JP2584526B2 - Microscope objective lens - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to an objective lens for a microscope which can be used in an ultraviolet region, particularly in a deep ultraviolet region having a wavelength of 300 nm or less.

(Conventional technology and its problems) As is well known, in a microscope, when the numerical aperture (NA) of the objective lens is the same, the resolution limit increases as the wavelength becomes shorter, It can be observed over the details of the sample. In addition, when the sample is irradiated with ultraviolet light, fluorescent light having higher intensity is often emitted as compared with the case where visible light is irradiated. Therefore, to obtain more information by observing the sample with a microscope,
It is desired to provide a microscope that can be used in the ultraviolet. For that purpose, an objective lens that can be used in the ultraviolet region or the far ultraviolet region is required.

Therefore, conventionally, for example, an objective lens for a microscope shown in FIG. 6 has been adopted as an objective lens usable in an ultraviolet region or a far ultraviolet region. FIG. 6 is a view showing the configuration of the objective lens 70 for a microscope. This objective lens 70 is described in the Optical Technology Contact Magazine Vol.25 No.2 (February 1987) P.187.

As shown in the figure, the objective lens 70 is composed of a first fluorite lens 71, a second lens 71, and a second lens sequentially arranged from the object side (the left side in the figure) to the imaging side (the right side in the figure). Third lens group 7
It consists of 2,73. The second lens group 72 is formed by joining a concave lens 72a made of quartz and convex lenses 72b and 72c made of fluorite. The third lens group 73 is a second lens group.
Similarly to the lens 72, the concave lens 73a made of quartz is replaced with the convex lens 7 made of fluorite.
It is the one sandwiched between 3b and 73c.

In this objective lens 70, each lens 71, 72a to 72c, 73a to 7
Since 3c is made of quartz or fluorite, it can transmit ultraviolet rays and far ultraviolet rays. Therefore, the objective lens 70
Can also be used in the ultraviolet or far ultraviolet region.

In addition, the second lens group 72 is composed of a concave lens 72a made of quartz and convex lenses 72b and 72c made of fluorite, and the third lens group 73 is a concave lens 73a made of quartz and convex lenses 73b and 73c made of fluorite.
Therefore, chromatic aberration can be corrected.

By the way, in the second lens group 72, the convex lens 72b,
Optical contact is made between the concave lens 72a and the convex lens 72c. Also in the third lens group 73, the convex lens 73b, the concave lens 73a, and the convex lens 73c are in optical contact with each other. The reason is that at present, there is no practical adhesive that transmits far ultraviolet rays. For this reason, the only way to prevent total reflection at the lens joint surface is to make optical contact at the joint surface. Therefore, it is required to process each joint surface with high precision, and there is a problem that the manufacturing cost of the objective lens 70 increases.

Therefore, the inventor of the present application has proposed a microscope objective lens in which the above-mentioned problem has been solved in an earlier application (hereinafter, simply referred to as “an earlier application” in JP-A-1-319719 and JP-A-1-319720). Proposed. FIG. 7 is a view showing one example of a microscope objective lens according to this proposal. According to this proposal, the microscope objective lens 60 is formed of quartz or fluorite lenses 61 to 63. The first to third lenses 61 to 63 are arranged in this order from the object side (left side in the figure) to the image side (right side in the figure) with a predetermined air interval, as shown in FIG. ing. Therefore, the microscope objective lens 60 can be used in an ultraviolet region or a far ultraviolet region. Moreover, the lenses 61 to 63 are separated from each other. In other words, the objective lens 60 has no bonding surface. Therefore, in the microscope objective lens 60, it is not necessary to use an optical contact, and the above problem is solved.

Incidentally, the objective lens 60 shown in FIG. 7 forms an image of an object on the focal plane of the imaging lens with a predetermined imaging magnification M in cooperation with an imaging lens (the detailed configuration thereof will be described later). The configuration is such that The imaging magnification M of the time, the ratio of the focal length f ₁ of the focal length f ₂ and the objective lens 60 of the imaging lens. That is, the imaging magnification M is as follows: M = −f ₂ / f ₁ (1)

In a microscope, the imaging lens is usually fixed,
Although the imaging magnification M is changed by replacing the objective lens, it is necessary to prepare objective lenses having mutually different focal lengths.

