JP2011164237A - Imaging lens - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a wide-angle imaging lens having superior optical performance, despite its small size, lightweight, and low cost, by suppressing failures, such as welds caused by jointing flows of molten resin in a mold, retaining high optical performance by the four-lens configuration, and appropriately setting the shapes of the lenses, the shapes of aspherical faces, and so on to reduce manufacturing tolerance. <P>SOLUTION: The imaging lens includes four lenses which are arranged, in the order starting from the object side: a first lens, which is a meniscus lens with negative refractive power, the convex face of which is oriented on the object side; a second lens with negative refractive power, the concave face of which is oriented on an image side; a third lens with positive refractive power, the convex face of which is oriented on the object side; an aperture stop; and a fourth lens with positive refractive power, the convex face of which is oriented on the image side, wherein if d1 represents the maximum thickness of the second lens, d2 represents the minimum thickness of the second lens, d3 represents the maximum thickness of the fourth lens, and d4 represents the minimum thickness of the fourth lens, the imaging lens satisfies the relations: d2/d1≤2 and d4/d3≤2. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a single-focus wide-angle imaging lens used for an imaging apparatus including a solid-state imaging device, such as a monitoring camera or an in-vehicle camera.

  Imaging lenses used for surveillance cameras and in-vehicle cameras are required to have good imaging performance over the entire screen while ensuring a wide angle of view. In addition, since the mounting space is often limited, it is required to be small and lightweight.

  The following Patent Documents 1 and 2 have been proposed as single-focus wide-angle imaging lenses that may be able to meet these demands. However, in the single focus lenses described in Patent Documents 1 and 2, since the ratio of the minimum thickness to the maximum thickness is large, a thin line is formed in the fused portion in the mold by the flow of the molten resin in the injection molding. In other words, there was a possibility of occurrence of a weld line. In addition, the effective diameter of the first lens is large, making it difficult to reduce the size.

JP 2004-29282 A JP 2005-345577 A

  The present invention has been made in view of the above points, and an object of the present invention is to suppress defects such as welds generated by the fusion of molten resin in a mold and to have high optical performance by a four-sheet configuration. On the other hand, it is to provide a small and thin wide-angle imaging lens by appropriately setting the shape of the lens, the shape of the aspherical surface and the like.

In order to achieve the above object, the lens of the present invention includes, in order from the object side, a first lens that is a meniscus lens having a negative refractive power with a convex surface facing the object side, and a negative refractive power with a concave surface facing the image side. A second lens having a spherical surface, a third lens having a positive refractive power with a convex surface facing the object side, an aperture stop, and a positive refractive power with a convex surface facing the image side, and at least one surface And an aspherical fourth lens, and satisfy the following conditional expressions (1) and (2).
d2 / d1 ≦ 2 (1)
d4 / d3 ≦ 2 (2)
However, d1 is the minimum thickness of the second lens, d2 is the maximum thickness of the second lens, d3 is the minimum thickness of the fourth lens, and d4 is the maximum thickness of the fourth lens.

  Preferably, the Abbe number for the d-line of the material constituting the first lens is 40 or more, the Abbe number for the d-line of the material constituting the second lens is 50 or more, and the d-line of the material constituting the third lens The Abbe number is set to 40 or less, and the Abbe number for the d-line of the material constituting the fourth lens is set to 50 or more. By selecting the material of each lens so as to satisfy such conditions, chromatic aberration can be corrected appropriately.

More preferably, the following conditional expression (3) is satisfied.
a1 / y ≦ 2.1 (3)
Here, a1 is the aperture diameter of the first lens, and y is the image height.

More preferably, the following conditional expressions (4) to (7) are satisfied.
−5 ≦ f1 / f ≦ −2 (4)
−5 ≦ f2 / f ≦ −3 (5)
3.0 ≦ f3 / f ≦ 5.0 (6)
0.5 ≦ f4 / f ≦ 2.5 (7)
Here, f1 is the focal length of the first lens, f2 is the focal length of the second lens, f3 is the focal length of the third lens, and f4 is the focal length of the fourth lens.

