WO2021114782A1 - 紧凑型长焦镜头 - Google Patents

紧凑型长焦镜头 Download PDF

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Publication number
WO2021114782A1
WO2021114782A1 PCT/CN2020/114609 CN2020114609W WO2021114782A1 WO 2021114782 A1 WO2021114782 A1 WO 2021114782A1 CN 2020114609 W CN2020114609 W CN 2020114609W WO 2021114782 A1 WO2021114782 A1 WO 2021114782A1
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Prior art keywords
lens
compact telephoto
object side
compact
light
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PCT/CN2020/114609
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English (en)
French (fr)
Inventor
田国兵
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瑞泰光学(常州)有限公司
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Publication of WO2021114782A1 publication Critical patent/WO2021114782A1/zh

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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/001Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras
    • G02B13/0015Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design
    • G02B13/002Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design having at least one aspherical surface
    • G02B13/004Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design having at least one aspherical surface having four lenses
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/18Optical objectives specially designed for the purposes specified below with lenses having one or more non-spherical faces, e.g. for reducing geometrical aberration

Definitions

  • the invention relates to the field of optical lenses, in particular to a compact telephoto lens.
  • the photosensitive devices of general photographic lenses are nothing more than photosensitive coupled devices (Charge Coupled Devic, CCD) or complementary metal oxide semiconductor devices (Complementary Metal Oxide Semiconductor).
  • CCD Charge Coupled Devic
  • CCD complementary metal oxide semiconductor
  • CMOS Sensor Metal-Oxide Se Miconductor Sensor
  • the pixel size of photosensitive devices has been reduced, and nowadays electronic products are developing trends with good functions, light, thin and short appearance, so ,
  • the miniaturized camera lens with good image quality has become the mainstream in the current market.
  • the miniaturized photographic lens load needs to have high spatial resolution, and the optical system is required to have a long focal length.
  • the current miniaturized photographic lens does not have a long focal length and cannot meet the needs of consumers.
  • the object of the present invention is to provide a compact telephoto lens capable of realizing a long focal length.
  • the present invention provides a compact telephoto lens, which includes an aperture, a secondary lens, and a primary lens in sequence from the object side to the image side.
  • the primary lens includes a first lens and a second lens.
  • the mirror includes a third lens, the first lens and the third lens are Mankin lenses, the image side surface of the first lens is a reflective surface, the object side surface of the third lens is a reflective surface, and the second lens
  • the lens is a transmissive lens, the light is reflected by the first lens to the third lens, the third lens reflects the light to the second lens, and the light is refracted on the image surface by the second lens Imaging.
  • the secondary mirror further includes a fourth lens, and the light rays are refracted by the fourth lens and then enter the first lens.
  • the third lens and the fourth lens are an integral structure.
  • the first lens and the second lens are an integral structure.
  • the compact telephoto lens further includes a field lens, and the field lens is arranged between the main lens and the image plane.
  • the effective diameter of the image side surface of the first lens is D1
  • the effective diameter of the object side surface of the third lens is D2
  • the first lens and the third lens satisfy the following relationship: D2/D1 ⁇ 0.70.
  • the first lens and the third lens satisfy the following relational expression: 0.35 ⁇ D2/D1 ⁇ 0.60.
  • the compact telephoto lens further includes a light-shielding sheet, and the light-shielding sheet and the diaphragm overlap in positions along the optical axis.
  • the F-number of the compact telephoto lens is less than or equal to 2.50.
  • the focal length of the compact telephoto lens is f
  • the total optical length of the compact telephoto lens is TTL
  • the total optical length is from the object side of the secondary lens to the image plane.
  • the compact telephoto lens satisfies the following relationship: 1.11 ⁇ f/TTL ⁇ 4.44.
  • the outer edge of the object side of the fourth lens is closer to the object side than the outer edge of the object side of the third lens.
  • the radius of curvature of the object side surface of the fourth lens is R1
  • the radius of curvature of the image side surface of the fourth lens is R2, which satisfies the conditional formula: 0.00 ⁇ R1/R2 ⁇ 80.00.
  • the compact telephoto lens satisfies the conditional formula: 0.50 ⁇ R1/R2 ⁇ 60.00.
  • the focal length of the first lens is f2
  • the focal length of the third lens in the opposite direction is f5, which satisfies the conditional formula: 2.00 ⁇ f5/f2 ⁇ 6.00.
  • the compact telephoto lens satisfies the conditional formula: 3.00 ⁇ f5/f2 ⁇ 5.00.
  • the focal length of the second lens is f6, and the focal length of the field lens is f7, which satisfies the conditional formula: -70.00 ⁇ f6/f7 ⁇ 50.00.
  • the compact telephoto lens satisfies the conditional formula: -55.00 ⁇ f6/f7 ⁇ 35.00.
  • the compact telephoto lens provided by the present invention increases the diffraction limit of the lens and realizes a long focal length by setting the optical path composed of the first, second and third lenses, and has a compact structure and a small volume.
  • FIG. 1 is a schematic structural diagram of a compact telephoto lens according to a first embodiment of the present invention
  • FIG. 2 is a schematic diagram of the propagation of a single beam of light in the compact telephoto lens shown in FIG. 1;
  • FIG. 3 is a schematic diagram of the propagation of multiple light beams in the compact telephoto lens shown in FIG. 1;
  • FIG. 4 is a schematic diagram of axial aberration of the compact telephoto lens shown in FIG. 1;
  • Fig. 5 is a schematic diagram of the chromatic aberration of magnification of the compact telephoto lens shown in Fig. 1;
  • Fig. 6 is a schematic diagram of field curvature and distortion of the compact telephoto lens shown in Fig. 1;
  • FIG. 7 is a schematic structural diagram of a compact telephoto lens according to a second embodiment of the present invention.
  • FIG. 8 is a schematic diagram of axial aberration of the compact telephoto lens shown in FIG. 7;
  • FIG. 9 is a schematic diagram of the chromatic aberration of magnification of the compact telephoto lens shown in FIG. 7;
  • FIG. 10 is a schematic diagram of field curvature and distortion of the compact telephoto lens shown in FIG. 7;
  • FIG. 11 is a schematic structural diagram of a compact telephoto lens according to a third embodiment of the present invention.
