JP2001228393A - Teleconverter lens - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an inexpensive teleconverter lens with simple constitution though it has excellent performance. SOLUTION: This teleconverter lens TC attached to the object side of a principal lens MS and displacing the focal distance of an entire system to the longer one consists of a front group FG having positive refractive power and a rear group RG having negative refractive power and constitutes an afocal system as a whole. Then, the front group FG consists of a 1st positive lens, a 2nd positive lens and a 3rd negative lens, and the rear group RG consists of a positive lens and a negative lens, and the lens satisfies a following conditional expression (1). (1) 0.07<ΣF/fF<0.14. Provided that ΣF is the thickness of the front group on an optical axis and fF is the synthetic focal distance of the front group.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a teleconverter lens mounted on the object side of a main lens and displacing the focal length of the entire system to a longer one.

[0002]

2. Description of the Related Art Conventionally, as a teleconverter lens which is mounted on the object side of a main lens system and displaces the focal length of the entire system to a longer one, A: JP-A-10-282412 B: JP-A-10-197792 C: U.S. Pat. No. 2,803,167 D: German Patent No. 1,127,102, which has the following number of components and a front group configuration.

[0003] ABCD number of components 34 to 5 65 5 front group configuration negative positive negative positive or negative positive positive positive positive negative positive positive negative

[0004]

However, these have the following problems.

[0005] 1. In A, the negative rear group is only a negative lens. This is disadvantageous in simultaneously correcting axial chromatic aberration and lateral chromatic aberration.

[0006] 2. In the cases of A and B, the lens closest to the object in the front group is a negative lens. The negative lens in the front group has a strong meniscus shape and is difficult to process.

[0007] 3. In the case of the first to third embodiments of A and B, the front group has two lenses. The positive lens in the front group has a strong biconvex lens shape, and is difficult to process. This is disadvantageous in correcting aberrations.

[0008] 4. C has a large number of components.

[0009] 5. D has many surfaces with strong refractive power, and as a result, the ratio (t / r) between the lens thickness (t) of the positive lens and the radius of curvature (r) is large. In this case, the volume of the lens tends to increase. It is disadvantageous in terms of lens weight and cost.

The present invention has been made in view of such a situation of the prior art, and an object of the present invention is to provide a low-cost teleconverter lens having a simple configuration while having good performance.

[0011]

A teleconverter lens according to the present invention for achieving the above object is mounted on the object side of a main lens and displaces the focal length of the entire system to a longer one. An afocal system is constituted as a whole by sequentially including a front group having a positive refractive power and a rear group having a negative refractive power. The front group includes, in order from the object side, a positive first lens, a positive second lens, and a negative second lens. The rear unit includes three lenses, and the rear unit includes a positive lens and a negative lens, and satisfies the following conditional expression (1).

0.07 <ΔF / f _F <0.14 (1) where ΔF: thickness on the optical axis of the front group f _F : composite focal length of the front group.

In this case, the following conditional expression (2) or (3)
It is desirable to satisfy at least one of the following.

0.9 <f _F1 / f _F2 <1.4 (2) 0.84 <r _2F / r _3R <1.5 (3) where f _{F1 is} the first group of the front group. Focal length of one lens f _F2 : focal length of the second lens of the front group r _2F : radius of curvature of the object side surface of the second lens of the front group r _3R : curvature of the image side surface of the third lens of the front group Radius.

Further, it is desirable to satisfy the following conditional expressions (4) to (7).

1.5 < _nd1 <1.54 (4) 1.5 < _nd2 <1.54 (5) 62 < _νd1 <67 (6) 62 <ν _d2 <67 ··· (7) However, n _d1: refractive index of d line of the first lens of the front group n _d2: refractive index of d line of the second lens of the front group [nu _d1: first lens of the front group Abbe number ν _d2 : Abbe number of the second lens in the front group.

Another teleconverter lens of the present invention is a teleconverter lens mounted on the object side of the main lens and displacing the focal length of the entire system to a longer one. And a rear group consisting of a negative refractive power and an afocal system as a whole. The front group includes, in order from the object side, a convex first flat lens having a convex surface facing the object side, and a convex lens having a convex surface facing the object side. The second lens unit includes a second flat lens and a third flat concave lens having a concave surface facing the image side, and the rear unit includes a positive lens and a negative lens, and satisfies conditional expressions (1) to (7). It is assumed that.

