JP5449947B2 - Objective optical system - Google Patents

Description

  The present invention relates to an objective optical system.

  Conventionally, microscopic observation using an objective optical system has been widespread. For example, in order to observe images of cells of living organisms in a cultured state or behavior of biological molecules in tissues, specific molecules, tissues, cells, etc. There is known a method in which a dye or a fluorescent marker is attached to this and observed with a fluorescent microscope or a confocal laser scanning microscope. In recent years, the behavior of molecules in living organisms of mammals such as mice may be different from that of cultured cells. Therefore, even if living organisms remain alive (in vivo) Various in vivo imaging techniques that can be observed have been proposed. Furthermore, for the purpose of observing living organisms in a minimally invasive manner, it is possible to observe living organisms in a minimally invasive manner by adopting an objective lens composed of a small-diameter optical system as an objective lens for a microscope and inserting it directly into the organism. A microscope has been proposed. (For example, refer to Patent Document 1).

JP 2006-119300 A

  However, the conventional objective optical system as disclosed in Patent Document 1 is an objective optical system when observing a relatively small organ such as a mouse brain or a deep part of a living body that is easily damaged by invasion. However, there is an inconvenience that the field of view (FOV) becomes narrower as the tip diameter of the objective lens is made thinner.

  In order to microscopically observe living cells such as small experimental animals, living tissues such as muscles, various organs such as the heart and liver, especially brain tissues, in a minimally invasive manner for a relatively long period of time. The tip diameter must be further reduced. However, if the conventional objective lens having a small diameter is further reduced, spherical aberration and curvature of field such as field curvature are likely to occur, which causes inconvenience in microscopic observation. This brings about the same inconvenience when it is intended to observe the objective lens having a small diameter in a wider field of view.

  The present invention has been made in view of the above-described circumstances, and provides an objective optical system that can perform accurate observation without reducing the numerical aperture on the object side as much as possible and suppressing curvature of field. The purpose is to do. Another object of the present invention is to provide an objective optical system that can realize further reduction in the diameter of the tip and / or widening of the field of view while suppressing the curvature of field without significantly reducing the numerical aperture on the object side. .

In order to achieve the above object, the present invention provides the following means.
In the present invention, in order from the object side, the first group of positive refractive power, the second group of positive refractive power, the third group of negative refractive power, the fourth group of positive refractive power, the intermediate imaging plane, the fifth group, and is constituted by a sixth unit having a positive refractive power, the first group is a lens surface is a plane closest to the object side, further comprising a plano-convex lens having a convex surface facing the image side, a divergent light beam from the object plane, and more into a small light flux divergence, the second group lens surface closest to the object side is a cemented lens having a convex surface on the object side lens surface of the third group of the most image side is a concave surface on the image side consists of a directed cemented lens, the object side lens surface of the fourth group lens where the image side lens surface of the lens disposed closest to the object side is arranged and a convex surface facing the image side, and the most image-side There comprises a lens having a convex surface directed toward the object side, converts the divergent light beam from the third group in the converging light flux, the fifth group wherein the intermediate It includes a lens surface closest to the image plane with the concave surface facing the intermediate image plane, the sixth group comprises a cemented lens convex and concave lenses are bonded, and the bonding surface is a negative refractive power, the joint The light beam diameter at the surface is larger than the light beam diameter between the first group and the fifth group, and has an intermediate imaging surface between the fourth group and the fifth group in an infinite design, Provided is an objective optical system characterized in that an image-side exit pupil position is located on the image side of a lens surface located closest to the image side of the objective optical system and satisfies the following conditional expression (1).
(1) 0.28 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
However,
t ₅ : distance from the intermediate imaging plane to the plane of the fifth group closest to the intermediate imaging plane
R ₅ : absolute value of the radius of curvature of the surface of the fifth group closest to the intermediate imaging surface
Dep: Depth of focus on one side at the intermediate image plane, defined by the following equation
Dep = λ / (NA / β) ²
Where λ is the wavelength of the d-line (0.5876 μm), β is the magnification from the object plane to the intermediate image plane
FOV: Object-side viewing range

According to the present invention, in a first unit having a positive refractive power, the most by the object side is flat surface, it is possible to ensure no air bubbles between the specimen and the objective optical system in an immersion observation. Further, by including a convex lens having a convex surface directed to the image side, it is possible to reduce the divergence of the diverging light from the specimen while reducing the occurrence of spherical aberration and coma aberration close to the aplanatic condition.

In the second group having positive refracting power, when the lens surface closest to the object side has a convex surface facing the object side, spherical aberration and coma aberration are greatly generated. Can be prevented, and the lens outer diameter can be reduced.
In the third group having negative refractive power, the lens surface closest to the image side has a concave surface facing the image side, so that the Petzval sum can be reduced without increasing the height of light in the third group. Surface curvature and spherical aberration can be corrected.

  In the fourth group having positive refracting power, the image side lens surface of the lens disposed closest to the object side has a convex surface directed toward the image side, so that it approaches the aplanatic condition, and the diverging light from the third group Can be made substantially convergent without increasing the generation of spherical aberration and coma. Furthermore, the object-side lens surface of the lens located closest to the image side has a convex surface facing the object side, so that it is close to the aplanatic condition, and convergent light can be obtained without increasing the generation of spherical aberration and coma aberration. it can.

  In the fifth group, by disposing a concave surface at a position close to the intermediate image plane, the Petzval sum can be reduced without relatively increasing the divergence of the light from the intermediate image position. At this time, when the Petzval sum is reduced by using the lens surface closest to the intermediate image forming position of the fourth group arranged on the object side of the intermediate image forming surface as a concave surface, the divergent light from the intermediate image forming surface is further diverged by the concave surface. Therefore, the tip lens diameter becomes large. In order to suppress the spread of the divergent light, it is inconvenient to suppress the divergence with a stronger positive refractive power because, for example, spherical aberration occurs.

  In addition, by disposing a concave surface on the image side with respect to the intermediate image plane, the Petzval sum can be reduced, the occurrence of curvature of field can be suppressed, and the focusing angle of the principal ray can be relaxed. It is possible to position the exit pupil position on the side closer to the image side than the lens surface located closest to the image side of the objective optical system, and it is optically possible to dispose the relay optical system on the image side of the objective optical system. It becomes easy.

