CN205679845U - A vehicle-mounted high-definition fisheye lens - Google Patents

Abstract

The utility model discloses an on-vehicle high definition fisheye camera lens is equipped with from the thing side to picture side in proper order: the front lens group comprises a first lens, a second lens and a third lens which are sequentially arranged from an object side to an image side, the focal power of the first lens and the focal power of the second lens are negative, the focal power of the third lens is positive, the rear lens group comprises a fourth lens, a fifth lens and a sixth lens which are sequentially arranged from the object side to the image side, the focal power of the fourth lens and the focal power of the sixth lens are positive, the focal power of the fifth lens is negative, and the third lens, the fourth lens, the fifth lens and the sixth lens are plastic aspheric lenses. The utility model discloses the angle of vision is big, and is with low costs, definition height, logical light ability reinforce.

Description

A vehicle-mounted high-definition fisheye lens

【Technical field】

The utility model relates to a vehicle-mounted high-definition fisheye lens.

【Background technique】

At present, driving disputes and traffic accidents are common. In order to ensure driving safety, many cars are equipped with on-board cameras. However, the current general vehicle lens has a limited field of view, poor definition, and weak light transmission, so the current vehicle lens can no longer meet social needs.

Therefore, the utility model proposes based on the shortcoming that the above-mentioned prior art exists.

【Content of utility model】

The purpose of the utility model is to overcome the deficiencies of the prior art, and provide a vehicle-mounted high-definition fisheye lens with a large field of view, low cost, high definition and strong light transmission ability.

The utility model is achieved through the following technical solutions:

A vehicle-mounted high-definition fisheye lens is characterized in that: from the object side to the image side, there are sequentially provided with: a front lens group 100 with positive refractive power, a diaphragm 200, a rear lens group 300 with positive refractive power, and an imaging surface 400. The front lens group 100 includes a first lens 1, a second lens 2, and a third lens 3 arranged sequentially from the object side to the image side, and the optical focal points of the first lens 1 and the second lens 2 are power is negative, the refractive power of the third lens 3 is positive, and the rear lens group 300 includes the fourth lens 4, the fifth lens 5 and the sixth lens 6 arranged in sequence from the object side to the image side , the refractive power of the fourth lens 4 and the sixth lens 6 is positive, the refractive power of the fifth lens 5 is negative, the third lens 3, the fourth lens 4, the fifth lens 5 and the sixth lens 6 are plastic aspherical lenses.

The vehicle-mounted high-definition fisheye lens as described above is characterized in that: the first lens 1 is a meniscus lens, and its surface facing the object side is convex, and the surface facing the image side is concave; Both surfaces of the lens 2 are concave; the surface of the third lens 3 facing the object side is concave, and the surface facing the image side is convex.

The vehicle-mounted high-definition fisheye lens as described above is characterized in that: both surfaces of the fourth lens 4 are convex; both surfaces of the fifth lens 5 are concave; the sixth lens Both surfaces of 6 are convex.

The vehicle-mounted high-definition fisheye lens described above is characterized in that: the front lens group 100 and the rear lens group 300 satisfy the following expressions: 3.14≤F _before ≤9.38, 2.35≤F _before /F≤7.8, 3.5 ≤F _after ≤5.12, 61≤F _after /F≤4.25, 0.62≤F _before /F _after ≤2.68; where, F _before is the focal length of the front lens group 100, F _after is the focal length of the rear lens group 300, F is the total focal length of the vehicle-mounted high-definition fisheye lens.

The vehicle-mounted high-definition fisheye lens described above is characterized in that: the first lens 1, the second lens 2 and the third lens 3 satisfy the following expressions: 1.7≤Nd ₁ ≤1.9, 56≤Vd ₁ ≤65, 1.6≤Nd ₂ ≤1.8, 50≤Vd ₂ ≤55, 1.51≤Nd ₃ ≤1.55, 50≤Vd ₃ ≤57; wherein, Nd ₁ , Nd ₂ , and Nd ₃ are the first lens 1, the second lens 2 and the The refractive indices of the third lens 3 , Vd ₁ , Vd ₂ , Vd ₃ are the Abbe numbers of the first lens 1 , the second lens 2 and the third lens 3 respectively.

The vehicle-mounted high-definition fisheye lens described above is characterized in that: the vehicle-mounted high-definition fisheye lens satisfies the following expressions: 0.72≤T2≤1.3, 0.65≤T1/T2≤1.97, 0.25≤(T1+T2+T3) /TTL≤0.44; where T1, T2, and T3 are the central thicknesses of the first lens 1, the second lens 2, and the third lens 3, respectively, and TTL is the total length of the vehicle-mounted high-definition fisheye lens.