For example, consider a case in which the objective lens 60 shown in FIG. 7 is replaced with a certain objective lens and the imaging magnification is reduced to 1/2.

In this case, as can be seen from equation (1), the imaging magnification is 1 /
In order to double, it is necessary to have a focal length to prepare the 2f ₁ objective lens. Here, if the focal length is simply doubled, for example, the objective lens 60 may be proportionally enlarged.

However, when the objective lens 60 is replaced with an objective lens that is enlarged by a factor of two, the distance from the objective lens to the object must be doubled as long as the position of the pupil is fixed. Later, it is necessary to refocus. This significantly reduces the operability of the microscope and is not preferable. Conversely, if the position of the object is fixed, the position of the pupil will move. Further, by replacing the objective lens, the size of the pupil is also doubled, and the amount of light used is reduced in a fixed illumination system.

Therefore, the imaging magnification is reduced to 1 /
In the case of 2, the objective lens after the replacement is (1) the focal length objective is twice as large as the lens 60, and (2) it is not necessary to refocus after the objective lens is replaced. (3) The position and size of the pupil are almost equal to those of the objective lens 60.

Is required.

(Object of the Invention) The present invention has been made in view of the above-mentioned problems, and has a configuration different from the objective lens according to the above-mentioned prior application, and can be used in an ultraviolet region or a far ultraviolet region. Is provided at low cost.

In addition, the present invention has a focal length almost twice that of the above-mentioned objective lens in which an image of an object is formed on a focal plane with a predetermined imaging magnification in cooperation with an imaging lens. Further, it is a second object of the present invention to provide a microscope objective lens which is confocal and has almost the same pupil position and size.

(Means for Achieving the Object) The invention according to claim 1 is directed to a microscope objective lens that forms an image of an object in cooperation with an imaging lens. In order to achieve the above, the first to third lenses are arranged in this order from the object side to the image side with a predetermined air gap. Among these first to third lenses, the first lens is a meniscus lens made of quartz or fluorite and having a positive power with the convex surface facing the object side, and the second lens is made of quartz and negative. Has the power of
The third lens is made of fluorite and has a positive power. The power of the second and third lenses is φ
When 2, φ3, the objective lens satisfies the inequality 1.1 <| φ ₃ / φ ₂ | <1.3.

The invention according to claim 2 is interchangeable with an objective lens that forms an image of an object on a focal plane of the imaging lens with a predetermined imaging magnification in cooperation with the imaging lens. The present invention is directed to a microscope objective lens that substantially reduces the imaging magnification by half when used in combination with the imaging lens instead of the objective lens.

In order to achieve the second object, the first to third lenses are arranged in this order from the object side to the image side with a predetermined air gap. Among these first to third lenses, the first lens is a meniscus lens made of quartz or fluorite and having a positive power with the convex surface facing the object side, and the second lens is made of quartz and having a negative power. The third lens is made of quartz and has a positive power.

Further, when the powers of the first to third lenses are respectively φ ₁ , φ ₂ , φ ₃ , the power of the combined system including the second and third lenses is φ ₂₃ , and the power of the entire system is φ, For the objective lens, 1.1 <| φ ₃ / φ ₂ | <1.3 0.90 | φ ₁₊ / φ | <| φ _1- / φ ₂₃ | 1.00 | φ ₁₊ / φ |> | φ _1- / φ ₂₃ | 0.80・ | (4φ / 3φ ₁₊ -1) / φ ₁₊ | <| 1 / φ _1- | 1.1 ・ | (4φ / 3φ ₁₊ -1) / φ ₁₊ |> | 1 / φ _1- | The inequality shown is satisfied.

Here, φ ₁₊ and φ ₁₋ are φ ₁₊ = (n−1) / r ₁ φ ₁ ⁻ = (1-n) / r ₂ where n is the refractive index of the first lens, r ₁ : Radius of curvature of the surface of the first lens facing the object side, r ₂ : radius of curvature of the surface of the first lens facing the image side.

(Operation) According to the invention of claim 1, the first lens is made of quartz or fluorite, the second lens is made of quartz, and the third lens is made of fluorite. Therefore, light in the ultraviolet region or the far ultraviolet region can pass through the objective lens, and can be used in the ultraviolet region and the far ultraviolet region. The first to third lenses are separated from each other with a predetermined air gap. Therefore, there is no need for an optical contact, and the objective lens can be provided at low cost. Moreover, the third lens has a positive power, while the second lens has a negative power. For this reason,
Various aberrations such as spherical aberration and chromatic aberration are corrected.