In the above invention, the intermediate imaging plane is disposed between the fourth group and the fifth group.
In this way, even if the outer diameter of the lens constituting the fifth group is increased, the outer diameter from the first group to the intermediate image plane is suppressed, and an objective optical system with a thinner outer diameter is provided. can do.

  In the sixth group having positive refracting power, in order to convert divergent light into parallel light, positive refracting power is given as a whole and a cemented lens having a cemented surface with negative refracting power is included. It is possible to correct spherical aberration, chromatic aberration, etc. that could not be corrected by the group.

Moreover, in the said invention, it is preferable to satisfy conditional expression (1). Conditional expression (1) causes field curvature due to the wide field of view range, and in order to correct the field curvature, the object side field of view range FOV of the objective optical system of the present invention and the middle of the fifth group. The absolute value R _{5 of the} radius of curvature of the lens surface closest to the intermediate image forming surface with the concave surface facing the image forming surface, and the distance t ₅ between the lens surface closest to the intermediate image forming surface of the fifth group and the intermediate image forming surface. And the optimum relationship between the depth of focus Dep at the intermediate image plane.

If conditional expression (1) is below 0.28, _{t 5} becomes shorter. t ₅ with a small and light high-low position must be reduced radius of curvature R ₅ to bend the light, reducing the R _5, is disadvantageous for the curvature of field is overcorrected. Further, when the visual field range FOV is increased, it is inconvenient because it is difficult to correct field curvature.

Conversely, if the conditional expression (1) exceeds 0.55, _{t 5} becomes longer. Then, curvature radius R ₅ increases and conversely, the disadvantage can not be correct curvature of field.
Furthermore, the expression (1) is more preferably within the following range in terms of aberration correction.
0.4 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
Therefore, according to the present invention configured in this way, the outer diameter is narrow, the field of view is wide, various aberrations are well corrected, and the high numerical aperture that can be used for two-photon excitation is used for in vivo observation. A suitable objective optical system can be provided.

Moreover, in the said invention, it is preferable to satisfy the following conditional expressions (2) to (6).
(2) 0.37 <F ₁₂ / (t ₁₃ · NA) <0.45
(3) 2.0 <φ ₆ / φ ₁₂ <2.5
(4) 1.75 <n ₁₂ <1.90
(5) 0.27 <Δn ₆ <0.45
(6) 30 <Δν ₆ <55
However,
F ₁₂ : Focal length of the first group to the second group t ₁₃ : Optical axis distance from the object plane to the image side surface of the third group NA: Object side numerical aperture φ ₆ : Most of the lenses in the sixth group Large lens diameter φ ₁₂ : The smallest lens diameter of the first and second lens groups n ₁₂ : The largest refractive index (d-line) of the first and second lens groups
Δn ₆ : refractive index difference (d line) of a cemented lens having a cemented surface with negative refractive power of the sixth group
Δν ₆ : Abbe number difference (d-line) of a cemented lens having a cemented surface with negative refractive power in the sixth group

Conditional expression (2) is preferable in terms of aberration correction by reducing the tip diameter, and the focal length F ₁₂ from the first group to the second group, the optical axis from the object plane to the most image side surface of the third group. distance t ₁₃ and defines the relationship between the object-side numerical aperture NA.
Condition (2) is the focal length F ₁₂ decreases the combined second group from the first group falls below 0.37, the refractive power of the first group and the second group becomes strong, the spherical aberration is largely generated However, the correction becomes difficult. Further, since the object-side numerical aperture NA becomes large, spherical aberration and the like are greatly generated, and the correction thereof becomes difficult.

Conversely, if the conditional expression (2) exceeds 0.45, the refractive power focal length F ₁₂ from the first group the combined second group becomes large decreases. As a result, inconveniences such as overcorrection of spherical aberration occur. Alternatively, since the object-side numerical aperture NA is small, aberrations such as spherical aberration are overcorrected, which is inconvenient.

  Conditional expression (3) relates to a condition for realizing an optical system that is as elongated as possible while maintaining good aberrations when both the FOV and the numerical aperture for an object on the specimen surface are increased. That is, when both the FOV and the numerical aperture for an object on the sample surface are increased, the divergent light from the sample surface becomes a light beam that is more easily spread, and the optical system on the image side becomes a large diameter as it is. So, on the contrary, a strong power optical system that is almost convergent light is adopted. At this time, immediately after the light beam having a large spread is formed by the lens closest to the object, the light beam is suddenly narrowed in the direction of convergence by the lens closest to the object. Along with this abrupt change in divergence angle, there arises a new problem that a relatively large aberration (mainly spherical aberration) occurs in the narrow tip portion. Therefore, in the present invention, the aberration generated at the tip is corrected by increasing the diameter of the light beam in the sixth group, and for this purpose, the largest lens in the sixth group with respect to the smallest lens outer diameter in the first and second groups. Conditional expression (3) defines the relationship between the outer diameters. In the present invention, in order to satisfy the conditional expression (3), the ratio of the largest lens diameter of the sixth group lens to the smallest lens diameter of the first group lens and the second group lens is from 2.0. By defining 2.5, divergent light from the specimen surface can be converged without spreading, and various aberrations can be sufficiently corrected while maintaining an elongated shape.

When conditional expression (3) is below 2.0, since the largest lens diameter phi ₆ of the sixth lens group becomes small, various aberrations including such as a spherical aberration generated in the fourth group from the first group Correction in the sixth group becomes difficult.
Conversely, when the conditional expression (3) exceeds 2.5, the largest lens diameter φ ₆ among the lenses in the sixth group becomes large, and the smallest lens diameter φ ₁₂ among the lenses in the first group and the second group. Therefore, correction of various aberrations including spherical aberration generated in the first group to the fourth group in the sixth group becomes excessive.

Conditional expression (4) requires that the refractive power of the first group and the second group at the tip portion be increased in order to reduce the tip diameter. It is preferable to optimally set the largest refractive index.
If conditional expression (4) is less than 1.75, the radius of curvature of the first and second lens groups becomes small, so that the spherical aberration becomes insufficiently corrected and field curvature occurs.
On the other hand, if the conditional expression (4) exceeds 1.90, the radius of curvature of the first and second lens groups becomes large, so that correction of spherical aberration becomes excessive and field curvature is excessively corrected, which is inconvenient. .

