CN220305555U - High-pixel wide-angle lens - Google Patents
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- CN220305555U CN220305555U CN202321629155.2U CN202321629155U CN220305555U CN 220305555 U CN220305555 U CN 220305555U CN 202321629155 U CN202321629155 U CN 202321629155U CN 220305555 U CN220305555 U CN 220305555U
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- 230000001681 protective effect Effects 0.000 claims description 9
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- 230000004075 alteration Effects 0.000 description 17
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- 238000012544 monitoring process Methods 0.000 description 2
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- 230000000007 visual effect Effects 0.000 description 2
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- 239000003086 colorant Substances 0.000 description 1
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Abstract
The utility model discloses a high-pixel wide-angle lens, which is sequentially arranged from an object side to an image side along an optical axis of the lens: the first lens is a glass spherical lens with negative focal power; the second lens is an aspheric plastic lens with negative focal power; the third lens is an aspheric plastic lens with negative focal power; a diaphragm sheet; the fourth lens is a spherical glass lens with positive focal power; a fifth lens which is an aspherical plastic lens having positive optical power; a sixth lens which is an aspherical plastic lens having negative optical power; optical filters, cover glass and image acquisition elements. The lens adopts the mixed combination of 2 pieces of spherical glass and 4 pieces of aspheric plastic, the lens is matched with a 1/2.4' chip, the view field angle DFOV=155 DEG, the lens can provide high definition image quality under the condition of large view field angle, and each lens is insensitive in manufacturability, easy to form and manufacture and has higher cost performance.
Description
Technical Field
The utility model relates to the field of optical lenses, in particular to a high-pixel wide-angle lens.
Background
Along with the continuous progress of society, the demands of people for visual and intelligent products are increasing, and the lens serving as a visual carrier and an eye of machine vision is widely applied to the fields of intelligent home, law enforcement instruments, unmanned aerial vehicle aerial photography and the like. However, in mainstream products in the fields of intelligent home, law enforcement instrument, unmanned aerial vehicle aerial photography and the like, phenomena of low pixel, low light sensitivity, high cost and the like exist.
Disclosure of Invention
Aiming at the defects in the prior art, the utility model provides a high-pixel wide-angle lens which adopts a mixed combination of 2 pieces of spherical glass and 4 pieces of aspheric plastic, can be matched with a 1/2.4 inch chip, can provide high-definition image quality under the condition of large viewing angle, is insensitive in manufacturability, is easy to mold and manufacture, and has higher cost performance.
The aim of the utility model is achieved by the following technical scheme:
a high-pixel wide-angle lens is provided in order from an object side to an image side along a lens optical axis: the first lens is a spherical glass lens with negative focal power, the object side surface of the first lens is a convex surface, and the image side surface of the first lens is a concave surface;
the second lens is an aspheric plastic lens with negative focal power, the object side surface of the second lens is a concave surface, and the image side surface of the second lens is a convex surface;
the third lens is an aspheric plastic lens with negative focal power, the object side surface of the third lens is a concave surface, and the image side surface of the third lens is a convex surface;
the fourth lens is a spherical glass lens with positive focal power, the object side surface of the fourth lens is a convex surface, and the image side surface of the fourth lens is a convex surface;
the fifth lens is an aspheric plastic lens with positive focal power, the object side surface of the fifth lens is a convex surface, and the image side surface of the fifth lens is a convex surface;
and the sixth lens is an aspheric plastic lens with negative focal power, the object side surface of the sixth lens is a concave surface, and the image side surface of the sixth lens is a concave surface.
Further, the object side surface of the third lens is a concave surface with reverse curvature, and the image side surface of the third lens is a convex surface with reverse curvature.
Further, the abbe number of the fourth lens is greater than 90.
Further, the image side surface of the second lens is a convex surface with reverse curvature.
Further, the high-pixel wide-angle lens is further provided with a diaphragm sheet, and the diaphragm sheet is arranged between the third lens and the fourth lens.
Further, the high-pixel wide-angle lens is also provided with an optical filter, protective glass and an image acquisition element; the optical filter is arranged on the image side surface of the sixth lens; the protective glass is arranged on the image side surface of the optical filter, the image acquisition element is arranged on the image side surface of the protective glass, and the protective glass is integrated on the image sensor.
