Optical shooting imaging system
By designing a compact optical intake imaging system, using a small number of lenses and aspherical lenses, combined with a specific focal length and aperture stop, the problems of large number of lenses and total optical length in the prior art are solved, and excellent optical under small volumes are achieved Performance and compact construction.
Patent Information
- Application Number
- CN202411399826.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-09
- Publication Date
- 2025-01-03
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The lens set structure of the existing optical intake imaging system has the problem of large number of lenses and long total optical length, which leads to large volume, high cost and poor performance under small volumes.
Design an optical intake imaging system, including a first lens group, a second lens group, a third lens group, a fourth lens group, a third lens group and a fourth lens group arranged along the optical axis from the object side to the image side. It contains only one lens, and the focal length of each lens group meets specific conditions. Combined with the aperture stop and aspherical lens, it achieves a compact structure and excellent optical performance.
A compact structural design and excellent optical performance are achieved in small volumes, suitable for large image field applications such as SLR photography, with small number of lenses and light weight, meeting the appropriate power distribution.
Smart Images
Figure CN119247591A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of optical imaging, and in particular to an optical imaging system. Background Art
[0002] Some existing optical imaging systems use lens group structures that have a large number of lenses and a long total optical length, and their structures are bloated and cannot be reduced in size.
[0003] For example, in the document with publication number JP2013137411A, multiple embodiments are disclosed in which the total optical length is longer and is more suitable for optical systems with long flange distances, while in the document with publication number CN218866211U, multiple embodiments adopt an inner focusing optical system, which also has the problem of a longer total optical length and a large number of lenses. Summary of the invention
[0004] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention provides an optical imaging system with a compact structure and excellent optical performance under the premise of a small size.
[0005] An optical imaging system according to an embodiment of the present invention comprises a first lens group, a second lens group, a third lens group and a fourth lens group arranged in sequence from the object side to the image side along the optical axis; The third lens group includes only one lens, and the fourth lens group includes only one lens; The first lens group, the second lens group, the third lens group and the fourth lens group respectively satisfy the following conditional expressions: 0.8≤F1 / F≤2.0, -3.0≤F2 / F≤3.0, -5.0≤F3 / F≤-2.0, 0.5≤F4 / F≤4.0, in, F1: focal length of the first lens group; F2: focal length of the second lens group; F3: focal length of the third lens group; F4: focal length of the fourth lens group; F: is the focal length of the optical imaging system.
[0006] The optical imaging system according to the embodiment of the present invention has at least the following beneficial effects: the third lens group and the fourth lens group only include one lens, the structure is compact and the volume is small, and the first lens group, the second lens group, the third lens group and the fourth lens group meet the conditional formula, have a suitable optical focal length distribution, and can have excellent optical performance under the premise of a small volume.
[0007] According to some embodiments of the present invention, an aperture stop is provided between the first lens group and the second lens group.
[0008] According to some embodiments of the present invention, during the focusing process from infinity to close distance on the object side, the first lens group and the second lens group move along the optical axis toward the object side.
[0009] According to some embodiments of the present invention, during the process of focusing from infinity to a close distance on the object side, the first lens group, the second lens group, the third lens group, and the fourth lens group move along the optical axis toward the object side.
[0010] According to some embodiments of the present invention, from the object side to the image side, the first lens group includes, in sequence, a first lens having positive power, a second lens having negative power, and a third lens having positive power.
[0011] According to some embodiments of the present invention, from the object side to the image side, the second lens group sequentially includes a fourth lens having negative optical power and a fifth lens having positive optical power.
[0012] According to some embodiments of the present invention, the second lens group includes at least one aspherical lens.
[0013] According to some embodiments of the present invention, the first lens group includes 3 lenses, the second lens group includes 2 lenses, the third lens group includes 1 lens, and the fourth lens group includes 1 lens. From the object side to the image side, the lenses are numbered L1 to L7 in sequence.
[0014] According to some embodiments of the present invention, both lens L1 and lens L7 satisfy the following conditional formula: 1.8≤Nd, wherein Nd is the refractive index of the lens material when transmitting light with a wavelength of 587.56 nm.
[0015] According to some embodiments of the present invention, lens L2, lens L4 and lens L6 all satisfy the following conditional formula: Vd≤40, wherein Vd is the Abbe number of the lens material when transmitting light with a wavelength of 587.56 nm.