Conditional expression (5) indicates that the refractive index difference (d-line) Δn _{6 of the} cemented lens having the cemented surface having the negative refractive power of the sixth group in order to correct the spherical aberration and the like generated up to the fifth group. It stipulates.
When the conditional expression (5) is less than 0.27, the refractive index difference at the joint surface having the negative refractive power becomes small, and it becomes difficult to correct aberrations such as spherical aberration generated in the first group to the fourth group. Become.
On the other hand, if the conditional expression (5) exceeds 0.45, the difference in the refractive index at the joint surface having the negative refractive power increases, resulting in inconveniences such as overcorrection of aberrations or an increase in ray height.

Conditional expression (6) defines the Abbe number difference (d-line) Δν ₆ of the cemented lens having the cemented surface having the negative refractive power of the sixth group in order to correct the chromatic aberration generated up to the fifth group. .
When conditional expression (6) is less than 30, chromatic aberration is undercorrected.
Conversely, if conditional expression (6) exceeds 55, the correction of chromatic aberration becomes excessive, which is inconvenient.

Moreover, in the said invention, you may have the substantially single diameter outer cylinder which accommodates the said 1st-3rd groups.
Moreover, in the said invention, the average internal diameter of the said outer cylinder may be 1 mm or less.
Moreover, in the said invention, the dimensional ratio of the outer diameter of the said outer cylinder and length may be 10 times or more.
In the above invention, the outer tube may have an outer diameter of about 1.8 mm or less and a length of about 20 mm or more.
Moreover, in the said invention, it is preferable that an object side visual field range is 0.25 or more, and an object side numerical aperture is 0.35 or more.

  According to the present invention, it is possible to widen the field of view while maintaining a small diameter, to suppress the curvature of field, and to perform an accurate observation with a high numerical aperture. In addition, according to the present invention, it is possible to realize further reduction in the diameter of the tip and / or wide field of view while suppressing the curvature of field, and to achieve an accurate observation with a high numerical aperture.

It is a block diagram of the objective optical system which concerns on the 1st Embodiment of this invention. It is a block diagram containing the outer cylinder which shows the objective optical system of FIG. It is a block diagram of the objective optical system which concerns on the 2nd Embodiment of this invention. It is a block diagram of the objective optical system which concerns on the 3rd Embodiment of this invention. FIG. 2 is an aberration diagram of an example of the objective optical system in FIG. 1, showing (a) spherical aberration, (b) sine condition violation amount, (c) astigmatism and field curvature, and (d) distortion aberration, respectively. Yes. FIG. 4 is an aberration diagram of an example of the objective optical system in FIG. 3, showing (a) spherical aberration, (b) sine condition violation amount, (c) astigmatism and field curvature, and (d) distortion aberration, respectively. Yes. FIG. 5 is an aberration diagram of an example of the objective optical system in FIG. 4, showing (a) spherical aberration, (b) sine condition violation amount, (c) astigmatism and field curvature, and (d) distortion aberration, respectively. Yes. It is a block diagram which shows an example of an imaging lens.

An objective optical system 1 according to a first embodiment of the present invention will be described with reference to the drawings.
The objective optical system 1 according to the present embodiment is an immersion objective optical system, and has an intermediate image plane with an infinite design as shown in FIGS.

The objective optical system 1, the most and the lens surface on the object side to the arranged object side is flat surface lens, a first lens unit including a convex lens having a convex surface directed toward the image side (first group) towards the G _1, and most second lens group lens surface on the object side of the positive refractive power has a convex surface on the object side (second group) G _2, a lens surface on the most image side of the concave surface on the image side negative refractive power a third lens group (the third group) G _3, most image side lens surface of the lens disposed on the object side has a convex surface directed toward the image side, a lens that is further disposed closest to the image side to have A fourth lens group (fourth group) G ₄ having positive refractive power in which the object-side lens surface faces the convex surface toward the object side, and the surface closest to the intermediate image-forming surface faces the concave surface toward the intermediate image-forming surface. 5 lens group (the fifth group) G _5, positive refractive power of the sixth lens including a cemented lens of a convex lens and a concave lens having a bonding surface having a negative refractive power It includes a (group 6) G _6, and arranged intermediate image plane between the fourth lens group G ₄ and the fifth lens group G _5.

More specifically, the first lens group G _1, the second lens refractive index of the d line with the convex surface facing the first lens L ₁ and the image surface side consisting of the parallel plate is made of a plano-convex lens is 1.883 L ₂ and has positive refracting power.
The second lens group G ₂ includes a cemented lens surface on the object side is bonded to the fourth lens L ₄ and a third lens L ₃ and a concave lens made of a convex lens facing a convex surface on the object side, a positive refractive power have.

The third lens group G ₃ includes a cemented lens surface of the fifth lens L ₅ and the image side, which is a biconvex lens is joined to the sixth lens L ₆ comprising a biconcave lens has a concave surface directed toward the image side, Has negative refractive power.
The fourth lens group G ₄ is image-side lens surface of the seventh lens L ₇ having a biconvex lens arranged on the most object side has a convex surface facing the image side, consisting of a plano-convex lens arranged on the most image side and the object-side lens surface of the eighth lens L ₈ is a convex surface facing the object side, and has positive refractive power as a whole.

The fifth lens group G ₅ includes a ninth lens L ₉ constituted of a meniscus lens closest lens surface on an intermediate image plane is a concave surface facing the intermediate image plane.
The sixth lens group G ₆ is a cemented lens of the cemented surface joining the eleventh lens L ₁₁ in which the tenth lens L ₁₀ which is a biconvex lens and a bi-concave lens having a negative refractive power, second lens L having a biconvex lens ₁₂ and has positive refracting power.
The position of the exit pupil of the image side is arranged on 3.29mm image side from the twelfth lens _{L 12.}

In the present embodiment, each lens is configured to satisfy the following conditional expressions (1) to (6).
(1) 0.28 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
(2) 0.37 <F ₁₂ / (t ₁₃ · NA) <0.45
(3) 2.0 <φ ₆ / φ ₁₂ <2.5
(4) 1.75 <n ₁₂ <1.90
(5) 0.27 <Δn ₆ <0.45
(6) 30 <Δν ₆ <55

Here, F ₁₂ is the focal length of the first lens group G ₁ to the second lens group G ₂ , t ₁₃ is the optical axis distance from the object plane to the most image side surface of the third lens group G ₃ , and NA is object-side numerical aperture of the objective optical system 1, t ₅ is the distance from the intermediate image surface to the nearest to the intermediate image plane surface of the fifth lens group G _5, R ₅ is intermediate image of the fifth lens group G ₅ The radius of curvature of the surface closest to the surface, Dep, is the one-sided focal depth at the intermediate image plane, and is defined by
Dep = λ / (NA / β) ²
Here, λ is the wavelength of the d-line ( 0.5876 μm ), and β is the magnification from the object plane to the intermediate image plane.