Further, the focal lengths, refractive indexes and radii of curvature of the first, second, third, fourth, fifth and sixth lenses respectively satisfy the following conditions:
f1 | -5.4~-4.2 | ND1 | 1.50~1.56 | R11 | +15.11~+200.21 | R12 | +2.01~+2.52 |
f2 | -161~+17.9 | ND2 | 1.53~1.68 | R21 | -13.60~-3.61 | R22 | -6.42~-4.09 |
f3 | -49.5~+4.9 | ND3 | 1.53~1.59 | R31 | -4.05~-19.37 | R32 | -5.07~-3.31 |
f4 | -6.9~+5.8 | ND4 | 1.45~1.65 | R41 | +3.53~+13.47 | R42 | -3.11~+1.85 |
f5 | +3.0~+4.6 | ND5 | 1.53~1.59 | R51 | +5.51~+6.79 | R52 | -3.37~-1.85 |
f6 | -8.0~-5.3 | ND6 | 1.60~1.68 | R61 | -3.36~-1.85 | R62 | -2.13~+12.52 |
wherein f1 is a focal length of the first lens element, ND1 is a refractive index of the first lens element, R11 is an object-side radius of curvature of the first lens element, and R12 is an image-side radius of curvature of the first lens element; f2 is a focal length of the second lens element, ND2 is a refractive index of the second lens element, R21 is an object-side radius of curvature of the second lens element, and R22 is an image-side radius of curvature of the second lens element; f is a focal length of the third lens element, ND3 is a refractive index of the third lens element, R31 is an object-side radius of curvature of the third lens element, and R32 is an image-side radius of curvature of the third lens element; f4 is a focal length of the fourth lens element, ND4 is a refractive index of the fourth lens element, R41 is an object-side radius of curvature of the fourth lens element, and R42 is an image-side radius of curvature of the fourth lens element; f5 is a focal length of the fifth lens element, ND5 is a refractive index of the fifth lens element, R51 is an object-side radius of curvature of the fifth lens element, and R52 is an image-side radius of curvature of the fifth lens element; f6 is a focal length of the sixth lens element, ND6 is a refractive index of the sixth lens element, R61 is an object-side radius of curvature of the sixth lens element, and R62 is an image-side radius of curvature of the sixth lens element; the "-" sign indicates that the surface is curved to the object plane side.
Further, the aspheres of the second, third, fifth and sixth lenses may be defined by the following even-order asphere equations:
wherein: z is the sagittal height of the lens along the optical axis, k is the conic coefficient of the curved surface, gamma is the lens height, c is the lens curvature, and A, B, C, D, E, F, G is the 4 th, 6 th, 8 th, 10 th, 12 th, 14 th and 16 th order coefficients of the aspherical polynomial.
Compared with the prior art, the utility model has the beneficial effects that: the total focal length F of the high-pixel wide-angle lens is less than or equal to 3.0mm, the aperture F# meets F# -2.0, and high-definition image quality can be provided under the condition of large field angle. In terms of manufacturability, the lens adopts the mixed combination of 2 pieces of spherical glass and 4 pieces of aspheric plastic, each lens is insensitive, the molding and the manufacturing are easy, the structure is compact, the characteristics of small volume, light weight, good performance and low cost can be realized, and the cost performance is higher. The utility model can be matched with 1/2.4 chip through reasonable lens material selection, focal power distribution and optical design optimization, realizes day-night confocal 24-hour all-weather high-definition monitoring, and has better reliability and stability.
Drawings
FIG. 1 is a schematic view of an optical structure according to an embodiment of the present utility model;
FIG. 2 is a schematic view of an optical path structure according to an embodiment of the present utility model;
FIG. 3 is a graph of the color spherical aberration of visible light of 0.435-0.656um according to an embodiment of the utility model;
FIG. 4 is a graph of field curvature of 0.435-0.656um for visible light according to an embodiment of the utility model;
FIG. 5 is a graph of distortion of 0.435-0.656um for visible light according to an embodiment of the utility model;
reference numerals: 1-first lens, 2-second lens, 3-third lens, 4-fourth lens, 5-fifth lens, 6-sixth lens, 7-diaphragm sheet, 8-optical filter, 9-protective glass and 10-image acquisition element.