Also, since the objective lens satisfies the inequality 1.1 <| φ ₃ / φ ₂ | <1.3 (2) using the powers φ ₂ and φ ₃ of the second and third lenses, the spherical aberration The reason is that when the value | φ ₃ / φ ₂ | becomes smaller than 1.1, the spherical aberration correction becomes excessive, and conversely,
If the value is larger than 1.3, the correction will be insufficient (under).

According to the invention of claim 2, achromatism is performed by a combination of the third lens having positive power and the second lens having negative power. Since the image-side surface of the first lens (hereinafter, referred to as “second surface”) has a large negative power, the objective lens becomes a so-called telephoto type, and the focal length of the objective lens is shorter than the entire length. become longer.

Further, an object-side surface of the first lens (hereinafter referred to as a “first surface”)
) Has a positive power, so that the objective lens has telecentric characteristics on the object side.

Here, looking at the above contents from another angle, the second
The surface, the combined system of the second lens and the third lens has a large focal length and plays the role of a teleconverter with respect to the first surface, ie, the combined system increases the power of the first surface. Thus, it can be said that the focal length of the objective lens is adjusted to a desired value.

In order to satisfy this condition accurately, it is necessary to satisfy the following expression: | φ ₁₊ / φ | = | φ _1- / φ ₂₃ | (3) However, in practice, the composite system does not need to be a perfect afocal system, and the composite system is composed of 0.90 | φ ₁₊ / φ | <| φ ₁₋ / φ ₂₃ | (4A) 1.00 | φ _{1 +} / φ |> | φ ₁₋ / φ ₂₃ |... (4B) It suffices to satisfy the inequalities (4A) and (4B).

Incidentally, achromatism is performed by combining the second and third lenses as described above. Here, when an image of an object is formed only by the combination of the second and third lenses, the value | φ ₃ / φ ₂ | is set in the range of 1.3 to 1.4 in consideration of dispersion of fluorite and quartz. It is desirable to set to. However, when the objective lens includes the first to third lenses, it is rather preferable to set the correction by the second and third lenses excessively in order to correct the aberration generated in the first lens. . Therefore, it is desirable to set the value | φ ₃ / φ ₂ | in the range of 1.1 to 1.3, that is, to set the objective lens so as to satisfy the inequality (2).

Next, the condition for making the parfocal distance uniform, that is, the objective lens is 0.80 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ | <| 1 / φ _1- |
A) The necessity of satisfying the inequality represented by 1.1 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ |> | 1 / φ _1- | (5B) will be described.
In the present application, the parfocal length is 3/3 of the focal length of the objective lens.
It is assumed that the focal length on the image side of the objective lens is nearly in close contact with the combined system of the second and third lenses so that the focal length becomes four times. Therefore, assuming that the distance between the principal points between the combined system and the second surface is e, the condition represented by the following equation e + 1 / φ ₁₊ ≒ 3/4 (1 / φ) is obtained. In addition, since the objective lens has telecentric characteristics on the object side, the second lens
It is necessary that the pupil of the combined system of the surface, the second lens and the third lens coincides with the focal point of the first surface. Therefore, the following equation e (1 + 1 / (1 + φ ₁₋ · e)) ≒ 3/4 (1 / φ) −2 / φ ₁₊
.. (7) are obtained. Taking these conditions (6) and (7) into account, the objective lens is required to satisfy the inequalities (5A) and (5B).

(Embodiment) A. First Embodiment FIG. 1 shows a first embodiment of a microscope objective lens according to the present invention.
It is a figure showing an example. As shown in FIG. 1, the objective lens 10 includes first to third lenses 11 to 13. The first to third lenses 11 to 13 are arranged in this order from the object side (left side in the figure) to the image side (right side in the figure) with a predetermined air gap. The first and third lenses 11, 13 both have positive power.
On the other hand, the second lens 12 has negative power. In addition,
As shown in the figure, the convex surface 11a of the first lens 11 faces the object side.

Table 1 shows lens data of the objective lens 10 configured as described above.