0.07 <ΣF / f _F <0.14 (1) 0.9 <f _F1 / f _F2 <1.4 (2) 0.84 <r _2F / r _3R < 1.5 (3) 1.5 < _nd1 <1.54 (4) 1.5 < _nd2 <1.54 (5) 62 < _νd1 <67 (6) 62 <ν _d2 <67 (7) where ΔF: thickness on the optical axis of the front group f _F : composite focal length of the front group f _F1 : focal length f _F2 of the first lens of the front group : Focal length of the second lens of the front group r _2F : radius of curvature of the object-side surface of the second lens of the front group r _3R : radius of curvature of the image-side surface of the third lens of the front group n _d1 : of the front group The refractive index of the d-line of the first lens n _d2 : the refractive index of the d-line of the second lens of the front group ν _d1 : the Abbe number of the first lens of the front group ν _d2 : the Abbe number of the second lens of the front group .

Hereinafter, the reason and operation of the above configuration in the present invention will be described.

In the basic configuration of the first teleconverter lens according to the present invention, a negative lens is disposed in the positive front group and a positive lens is disposed in the negative rear group in order to satisfactorily correct chromatic aberration. . Furthermore, the configuration of the front group is particularly important for aberration correction of the lens and cost reduction. The front group is furthest from the main lens, so that off-axis rays are high and the lens has a large outer shape. Therefore, optimizing the configuration of the front group has a great effect on aberration correction, weight reduction, and cost reduction as a whole.

In the present invention, the positive refractive power of the front group is shared by two positive lenses. The negative lens of the front group is arranged closest to the image side of the front group. By placing a positive refractive power on the object side of the front group and a negative refractive power on the image side of the front group, the principal point of the front group can be easily located on the object side, and the front group can be downsized. This is advantageous.

Under these circumstances, it is necessary to satisfy conditional expression (1). Conditional expression (1) defines the ratio between the thickness on the optical axis of the front group and the combined focal length of the front group. If the upper limit of 0.14 to condition (1) is exceeded, the volume or weight of the lens tends to increase, which is not preferable in terms of cost. If the lower limit of 0.07 to condition (1) is exceeded, the rigidity of the lens will decrease, making processing difficult, which is not preferred.

It is more preferable to satisfy conditional expressions (2) and / or (3). Conditional expressions (2) and (3) relate to miniaturization of the front group. Conditional expression (2) is to make the first lens of the front group share a sufficient positive refractive power, and to arrange the principal point position of the front group on the object side. If the upper limit of 1.4 to condition (2) is exceeded, the amount of positive refractive power shared by the first lens will be small, which is disadvantageous for miniaturization. Exceeding the lower limit of 0.9 to condition (2) is disadvantageous in terms of aberration correction.

Conditional expression (3), like conditional expression (2), also relates to the arrangement of principal point positions in the front group. 1. Upper limit of conditional expression (3)
If it exceeds 5, it is disadvantageous for aberration correction. Exceeding the lower limit of 0.84 to condition (3) is disadvantageous for miniaturization.

It is desirable that conditional expressions (4) to (7) be satisfied. Conditional expressions (4) to (7) relate to cost. The conditional expressions (4) to (7) define the glass types of the first and second lenses having the largest lens diameters. It is most preferable to use a borosilicate crown glass type glass as the first and second lenses in order to reduce the cost while satisfying the correction of the chromatic aberration, and the effect is large. These conditional expressions define the range of the borosilicate crown glass system, and it is preferable to use glass types having characteristics in this range.

As a borosilicate crown glass system, BK7 and its equivalent are particularly advantageous in terms of cost. Glass materials equivalent to BK7 are as follows in each manufacturer.

Name Maker n _d ν _d BK7 SCHOTT 1.51680 64.17 BSC7 HOYA 1.51680 64.20 S-BSL7 OHARA 1.51633 64.14 Regarding another teleconverter lens of the present invention, in order to reduce the cost of the lens, the workability of the lens is improved. It is also important. In particular, it is effective to devise the lens shape of the front group having a large lens diameter. In order to improve workability while arranging a positive refractive power on the object side and a negative refractive power on the image side of the front group, the first and second lenses on the image side,
It is preferable that the object side surface of the lens is set to a flat surface. With such a configuration, the workability of the lens can be improved while maintaining good performance, which is advantageous in cost.

