 40. The beginning and end of adjacent concentric arcs 431 are connected by a short connecting segment 432, so that these concentric arcs 431 are connected to form a complete conductive line 43. With the above structure, the electrode leads that provide driving voltage to each electrode unit can be connected from below or above the second electrode layer 40.

[0061] In this embodiment, the conductive lines 43 of the electrode unit adopt a regular concentric ring structure, and there is no need to change the spacing between the wires. When the spacing between adjacent wires is the same and less than 100μm, a precise parabolic potential distribution can be formed, making the optical effect of the liquid crystal lens closer to that of an ideal Fresnel lens. Moreover, this structure has low complexity, so the manufacturing cost is also low.

[0062] like Figure 7 As shown, as an optional but advantageous implementation, in this embodiment, the conductive wire 43 is in the shape of a spiral. The starting point of the spiral can be located at the position closest to the center of the second electrode layer 40 in the electrode unit. Figure 8As shown, the spiral extends from the starting position in the circumferential direction towards the edge of the second electrode layer 40. As the spiral extends from the center of the second electrode layer 40 to the edge of the second electrode layer 40, the spiral passes through most of the area of ​​the electrode unit from the inside to the outside. The potential of the electrode unit along the first direction also gradually changes with the extension of the spiral. Therefore, a relatively ideal potential distribution can be obtained when the spacing between adjacent conductive lines 43 is less than or equal to 100 μm.

[0063] In this embodiment, the liquid crystal lens only needs to have the conductive line 43 spirally shaped to obtain a precise potential distribution that meets the functional requirements of various liquid crystal lenses. The specific method for setting the shape of the conductive line 43 is as follows:

[0064] In this embodiment, the conductive wire 43 in the electrode unit has a spiral shape obtained from the first spiral equation, which is:

[0065] ,in

[0066] in Represents the radius in polar coordinates. Polar angle, The parameters of the equation.

[0067] like Figure 8 As shown, The size determines the density of the spiral. The larger the diameter, the denser the spiral lines. By using the aforementioned method to set the conductive lines 43, a precise parabolic potential distribution can be obtained, thereby ensuring that the wavefront distribution of the resulting liquid crystal lens is also a precise parabolic distribution.

[0068] In this embodiment, the shape of the conductive wire 43 is a helix obtained by the second helix equation, which is:

[0069]

[0070] in

[0071] in Represents the radius in polar coordinates. is the polar angle, m is a parameter related to the liquid crystal material, and R is the radius of curvature of the lens.

[0072] The conductive lines 43, arranged in the aforementioned manner, can achieve a precisely spherically distributed potential, thereby ensuring that the wavefront distribution of the resulting liquid crystal lens is also precisely spherically distributed. Lenses with spherical wavefronts exhibit the most ideal imaging effect. However, ordinary lenses require complex and precise shaping processes to achieve an approximate spherical wavefront distribution. In contrast, the present invention only requires the conductive lines to meet the aforementioned requirements to obtain a lens with a precisely spherical wavefront distribution. A high-precision spherical wavefront distribution lens can be obtained without complex processing, significantly reducing product manufacturing costs.

[0073] The conductive wire 43 has a spiral shape obtained from the third spiral equation, which is:

[0074]

[0075] in Represents the radius in polar coordinates. Polar angle,

[0076] Where c is an arbitrary constant. represents the parameters of the equation.

[0077] By using the aforementioned conductive lines 43, a precise conical potential distribution can be obtained, thereby ensuring that the wavefront distribution of the resulting liquid crystal lens is also a precise conical distribution.

[0078] In one implementation, the electrode unit 430 has a parabolic shape, and the mathematical equation representing this shape is: , where x and y are in μm.

[0079] In one embodiment, the conductive wire 43431 is arc-shaped, and the mathematical equation representing this shape is: The units for x and y are μm.

[0080] In one embodiment, the conductive wire 43 is shaped like an Archimedean spiral, and the mathematical equation for this shape is:

[0081] The units for x and y are μm.