[0016] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments, wherein: Figure 1 is a schematic diagram of a first structure of an optical imaging system according to an embodiment of the present invention; Figure 2 for Figure 1 Spherical aberration diagram of the system structure; Figure 3 for Figure 1 Astigmatism field curvature diagram of the system structure; Figure 4 for Figure 1 Distortion diagram of the system structure; Figure 5 is a schematic diagram of a second structure of the optical imaging system according to an embodiment of the present invention; Figure 6 for Figure 5 Spherical aberration diagram of the system structure; Figure 7 for Figure 5 Astigmatism field curvature diagram of the system structure; Figure 8 for Figure 5 Distortion diagram of the system structure; Fig. 9 is a schematic diagram of a third structure of the optical imaging system according to an embodiment of the present invention; Fig.10 for Fig. 9 Spherical aberration diagram of the system structure; Fig.11 for Fig. 9 Astigmatism field curvature diagram of the system structure; Fig.12 for Fig. 9 Distortion diagram of the system structure.
[0018] Figure Number: A first lens group 100 , a second lens group 200 , a third lens group 300 , a fourth lens group 400 , and an aperture stop 500 . DETAILED DESCRIPTION
[0019] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.
[0020] In the description of the present invention, it should be understood that descriptions involving orientation, such as orientation or positional relationship indicated as up, down, etc., are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.
[0021] In the description of the present invention, "a plurality" means more than two. If there is a description of "first" or "second", it is only used for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.
[0022] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.
[0023] Some existing large-aperture optical lenses for photography have a lens group structure with a large number of lenses and high costs. After reducing the number of lenses, the performance is poor at large apertures and the resolution is low.
[0024] Some existing optical imaging systems use lens group structures that have a large number of lenses and a long total optical length, and their structures are bloated and cannot be reduced in size.
[0025] For example, in the document with publication number JP2013137411A, multiple embodiments are disclosed in which the total optical length is longer and is more suitable for optical systems with long flange distances, while in the document with publication number CN218866211U, multiple embodiments adopt an inner focusing optical system, which also has the problem of a longer total optical length and a large number of lenses.
[0026] Reference Figure 1 As shown, an optical imaging system according to an embodiment of the present invention comprises a first lens group (100), a second lens group (200), a third lens group (300) and a fourth lens group (400) which are arranged in sequence from the object side to the image side along the optical axis; The third lens group (300) includes only one lens, and the fourth lens group (400) includes only one lens; The first lens group (100), the second lens group (200), the third lens group (300) and the fourth lens group (400) respectively satisfy the following conditional expressions: 0.8≤F1 / F≤2.0(1) -3.0≤F2 / F≤3.0(2) -5.0≤F3 / F≤-2.0(3) 0.5≤F4 / F≤4.0(4) in, F1: is the focal length of the first lens group (100); F2: is the focal length of the second lens group (200); F3: is the focal length of the third lens group (300); F4: is the focal length of the fourth lens group (400); F: is the focal length of the optical imaging system.
[0027] The optical imaging system of the embodiment of the present invention is mainly suitable for applications with a large image field, such as single-lens reflex photography, etc. Under the large image field, it has a compact size.
[0028] For example, the third lens group 300 and the fourth lens group 400 include only one lens, have a compact structure and a small size, and the first lens group 100, the second lens group 200, the third lens group 300 and the fourth lens group 400 meet the above conditional formula, have a suitable optical power distribution, and can have excellent optical performance under the premise of a small size.
[0029] It should be understood that an aperture stop 500 is provided between each lens group. Preferably, an aperture stop 500 is provided between the first lens group 100 and the second lens group 200 .
[0030] It can be understood that the optical imaging system of the embodiment of the present invention is preferably provided with 7 lenses, wherein the first lens group 100 includes 3 lenses, the second lens group 200 includes 2 lenses, and the third lens group 300 and the fourth lens group 400 each include 1 lens. In the embodiment, along the direction from the object side to the image side of the optical axis, the above lenses are numbered L1 to L7 in sequence.
[0031] Preferably, the lens L1 and the lens L7 also satisfy the following conditional formula: 1.8≤Nd(5), Wherein, Nd is the refractive index of the lens material when transmitting light with a wavelength of 587.56 nm.
[0032] Preferably, the lenses L2, L4 and L6 also satisfy the following conditional formula: Vd≤40(6) Wherein, Vd is the Abbe number of the lens material when transmitting light with a wavelength of 587.56 nm.
