JP2019039991A - Optical system and imaging apparatus having the same - Google Patents
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本発明は、光学系に関し、デジタルビデオカメラ、デジタルスチルカメラ、放送用カメラ、銀塩フィルム用カメラ、監視用カメラ等の撮像装置に好適なものである。 The present invention relates to an optical system and is suitable for an imaging apparatus such as a digital video camera, a digital still camera, a broadcast camera, a silver salt film camera, and a surveillance camera.
小型な光学系として、光の反射と屈折を用いたカタディオプトリック光学系が知られている。 As a compact optical system, a catadioptric optical system using reflection and refraction of light is known.
特許文献１には、自由曲面ミラーと屈折光学系を有する投射光学系が記載されている。特許文献１には、屈折光学系の一部を移動させてフォーカシングを行う投射光学系が記載されている。 Patent Document 1 describes a projection optical system having a free-form surface mirror and a refractive optical system. Patent Document 1 describes a projection optical system that performs focusing by moving a part of a refractive optical system.
非共軸の光学系では、軸上で生じる収差量が物体距離の変化によって非対称に変動する。特許文献１の投射光学系では、回転対称に構成された屈折光学系を移動させてフォーカシングを行っている。このため、特許文献１の投射光学系では軸上の非対称な収差（軸上アスと称する）量を各物体距離において低減させることは難しい。 In a non-coaxial optical system, the amount of aberration generated on the axis fluctuates asymmetrically with changes in the object distance. In the projection optical system of Patent Document 1, focusing is performed by moving a refractive optical system configured to be rotationally symmetric. For this reason, in the projection optical system of Patent Document 1, it is difficult to reduce the amount of axial asymmetrical aberration (referred to as axial ascending) at each object distance.
本発明の目的は、物体距離の変化による収差量の変化を低減させることのできる光学系を提供することである。 An object of the present invention is to provide an optical system capable of reducing a change in aberration amount due to a change in object distance.
本発明の光学系は、物体側から像側へ順に、入射光を反射する反射光学系と、前記反射光学系によって反射された光を屈折する屈折光学系を有し、前記反射光学系は自由曲面ミラーを備え、前記屈折光学系は無限遠から至近距離までのフォーカシングに際して物体側に移動するフォーカスレンズ群を含み、光軸に直交し前記反射光学系の焦点距離が最も小さくなる方向を第１の方向、前記第１の方向に直交する方向を第２の方向、前記第１の方向における前記フォーカスレンズ群の焦点距離をｆｙ、前記第２の方向における前記フォーカスレンズ群の焦点距離をｆｘとしたとき、
ｆｘ＞ｆｙ
なる条件式を満足することを特徴とする。
The optical system of the present invention includes a reflective optical system that reflects incident light and a refractive optical system that refracts light reflected by the reflective optical system in order from the object side to the image side, and the reflective optical system is free The refractive optical system includes a focus lens group that moves to the object side during focusing from infinity to a close distance, and has a first direction perpendicular to the optical axis and having the smallest focal length of the reflective optical system. Direction, the direction orthogonal to the first direction is the second direction, the focal length of the focus lens group in the first direction is fy, and the focal length of the focus lens group in the second direction is fx. When
fx> fy
The following conditional expression is satisfied.
また、本発明の他の光学系は、物体側から像側へ順に、入射光を反射する反射光学系と、前記反射光学系によって反射された光を屈折する屈折光学系を有し、前記反射光学系は自由曲面ミラーを備え、前記屈折光学系は無限遠から至近距離までのフォーカシングに際して像側に移動するフォーカスレンズ群を含み、光軸に直交し前記反射光学系の焦点距離が最も小さくなる方向を第１の方向、前記第１の方向に直交する方向を第２の方向、前記第１の方向における前記フォーカスレンズ群の焦点距離をｆｙ、前記第２の方向における前記フォーカスレンズ群の焦点距離をｆｘとしたとき、
ｆｙ＞ｆｘ
なる条件式を満足することを特徴とする。
Another optical system of the present invention includes a reflective optical system that reflects incident light and a refractive optical system that refracts light reflected by the reflective optical system in order from the object side to the image side. The optical system includes a free-form surface mirror, and the refractive optical system includes a focus lens group that moves to the image side during focusing from infinity to a close distance, and is perpendicular to the optical axis and has the smallest focal length of the reflective optical system Is the first direction, the direction orthogonal to the first direction is the second direction, the focal length of the focus lens group in the first direction is fy, and the focal length of the focus lens group in the second direction is Is fx,
fy> fx
The following conditional expression is satisfied.
本発明によれば、物体距離の変化による収差量の変化を低減させることのできる光学系を実現できる。 According to the present invention, it is possible to realize an optical system capable of reducing a change in aberration amount due to a change in object distance.
以下、本発明の光学系及びそれを有する撮像装置の実施例について、添付の図面に基づいて説明する。各実施例の光学系は、物体側から像側へ順に、反射光学系と、屈折光学系を有する。屈折光学系はフォーカシングに際して移動するフォーカスレンズ群を含む。 Embodiments of an optical system of the present invention and an image pickup apparatus having the same will be described below with reference to the accompanying drawings. The optical system of each embodiment has a reflective optical system and a refractive optical system in order from the object side to the image side. The refractive optical system includes a focus lens group that moves during focusing.
図１，３，５，７，９，１１，１３，１５は、それぞれ実施例１乃至８の光学系の無限遠合焦時における断面図である。各実施例の光学系はビデオカメラやデジタルカメラ、銀塩フィルムカメラ、テレビカメラ等の撮像装置に用いられる撮影光学系である。 1, 3, 5, 7, 9, 11, 13, and 15 are cross-sectional views of the optical systems of Examples 1 to 8, respectively, when focusing on infinity. The optical system of each embodiment is a photographing optical system used in an imaging apparatus such as a video camera, a digital camera, a silver salt film camera, or a television camera.
各レンズ断面図において左方が物体側（前方）で、右方が像側（後方）である。また、Ｌは各実施例の光学系であり、Ｍ０は反射光学系、Ｌ０は屈折光学系、ＬＦはフォーカスレンズ群である。 In each lens cross-sectional view, the left side is the object side (front), and the right side is the image side (rear). Further, L is an optical system of each embodiment, M0 is a reflection optical system, L0 is a refractive optical system, and LF is a focus lens group.
また、ＳＰは開口絞り、ＩＰは像面を表す。各実施例の光学系Ｌをビデオカメラやデジタルカメラの撮影光学系として用いる際には像面ＩＰに矩形のＣＣＤセンサやＣＭＯＳセンサ等の撮像素子（光電変換素子）が配置される。各実施例の光学系Ｌ０を銀塩フィルム用カメラの撮像光学系として用いる際には像面ＩＰにフィルムが配置される。 SP represents an aperture stop, and IP represents an image plane. When the optical system L of each embodiment is used as a photographing optical system for a video camera or a digital camera, an image pickup device (photoelectric conversion device) such as a rectangular CCD sensor or CMOS sensor is disposed on the image plane IP. When the optical system L0 of each embodiment is used as an imaging optical system for a silver salt film camera, a film is disposed on the image plane IP.
実施例１乃至４において、反射光学系Ｍ０は３枚の反射面Ｍ１乃至Ｍ３を有する。実施例５乃至８において、反射光学系Ｍ０は４枚の反射面Ｍ１乃至Ｍ４を有する。各反射面は自由曲面となっている。光学系Ｌに入射した入射光は反射光学系Ｍ０の各反射面で反射され、屈折光学系Ｌ０に導かれる。 In Examples 1 to 4, the reflective optical system M0 has three reflecting surfaces M1 to M3. In Examples 5 to 8, the reflective optical system M0 has four reflecting surfaces M1 to M4. Each reflecting surface is a free-form surface. Incident light that has entered the optical system L is reflected by the reflecting surfaces of the reflective optical system M0 and guided to the refractive optical system L0.
