Wide-angle lens

Through specific lens combinations and optical parameter design, the problem that wide-angle lenses cannot meet the large field of view and high resolution at the same time is solved, and the field of view is increased and resolution improved while maintaining good optical performance.

CN120507865APending Publication Date: 2025-08-19ASIA OPTICAL CO INC
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202410185585.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-02-19
Publication Date
2025-08-19

Smart Images

  • Figure CN120507865A_ABST
    Figure CN120507865A_ABST
Patent Text Reader

Abstract

A wide-angle lens includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and a sixth lens. The first lens has negative refractive power. The second lens has refractive power. The third lens has positive refractive power. The fourth lens has negative refractive power and comprises a concave surface facing the image side. The fifth lens element has refractive power and includes a convex surface facing the image side. The sixth lens element has refractive power and includes a convex surface facing the object side. The first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens are sequentially arranged from the object side to the image side along an optical axis.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The invention relates to a wide-angle lens. Background Art

[0002] The current development trend of wide-angle lenses is not only towards a larger field of view, but also requires high resolution to meet different application requirements. Existing wide-angle lenses can no longer meet today's needs. A new wide-angle lens architecture is needed to meet the requirements of both a large field of view and high resolution. Summary of the Invention

[0003] In view of this, a main object of the present invention is to provide a wide-angle lens with higher resolution.

[0004] The present invention provides a wide-angle lens comprising a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and a sixth lens. The first lens has negative refractive power. The second lens has refractive power. The third lens has positive refractive power. The fourth lens has negative refractive power and includes a concave surface facing the image side. The fifth lens has refractive power and includes a convex surface facing the image side. The sixth lens has refractive power and includes a convex surface facing the object side. The first lens, the second lens, the third lens, the fourth lens, the fifth lens, and the sixth lens are arranged in order along the optical axis from the object side to the image side. The wide-angle lens satisfies at least one of the following conditions: 1.03 ≤ BFL / f ≤ 1.22; 0.44 ≤ |f / R31| ≤ 0.57; 0.5 ≤ R52 / R61 ≤ 1.3; 17.2 degrees / mm ≤ FOV / f ≤ 17.5 degrees / mm; 45 degrees ≤ FOV / Fno ≤ 47 degrees; and 2.58 mm ≤ f / Fno ≤ 2.72 mm. Wherein, f is the effective focal length of the wide-angle lens, R31 is the radius of curvature of the object-side surface of the third lens element, R52 is the radius of curvature of the image-side surface of the fifth lens element, R61 is the radius of curvature of the object-side surface of the sixth lens element, BFL is the distance between the image-side surface of the sixth lens element and the imaging plane on the optical axis, FOV is the maximum field of view of the wide-angle lens, and Fno is the aperture value of the wide-angle lens. When the wide-angle lens of the present invention satisfies the above characteristics and at least one of the conditions, and no additional characteristics or conditions are required, the basic functions of the wide-angle lens of the present invention can be achieved.

[0005] The second lens has positive refractive power, the fifth lens has positive refractive power, and the sixth lens has positive refractive power.

[0006] The first lens includes a concave surface facing the image side, the second lens includes a convex surface facing the object side, the third lens is a biconvex lens and includes a convex surface facing the object side and another convex surface facing the image side, the fourth lens is a biconcave lens and may further include another concave surface facing the object side, and the fifth lens is a meniscus lens and may further include a concave surface facing the object side.

[0007] The second lens is a meniscus lens and may further include a concave surface facing the image side. The sixth lens is a meniscus lens and may further include a concave surface facing the image side.

[0008] The first lens is a meniscus lens and may further include a convex surface facing the object side.

[0009] The first lens is a biconcave lens and may further include another concave surface facing the object side.

[0010] The second lens is a biconvex lens and may further include another convex surface facing the image side. The sixth lens is a biconvex lens and may further include another convex surface facing the image side.

[0011] The method may further include an aperture disposed between the third lens and the fourth lens.