For conditional expression (1), the lower limit is set to 0.
09 and / or the upper limit is more preferably set to 0.13.

For conditional expression (2), the lower limit is set to 1.
It is more preferable to set 1 and / or the upper limit to 1.3.

For conditional expression (3), the lower limit is set to 0.
9 and / or the upper limit is more preferably 1.3.

For conditional expression (4), the lower limit is set to 1.
More preferably, 51 and / or the upper limit is 1.52.

For conditional expression (5), the lower limit is set to 1.
More preferably, 51 and / or the upper limit is 1.52.

For conditional expression (6), the lower limit is 63.
And / or the upper limit is more preferably set to 65.

For conditional expression (7), the lower limit is 63.
And / or the upper limit is more preferably set to 65.

Incidentally, in the teleconverter lens of the present invention, an aspherical surface may be used for the purpose of aberration correction and the like. Further, a plastic lens may be used for any lens for the purpose of cost reduction or the like. Further, the second lens and the third lens of the front group may be joined or separated. If joined
Workability when incorporating the lens into the lens frame is improved.

[0036]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments 1 to 3 of the teleconverter lens of the present invention will be described below. In all embodiments, the afocal magnification of the teleconverter lens is 1.42.

FIG. 1 is a sectional view showing a state in which the teleconverter lens TC of the first embodiment is mounted on the master lens MS.
Shown in In the drawing, L0 indicates an on-axis principal ray, and L1 indicates an off-axis principal ray. FIGS. 2 and 3 show lens sectional views of only the teleconverter lens TC of Examples 2 and 3, respectively. Numerical data of the master lens MS and the teleconverter lens TC of each embodiment will be described later.

Teleconverter lens TC of Embodiments 1 and 2
Is composed of a first lens of a convex plano-positive lens, a second lens of a convex plano-positive lens, and a third lens of a plano-concave negative lens, and the second lens and the third lens are cemented in a plane. The rear group RG includes a cemented lens of a convex positive lens and a biconcave negative lens.

The teleconverter lens TC of the third embodiment is
The first lens unit is a convex positive positive lens, the second lens is a positive convex positive lens, and the third lens is a negative plano-concave lens. Rear group R composed of a cemented lens of a negative meniscus lens having a convex surface and a positive meniscus lens having a convex surface facing the object side
G.

The teleconverter lens T of each embodiment
Japanese Patent Application No. 11-61897 (Japanese Patent Application No. 2000-17311) discloses a master lens MS for mounting C on the object side.
The telephoto end of the zoom lens according to the third embodiment is used. The master lens MS will be briefly described.

As shown in FIG. 1, the master lens MS is composed of a first group G1 having a positive refractive power, which is a combination of a negative meniscus lens having a convex surface facing the object side and a positive meniscus lens having a convex surface facing the object side. The second group G2, which includes a lens and a positive meniscus lens having a convex surface facing the object side and has a negative refractive power, includes a negative meniscus lens having a convex surface facing the object side, a biconcave lens, and a biconcave lens. A third lens unit G3 having a positive meniscus lens having a positive refractive power, a positive meniscus lens having a convex surface facing the object side, a biconvex lens, and a positive lens. The fourth group G4, which includes three negative meniscus lenses having a convex surface facing the side and has a positive refractive power, includes a negative meniscus lens having a convex surface facing the image side and a positive meniscus lens having a convex surface facing the image side. With a cemented lens Consisting of four sheets with two biconvex lens. The aspherical surface is used for two surfaces, the object side surface of the biconvex lens of the third group G3 and the most image side surface of the fourth group G4. In the drawing, S is a stop, and F is a member such as an optical path dividing member and an optical filter.

Of course, the teleconverter lens TC of each embodiment according to the present invention may be mounted on another master lens.

[0043] Hereinafter, numerical data of teleconverter lens TC and master lens MS of the above _{embodiments, r 1, r 2, r} 3, r 4, r 5, r 6, r 7, r 8
Is the radius of curvature of each lens surface of the teleconverter lens TC,
d ₁ , d ₂ , d ₃ , d ₄ , d ₅ , d ₆ , d ₇ are the distances between the lens surfaces of the tele-converter lens TC, and d ₈ is the distance from the most image-side surface of the tele-converter lens TC to the master lens MS. On-axis distance to the most object side surface of n _d1 , n _d2 , n
_d3, n _d4, n _d5 is the refractive index of the d-line of each lens of the teleconverter lens _{TC, ν d1, ν d2,} ν d3, ν d4, ν d5 is the Abbe number of each lens in the teleconverter lens TC.