反射光学系Ｍ０の焦点距離は光軸に対して非対称性を有する。以下の説明では、屈折光学系Ｌ０の光軸に直交し反射光学系Ｍ０の焦点距離が最も小さくなる方向を第１の方向とし、第１の方向における反射光学系Ｍ０の焦点距離をＦｙと称する。また、屈折光学系Ｌ０の光軸および第１の方向に直交する方向を第２の方向とし、第２の方向における反射光学系Ｍ０の焦点距離をＦｘと称する。すなわち、Ｆｘ＞Ｆｙである。 The focal length of the reflective optical system M0 is asymmetric with respect to the optical axis. In the following description, the direction orthogonal to the optical axis of the refractive optical system L0 and having the smallest focal length of the reflective optical system M0 is referred to as a first direction, and the focal length of the reflective optical system M0 in the first direction is referred to as Fy. . A direction orthogonal to the optical axis of the refractive optical system L0 and the first direction is referred to as a second direction, and the focal length of the reflective optical system M0 in the second direction is referred to as Fx. That is, Fx> Fy.
各実施例の光学系Ｌにおいて、屈折光学系Ｌ０はフォーカシングに際して移動するフォーカスレンズ群ＬＦとフォーカシングに際して移動しないレンズ群を有する。フォーカスレンズ群ＬＦは、フォーカシングに際して物体側または像側に移動する。なお、フォーカシングに際してのフォーカスレンズ群ＬＦの移動方向は、屈折光学系Ｌ０の光軸に沿う方向の成分を含んでいればよく、必ずしも屈折光学系Ｌ０の光軸に平行に移動していなくても良い。 In the optical system L of each embodiment, the refractive optical system L0 includes a focus lens group LF that moves during focusing and a lens group that does not move during focusing. The focus lens unit LF moves to the object side or the image side during focusing. Note that the moving direction of the focus lens group LF at the time of focusing only needs to include a component in a direction along the optical axis of the refractive optical system L0, and does not necessarily move parallel to the optical axis of the refractive optical system L0. good.
なお、各実施例において「光軸」とは、開口絞りＳＰが形成する開口部（絞り面）の中心を通り、絞り面に対して垂直に入射する光線の光路を言う。 In each embodiment, the “optical axis” refers to the optical path of a light beam that passes through the center of the aperture (diaphragm surface) formed by the aperture stop SP and is perpendicular to the aperture surface.
図２（ａ），４（ａ），６（ａ），８（ａ），１０（ａ），１２（ａ），１４（ａ），１６（ａ）は、それぞれ実施例１乃至８の光学系が無限遠に合焦している時の横収差図である。図２（ｂ），４（ｂ），６（ｂ），８（ｂ），１０（ｂ），１２（ｂ），１４（ｂ），１６（ｂ）は、それぞれ実施例１乃至８の光学系が最至近距離に合焦している時の横収差図である。 2 (a), 4 (a), 6 (a), 8 (a), 10 (a), 12 (a), 14 (a), and 16 (a) show the optical characteristics of Examples 1 to 8, respectively. It is a lateral aberration diagram when the system is focused at infinity. 2 (b), 4 (b), 6 (b), 8 (b), 10 (b), 12 (b), 14 (b), and 16 (b) show the optical characteristics of Examples 1 to 8, respectively. FIG. 6 is a lateral aberration diagram when the system is focused on the closest distance.
各横収差図において、向かって左側に短辺方向の収差図、向かって右側に長辺方向の収差図を示している。ここで、短辺方向とは、像面ＩＰに矩形の撮像素子が配置された場合に撮像素子の短辺に平行な方向を言う。これは例えば図１に示した光学系Ｌの断面図においてｙ軸に平行な方向に相当する。また、長辺方向とは像面ＩＰに矩形の撮像素子が配置された場合に撮像素子の長辺に平行な方向を言う。これは例えば図１に示した光学系Ｌの断面図においてｘ軸に平行な方向に相当する。各方向に対して０割像高と７割像高における横収差図を示している。 In each lateral aberration diagram, an aberration diagram in the short side direction is shown on the left side, and an aberration diagram in the long side direction is shown on the right side. Here, the short side direction refers to a direction parallel to the short side of the image sensor when a rectangular image sensor is arranged on the image plane IP. This corresponds to, for example, a direction parallel to the y-axis in the cross-sectional view of the optical system L shown in FIG. The long side direction refers to a direction parallel to the long side of the image sensor when a rectangular image sensor is arranged on the image plane IP. For example, this corresponds to a direction parallel to the x-axis in the cross-sectional view of the optical system L shown in FIG. Horizontal aberration diagrams at 0% image height and 70% image height are shown for each direction.
各実施例の光学系Ｌのように非共軸の光学系では、物体距離の変化によって反射光学系Ｍ０で生じる軸上アス量が変化する。そこで、各実施例の光学系Ｌでは、フォーカスレンズ群ＬＦをアナモルフィックなレンズ群とすることで、反射光学系Ｍ０での軸上アス量の変化の補正を可能としている。具体的には、各実施例の光学系は、無限遠から最至近距離へのフォーカシングに際してフォーカスレンズ群ＬＦが物体側に移動する場合は以下の条件式（１）を満たし、像側に移動する場合には以下の条件式（２）を満たす。
ｆｘ＞ｆｙ （１）
ｆｙ＞ｆｘ （２）
In a non-coaxial optical system such as the optical system L of each embodiment, the axial asphalt amount generated in the reflective optical system M0 changes due to the change in the object distance. Therefore, in the optical system L of each embodiment, the focus lens group LF is an anamorphic lens group, thereby making it possible to correct a change in the axial asphalt amount in the reflective optical system M0. Specifically, the optical system of each embodiment satisfies the following conditional expression (1) when the focus lens group LF moves to the object side during focusing from infinity to the closest distance, and moves to the image side: Satisfies the following conditional expression (2).
fx> fy (1)
fy> fx (2)
式（１）および（２）において、ｆｙは第１の方向におけるフォーカスレンズ群ＬＦの焦点距離であり、ｆｘは第２の方向におけるフォーカスレンズ群ＬＦの焦点距離である。 In equations (1) and (2), fy is the focal length of the focus lens group LF in the first direction, and fx is the focal length of the focus lens group LF in the second direction.
式（１）は、無限遠から最至近距離へのフォーカシングに際してフォーカスレンズ群ＬＦが物体側に移動する場合において物体距離の変化による収差量の変動を低減させるためにフォーカスレンズ群ＬＦが満たすべき条件である。 Expression (1) is a condition that the focus lens group LF must satisfy in order to reduce fluctuations in the amount of aberration due to changes in the object distance when the focus lens group LF moves to the object side during focusing from infinity to the closest distance. is there.
最至近距離に合焦している時に反射光学系Ｍ０で生じる球面収差量は第２の方向に対して第１の方向が相対的にオーバーとなる。 The amount of spherical aberration generated in the reflective optical system M0 when focusing on the closest distance is relatively over in the first direction relative to the second direction.