  According to the present invention, defects such as welds can be suppressed by limiting the ratio between the maximum thickness and the minimum thickness. In addition, by reducing the aperture diameter of the first lens, it is possible to provide a small-angle wide-angle imaging lens in which various aberrations are favorably corrected.

It is a figure which shows the basic composition of the imaging lens of this embodiment. In this embodiment, it is a figure which shows the aperture | diaphragm | squeeze part of an imaging lens, and the surface number provided with respect to each lens. In Example 1, it is an aberrational figure which shows spherical aberration, distortion aberration, and astigmatism. 6 is a diagram illustrating a configuration of an imaging lens employed in Example 2. FIG. In Example 2, it is an aberrational figure which shows spherical aberration, distortion aberration, and astigmatism. 6 is a diagram illustrating a configuration of an imaging lens employed in Example 3. FIG. In Example 3, it is an aberrational figure which shows spherical aberration, distortion aberration, and astigmatism. 6 is a diagram illustrating a configuration of an imaging lens employed in Example 4. FIG. In Example 4, it is an aberrational figure which shows spherical aberration, a distortion aberration, and astigmatism. 6 is a diagram illustrating a configuration of an imaging lens employed in Example 5. FIG. FIG. 10 is an aberration diagram showing spherical aberration, distortion, and astigmatism in Example 5.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 shows the lens configuration of the embodiment in an optical section. In these embodiments, in order from the object side, a CCD (Charge Coupled Device) or a CMOS (Complementary) having a first lens 110, a second lens 120, a third lens 130, an aperture stop 140, a fourth lens 150, and an image plane 160. This is a four-lens single-focus lens 100 in which an image sensor such as a mental-oxide semiconductor device is arranged.

The imaging lens embodying the present invention is preferably configured to satisfy conditional expressions (1) and (2).
d2 / d1 ≦ 2 (1)
d4 / d3 ≦ 2 (2)
However, d1 is the minimum thickness of the second lens, d2 is the maximum thickness of the second lens, d3 is the minimum thickness of the fourth lens, and d4 is the maximum thickness of the fourth lens.
When the upper limit of (1) and (2) is exceeded, the ratio of the minimum thickness to the maximum thickness is large. Lines can be generated, which makes manufacturing difficult.

  The four lenses in the imaging lens embodying the present invention are meniscus lenses that are advantageous for obtaining a wide angle of view by having a negative refractive power with a convex surface facing the object side in order from the object side. The lens 110, the second lens 120, which is a meniscus lens having a negative refractive power that is advantageous for downsizing and has a low manufacturing difficulty by directing the concave surface to the object side, and the positive refractive power by directing the convex surface to the object side Of the third lens 130 that makes it easy to correct aberrations, and the fourth lens 150 that has a positive refractive power with the convex surface facing the aperture stop 140 and the image side, thereby reducing the incident angle on the image plane. Are arranged as follows.

  In the imaging lens 100, the light incident from the object side OBJS is the object side R1 surface 1, the image surface side R2 surface 2 of the first lens 110, the object side R3 surface 3, the image surface side R4 surface 4 of the second lens 120, An image sensor that sequentially passes through the object side R5 surface 5, the image surface side R6 surface 6, the surface 7 of the aperture stop 140, the object side R7 surface 8 and the image surface side R8 surface 9 of the fourth lens 150 of the third lens 130. The light is condensed to 160.

  By forming the second lens 120 and the fourth lens 150 from a resin material, it is possible to realize weight reduction and cost reduction, and it is easy to manufacture an aspherical shape. Each of these lenses has at least one aspherical shape. By having an aspherical shape, aberration correction becomes easy, and it is possible to obtain a good resolution performance while being small.

  In addition, since the combination of the power of the second lens 120 and the fourth lens 150 made of a resin material is negative and positive, the temperature characteristics of the refractive index can be offset. In general, a resin material has a larger change in refractive index due to a temperature change than a glass material, and its refractive power is small at high temperature and large at low temperature. Therefore, in the present invention, each of the negative and positive lenses is made of a resin material, thereby canceling this change in refractive power and reducing the change in focal length in the entire lens system. As a result, it is desirable even in a wide temperature range. Performance can be obtained.