  • FIG. 12 is a schematic diagram of axial aberration of the compact telephoto lens shown in FIG. 11;
  • FIG. 13 is a schematic diagram of the chromatic aberration of magnification of the compact telephoto lens shown in FIG. 11;
  • Fig. 14 is a schematic diagram of field curvature and distortion of the compact telephoto lens shown in Fig. 11.
  • the compact telephoto lens 100 provided according to the present invention includes an aperture 20, a secondary lens 30, a primary lens 40, and a field lens 50, which are arranged in sequence from the object side to the image side, and the light shielding film 10
  • the optical filter 60 may be arranged between the field lens 50 and the image plane 70 to overlap the diaphragm 20 in the direction along the optical axis OO', and the field lens 50 is used to further eliminate aberrations.
  • the field lens 50 may not be provided, and only the primary mirror 40 and the secondary mirror 30 are used to eliminate aberrations.
  • the primary lens 40 includes a first lens 41 and a second lens 42
  • the secondary lens 30 includes a third lens 32 and a fourth lens 31
  • the first lens 41 and the third lens 32 are both Mankind lenses.
  • the surface of the first lens 41 close to the image surface is a reflective surface
  • the surface of the third lens 32 close to the object side is a reflective surface.
  • the first lens 41 and the second lens 42 are an integral structure, the dotted line in the figure indicates the virtual dividing line between the two, and the first lens 41 extends outward from the edge of the second lens 42
  • the first lens and the second lens may be a separate structure, that is, two lenses are connected; the third lens 32 and the fourth lens 31 are an integral structure, so The fourth lens 31 extends outward from the edge of the third lens 32.
  • the fourth lens 31 may not be provided, and the light L is directly incident from the first lens 41.
  • the light-shielding sheet 10 blocks the incident light L at the corresponding position, so that the incident light L is a hollow ring.
  • the outer diameter of the light-shielding sheet 10 is greater than the outer diameter of the reflective surface of the secondary mirror 30, which is more conducive to reducing stray light; in other implementations
  • the light shielding sheet 10 may not be provided, and only the reflection surface of the secondary mirror 30 blocks the light in the central area so that the incident light L has a ring shape.
  • the first lens 41 includes a first surface 411 close to the object side and a second surface 412 close to the image side.
  • the second lens 42 includes a third surface 421 close to the object side and a fourth surface 421 close to the image side.
  • Surface 422 said first surface 411, said third surface 421, and said fourth surface 422 are all transmissive surfaces
  • said second surface 412 is a reflective surface
  • said first surface 411 and said third surface 421 are both concave surfaces and are connected together
  • the second surface 412 and the fourth surface 422 are convex surfaces and are connected together.
  • the third lens 32 includes a fifth surface 321 close to the object side and a sixth surface 322 close to the image side.
  • the fourth lens 31 includes a seventh surface 311 close to the object side and an eighth surface 312 close to the image side.
  • the fifth surface 321 is a reflective surface
  • the sixth surface 322, the seventh surface 311, and the eighth surface 312 are all transmissive surfaces
  • the fifth surface 321 and the seventh surface 311 are inner surfaces.
  • the fifth surface 321 and the seventh surface 311 are arranged in a step shape
  • the sixth surface 322 and the eighth surface 312 are both convex surfaces and are connected together. It can be understood that the third lens 32 has a ring shape, and the center blank is filled by the fourth lens 31.
  • the image side surface of the third lens 32 and the image side surface of the fourth lens 31 form a convex surface.
  • the outer edge of the fifth surface 321 is closer to the object side than the outer edge of the seventh surface 311, which helps reduce the difficulty of processing the secondary mirror; in other embodiments, the seventh surface
  • the outer edge of 311 may also be closer to the object side than the outer edge of the fifth surface.
  • the field lens 50 includes a ninth surface 51 close to the main mirror 40 and a tenth surface 52 far from the main mirror 40.
  • the ninth surface 51 and the tenth surface 52 are both transmissive surfaces, and the ninth surface 51 is a concave surface.
  • the tenth surface 52 is a convex surface.
  • the light L enters the fourth lens 41 through the aperture 20, and the light L is refracted by the seventh surface 311 and the eighth surface 312. Enter the first surface 411 of the first lens 41; then, the light L is refracted by the first surface 411 and then enters the second surface 412, and the second surface 412 transmits the light L is reflected back to the first surface 411 and refracted to the sixth surface 322 of the third lens 32; then, the sixth surface 322 refracts the light L to the fifth surface 321, and the The fifth surface 321 reflects the light L back to the sixth surface 322, and the sixth surface 322 refracts the light L to the second lens 42; finally, the light L passes through the first lens in turn.
  • the light L passes through the optical filter 60 and forms an image on the image plane 70.
  • the propagation path of the light L in the compact telephoto lens 100 is to pass through the fourth lens 31, hit the first lens 41, and be reflected by the first lens 41 to the third lens 32, and then by the third lens 32 is reflected to the second lens 42, passes through the second lens 42 to the field lens 50, and then passes through the field lens 50 to the image surface 70.
  • the effective diameter of the image side surface of the first lens 41 (the maximum diameter of the optical region for actual light reflection) is D1
  • the effective diameter of the object side surface of the third lens 32 is D2
  • the first lens 41 and the third lens 32 satisfy the following relationship: D2/D1 ⁇ 0.7, that is, the blocking ratio of the compact telephoto lens 100 is less than or equal to 0.7.
  • the first lens 41 and the third lens 32 satisfy the following relationship: 0.35 ⁇ D2/D1 ⁇ 0.60, that is, the blocking ratio of the compact telephoto lens 100 is not less than 0.35 and less than or equal to 0.60.
  • D1 9.889mm
  • D2 4.449mm
  • the blocking ratio is equal to 0.45
  • the optical performance is excellent.
  • the aperture F number of the compact telephoto lens 100 is less than or equal to 2.50. Large aperture, good imaging performance. Preferably, the aperture F number is less than or equal to 2.2.