無限遠から最至近距離へのフォーカシングに際してフォーカスレンズ群ＬＦは物体側に移動するため、無限遠から最至近距離へのフォーカシングに際して軸上光束がフォーカスレンズ群ＬＦに入射する位置は高くなっていく。ゆえに、フォーカスレンズ群ＬＦのｆｙをｆｘよりも小さくすることで、最至近距離で反射光学系Ｍ０において生じる軸上アス量をフォーカスレンズ群ＬＦで補正することができる。したがって、式（１）を満たすことで物体距離の変化による収差量の変化を効果的に低減させることができる。 Since the focus lens unit LF moves to the object side during focusing from infinity to the closest distance, the position at which the axial light beam enters the focus lens group LF is increased during focusing from infinity to the closest distance. Therefore, by making fy of the focus lens group LF smaller than fx, the on-axis astigmatism generated in the reflective optical system M0 at the closest distance can be corrected by the focus lens group LF. Therefore, by satisfying Expression (1), the change in the amount of aberration due to the change in the object distance can be effectively reduced.
式（２）は、無限遠から最至近距離へのフォーカシングに際してフォーカスレンズ群ＬＦが像側に移動する場合において物体距離の変化による収差量の変動を低減させるためにフォーカスレンズ群ＬＦが満たすべき条件である。 Expression (2) is a condition that the focus lens group LF must satisfy in order to reduce the variation in the amount of aberration due to the change in the object distance when the focus lens group LF moves to the image side during focusing from infinity to the closest distance. is there.
無限遠距離に合焦している時に反射光学系Ｍ０で生じる球面収差量は第１の方向に対して第２の方向が相対的にオーバーとなる。 The amount of spherical aberration generated in the reflective optical system M0 when focusing on an infinite distance is relatively over in the second direction relative to the first direction.
最至近距離から無限遠へのフォーカシングに際してフォーカスレンズ群ＬＦは物体側に移動するため、最至近距離から無限遠へのフォーカシングに際して軸上光束がフォーカスレンズ群ＬＦに入射する位置は高くなっていく。ゆえに、フォーカスレンズ群ＬＦのｆｘをｆｙよりも小さくすることで、無限遠で反射光学系Ｍ０において生じる軸上アス量をフォーカスレンズ群ＬＦで補正することができる。したがって、式（２）を満たすことで物体距離の変化による収差量の変化を効果的に低減させることができる。 Since the focus lens group LF moves to the object side during focusing from the closest distance to infinity, the position where the axial light beam enters the focus lens group LF becomes higher during focusing from the closest distance to infinity. Therefore, by setting fx of the focus lens group LF to be smaller than fy, the axial lens amount generated in the reflection optical system M0 at infinity can be corrected by the focus lens group LF. Therefore, by satisfying Expression (2), it is possible to effectively reduce the change in the amount of aberration due to the change in the object distance.
また、フォーカスレンズ群ＬＦが無限遠から最至近距離へのフォーカシングに際して物体側に移動する場合、ｆｙが０より大きい場合は以下の式（３）を、ｆｘが０より小さい場合には以下の式（４）を満たすことが好ましい。
１．００＜ｆｘ／ｆｙ＜２．８０ （３）
０．３００＜ｆｘ／ｆｙ＜１．００ （４）
Further, when the focus lens unit LF moves to the object side during focusing from infinity to the closest distance, the following equation (3) is obtained when fy is larger than 0, and the following equation (3) when fx is smaller than 0: It is preferable to satisfy 4).
1.00 <fx / fy <2.80 (3)
0.300 <fx / fy <1.00 (4)
フォーカスレンズ群ＬＦが無限遠から最至近距離へのフォーカシングに際して物体側に移動する場合、最至近距離において相対的にオーバーとなる第１の方向の球面収差をフォーカスレンズ群ＬＦで補正している。式（３）、（４）は最至近距離における軸上アスを十分に補正するためのフォーカスレンズ群ＬＦにおける第１の方向の焦点距離と第２の方向の焦点距離の比を規定するものである。式（３）と式（４）で場合分けをしているのは、フォーカスレンズ群ＬＦの焦点距離が正である場合と負である場合で球面収差の出る方向が異なるためである。 When the focus lens group LF moves to the object side during focusing from infinity to the closest distance, the spherical aberration in the first direction, which is relatively over at the closest distance, is corrected by the focus lens group LF. Expressions (3) and (4) define the ratio of the focal length in the first direction to the focal length in the second direction in the focus lens group LF for sufficiently correcting the axial ass at the closest distance. is there. The reason why the expression (3) and the expression (4) are divided is that the direction in which the spherical aberration occurs differs depending on whether the focal length of the focus lens group LF is positive or negative.
式（３）の下限値または式（４）の上限値は式（１）に対応している。 The lower limit value of Expression (3) or the upper limit value of Expression (4) corresponds to Expression (1).
式（３）の上限値を超える場合または式（４）の下限値を下回る場合、フォーカスレンズ群の焦点距離の非対称性が大きくなりすぎ、最至近距離での軸上アスを過剰に補正してしまう。したがって軸上アスを十分に低減させることが困難となる。 When the upper limit value of Equation (3) is exceeded or below the lower limit value of Equation (4), the asymmetry of the focal length of the focus lens group becomes too large, and the axial ass at the closest distance is excessively corrected. End up. Therefore, it is difficult to sufficiently reduce axial asphalt.
なお、ｆｘ／ｆｙの値が１に近すぎる場合、フォーカスレンズ群の焦点距離の非対称性が小さくなりすぎ、最至近距離における軸上アスを十分に補正できないことがある。このため、式（３）の数値範囲を以下の式（３ａ）のように設定することがより好ましく、式（３ｂ）のように設定することがさらに好ましい。また、式（４）の数値範囲を以下の式（４ａ）のように設定することがより好ましく、式（４ｂ）のように設定することがさらに好ましい。
１．１０＜ｆｘ／ｆｙ＜２．５０ （３ａ）
１．３０＜ｆｘ／ｆｙ＜２．１０ （３ｂ）
０．４００＜ｆｘ／ｆｙ＜０．９００ （４ａ）
０．５００＜ｆｘ／ｆｙ＜０．８００ （４ｂ）
When the value of fx / fy is too close to 1, the asymmetry of the focal length of the focus lens group becomes too small, and the axial ass at the closest distance may not be sufficiently corrected. For this reason, it is more preferable to set the numerical value range of Formula (3) like the following formula | equation (3a), and it is still more preferable to set like Formula (3b). Moreover, it is more preferable to set the numerical range of the formula (4) as the following formula (4a), and it is more preferable to set as the formula (4b).
1.10 <fx / fy <2.50 (3a)
1.30 <fx / fy <2.10 (3b)
0.400 <fx / fy <0.900 (4a)
0.500 <fx / fy <0.800 (4b)
また、フォーカスレンズ群ＬＦが無限遠から最至近距離へのフォーカシングに際して像側に移動する場合、ｆｘが０より大きい場合は以下の式（５）を、ｆｙが０より小さい場合には以下の式（６）を満たすことが好ましい。
０．３００＜ｆｘ／ｆｙ＜１．００ （５）
１．００＜ｆｘ／ｆｙ＜２．８０ （６）
When the focus lens unit LF moves to the image side during focusing from infinity to the closest distance, the following expression (5) is obtained when fx is larger than 0, and the following expression (when fy is smaller than 0) ( It is preferable to satisfy 6).
0.300 <fx / fy <1.00 (5)
1.00 <fx / fy <2.80 (6)
フォーカスレンズ群ＬＦが無限遠から最至近距離へのフォーカシングに際して像側に移動する場合、無限遠において相対的にオーバーとなる第２の方向の球面収差をフォーカスレンズ群ＬＦで補正している。式（５）、（６）は無限遠における軸上アスを十分に補正するためのフォーカスレンズ群ＬＦにおける第１の方向の焦点距離と第２の方向の焦点距離の比を規定するものである。式（５）と式（６）で場合分けをしているのは、フォーカスレンズ群ＬＦの焦点距離が正である場合と負である場合で球面収差の出る方向が異なるためである。 When the focus lens group LF moves to the image side during focusing from infinity to the closest distance, spherical aberration in the second direction, which is relatively over at infinity, is corrected by the focus lens group LF. Expressions (5) and (6) define the ratio of the focal length in the first direction to the focal length in the second direction in the focus lens group LF for sufficiently correcting the axial ass at infinity. . The reason why the expression (5) and the expression (6) are divided is that the direction in which the spherical aberration occurs differs depending on whether the focal length of the focus lens group LF is positive or negative.
