JP2005284003A - Photographic lens - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a photographic lens capable of obtaining sufficient brightness and high resolution in spite of simple and compact constitution, such as two-lens constitution, suitably mounted on a small-sized electronic equipment in particular. <P>SOLUTION: The photographic lens is equipped with a diaphragm, a positive lens G1 whose surface on an image side is constituted as an aspherical surface convex to the image side near an optical axis and a negative lens G2 whose surface on the image side is constituted as an aspherical surface convex to the image side near the optical axis in order from an object side. The photographic lens satisfies following conditional expressions (1) to (3). Provided that T is a conjugate distance, f is the focal distance of an entire system, ν2 is the Abbe number of the negative lens G2, and D3 is space on the optical axis Z1 between the surface S3 on the image side of the positive lens G1 and the surface S4 on the object side of the negative lens G2. A conditional expression (1) is 1.41<T/f<1.66, a conditional expression (2) is ν2<29.5, and a conditional expression (3) is D3/f>0.05. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a photographic lens suitable for mounting on a small electronic device such as a mobile phone with a camera or a PDA (Personal Digital Assistant).

  In recent years, with the spread of personal computers to ordinary homes and the like, digital still cameras (hereinafter simply referred to as digital cameras) capable of inputting image information such as photographed landscapes and human images to personal computers have rapidly spread. It's getting on. As mobile phones become more sophisticated, camera-equipped mobile phones equipped with a small imaging module are also rapidly spreading. In addition, small information terminal devices such as PDAs that are equipped with an imaging module have become widespread.

  In an electronic device having these imaging functions, an imaging element such as a CCD (Charge Coupled Device) or a CMOS (Complementary Metal Oxide Semiconductor) is used. In recent years, these image sensors have been extremely reduced in size and increased in pixels, and accordingly, the electronic device main body and the photographic lens mounted thereon are also required to have a compact configuration with high resolution performance. ing. For example, camera-equipped mobile phones and the like that are compatible with megapixels of 1 million pixels or more have been put into practical use, and the demand for performance has been increasing.

  2. Description of the Related Art Conventionally, as a lens system mounted on such a small and high-pixel electronic device, a two-lens imaging lens (imaging lens) including an aspheric lens is known (for example, Patent Documents 1 and 2). And 3).

  The photographic lens of Patent Document 1 includes, in order from the object side, a positive lens having both aspheric surfaces and a biconvex shape, and a positive meniscus lens having both surfaces aspheric and convex to the image surface side. This photographic lens is configured to satisfy both the conditional expression that defines the lens surface spacing and the conditional expression that defines the curvature of the lens surface, shortening the overall length and improving peripheral performance over the single lens configuration. I try to let them.

  The imaging lens of Patent Literature 2 includes, in order from the object side, an aperture stop, a biconvex positive lens including at least one aspheric surface, and a meniscus lens including at least one aspheric surface and concave on the object side. I have. This imaging lens is configured to satisfy both the conditional expression that defines the power of the positive lens and the conditional expression that defines the distance from the aperture stop to the imaging surface, and ensures an angle of view exceeding 30 °. However, efforts are made to reduce the size and cost.

In addition, the imaging lens of Patent Document 3 includes, in order from the object side, an aperture stop, a first lens having a positive refractive power with a convex surface facing the image side, and a meniscus second lens with a concave surface facing the object side. It is comprised by. The first and second lenses have at least one aspheric surface. Furthermore, by satisfying both the conditional expression for defining the focal length of the first lens and the conditional expression for defining the curvature radii of both surfaces of the first lens, the size can be reduced while ensuring good aberrations. Yes.
JP 2003-75719 A JP 2003-329921 A Japanese Patent Laid-Open No. 2004-4742

  Recently, an imaging module mounted on an electronic device as described above is required to have a bright photographing lens having a high resolving power and an F number of, for example, 2.8 or less. Furthermore, there is an increasing demand for downsizing of the entire electronic device, and further downsizing of the taking lens that affects the size is desired. In addition, since the number of pixels of the image sensor tends to further increase in the future, it is expected that higher resolution is required for the imaging lens.