Detailed Description
The following description of the embodiments of the present utility model will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present utility model, but not all embodiments. In this specification, the expressions of first, second, third, etc. are used merely to distinguish one feature from another feature and do not denote any limitation of feature. The shape of the spherical or aspherical surface is not limited to the shape of the spherical or aspherical surface shown in the drawings. The figures are merely examples and are not drawn to scale.
In the present utility model, the paraxial region refers to a region near the optical axis. If the lens surface is convex and the convex position is not defined, then the lens surface is convex at least in the paraxial region; if the lens surface is concave and the concave position is not defined, the lens surface is concave at least in the paraxial region; when the lens surface is not limited to a convex surface, a concave surface or a plane surface, it means that the lens surface may be a convex surface, a concave surface or a plane surface. The surface of each lens closest to the object is referred to as the object side of the lens, and the surface of each lens closest to the imaging plane is referred to as the image side of the lens.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. All other embodiments, which can be made by those skilled in the art based on the embodiments of the utility model without making any inventive effort, are intended to be within the scope of the utility model. For a better understanding and implementation, the present utility model is described in detail below with reference to the drawings.
The utility model provides a high-pixel wide-angle lens, wherein the surface of a lens adjacent to an object plane side is an object side, the surface of the lens adjacent to an image plane side is an image side, and a first lens 1, a second lens 2, a third lens 3, a diaphragm sheet 7, a fourth lens 4, a fifth lens 5, a sixth lens 6, an optical filter 8, a protective glass 9 and an image acquisition element 10 are sequentially arranged from the object side to the image side along an optical axis of the lens. The diaphragm 7 is positioned between the third lens 3 and the fourth lens 4; the filter 8 is provided on the image side surface of the sixth lens 6, and the filter 8 is made of H-K9L. The cover glass 9 is disposed on the image side of the filter 8, the image pickup element 10 is disposed on the image side of the cover glass 9, and the cover glass 9 is integrated on the image sensor.
In the utility model, in order to make the optical system exhibit better performance, in the design process, lens materials are reasonably selected, focal lengths of all lenses are reasonably distributed, the optical system is reasonably optimized, and finally, the performance of the optical system is optimized, generally, the imaging quality of the optical system is affected by the existence of aberration of the optical system, the aberration correction is the key point of optimizing the optical system, various methods for correcting the aberration are provided, for example, lenses with different refractive indexes and larger Abbe number are selected for being matched for use, chromatic aberration and spherical aberration can be eliminated to a certain extent, and the focal length and shape of all lenses can be reasonably distributed and optimized, so that the aberration of the system can be corrected.
In the utility model, the focal length, refractive index and curvature radius of each lens respectively meet the following conditions in consideration of the problems of aberration and balance temperature drift of an optical system:
f1 | -5.4~-4.2 | ND1 | 1.50~1.56 | R11 | +15.11~+200.21 | R12 | +2.01~+2.52 |
f2 | -161~+17.9 | ND2 | 1.53~1.68 | R21 | -13.60~-3.61 | R22 | -6.42~-4.09 |
f3 | -49.5~+4.9 | ND3 | 1.53~1.59 | R31 | -4.05~-19.37 | R32 | -5.07~-3.31 |
f4 | -6.9~+5.8 | ND4 | 1.45~1.65 | R41 | +3.53~+13.47 | R42 | -3.11~+1.85 |
f5 | +3.0~+4.6 | ND5 | 1.53~1.59 | R51 | +5.51~+6.79 | R52 | -3.37~-1.85 |
f6 | -8.0~-5.3 | ND6 | 1.60~1.68 | R61 | -3.36~-1.85 | R62 | -2.13~+12.52 |
wherein f1 is a focal length of the first lens element, ND1 is a refractive index of the first lens element, R11 is an object-side radius of curvature of the first lens element, and R12 is an image-side radius of curvature of the first lens element; f2 is a focal length of the second lens element, ND2 is a refractive index of the second lens element, R21 is an object-side radius of curvature of the second lens element, and R22 is an image-side radius of curvature of the second lens element; f is a focal length of the third lens element, ND3 is a refractive index of the third lens element, R31 is an object-side radius of curvature of the third lens element, and R32 is an image-side radius of curvature of the third lens element; f4 is a focal length of the fourth lens element, ND4 is a refractive index of the fourth lens element, R41 is an object-side radius of curvature of the fourth lens element, and R42 is an image-side radius of curvature of the fourth lens element; f5 is a focal length of the fifth lens element, ND5 is a refractive index of the fifth lens element, R51 is an object-side radius of curvature of the fifth lens element, and R52 is an image-side radius of curvature of the fifth lens element; f6 is a focal length of the sixth lens element, ND6 is a refractive index of the sixth lens element, R61 is an object-side radius of curvature of the sixth lens element, and R62 is an image-side radius of curvature of the sixth lens element; the "-" sign indicates that the surface is curved to the object plane side.