The vehicle-mounted high-definition fisheye lens as described above is characterized in that: the vehicle-mounted high-definition fisheye lens satisfies the following formula: 2W≥210°, 8.8≤TTL/F≤11.17; wherein, 2W is the value of the vehicle-mounted high-definition fisheye lens Field of view, TTL is the total length of the car HD fisheye lens, F is the total focal length of the car HD fisheye lens.

The vehicle-mounted high-definition fisheye lens as described above is characterized in that: the first lens 1 and the second lens 2 are glass spherical lenses, and a filter 500 is provided between the sixth lens 6 and the imaging surface 400 .

The vehicle-mounted high-definition fisheye lens as described above is characterized in that: the aspheric surface shapes of the third lens 3, the fourth lens 4, the fifth lens 5 and the sixth lens 6 satisfy the following equation:

$\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; cy</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 16</span>}}<span\; class="notranslate">\; ,</span>$

In the formula, the parameter c is the curvature corresponding to the radius, y is the radial coordinate, and its unit is the same as that of the lens length, and k is the coefficient of the conic conic curve; when the k coefficient is less than -1, the surface curve of the lens is a hyperbola , when the coefficient k is equal to -1, the surface curve of the lens is a parabola; when the coefficient k is between -1 and 0, the surface curve of the lens is an ellipse; when the coefficient k is equal to 0, the surface curve of the lens is a circle, and when the k coefficient is greater than 0, the surface curve of the lens is oblate; a ₁ to a ₈ represent the coefficients corresponding to each radial coordinate.

Compared with the prior art, the utility model has the following advantages:

1. The utility model is sequentially provided with a front lens group with positive refractive power, a diaphragm and a rear lens group with positive refractive power from the object side to the image side. This structure enables the utility model to become a super wide-angle lens with a maximum viewing angle of 220°, a large relative aperture, and a high-definition lens with 4 million pixels, and it can also ensure that it still has a high-definition lens in the temperature range of -40°C to +85°C. High definition, especially suitable for harsh environment vehicle environment.

2. The utility model can effectively converge a wide field of view into the vehicle lens optical system, reduce the tolerance sensitivity of the vehicle lens optical system, and improve the optical performance of the lens.

3. The utility model effectively corrects the excessive axial chromatic aberration of the system, and can ensure that the first lens has a smaller aperture, which is more beneficial to the miniaturization of the lens.

4. The utility model effectively shortens the total length of the lens, so that the optical system of the vehicle lens has a larger aperture, and the aperture number reaches F2.0.

5. The optical filter of the present invention can filter part of the light to reduce stray light and light spots, etc., so that the image color is bright and sharp and has good color reproduction; the third lens, the fourth lens, the fifth lens and the third lens The six lenses are plastic aspheric lenses, so as to achieve higher resolution and match the 4 million pixel optical sensor, so that the sharpness and color reproduction of the utility model are significantly improved.

6. The utility model has a large field of view, low cost, high definition, and strong light transmission ability, and is suitable for popularization and application.

【Description of drawings】

Fig. 1 is a schematic diagram of the utility model;

Fig. 2 is a schematic diagram of the optical path of the present invention.

【detailed description】

Below in conjunction with accompanying drawing, the utility model will be further described:

A vehicle-mounted high-definition fisheye lens is provided in sequence from the object side to the image side: a front lens group 100 with positive refractive power, a diaphragm 200, a rear lens group 300 with positive refractive power, and an imaging surface 400. The front lens group 100 includes a first lens 1, a second lens 2 and a third lens 3 arranged in sequence from the object side to the image side, the refractive power of the first lens 1 and the second lens 2 is negative, The refractive power of the third lens 3 is positive, and the rear lens group 300 includes a fourth lens 4, a fifth lens 5 and a sixth lens 6 arranged in sequence from the object side to the image side, and the said The refractive power of the fourth lens 4 and the sixth lens 6 is positive, the refractive power of the fifth lens 5 is negative, and the third lens 3, the fourth lens 4, the fifth lens 5 and the sixth lens The lenses 6 are all plastic aspherical lenses. This structure enables the utility model to become a super wide-angle lens with a maximum viewing angle of 220°, a large relative aperture, and a high-definition lens with 4 million pixels, and it can also ensure that it still has a high-definition lens in the temperature range of -40°C to +85°C. High definition, especially suitable for harsh environment vehicle environment. The third lens 3, the fourth lens 4, the fifth lens 5, and the sixth lens 6 are plastic aspheric lenses, which reduce the number and quality of the lenses on the one hand, and reduce the cost. On the other hand, they can achieve higher resolution and can match 400 The 10,000-pixel optical sensor significantly improves the sharpness and color reproduction of the utility model.