[0012] The wide-angle lens of the present invention satisfies at least one of the following conditions: 2≤Vd1 / Vd2≤3; 3.4≤TTL / BFL≤4.2; 2.2≤|R21 / R12|≤6.3; 1.35≤f1 / f4≤2.05; wherein Vd1 is the Abbe coefficient of the first lens element, Vd2 is the Abbe coefficient of the second lens element, TTL is the distance between the object side surface of the first lens element and the imaging plane on the optical axis, BFL is the distance between the image side surface of the sixth lens element and the imaging plane on the optical axis, R12 is the curvature radius of the image side surface of the first lens element, R21 is the curvature radius of the object side surface of the second lens element, f1 is the effective focal length of the first lens element, and f4 is the effective focal length of the fourth lens element.

[0013] The wide-angle lens of the present invention has the following beneficial effects: it has a large field of view and a high resolution while still having good optical performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to make the above-mentioned objects, features, and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings.

[0015] Figure 1 2 is a schematic diagram of the lens configuration and optical path of the first embodiment of the wide-angle lens according to the present invention.

[0016] Figure 2 、 3, 4, and 5 are respectively a field curvature diagram, a distortion diagram, a modulation transfer function diagram, and a through focus modulation transfer function diagram of the first embodiment of the wide-angle lens according to the present invention.

[0017] Figure 6 FIG. 4 is a schematic diagram of the lens configuration and optical path of a second embodiment of a wide-angle lens according to the present invention.

[0018] Figure 7 、 8 9 and 10 are respectively a field curvature diagram, a distortion diagram, a modulation transfer function diagram, and a defocus modulation transfer function diagram of the second embodiment of the wide-angle lens according to the present invention.

[0019] Figure 11 FIG. 4 is a schematic diagram of the lens configuration and optical path of a third embodiment of a wide-angle lens according to the present invention.

[0020] Figure 12 、 13 14 and 15 are respectively a field curvature diagram, a distortion diagram, a modulation transfer function diagram, and a defocus modulation transfer function diagram of the third embodiment of the wide-angle lens according to the present invention. DETAILED DESCRIPTION

[0021] The present invention provides a wide-angle lens, comprising: a first lens having negative refractive power; a second lens having refractive power; a third lens having positive refractive power; a fourth lens having negative refractive power, the fourth lens including a concave surface facing the image side; a fifth lens having refractive power, the fifth lens including a convex surface facing the image side; and a sixth lens having refractive power, the sixth lens including a convex surface facing the object side; wherein the first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens are arranged in sequence from the object side to the image side along the optical axis; wherein the wide-angle lens satisfies at least one of the following conditions: 1.03≤BFL / f≤1.22; 0.4 4≤|f / R31|≤0.57;0.5≤R52 / R61≤1.3;17.2 degrees / mm≤FOV / f≤17.5 degrees / mm;45 degrees≤FOV / Fno≤47 degrees;2.58mm≤f / Fno≤2.72mm;wherein, f is the effective focal length of the wide-angle lens, R31 is the radius of curvature of the object-side surface of the third lens element, R52 is the radius of curvature of the image-side surface of the fifth lens element, R61 is the radius of curvature of the object-side surface of the sixth lens element, BFL is the distance between the image-side surface of the sixth lens element and the imaging plane on the optical axis, FOV is the maximum field of view of the wide-angle lens, and Fno is the aperture value of the wide-angle lens. When the wide-angle lens of the present invention meets the above characteristics and at least one of the conditions, it is a preferred embodiment of the present invention.

[0022] Please refer to Table 1, Table 3, and Table 5 below, where Table 1, Table 3, and Table 5 are tables showing parameters of the various lenses of the wide-angle lens according to the first to third embodiments of the present invention.

[0023] Figure 1 、 6 11 and 12 are schematic diagrams of the lens configurations and optical paths of the first, second, and third embodiments of the wide-angle lens of the present invention, respectively. First lens elements L11, L21, and L31 have negative refractive power, their image-side surfaces S12, S22, and S32 are concave, and their object-side surfaces S11, S21, S31 and image-side surfaces S12, S22, and S32 are spherical.

[0024] The second lenses L12 , L22 , and L32 have positive refractive power, and their object-side surfaces S13 , S23 , and S33 are convex. The object-side surfaces S13 , S23 , and S33 and the image-side surfaces S14 , S24 , and S34 are all spherical surfaces.