FOV is the object-side visual field range of the immersion objective optical system, φ ₆ is the largest lens diameter among the lenses of the sixth lens group G ₆ , and φ ₁₂ is the lenses of the first lens group G ₁ and the second lens group G ₂ . smallest lens diameter of, n ₁₂ is the largest refractive index of the first lens group G ₁ and second lens group G ₂ of the lens (d line), [Delta] n ₆ is the negative refractive power of the sixth lens group G ₆ The refractive index difference (d line) of the cemented lens having the cemented surface, Δν ₆ is the Abbe number difference (d line) of the cemented lens having the cemented surface having the negative refractive power of the sixth lens group G ₆ .

In the conditional expression (1), the field curvature is generated by widening the field range, and in order to correct the field curvature, the object-side field range FOV of the objective optical system of the present invention and the fifth lens group G ₅ and the radius of curvature of the magnitude R ₅ nearest lens surface on an intermediate image plane with the concave surface facing the intermediate image plane of the closest lens surface on an intermediate image plane of the fifth lens group G ₅ and the intermediate image a distance t ₅ between the surface defines an optimal relationship between the focal depth Dep at the intermediate image plane.

If conditional expression (1) is below 0.28, _{t 5} becomes shorter. t ₅ with a small and light high-low position must be reduced radius of curvature R ₅ to bend the light, reducing the R _5, is disadvantageous for the curvature of field is overcorrected. Further, when the visual field range FOV is increased, it is inconvenient because it is difficult to correct field curvature.

Conversely, if the conditional expression (1) exceeds 0.55, _{t 5} becomes longer. Then, curvature radius R ₅ increases and conversely, the disadvantage can not be correct curvature of field.
Furthermore, the expression (1) is more preferably within the following range in terms of aberration correction.
0.4 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
Therefore, by satisfying this conditional expression (1), the outer diameter is narrow, the field of view is wide, various aberrations are well corrected, and it is suitable for in vivo observation with a high numerical aperture that can also be used for two-photon excitation. An objective optical system can be provided.

Conditional expression (2) is preferable in terms of aberration correction by reducing the tip diameter, and the focal length F ₁₂ from the first lens group G ₁ to the second lens group G ₂ and the third lens group G from the object plane are preferred. to the most image side surface of the _third defines the relationship between the optical axis distance t ₁₃ and the object-side numerical aperture NA.
Condition (2) is from the first lens group _{G 1} falls below 0.37 focal length _{F 12} obtained by combining the second lens group _{G 2} becomes small, the first lens group _{G 1} and the second lens group _{G 2} Since the refractive power becomes strong, a large amount of spherical aberration occurs, making correction difficult. Further, since the object-side numerical aperture NA becomes large, spherical aberration and the like are greatly generated, and the correction thereof becomes difficult.

Conversely, if the conditional expression (2) exceeds 0.45, the refractive power focal length _{F 12} from the first lens group _{G 1} combined second lens group _{G 2} is increased is reduced. As a result, inconveniences such as overcorrection of spherical aberration occur. Alternatively, since the object-side numerical aperture NA is small, aberrations such as spherical aberration are overcorrected, which is inconvenient.

Conditional expression (3) requires that the convergent light be diverged before the divergent light from the sample surface spreads in order to reduce the tip diameter, and that aberration (mainly spherical aberration) occurs at the tip diameter portion. Is big. Therefore, it is necessary to correct the aberrations generated at the tip by increasing the beam diameter of the sixth lens group G _6. Therefore, it defines the smallest lens diameter in the first and second groups, the relationship between the largest lens diameter in the sixth lens group G _6.

When conditional expression (3) is below 2.0, since the largest lens diameter phi ₆ of the lenses of the sixth lens group G ₆ becomes smaller, from the first lens group G ₁ generated in the fourth lens group G ₄ correction in the sixth lens group G ₆ of the various aberrations including such as spherical aberration becomes difficult.
Conversely, if the conditional expression (3) exceeds 2.5, the largest lens diameter phi ₆ of the lenses of the sixth lens group G ₆ becomes large, the first lens group G ₁ and the second lens group G ₂ since the smallest lens diameter phi ₁₂ of the lens is small, the correction in the sixth lens group G ₆ of the various aberrations including such a first lens group G ₁ spherical aberration generated in the fourth lens group G ₄ It becomes excessive.

Condition (4) is not necessary to strongly first lens group G ₁ and the refractive power of the second lens group G ₂ of the tip portion to narrow the tip diameter, aberration correction, the first lens group G ₁ and preferably optimally set the largest refractive index in the second lens group G ₂ of the lens.
If the conditional expression (4) is less than 1.75, the curvature radii of the _first and second lens groups G ₁ and G ₂ become small, so that the spherical aberration becomes insufficiently corrected, and field curvature occurs. is there.
Conversely, if the conditional expression (4) exceeds 1.90, the curvature radii of the _first and second lens groups G ₁ and G ₂ become large, so that the spherical aberration is excessively corrected and the field curvature is excessively corrected. This is inconvenient.

Condition (5), in order to correct the various aberrations such as spherical aberration generated in up the fifth lens group G _5, the refractive index difference between the cemented lens having a cemented surface of the negative refractive power of the sixth lens group G ₆ (D line) Δn ₆ is defined.
When conditional expression (5) is below 0.27, the aberration such as spherical aberration generated refractive index difference from the first lens group G ₁ becomes small in the fourth lens group G ₄ at the bonding surface of the negative refractive power It becomes difficult to correct.
On the other hand, if the conditional expression (5) exceeds 0.45, the difference in the refractive index at the joint surface having the negative refractive power increases, resulting in inconveniences such as overcorrection of aberrations or an increase in ray height.