F is the focal length of the master lens MS.
Release, F_NOIs the F-number of the master lens MS, ω is the mass
Half angle of view of the tar lens MS, r₉, R_Ten... is Master Len
Radius of curvature of each lens surface of the lens MS, d₉, D_Ten... is the master
-Spacing between lens surfaces of lens MS, n_d6, N_d7... ha
D-line refractive index of each lens of the star lens MS, ν_d6, Ν
_d7... is the Abbe number of each lens of the master lens MS.
You. In addition, as for the aspherical shape, x is defined as the light traveling direction is positive.
When y is taken in the direction orthogonal to the optical axis as the optical axis, the following equation is obtained.
Is represented by

X = (y ² / r) / [1+ ｛1- (1+
^{K) (y / r) 2} } 1/2] + A 4 y 4 + A 6 y 6 + A 8 y 8 +
A ₁₀ y ¹⁰ where r is the paraxial radius of curvature, K is the conic coefficient, A ₄ , A ₆ ,
A ₈ and A ₁₀ are fourth-order, sixth-order, eighth-order, and tenth-order aspherical coefficients, respectively.

Example 1 r ₁ = 101.6565 d ₁ = 10.0231 nd ₁ = 1.51680 ν _d1 = 64.20 r ₂ = ∞ d ₂ = 0.3000 r ₃ = 90.1960 d ₃ = 11.0034 nd ₂ = 1.51680 ν _d2 = 64.20 r ₄ = ∞ _{d 4 = 3.4800 n d3 = 1.58144} ν d3 = 40.75 r 5 = 80.8440 d 5 = 26.8800 r 6 = 170.6070 d 6 = 7.3700 n d4 = 1.60342 ν d4 = 38.03 r 7 = -112.5660 d 7 = 2.9800 n d5 = 1.77250 ν _{d5 = 49.60 r 8 = 91.2290 d} 8 = 3.5000.

Example 2 r ₁ = 99.4980 d ₁ = 10.0953 nd ₁ = 1.51633 ν _d1 = 64.14 r ₂ = ∞ d ₂ = 0.3000 r ₃ = 88.5894 d ₃ = 11.0002 nd ₂ = 1.51633 ν _d2 = 64.14 r ₄ = ∞ _{d 4 = 3.4823 n d3 = 1.58144} ν d3 = 40.75 r 5 = 77.2363 d 5 = 26.7890 r 6 = 166.6391 d 6 = 7.4480 n d4 = 1.60342 ν d4 = 38.03 r 7 = -106.1457 d 7 = 2.9879 n d5 = 1.77250 ν _{d5 = 49.60 r 8 = 92.2234 d} 8 = 3.5000.

Example 3 r ₁ = 107.2327 d ₁ = 9.5969 nd ₁ = 1.51633 ν _d1 = 64.14 r ₂ = ∞ d ₂ = 0.3000 r ₃ = 84.3412 d ₃ = 9.7050 nd ₂ = 1.51633 ν _d2 = 64.14 r ₄ = ∞ _{d 4 = 3.4556 n d3 = 1.58144} ν d3 = 40.75 r 5 = 90.9561 d 5 = 28.4974 r 6 = 417.1787 d 6 = 3.0000 n d4 = 1.77250 ν d4 = 49.60 r 7 = 44.9714 d 7 = 6.2976 n d5 = 1.60342 ν d5 _{= 38.03 r 8 = 111.7222 d 8} = 3.0000.