[0025] The third lens L13, L23, and L33 are biconvex lenses with positive refractive power. Their object-side surfaces S15, S25, and S35 are convex, and their image-side surfaces S16, S26, and S36 are convex. All of the object-side surfaces S15, S25, and S35 and the image-side surfaces S16, S26, and S36 are spherical surfaces.

[0026] The fourth lens L14, L24, L34 is a biconcave lens with negative refractive power. Its object-side surfaces S18, S28, S38 are concave, and its image-side surfaces S19, S29, S39 are concave. All of the object-side surfaces S18, S28, S38 and the image-side surfaces S19, S29, S39 are spherical surfaces.

[0027] The fifth lens L15, L25, and L35 are meniscus lenses with positive refractive power. Their object-side surfaces S110, S210, and S310 are concave, and their image-side surfaces S111, S211, and S311 are convex. All of the object-side surfaces S110, S210, and S310 and the image-side surfaces S111, S211, and S311 are spherical surfaces.

[0028] The sixth lens L16, L26, L36 has positive refractive power, and its object-side surfaces S112, S212, S312 are convex, and the object-side surfaces S112, S212, S312 and image-side surfaces S113, S213, S313 are spherical surfaces.

[0029] In addition, the wide-angle lenses 1, 2, and 3 satisfy at least one of the following conditions (1) to (10):

[0030] 2 ≤ Vd1 / Vd2 ≤ 3; (1)

[0031] 3.4 ≤ TTL / BFL ≤ 4.2; (2)

[0032] 1.03 ≤ BFL / f ≤ 1.22; (3)

[0033] 0.44 ≤ |f / R31| ≤ 0.57; (4)

[0034] 0.5 ≤ R52 / R61 ≤ 1.3; (5)

[0035] 2.2 ≤ |R21 / R12| ≤ 6.3; (6)

[0036] 1.35 ≤ f1 / f4 ≤ 2.05; (7)

[0037] 17.2 degrees / mm≤FOV / f≤17.5 degrees / mm; (8)

[0038] 45 degrees ≤ FOV / Fno ≤ 47 degrees; (9)

[0039] 2.58 mm ≤ f / Fno ≤ 2.72 mm; (10)

[0040] Wherein, f is the effective focal length of the wide-angle lenses 1, 2, and 3 in the first to third embodiments, f1 is the effective focal length of the first lens L11, L21, and L31 in the first to third embodiments, f4 is the effective focal length of the fourth lens L14, L24, and L34 in the first to third embodiments, R12 is the curvature radius of the image-side surfaces S12, S22, and S32 of the first lens L11, L21, and L31 in the first to third embodiments, R21 is the curvature radius of the image-side surfaces S12, S22, and S32 of the first lens L11, L21, and L31 in the first to third embodiments, In the embodiments, the curvature radii S13, S23, and S33 of the object-side surfaces of the second lens elements L12, L22, and L32 are shown; R31 is the curvature radii S15, S25, and S35 of the object-side surfaces of the third lens elements L13, L23, and L33 in the first to third embodiments; R52 is the curvature radii S111, S211, and S311 of the image-side surfaces of the fifth lens elements L15, L25, and L35 in the first to third embodiments; and R61 is the curvature radii S111, S211, and S311 of the image-side surfaces of the sixth lens elements L15, L25, and L35 in the first to third embodiments. TTL is the distance between the object-side surfaces S11, S21, S31 of the first lens element L11, L21, L31 and the imaging surfaces IMA1, IMA2, IMA3 on the optical axes OA1, OA2, OA3 in the first to third embodiments. BFL is the distance between the image-side surfaces S113, S213, S313 of the sixth lens element L16, L26, L36 and the imaging surfaces IMA1, IMA2, IMA3 on the optical axes OA1, OA2, OA3 in the first to third embodiments. The spacing between IMA1, IMA2, and IMA3 on the optical axes OA1, OA2, and OA3, Vd1 is the Abbe coefficient of the first lens L11, L21, and L31 in the first to third embodiments, Vd2 is the Abbe coefficient of the second lens L12, L22, and L32 in the first to third embodiments, FOV is the maximum field of view of the wide-angle lenses 1, 2, and 3 in the first to third embodiments, and Fno is the aperture value of the wide-angle lenses 1, 2, and 3 in the first to third embodiments. This allows the wide-angle lenses 1, 2, and 3 to effectively improve the field of view, effectively improve the resolution, and effectively correct aberrations.