式（５）の上限値または式（６）の下限値は式（２）に対応している。 The upper limit value of Expression (5) or the lower limit value of Expression (6) corresponds to Expression (2).
式（５）の下限値を下回る場合または式（６）の上限値を超える場合、フォーカスレンズ群の焦点距離の非対称性が大きくなりすぎ、無限遠での軸上アスを過剰に補正してしまう。したがって軸上アスを十分に低減させることが困難となる。 When the lower limit value of Expression (5) is not reached or when the upper limit value of Expression (6) is exceeded, the asymmetry of the focal length of the focus lens group becomes too large, and the on-axis astigmatism at infinity is excessively corrected. . Therefore, it is difficult to sufficiently reduce axial asphalt.
なお、ｆｘ／ｆｙの値が１に近すぎる場合、フォーカスレンズ群の焦点距離の非対称性が小さくなりすぎ、無限遠における軸上アスを十分に補正できないことがある。このため、式（５）の数値範囲を以下の式（５ａ）のように設定することがより好ましく、式（５ｂ）のように設定することがさらに好ましい。また、式（６）の数値範囲を以下の式（６ａ）のように設定することがより好ましく、式（６ｂ）のように設定することがさらに好ましい。
０．４００＜ｆｘ／ｆｙ＜０．９００ （５ａ）
０．５００＜ｆｘ／ｆｙ＜０．８００ （５ｂ）
１．１０＜ｆｘ／ｆｙ＜２．５０ （６ａ）
１．３０＜ｆｘ／ｆｙ＜２．１０ （６ｂ）
If the value of fx / fy is too close to 1, the asymmetry of the focal length of the focus lens group becomes too small, and the axial astigmatism at infinity may not be sufficiently corrected. For this reason, it is more preferable to set the numerical range of Formula (5) like the following formula | equation (5a), and it is still more preferable to set like Formula (5b). Moreover, it is more preferable to set the numerical range of the equation (6) as the following equation (6a), and it is more preferable to set it as the equation (6b).
0.400 <fx / fy <0.900 (5a)
0.500 <fx / fy <0.800 (5b)
1.10 <fx / fy <2.50 (6a)
1.30 <fx / fy <2.10 (6b)
また、各実施例の光学系は以下の式（７）を満たすことが好ましい。
１．０１＜｜Ｆｘ｜／｜Ｆｙ｜＜１．５０ （７）
Moreover, it is preferable that the optical system of each Example satisfies the following formula (7).
1.01 <| Fx | / | Fy | <1.50 (7)
式（７）は反射光学系Ｍ０における第１の方向の焦点距離と第２の方向の焦点距離の比に関する。 Expression (7) relates to the ratio between the focal length in the first direction and the focal length in the second direction in the reflective optical system M0.
｜Ｆｘ｜／｜Ｆｙ｜の値が式（７）の下限値を下回る場合、ＦｘとＦｙの値が近くなりすぎる。この場合、良好な光学性能を得るようとすると反射光学系Ｍ０が大型化してしまうため好ましくない。｜Ｆｘ｜／｜Ｆｙ｜の値が式（７）の上限値を超える場合、反射光学系Ｍ０における焦点距離の非対称性が強くなり、反射光学系Ｍ０で生じる軸上アスを屈折光学系Ｌ０で十分に補正することが困難となる。 When the value of | Fx | / | Fy | is lower than the lower limit value of Expression (7), the values of Fx and Fy are too close. In this case, it is not preferable to obtain good optical performance because the reflective optical system M0 is enlarged. When the value of | Fx | / | Fy | exceeds the upper limit of the expression (7), the asymmetry of the focal length in the reflective optical system M0 becomes strong, and the axial astigmatism generated in the reflective optical system M0 is reduced in the refractive optical system L0. It becomes difficult to correct sufficiently.
また、各実施例の光学系は少なくとも３面の反射面を備えて構成されていることが好ましい。また、この時それぞれの反射面は自由曲面であることが好ましい。これによって、反射光学系Ｍ０を小型に構成しつつ良好な光学性能を得ることができる。 Moreover, it is preferable that the optical system of each embodiment is configured to include at least three reflecting surfaces. At this time, each reflecting surface is preferably a free-form surface. This makes it possible to obtain good optical performance while making the reflective optical system M0 compact.
この場合、反射光学系に入射した光を最初に反射する反射面Ｍ１は、以下の式（８）を満たすことが好ましい。また、反射面Ｍ１で反射された光を反射する反射面Ｍ２は以下の式（９）を満たすことが好ましい。また、反射面Ｍ２で反射された光を反射する反射面Ｍ３は以下の式（１０）を満たすことが好ましい。また、反射面Ｍ３で反射された光を反射する反射面Ｍ４を有する場合、反射面Ｍ４は以下の式（１１）を満たすことが好ましい。
１．０５＜｜Ｆｕ１｜／｜Ｆｖ１｜＜５．００ （８）
１．０５＜｜Ｆｕ２｜／｜Ｆｖ２｜＜５．００ （９）
１．２０＜｜Ｆｕ３｜／｜Ｆｖ３｜＜６０．０ （１０）
１．２０＜｜Ｆｕ４｜／｜Ｆｖ４｜＜３．００ （１１）
In this case, it is preferable that the reflective surface M1 that first reflects the light incident on the reflective optical system satisfies the following formula (8). Moreover, it is preferable that the reflective surface M2 that reflects the light reflected by the reflective surface M1 satisfies the following formula (9). Moreover, it is preferable that the reflective surface M3 that reflects the light reflected by the reflective surface M2 satisfies the following formula (10). Moreover, when it has the reflective surface M4 which reflects the light reflected by the reflective surface M3, it is preferable that the reflective surface M4 satisfy | fills the following formula | equation (11).