[0033] In the embodiment, the first lens group 100 is also recorded as G1, the second lens group 200 is also recorded as G2, the third lens group 300 is also recorded as G3, and the fourth lens group 400 is also recorded as G4. Therefore, among the above lenses, the lens G1L1 and the lens G4L7 satisfy the conditional formula 1.8≤Nd. The lens G1L2, the lens G2L4 and the lens G3L6 satisfy the conditional formula Vd≤40.
[0034] It is understandable that the first lens group 100 includes three lenses, and the specific distribution method can be from the object side to the image side along the optical axis. The first lens group 100 includes a first lens with positive focal power, a second lens with negative focal power, and a third lens with positive focal power in sequence. It should be understood that the first lens here is only a naming method for distinguishing the lenses in the first lens group 100, and the first of the first lens does not limit the arrangement position of the lens. Similarly, the second lens and the third lens are also the same. In a specific embodiment, the arrangement position of the lenses is marked with L1, L2, Ln, etc.
[0035] It is understandable that the second lens group 200 includes two lenses, and the specific distribution method can be that along the optical axis direction from the object side to the image side, the second lens group 200 includes a fourth lens with negative optical power and a fifth lens with positive optical power in sequence. Preferably, the second lens group 200 includes an aspherical lens.
[0036] In an embodiment, the aspherical lens satisfies the following curve driving equation: , in, R: is the radius of curvature of the aspheric surface; Y: radial coordinate; K: is the cone coefficient of the quadratic surface; Z: is the sagittal height of the surface along the optical axis; A: 4th order aspheric coefficient; B: 6th order aspheric coefficient; C: 8th order aspheric coefficient; D: is the 10th order aspheric coefficient.
[0037] It can be understood that in the optical imaging system of the embodiment of the present invention, there are two focusing methods. The first focusing method is: during the focusing process from infinity to close distance on the object side, the first lens group 100 and the second lens group 200 move along the optical axis toward the object side. The second focusing method is: during the focusing process from infinity to close distance on the object side, the first lens group 100, the second lens group 200, the third lens group 300 and the fourth lens group 400 move along the optical axis toward the object side.
[0038] Three specific embodiments with parameters are provided below.
[0039] Embodiment 1: The parameters of the optical imaging system of this embodiment are as follows: EFL:40mm; Fno: 2.8; 2ω: 56.1°; Among them, EFL is the effective focal length of the optical lens, Fno is the aperture, and 2ω is the field of view.
[0040] F1 / F=1.4, satisfies conditional formula (1); F2 / F=1.7, satisfies conditional formula (2); F3 / F=-2.4, satisfies conditional formula (3); F4 / F=2.4, satisfies conditional formula (4); Nd =1.83 (G1L1), Nd=1.90 (G4L7) satisfies conditional formula (5); Vd=30.0 (G1L2), Vd=33.8 (G2L4), Vd=28.3 (G3L6), satisfies conditional formula (6).
[0041] It should be understood that in the imaging system shown in the drawings, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. For example, lens G2L4 refers to the 4th lens, and the lens belongs to the second lens group 200. Among them, the image plane is denoted as IMA, and the protective glass is denoted as CG.
[0042] The parameters of the optical imaging system of this embodiment also satisfy the contents of Table 1, Table 2 and Table 3.
[0043] Table 1 Parameters of the optical imaging system of Example 1
[0044] In Table 1, Image is the image side; Radius is the radius of curvature of each surface; Thickness is the distance between each lens and the thickness of the lens; Nd is the refractive index of each glass of d line; Vd is the Abbe number of the glass; ASP indicates that the surface is aspherical.
[0045] Table 2 Focus interval parameters of the optical imaging system of Example 1
[0046] In Table 2, FAR stands for far side, that is, the lens focuses on far view; NEAR stands for near side, that is, the lens focuses on near view.
[0047] Table 3 Aspherical lens parameters of the optical imaging system of Example 1
[0048] In Table 3, R is the radius of curvature of the aspheric surface; K is the conic coefficient of the quadratic surface; A is the 4th-order aspheric coefficient; B is the 6th-order aspheric coefficient; C is the 8th-order aspheric coefficient; and D is the 10th-order aspheric coefficient.
[0049] Among them, 2.9710e-006 refers to 2.9710×10 -6 , and the same goes for the rest.
[0050] The lens arrangement structure of the optical imaging system of Example 1 can refer to Figure 1 As shown. And Figure 2 , Figure 3 , Figure 4 The spherical aberration, astigmatism field curvature and distortion diagram of the optical imaging system of Example 1 are shown.