[0041] When condition (1): 2≤Vd1 / Vd2≤3 is met, chromatic aberration can be effectively reduced and resolution can be improved. When condition (2): 3.4≤TTL / BFL≤4.2 is met, back focus length can be effectively controlled to improve production yield. When condition (3): 1.03≤BFL / f≤1.22, condition (4): 0.44≤|f / R31|≤0.57 and condition (5): 0.5≤R52 / R61≤1.3 are met simultaneously, field curvature can be effectively reduced and resolution can be improved. When condition (6): 2.2≤|R21 / R12|≤6.3 is met, resolution can be effectively improved. When condition (7): 1.35≤f1 / f4≤2.05 is met, light collection capability can be effectively improved. When the following conditions are met simultaneously: (8) 17.2 degrees / mm ≤ FOV / f ≤ 17.5 degrees / mm, (9) 45 degrees ≤ FOV / Fno ≤ 47 degrees, and (10) 2.58 mm ≤ f / Fno ≤ 2.72 mm, the wide-angle lens aperture can be effectively increased, thus improving image brightness.

[0042] The first embodiment of the wide-angle lens of the present invention will now be described in detail. Figure 1 Wide-angle lens 1 includes, in order from the object side to the image side along optical axis OA1, first lens L11, second lens L12, third lens L13, aperture ST1, fourth lens L14, fifth lens L15, sixth lens L16, optical filter OF1, and cover glass CG1. When imaging, light from the object side is ultimately focused on imaging surface IMA1. According to the first to eighth paragraphs of the [Specific Implementation], the first lens L11 is a biconcave lens, and its object side surface S11 is a concave surface; the second lens L12 is a meniscus lens, and its image side surface S14 is a concave surface; the sixth lens L16 is a meniscus lens, and its image side surface S113 is a concave surface; the object side surface S114 and the image side surface S115 of the filter OF1 are both planes; the object side surface S116 and the image side surface S117 of the protective glass CG1 are both planes; by utilizing the above-mentioned lens, aperture ST1 and the design that satisfies at least one of conditions (1) to (10), the wide-angle lens 1 can effectively improve the field of view, effectively improve the resolution, and effectively correct aberrations. When the wide-angle lens of the present invention only satisfies the refractive surface shape characteristics in conditions (3), (4), (5), (8), (9) or (10) and the independent items, the basic actuation requirements can be met.

[0043] Table 1 Figure 1 Table of relevant parameters of each lens of medium wide-angle lens 1.

[0044] Table 1

[0045]

[0046] Table 2 shows the relevant parameter values of the wide-angle lens 1 of the first embodiment and the calculated values corresponding to conditions (1) to (10). It can be seen from Table 2 that the wide-angle lens 1 of the first embodiment can meet the requirements of conditions (1) to (10). Table 2

[0047]

[0048] In addition, the optical performance of the wide-angle lens 1 of the first embodiment can also meet the requirements. Figure 2 It can be seen that the field curvature of the wide-angle lens 1 of the first embodiment is between -0.06mm and 0.03mm. Figure 3 It can be seen that the distortion of the wide-angle lens 1 of the first embodiment is between -25% and 0%. Figure 4 It can be seen that the modulation transfer function value of the wide-angle lens 1 of the first embodiment is between 0.36 and 1.0. Figure 5 As can be seen, the modulation transfer function value of the wide-angle lens 1 of the first embodiment ranges from 0.0 to 0.83 when the focus offset is between -0.05mm and 0.05mm. Clearly, the field curvature and distortion of the wide-angle lens 1 of the first embodiment are effectively corrected, while the lens resolution and depth of focus also meet requirements, resulting in excellent optical performance.