  The photographing lenses (imaging lenses) described in Patent Documents 1 and 2 realize a bright and high-resolution lens system while achieving a certain size reduction by effectively using an aspheric surface in a two-lens configuration. However, due to the demand for higher resolution in the future and the demand for miniaturization of the entire electronic device, it is desired to develop a lens system that is smaller and higher performance than these. For example, the imaging lens of Patent Document 2 satisfies the condition of T / f <2.4 (T: conjugate distance, f: focal length of the entire system) with respect to miniaturization. Thus, T / f> 1.7 is substantially satisfied, and it is desired to develop a lens system that is further downsized. Further, although optical resin is used as a lens material, it is effective to use a glass mold lens positively in order to improve chromatic aberration. Furthermore, in the imaging lens of Patent Document 2, since an optical resin having a linear expansion coefficient with respect to temperature larger than that of glass is used for a strong lens, the focus position changes greatly due to a temperature change. For this reason, it is necessary to provide a focus correction function such as autofocus on the camera side. Similarly, the photographic lens of Patent Document 1 still has room for improvement in terms of miniaturization and selection of lens materials. In addition, the imaging lens of Patent Document 3 has a relatively long overall length and still has room for improvement in terms of brightness.

  The present invention has been made in view of such problems, and the object thereof is a simple and compact configuration suitable for mounting on a small electronic device having a two-sheet configuration, with sufficient brightness, high resolution, and the like. An object of the present invention is to provide a photographing lens that can obtain the above.

The photographic lens of the present invention is a photographic lens having a two-piece structure, in order from the object side, a stop, and a positive lens composed of an aspherical surface in which the image side surface is convex to the image side in the vicinity of the paraxial axis, A negative lens composed of an aspherical surface in which the image-side surface is convex toward the image side in the vicinity of the paraxial axis. This photographing lens further satisfies the following conditional expressions (1) to (3).
1.41 <T / f <1.66 (1)
ν2 <29.5 (2)
D3 / f> 0.05 (3)
Where T is a conjugate distance (distance from the stop to the imaging surface), f is the focal length of the entire system, ν2 is the Abbe number of the negative lens, and D3 is the image side surface of the positive lens and the negative lens Is the distance from the object side surface.

  In the photographic lens of the present invention, with the above basic configuration, the aspherical surface is positively used while the number of lenses is as small as two, and by satisfying a predetermined conditional expression, various aberrations are excellent without increasing the total length. In addition, it is possible to obtain sufficient brightness. In particular, since the ratio (T / f) between the conjugate distance T and the focal length f of the entire system is optimized by the conditional expression (1), the overall length can be suppressed to be short. In addition, sufficient brightness is ensured by disposing the diaphragm on the most object side. By satisfying conditional expression (2), axial chromatic aberration is mainly reduced. Furthermore, by satisfying the conditional expression (3) and making the surface distance between the positive lens and the negative lens appropriate, the dispersion of the lens material is effectively used, and the chromatic aberration is corrected well.

The photographic lens of the present invention realizes a higher-performance lens system by appropriately adopting the following preferable conditions in accordance with required specifications in addition to the above basic configuration. That is, it is desirable that this photographic lens is further configured to satisfy the following conditional expressions (4) to (6). Where ν1 is the Abbe number of the positive lens, R2 is the radius of curvature near the paraxial axis on the object side surface of the positive lens, and f1 is the focal length of the positive lens. By satisfying conditional expression (4), axial chromatic aberration is mainly reduced. Further, the object side surface of the first lens (positive lens) from the object side that satisfies the conditional expression (5) is made relatively close to a plane, and further the conditional expression (6) is satisfied, By making the power relatively strong, more brightness is secured.
ν1> 54 (4)
| F / R2 | <10 (5)
0.4 <f1 / f <0.75 (6)

It is desirable that the imaging lens of the present invention is further configured to satisfy the following conditional expression (7). Here, fi is the focal length (i = 1, 2) of the i-th lens from the object side, and νi is the Abbe number (i = 1, 2) of the i-th lens from the object side. By satisfying conditional expression (6), axial and magnification chromatic aberrations are reduced.
| F / D3 · Σ (fi / νi) | <1.0 (7)

It is desirable that the imaging lens of the present invention is further configured to satisfy the following conditional expression (8). However, R3 is a radius of curvature near the paraxial axis on the image side surface of the positive lens, and R4 is a radius of curvature near the paraxial axis on the object side surface of the negative lens. By satisfying conditional expression (8), field curvature is reduced.
R3 <R4 (8)