Conditional expression (6) indicates that the Abbe number difference (d-line) Δν of the cemented lens having the cemented surface having the negative refractive power of the sixth lens group G ₆ is used to correct the chromatic aberration generated up to the fifth lens group G _{5. 6} is stipulated.
When conditional expression (6) is less than 30, chromatic aberration is undercorrected.
Conversely, if conditional expression (6) exceeds 55, the correction of chromatic aberration becomes excessive, which is inconvenient.
Therefore, by satisfying these conditional expressions (2) to (6), various aberrations such as spherical aberration, field curvature, and chromatic aberration generated in each lens group can be corrected appropriately.

  Table 1 shows lens data of an example of the objective optical system 1 according to this embodiment, FIG. 1 shows an optical path diagram of this example, and FIG. 5 shows aberration diagrams.

In this example, each value in conditional expressions (1) to (6) is as follows.
F ₁₂ = 0.63
t ₁₃ = 3.87
NA = 0.38
φ ₁₂ = 0.8
φ ₆ = 1.8
t ₅ = 2.0
R ₅ = 3.423
Dep = 54.7
β = 3.67
FOV = 0.3

Therefore,
(1) (t ₅ · R ₅ ) / (Dep · FOV) = 0.42
(2) F ₁₂ / (t ₁₃ · NA) = 0.43
(3) φ ₆ / φ ₁₂ = 2.3
(4) n ₁₂ = 1.88
(5) Δn ₆ = 0.44
(6) Δν ₆ = 54.1
It becomes.

In the objective optical system 1 according to the present embodiment, as shown in FIG. 2, the lens diameters of the lenses L _{1 to} L ₆ are 0.8 mm at maximum (effective diameter is 0.6 mm), and the lenses L _{7 to} L _8. maximum 1.2mm are lens diameter (effective diameter 1.0 mm), the lens diameter of the lens _L 9 _{~L 13} is maximum 1.8 mm (effective diameter 1.6 mm), until the lens _L 1 ~L ₆ The tip portion is composed only of a lens having a very small diameter. For this reason, the outer cylinder 11 that accommodates the lenses L _{1 to} L ₁₂ , particularly the lenses L _{1 to} L ₆ of the _first to third lens groups G _{1 to} G ₃ , can be configured to be extremely thin, such as a mouse. It is suitable for in vivo observation over a relatively long period of time in a wide range deep in the body of experimental small animals. Moreover, in the said invention, the average internal diameter of the said outer cylinder may be 1 mm or less. Here, the outer cylinder holding the objective optical system of the present invention is much longer than that of the conventional one. For example, the outer diameter is about 2 mm or less (lens diameter is 1.8 mm or less) and the length is about 20 mm or more ( The table may be 22.53 mm). In other words, the present invention has a wider field of view than the conventional one in an elongated shape in which the dimensional ratio between the outer diameter and the length of the portion where the objective optical system is arranged in series along the optical axis is 10 times or more. An objective lens can be provided. This makes it possible to perform microscopic observation that is most advantageous for objects in the observation field where the dimensional ratio is required. In addition, it is suitable for application to any small apparatus in which only the arrangement space having the dimensional ratio is allowed regardless of the presence or absence of the outer cylinder.

In this embodiment, not only visible light but also aberrations are corrected well up to the near-infrared region, and not only the surface of the sample but also the inside of the living body can be relatively affected by scattering. Can be observed. Furthermore, since the object-side numerical aperture is relatively large, it can also be used for multiphoton excitation. Furthermore, the present invention satisfies all of the large FOV (wide field of view) and high numerical aperture (high resolution) required for in vivo observation. The objective optical system adopting the present invention has, for example, an object-side visual field range of 0.25 or more, an object-side numerical aperture of 0.35 or more, a tip lens diameter of 0.9 mm or less, and a lens from the tip. The lens barrel has an outer diameter of approximately 1 mm or less.
The symbols in the table are r: radius of curvature, d: spacing, nd: refractive index (d line), νd: Abbe number (d line), and the unit of length is mm.

Next, an objective optical system 2 according to a second embodiment of the present invention will be described with reference to the drawings.
As shown in FIG. 3, the objective optical system 2 according to the present embodiment has an intermediate image plane with an infinity design.

The objective optical system 2, the most and the lens surface on the object side of the object side to the lens disposed is a flat surface lens, a first lens unit including a plano-convex lens having a convex surface on the image side G ₁ When the most object side lens surface of the second lens group G ₂ having a positive refractive power which has a surface convex toward the object side, having negative refracting power and a lens surface closest to the image side is a concave surface facing the image side third a lens group G _3, most image side lens surface of the lens disposed on the object side is a convex surface facing the image side, and most object-side lens surface of the lens disposed on the image side is a convex surface on the object side and a fourth lens group G ₄ having a positive refractive power, a fifth lens group G ₅ to the surface closest to the intermediate image plane is a concave surface facing the intermediate image plane, and a convex lens having a bonding surface having a negative refractive power and a sixth lens group G ₆ having a positive refractive power, including a cemented lens of a concave lens, and the fourth lens group G ₄ 5 Len Intermediate image plane is arranged between's group G _5.

More specifically, the first lens group G ₁ has a first lens L ₁ composed of parallel plate, a second lens having a refractive index of d line convex surface faces the image surface side is a plano-convex lens is 1.883 and a L _2, and has a positive refractive power.
The second lens group G ₂ comprises a third lens L _3, which is a biconvex lens having a surface on the object side is facing convex surface on the object side, a cemented lens of a fourth lens L _4, which is a plano-convex lens, Has positive refractive power.

The third lens group G ₃ includes a cemented lens surface of the fifth lens L ₅ and the image side, which is a biconvex lens is joined to the sixth lens L ₆ comprising a biconcave lens has a concave surface directed toward the image side, Has negative refractive power.
The fourth lens group G ₄ includes a biconvex lens arranged on the most object side, a seventh lens L ₇ image side lens surface having a convex surface directed toward the image side, the eighth lens L ₈ ninth lens L ₉ a cemented lens joined to the object-side lens surface is a convex surface facing the object side bets, tenth lens L ₁₀ and the object-side lens surface by joining a eleventh lens L ₁₁ disposed nearest to the image side to the object side It has a cemented lens with a convex surface and has positive refractive power as a whole.