1.05 <| Fu1 | / | Fv1 | <5.00 (8)
1.05 <| Fu2 | / | Fv2 | <5.00 (9)
1.20 <| Fu3 | / | Fv3 | <60.0 (10)
1.20 <| Fu4 | / | Fv4 | <3.00 (11)
式（８）において、Ｆｖ１は、光軸に直交し反射面Ｍ１の焦点距離が最も小さくなる方向における反射面Ｍ１の焦点距離であり、Ｆｕ１は反射面Ｍ１の焦点距離が最も小さくなる光軸に直交する方向に直交する方向における反射面Ｍ１の焦点距離である。式（９）において、Ｆｖ２は、光軸に直交し反射面Ｍ２の焦点距離が最も小さくなる方向における反射面Ｍ２の焦点距離であり、Ｆｕ２は反射面Ｍ２の焦点距離が最も小さくなる光軸に直交する方向に直交する方向における反射面Ｍ２の焦点距離である。式（１０）において、Ｆｖ３は、光軸に直交し反射面Ｍ３の焦点距離が最も小さくなる方向における反射面Ｍ３の焦点距離であり、Ｆｕ３は反射面Ｍ３の焦点距離が最も小さくなる光軸に直交する方向に直交する方向における反射面Ｍ３の焦点距離である。式（１１）において、Ｆｖ４は、光軸に直交し反射面Ｍ４の焦点距離が最も小さくなる方向における反射面Ｍ４の焦点距離であり、Ｆｕ４は反射面Ｍ４の焦点距離が最も小さくなる光軸に直交する方向に直交する方向における反射面Ｍ４の焦点距離である。 In Equation (8), Fv1 is the focal length of the reflecting surface M1 in the direction perpendicular to the optical axis and the focal length of the reflecting surface M1 is smallest, and Fu1 is the optical axis where the focal length of the reflecting surface M1 is smallest. This is the focal length of the reflecting surface M1 in the direction orthogonal to the orthogonal direction. In equation (9), Fv2 is the focal length of the reflecting surface M2 in the direction orthogonal to the optical axis and the focal length of the reflecting surface M2 is smallest, and Fu2 is the optical axis where the focal length of the reflecting surface M2 is smallest. This is the focal length of the reflecting surface M2 in the direction orthogonal to the orthogonal direction. In Formula (10), Fv3 is the focal length of the reflecting surface M3 in the direction orthogonal to the optical axis and the focal length of the reflecting surface M3 is the smallest, and Fu3 is the optical axis where the focal length of the reflecting surface M3 is the smallest. This is the focal length of the reflecting surface M3 in the direction orthogonal to the orthogonal direction. In Expression (11), Fv4 is a focal length of the reflecting surface M4 in a direction orthogonal to the optical axis and having the smallest focal length of the reflecting surface M4, and Fu4 is an optical axis having the smallest focal length of the reflecting surface M4. This is the focal length of the reflecting surface M4 in the direction orthogonal to the orthogonal direction.
式（８）から（１１）は、各反射面における焦点距離の非対称性に関する。各式において下限値を下回る場合、各反射面における焦点距離の非対称性が小さくなりすぎる。この場合、良好な光学性能を得るようとすると反射光学系Ｍ０が大型化してしまうため好ましくない。また、各式において上限値を上回る場合、各反射面における焦点距離の非対称性が大きくなりすぎ、反射光学系Ｍ０で生じる軸上アスを屈折光学系Ｌ０で十分に補正することが困難となる。 Expressions (8) to (11) relate to the asymmetry of the focal length at each reflecting surface. When the value is below the lower limit in each equation, the asymmetry of the focal length on each reflecting surface becomes too small. In this case, it is not preferable to obtain good optical performance because the reflective optical system M0 is enlarged. In addition, when the upper limit value is exceeded in each expression, the asymmetry of the focal length at each reflecting surface becomes too large, and it is difficult to sufficiently correct on-axis astigmatism generated in the reflecting optical system M0 with the refractive optical system L0.
なお、式（８）乃至（１１）の数値範囲を以下の式（８ａ）乃至（１１ａ）のように設定することがより好ましく、式（８ｂ）乃至（１１ｂ）のように設定することがさらに好ましい。
１．１０＜｜Ｆｕ１｜／｜Ｆｖ１｜＜４．５０ （８ａ）
１．１０＜｜Ｆｕ２｜／｜Ｆｖ２｜＜４．５０ （９ａ）
１．２５＜｜Ｆｕ３｜／｜Ｆｖ３｜＜５５．０ （１０ａ）
１．２５＜｜Ｆｕ４｜／｜Ｆｖ４｜＜２．５０ （１１ａ）
１．１５＜｜Ｆｕ１｜／｜Ｆｖ１｜＜４．００ （８ｂ）
１．１５＜｜Ｆｕ２｜／｜Ｆｖ２｜＜４．００ （９ｂ）
１．３０＜｜Ｆｕ３｜／｜Ｆｖ３｜＜５０．０ （１０ｂ）
１．３０＜｜Ｆｕ４｜／｜Ｆｖ４｜＜２．００ （１１ｂ）
In addition, it is more preferable to set the numerical ranges of the expressions (8) to (11) as the following expressions (8a) to (11a), and it is more preferable to set them as the expressions (8b) to (11b). preferable.
1.10 <| Fu1 | / | Fv1 | <4.50 (8a)
1.10 <| Fu2 | / | Fv2 | <4.50 (9a)
1.25 <| Fu3 | / | Fv3 | <55.0 (10a)
1.25 <| Fu4 | / | Fv4 | <2.50 (11a)
1.15 <| Fu1 | / | Fv1 | <4.00 (8b)
1.15 <| Fu2 | / | Fv2 | <4.00 (9b)
1.30 <| Fu3 | / | Fv3 | <50.0 (10b)
1.30 <| Fu4 | / | Fv4 | <2.00 (11b)
さらに、各実施例の光学系は以下の条件式（１２）を満足することが好ましい。
３．００＜Ｄ／ｙ０＜２０．０ （１２）
Furthermore, it is preferable that the optical system of each example satisfies the following conditional expression (12).
3.00 <D / y0 <20.0 (12)
式（１２）において、Ｄは開口絞りＳＰが開放である時の入射瞳径である。各実施例の光学系では物体側から数えて第一番目に光線が通過する面である絞り面の軸上光束の有効径（絞り径）に相当する。また、ｙ０は最大像高である。最大像高は無限遠合焦時のイメージサークル径の半径によって定めれば良い。イメージサークル径は、イメージサークルの中心の明るさに対して明るさが１０％となる領域の径とすれば良い。 In Expression (12), D is the entrance pupil diameter when the aperture stop SP is open. In the optical system of each embodiment, this corresponds to the effective diameter (diaphragm diameter) of the axial light beam on the diaphragm surface, which is the first surface through which the light beam passes from the object side. Y0 is the maximum image height. The maximum image height may be determined by the radius of the image circle diameter when focusing on infinity. The image circle diameter may be a diameter of a region where the brightness is 10% with respect to the brightness of the center of the image circle.
なお、通常はイメージサークル径と撮像素子の対角長は略同等である。そのため、各実施例の光学系が装着される撮像装置に設けられた撮像素子の対角長の半分の値をｙ０としても良い。 In general, the image circle diameter and the diagonal length of the image sensor are substantially the same. For this reason, a value that is half the diagonal length of the imaging element provided in the imaging apparatus to which the optical system of each embodiment is mounted may be set to y0.
式（１２）の下限値を下回るほどにＤが小さくなると、光学系Ｌに入射する光の光量を十分に確保することが難しくなる。この場合、各実施例の光学系Ｌを望遠タイプの撮影光学系として用いることが難しくなる。式（１２）の上限値を上回るほどにＤが大きくなると、光学系Ｌが大型化するため好ましくない。 If D becomes smaller as it falls below the lower limit of Expression (12), it becomes difficult to ensure a sufficient amount of light incident on the optical system L. In this case, it becomes difficult to use the optical system L of each embodiment as a telephoto imaging optical system. If D is increased so as to exceed the upper limit value of Expression (12), the optical system L is increased in size, which is not preferable.
さらに、各実施例の光学系Ｌにおいて、フォーカスレンズ群ＬＦはフォーカシングに際して光軸に平行な方向に移動することが好ましい。これによってフォーカスレンズ群ＬＦを光軸に対して斜めに移動させる場合と比較して、フォーカスレンズ群ＬＦを移動させるための機構を簡略化することができる。 Further, in the optical system L of each embodiment, it is preferable that the focus lens group LF moves in a direction parallel to the optical axis during focusing. As a result, a mechanism for moving the focus lens group LF can be simplified as compared with the case where the focus lens group LF is moved obliquely with respect to the optical axis.
次に、各実施例の光学系について述べる。 Next, the optical system of each example will be described.