  By forming the third lens 130 from a glass material, a material having a wide range of dispersion values can be selected. As a result, it is possible to satisfactorily correct lateral chromatic aberration. Specifically, by using a glass material having a high dispersion value for the third lens 130, an advantageous effect for correcting chromatic aberration generated in the first lens and the second lens 120 is obtained.

  That is, in the present invention, the second lens 120 and the fourth lens 150 are made of a resin material to reduce the weight and reduce the cost, and form an aspheric shape that can be easily manufactured to correct aberrations. Furthermore, the temperature characteristics are offset by the combination of the negative and positive powers of these lenses. In addition, by selecting a high dispersion value using the third lens 130 as a glass material, it is also effective in correcting chromatic aberration, so that it is a compact, lightweight, high resolution performance, and a wide angle with excellent temperature characteristics. The lens is realized.

  The aspherical shape of the lens described in the following numerical examples is positive in the direction from the object side to the image plane side, k is a conical coefficient, and A, B, C, and D are aspherical coefficients. , R is the central radius of curvature, h represents the height of the light beam, and c represents the reciprocal of the central radius of curvature. Where Z is the depth from the tangent plane to the surface vertex, A is the fourth-order aspheric coefficient, B is the sixth-order aspheric coefficient, C is the eighth-order aspheric coefficient, and D is the tenth-order non-spherical coefficient. Each spherical coefficient is represented.

  Preferably, in the imaging lens embodying the present invention, the Abbe number of the material constituting the first lens 110 with respect to the d-line is 40 or more, and the Abbe number of the material constituting the second lens 120 with respect to the d-line is 50 or more. The Abbe number of the material constituting the third lens 130 with respect to the d-line is set to 40 or less, and the Abbe number of the material constituting the fourth lens with respect to the d-line is set to 50 or more. The first lens 110 and the second lens 120 that are located on the object side of the aperture stop 140 and are negative lenses have a magnification that is generated in the first lens 110 and the second lens 120 as the Abbe number of each material constituting them increases. Chromatic aberration is reduced. Further, this is because the chromatic aberration of magnification can be corrected more favorably as the Abbe number of the material constituting the third lens 130 that is a positive lens is closer to the object side than the aperture stop 140.

The imaging lens embodying the present invention is preferably configured to satisfy the conditional expression (3).
a1 / y ≦ 2.1 (3)
Here, a1 is the aperture diameter of the first lens, and y is the image height.
When the upper limit value of (3) is exceeded, the first lens is the largest in the lens design that realizes a wide angle, and thus it is difficult to reduce the size compared to the existing design.

The imaging lens embodying the present invention is preferably configured to satisfy conditional expressions (4) to (7).
−5 ≦ f1 / f ≦ −2 (4)
−5 ≦ f2 / f ≦ −3 (5)
3.0 ≦ f3 / f ≦ 5.0 (6)
0.5 ≦ f4 / f ≦ 2.5 (7)
Where f is the focal length of the entire lens system, f1 is the focal length of the first lens 110, f2 is the focal length of the second lens 120, f3 is the focal length of the third lens 130, and f4 is the focal length of the fourth lens 150. It is.
When the upper limit of (4) is exceeded, negative refractive power increases and correction of chromatic aberration of magnification becomes easy, but the curvature of the side surface of the first lens image becomes too small, making manufacture difficult. When the lower limit is exceeded, the curvature of the side surface of the first lens object becomes small, the effective diameter becomes large, and it becomes difficult to reduce the size of the lens system. If the upper limit of (5) is exceeded, the negative refractive power becomes strong, so the curvature of the second lens image side surface becomes too small. In addition, the curvature of the side surface of the third lens object becomes too small along with this, so that the manufacture becomes difficult. If the lower limit is exceeded, the negative refractive power decreases and the positive refractive power of the third lens decreases, making it difficult to correct lateral chromatic aberration. Exceeding the upper limit of (6) makes it difficult to correct chromatic aberration of magnification because the positive refractive power is insufficient. If the lower limit is exceeded, the curvature of the third lens object side surface becomes too small, making manufacture difficult. Since the fourth lens, particularly the image side surface, is greatly corrected for aberrations, if the upper limit of (7) is exceeded, the positive refractive power becomes too small, making it difficult to correct the aberration. On the contrary, when the lower limit is exceeded, the curvature of the side surface of the fourth lens image becomes too small, which makes manufacture difficult.