[0049] The second embodiment of the wide-angle lens of the present invention will now be described in detail. Figure 6 Wide-angle lens 2 includes, in order from the object side to the image side along optical axis OA2, a first lens L21, a second lens L22, a third lens L23, an aperture ST2, a fourth lens L24, a fifth lens L25, a sixth lens L26, a filter OF2, and cover glass CG2. When imaging, light from the object side is ultimately focused on imaging surface IMA2. According to the first to eighth paragraphs of the [Specific Implementation], the first lens L21 is a meniscus lens, and its object side surface S21 is convex; the second lens L22 is a meniscus lens, and its image side surface S24 is concave; the sixth lens L26 is a meniscus lens, and its image side surface S213 is concave; the object side surface S214 and the image side surface S215 of the filter OF2 are both planes; the object side surface S216 and the image side surface S217 of the protective glass CG2 are both planes; by utilizing the above-mentioned lens, aperture ST2 and a design that satisfies at least one of conditions (1) to (10), the wide-angle lens 2 can effectively improve the field of view, effectively improve the resolution, and effectively correct aberrations. When the wide-angle lens of the present invention only satisfies condition (1) or condition (2) and the refractive surface shape characteristics in the independent item, the basic actuation requirements can be met.

[0050] Table 3 is Figure 6 Table of relevant parameters of each lens of medium wide-angle lens 2.

[0051] Table 3

[0052]

[0053]

[0054] Table 4 shows the relevant parameter values of the wide-angle lens 2 of the second embodiment and the calculated values corresponding to conditions (1) to (10). It can be seen from Table 4 that the wide-angle lens 2 of the second embodiment can meet the requirements of conditions (1) to (10). Table 4

[0055]

[0056] In addition, the optical performance of the wide-angle lens 2 of the second embodiment can also meet the requirements. Figure 7 It can be seen that the field curvature of the wide-angle lens 2 of the second embodiment is between -0.06mm and 0.04mm. Figure 8 It can be seen that the distortion of the wide-angle lens 2 of the second embodiment is between -25% and 0%. Figure 9 It can be seen that the modulation transfer function value of the wide-angle lens 2 of the second embodiment is between 0.33 and 1.0. Figure 10 As can be seen, the modulation transfer function value of the wide-angle lens 2 of the second embodiment ranges from 0.0 to 0.83 when the focus offset is between -0.05mm and 0.05mm. Clearly, the field curvature and distortion of the wide-angle lens 2 of the second embodiment are effectively corrected, while the lens resolution and depth of focus also meet requirements, resulting in excellent optical performance.

[0057] The third embodiment of the wide-angle lens of the present invention will now be described in detail. Figure 11 The wide-angle lens 3 includes, in order from the object side to the image side along optical axis OA3, a first lens L31, a second lens L32, a third lens L33, an aperture ST3, a fourth lens L34, a fifth lens L35, a sixth lens L36, a filter OF3, and a cover glass CG3. When imaging, light from the object side is ultimately focused on the imaging surface IMA3. According to the first to eighth paragraphs of the [Specific Implementation], the first lens L31 is a biconcave lens, and its object side surface S31 is concave; the second lens L32 is a biconvex lens, and its image side surface S34 is convex; the sixth lens L36 is a biconvex lens, and its image side surface S313 is convex; the object side surface S314 and the image side surface S315 of the filter OF3 are both planes; the object side surface S316 and the image side surface S317 of the protective glass CG3 are both planes; by utilizing the above-mentioned lenses, aperture ST3 and a design that satisfies at least one of conditions (1) to (10), the wide-angle lens 3 can effectively improve the field of view, effectively improve the resolution, and effectively correct aberrations. When the wide-angle lens of the present invention only satisfies condition (6) or condition (7) and the refractive surface shape characteristics in the independent item, the basic actuation requirements can be met.

[0058] Table 5 is a table of relevant parameters of each lens of the wide-angle lens 3 in Figure 11.

[0059] Table 5

[0060]

[0061] Table 6 shows the relevant parameter values of the wide-angle lens 3 of the third embodiment and the calculated values corresponding to conditions (1) to (10). It can be seen from Table 6 that the wide-angle lens 3 of the third embodiment can meet the requirements of conditions (1) to (10).