[0051] The third lens group 300 and the fourth lens group 400 of Example 1 each include only one lens, are light in weight and small in number, have a compact structure, and can have excellent optical performance under the premise of a small volume. Each lens group of Example 1 satisfies the conditional formula and has a reasonable optical power distribution.
[0052] It is important to understand that Figure 1 In the embodiment, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. The image plane is denoted as IMA, and the protective glass is denoted as CG.
[0053] Embodiment 2: The parameters of the optical imaging system of this embodiment are as follows: EFL:40mm; Fno: 2.8; 2ω: 55.6°; Among them, EFL is the effective focal length of the optical lens, Fno is the aperture, and 2ω is the field of view.
[0054] F1 / F=1.3, satisfies conditional formula (1); F2 / F=1.7, satisfies conditional formula (2); F3 / F=-3.6, satisfies conditional formula (3); F4 / F=3.8, satisfies conditional formula (4); Nd =1.88 (G1L1), Nd=1.85 (G4L7) satisfies conditional formula (5); Vd=30.0 (G1L2), Vd=33.8 (G2L4), Vd=25.5 (G3L6), satisfies conditional formula (6).
[0055] It should be understood that in the imaging system shown in the drawings, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. For example, lens G2L4 refers to the 4th lens, and the lens belongs to the second lens group 200. Among them, the image plane is denoted as IMA, and the protective glass is denoted as CG.
[0056] The parameters of the optical imaging system of this embodiment also satisfy the contents of Table 4, Table 5 and Table 6.
[0057] Table 4 Parameters of the optical imaging system of Example 2
[0058] In Table 4, Image is the image side; Radius is the radius of curvature of each surface; Thickness is the distance between each lens and the thickness of the lens; Nd is the refractive index of each glass of d line; Vd is the Abbe number of the glass; ASP indicates that the surface is aspherical.
[0059] Table 5 Focus interval parameters of the optical imaging system of Example 2
[0060] In Table 5, FAR stands for far side, that is, the lens focuses on far view; NEAR stands for near side, that is, the lens focuses on near view.
[0061] Table 6 Aspherical lens parameters of the optical imaging system of Example 2
[0062] In Table 6, R is the radius of curvature of the aspheric surface; K is the conic coefficient of the quadratic surface; A is the 4th-order aspheric coefficient; B is the 6th-order aspheric coefficient; C is the 8th-order aspheric coefficient; and D is the 10th-order aspheric coefficient.
[0063] Among them, 1.6866e-006 refers to 1.6866×10 -6 , and the same goes for the rest.
[0064] The lens arrangement structure of the optical imaging system of Example 2 can refer to Figure 5 As shown. And Figure 6 , Figure 7 , Figure 8 The spherical aberration, astigmatism field curvature and distortion diagram of the optical imaging system of Example 2 are shown.
[0065] The third lens group 300 and the fourth lens group 400 of Example 2 each include only one lens, are light in weight and small in number, have a compact structure, and can have excellent optical performance under the premise of a small volume. Each lens group of Example 2 satisfies the conditional formula and has a reasonable optical power distribution.
[0066] It is important to understand that Figure 5 In the embodiment, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. The image plane is denoted as IMA, and the protective glass is denoted as CG.
[0067] Embodiment 3: The parameters of the optical imaging system of this embodiment are as follows: EFL:40mm; Fno: 2.8; 2ω: 55.9°; Among them, EFL is the effective focal length of the optical lens, Fno is the aperture, and 2ω is the field of view.
[0068] F1 / F=1.09, satisfies conditional formula (1); F2 / F=-1.95, satisfies conditional formula (2); F3 / F=-4.03, satisfies conditional formula (3); F4 / F=0.93, satisfies conditional formula (4); Nd =1.83(G1L1), Nd=1.83(G4L7)satisfies conditional formula (5); Vd=30.0(G1L2), Vd=36.3(G2L4), Vd=25.5(G3L6)satisfies conditional formula (6).
[0069] It should be understood that in the imaging system shown in the drawings, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. For example, lens G2L4 refers to the 4th lens, and the lens belongs to the second lens group 200. Among them, the image plane is denoted as IMA, and the protective glass is denoted as CG.
[0070] The parameters of the optical imaging system of this embodiment also satisfy the contents of Table 7, Table 8 and Table 9.
[0071] Table 7 Parameters of the optical imaging system of Example 3
[0072] In Table 7, Image is the image side; Radius is the radius of curvature of each surface; Thickness is the distance between each lens and the thickness of the lens; Nd is the refractive index of each glass of d line; Vd is the Abbe number of the glass; ASP indicates that the surface is aspherical.