[0082] In the parametric equation of a helix, k represents the period that the helix takes from the center to the edge.

[0083] In one preferred embodiment, the electrode unit has a Fermat spiral shape, the mathematical equation of which is:

[0084] The units for x and y are μm.

[0085] Electrode units with spirals and a second electrode layer 40, as shown Figure 9 and Figure 10 As shown, Figure 9 The second electrode layer 40 is provided with three electrode units, namely the first electrode unit 411, the second electrode unit 412 and the third electrode unit 413 from the inside to the outside.

[0086] When the number of conductive wires 43 is greater than one, the electrode unit used in this embodiment further includes a first electrical connector and a second electrical connector. The first electrical connector is configured to provide the same first voltage to the ends of each conductive wire 43 electrically connected to it in the same electrode unit. The second electrical connector is configured to provide the same second voltage to the ends of each conductive wire 43 electrically connected to it in the same electrode unit.

[0087] like Figure 9 As shown, the liquid crystal Fresnel lens of this embodiment also includes a lead assembly 44, which includes a first lead 441 and a second lead 442, as shown... Figure 10 As shown, the conductive wire 43 of the electrode unit includes multiple curved segments arranged along a first direction. Each curved segment has a certain distance between its two ends to allow the first lead 441 and / or the second lead 442 to pass through. One end of the outermost curved segment 433 is electrically connected to the second lead 442, and the other end is connected to an adjacent curved segment on the same side of the lead assembly 44. One end of the innermost curved segment 434 is electrically connected to the first lead 441, and the other end is connected to an adjacent curved segment on the same side of the lead assembly 44. One end of the remaining curved segments 435 is connected to an adjacent curved segment on the same side of the lead assembly 44, and the other end is connected to another adjacent curved segment on the same side of the lead assembly 44. In this embodiment, the first lead 441 and the second lead 442 introduce a first voltage and a second voltage to the electrode unit, respectively. The first lead 441 is electrically connected to the end of the conductive wire 43 near the center of the electrode, while the second lead 442 is electrically connected to the end of the conductive wire 43 away from the center of the electrode. The first lead 441 and the second lead 442 are both led outward from a position close to the center of the second electrode layer 40.

[0088] In this embodiment, a conductive wire 43 can be considered as being composed of multiple curved segments connected end to end. These curved segments are arranged along a first direction from a position close to the center of the second electrode layer 40 to a position away from the center of the second electrode layer 40. Each curved segment has two ends, which are not directly connected but are spaced a certain distance apart. This allows the lead assembly 44 to pass through the gap between the two ends without interfering with the conductive wire 43.

[0089] like Figure 10 As shown, among the multiple curved segments constituting the conductive line 43, two are particularly special. One is the outermost curved segment of the electrode unit, which is the segment furthest from the center of the second electrode layer 40. The other is the innermost curved segment 434, which is the segment closest to the center of the second electrode layer 40. One end of the outermost curved segment 433 is electrically connected to the second lead 442, and the other end is electrically connected to an adjacent curved segment that is closer to the center of the second electrode layer 40 in the first direction. One end of the innermost curved segment 434 is electrically connected to the second lead 442, and the other end is connected to an adjacent curved segment that is further away from the center of the second electrode layer 40 in the first direction. Of all the curved segments constituting the conductive line 43, except for the two mentioned above, both ends of the remaining curved segments 435 are connected to adjacent curved segments. One end of these segments is connected to an adjacent curved segment that is closer to the center of the second electrode layer 40, and the other end is connected to an adjacent curved segment that is closer to the center of the second electrode layer 40. In this way, these curved segments are connected end to end to form a conductive line 43 that extends continuously from the center of the electrode unit 412 to the edge of the second electrode unit 40 and fully fills the second electrode layer 40. At the same time, they cleverly avoid the lead assembly 44, thus achieving precise potential distribution while avoiding the influence of the lead assembly 44. In this embodiment, the beginning and end of two adjacent curved segments can be connected by a connecting segment 432.