The fifth lens group G ₅ includes a twelfth lens L ₁₂ constituted of a meniscus lens closest lens surface on an intermediate image plane is a concave surface facing the intermediate image plane.
The sixth lens group G ₆ includes a thirteenth lens L ₁₃ and the cemented lens of the cemented surface by joining a fourteenth lens L ₁₄ which is a biconcave lens is a negative refractive power is a biconvex lens, 15 lens L having a biconvex lens ₁₅ and has positive refracting power.
The position of the exit pupil of the image side is arranged at a position of the image side 3.56mm fifteenth lens _{L 15.}

In the present embodiment, each lens is configured to satisfy the following conditional expressions (1) to (6).
(1) 0.28 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
(2) 0.37 <F ₁₂ / (t ₁₃ · NA) <0.45
(3) 2.0 <φ ₆ / φ ₁₂ <2.5
(4) 1.75 <n ₁₂ <1.90
(5) 0.27 <Δn ₆ <0.45
(6) 30 <Δν ₆ <55

Here, F ₁₂ is the focal length of the first lens group G ₁ to the second lens group G ₂ , t ₁₃ is the optical axis distance from the object plane to the most image side surface of the third lens group G ₃ , and NA is the object-side numerical aperture, t ₅ is the distance from the intermediate image surface to the nearest to the intermediate image plane surface of the fifth lens group G _5, R ₅ is most intermediate image plane of the fifth lens group G ₅ The radius of curvature of the near surface, Dep, is the unilateral depth of focus at the intermediate image plane and is defined by the following equation.
Dep = λ / (NA / β) ²
Here, λ is the wavelength of the d-line ( 0.5876 μm ), and β is the magnification from the object plane to the intermediate image plane.

FOV is the object-side visual field range, φ ₆ is the largest lens diameter of the lenses of the sixth lens group G ₆ , φ ₁₂ is the smallest lens diameter of the lenses of the first lens group G ₁ and the second lens group G ₂ , n ₁₂ is the largest refractive index of the first lens group G ₁ and second lens group G ₂ of the lens (d line), [Delta] n ₆ is a cemented lens having a cemented surface of the negative refractive power of the sixth lens group G ₆ The refractive index difference (d-line), Δν ₆ is the Abbe number difference (d-line) of the cemented lens having the cemented surface having the negative refractive power of the sixth lens group G ₆ .

  Table 2 shows lens data of one example of the objective optical system 1 according to this embodiment, FIG. 3 shows an optical path diagram of this example, and FIG. 6 shows aberration diagrams.

In this example, each value in conditional expressions (1) to (6) is as follows.
F ₁₂ = 0.56
t ₁₃ = 3.66
NA = 0.38
φ ₁₂ = 0.8
φ ₆ = 1.8
t ₅ = 2.1
R ₅ = 4.901
Dep = 64.7
β = 3.99
FOV = 0.3

Therefore,
(1) (t ₅ · R ₅ ) / (Dep · FOV) = 0.53
(2) F ₁₂ / (t ₁₃ · NA) = 0.4
(3) φ ₆ / φ ₁₂ = 2.3
(4) n ₁₂ = 1.88
(5) Δn ₆ = 0.44
(6) Δν ₆ = 54.1
It becomes.

  The objective optical system 2 according to the present embodiment is basically the same as the first embodiment, but corrects spherical aberration, axial chromatic aberration, and coma aberration more than the first embodiment, so This is an example in which the imaging performance is improved.

In the objective optical system 2 according to the present embodiment, the lens _L 1 ~L lens diameter of ₆ up to 0.8 mm, the lens _L 7 _~L lens diameter of ₁₁ up to 1.2 mm, the lens of the lens _L 12 _{~L 15} The diameter is 1.8 mm at the maximum, and the tip portions of the lenses L _{1 to} L ₆ are constituted only by lenses having a very small diameter. For this reason, it is suitable for in vivo observation over a relatively long period of time in a wide range deep inside the body of small experimental animals such as mice.
Here, the outer cylinder holding the objective optical system of the present invention is much longer than that of the conventional one. For example, the outer diameter is about 2 mm or less (lens diameter is 1.8 mm or less) and the length is about 20 mm or more ( 24.43 mm in the table). In other words, the present invention has a wider field of view than the conventional one in an elongated shape in which the dimensional ratio between the outer diameter and the length of the portion where the objective optical system is arranged in series along the optical axis is 10 times or more. An objective optical system can be provided. This makes it possible to perform microscopic observation that is most advantageous for objects in the observation field where the dimensional ratio is required. In addition, it is suitable for application to any small apparatus in which only the arrangement space of the above dimensional ratio is allowed regardless of the presence or absence of the outer cylinder.

In addition, this embodiment corrects aberrations up to the near infrared region as well as visible light, and uses the near infrared light to observe not only the surface of the sample but also the inside of the living body relatively without the influence of scattering. be able to. Furthermore, since the object-side numerical aperture is relatively large, it can also be used for multiphoton excitation.
The symbols in the table are r: radius of curvature, d: spacing, nd: refractive index (d line), νd: Abbe number (d line), and the unit of length is mm.

Next, an objective optical system 3 according to a third embodiment of the present invention will be described below with reference to the drawings.
As shown in FIG. 4, the objective optical system 3 according to the present embodiment has an intermediate image plane with an infinity design.

Objective optical system 3 according to this embodiment, the positive refractive power including a lens the object-side lens surface of the lens disposed closest to the object side is flat surface, and a plano-convex lens having a convex surface facing the image side first a first lens group G _1, the negative lens surface on the most object side are directed second lens group G ₂ having a positive refractive power which has a surface convex toward the object side, a lens surface on the most image side of the concave surface on the image side a third lens group G ₃ refractive power, the object side lens surface of the most image side lens surface of the lens disposed on the object side has a convex surface directed toward the image side, a lens disposed and most image side object a fourth lens group G ₄ having a positive refractive power with a convex surface facing the side, the fifth lens group G ₅ to the surface closest to the intermediate image plane is a concave surface facing the intermediate image plane, bonding a negative refractive power and a sixth lens group G ₆ having a positive refractive power, including a cemented lens of a convex lens and a concave lens having a surface.
The intermediate image plane is arranged between the fourth lens group G ₄ of the fifth lens group G _5.

More specifically, the first lens group G ₁ has a first lens L ₁ composed of parallel plate, a second lens having a refractive index of d line convex surface faces the image surface side is a plano-convex lens is 1.773 and a L _2, and has a positive refractive power.
The second lens group G ₂ includes a cemented lens of a fourth lens L ₄ surface on the object side and a third lens L ₃ and the plano-convex lens having a biconvex lens facing a convex surface on the object side, a positive Has refractive power.