実施例１および２の光学系Ｌにおける反射光学系Ｍ０は、３枚の反射面Ｍ１乃至Ｍ３で構成されている。また、フォーカスレンズ群ＬＦは無限遠から最至近距離へのフォーカシングに際して像側に移動する。 The reflective optical system M0 in the optical system L of the first and second embodiments includes three reflective surfaces M1 to M3. The focus lens unit LF moves to the image side during focusing from infinity to the closest distance.
実施例３および４の光学系における反射光学系Ｍ０は、３枚の反射面Ｍ１乃至Ｍ３で構成されている。また、フォーカスレンズ群ＬＦは無限遠から最至近距離へのフォーカシングに際して物体側に移動する。 The reflective optical system M0 in the optical systems of Examples 3 and 4 includes three reflective surfaces M1 to M3. The focus lens unit LF moves to the object side during focusing from infinity to the closest distance.
実施例５および６の光学系における反射光学系Ｍ０は、４枚の反射面Ｍ１乃至Ｍ４で構成されている。フォーカスレンズ群ＬＦは無限遠から最至近距離へのフォーカシングに際して物体側に移動する。 The reflecting optical system M0 in the optical systems of Examples 5 and 6 is composed of four reflecting surfaces M1 to M4. The focus lens unit LF moves to the object side during focusing from infinity to the closest distance.
実施例７および８の光学系における反射光学系Ｍ０は、４枚の反射面Ｍ１乃至Ｍ４で構成されている。フォーカスレンズ群ＬＦは無限遠から最至近距離へのフォーカシングに際して像側に移動する。 The reflecting optical system M0 in the optical systems of Examples 7 and 8 is composed of four reflecting surfaces M1 to M4. The focus lens unit LF moves to the image side during focusing from infinity to the closest distance.
以下に、実施例１乃至８に対応する数値実施例１乃至８を示す。 Numerical examples 1 to 8 corresponding to the first to eighth examples will be shown below.
面データにおいて、面番号は物体側から順に数えた光学面の番号である。光学面は、絞り面、反射面、屈折面を含む。Ｘ，Ｙ，Ｚは、第１面Ｓ１の中心を原点（０，０，０）として、図中に示したｙ軸とｚ軸と紙面の奥向きを正としたｘ軸からなる座標系における各面の面頂点の座標（Ｘ，Ｙ，Ｚ）である。Ａは図中で反時計回り方向を正方向とするｘ軸回りの回転角度（°）である。Ｒｙは各面のｙ方向の曲率半径である。Ｒｙが０である面は平面であることを表す。Ｎｄはｄ線（５８７．６ｎｍ）に対する屈折率である。νｄはアッベ数である。なおアッベ数νｄとは、Ｆ線（４８６．１ｎｍ）、Ｃ線（６５６．３ｎｍ）、ｄ線に対する屈折率をそれぞれＮＦ、ＮＣ、Ｎｄとしたとき、以下の式（１３）で定義される値である。
νｄ＝（Ｎｄ−１）／（ＮＦ−ＮＣ） （１３）
In the surface data, the surface number is the number of the optical surface counted in order from the object side. The optical surface includes a diaphragm surface, a reflective surface, and a refractive surface. X, Y, and Z are in a coordinate system composed of the x-axis with the center of the first surface S1 as the origin (0, 0, 0) and the y-axis and z-axis shown in the figure and the depth direction of the paper surface being positive. It is the coordinate (X, Y, Z) of the surface vertex of each surface. A is a rotation angle (°) about the x-axis with the counterclockwise direction as the positive direction in the figure. Ry is the radius of curvature of each surface in the y direction. The surface where Ry is 0 represents that it is a plane. Nd is a refractive index with respect to d line (587.6 nm). νd is the Abbe number. The Abbe number νd is a value defined by the following equation (13) when the refractive indexes for the F-line (486.1 nm), C-line (656.3 nm), and d-line are NF, NC, and Nd, respectively. It is.
νd = (Nd−1) / (NF-NC) (13)
面データにおいて自由曲面には面番号の隣にアスタリスク（＊）を付している。自由曲面の面形状は以下の式（１４）で表される。
ｚ＝ｃｒ２／｛１＋√［１−ｃ２ｒ２］｝＋ΣｊＣｊＸｍＹｎ （１４）
In the surface data, an asterisk (*) is added to the free curved surface next to the surface number. The surface shape of the free-form surface is expressed by the following formula (14).
z = cr 2 / {1 + √ [1-c 2 r 2 ]} + Σ j C j X m Y n (14)
ただし、ｒ２＝Ｘ２＋Ｙ２、ｊ＝［（ｍ＋ｎ）２＋ｍ＋３ｎ］／２＋１である。また、ｃはｙ方向の曲率（＝１／Ｒｙ）であり、ＣｊはＸｍＹｎの係数である。各面のＣｊの値はＦＦＳの項目中にＸｍＹｎと対応させて示されている。ＦＦＳの隣の数字は面番号を表す。また、ＸｍＹｎとして示された数字は式（１４）におけるＸｍＹｎの係数Ｃｊである。 However, r 2 = X 2 + Y 2 , j = [(m + n) 2 + m + 3n] / 2 + 1. C is a curvature in the y direction (= 1 / Ry), and C j is a coefficient of X m Y n . The value of C j for each surface is shown in correspondence with X m Y n in the item of FFS. The number next to FFS represents the surface number. Also, the numbers shown as XmYn is the coefficient C j of X m Y n in the formula (14).
以下の数値実施例において、「Ｅ−Ｐ」とは、１０−Ｐを表す。 In the following numerical examples, “E-P” represents 10 −P .