  Examples 1 to 5 according to specific numerical values of the imaging lens are shown below. In the numerical examples 1 to 5, the focal length, F number, field angle, image height, total lens length, and back focus (BF) are as shown in Table 1 below. Similarly, in the numerical examples of 1 to 5, the numerical data of the conditional expressions (1) to (6) are the values described in Table 2 below.

  The basic configuration of the lens system in the first embodiment is shown in FIG. 2, each numerical data (setting value) is shown in Tables 3 and 4, and the aberration diagram showing spherical aberration, distortion, and astigmatism is shown in FIG. Each is shown.

  As shown in FIG. 2, the first lens 110 has a meniscus shape with a convex surface facing the object side, the second lens 120 has a biconcave shape, the third lens 130 has a biconvex shape, and is arranged on the image side of the aperture stop 140. The fourth lens 150 has a biconvex shape. Each of the second lens 120 and the fourth lens 150 has an aspheric surface on both sides. Further, as shown in the figure, the distance between the R1 surface 1 and the R2 surface 2 which is the thickness of the first lens 110 is D1, and the distance between the R2 surface 2 of the first lens 110 and the R3 surface 3 of the second lens 120 is D2. The distance between the R3 surface 3 and the R4 surface 4 that is the thickness of the second lens 120 is D3, the distance between the R4 surface 4 of the second lens 120 and the R5 surface 5 of the third lens 130 is D4, and The distance between the R5 surface 5 and the R6 surface 6 that is the thickness is D5, the distance between the R6 surface 6 of the third lens 130 and the surface 7 of the aperture portion is D6, the surface 7 of the aperture portion and the R7 surface 8 of the fourth lens 150. The distance between them is D7, and the distance between the R7 surface 8 and the R8 surface 9 that is the thickness of the fourth lens 150 is D8.

Table 3 shows the stop corresponding to each surface number of the imaging lens in Example 1, the radius of curvature R, the interval D, the refractive index Nd, and the dispersion value νd of each lens. In Table 3, the surface with * in the surface number indicates an aspherical shape. Table 4 shows the aspheric coefficient of the predetermined surface.
<Numerical Example 1>

  3A is a spherical aberration (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, 656.3 nm from the left), and FIG. 3B is an astigmatism (solid line: left) in Example 1. 35.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm sagittal rays, dotted line: 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm tangential rays from the left), Figure 3 (C) Distortion aberrations (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm overlap) are shown. 3B and 3C, the vertical axis represents the half angle of view ω. In FIG. 3B, the solid line M represents the value of the meridional image plane, and the broken line S represents the value of the sagittal image plane ( The same applies to FIGS. 5, 7, 9, and 11). As can be seen from FIG. 3, according to the first embodiment, spherical, distorted, and astigmatism aberrations are satisfactorily corrected, and an imaging lens excellent in imaging performance can be obtained.

  The basic configuration of the lens system in the second embodiment is shown in FIG. 4, each numerical data (setting value) is shown in Tables 5 and 6, and aberration diagrams showing spherical aberration, distortion, and astigmatism are shown in FIG. Each is shown.

  The imaging lens in Example 2 is designed for the purpose of miniaturization by minimizing the occurrence of distortion near the center by superimposing MTFs having various angles of view.

  As shown in FIG. 4, the first lens 110 has a meniscus shape with a convex surface facing the object side, the second lens 120 has a biconcave shape, the third lens 130 has a biconvex shape, and is arranged on the image side of the aperture stop 140. The fourth lens 150 has a biconvex shape. Each of the second lens 120 and the fourth lens 150 has an aspheric surface on both sides.