The master lens f = 9.099 ~ 18.100 ~ 35.998 F NO = 2.008 ~ 2.065 ~ 2.481 ω = 34.2 ° ~ 17.9 ° ~ 9.3 ° r 9 = 74.1213 d 9 = 2.5000 n d6 = 1.84666 ν d6 = 23.78 r 10 = 45.2920 _{d 10 = 7.6976 n d7 = 1.61800} ν d7 = 63.33 r 11 = 200.0000 d 11 = 0.1500 r 12 = 53.6322 d 12 = 5.1636 n d8 = 1.77250 ν d8 = 49.60 r 13 = 160.3763 d 13 = 28.3598 r 14 = 86.4469 d 14 _{= 1.8938 n d9 = 1.77250 ν d9} = 49.60 r 15 = 12.9947 d 15 = 6.5582 r 16 = -633.9388 d 16 = 1.3849 n d10 = 1.84666 ν d10 = 23.78 r 17 = 53.5036 d 17 = 3.0086 r 18 = -70.1852 d 18 _{= 1.3000 n d11 = 1.48749 ν d11} = 70.21 r 19 = 19.4251 d 19 = 4.0971 n d12 = 1.80518 ν d12 = 25.42 r 20 = 567.6091 d 20 = 1.5971 r 21 = ∞ ( _{stop) d 21 = 1.4993 r 22 =} 35.5332 d _{22 = 2.9155 n d13 = 1.84666 ν} d13 = 23.78 r 23 = 149.5334 d 23 = 1.9951 r 24 = 23.1874 ( _{aspherical) d 24 = 3.2540 n d14 =} 1.69350 ν d14 = 53.20 r 25 = -136.5790 d _{25 = 0.1500 r 26 = 54.2006 d} 26 = 1.1258 n d15 = 1.80518 ν d15 = 25.42 r 27 = 17.2110 d 27 = 10.6294 r 28 = -12.6096 d 28 = 1.1000 n d16 = 1.80518 ν d16 = 25.42 r 29 = -55.3792 d _{29 = 3.1600 n d17 = 1.61800 ν} d17 = 63.33 r 30 = -15.6001 d 30 = 0.1500 r 31 = 74.9447 d 31 = 3.2661 n d18 = 1.61800 ν d18 = 63.33 r 32 = -30.4739 d 32 = 0.1500 r 33 = 124.0475 d ₃₃ = 2.5117 n _d19 = 1.69350 ν _d19 = 53.20 r ₃₄ = -68.0400 (aspheric surface) d ₃₄ = 8.5887 r ₃₅ = ∞ d ₃₅ = 24.0000 nd ₂₀ = 1.51633 ν _d20 = 64.14 r ₃₆ = ｄ d ₃₆ = 1.0000 r _{37 = ∞ d 37 = 1.5700 n d21} = 1.54771 ν d21 = 62.84 r 38 = ∞ d 38 = 1.0000 r 39 = ∞ d 39 = 0.8000 n d22 = 1.52300 ν d22 = 55.00 r 40 = ∞ d 40 = 1.2900 r 41 = ∞ (Image plane) Aspheric surface 24th surface K = 0 A ₄ = -1.3659 × 10 ^-5 A ₆ = -5.3156 × 10 ^-9 A ₈ = -2.4548 × 10 ^-11 A ₁₀ = 2.2544 × 10 ^-12 34th surface K = 0 A ₄ = 6.6763 x 10 ^-6 A ₆ = 3.7977 x 10 ^-8 A ₈ = -4.9995 x 10 ^-10 A ₁₀ = 2.3437 x 10 ^-12 .

FIGS. 4 to 6 show aberration diagrams when the teleconverter lenses TC of the first to third embodiments are mounted on the master lens MS at the telephoto end and focused on infinity.
FIG. 7 shows an aberration diagram at the telephoto end of the master lens MS when focused on infinity. In each aberration diagram, (a) is the wide-angle end,
(B) is the middle position, (c) is the spherical aberration S at the telephoto end.
A, astigmatism AS, distortion DT, and lateral chromatic aberration CC are shown. In the drawing, “FIY” represents the image height.

Next, the conditional expression (1) in each of the above embodiments is used.
The values of (7) and the values of the basic parameters are shown below.

Conditional expressions Example 1 Example 2 Example 3 (1) 0.11 0.11 0.12 (2) 1.13 1.12 1.27 (3) 1.12 1.15 0.93 (4) 1.51680 1.51633 1.51633 (5) 1.51680 1.51633 1.51633 (6) 64.20 64.14 64.14 (7) 64.20 64.14 64.14 basic parameters example 1 example 2 example _{3 f F 227.561 231.461 194.454 f F1} 196.704 192.702 207.683 f F2 174.528 171.575 163.348 ΣF 24.807 24.878 23.057 r 2F 90.196 88.589 84.341 r 3R 80.844 77.236 90.956 n d1 1.51680 1.51633 _{1.51633 n d2 1.51680 1.51633 1.51633 ν d1} 64.20 64.14 64.14 ν d2 64.20 64.14 64.14
.