［数値実施例１］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 110.000 -25.0 -706.955 反射面
3* 0.000 59.390 60.166 -80.0 -388.855 反射面
4* 0.000 82.190 8.635 -145.0 -132.457 反射面
5* 0.000 82.190 78.559 -180.0 -35.233 1.64746 34.10 屈折面
6 0.000 82.190 91.262 -180.0 46.392 1.73743 32.11 屈折面
7 0.000 82.190 93.762 -180.0 -37.300 屈折面
8 0.000 82.190 106.675 -180.0 42.597 1.65964 56.73 屈折面
9 0.000 82.190 109.175 -180.0 -77.889 屈折面
10 0.000 82.190 149.175 -180.0 -60.000 1.54256 53.00 屈折面
11 0.000 82.190 157.175 -180.0 22.932 1.83421 36.84 屈折面
12 0.000 82.190 159.675 -180.0 -260.000 屈折面
13 0.000 82.190 163.675 -180.0 408.137 1.84030 28.67 屈折面
14 0.000 82.190 171.671 -180.0 38.233 屈折面
15 0.000 82.190 192.332 -180.0 0.000 像面
FFS2
X2: 4.6092E-04 Y2: -9.1545E-06 X2Y: -1.9632E-07
Y3: -5.9293E-06 X4: -2.8306E-09 X2Y2: -3.4147E-09
Y4: -1.3647E-08 X4Y: -1.2387E-11 X2Y3: -1.7808E-11
Y5: -1.9977E-10 X6: 3.3513E-13 X4Y2: 6.6638E-13
X2Y4: 6.1861E-13 Y6: -1.1994E-12 X6Y: 2.2193E-15
X4Y3: 3.6873E-15 X2Y5: -7.0263E-15 Y7: -1.5823E-14
X8: -1.3284E-17 X6Y2: 1.4358E-17 X4Y4: 3.4557E-17
X2Y6: -2.0332E-18 Y8: -1.9102E-16
FFS3
X2: 1.8920E-03 Y2: 2.6591E-03 X2Y: -4.9079E-07
Y3: -1.1042E-05 X4: -2.6256E-09 X2Y2: 7.9037E-09
Y4: -4.2409E-08 X4Y: -5.8714E-12 X2Y3: 3.2023E-11
Y5: -1.9329E-10 X6: 4.4727E-13 X4Y2: 1.2779E-12
FFS4
X2: 3.4485E-03 Y2: -1.3946E-03 X2Y: 3.0775E-06
Y3: -8.9033E-06 X4: 5.9035E-08 X2Y2: 7.5964E-08
Y4: -1.5236E-07 X4Y: -2.2777E-10 X2Y3: 1.5594E-10
Y5: -1.9086E-09 X6: -5.5594E-12 X4Y2: -1.5770E-11
X2Y4: -1.6262E-11 Y6: -1.9315E-11
FFS5
X2: -3.4856E-04 Y2: -8.4318E-04 Y3: 9.2591E-07
X4: -2.1866E-06 X2Y2: -4.5135E-06 Y4: -3.3114E-06
X4Y: 1.6075E-09 X3Y2: -2.4550E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
[Numerical Example 1]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd vd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 110.000 -25.0 -706.955 Reflective surface
3 * 0.000 59.390 60.166 -80.0 -388.855 Reflecting surface
4 * 0.000 82.190 8.635 -145.0 -132.457 Reflective surface
5 * 0.000 82.190 78.559 -180.0 -35.233 1.64746 34.10 Refractive surface
6 0.000 82.190 91.262 -180.0 46.392 1.73743 32.11 Refractive surface
7 0.000 82.190 93.762 -180.0 -37.300 Refractive surface
8 0.000 82.190 106.675 -180.0 42.597 1.65964 56.73 Refractive surface
9 0.000 82.190 109.175 -180.0 -77.889 Refractive surface
10 0.000 82.190 149.175 -180.0 -60.000 1.54256 53.00 Refractive surface
11 0.000 82.190 157.175 -180.0 22.932 1.83421 36.84 Refractive surface
12 0.000 82.190 159.675 -180.0 -260.000 Refractive surface
13 0.000 82.190 163.675 -180.0 408.137 1.84030 28.67 Refractive surface
14 0.000 82.190 171.671 -180.0 38.233 Refractive surface
15 0.000 82.190 192.332 -180.0 0.000 Image plane
FFS2
X2: 4.6092E-04 Y2: -9.1545E-06 X2Y: -1.9632E-07
Y3: -5.9293E-06 X4: -2.8306E-09 X2Y2: -3.4147E-09
Y4: -1.3647E-08 X4Y: -1.2387E-11 X2Y3: -1.7808E-11
Y5: -1.9977E-10 X6: 3.3513E-13 X4Y2: 6.6638E-13
X2Y4: 6.1861E-13 Y6: -1.1994E-12 X6Y: 2.2193E-15
X4Y3: 3.6873E-15 X2Y5: -7.0263E-15 Y7: -1.5823E-14
X8: -1.3284E-17 X6Y2: 1.4358E-17 X4Y4: 3.4557E-17
X2Y6: -2.0332E-18 Y8: -1.9102E-16
FFS3
X2: 1.8920E-03 Y2: 2.6591E-03 X2Y: -4.9079E-07
Y3: -1.1042E-05 X4: -2.6256E-09 X2Y2: 7.9037E-09
Y4: -4.2409E-08 X4Y: -5.8714E-12 X2Y3: 3.2023E-11
Y5: -1.9329E-10 X6: 4.4727E-13 X4Y2: 1.2779E-12
FFS4
X2: 3.4485E-03 Y2: -1.3946E-03 X2Y: 3.0775E-06
Y3: -8.9033E-06 X4: 5.9035E-08 X2Y2: 7.5964E-08
Y4: -1.5236E-07 X4Y: -2.2777E-10 X2Y3: 1.5594E-10
Y5: -1.9086E-09 X6: -5.5594E-12 X4Y2: -1.5770E-11
X2Y4: -1.6262E-11 Y6: -1.9315E-11
FFS5
X2: -3.4856E-04 Y2: -8.4318E-04 Y3: 9.2591E-07
X4: -2.1866E-06 X2Y2: -4.5135E-06 Y4: -3.3114E-06
X4Y: 1.6075E-09 X3Y2: -2.4550E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
［数値実施例２］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 110.000 -25.0 -714.372 反射面
3* 0.000 60.932 58.872 -80.0 -380.884 反射面
4* 0.000 -80.465 7.408 -145.0 -126.742 反射面
5* 0.000 -80.465 77.408 -180.0 -39.809 1.63811 38.86 屈折面
6 0.000 -80.465 89.314 -180.0 213.373 1.69897 44.47 屈折面
7 0.000 -80.465 91.814 -180.0 -22.462 屈折面
8 0.000 -80.465 100.814 -180.0 72.324 1.64913 33.94 屈折面
9 0.000 -80.465 103.314 -180.0 226.053 屈折面
10 0.000 -80.465 123.800 -180.0 -60.000 1.75764 30.67 屈折面
11 0.000 -80.465 131.800 -180.0 52.051 1.76352 44.00 屈折面
12 0.000 -80.465 134.300 -180.0 -260.000 屈折面
13 0.000 -80.465 138.300 -180.0 51.268 1.84600 23.80 屈折面
14 0.000 -80.465 140.800 -180.0 199.468 屈折面
15 0.000 -80.465 147.721 -180.0 45.907 1.48749 70.41 屈折面
16 0.000 -80.465 152.337 -180.0 -27.799 屈折面
17 0.000 -80.465 177.337 -180.0 0.000 像面
FFS2
X2: 4.6791E-04 Y2: -4.0604E-06 X2Y: -1.3361E-07
Y3: -5.5690E-06 X4: 3.6075E-09 X2Y2: 8.8156E-09
Y4: -9.2017E-09 X4Y: -3.0575E-12 X2Y3: 5.8158E-12
Y5: -1.9240E-10 X6: -1.1889E-12 X4Y2: -1.4154E-12
X2Y4: -4.6113E-13 Y6: -9.5631E-13 X6Y: 2.2064E-16
X4Y3: 4.3494E-15 X2Y5: 9.8654E-16 Y7: -1.0401E-14
X8: -5.8401E-18 X6Y2: 1.7618E-17 X4Y4: -4.6248E-17
X2Y6: -1.1867E-16 Y8: -1.8088E-16
FFS3
X2: 1.8958E-03 Y2: 2.6199E-03 X2Y: -6.7973E-07
Y3: -1.0715E-05 X4: 6.6024E-09 X2Y2: 3.3837E-08
Y4: -2.9170E-08 X4Y: -1.3093E-11 X2Y3: 1.4106E-10
Y5: -1.3573E-10 X6: -2.1851E-12 X4Y2: -3.1550E-12
X2Y4: -1.3855E-12 Y6: -1.2415E-12
FFS4