Table 3 shows the stop corresponding to each surface number of the imaging lens in Example 1, the radius of curvature R, the interval D, the refractive index Nd, and the dispersion value νd of each lens. In Table 5, the surface numbered with * indicates that the surface is aspherical. Table 6 shows the aspheric coefficient of the predetermined surface.
<Numerical Example 2>

  5A is a spherical aberration (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, 656.3 nm from the left) and FIG. 5B is an astigmatism (solid line: left) in Example 2. (5) to 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm sagittal ray, dotted line: 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm tangential rays from the left) Distortion aberrations (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm overlap) are shown. As can be seen from FIG. 5, according to the second embodiment, the spherical lens, the distortion, and the astigmatism are satisfactorily corrected, and an imaging lens excellent in imaging performance can be obtained.

  The basic configuration of the lens system according to Embodiment 3 is shown in FIG. 6, each numerical data (setting value) is shown in Tables 7 and 8, and the aberration diagram showing spherical aberration, distortion, and astigmatism is shown in FIG. Each is shown.

  The imaging lens in Example 3 is designed for the purpose of miniaturization by suppressing the occurrence of distortion near the center.

  As shown in FIG. 6, the first lens 110 has a meniscus shape with a convex surface facing the object side, the second lens 120 has a meniscus shape with a concave surface facing the object side, and the third lens 130 has a meniscus shape with a convex surface facing the object side. The fourth lens 150 arranged on the image side of the aperture stop 140 has a biconvex shape. Each of the second lens 120 and the fourth lens 150 has an aspheric surface on both sides.

Table 7 shows the stop corresponding to each surface number of the imaging lens in Example 3, the radius of curvature R, the interval D, the refractive index Nd, and the dispersion value νd of each lens. In Table 7, the surface numbered with * indicates that the surface is aspherical. Table 8 shows the aspheric coefficient of the predetermined surface.
<Numerical Example 3>

  FIG. 7 shows the spherical aberration (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, 656.3 nm from the left) and FIG. 7B shows the astigmatism (solid line: solid line) in Example 3. Sagittal rays of 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm from the left, dotted line: 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm tangential rays from the left), Fig. 7 (C) Shows distortion aberrations (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm are overlapped), respectively. As can be seen from FIG. 7, according to the third embodiment, spherical, distorted, and astigmatism aberrations are satisfactorily corrected, and an imaging lens excellent in imaging performance can be obtained.

  The basic configuration of the lens system in the fourth embodiment is shown in FIG. 8, each numerical data (setting value) is shown in Tables 9 and 10, and the aberration diagram showing spherical aberration, distortion, and astigmatism is shown in FIG. Each is shown.

  The imaging lens in Example 4 is designed for the purpose of improving the MTF and reducing the size.

  As shown in FIG. 8, the first lens 110 has a meniscus shape with a convex surface facing the object side, the second lens 120 has a meniscus shape with a concave surface facing the object side, and the third lens 130 has a meniscus shape with a convex surface facing the object side. The fourth lens 150 arranged on the image side of the aperture stop 140 has a biconvex shape. Each of the second lens 120 and the fourth lens 150 has an aspheric surface on both surfaces, and in particular, the image side surface 4 of the second lens has an inflection point where the sign of the curvature is reversed near the center.

Table 9 shows the diaphragm corresponding to each surface number of the imaging lens in Example 1, the radius of curvature R, the interval D, the refractive index Nd, and the dispersion value νd of each lens. In Table 9, the surface numbered with * indicates that the surface is aspherical. Table 10 shows the aspheric coefficient of the predetermined surface.
<Numerical Example 4>

  9A is a spherical aberration (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, 656.3 nm from the left), and FIG. 9B is an astigmatism (solid line: solid line: Example 4). Sagittal rays of 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm from the left, dotted line: tangential rays of 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm from the left), Fig. 9 (C) Shows distortion aberrations (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm are overlapped), respectively. As can be seen from FIG. 9, according to Example 4, various aberrations of spherical surface, distortion, and astigmatism are satisfactorily corrected, and an imaging lens excellent in imaging performance can be obtained.