  According to the photographic lens of the present invention, a photographic lens having a two-lens configuration, in order from the object side, a stop and a positive lens composed of an aspherical surface in which the image side surface is convex to the image side in the vicinity of the paraxial axis And a negative lens composed of an aspherical surface in which the image-side surface is convex toward the image side in the vicinity of the paraxial axis, and further satisfies predetermined conditional expressions (1) to (3). Although it is a simple and compact configuration suitable for mounting on a small electronic device, which is a two-sheet configuration, sufficient brightness and high resolution can be obtained while correcting aberrations well.

  Further, when the predetermined conditional expression (4) regarding the Abbe number of the positive lens is satisfied, in particular, the longitudinal chromatic aberration can be further reduced. Further, the object side surface of the first lens (positive lens) from the object side that satisfies the conditional expression (5) is made relatively close to a plane, and further the conditional expression (6) is satisfied, By making the power relatively strong, it is possible to secure even more brightness.

  Further, when the predetermined conditional expression (7) relating to the surface distance between the positive lens and the negative lens is satisfied, in particular, axial and magnification chromatic aberration can be reduced.

  Further, when the conditional expression (8) relating to the radius of curvature near the paraxial axis in the positive lens and the negative lens is satisfied, it is possible to reduce field curvature, in particular.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 shows a configuration example of a photographic lens according to an embodiment of the present invention. This configuration example corresponds to a lens configuration of a first numerical example (FIGS. 5A and 5B) described later. 2 to 4 show other configuration examples of the photographing lens according to the present embodiment. 2 to 4 correspond to lens configurations of second to fourth numerical examples (FIGS. 6A, 6B to 8A, 8B) described later. . Since the basic configuration is the same in each configuration example, the following description is based on the configuration of the photographic lens shown in FIG.

  This photographic lens has a brightness of, for example, F2.8, and is particularly suitable for mounting on an imaging device including an imaging device having high pixels (for example, about 800 to 1,000,000 pixels). In FIG. 1, the side indicated by reference sign Zobj is the object side, and the side indicated by reference sign Zimg is the image side. The reference symbol Ri (R1 to R7) represents the i-th component that increases sequentially toward the image side, with the surface of the most object-side component including the aperture stop (hereinafter simply referred to as the stop) St as the first. The curvature radius of surface Si (i = 1-7) is shown. Here, the aperture stop St corresponds to the surface S1. The symbol Di indicates the surface interval on the optical axis Z1 between the i-th surface Si and the i + 1-th surface Si + 1.

  This photographing lens is a simple two-lens lens system, and includes an aperture stop St, a positive lens G1, and a negative lens G2 in order from the object side along the optical axis Z1. Both the positive lens G1 and the negative lens G2 are aspheric on both surfaces (that is, the surfaces S2 to S5). Further, in the vicinity of the paraxial axis of the positive lens G1, the object-side surface S2 is concave on the object side, and the image-side surface S3 is convex on the image side. On the other hand, in the vicinity of the paraxial axis, the negative lens G2 has a meniscus shape in which the object side surface S4 is concave on the object side and the image side surface S5 is convex on the image side. However, as in the configuration example shown in FIGS. 2 and 3, the object-side surface S2 of the positive lens G1 may be convex toward the object side. As shown in FIG. 2 and FIG. 3, the surface S2 has an absolute value of curvature that gradually increases toward the periphery, and is further concaved on the object side via an inflection point so that it differs from the vicinity of the paraxial. May be. 2 and 3, the surfaces S4 and S5 of the negative lens G2 have an absolute value of curvature that gradually increases toward the periphery. It may be made to be convex on the object side (concave on the image side).

  An imaging element such as a CCD (not shown) is disposed on the imaging surface (imaging surface) Simg of the photographing lens. Various optical members may be arranged between the negative lens G2, which is the final lens, and the imaging surface Simg depending on the configuration of the camera on which the lens is mounted. In the configuration example of FIG. 1, a cover glass GC for protecting the imaging surface Simg is disposed. In addition, optical members such as an infrared cut filter and a low-pass filter may be disposed.