In the table (and in Table 3 described later),
r _i is the radius of curvature of the i-th (i = 1 to 6) lens surface as taught from the object side, and d _i is the i-th (i =
It shows the distance between the lens surfaces 1-5) on the optical axis Z between the (i + 1) -th lens surface. As can be seen from the table, the first and second lenses 11 and 12 are made of quartz, and the third lens 13 is made of fluorite.

The focal length f of the objective lens 10 is 60, the numerical aperture (NA) is 1/24, and the image size is 10.6.

Further, the power φ ₁₊ of the convex surface 11a of the first lens 11 with respect to the wavelength 298.06 (nm) and the surface 1 facing the image side of the first lens 11
The power φ _{1− of} 1b is φ ₁₊ = 0.1864 and φ ₁₋ = 0.2467, respectively. Further, for the wavelength of 298.06 (nm), the powers φ ₂ and φ ₃ of the second and third lenses 12 and 13, the power φ _{23 of the} combined system including the second lens 12 and the third lens 13, and the total system (objective) The power φ of the lens 10) is as follows.

φ ₂ = −0.07670, φ ₃ = 0.09208, φ ₂₃ = 0.02266, φ = 0.01667 Therefore, from the above data, | φ ₃ / φ ₂ | = 1.201 is obtained, and the objective lens 10 satisfies the inequality (2). That is clear.

From the above data, 0.90 | φ ₁₊ /φ|=10.07, 1.00 | φ ₁₊ /φ|=11.18, | φ ₁₋ / φ ₂₃ | = 10.84 are obtained. Therefore, it is clear that the objective lens 10 satisfies the inequalities (4A) and (4B).

Further, from the above data, 0.80 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ | = 3.780, 1.1 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ | = 5.198, | 1 / φ _1- | = 4.071 is obtained respectively. Therefore, it is apparent that the objective lens 10 satisfies the inequalities (5A) and (5B).

Incidentally, this objective lens 10 is a so-called infinity correction system in consideration of application to an epi-illumination type microscope. That is, it is configured to form an image of an object on a predetermined imaging plane in combination with an imaging lens described below.

<Imaging Lens> FIG. 2 is a diagram showing a configuration of the imaging lens, which is the same as the imaging lens shown in the earlier application. As shown in the figure, the imaging lens 50 includes first to third lenses.
It is composed of 51-53. The first to third lenses 51 to 53 are arranged in this order from the object side (left side in the figure) to the image side (right side in the figure) with a predetermined air gap.

Table 2 shows lens data of the imaging lens 50 configured as described above.

Incidentally, in the table, R _i is the radius of curvature of the lens surface of i-th counted from the object side (i = 1 to 6), also D _i is the i-th counted from the object side (i = 1 to 5) The lens surface and (i +
1) shows the distance between the lens surface on the optical axis Z and the first lens surface. As can be seen from the table, the first lens 51 is made of fluorite, and the second and third lenses 52 and 53 are made of quartz. The focal distance f 'of the imaging lens 50 is 30
It is 0.

Therefore, the imaging magnification M of the microscope including the imaging lens 50 and the objective lens 10 according to the first embodiment is M = −f ′ / f = −300 / 60 = −5.0.

3A and 3B are diagrams showing the spherical aberration and the sine condition of a lens system in which the objective lens 10 and the imaging lens 50 are combined, respectively. Note that both sides (and the later-described
In FIGS. 5A and 5B), reference numerals A to D indicate wavelengths 29, respectively.
8.06 (nm), 202.54 (nm), 398.84 (nm), 253.70 (nm)
3 shows the results for the light.

3C and 3D are diagrams respectively showing astigmatism and distortion at a wavelength of 298.08 (nm). In FIG. 3C (and FIG. 5C described later), a solid line S indicates a sagittal image plane, and a broken line M indicates a meridional image plane.

From FIGS. 3A and 3B, it can be seen that the objective lens 10 has less aberration with respect to light in the ultraviolet region and the far ultraviolet region. Therefore, it is clear that this objective lens 10 can be used in the ultraviolet region or the far ultraviolet region.
Further, from FIGS. 3C and 3D, it is clear that the lens system using the objective lens 10 has less astigmatism and distortion.

B. Second Embodiment FIG. 4 shows a second embodiment of the microscope objective lens according to the present invention.
It is a figure showing an example. The objective lens 20 according to the second embodiment has basically the same configuration as the objective lens 10. That is, the objective lens 20 is composed of first to third lenses 21 to 23 arranged in this order from the object side (left side in the figure) to the image side (right side in the figure) with a predetermined air spacing. .