[0062] Table 6

[0063]

[0064] In addition, the optical performance of the wide-angle lens 3 of the third embodiment can also meet the requirements. Figure 12 It can be seen that the field curvature of the wide-angle lens 3 of the third embodiment is between -0.025mm and 0.03mm. Figure 13 It can be seen that the distortion of the wide-angle lens 3 of the third embodiment is between -30% and 0%. Figure 14 It can be seen that the modulation transfer function value of the wide-angle lens 3 of the third embodiment is between 0.37 and 1.0. Figure 15 As can be seen, the wide-angle lens 3 of the third embodiment has a modulation transfer function value between 0.01 and 0.85 when the focus offset is between -0.05mm and 0.05mm. Clearly, the wide-angle lens 3 of the third embodiment effectively corrects both field curvature and distortion, while also meeting requirements for lens resolution and depth of focus, resulting in superior optical performance.

[0065] Although the present invention has been disclosed above in terms of preferred embodiments, this is not intended to limit the present invention. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A wide-angle lens, characterized in that: include: The first lens has negative refractive power; The second lens has refractive power; The third lens has positive refractive power; The fourth lens has negative refractive power and includes a concave surface facing the image side; The fifth lens has refractive power, and the fifth lens includes a convex surface facing the image side; and The sixth lens has refractive power and includes a convex surface facing the object side; wherein the first lens, the second lens, the third lens, the fourth lens, the fifth lens, and the sixth lens are arranged in sequence from the object side to the image side along the optical axis; The wide-angle lens satisfies at least one of the following conditions: 1.03≤BFL / f≤1.22; 0.44≤|f / R31|≤0.57; 0.5≤R52 / R61≤1.3; 17.2 degrees / mm≤FOV / f≤17.5 degrees / mm; 45 degrees ≤ FOV / Fno ≤ 47 degrees; 2.58mm≤f / Fno≤2.72mm; Wherein, f is the effective focal length of the wide-angle lens, R31 is the curvature radius of the object side surface of the third lens, R52 is the curvature radius of the image side surface of the fifth lens, R61 is the curvature radius of the object side surface of the sixth lens, BFL is the distance between the image side surface of the sixth lens and the imaging plane on the optical axis, FOV is the maximum field of view of the wide-angle lens, and Fno is the aperture value of the wide-angle lens.

2. The wide-angle lens according to claim 1, wherein: The second lens has positive refractive power; The fifth lens has positive refractive power; and The sixth lens has positive refractive power.

3. The wide-angle lens according to claim 2, wherein: The first lens comprises a concave surface facing the image side; The second lens comprises a convex surface facing the object side; The third lens is a biconvex lens and includes a convex surface facing the object side and another convex surface facing the image side; The fourth lens is a biconcave lens and further includes another concave surface facing the object side; and The fifth lens is a meniscus lens and further includes a concave surface facing the object side.

4. The wide-angle lens according to claim 3, wherein: The second lens is a meniscus lens and further includes a concave surface facing the image side; and The sixth lens is a meniscus lens and further includes a concave surface facing the image side.

5. The wide-angle lens according to claim 4, wherein: The first lens is a meniscus lens and further includes a convex surface facing the object side.

6. The wide-angle lens according to claim 3, wherein: The first lens is a biconcave lens and further includes another concave surface facing the object side.

7. The wide-angle lens according to claim 3, wherein: The second lens is a biconvex lens and further includes another convex surface facing the image side; and The sixth lens is a biconvex lens and further includes another convex surface facing the image side.

8. The wide-angle lens according to claim 1, wherein: The invention further includes an aperture disposed between the third lens and the fourth lens.

9. The wide-angle lens according to any one of claims 1 to 8, wherein: The wide-angle lens meets at least one of the following conditions: 2≤Vd1 / Vd2≤3; 3.4≤TTL / BFL≤4.2; 2.2≤|R21 / R12|≤6.3; 1.35≤f1 / f4≤2.05; Wherein, Vd1 is the Abbe coefficient of the first lens, Vd2 is the Abbe coefficient of the second lens, TTL is the distance between the object side surface of the first lens and the imaging plane on the optical axis, BFL is the distance between the image side surface of the sixth lens and the imaging plane on the optical axis, R12 is the curvature radius of the image side surface of the first lens, R21 is the curvature radius of the object side surface of the second lens, f1 is the effective focal length of the first lens, and f4 is the effective focal length of the fourth lens.