  • the focal length of the compact telephoto lens 100 as f
  • the focal length of the fourth lens 31 as f1
  • f1 which satisfies the relationship -35.00 ⁇ f1/f ⁇ 5.00
  • the focal length of the compact telephoto lens 100 as f
  • the focal length of the first lens 41 as f2
  • the ratio of the focal length f2 of the first lens 41 to the total focal length f of the system is specified.
  • the spherical aberration and field curvature of the system can be effectively balanced within the scope of the conditional formula.
  • the focal length of the compact telephoto lens 100 as f
  • the focal length of the inverted first lens 41 as f3 which satisfies the relation -1.80 ⁇ f3/f ⁇ -0.80.
  • the reasonable distribution of the optical power makes the system better High imaging quality and low sensitivity.
  • the focal length of the compact telephoto lens 100 as f
  • the focal length of the inverted third lens 32 as f5
  • the reasonable distribution of the optical power enables the system to have better imaging Quality and low sensitivity.
  • the focal length of the compact telephoto lens 100 as f
  • the focal length of the second lens 42 as f6, which satisfies the relationship -20.00 ⁇ f6/f ⁇ 25.00, and specifies the ratio of the focal length f6 of the second lens 42 to the total focal length f of the system.
  • the spherical aberration and field curvature of the system can be effectively balanced within the scope of the conditional formula.
  • R1 the radius of curvature of the object side surface of the fourth lens 31 as R1
  • R2 the radius of curvature of the image side surface of the fourth lens 31
  • R1/R2 the radius of curvature of the image side surface of the fourth lens 31
  • the focal length of the first lens 41 as f2
  • the focal length of the inverted third lens 32 as f5, which satisfies the conditional formula: 2.00 ⁇ f5/f2 ⁇ 6.00.
  • it is beneficial to increase the overall compact telephoto lens Focal length; preferably, 3.00 ⁇ f5/f2 ⁇ 5.00; in this embodiment, f5/f2 4.404.
  • the focal length of the second lens 42 as f6, and the focal length of the field lens 50 as f7, which satisfies the conditional formula: -70.00 ⁇ f6/f7 ⁇ 50.00.
  • f6/f7 -49.155.
  • the focal length of the compact telephoto lens 100 as f
  • the total optical length of the compact telephoto lens 100 (the distance from the object side of the secondary lens 30 to the image plane along the direction parallel to the optical axis OO', In this embodiment, the distance from the outer edge of the object side of the fourth lens 31 to the imaging surface along the optical axis OO') is TTL
  • the compact telephoto lens 100 satisfies the following relationship: 1.11 ⁇ f/TTL ⁇ 4.44.
  • the lens can be miniaturized and long focal length.
  • the sagittal height Sag312 at the effective diameter of the object side of the fourth lens 31 (the maximum diameter of the optical area through which light passes) is -1.361mm
  • the total optical length TTL is 6.756mm
  • the focal length f is 15.004mm
  • f/ TTL 2.22.
  • the symbols described in the compact telephoto lens 100 of the first embodiment of the present invention are as follows.
  • the unit of focal length, on-axis distance, radius of curvature, and on-axis thickness is mm.
  • Table 1 and Table 2 show the design data of the compact telephoto lens 100 of the first embodiment.
  • R The radius of curvature of the optical surface, and the radius of curvature of the center of the lens
  • R1 the radius of curvature of the object side surface of the fourth lens 31;
  • R2 the radius of curvature of the image side surface of the fourth lens 31;
  • R3 the radius of curvature of the object side surface of the first lens 41
  • R4 the radius of curvature of the image side surface of the first lens 41
  • R5 The radius of curvature of the object side of the reverse first lens 41 (after reflection, from the analysis of the propagation path of the light, the position of the object side and the image side of the first lens are reversed, and the original image side is closer to the original object side Object side);
  • R6 the radius of curvature of the image side surface of the reverse first lens 41
  • R7 the radius of curvature of the object side surface of the inverted third lens 32
  • R8 the radius of curvature of the image side surface of the reverse third lens 32
  • R9 the radius of curvature of the object side surface of the third lens 32 (after being reflected again, the position is restored to the same direction as the lens position, and the object side surface is closer to the object);
  • R10 the radius of curvature of the image side surface of the third lens 32
  • R11 the radius of curvature of the object side surface of the second lens 42;
  • R12 the radius of curvature of the image side surface of the second lens 42
  • R13 the radius of curvature of the object side of the field lens 50
  • R14 the radius of curvature of the image side surface of the field lens 50
  • d0 The on-axis distance from the diaphragm 20 to the object side of the fourth lens 31 (the central area of the object side of the fourth lens is the virtual surface of the design, see the dotted line in the figure, the intersection with the optical axis is the calculation of d0
  • the end point is also the starting point for calculating the thickness d1 on the axis of the fourth lens
  • d2 the on-axis distance from the image side surface of the fourth lens 31 to the object side surface of the first lens 41;
  • d4 the on-axis distance from the image side surface of the first lens 41 to the opposite object side surface of the first lens 41;
  • d5 the on-axis thickness of the reverse first lens 41
  • d6 the on-axis distance from the image side surface of the reverse first lens 41 to the object side surface of the third lens 32;
  • d8 the on-axis distance from the image side surface of the inverted third lens 32 to the object side surface of the inverted third lens 32;
  • d10 the on-axis distance from the image side surface of the third lens 32 to the object side surface of the second lens 42;
  • d11 the on-axis thickness of the second lens 42
  • d12 the on-axis distance from the image side surface of the second lens 42 to the object side surface of the field lens
  • d14 the on-axis distance from the image side surface of the field lens 50 to the image surface
  • nd refractive index of d-line
  • nd1 the refractive index of the d-line of the fourth lens 31;
  • nd2 the refractive index of the d-line of the first lens 41
  • nd3 the refractive index of the d-line of the reverse first lens 41;
  • nd4 the refractive index of the d-line of the inverted third lens 32;
  • nd5 the refractive index of the d-line of the third lens 32;
  • nd6 the refractive index of the d-line of the second lens 42
  • nd7 the refractive index of the d-line of the field lens 50
  • ndg the refractive index of the d-line of the optical filter 60
  • v4 Abbe number of the inverted third lens 32
  • vg Abbe number of the optical filter 60.
  • Table 2 shows the aspheric surface data of each lens in the compact telephoto lens 100 according to the first embodiment of the present invention.