The photographing lens is further configured to satisfy the following conditional expressions (1) to (3). However, T is a conjugate distance (in this embodiment, it means the distance from the stop St to the imaging plane Simg), f is the focal length of the entire system, and ν2 is the Abbe number of the negative lens G2. , D3 is the distance on the optical axis between the image side surface S3 of the positive lens G1 and the object side surface S4 of the negative lens G2. Here, it is desirable that the negative lens G2 is a glass mold lens.
1.41 <T / f <1.66 (1)
ν2 <29.5 (2)
D3 / f> 0.05 (3)

In particular, in the case of the configuration example shown in FIG. 1, it is desirable that the following conditional expression (3-1) is satisfied. This is because chromatic aberration can be corrected more favorably.
D3 / f ≧ 0.2 (3-1)

Further, it is desirable that the taking lens is configured to satisfy the following conditional expressions (4) to (6). Where ν1 is the Abbe number of the positive lens G1, R2 is the radius of curvature near the paraxial axis on the object side surface S2 of the positive lens G1, and f1 is the focal length of the positive lens G1. Here, it is desirable that the positive lens G1 is also a glass mold lens.
ν1> 54 (4)
| F / R2 | <10 (5)
0.4 <f1 / f <0.75 (6)

Furthermore, it is desirable that this photographic lens is configured to satisfy the following conditional expression (7). Here, fi is the focal length (i = 1, 2) of the i-th lens from the object side, and νi is the Abbe number (i = 1, 2) of the i-th lens from the object side.
| F / D3 · Σ (fi / νi) | <1.0 (7)

Further, it is desirable that the photographing lens is configured to satisfy the following conditional expression (8). However, R3 is a radius of curvature near the paraxial axis on the image side surface S3 of the positive lens G1, and R4 is a radius of curvature near the paraxial axis on the object side surface S4 of the negative lens G2.
R3 <R4 (8)

  Next, operations and effects of the photographic lens configured as described above will be described.

  In this photographic lens, the positive lens G1 and the negative lens G2 are positively used to correct the shape of each lens by positively correcting the shape of each lens, thereby performing good aberration correction while the number of lenses is as small as two. . In addition, since the ratio (T / f) between the conjugate distance T and the focal length f of the entire system is optimized and the stop St is disposed closest to the object side, the overall length of the system can be further shortened. Furthermore, the aperture St is disposed closest to the object side, the radius of curvature R2 of the positive lens G1 is relatively close to a plane, and the power of the positive lens G1 is relatively increased, thereby ensuring sufficient brightness. I am trying.

  Here, the significance of the conditional expressions (1) to (8) will be described in detail.

  Conditional expression (1) is an advantageous condition for downsizing. By satisfying conditional expression (1), the ratio (T / f) between the conjugate distance T and the focal length f of the entire system can be optimized, and the overall length can be shortened. If the glass material of the negative lens G2 is selected so as to satisfy the conditional expression (2), especially the axial chromatic aberration can be corrected well. Furthermore, by satisfying conditional expression (3), the surface distance D3 between the positive lens G1 and the negative lens G2 can be optimized, and chromatic aberration can be corrected well by effectively using dispersion of the glass material.

Further, if the glass material of the positive lens G1 is selected so as to satisfy the conditional expression (4), in particular, axial chromatic aberration can be corrected more satisfactorily. Conditional expression (5) is a conditional expression for optimizing the radius of curvature R2 on the surface S2 of the positive lens G1, and conditional expression (6) is that of the positive lens G1 with respect to the refractive power (1 / f) of the entire system. It is a formula representing an appropriate range of an amount (f1 / f) representing the magnitude of refractive power (1 / f1). The aperture stop St is disposed closest to the object side, the radius of curvature R2 is made closer to a plane so as to satisfy these conditional expressions (5) and (6), and the power of the positive lens G1 is increased. Thus, sufficient brightness can be obtained. Here, in order to ensure even more brightness, in the conditional expression (5),
| F / R2 | <3.3
It is desirable to satisfy
| F / R2 | <0.4
It is desirable to satisfy

  Furthermore, by satisfying conditional expression (7), it is possible to correct axial and lateral chromatic aberrations more satisfactorily.

  In addition, when the conditional expression (8) is satisfied, it is possible to particularly favorably correct curvature of field.