  The basic configuration of the lens system according to Embodiment 5 is shown in FIG. 10, each numerical data (setting value) is shown in Tables 11 and 12, and aberration diagrams showing spherical aberration, distortion, and astigmatism are shown in FIG. Each is shown.

  The imaging lens in Example 5 is designed for the purpose of downsizing, in particular, reducing the maximum effective diameter of the lens.

  As shown in FIG. 10, the first lens 110 has a meniscus shape with a convex surface facing the object side, the second lens 120 has a meniscus shape with a concave surface facing the object side, the third lens 130 has a biconvex shape, and the aperture stop 140 The fourth lens 150 disposed on the image side has a biconvex shape. Each of the second lens 120 and the fourth lens 150 has an aspheric surface on both surfaces, and in particular, the image side surface 9 of the fourth lens has an inflection point where the sign of the curvature is reversed around the periphery.

Table 11 shows the stop corresponding to each surface number of the imaging lens in Example 5, the radius of curvature R, the interval D, the refractive index Nd, and the dispersion value νd of each lens. In Table 11, a surface numbered with * indicates that it has an aspherical shape. Table 12 shows the aspheric coefficient of the predetermined surface.
<Numerical example 5>

  11A is a spherical aberration (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, 656.3 nm from the left), and FIG. 11B is an astigmatism (solid line: left) in Example 5. 115.8C, 486.1nm, 546.1nm, 587.6nm, 656.3nm sagittal rays, dotted line: 435.8nm, 486.1nm, 546.1nm, 587.6nm, 656.3nm tangential rays from the left), Fig. 11 (C) Distortion aberrations (435.8 nm, 486.1 nm, 546.1 nm, 587.6 nm, and 656.3 nm overlap) are shown. As can be seen from FIG. 11, according to the fifth embodiment, spherical, distorted, and astigmatism aberrations are corrected well, and an imaging lens excellent in imaging performance can be obtained.

100, 100A, 100B, 100C, 100D, 100E ... Imaging lens 110 ... First lens 120 ... Second lens 130 ... Third lens 140 ... Aperture stop 150 ... Fourth lens 160 ... Imaging surface

Claims (4)

In order from the object side, a first lens which is a meniscus lens having a negative refractive power with a convex surface facing the object side, a second lens having a negative refractive power with a concave surface facing the object side, and a spherical surface, the object side A third lens having a positive refractive power with a convex surface facing the lens, an aperture stop, and a fourth lens having a positive refractive power with the convex surface facing the image side and at least one surface being an aspherical surface. An imaging lens satisfying the following conditional expressions (1) and (2).
d2 / d1 ≦ 2 (1)
d4 / d3 ≦ 2 (2)
However, d1 is the minimum thickness of the second lens, d2 is the maximum thickness of the second lens, d3 is the minimum thickness of the fourth lens, and d4 is the maximum thickness of the fourth lens. The Abbe number of the material constituting the first lens with respect to the d-line is 40 or more, the Abbe number with respect to the d-line of the material constituting the second lens is 50 or more, and the Abbe number of the material constituting the third lens with respect to the d-line The imaging lens according to claim 1, wherein the imaging lens is set to 40 or less, and the Abbe number for the d-line of the material constituting the fourth lens is set to 50 or more. The imaging lens according to claim 1, wherein the following conditional expression (3) is satisfied.
a1 / y ≦ 2.1 (3)
Here, a1 is the aperture diameter of the first lens, and y is the image height. The imaging lens according to any one of claims 1 to 3, wherein the following conditional expressions (4) to (7) are satisfied.
−5 ≦ f1 / f ≦ −2 (4)
−5 ≦ f2 / f ≦ −3 (5)
3.0 ≦ f3 / f ≦ 5.0 (6)
0.5 ≦ f4 / f ≦ 2.5 (7)
Here, f1 is the focal length of the first lens, f2 is the focal length of the second lens, f3 is the focal length of the third lens, and f4 is the focal length of the fourth lens.

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