  • k is the conic coefficient
  • A4, A6, A8, A10, A12, A14, A16 are the aspheric coefficients
  • x is the vertical distance between the point on the aspheric curve and the optical axis
  • y is the aspheric depth (the distance from the aspheric surface to the optical axis is The vertical distance between the point of x and the tangent plane tangent to the vertex on the optical axis of the aspherical surface).
  • the aspheric surface of each lens surface uses the aspheric surface shown in the above formula (1).
  • the present invention is not limited to the aspheric polynomial form represented by the formula (1).
  • FIGS. 4 and 5 respectively show schematic diagrams of axial aberration and chromatic aberration of magnification after light with wavelengths of 470 nm, 510 nm, 570 nm, 610 nm, and 650 nm pass through the compact telephoto lens 100 of the 7-lens embodiment.
  • Figure 6 shows a schematic diagram of field curvature and distortion of light with a wavelength of 570nm after passing through the compact telephoto lens 100 of the first embodiment.
  • the field curvature S in Figure 6 is the field curvature in the sagittal direction, and T is the meridian direction. Field song.
  • the compact telephoto lens 100 has a full field of view image height of 3.095mm, a diagonal field of view angle of 22.88°, an aperture F number of 1.979, a large aperture, and excellent optics. feature.
  • the second embodiment is basically the same as the first embodiment, and the meaning of the symbols is the same as that of the first embodiment, and only the differences are listed below.
  • Table 3 and Table 4 show the design data of the compact telephoto lens 200 according to the second embodiment of the present invention.
  • Table 4 shows the aspheric surface data of each lens in the compact telephoto lens 200 of the second embodiment of the present invention.
  • FIG. 7 shows a schematic structural diagram of a compact telephoto lens 200.
  • D1 5.073mm
  • D2 2.225mm
  • the blocking ratio is equal to 0.44
  • the optical performance is excellent.
  • Figures 8 and 9 respectively show schematic diagrams of axial aberration and chromatic aberration of magnification after light with wavelengths of 470 nm, 510 nm, 570 nm, 610 nm and 650 nm passes through the compact telephoto lens 200 of the 7-lens embodiment.
  • Figure 10 shows a schematic diagram of field curvature and distortion of light with a wavelength of 570nm after passing through the compact telephoto lens 200 of the second embodiment.
  • the field curvature S in Figure 10 is the field curvature in the sagittal direction, and T is the meridian direction. Field song.
  • the compact telephoto lens 200 has a full field of view image height of 3.095mm, a diagonal field of view angle of 21.82°, an aperture F number of 1.993, a large aperture, and excellent optics feature.
  • the third embodiment is basically the same as the first embodiment, and the meaning of the symbols is the same as that of the first embodiment, and only the differences are listed below.
  • Table 5 and Table 6 show the design data of the compact telephoto lens 300 according to the third embodiment of the present invention.
  • Table 6 shows the aspheric surface data of each lens in the compact telephoto lens 300 of the third embodiment of the present invention.
  • D1 5.228mm
  • D2 1.869mm
  • the blocking ratio is equal to 0.54
  • the imaging performance is excellent.
  • f1 -32.428
  • f2 3.746
  • f3 -17.025
  • f4 -2.348
  • f5 13.442
  • f6 211.356
  • f7 -8.173
  • R1/R2 0.694
  • f5/f2 3.588
  • the total optical length TTL of the compact telephoto lens 300 is the distance along the optical axis from the outer edge of the object side of the fourth lens 31 to the imaging surface 70, and the effective length of the object side of the fourth lens 31
  • the sag312 at the maximum diameter (the maximum diameter of the optical area through which the light passes) is -1.845mm
  • the total optical length TTL is 8.033mm
  • the focal length f is 15.013mm
  • f/TTL 1.87.
  • Figures 12 and 13 respectively show schematic diagrams of axial aberration and chromatic aberration of magnification after light with wavelengths of 470 nm, 510 nm, 570 nm, 610 nm and 650 nm passes through the compact telephoto lens 300 of the 7-lens embodiment.
  • Figure 14 shows a schematic diagram of field curvature and distortion of light with a wavelength of 570nm after passing through the compact telephoto lens 300 of the third embodiment.
  • the field curvature S in Figure 14 is the field curvature in the sagittal direction and T is the meridian direction Field song.
  • the compact telephoto lens 300 has a full field of view image height of 3.095mm, a diagonal field of view angle of 23.01°, an aperture F number of 1.909, a large aperture, and excellent Optical characteristics.
  • the compact telephoto lens provided by the present invention improves the diffraction limit of the lens and realizes a long focal length by arranging an optical path composed of a first lens, a second lens and a third lens, and has a compact structure and a small volume.