The third lens group G ₃ includes a cemented lens surface of the fifth lens L ₅ and the image side, which is a biconvex lens is joined to the sixth lens L ₆ comprising a biconcave lens has a concave surface directed toward the image side, Has negative refractive power.
The fourth lens group G ₄ is image-side lens surface of the seventh lens L ₇ made of a plano-convex lens disposed on the most object side is convex is facing the image side, consisting of a plano-convex lens arranged on the most image side and the object-side lens surface of the eighth lens L ₈ is a convex surface facing the object side, and has positive refractive power as a whole.

The fifth lens group G ₅ includes a ninth lens L ₉ constituted of a meniscus lens closest lens surface on an intermediate image plane is a concave surface facing the intermediate image plane.
The sixth lens group G ₆ is a cemented lens of the cemented surface joining the eleventh lens L ₁₁ in which the tenth lens L ₁₀ which is a biconvex lens and a bi-concave lens having a negative refractive power, second lens L having a biconvex lens ₁₂ and has positive refracting power.
The position of the exit pupil of the image side is arranged on 3.51mm image side from the twelfth lens _{L 12.}

In the present embodiment, each lens is configured to satisfy the following conditional expressions (1) to (6).
(1) 0.28 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
(2) 0.37 <F ₁₂ / (t ₁₃ · NA) <0.45
(3) 2.0 <φ ₆ / φ ₁₂ <2.5
(4) 1.75 <n ₁₂ <1.90
(5) 0.27 <Δn ₆ <0.45
(6) 30 <Δν ₆ <55

Here, F ₁₂ is the focal length of the first lens group G ₁ to the second lens group G ₂ , t ₁₃ is the optical axis distance from the object plane to the most image side surface of the third lens group G 3, and NA object-side numerical aperture of the objective optical system 3, t ₅ is the distance from the intermediate image surface to the nearest to the intermediate image plane surface of the fifth lens group G _5, R ₅ is the fifth lens group G ₅ intermediate The radius of curvature of the surface closest to the imaging plane, Dep, is the unilateral depth of focus at the intermediate imaging plane and is defined by the following equation.
Dep = λ / (NA / β) ²
Here, λ is the wavelength of the d-line ( 0.5876 μm ), and β is the magnification from the object plane to the intermediate image plane.

FOV is the object-side visual field range of the objective optical system, φ ₆ is the largest lens diameter of the lenses of the sixth lens group G ₆ , and φ ₁₂ is the lens of the first lens group G ₁ and the second lens group G ₂ smallest lens diameter, n ₁₂ is the largest refractive index (d line), [Delta] n ₆ bonding surface of the negative refractive power of the sixth lens group G ₆ of the first lens group G ₁ and second lens group G ₂ of the lens refractive index difference of the cemented lens having a (d-line), .DELTA..nu ₆ is the Abbe number difference between the cemented lens having a cemented surface of the negative refractive power of the sixth lens group G ₆ (d line).

  Table 3 shows lens data of one example of the objective optical system 3 according to this embodiment, FIG. 4 shows an optical path diagram of this example, and FIG. 7 shows aberration diagrams.

In this example, each value in conditional expressions (1) to (6) is as follows.
F ₁₂ = 0.55
t ₁₃ = 3.68
NA = 0.38
φ ₁₂ = 0.8
φ ₆ = 1.8
t ₅ = 1.71
R ₅ = 2.989
Dep = 56.9
β = 3.74
FOV = 0.3

Therefore,
(1) (t ₅ · R ₅ ) / (Dep · FOV) = 0.30
(2) F ₁₂ / (t ₁₃ · NA) = 0.39
(3) φ ₆ / φ ₁₂ = 2.3
(4) n ₁₂ = 1.773
(5) Δn ₆ = 0.276
(6) Δν ₆ = 31.9
It becomes.

The objective optical system 3 according to the present embodiment is basically the same as the first embodiment, but is an example in which distortion aberration is corrected and image distortion is reduced as compared with the first embodiment. In the objective optical system 3 according to the present embodiment, the lens diameters of the lenses L _{1 to} L ₆ are 0.8 mm at the maximum, the lens diameters of the lenses L _{7 to} L ₈ are 1.4 mm at the maximum, and the lenses L _{9 to} L ₁₂ The lens diameter is 1.8 mm at the maximum, and the tip portions of the lenses L _{1 to} L ₆ are composed of only lenses having a very small diameter.

For this reason, it is suitable for in vivo observation over a relatively long period of time in a wide range deep in the body of a small experimental animal such as a mouse with minimal image distortion and minimal invasiveness.
Here, the outer cylinder holding the objective optical system of the present invention is much longer than that of the conventional one. For example, the outer diameter is about 2 mm or less (lens diameter is 1.8 mm or less) and the length is about 20 mm or more ( 21.58 mm in the table). In other words, the present invention has a wider field of view than the conventional one in an elongated shape in which the dimensional ratio between the outer diameter and the length of the portion where the objective optical system is arranged in series along the optical axis is 10 times or more. An objective optical system can be provided. This makes it possible to perform microscopic observation that is most advantageous for objects in the observation field where the dimensional ratio is required. In addition, it is suitable for application to any small apparatus in which only the arrangement space of the above dimensional ratio is allowed regardless of the presence or absence of the outer cylinder.

In addition, this embodiment corrects aberrations up to the near infrared region as well as visible light, and uses the near infrared light to observe not only the surface of the sample but also the inside of the living body relatively without the influence of scattering. be able to. Furthermore, since the object-side numerical aperture is relatively large, it can also be used for multiphoton excitation.
The symbols in the table are r: radius of curvature, d: spacing, nd: refractive index (d line), νd: Abbe number (d line), and the unit of length is mm.

  In all of Examples 1 to 3, since the light emitted to the image side becomes parallel light, no image is formed by itself. Therefore, for example, the lens data shown in Table 4 below is used and used in combination with an imaging lens whose lens configuration is shown in FIG. Again, since the maximum diameter of the lens is within 1.8 mm (effective diameter is within 1.6 mm) over a length range of 6.1 mm corresponding to the working distance of the imaging optical system, the objective optical system can be maintained. It can be seen that the small diameter can be maintained for the total length of the optical system that is the sum of the system and the imaging optical system (according to the above embodiment, 27.63 to 30.53 mm). At this time, it is also possible to observe by connecting the light receiving surfaces of the image fiber and the CCD so as to be positioned on the fourth image plane (imaging plane). The lens data shown in Table 4 shows an example in which flat glass for preventing reflection is attached so as to be in contact with the image plane.