The first lens 1 is a meniscus lens, and its surface towards the object side is convex, and the surface towards the image side is concave; both surfaces of the second lens 2 are concave; the second lens 2 is concave; The surface of the three lenses 3 facing the object side is concave, and the surface facing the image side is convex.

Both surfaces of the fourth lens 4 are convex; both surfaces of the fifth lens 5 are concave; and both surfaces of the sixth lens 6 are convex.

The first lens 1 and the second lens 2 are glass spherical lenses, and a filter 500 is provided between the sixth lens 6 and the imaging surface 400 . The first lens 1 of the fisheye lens adopts a glass lens, which can effectively protect the lens from being scratched during use, and can also make the lens resist changes in harsh environments. The filter 500 can filter a part of light to reduce stray light and light spots, etc., so that the color of the image is bright and sharp and has good color reproduction.

The front lens group 100 and the rear lens group 300 satisfy the following expressions: 3.14≤F _before ≤9.38, 2.35≤F _before /F≤7.8, 3.5≤F _after ≤5.12, 61≤F _after /F≤4.25 , 0.62≤F _before /F _after ≤2.68; wherein, F _before is the focal length of the front lens group 100, F _after is the focal length of the rear lens group 300, and F is the total focal length of the vehicle-mounted high-definition fisheye lens. The focal length allocation that satisfies the above expression can effectively converge a wide field of view into the fisheye lens optical system, reduce the tolerance sensitivity of the optical system, and improve the relative brightness of the optical system.

The first lens 1, the second lens 2 and the third lens 3 satisfy the following expressions: 1.7≤Nd ₁ ≤1.9, 56≤Vd ₁ ≤65, 1.6≤Nd ₂ ≤1.8, 50≤Vd ₂ ≤55, 1.51≤Nd ₃ ≤1.55, 50≤Vd ₃ ≤57; wherein, Nd ₁ , Nd ₂ , and Nd ₃ are the refractive indices of the first lens 1, the second lens 2, and the third lens 3, respectively, and Vd ₁ , Vd ₂ , Vd ₃ is the Abbe number of the first lens 1 , the second lens 2 and the third lens 3 respectively. The refractive index and Abbe number of the first lens 1, the second lens 2 and the third lens 3 satisfy the above expression, which can effectively correct the excessive axial chromatic aberration of the fisheye lens optical system, and can ensure that the first lens 1 has a small caliber, which is more beneficial to lens miniaturization.

The vehicle-mounted high-definition fisheye lens satisfies the following expressions: 0.72≤T2≤1.3, 0.65≤T1/T2≤1.97, 0.25≤(T1+T2+T3)/TTL≤0.44; wherein, T1, T2, and T3 are respectively The central thickness of the first lens 1, the second lens 2 and the third lens 3, TTL is the total length of the vehicle-mounted high-definition fisheye lens. Therefore, the total length of the lens can be effectively shortened, so that the vehicle lens optical system has a larger aperture, and the aperture number reaches F2.0.

The vehicle-mounted high-definition fisheye lens satisfies the following formula: 2W≥210°, 8.8≤TTL/F≤11.17; wherein, 2W is the field of view of the vehicle-mounted high-definition fisheye lens, and TTL is the total length of the vehicle-mounted high-definition fisheye lens, F is the total focal length of the car HD fisheye lens. Therefore, the optical performance of the fisheye lens is improved, with high definition and strong light transmission ability.

The aspherical surface shapes of the third lens 3, the fourth lens 4, the fifth lens 5 and the sixth lens 6 satisfy the following equation:

$\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; cy</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 16</span>}}<span\; class="notranslate">\; ,</span>$

In the formula, the parameter c is the curvature corresponding to the radius, y is the radial coordinate, and its unit is the same as that of the lens length, and k is the coefficient of the conic conic curve; when the k coefficient is less than -1, the surface curve of the lens is a hyperbola , when the coefficient k is equal to -1, the surface curve of the lens is a parabola; when the coefficient k is between -1 and 0, the surface curve of the lens is an ellipse; when the coefficient k is equal to 0, the surface curve of the lens is a circle, and when the k coefficient is greater than 0, the surface curve of the lens is oblate; a ₁ to a ₈ represent the coefficients corresponding to each radial coordinate.