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Abstract

一种紧凑型长焦镜头,紧凑型长焦镜头由物侧至像侧依次包括光阑(20)、次镜(30)和主镜(40),主镜(40)包括第一透镜(41)和第二透镜(42),次镜(30)包括第三透镜(32),第一透镜(41)和第三透镜(32)为曼金镜,第一透镜(41)的像侧面为反射面,第三透镜(32)的物侧面为反射面,第二透镜(42)为透射镜,光线经第一透镜(41)反射至第三透镜(32),第三透镜(32)将光线反射至第二透镜(42),光线经第二透镜(42)折射于像面(70)成像。上述紧凑型长焦镜头通过设置由第一、第二以及第三透镜组成的光路,提高了镜头的衍射极限及实现长焦距,且结构紧凑、体积小。

Description

紧凑型长焦镜头 【技术领域】
本发明涉及光学镜头领域,尤其涉及一种紧凑型长焦镜头。
【背景技术】
近年来,随着智能手机的兴起,小型化摄影镜头的需求日渐提高,而一般摄影镜头的感光器件不外乎是感光耦合器件(Charge Coupled Devic e,CCD)或互补性氧化金属半导体器件(Complementary Metal-Oxide Se miconductor Sensor,CMOS Sensor)两种,且由于半导体制造工艺技术的精进,使得感光器件的像素尺寸缩小,再加上现今电子产品以功能佳且轻薄短小的外型为发展趋势,因此,具备良好成像品质的小型化摄像镜头俨然成为目前市场上的主流。
为获取较高的图像成像质量,小型化摄影镜头载荷需要具备高的空间分辨力,要求光学系统具有长焦距。但是,目前的小型化摄影镜头不具备长焦距,无法满足消费者的使用需求。
因此,必须提供一种新的紧凑型长焦镜头以解决上述技术问题。
【发明内容】
本发明的目的在于提供一种能实现长焦距的紧凑型长焦镜头。
为了达到上述目的,本发明提供了一种紧凑型长焦镜头,由物侧至像侧依次包括光阑、次镜和主镜,所述主镜包括第一透镜和第二透镜,所述次镜包括第三透镜,所述第一透镜和所述第三透镜为曼金镜,所述第一透镜的像侧面为反射面,所述第三透镜的物侧面为反射面,所述第二透镜为透射镜,光线经所述第一透镜反射至所述第三透镜,所述第三透镜将所述光线反射至所述第二透镜,所述光线经所述第二透镜折射于像面成像。
优选地,所述次镜还包括第四透镜,所述光线经所述第四透镜折射后射入所述第一透镜。
优选地,所述第三透镜和所述第四透镜为一体结构。
优选地,所述第一透镜和所述第二透镜为一体结构。
优选地,所述的紧凑型长焦镜头还包括场镜,所述场镜设于所述主镜与所述像面之间。
优选地,所述第一透镜的像侧面的有效径为D1,所述第三透镜的物侧面的有效径为D2,所述第一透镜和所述第三透镜满足下列关系式:D2/D1≤0.70。
优选地,所述第一透镜和所述第三透镜满足下列关系式:0.35≤D2/D1≤0.60。
优选地,所述的紧凑型长焦镜头还包括遮光片,所述遮光片和所述光阑沿光轴方向的位置重叠。
优选地,所述紧凑型长焦镜头的光圈F数小于或等于2.50。
优选地,所述紧凑型长焦镜头的焦距为f,所述紧凑型长焦镜头的光学总长为TTL,所述光学总长为自所述次镜的物侧面至所述像面的沿平行于光轴方向的距离,所述紧凑型长焦镜头满足以下关系式:1.11≤f/TTL≤4.44。
优选地,所述第四透镜的物侧面的外缘比所述第三透镜的物侧面的外缘更靠近物侧。
优选地,所述第四透镜的物侧面的曲率半径为R1,所述第四透镜的像侧面的曲率半径为R2,满足条件式:0.00≤R1/R2≤80.00。
优选地,所述的紧凑型长焦镜头满足条件式:0.50≤R1/R2≤60.00。
优选地,所述第一透镜的焦距为f2,反向的所述第三透镜的焦距为f5,满足条件式:2.00≤f5/f2≤6.00。
优选地,所述的紧凑型长焦镜头满足条件式:3.00≤f5/f2≤5.00。
优选地,所述第二透镜的焦距为f6,所述场镜的焦距为f7,满足条件式:-70.00≤f6/f7≤50.00。
优选地,所述的紧凑型长焦镜头满足条件式:-55.00≤f6/f7≤35.00。
与相关技术相比,本发明提供的紧凑型长焦镜头通过设置由第一、第 二以及第三透镜组成的光路,提高了镜头的衍射极限及实现长焦距,且结构紧凑、体积小。
【附图说明】
为了更清楚地说明本发明实施例中的技术方案,下面将对实施例描述中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其它的附图,其中:
图1为本发明第一实施方式的紧凑型长焦镜头的结构示意图;
图2为单束光线在图1所示的所述紧凑型长焦镜头中的传播示意图;
图3为多束光线在图1所示的所述紧凑型长焦镜头中的传播示意图;
图4是图1所示紧凑型长焦镜头的轴向像差示意图;
图5是图1所示紧凑型长焦镜头的倍率色差示意图;
图6是图1所示紧凑型长焦镜头的场曲及畸变示意图;
图7为本发明第二实施方式的紧凑型长焦镜头的结构示意图;
图8是图7所示紧凑型长焦镜头的轴向像差示意图;
图9是图7所示紧凑型长焦镜头的倍率色差示意图;
图10是图7所示紧凑型长焦镜头的场曲及畸变示意图;
图11为本发明第三实施方式的紧凑型长焦镜头的结构示意图;
图12是图11所示紧凑型长焦镜头的轴向像差示意图;
图13是图11所示紧凑型长焦镜头的倍率色差示意图;
图14是图11所示紧凑型长焦镜头的场曲及畸变示意图。
【具体实施方式】
下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅是本发明的一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例,都属于本发明保护的范围。
(实施例一)
请同时参阅图1-3,根据本发明提供的紧凑型长焦镜头100包括自物侧到像侧依次设置的光阑20、次镜30、主镜40以及场镜50,所述遮光片10和所述光阑20在沿光轴OO’方向的位置重叠,所述场镜50与像面70之间可设置光学过滤片60,所述场镜50用于进一步消除像差。在其他实施例中,也可以不设置场镜50,仅通过主镜40和次镜30消除像差。