[0053]

As described above, according to the present invention, it is possible to provide a low-cost teleconverter lens having a simple structure while having good performance.

[Brief description of the drawings]

FIG. 1 is a lens cross-sectional view showing a state where a teleconverter lens according to a first embodiment of the present invention is mounted on a telephoto end of a master lens.

FIG. 2 is a lens cross-sectional view of a teleconverter lens according to a second embodiment of the present invention.

FIG. 3 is a sectional view of a teleconverter lens according to a third embodiment of the present invention.

FIG. 4 is an aberration diagram when the attachment lens of Example 1 is attached to a telephoto end of a master lens.

FIG. 5 is an aberration diagram when the attachment lens of Example 2 is attached to the telephoto end of the master lens.

FIG. 6 is an aberration diagram when the attachment lens of Example 3 is attached to the telephoto end of the master lens.

FIG. 7 is an aberration diagram at a telephoto end of a master lens in an infinity in-focus state.

[Description of Signs] TC: Teleconverter lens FG: Front group of teleconverter lens RG: Rear group of teleconverter lens MS: Master lens G1: First group of master lens G2: Second group of master lens G3: Master lens G4: fourth group of master lenses S: stop of master lens F: members such as optical path splitting member and optical filter of master lens

Claims (4)

[Claims] 1. A teleconverter lens mounted on the object side of a main lens and displacing the focal length of the whole system to a longer one, comprising, in order from the object side, a front group having a positive refractive power and a rear group having a negative refractive power. The whole group constitutes an afocal system,
In order from the object side, the first lens unit includes a first positive lens, a second positive lens, and a third negative lens. The rear unit includes a positive lens and a negative lens, and satisfies the following conditional expression (1). Teleconverter lens. 0.07 <ΔF / f _F <0.14 (1) where ΔF: thickness on the optical axis of the front group f _F : composite focal length of the front group. 2. The teleconverter lens according to claim 1, wherein at least one of the following conditional expressions (2) and (3) is satisfied. . _{0.9 <f F1 / f F2 <} 1.4 ··· (2) 0.84 <r 2F / r 3R <1.5 ··· (3) However, f _F1: the first lens of the front group Focal length f _F2 : focal length of the second lens of the front group r _2F : radius of curvature of the object side surface of the second lens of the front group r _3R : radius of curvature of the image side surface of the third lens of the front group . 3. The teleconverter lens according to claim 2, wherein the following conditional expressions (4) to (7) are satisfied. 1.5 < _nd1 <1.54 (4) 1.5 < _nd2 <1.54 (5) 62 < _νd1 <67 (6) 62 < _νd2 <67 (7) where n _d1 : refractive index of d-line of the first lens of the front group n _d2 : refractive index of d-line of the second lens of the front group ν _d1 : Abbe number of the first lens of the front group ν _d2 : Abbe number of the second lens in the front group. 4. A teleconverter lens mounted on the object side of a main lens and displacing the focal length of the whole system to a longer one, comprising, in order from the object side, a front group having a positive refractive power and a rear group having a negative refractive power. The whole group constitutes an afocal system,
In order from the object side, a first convex convex lens having a convex surface facing the object side, a second convex convex lens having a convex surface facing the object side, and a third plano-concave lens having a concave surface facing the image side. And the rear group comprises a positive lens and a negative lens, and satisfies conditional expressions (1) to (7). 0.07 <ΣF / f _F <0.14 (1) 0.9 <f _F1 / f _F2 <1.4 (2) 0.84 <r _2F / r _3R <1.5 (3) 1.5 < _nd1 <1.54 (4) 1.5 < _nd2 <1.54 (5) 62 < _νd1 <67 (6) 62 <ν _d2 <67 (7) where ΔF: thickness on the optical axis of the front group f _F : composite focal length of the front group f _F1 : focal length of the first lens of the front group f _F2 : front group R _2F : radius of curvature of the object-side surface of the second lens of the front group r _3R : radius of curvature of the image-side surface of the third lens of the front group n _d1 : first lens of the front group N _d2 : the refractive index of the d line of the second lens of the front group ν _d1 : the Abbe number of the first lens of the front group ν _d2 : the Abbe number of the second lens of the front group.