  As described above, according to the photographic lens of the present embodiment, since the aspherical surface is used positively and the conditional expressions (1) to (8) are satisfied, the number of lenses can be as small as two. Bright and good optical performance can be ensured while achieving low cost and shortening the overall length.

  Next, specific numerical examples of the photographing lens according to the present embodiment will be described. Below, the 1st-4th numerical example (Examples 1-4) is demonstrated collectively. FIGS. 5A and 5B show specific lens data corresponding to the configuration of the photographing lens shown in FIG. FIGS. 6A, 6B, 7A, 7B, 8A, and 8B are specific examples corresponding to the configuration of the zoom lens shown in FIGS. Lens data is shown. 5A, FIG. 6A, FIG. 7A, and FIG. 8A (hereinafter collectively referred to as FIG. 5A, etc.) include lens data of the examples. FIG. 5B, FIG. 6B, FIG. 7B, and FIG. 8B (hereinafter collectively referred to as FIG. 5B, etc.) show the basic data portion. The data part regarding an aspherical shape is shown among the lens data of an example.

  In the field of the surface number Si in each lens data such as FIG. 5 (A), the surface of the constituent element closest to the object side including the aperture stop St and the cover glass GC is set as the first for the photographing lens of each example. The number of the i-th (i = 1-7) surface which attached | subjected the code | symbol so that it may increase sequentially as it goes to the side is shown. In the column of the curvature radius Ri, the value of the curvature radius of the i-th surface Si from the object side including the stop St is shown in correspondence with the reference symbol Ri in FIG. Also in the column of the surface interval Di, the interval on the optical axis between the i-th surface Si and the i + 1-th surface Si + 1 from the object side is shown in correspondence with the reference numerals given in FIG. The unit of the value of the curvature radius Ri and the surface interval Di is millimeter (mm). In the columns of Ndj and νdj, the refractive index for the d-line (587.6 nm) and the Abbe number of the j-th (j = 1 to 3) optical element from the object side including the cover glass GC are shown.

  In each lens data such as FIG. 5A, the symbol “*” attached to the left side of the surface number indicates that the lens surface is aspherical. In the photographic lenses of Examples 1 to 4, all the surfaces of the positive lens G1 and the negative lens G2, that is, the surfaces S2 to S5 are aspherical. In the basic lens data such as FIG. 5A, numerical values of the radius of curvature near the optical axis (near the paraxial axis) are shown as the radius of curvature of these aspheric surfaces.

In the numerical value of each aspherical data such as FIG. 5B, the symbol “E” indicates that the next numerical value is a “power exponent” with 10 as the base, and an exponent function with 10 as the base. The numerical value represented by “E” is multiplied by the numerical value before “E”. For example, “1.0E-02” indicates “1.0 × 10 ⁻² ”.

In each aspheric surface data, the values of the coefficients A _k and KA in the aspheric surface expression represented by the following expression (A) are described. More specifically, Z is the length (mm) of a perpendicular line drawn from a point on the aspheric surface at a height h from the optical axis to the tangential plane (plane perpendicular to the optical axis) of the apex of the aspheric surface. Show.

Z = C · h ² / {1+ (1−KA · C ² · h ² ) ^1/2 } + ΣA _k · h ^k (A)
However,
Z: Depth of aspheric surface (mm)
h: Distance from the optical axis to the lens surface (height) (mm)
KA: eccentricity C: paraxial curvature = 1 / R
(R: paraxial radius of curvature)
A _k : k-th order (k = 3 to 12) aspheric coefficient

  FIG. 9 collectively shows values relating to the conditional expressions (1) to (7) described above for the respective examples. As is clear from the data shown in FIG. 9, the photographing lenses of Examples 1 to 4 satisfy the above conditional expressions (1) to (7). Further, as is clear from the lens data in FIG. 5A and the like, the photographing lenses of Examples 1 to 4 satisfy the conditional expression (8).

  10A to 10C show spherical aberration, astigmatism, and distortion (distortion aberration) in the photographing lens of Example 1. FIG. In FIG. 10A showing spherical aberration and FIG. 10B showing astigmatism, values at wavelengths of 420 nm, 560 nm and 680 nm are shown. In FIG. 10B, the solid line indicates the sagittal aberration, and the broken line indicates the tangential aberration. FIG. 10C shows aberration at a wavelength of 560 nm.