所述主镜40包括第一透镜41和第二透镜42,所述次镜30包括第三透镜32和第四透镜31,所述第一透镜41和所述第三透镜32均为曼金镜,具体的,所述第一透镜41的靠近像面的表面为反射面,所述第三透镜32的靠近物侧的表面为反射面。可选地,所述第一透镜41和所述第二透镜42为一体结构,图中虚线示意了二者的虚拟分界线,所述第一透镜41自所述第二透镜42的边沿向外延伸而成,在其他实施例中,第一透镜和第二透镜可为分体结构,即由两个透镜连接而成;所述第三透镜32和所述第四透镜31为一体结构,所述第四透镜31自所述第三透镜32的边沿向外延伸而成。在其他实施例中,也可以不设置第四透镜31,光线L直接从第一透镜41入射。
另外,遮光片10挡住对应位置的入射光线L,使得入射光线L为中空的环形,其中遮光片10的外径大于次镜30的反射面的外径,更有利于消减杂散光;在其他实施例中,也可以不设置遮光片10,仅通过次镜30的反射面挡住中心区域光线使得入射光线L呈环形。
具体地,所述第一透镜41包括靠近物侧的第一表面411和靠近像侧的第二表面412,所述第二透镜42包括靠近物侧的第三表面421和靠近像侧的第四表面422,所述第一表面411、所述第三表面421以及所述第四表面422均为透射面,所述第二表面412为反射面,所述第一表面411和所述第三表面421均为内凹面且衔接在一起,所述第二表面412和所述第四表面422为外凸面且衔接在一起。
所述第三透镜32包括靠近物侧的第五表面321和靠近像侧的第六表面322,所述第四透镜31包括靠近物侧的第七表面311和靠近像侧的第八表 面312,所述第五表面321为反射面,所述第六表面322、所述第七表面311以及所述第八表面312均为透射面,所述第五表面321和所述第七表面311为内凹面,且所述第五表面321和所述第七表面311呈台阶状设置,所述第六表面322和所述第八表面312均为外凸面且衔接在一起。可以理解,所述第三透镜32呈环状,其中心空白处由所述第四透镜31填补,所述第三透镜32的像侧面与所述第四透镜31的像侧面形成外凸面。本实施例中,所述第五表面321的外缘比所述第七表面311的外缘更靠近物侧,有利于减小次镜的加工难度;在其他实施例中,所述第七表面311的外缘也可以比所述第五表面的外缘更靠近物侧。
场镜50包括靠近主镜40的第九表面51和远离主镜40的第十表面52,所述第九表面51和所述第十表面52均为透射面,且第九表面51为内凹面,所述第十表面52为外凸面。
其中,沿物侧到像侧方向,首先,光线L通过所述光阑20射入所述第四透镜41,所述光线L经过所述第七表面311和所述第八表面312的折射后射入所述第一透镜41的所述第一表面411;然后,所述光线L经所述第一表面411折射后射入所述第二表面412,所述第二表面412将所述光线L反射回所述第一表面411并折射至所述第三透镜32的所述第六表面322;接着,所述第六表面322将所述光线L折射至所述第五表面321,所述第五表面321将所述光线L反射回所述第六表面322,所述第六表面322再将所述光线L折射至所述第二透镜42;最后,所述光线L依次经过所述第三表面421、所述第四表面422、所述第九表面51和所述第十表面52的折射后,所述光线L透过所述光学滤片60并在所述像面70成像。简而言之,光线L在紧凑型长焦镜头100的传播路径为穿过第四透镜31,射向第一透镜41,并经由第一透镜41反射至第三透镜32,再由第三透镜32反射至第二透镜42,穿过第二透镜42至场镜50,再经场镜50射向像面70。
进一步地,所述第一透镜41的像侧面的有效径(实际供光线反射的光学区域的最大直径)为D1,所述第三透镜32的物侧面的有效径为D2,所述第一透镜41和所述第三透镜32满足下列关系式:D2/D1≤0.7,即紧凑 型长焦镜头100的遮拦比小于或等于0.7。优选地,所述第一透镜41和所述第三透镜32满足下列关系式:0.35≤D2/D1≤0.60,即紧凑型长焦镜头100的遮拦比不小于0.35且小于或等于0.60。在条件式范围内有助于所述紧凑型长焦镜头100实现长焦距,并且有助于摄像性能的提升。本实施例中,D1=9.889mm,D2=4.449mm,遮拦比等于0.45,光学性能优秀。
进一步地,所述紧凑型长焦镜头100的光圈F数小于或等于2.50。大光圈,成像性能好。优选的,光圈F数小于或等于2.2。
定义紧凑型长焦镜头100的焦距为f,第四透镜31的焦距为f1,满足关系式-35.00≤f1/f≤5.00,规定了第四透镜31的焦距f1与系统总焦距f的比值,在条件式范围内有助于提高光学系统性能。
定义紧凑型长焦镜头100的焦距为f,第一透镜41的焦距为f2,满足关系式0.12≤f2/f≤0.48,规定了第一透镜41的焦距f2与系统总焦距f的比值,在条件式范围内可以有效地平衡系统的球差以及场曲量。
定义紧凑型长焦镜头100的焦距为f,反向的第一透镜41的焦距为f3,满足关系式-1.80≤f3/f≤-0.80,通过光焦度的合理分配,使得系统具有较佳的成像品质和较低的敏感性。
定义紧凑型长焦镜头100的焦距为f,反向的第三透镜32的焦距为f5,满足关系式0.70≤f5/f≤1.50,通过光焦度的合理分配,使得系统具有较佳的成像品质和较低的敏感性。
定义紧凑型长焦镜头100的焦距为f,第二透镜42的焦距为f6,满足关系式-20.00≤f6/f≤25.00,规定了第二透镜42的焦距f6与系统总焦距f的比值,在条件式范围内可以有效地平衡系统的球差以及场曲量。
本实施例中,f1=-418.55,f2=3.62,f3=-15.875,f4=-2.459,f5=15.941,f6=297.976,f7=-6.062,满足以上条件式。
定义第四透镜31的物侧面的曲率半径为R1,第四透镜31的像侧面的曲率半径为R2,满足条件式:0.00≤R1/R2≤80.00,在范围内时,有利于实现大光圈,增大衍射极限,提高成像质量;优选的,0.50≤R1/R2≤60.00;本实施例中,R1/R2=0.949。
定义第一透镜41的焦距为f2,反向的第三透镜32的焦距为f5,满足条件式:2.00≤f5/f2≤6.00,在范围内时,有利于增大紧凑型长焦镜头的整体焦距;优选的,3.00≤f5/f2≤5.00;本实施例中,f5/f2=4.404。
定义第二透镜42的焦距为f6,场镜50的焦距为f7,满足条件式:-70.00≤f6/f7≤50.00,在范围内时,有利于消除系统像差;优选的,-55.00≤f6/f7≤35.00;本实施例中,f6/f7=-49.155。