Table 3 shows lens data of the objective lens 20 configured as described above.

As can be seen from the table, the second lens 22 is made of quartz, and the first and third lenses 21 and 23 are made of fluorite.

The focal length f of the objective lens 20 is 60, the numerical aperture (NA) is 1/24, and the image size is 10.6.

Further, the power φ ₁₊ of the convex surface 21a of the first lens 21 with respect to the wavelength 298.06 (nm) and the surface 2 facing the image side of the first lens 21
The power φ _{1− of} 1b is φ ₁₊ = 0.1637, φ ₁₋ = −0.2207, respectively. Further, the powers φ ₂ and φ ₃ of the second and third lenses 22 and ₂₃ , the power φ _{23 of the} combined system including the second lens 22 and the third lens 23, and the power φ of the entire system (objective lens 20) Are as follows.

φ ₂ = −0.07676, φ ₃ = 0.09283, φ ₂₃ = 0.02313, φ = 0.01667 Therefore, from the above data, | φ ₃ / φ ₂ | = 1.210 is obtained, and the objective lens 20 satisfies the inequality (2). That is clear.

From the above data, 0.90 | φ ₁₊ /φ|=8.839, 1.00 | φ ₁₊ /φ|=9.821, | φ ₁₋ / φ ₂₃ | = 9.541, respectively. Therefore, it is clear that the objective lens 20 satisfies the inequalities (4A) and (4B).

Further, from the above data, 0.80 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ | = 4.224, 1.1 · | (4φ / 3φ ₁₊ -1) / φ ₁₊ | = 5.808, | 1 / φ _1- | = 4.531 is obtained respectively. Therefore, it is also clear that the objective lens 20 satisfies the inequalities (5A) and (5B).

This objective lens 20 is also a so-called infinity correction system as in the first embodiment, and is combined with an imaging lens 50 shown in FIG. Therefore, the imaging magnification M of the microscope including the imaging lens 50 and the objective lens 20 according to the second embodiment is also M = -f '/ f = -300 / 60 = -5.0.

5A and 5B are diagrams showing the spherical aberration and the sine condition of a lens system in which the objective lens 20 and the imaging lens 50 are combined, respectively. FIGS. 5C and 5D are diagrams respectively showing astigmatism and distortion at a wavelength of 298.06 (nm).

From FIGS. 5A and 5B, it can be seen that the objective lens 20 has a small aberration with respect to light in the ultraviolet region and the far ultraviolet region. Therefore, it is clear that this objective lens 20 can be used in the ultraviolet region or the far ultraviolet region.
5C and 5D show that the lens system using the objective lens 20 has less astigmatism and distortion.

C. Effects of First and Second Embodiments As described above, the objective lenses 10 and 20 according to the first and second embodiments can be used in an ultraviolet region or a deep ultraviolet region, and are excellent in these wavelength regions. Has characteristics. Also, in any of the embodiments, the first to third
The lenses are spaced from each other. Therefore, there is no need for an optical contact, and an objective lens can be provided at low cost.

In the above, although not particularly described, in each embodiment, both aberrations are small in the visible region and the infrared region, and each of the objective lenses 10 and 20 is in the range from the infrared region to the far ultraviolet region. It was confirmed that it could be used.

By the way, the objective lens 60 previously disclosed by the inventor of the present application.
(FIG. 7) is combined with the imaging lens 50 (FIG. 2) to form a lens system having an imaging magnification M of -10. That is, the focal length of the objective lens 60 is 30. On the other hand, the focal lengths of the objective lenses 10 and 20 according to the above embodiments are both 60. Therefore, the imaging lens 50 is fixed, and for example, the objective lens 10 of the first embodiment is
By exchanging with 60, the imaging magnification M is changed from -10 times to-
It can be changed five times.

In addition, both the objective lenses 10 and 20 are confocal with the objective lens 60. As a result, after replacement of the objective lens (for example, replacement of the objective lens 60 to the objective lens 10),
There is no need to refocus, and the operability of the microscope is improved.

In addition, the pupil diameter of each of the objective lenses 10 and 20 is substantially the same as that of the objective lens 60. Therefore, even when the lens is replaced, a large change in the amount of light illuminating the object is not recognized, and the object can be observed in a favorable state.