Claims (9)

1. A vehicle-mounted high-definition fisheye lens, characterized in that: from the object side to the image side, there are successively provided with: a front lens group (100) with positive refractive power, a diaphragm (200), and a rear lens with positive refractive power group (300) and imaging surface (400), the front lens group (100) includes a first lens (1), a second lens (2) and a third lens ( 3), the refractive power of the first lens (1) and the second lens (2) is negative, the refractive power of the third lens (3) is positive, and the rear lens group ( 300) includes a fourth lens (4), a fifth lens (5) and a sixth lens (6) arranged in sequence from the object side to the image side, and the fourth lens (4) and the sixth lens (6) The refractive power is positive, the refractive power of the fifth lens (5) is negative, and the third lens (3), the fourth lens (4), the fifth lens (5) and the sixth lens ( 6) All are plastic aspheric lenses. 2. The vehicle-mounted high-definition fisheye lens according to claim 1, characterized in that: the first lens (1) is a meniscus lens, and its surface toward the object side is a convex surface, and the surface toward the image side is Concave surface; both surfaces of the second lens (2) are concave; the surface of the third lens (3) facing the object side is concave, and the surface facing the image side is convex. 3. The vehicle-mounted high-definition fisheye lens according to claim 2, characterized in that: both surfaces of the fourth lens (4) are convex; both surfaces of the fifth lens (5) are convex. It is concave; both surfaces of the sixth lens (6) are convex. 4. The vehicle-mounted high-definition fisheye lens according to claim 1, 2 or 3, characterized in that: the front lens group (100) and the rear lens group (300) satisfy the following expression: 3.14≤F _before ≤9.38, 2.35≤F _before /F≤7.8, 3.5≤F _after ≤5.12, 61≤F _after /F≤4.25, 0.62≤F _before /F _after ≤2.68; where, F _before is the front lens group (100) The focal length of , F _after is the focal length of the rear lens group (300), and F is the total focal length of the vehicle-mounted high-definition fisheye lens. 5. The vehicle-mounted high-definition fisheye lens according to claim 4, characterized in that: the first lens (1), the second lens (2) and the third lens (3) satisfy the following expression: 1.7≤Nd ₁ ≤1.9, 56≤Vd ₁ ≤65, 1.6≤Nd ₂ ≤1.8, 50≤Vd ₂ ≤55, 1.51≤Nd ₃ ≤1.55, 50≤Vd ₃ ≤57; where Nd ₁ , Nd ₂ , Nd ₃ is the refractive index of the first lens (1), the second lens (2) and the third lens (3), Vd ₁ , Vd ₂ , Vd ₃ are the first lens (1), the second lens (2) and the third lens respectively The Abbe number of the three lenses (3). 6. The vehicle-mounted high-definition fisheye lens according to claim 5, characterized in that: the vehicle-mounted high-definition fisheye lens satisfies the following expressions: 0.72≤T2≤1.3, 0.65≤T1/T2≤1.97, 0.25≤(T1 +T2+T3)/TTL≤0.44; among them, T1, T2, T3 are the center thicknesses of the first lens (1), the second lens (2) and the third lens (3) respectively, and TTL is the vehicle-mounted high-definition fisheye lens total length. 7. The vehicle-mounted high-definition fisheye lens according to claim 6, characterized in that: the vehicle-mounted high-definition fisheye lens satisfies the following formula: 2W≥210°, 8.8≤TTL/F≤11.17; wherein, 2W is the vehicle-mounted The field of view of the high-definition fisheye lens, TTL is the total length of the car HD fisheye lens, and F is the total focal length of the car high-definition fisheye lens. 8. The vehicle-mounted high-definition fisheye lens according to claim 7, characterized in that: the first lens (1) and the second lens (2) are glass spherical lenses, and the sixth lens (6) and A filter (500) is arranged between the imaging surfaces (400). 9. The vehicle-mounted high-definition fisheye lens according to claim 1, characterized in that: the third lens (3), the fourth lens (4), the fifth lens (5) and the sixth lens (6) The shape of the aspheric surface satisfies the following equation: $\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; cy</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 16</span>}}<span\; class="notranslate">\; ,</span>$ In the formula, the parameter c is the curvature corresponding to the radius, y is the radial coordinate, and its unit is the same as that of the lens length, and k is the coefficient of the conic conic curve; when the k coefficient is less than -1, the surface curve of the lens is a hyperbola , when the coefficient k is equal to -1, the surface curve of the lens is a parabola; when the coefficient k is between -1 and 0, the surface curve of the lens is an ellipse; when the coefficient k is equal to 0, the surface curve of the lens is a circle, and when the k coefficient is greater than 0, the surface curve of the lens is oblate; a ₁ to a ₈ represent the coefficients corresponding to each radial coordinate.