  Here, as can be seen from the various embodiments described above, the exit pupil position of the objective optical system of the present invention is located on the image side with respect to the lens surface located on the most image side of the objective optical system. Even when the pupil position of the imaging lens is located within the imaging lens, it is relatively easy to optically combine them. As described above, in the present invention, it is possible to correct the curvature of field by disposing the concave surface of the lens on the rear side of the primary image, and to further narrow the tip of the objective optical system. In addition, the angle of the chief ray with respect to the optical axis (degree of light collection) is relaxed, and the point where the chief ray and the optical axis intersect can be brought close to the image position. Can be put out.

  The symbols in the table are r: radius of curvature, d: spacing, nd: refractive index (d line), νd: Abbe number (d line), and the unit of length is mm.

Although the present invention has been described above, the following modifications and applications can be made within the above spirit.
In (A) above embodiment has exemplified the case of arranging the intermediate image plane between the fourth lens group G ₄ and the fifth lens group G _5, instead of this, the fifth lens group G ₅ If may be disposed intermediate image plane between the sixth lens group G _6, in this case, that the concave surface of the fifth lens group G ₅ is to place toward the intermediate image plane on the image side do it.
(B) In vivo observation is not limited to a so-called microscope and can be applied to an endoscope or the like as long as it is a microscopic optical system that magnifies and observes a predetermined observation site of a living animal or plant.
(C) The immersion type means an optical system that performs observation in a state in which the tip on the objective optical system side is immersed in a liquid such as a body fluid or a culture solution when microscopic observation is performed close to a living body or the like. The present invention is particularly suitable for such an immersion type optical system.
(D) In the case of an elongated objective optical system, since the diameter of the outer cylinder does not increase from the distal end portion of the objective optical system toward the image side, it becomes possible to approach the observation site with minimal invasiveness, and the observation target ( For example, it is suitable for an arbitrary application in which observation in a deep place is performed with a wide field of view while minimizing damage in a path leading to an observation target.
(E) It is easy to apply to an observation target that wants to directly observe a deep part with low invasiveness without reducing resolution.
(F) The objective optical system of the present invention is not limited to the observation means having a cylindrical appearance, but is applied to various small optical devices (for example, capsule endoscopes, ultra-small cameras) that are desirably mounted in an elongated space Can be arranged.

G ₁ first lens group (first group)
G2 _second lens group (second group)
G ₃ third lens group (Group 3)
G ₄ fourth lens group (group 4)
G ₅ the fifth lens group (Group 5)
G6 _sixth lens group (sixth group)
L ₁ 1st lens L ₂ 2nd lens L ₃ 3rd lens L ₄ 4th lens L ₅ 5th lens L ₆ 6th lens L ₇ 7th lens L ₈ 8th lens L ₉ 9th lens L ₁₀ 10th lens L ₁₁ 11th lens L ₁₂ 12th lens L ₁₃ 13th lens L ₁₄ 14th lens L ₁₅ 15th lens t ₁₃ Optical axis distance t ₅ from the object surface to the image side surface of the third lens group The distance to the surface closest to the intermediate image plane of the 5 lens group

Claims (2)

In order from the object side, the first group of positive refractive power, the second group of positive refractive power, the third group of negative refractive power, the fourth group of positive refractive power, the intermediate image plane, the fifth group, and the positive refractive power Of the sixth group,
The first group includes a plano-convex lens whose lens surface closest to the object side is flat and further has a convex surface facing the image side, and converts a divergent light beam from the object surface into a light beam having a smaller divergence;
The second group is composed of a cemented lens in which the lens surface closest to the object side has a convex surface facing the object side,
The third group is composed of a cemented lens in which the lens surface closest to the image side has a concave surface facing the image side ,
In the fourth group, the image side lens surface of the lens arranged closest to the object side has the convex surface facing the image side, and the object side lens surface of the lens arranged closest to the image side has the convex surface facing the object side. Including a lens , converting a divergent light beam from the third group into a convergent light beam,
The fifth group includes a lens in which a surface closest to the intermediate imaging plane faces a concave surface to the intermediate imaging plane;
The sixth group includes a cemented lens in which a convex lens and a concave lens are cemented and the cemented surface has a negative refractive power, and the beam diameter at the cemented surface is larger than the beam diameter between the first group and the fifth group. It ’s getting bigger ,
With an infinite design and an intermediate imaging surface between the fourth group and the fifth group, the image-side exit pupil position is positioned on the image side of the lens surface positioned on the most image side of the objective optical system,
An objective optical system satisfying the following conditional expression (1):
(1) 0.28 <(t ₅ · R ₅ ) / (Dep · FOV) <0.55
However,
t ₅ : distance from the intermediate imaging plane to the plane of the fifth group closest to the intermediate imaging plane
R ₅ : absolute value of the radius of curvature of the surface of the fifth group closest to the intermediate imaging surface
Dep: Depth of focus on one side at the intermediate image plane, defined by the following equation
Dep = λ / (NA / β) ²
Where λ is the wavelength of the d-line (0.5876 μm), β is the magnification from the object plane to the intermediate image plane
FOV: Object-side viewing range The objective optical system according to claim 1, wherein the following conditional expressions (2) to (6) are satisfied.
(2) 0.37 <F ₁₂ / (t ₁₃ · NA) <0.45
(3) 2.0 <φ ₆ / φ ₁₂ <2.5
(4) 1.75 <n ₁₂ <1.90
(5) 0.27 <Δn ₆ <0.45
(6) 30 <Δν ₆ <55
However,
F ₁₂ : Focal length of the first group to the second group t ₁₃ : Optical axis distance from the object plane to the image side surface of the third group NA: Object side numerical aperture φ ₆ : Most of the lenses in the sixth group Large lens diameter φ ₁₂ : The smallest lens diameter of the first and second lens groups n ₁₂ : The largest refractive index (d-line) of the first and second lens groups
Δn ₆ : refractive index difference (d line) of a cemented lens having a cemented surface with negative refractive power of the sixth group
Δν ₆ : Abbe number difference (d-line) of a cemented lens having a cemented surface with negative refractive power in the sixth group

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