定义紧凑型长焦镜头100的焦距为f,所述紧凑型长焦镜头100的光学总长(自所述次镜30的物侧面至所述像面的沿平行于光轴OO’方向的距离,本实施例中,第四透镜31的物侧面的外缘到成像面的沿光轴OO’方向的距离)为TTL,所述紧凑型长焦镜头100满足以下关系式:1.11≤f/TTL≤4.44。在条件式范围内,可使镜头实现小型化的长焦距。本实施例中,第四透镜31物侧面的有效径(实际供光线经过的光学区域的最大直径)处的矢高Sag312为-1.361mm,光学总长TTL为6.756mm,焦距f为15.004mm,f/TTL=2.22。
本发明的实施例一的紧凑型长焦镜头100中所记载的符号如下所示。焦距、轴上距离、曲率半径、轴上厚度的单位为mm。
表1、表2示出了实施例一的紧凑型长焦镜头100的设计数据。
【表1】
Figure PCTCN2020114609-appb-000001
其中,各符号的含义如下:
S1:光阑20;
R:光学面的曲率半径、透镜时为中心曲率半径;
R1:第四透镜31的物侧面的曲率半径;
R2:第四透镜31的像侧面的曲率半径;
R3:第一透镜41的物侧面的曲率半径;
R4:第一透镜41的像侧面的曲率半径;
R5:反向的第一透镜41的物侧面的曲率半径(经反射后,从光线的传播路径分析,第一透镜的物侧面和像侧面对调位置,原来的像侧面与原来的物侧面更靠近物侧);
R6:反向的第一透镜41的像侧面的曲率半径;
R7:反向的第三透镜32的物侧面的曲率半径;
R8:反向的第三透镜32的像侧面的曲率半径;
R9:第三透镜32的物侧面的曲率半径(经再次反射后,位置还原为与镜片位置方向一致,物侧面更靠近被摄物体);
R10:第三透镜32的像侧面的曲率半径;
R11:第二透镜42的物侧面的曲率半径;
R12:第二透镜42的像侧面的曲率半径;
R13:场镜50的物侧面的曲率半径;
R14:场镜50的像侧面的曲率半径;
d:透镜的轴上厚度与透镜之间的轴上距离;
d0:光阑20到第四透镜31的物侧面的轴上距离(第四透镜物侧面的中心区域为设计的虚拟面,见附图中虚线所示,其与光轴的交点是d0的计算终点,也是第四透镜轴上厚度d1的计算起点);
d1:第四透镜31的轴上厚度;
d2:第四透镜31的像侧面到第一透镜41的物侧面的轴上距离;
d3:第一透镜41的轴上厚度;
d4:第一透镜41的像侧面到反向的第一透镜41的物侧面的轴上距离;
d5:反向的第一透镜41的轴上厚度;
d6:反向的第一透镜41的像侧面到第三透镜32的物侧面的轴上距离;
d7:反向的第三透镜32的轴上厚度;
d8:反向的第三透镜32的像侧面到反向的第三透镜32的物侧面的轴上距离;
d9:第三透镜32的轴上厚度;
d10:第三透镜32的像侧面到第二透镜42的物侧面的轴上距离;
d11:第二透镜42的轴上厚度;
d12:第二透镜42的像侧面到场镜的物侧面的轴上距离;
d13:场镜50的轴上厚度;
d14:场镜50的像侧面到像面的轴上距离;
nd:d线的折射率;
nd1:第四透镜31的d线的折射率;
nd2:第一透镜41的d线的折射率;
nd3:反向的第一透镜41的d线的折射率;
nd4:反向的第三透镜32的d线的折射率;
nd5:第三透镜32的d线的折射率;
nd6:第二透镜42的d线的折射率;
nd7:场镜50的d线的折射率;
ndg:光学过滤片60的d线的折射率;
vd:阿贝数;
v1:第四透镜31的阿贝数;
v2:第一透镜41的阿贝数;
v3:反向的第一透镜41的阿贝数;
v4:反向的第三透镜32的阿贝数;
v5:第三透镜32的阿贝数;
v6:第二透镜42的阿贝数;
v7:场镜50的阿贝数;
vg:光学过滤片60的阿贝数。
表2示出了本发明实施例一的紧凑型长焦镜头100中各透镜的非球面数据。
【表2】
Figure PCTCN2020114609-appb-000002
其中,k是圆锥系数,A4、A6、A8、A10、A12、A14、A16是非球面系数,x是非球面曲线上的点与光轴的垂直距离,y是非球面深度(非球面上距离光轴为x的点,与相切于非球面光轴上顶点的切面两者间的垂直距离)。
IH:像高
y=(x 2/R)/[1+{1-(k+1)(x 2/R 2)} 1/2]+A4x 4+A6x 6+A8x 8+A10x 10+A12x 12+A14x 14+A16x 16      (1)
为方便起见,各个透镜面的非球面使用上述公式(1)中所示的非球面。但是,本发明不限于该公式(1)表示的非球面多项式形式。
图4、图5分别示出了波长为470nm、510nm、570nm、610nm和650nm的光经过7镜片实施方式的紧凑型长焦镜头100后的轴向像差以及倍率色差示意图。图6则示出了,波长为570nm的光经过实施例一的紧凑型长焦镜头100后的场曲及畸变示意图,图6的场曲S是弧矢方向的场曲,T是 子午方向的场曲。
在本实施例中,所述紧凑型长焦镜头100的全视场像高为3.095mm,对角线方向的视场角为22.88°,光圈F数为1.979,大光圈、且具有优秀的光学特征。
(实施例二)
实施例二与实施例一基本相同,符号含义与实施例一相同,以下只列出不同点。
表3、表4示出本发明实施例二的紧凑型长焦镜头200的设计数据。
【表3】
Figure PCTCN2020114609-appb-000003
表4示出本发明实施例二的紧凑型长焦镜头200中各透镜的非球面数据。
【表4】
Figure PCTCN2020114609-appb-000004
图7示意出了紧凑型长焦镜头200的结构示意图,本实施例中,D1=5.073mm,D2=2.225mm,遮拦比等于0.44,光学性能优秀。
本实施例中,f1=19.471,f2=5.208,f3=-19.145,f4=-2.598,f5=19.122,f6=-224.019,f7=-7.109,R1/R2=54.436,f5/f2=3.672,f6/f7=31.512,满足实施例一中详细描述的各个条件式。
本实施方式中,紧凑型长焦镜头200的光学总长TTL为第三透镜32的物侧面的外缘到成像面70的沿光轴方向的距离,所述第三透镜32物侧面的有效径(实际供光线经过的光学区域的最大直径)处的矢高Sag322为-0.389mm,光学总长TTL为6.715mm,焦距f为15.939mm,f/TTL=2.374,满足:1.11≤f/TTL≤4.44,可使镜头实现小型化的长焦距。