[0090] In this embodiment, the curved segment is an arc, and the spacing between adjacent conductive lines 43 is the same. This method not only yields a precise parabolic potential distribution but also reduces manufacturing costs through a simple structural design.

[0091] As an optional but advantageous implementation, in this embodiment, the spacing between at least some adjacent curve segments is unequal. This embodiment can also control the potential distribution of the electrode units, thereby controlling the modulation effect of the liquid crystal lens on light, by setting the spacing between the curve segments.

[0092] The spacing between adjacent curve segments satisfies the requirement that the potential distribution formed by the liquid crystal lens is spherical. When the spacing between adjacent curve segments meets the aforementioned requirement, the wavefront distribution of the resulting liquid crystal lens is spherical. Lenses with spherical wavefronts have the most ideal effect in imaging. However, ordinary lenses require complex and precise shaping processes to obtain lenses with approximately spherical wavefront distributions. This method, however, only requires the spacing between adjacent curve segments to meet the aforementioned requirement to obtain a lens with a precise spherical wavefront distribution. The spacing between adjacent curve segments also satisfies the requirement that the potential distribution formed by the liquid crystal lens is conical. When the spacing between adjacent curve segments meets the aforementioned requirement, the wavefront distribution of the resulting liquid crystal lens is conical.

[0093] As an optional but advantageous implementation, a high-impedance film is disposed between the second electrode layer 40 and the liquid crystal layer 30 in this embodiment. Unlike current methods that primarily utilize high-impedance films to guide the potential distribution of liquid crystal lenses, this embodiment uses a high-impedance film between adjacent conductive lines 43 primarily to reduce spatial variations in the electric field near the conductive lines 43. Since the spacing between adjacent conductive lines 43 is less than 100 μm, the potential distribution is mainly determined by the conductive lines 43; therefore, the effect of changes in the characteristics of the high-impedance film on the potential distribution in this embodiment is negligible.

[0094] Furthermore, an insulating layer can be placed between the second electrode layer 40 and the liquid crystal layer 30, or an insulating layer can be placed between the second electrode layer 40 and the liquid crystal layer 30, and a high-impedance film can be placed between the insulating layer and the liquid crystal layer 30 to reduce the spatial variation of the electric field near the conductive line 43. Because the voltage jumps from a first voltage to a second voltage at the junction of two adjacent electrode units, a sudden change in voltage occurs in this region, resulting in a stronger electric field compared to other regions. This electric field affects the potential distribution within a certain range at the junction, thereby reducing the imaging quality of the liquid crystal lens. In response, as... Figure 11 As shown, in this embodiment, the liquid crystal lens further includes a conductive element. The projection of the conductive element on the second electrode layer 40 is located at the junction of adjacent electrode units. The conductive element is used to receive a third driving voltage.

[0095] like Figure 12 As shown, Figure 12 To intercept Figure 11The diagram shows an enlarged view of any small segment within the annulus. In the diagram, a and b represent the portions of the conductive lines 43 of two electrode units adjacent to the other electrode unit, respectively. Since each electrode unit is composed of conductive lines 43, the boundary between adjacent electrode units includes the portions of the conductive lines 43 of each of the two electrode units adjacent to the other electrode unit, and the area between the two adjacent portions, i.e., portions a, b, and portion c between portions a and b in the diagram. The projection of the conductive element onto the second electrode layer 40 can be located between two adjacent electrode units, or it can partially cover the portions of the conductive lines 43 of the two electrode units adjacent to the other electrode unit. The conductive element can be located on the side of the second electrode layer 40 facing the second substrate 50, or it can be located on the side of the second electrode layer 40 away from the second substrate 50. In this embodiment, an insulating layer is also included between the conductive element and the second electrode layer 40.