In the utility model, f is the total focal length of the lens; TTL is the total optical length of the lens; the OBFL is an optical back intercept of the lens, and the optical back intercept of the lens is a distance from a point of the sixth lens 6 closest to the image plane; the IC is the total image height of a 1/2.4' chip matched with the lens system; they satisfy the following conditions: f is less than or equal to 3.0, TTL is less than or equal to 16.5mm, IC/TTL is more than or equal to 0.45, TTL/f is less than or equal to 5.4, and OBFL/TTL is more than or equal to 0.22.
In the utility model, the aperture of the lens is F#, and F# -2.0 is satisfied.
The main element symbols in the present utility model are shown in Table 1.
TABLE 1
S1 | First lens object side surface | S10 | Fifth lens object side surface |
S2 | The image side surface of the first lens | S11 | Fifth lens image-side surface |
S3 | Second lens object side surface | S12 | Sixth lens object side surface |
S4 | Second lens image side surface | S13 | Image side surface of sixth lens |
S5 | Third lens object side surface | S14 | Optical filter object side surface |
S6 | Image side surface of the third lens | S15 | Image side of optical filter |
S7 | Diaphragm | S16 | Protecting glass object side surfaces |
S8 | Fourth lens object side surface | S17 | Protecting glass image side |
S9 | Fourth lens image side surface | S18 | Image plane |
In one embodiment, reference is made to fig. 1 and 2, which are respectively an optical structure schematic diagram and an optical path structure schematic diagram of the present embodiment. In this embodiment, parameters of the high-pixel wide-angle lens are shown in table 2.
TABLE 2
The high-pixel wide-angle lens in the present embodiment is provided with a first lens 1, a second lens 2, a third lens 3, a diaphragm sheet 7, a fourth lens 4, a fifth lens 5, a sixth lens 6, an optical filter 8, a cover glass 9 and an image capturing element 10 in order from an object side to an image side along an optical axis of the lens, wherein:
the first lens 1 is a spherical glass lens with negative focal power, the object side surface of the first lens 1 is a convex surface, and the image side surface of the first lens 1 is a concave surface;
the second lens 2 is an aspheric plastic lens with negative focal power, the object side surface of the second lens 2 is a concave surface, and the image side surface of the second lens 2 is a convex surface with reverse curvature;
the third lens 3 is an aspheric plastic lens with negative focal power, the object side surface of the third lens 3 is a concave surface with reverse curvature, and the image side surface of the third lens is a convex surface with reverse curvature;
the fourth lens element 4 is a spherical glass lens element with positive refractive power, wherein the object-side surface of the fourth lens element 4 is convex, and the image-side surface thereof is convex;
the fifth lens element 5 is an aspheric plastic lens with positive refractive power, wherein an object-side surface of the fifth lens element 5 is a convex surface, and an image-side surface thereof is a convex surface;
the sixth lens element 6 is an aspheric plastic lens element with negative refractive power, wherein the object-side surface of the sixth lens element 6 is concave, and the image-side surface thereof is concave.
In this embodiment, the first lens 1 is a glass spherical lens with negative focal power, the object side surface is a convex surface, and the image side surface is a concave surface, so as to form a lens with meniscus negative focal power, which is used for rapidly converging light; the Abbe number of the fourth lens 4 is larger than 90, so that the chromatic aberration of the system can be reduced by the combination, and the day-night confocal and other problems can be further realized; the second lens 2, the third lens 3 and the fifth lens 5 and the sixth lens 6 are plastic aspheric lenses, and the functions of the lens are mainly to correct various optical aberrations, and finally optimize the performance of the optical system.