  Similarly, various aberrations in the photographic lens of Example 2 are shown in FIGS. 11A to 11C, and various aberrations in the photographic lens of Example 3 are shown in FIGS. 12A to 12C. Various aberrations in the photographic lens are shown in FIGS.

  As described above, as shown in each numerical data and each aberration diagram, in each example, sufficient brightness and good aberration performance are obtained while reducing the overall length and reducing the size.

  In addition, this invention is not limited to the said embodiment and each Example, A various deformation | transformation implementation is possible. For example, the radius of curvature, the surface interval, and the refractive index of each lens component are not limited to the values shown in the above numerical examples, and may take other values.

1 is a cross-sectional view of a lens corresponding to Example 1 and illustrating a configuration example of a photographing lens according to an embodiment of the present invention. FIG. FIG. 2 is a lens cross-sectional view illustrating a second configuration example of a photographing lens according to an embodiment of the present invention and corresponding to Example 2; FIG. 9 is a lens cross-sectional view illustrating a third configuration example of a photographing lens according to an embodiment of the present invention and corresponding to Example 3; FIG. 9 is a lens cross-sectional view illustrating a fourth configuration example of a photographing lens according to an embodiment of the present invention and corresponding to Example 4; FIG. 3 is a diagram illustrating lens data of a photographing lens according to Example 1. 6 is a diagram illustrating lens data of a photographing lens according to Example 2. FIG. 6 is a diagram illustrating lens data of a photographing lens according to Example 3. FIG. 6 is a diagram illustrating lens data of a photographic lens according to Example 4. FIG. It is a figure which shows the value regarding the conditional expression which the imaging lens which concerns on each Example satisfy | fills. FIG. 6 is an aberration diagram illustrating spherical aberration, astigmatism, and distortion of the imaging lens according to Example 1; FIG. 6 is an aberration diagram illustrating spherical aberration, astigmatism, and distortion of the photographing lens according to Example 2. FIG. 6 is an aberration diagram illustrating spherical aberration, astigmatism, and distortion of the photographing lens according to Example 3; FIG. 6 is an aberration diagram illustrating spherical aberration, astigmatism, and distortion of the photographing lens according to Example 4;

Explanation of symbols

G1 ... positive lens, G2 ... negative lens, GC ... cover glass, Si ... i-th lens surface from the object side, Ri ... curvature radius of the i-th lens surface from the object side, Di ... i-th from the object side And the i + 1th lens surface, Simg ... imaging surface (imaging surface), Z1 ... optical axis.

Claims (4)

A two-lens photographic lens,
In order from the object side, a stop, a positive lens composed of an aspherical surface in which the image side surface is convex toward the image side in the vicinity of the paraxial axis, and an aspherical surface in which the image side surface is convex toward the image side in the vicinity of the paraxial direction And a negative lens composed of
Furthermore, it is comprised so that the following conditional expressions (1)-(3) may be satisfied.
1.41 <T / f <1.66 (1)
ν2 <29.5 (2)
D3 / f> 0.05 (3)
However,
T: conjugate distance f: focal length of entire system ν2: Abbe number of negative lens D3: distance on the optical axis between the image side surface of the positive lens and the object side surface of the negative lens Furthermore, it is comprised so that the following conditional expression (4)-(6) may be satisfied. The imaging lens of Claim 1 characterized by the above-mentioned.
ν1> 54 (4)
| F / R2 | <10 (5)
0.4 <f1 / f <0.75 (6)
However,
ν1: Abbe number of the positive lens R2: radius of curvature near the paraxial axis on the object side surface of the positive lens f1: focal length of the positive lens Furthermore, it is comprised so that the following conditional expressions (7) may be satisfy | filled. The imaging lens of Claim 2 characterized by the above-mentioned.
| F / D3 · Σ (fi / νi) | <1.0 (7)
However,
fi: focal length at the i-th lens from the object side (i = 1, 2)
νi: Abbe number at the i-th lens from the object side (i = 1, 2) Furthermore, it is comprised so that the following conditional expressions (8) may be satisfy | filled. The imaging lens of Claim 3 characterized by the above-mentioned.
R3 <R4 (8)
However,
R3: radius of curvature near the paraxial axis on the image side surface of the positive lens R4: radius of curvature near the paraxial axis on the object side surface of the negative lens

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