[0096] In this embodiment, an insulating layer separates the conductive element and the second electrode layer 40 to avoid mutual interference. By applying a third driving voltage V3 to the aforementioned conductive element, the range of the strong electric field influence at the junction of two adjacent electrode units can be reduced, thereby improving the imaging quality of the liquid crystal lens.

[0097] Example 2

[0098] This embodiment provides a method for driving a liquid crystal Fresnel lens. This method is used to drive the liquid crystal Fresnel lens described in Embodiment 1. Let V1 be the voltage applied between the first electrical connector and the first electrode layer 2020, and V2 be the voltage applied between the second electrical connector and the first electrode layer 2020. Figure 12 As shown, the method includes the following steps:

[0099] S1: Obtain the liquid crystal linear response voltage range of the liquid crystal Fresnel lens;

[0100] The linear operating range of a liquid crystal refers to the voltage range in which the phase delay of the liquid crystal is linearly related to the driving voltage.

[0101] S2: Obtain the minimum voltage V within the linear operating range of the liquid crystal based on the liquid crystal linear response voltage range. min and maximum voltage V max ;

[0102] S3: Based on the minimum voltage V min and maximum voltage V max Adjusting the voltage difference between V1 and V2 adjusts the optical power of the liquid crystal Fresnel lens, where V... min ≤V1≤V max And V min ≤V2≤V max .

[0103] This step adjusts the optical power of the liquid crystal Fresnel lens by adjusting the values ​​of V1 and V2. Specifically, you can keep V1 constant while adjusting V2; you can keep V1 constant while adjusting V2; or you can change both V1 and V2 simultaneously. When keeping V1 constant while adjusting V2, you can set V1 = V... min Or V1=V max To adjust the size of V2, keep V2 constant while adjusting the size of V1; you can set V2 = V1. min Or V2=V max The size of V1 is adjusted accordingly. Furthermore, this embodiment can switch between the positive and negative lens states of the liquid crystal Fresnel lens by changing the relationship between the sizes of V1 and V2.

[0104] Example 3

[0105] This embodiment provides a pair of eyeglasses, which includes the liquid crystal Fresnel lens described in Embodiment 1. The eyeglasses include a left lens and a right lens, each containing a liquid crystal Fresnel lens as described in Embodiment 1. The eyeglasses also include a control circuit, comprising a first focusing circuit and a second focusing circuit. The first focusing circuit is electrically connected to the liquid crystal Fresnel lens in the left lens and is used to adjust the optical power of the liquid crystal Fresnel lens in the left lens. The second focusing circuit is electrically connected to the liquid crystal Fresnel lens in the right lens and is used to adjust the optical power of the liquid crystal Fresnel lens in the right lens.

[0106] Example 4

[0107] This embodiment provides an electronic product, which includes a control circuit and a liquid crystal lens as described in any one of Embodiments 1. The control circuit is electrically connected to the liquid crystal Fresnel lens. The electronic product includes, but is not limited to, imaging devices, display devices, mobile phones, wearable devices, etc.

[0108] Example 5

[0109] This embodiment provides an AR device, including the liquid crystal Fresnel lens described in Embodiment 1. Furthermore, the AR device includes a first lens assembly and a second lens assembly. The first lens assembly includes at least one liquid crystal Fresnel lens as described in Embodiment 1, and the second lens assembly includes at least one liquid crystal Fresnel lens as described in Embodiment 1. The AR device also includes a first focusing circuit and a second focusing circuit. The first focusing circuit is electrically connected to the liquid crystal Fresnel lens in the first lens assembly and is used to adjust the optical power of the liquid crystal Fresnel lens in the first lens assembly. The second focusing circuit is electrically connected to the liquid crystal Fresnel lens in the second lens assembly and is used to adjust the optical power of the liquid crystal lens in the second lens assembly. In this embodiment, the first lens assembly corresponds to the user's left eye, and the second lens assembly corresponds to the user's right eye.