In this embodiment, the radius of curvature, center thickness, refractive index, abbe constant, and aspherical K value of each lens are designed as shown in table 3 in consideration of the problems of aberration and equilibrium temperature drift of the optical system.
Table 3 shows the radius of curvature R (unit: mm) of each lens, the center thickness d (unit: mm) of each lens, the refractive index (ND) of each lens, the Abbe constant (VD), and the aspherical K value (Conic) of each lens.
TABLE 3 Table 3
In Table 3, the radius of curvature represents the degree of curvature of the lens surface, a positive value represents the surface curved to the image plane side, a negative value represents the surface curved to the object plane side, where "Infinity" represents the surface as a plane; the thickness represents the center axial distance from the current surface to the next surface, the refractive index represents the deflection capability of the current lens material to light, and the Abbe number represents the dispersion characteristic of the current lens material to light; the K value represents the magnitude of the best fit conic coefficient for the aspheric surface.
In the present embodiment, the aspherical surfaces of the second lens 2, the third lens 3, the fifth lens 5 and the sixth lens 6 can be defined by the following even aspherical equations:
wherein Z is the sagittal height of the lens along the optical axis, k is the conic coefficient of the curved surface, gamma is the lens height, c is the lens curvature, and A, B, C, D, E, F, G is the 4 th, 6 th, 8 th, 10 th, 12 th, 14 th and 16 th order polynomial coefficients of the aspherical surface.
Table 4 gives the individual coefficients of aspheres of the optical surfaces of the second lens 2, the third lens 3, the fifth lens 5 and the sixth lens 6.
TABLE 4 Table 4
Referring to fig. 3, a graph of the color spherical aberration of the lens of the present embodiment, which is 0.435-0.656um, shows the longitudinal spherical aberration values of the spectrum of 5 different colors. Where LONGITUDINAL SPHERICAL ABER represents the different fields of view and FOCUS (MILLIMETERS) represents the longitudinal spherical aberration. The image can reflect the aberration of the wide-angle lens to a certain extent and is well corrected.
Referring to fig. 4, a graph of field CURVES of 0.435-0.656um of visible light of the lens according to the present embodiment is shown, wherein an ordinate ASTIGMATIC FIELD CURVES represents different fields of view and an abscissa FOCUS (MILLIMETERS) represents field quantity (mm). The image can reflect the aberration of the wide-angle lens to a certain extent and is well corrected.
Referring to fig. 5, in the distortion graph of the visible light 0.435-0.656um of the lens according to the embodiment, the horizontal axis represents the distortion (unit:%) of F-tan (Theta), and the vertical axis represents the half angle of view (unit: °), it can be seen from the graph that the distortion of tan (Theta) of the lens is smaller, and is less than-70%, which indicates that the distortion of the lens is well corrected, and the real shot image and the real scene cannot be deformed too much.
As can be seen from fig. 3, 4 and 5, curvature of field, distortion and chromatic aberration can be well corrected in this embodiment.
In this embodiment, the total focal length f=3.0 mm, the aperture f# =2.0, the total length ttl=16.4 mm, the optical back intercept obfl=3.6 mm, and the field angle dfov=155° of the lens matching 1/2.5″ chip.
The embodiment above shows that the high-pixel wide-angle lens provided by the utility model has the total focal length F of the optical lens less than or equal to 3.0mm, the aperture F# meets F# -2.0, and the high-definition image quality can be provided under the condition of a large field angle. In terms of manufacturability, the lens adopts the mixed combination of 2 pieces of spherical glass and 4 pieces of aspheric plastic, each lens is insensitive, the molding and the manufacturing are easy, the characteristics of small volume, light weight, good performance and low cost can be realized, and the lens has higher cost performance. The utility model can be matched with 1/2.4 chip through reasonable lens material selection, focal power distribution and optical design optimization, realizes day-night confocal 24-hour all-weather high-definition monitoring, and has better reliability and stability.