That is, it can be said that the objective lenses 10 and 20 according to the above-described embodiments are both objective lenses that meet the second object of the present invention.

(Effects of the Invention) As described above, according to the first aspect of the present invention, the first lens made of quartz or fluorite, the second lens made of quartz, and the third lens made of fluorite are placed on the object. The objective lens can be used in an ultraviolet region or a deep ultraviolet region since the objective lens is arranged from the side to the image side in this order with a predetermined air gap.

In addition, since the lenses are separated from each other with a predetermined air gap, there is no need for an optical contact, and the objective lens can be provided at a low cost.

Moreover, while the third lens has a positive power,
Since the second lens has negative power, various aberrations such as spherical aberration and chromatic aberration can be corrected.

Further, since the objective lens satisfies the inequality (2), spherical aberration and the like can be further reduced.

According to the second aspect of the present invention, the second surface of the first lens has a large negative power, and the second surface, the second lens, and the third lens are arranged in this order from the object side to the image side. Then, it has a so-called telephoto type configuration. Therefore, the focal length of the objective lens of the present application can be approximately twice that of the objective lens of the earlier application.

Further, since the objective lens of the present application is configured so as to satisfy the inequalities (5A) and (5B), the objective lens can be made substantially confocal with the exchangeable objective lens of the earlier application.

[Brief description of the drawings]

FIG. 1 is a first view of a microscope objective lens according to the present invention.
FIG. 2 is a diagram showing an embodiment, FIG. 2 is a diagram showing a configuration of an imaging lens, and FIGS. 3A, 3B, 3C, and 3D each show a first example.
FIG. 4 is a diagram showing spherical aberration, sine condition, astigmatism, and distortion of a lens system obtained by combining the objective lens shown in the figure and the above-mentioned imaging lens. FIG. 4 is a diagram showing a microscope objective lens according to the present invention. 2
FIGS. 5A, 5B, 5C, and 5D each show an embodiment.
FIGS. 6 and 7 are diagrams showing spherical aberration, sine condition, astigmatism and distortion of a lens system in which the objective lens shown in FIG. 1 and the above-mentioned imaging lens are combined. FIGS. FIG. 3 is a diagram illustrating a configuration of a lens. 10, 20 ... objective lens, 11, 21 ... first lens, 11a, 21a ... convex surface, 12, 22 ... second lens, 13,23 ... third lens, 50 ... imaging lens, 60 …… Objective lens

Claims (2)

(57) [Claims] An objective lens for a microscope for forming an image of an object in cooperation with an imaging lens, comprising:
The third lens is a meniscus lens made of quartz or fluorite and having a positive power with its convex surface facing the object side, and the first lens is made of quartz or fluorite. The lens is made of quartz and has a negative power, the third lens is made of fluorite and has a positive power, and the powers of the second and third lenses are φ2 and φ3, respectively.
Where 1.1 <| φ3 / φ2 | <1.3. 2. An imaging lens which is interchangeable with an objective lens for forming an image of an object on an imaging surface at a predetermined imaging magnification in cooperation with an imaging lens, and wherein said objective lens is replaced with said objective lens. A microscope objective lens for reducing the imaging magnification by almost half when used in combination with the first to third lenses arranged in this order from the object side to the image side with a predetermined air gap. The first lens is a meniscus lens made of quartz or fluorite and having a positive power with the convex surface facing the object side, the second lens is made of quartz and has a negative power, and the third lens is It is made of fluorite and has a positive power. The power of the first to third lenses is φ1, φ
2, φ3, when the power of the combined system including the second and third lenses is φ23 and the power of the entire system is φ, 1.1 <| φ3 / φ2 | <1.3 0.90 | φ1 + / φ | <| φ1- / φ23 | 1.00 | φ1 + / φ |> | φ1- / φ23 | 0.80 · | (4φ / 3φ1 + -1) / φ1 + | <| 1 / φ1-
| 1.1 · | (4φ / 3φ1 + -1) / φ1 + |> | 1 / φ1- | φ1 + = (n-1) / r1 φ1-= (1-n) / r2, where n: the first lens R1: a radius of curvature of a surface of the first lens facing the object side, and r2: a radius of curvature of a surface of the first lens facing the image side.