[0073] Table 8 Focus interval parameters of the optical imaging system of Example 3
[0074] In Table 8, FAR stands for far side, that is, the lens focuses on far view; NEAR stands for near side, that is, the lens focuses on near view.
[0075] Table 9 Aspherical lens parameters of the optical imaging system of Example 3
[0076] In Table 9, R is the radius of curvature of the aspheric surface; K is the cone coefficient of the quadratic surface; A is the 4th-order aspheric coefficient; B is the 6th-order aspheric coefficient; C is the 8th-order aspheric coefficient; and D is the 10th-order aspheric coefficient.
[0077] Among them, 1.59e-004 refers to 1.59×10 -4 , and the same goes for the rest.
[0078] The lens arrangement structure of the optical imaging system of Example 3 can refer to Fig. 9 As shown. And Fig.10 , Fig.11 , Fig.12 The spherical aberration, astigmatism field curvature and distortion diagram of the optical imaging system of Example 3 are shown.
[0079] The third lens group 300 and the fourth lens group 400 of Example 3 each include only one lens, are light in weight and small in number, have a compact structure, and can have excellent optical performance under the premise of a small volume. Each lens group of Example 3 satisfies the conditional formula and has a reasonable optical power distribution.
[0080] It is important to understand that Fig. 9 In the embodiment, the first lens group 100 is also denoted as G1, the second lens group 200 is also denoted as G2, the third lens group 300 is also denoted as G3, and the fourth lens group 400 is also denoted as G4. In the entire system, the order of lens arrangement from the object side to the image side is L1 for the first lens, L2 for the second lens, and Ln for the nth lens in this order. The image plane is denoted as IMA, and the protective glass is denoted as CG.
[0081] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in the relevant technical field without departing from the purpose of the present invention.
Claims
1. An optical imaging system, characterized in that: include: A first lens group (100), a second lens group (200), a third lens group (300) and a fourth lens group (400) are arranged in sequence from the object side to the image side along the optical axis; The third lens group (300) includes only one lens, and the fourth lens group (400) includes only one lens; The first lens group (100), the second lens group (200), the third lens group (300) and the fourth lens group (400) respectively satisfy the following conditional expressions: 0.8≤F1 / F≤2.0, -3.0≤F2 / F≤3.0, -5.0≤F3 / F≤-2.0, 0.5≤F4 / F≤4.0, in, F1: is the focal length of the first lens group (100); F2: is the focal length of the second lens group (200); F3: is the focal length of the third lens group (300); F4: is the focal length of the fourth lens group (400); F: is the focal length of the optical imaging system.
2. The optical imaging system according to claim 1, characterized in that: An aperture stop (500) is provided between the first lens group (100) and the second lens group (200).
3. The optical imaging system according to claim 1, characterized in that: In the process of focusing from infinity to a close distance on the object side, the first lens group (100) and the second lens group (200) move along the optical axis toward the object side.
4. The optical imaging system according to claim 1, characterized in that: During the process of focusing from infinity to a close distance on the object side, the first lens group (100), the second lens group (200), the third lens group (300) and the fourth lens group (400) move along the optical axis toward the object side.
5. The optical imaging system according to claim 1, characterized in that: From the object side to the image side, the first lens group (100) comprises, in sequence, a first lens having positive focal power, a second lens having negative focal power, and a third lens having positive focal power.
6. The optical imaging system according to claim 1, characterized in that: From the object side to the image side, the second lens group (200) comprises, in sequence, a fourth lens having negative optical power and a fifth lens having positive optical power.
7. The optical imaging system according to claim 6, characterized in that: The second lens group (200) comprises at least one aspherical lens.
8. The optical imaging system according to claim 1, characterized in that: The first lens group (100) comprises three lenses, the second lens group (200) comprises two lenses, the third lens group (300) comprises one lens, and the fourth lens group (400) comprises one lens. From the object side to the image side, the lenses are numbered L1 to L7 in sequence.
9. The optical imaging system according to claim 8, characterized in that: Both lens L1 and lens L7 satisfy the following conditional formula: 1.8≤Nd, Wherein, Nd is the refractive index of the lens material when transmitting light with a wavelength of 587.56 nm.
10. The optical imaging system according to claim 8, characterized in that: Lens L2, lens L4 and lens L6 all satisfy the following conditional formula: Vd≤40, Wherein, Vd is the Abbe number of the lens material when transmitting light with a wavelength of 587.56 nm.