[0110] In AR devices, since the left and right eyes correspond to different screens, there are two sets of lens assemblies corresponding to the left and right eyes respectively. Because the interpupillary distance varies among different users, if the focal length of the lens assemblies remains constant, it will inevitably lead to a different experience for some users when wearing AR glasses. Since different consumers have different facial features, the AR glasses in this embodiment can utilize the liquid crystal Fresnel lens from Embodiment 1 to achieve focal length adjustment. Adjusting both the interpupillary distance and the focal length to appropriate positions will allow the image to accurately fall on the retina, resulting in a clear image and thus a better user experience.

[0111] Example 6

[0112] This embodiment provides a VR device, including the liquid crystal Fresnel lens described in Embodiment 1. The VR device includes a third lens assembly and a fourth lens assembly. The third lens assembly includes at least one liquid crystal Fresnel lens as described in Embodiment 1, and the fourth lens assembly includes at least one liquid crystal lens as described in Embodiment 1. The VR device also includes a third focusing circuit and a fourth focusing circuit. The third focusing circuit is electrically connected to the liquid crystal lens in the third lens assembly and is used to adjust the optical power of the liquid crystal lens in the third lens assembly. The fourth focusing circuit is electrically connected to the liquid crystal lens in the fourth lens assembly and is used to adjust the optical power of the liquid crystal lens in the fourth lens assembly. In this embodiment, the third lens assembly corresponds to the user's left eye, and the fourth lens assembly corresponds to the user's right eye.

[0113] In VR devices, since the left and right eyes correspond to different screens, there are two sets of lens assemblies corresponding to the left and right eyes respectively. Because the interpupillary distance varies among different users, if the focal length of the lens assemblies remains constant, it will inevitably lead to a different experience for some users when wearing VR glasses. Since different consumers have different facial features, the VR glasses in this embodiment can utilize the liquid crystal lens from Embodiment 1 to achieve focal length adjustment. Adjusting both the interpupillary distance and the focal length to appropriate positions will ensure that the image accurately falls on the retina, resulting in a clear image and thus providing the user with a better experience.

[0114] The above is a detailed description of the liquid crystal lens driving method, apparatus, device, and storage medium provided in the embodiments of the present invention.

[0115] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention. The functional blocks shown in the above-described block diagrams can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present invention are programs or code segments used to perform the required tasks. The programs or code segments can be stored in a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. The code segment can be downloaded via computer networks such as the Internet or intranets. It should also be noted that the exemplary embodiments mentioned in this invention describe methods or systems based on a series of steps or apparatus. However, this invention is not limited to the order of the steps described above; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0116] The above description is merely a specific embodiment of the present invention. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the protection scope of the present invention.

Claims

1. A liquid crystal Fresnel lens, characterized in that, It includes a first substrate, a first electrode layer, a liquid crystal layer, a second electrode layer, and a second substrate, which are stacked sequentially. The first electrode layer is a surface electrode; The second electrode layer includes a plurality of electrode units, which are arranged sequentially from the position near the center of the second electrode layer to the position away from the center of the second electrode layer. The plurality of electrode units are divided into a first electrode unit group and a second electrode unit group along a first direction, where the first direction is from the center of the second electrode layer to the edge of the second electrode layer. Each electrode unit includes at least one conductive wire extending from a position near the center of the second electrode layer toward a position away from the center of the second electrode layer; a first voltage is applied to one end of the conductive wire and a second voltage is applied to the other end. The surface electrode and the electrode units of the first electrode unit group, driven by the first voltage and the second voltage, deflect the liquid crystal in the liquid crystal layer to form a liquid crystal Fresnel lens. The change in width of each electrode unit in the second electrode unit group from the width of the adjacent electrode unit closer to the center of the second electrode layer is less than or equal to a first preset value. Let the outer boundary radius of the first electrode unit be r0, and the outer boundary radius of the i-th electrode unit arranged from the center of the second electrode layer to the edge of the second electrode layer be r. i If the i-th electrode unit belongs to the second electrode unit group, then r satisfies i =r0i x , where i is an integer greater than or equal to 1, 0.5 < x ≤ 1, and the first preset value is the maximum value of the change in width between each electrode unit in the second electrode unit group that satisfies the aforementioned conditions and the width of the adjacent electrode unit that is closer to the center of the second electrode layer.