图8、图9分别示出了波长为470nm、510nm、570nm、610nm和650nm的光经过7镜片实施方式的紧凑型长焦镜头200后的轴向像差以及倍率色 差示意图。图10则示出了,波长为570nm的光经过实施例二的紧凑型长焦镜头200后的场曲及畸变示意图,图10的场曲S是弧矢方向的场曲,T是子午方向的场曲。
在本实施例中,所述紧凑型长焦镜头200的全视场像高为3.095mm,对角线方向的视场角为21.82°,光圈F数为1.993,大光圈、且具有优秀的光学特征。
(实施例三)
实施例三与实施例一基本相同,符号含义与实施例一相同,以下只列出不同点。
表5、表6示出本发明实施例三的紧凑型长焦镜头300的设计数据。
【表5】
Figure PCTCN2020114609-appb-000005
表6示出本发明实施例三的紧凑型长焦镜头300中各透镜的非球面数据。
【表6】
Figure PCTCN2020114609-appb-000006
本实施例中,D1=5.228mm,D2=1.869mm,遮拦比等于0.54,摄像性能优秀。
本实施例中,f1=-32.428,f2=3.746,f3=-17.025,f4=-2.348,f5=13.442,f6=211.356,f7=-8.173,R1/R2=0.694,f5/f2=3.588,f6/f7=-25.860,满足实施例一中的各条件式。
本实施例中,紧凑型长焦镜头300的光学总长TTL为所述第四透镜31的物侧面的外缘到成像面70的沿光轴方向的距离,所述第四透镜31物侧面的有效径(实际供光线经过的光学区域的最大直径)处的矢高Sag312为-1.845mm,光学总长TTL为8.033mm,焦距f为15.013mm,f/TTL=1.87。
图12、图13分别示出了波长为470nm、510nm、570nm、610nm和650nm的光经过7镜片实施方式的紧凑型长焦镜头300后的轴向像差以及倍率色差示意图。图14则示出了,波长为570nm的光经过实施例三的紧凑型长 焦镜头300后的场曲及畸变示意图,图14的场曲S是弧矢方向的场曲,T是子午方向的场曲。
在本实施方式例中,所述紧凑型长焦镜头300的全视场像高为3.095mm,对角线方向的视场角为23.01°,光圈F数为1.909,大光圈、且具有优秀的光学特征。
与相关技术相比,本发明提供的紧凑型长焦镜头通过设置由第一、第二以及第三透镜组成的光路,提高了镜头的衍射极限及实现长焦距,且结构紧凑、体积小。
以上所述的仅是本发明的实施方式,在此应当指出,对于本领域的普通技术人员来说,在不脱离本发明创造构思的前提下,还可以做出改进,但这些均属于本发明的保护范围。

Claims (17)

  1. 一种紧凑型长焦镜头,其特征在于,所述紧凑型长焦镜头由物侧至像侧依次包括光阑、次镜和主镜,所述主镜包括第一透镜和第二透镜,所述次镜包括第三透镜,所述第一透镜和所述第三透镜为曼金镜,所述第一透镜的像侧面为反射面,所述第三透镜的物侧面为反射面,所述第二透镜为透射镜,光线经所述第一透镜反射至所述第三透镜,所述第三透镜将所述光线反射至所述第二透镜,所述光线经所述第二透镜折射于像面成像。
  2. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述次镜还包括第四透镜,所述光线经所述第四透镜折射后射入所述第一透镜。
  3. 根据权利要求2所述的紧凑型长焦镜头,其特征在于,所述第三透镜和所述第四透镜为一体结构。
  4. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述第一透镜和所述第二透镜为一体结构。
  5. 根据权利要求1或2所述的紧凑型长焦镜头,其特征在于,还包括场镜,所述场镜设于所述主镜与所述像面之间。
  6. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述第一透镜的像侧面的有效径为D1,所述第三透镜的物侧面的有效径为D2,所述第一透镜和所述第三透镜满足下列关系式:D2/D1≤0.70。
  7. 根据权利要求6所述的紧凑型长焦镜头,其特征在于,所述第一透镜和所述第三透镜满足下列关系式:0.35≤D2/D1≤0.60。
  8. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,还包括遮光片,所述遮光片和所述光阑沿光轴方向的位置重叠。
  9. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述紧凑型长焦镜头的光圈F数小于或等于2.50。
  10. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述紧凑型长焦镜头的焦距为f,所述紧凑型长焦镜头的光学总长为TTL,所述光学总长为自所述次镜的物侧面至所述像面的沿平行于光轴方向的距离,所述紧 凑型长焦镜头满足以下关系式:1.11≤f/TTL≤4.44。
  11. 根据权利要求2所述的紧凑型长焦镜头,其特征在于,所述第四透镜的物侧面的外缘比所述第三透镜的物侧面的外缘更靠近物侧。
  12. 根据权利要求2所述的紧凑型长焦镜头,其特征在于,所述第四透镜的物侧面的曲率半径为R1,所述第四透镜的像侧面的曲率半径为R2,满足条件式:0.00≤R1/R2≤80.00。
  13. 根据权利要求12所述的紧凑型长焦镜头,其特征在于,满足条件式:0.50≤R1/R2≤60.00。
  14. 根据权利要求1所述的紧凑型长焦镜头,其特征在于,所述第一透镜的焦距为f2,反向的所述第三透镜的焦距为f5,满足条件式:2.00≤f5/f2≤6.00。
  15. 根据权利要求14所述的紧凑型长焦镜头,其特征在于,满足条件式:3.00≤f5/f2≤5.00。
  16. 根据权利要求5所述的紧凑型长焦镜头,其特征在于,所述第二透镜的焦距为f6,所述场镜的焦距为f7,满足条件式:-70.00≤f6/f7≤50.00。
  17. 根据权利要求16所述的紧凑型长焦镜头,其特征在于,满足条件式:-55.00≤f6/f7≤35.00。
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