The foregoing description of only a few embodiments of the present utility model has been presented for purposes of illustration and description, but is not intended to limit the scope of the utility model. It should be noted that modifications and improvements can be made by those skilled in the art without departing from the spirit of the utility model, and the utility model is intended to encompass such modifications and improvements.
Claims (9)
1. The utility model provides a high pixel wide angle lens which characterized in that: the lens is sequentially arranged from an object side to an image side along the optical axis of the lens:
the first lens is a spherical glass lens with negative focal power, the object side surface of the first lens is a convex surface, and the image side surface of the first lens is a concave surface;
the second lens is an aspheric plastic lens with negative focal power, the object side surface of the second lens is a concave surface, and the image side surface of the second lens is a convex surface;
the third lens is an aspheric plastic lens with negative focal power, the object side surface of the third lens is a concave surface, and the image side surface of the third lens is a convex surface;
the fourth lens is a spherical glass lens with positive focal power, the object side surface of the fourth lens is a convex surface, and the image side surface of the fourth lens is a convex surface; the abbe number of the fourth lens is more than 90;
the fifth lens is an aspheric plastic lens with positive focal power, the object side surface of the fifth lens is a convex surface, and the image side surface of the fifth lens is a convex surface;
the object side surface of the sixth lens is a concave surface, and the image side surface of the sixth lens is a concave surface;
the high-pixel wide-angle lens is further provided with a diaphragm sheet, and the diaphragm sheet is arranged between the third lens and the fourth lens;
the total focal length of the lens is f which is less than or equal to 3.0mm.
2. The high-pixel wide-angle lens of claim 1, wherein: the object side surface of the third lens is a concave surface with reverse curvature, and the image side surface of the third lens is a convex surface with reverse curvature.
3. The high-pixel wide-angle lens of claim 1, wherein: the image side surface of the second lens is a convex surface with reverse curvature.
4. The high-pixel wide-angle lens of claim 1, wherein: the high-pixel wide-angle lens is also provided with an optical filter, protective glass and an image acquisition element; the optical filter is arranged on the image side surface of the sixth lens; the protective glass is arranged on the image side surface of the optical filter, the image acquisition element is arranged on the image side surface of the protective glass, and the protective glass is integrated on the image sensor.
5. The high-pixel wide-angle lens of claim 1, wherein: the focal length value ranges of the first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens which are sequentially corresponding are respectively-5.4 to-4.2, -161 to +17.9, -49.5 to +4.9, -6.9 to +5.8, +3.0 to +4.6, -8.0 to-5.3; the "-" sign indicates that the surface is curved to the object plane side.
6. The high-pixel wide-angle lens of claim 1, wherein: the refractive index values of the first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens, which are sequentially corresponding, are respectively 1.50-1.56, 1.53-1.68, 1.53-1.59, 1.45-1.65, 1.53-1.59 and 1.60-1.68.
7. The high-pixel wide-angle lens of claim 1, wherein: the object side surface curvature radius value ranges of the first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens which are sequentially corresponding are respectively +15.11- +200.21, -13.60-3.61, -4.05-19.37, +3.53- +13.47, +5.51- +6.79, -3.36-1.85; the "-" sign indicates that the surface is curved to the object plane side.
8. The high-pixel wide-angle lens of claim 1, wherein: the values of the image side surface curvature radiuses of the first lens, the second lens, the third lens, the fourth lens, the fifth lens and the sixth lens, which are sequentially corresponding, are respectively +2.01 to +2.52, -6.42 to-4.09, -5.07 to-3.31, -3.11 to +1.85, -3.37 to-1.85, -2.13 to +12.52; the "-" sign indicates that the surface is curved to the object plane side.
9. The high-pixel wide-angle lens of claim 1, wherein: the aspherical surfaces of the second lens, the third lens, the fifth lens and the sixth lens satisfy the following formula:
wherein: z is the sagittal height of the lens along the optical axis, k is the conic coefficient of the curved surface, gamma is the lens height, c is the lens curvature, and A, B, C, D, E, F, G is the 4 th, 6 th, 8 th, 10 th, 12 th, 14 th and 16 th order coefficients of the aspherical polynomial.
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