2. The liquid crystal Fresnel lens according to claim 1, characterized in that, Let the outer boundary radius of the first electrode unit be r0, and the outer boundary radius of the i-th electrode unit arranged from the center of the second electrode layer to the edge of the second electrode layer be r. i If the i-th electrode unit belongs to the second electrode unit group, then r satisfies i =r0i x , where i is an integer greater than or equal to 1, and 0.5 < x ≤ 1.

3. The liquid crystal Fresnel lens according to claim 1, characterized in that, In the second electrode unit group, the width of each electrode unit in the second electrode unit group is equal to the width of the adjacent electrode unit that is closer to the center of the second electrode layer, and the change in width is equal to 0.

4. The liquid crystal Fresnel lens according to claim 1, characterized in that, The conductive line includes several concentric arcs arranged along a first direction, and adjacent concentric arcs are connected by connecting segments, or the conductive line is parabolic or spiral.

5. The liquid crystal Fresnel lens according to claim 1, characterized in that, The spacing between adjacent conductive lines is less than or equal to 100 μm.

6. The liquid crystal Fresnel lens according to claim 1, characterized in that, It also includes a lead assembly, which includes a first lead and a second lead. The conductive wire of the electrode unit includes a plurality of curved segments arranged along a first direction. The two ends of each curved segment are spaced a certain distance apart to allow the first lead and / or the second lead to pass through. One end of the outermost curved segment is electrically connected to the second lead, and the other end is connected to the adjacent curved segment on the same side of the lead assembly. One end of the innermost curved segment is electrically connected to the first lead, and the other end is connected to the adjacent curved segment on the same side of the lead assembly. One end of the remaining curved segments is connected to an adjacent curved segment on the same side of the lead assembly, and the other end is connected to another adjacent curved segment on the same side of the lead assembly.

7. The liquid crystal Fresnel lens according to claim 6, characterized in that, The curve segment is an arc, and the spacing between adjacent conductive lines is the same or at least some of the spacing between adjacent curve segments is not equal.

8. The liquid crystal Fresnel lens according to claim 1, characterized in that, A high-resistance film is disposed between the second electrode layer and the liquid crystal layer, or an insulating layer is disposed between the second electrode layer and the liquid crystal layer, or an insulating layer is disposed between the second electrode layer and the liquid crystal layer and a high-resistance film is disposed between the insulating layer and the liquid crystal layer.

9. The liquid crystal Fresnel lens according to any one of claims 1 to 8, characterized in that, The liquid crystal Fresnel lens also includes a conductive element, the projection of which on the second electrode layer is located at the junction of adjacent electrode units, and the conductive element is used to receive a third driving voltage.

10. Eyeglasses, characterized in that, The liquid crystal Fresnel lens includes any one of claims 1 to 9.

11. An electronic product, characterized in that, It includes a control circuit and a liquid crystal Fresnel lens according to any one of claims 1 to 9, wherein the control circuit is electrically connected to the liquid crystal Fresnel lens.

12. A liquid crystal Fresnel lens driving method, characterized in that, For driving a liquid crystal Fresnel lens according to any one of claims 1 to 9, wherein the first driving voltage is V1 and the second driving voltage is V2, the method includes the following steps: S1: Obtain the liquid crystal linear response voltage range of the liquid crystal Fresnel lens; S2: Obtain the minimum voltage V within the linear operating range of the liquid crystal based on the liquid crystal linear response voltage range. min and maximum voltage V max ; S3: Based on the minimum voltage V min and maximum voltage V max Adjusting the voltage difference between V1 and V2 adjusts the optical power of the liquid crystal lens and / or switches the state of the liquid crystal Fresnel lens between a positive and a negative lens, where V... min ≤V1≤V max And V min ≤V2≤V max .