X2: 3.3860E-03 Y2: -1.6475E-03 X2Y: 2.3172E-06
Y3: -1.1636E-05 X4: 3.9637E-08 X2Y2: 8.5526E-08
Y4: -2.2802E-07 X4Y: -2.2658E-10 X2Y3: 9.0009E-10
Y5: -3.3036E-09 X6: 2.8296E-12 X4Y2: 1.5755E-11
X2Y4: 9.5846E-12 Y6: -3.9534E-11
FFS5
X2: -7.8014E-04 Y2: -7.8969E-03 Y3: 4.6269E-06
X4: 4.0288E-06 X2Y2: -3.9569E-07 Y4: -1.6730E-06
X4Y: -1.4780E-09 X3Y2: 9.1076E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
[Numerical Example 2]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 110.000 -25.0 -714.372 Reflecting surface
3 * 0.000 60.932 58.872 -80.0 -380.884 Reflecting surface
4 * 0.000 -80.465 7.408 -145.0 -126.742 Reflecting surface
5 * 0.000 -80.465 77.408 -180.0 -39.809 1.63811 38.86 Refractive surface
6 0.000 -80.465 89.314 -180.0 213.373 1.69897 44.47 Refractive surface
7 0.000 -80.465 91.814 -180.0 -22.462 Refractive surface
8 0.000 -80.465 100.814 -180.0 72.324 1.64913 33.94 Refractive surface
9 0.000 -80.465 103.314 -180.0 226.053 Refractive surface
10 0.000 -80.465 123.800 -180.0 -60.000 1.75764 30.67 Refractive surface
11 0.000 -80.465 131.800 -180.0 52.051 1.76352 44.00 Refractive surface
12 0.000 -80.465 134.300 -180.0 -260.000 Refractive surface
13 0.000 -80.465 138.300 -180.0 51.268 1.84600 23.80 Refractive surface
14 0.000 -80.465 140.800 -180.0 199.468 Refractive surface
15 0.000 -80.465 147.721 -180.0 45.907 1.48749 70.41 Refractive surface
16 0.000 -80.465 152.337 -180.0 -27.799 Refractive surface
17 0.000 -80.465 177.337 -180.0 0.000 Image plane
FFS2
X2: 4.6791E-04 Y2: -4.0604E-06 X2Y: -1.3361E-07
Y3: -5.5690E-06 X4: 3.6075E-09 X2Y2: 8.8156E-09
Y4: -9.2017E-09 X4Y: -3.0575E-12 X2Y3: 5.8158E-12
Y5: -1.9240E-10 X6: -1.1889E-12 X4Y2: -1.4154E-12
X2Y4: -4.6113E-13 Y6: -9.5631E-13 X6Y: 2.2064E-16
X4Y3: 4.3494E-15 X2Y5: 9.8654E-16 Y7: -1.0401E-14
X8: -5.8401E-18 X6Y2: 1.7618E-17 X4Y4: -4.6248E-17
X2Y6: -1.1867E-16 Y8: -1.8088E-16
FFS3
X2: 1.8958E-03 Y2: 2.6199E-03 X2Y: -6.7973E-07
Y3: -1.0715E-05 X4: 6.6024E-09 X2Y2: 3.3837E-08
Y4: -2.9170E-08 X4Y: -1.3093E-11 X2Y3: 1.4106E-10
Y5: -1.3573E-10 X6: -2.1851E-12 X4Y2: -3.1550E-12
X2Y4: -1.3855E-12 Y6: -1.2415E-12
FFS4
X2: 3.3860E-03 Y2: -1.6475E-03 X2Y: 2.3172E-06
Y3: -1.1636E-05 X4: 3.9637E-08 X2Y2: 8.5526E-08
Y4: -2.2802E-07 X4Y: -2.2658E-10 X2Y3: 9.0009E-10
Y5: -3.3036E-09 X6: 2.8296E-12 X4Y2: 1.5755E-11
X2Y4: 9.5846E-12 Y6: -3.9534E-11
FFS5
X2: -7.8014E-04 Y2: -7.8969E-03 Y3: 4.6269E-06
X4: 4.0288E-06 X2Y2: -3.9569E-07 Y4: -1.6730E-06
X4Y: -1.4780E-09 X3Y2: 9.1076E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
［数値実施例３］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 110.000 -25.0 -700.914 反射面
3* 0.000 60.707 59.061 -80.0 -385.672 反射面
4* 0.000 -81.007 7.481 -145.0 -131.035 反射面
5* 0.000 -81.007 76.643 -180.0 -62.863 1.61382 37.93 屈折面
6 0.000 -81.007 87.593 -180.0 41.994 1.73887 47.42 屈折面
7 0.000 -81.007 90.093 -180.0 -70.000 屈折面
8 0.000 -81.007 100.712 -180.0 -60.000 1.60497 39.17 屈折面
9 0.000 -81.007 108.712 -180.0 30.497 1.73133 45.87 屈折面
10 0.000 -81.007 111.212 -180.0 -260.000 屈折面
11 0.000 -81.007 115.212 -180.0 51.268 1.74896 29.74 屈折面
12 0.000 -81.007 117.712 -180.0 199.468 屈折面
13 0.000 -81.007 138.712 -180.0 36.637 1.51630 64.15 屈折面
14 0.000 -81.007 144.892 -180.0 136.353 屈折面
15 0.000 -81.007 186.885 -180.0 0.000 像面
FFS2
X2: 4.2679E-04 Y2: -6.7326E-06 X2Y: -2.5337E-07
Y3: -5.5785E-06 X4: 4.6918E-09 X2Y2: 3.1150E-09
Y4: -7.1031E-09 X4Y: 1.2675E-11 X2Y3: 1.3406E-11
Y5: -1.8411E-10 X6: -2.8735E-14 X4Y2: -3.3803E-13
X2Y4: 4.6457E-14 Y6: -1.0449E-12 X6Y: -4.3111E-15
X4Y3: -3.0096E-16 X2Y5: -3.0692E-15 Y7: -9.3337E-15
X8: 4.2814E-18 X6Y2: -2.0280E-17 X4Y4: 3.2794E-18
X2Y6: -2.9687E-17 Y8: -1.7517E-16
FFS3
X2: 1.9184E-03 Y2: 2.6282E-03 X2Y: -4.6018E-07
Y3: -1.0651E-05 X4: 5.9470E-09 X2Y2: 1.9750E-08
Y4: -3.0035E-08 X4Y: -1.8519E-11 X2Y3: 1.0906E-10
Y5: -9.9070E-11 X6: 2.0163E-13 X4Y2: -5.1714E-13
X2Y4: 1.0605E-12 Y6: -9.1935E-13
FFS4
X2: 3.6035E-03 Y2: -1.5901E-03 X2Y: 3.6039E-06
Y3: -1.0138E-05 X4: -9.9592E-09 X2Y2: 6.6281E-08
Y4: -2.3389E-07 X4Y: -8.3471E-11 X2Y3: 7.1406E-10
Y5: -3.0766E-09 X6: 2.9222E-11 X4Y2: 2.3080E-11
X2Y4: 7.3342E-12 Y6: -3.6033E-11
FFS5
X2: 1.7546E-03 Y2: -7.1812E-03 Y3: -8.1649E-07
X4: 1.5257E-06 X2Y2: 2.7020E-06 Y4: 1.5931E-06
X4Y: -3.5981E-10 X3Y2: 2.8625E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
[Numerical Example 3]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 110.000 -25.0 -700.914 Reflective surface
3 * 0.000 60.707 59.061 -80.0 -385.672 Reflective surface
4 * 0.000 -81.007 7.481 -145.0 -131.035 Reflective surface
5 * 0.000 -81.007 76.643 -180.0 -62.863 1.61382 37.93 Refractive surface
6 0.000 -81.007 87.593 -180.0 41.994 1.73887 47.42 Refractive surface
7 0.000 -81.007 90.093 -180.0 -70.000 Refractive surface
8 0.000 -81.007 100.712 -180.0 -60.000 1.60497 39.17 Refractive surface
9 0.000 -81.007 108.712 -180.0 30.497 1.73133 45.87 Refractive surface
10 0.000 -81.007 111.212 -180.0 -260.000 Refractive surface
11 0.000 -81.007 115.212 -180.0 51.268 1.74896 29.74 Refractive surface
12 0.000 -81.007 117.712 -180.0 199.468 Refractive surface
13 0.000 -81.007 138.712 -180.0 36.637 1.51630 64.15 Refractive surface
14 0.000 -81.007 144.892 -180.0 136.353 Refractive surface
15 0.000 -81.007 186.885 -180.0 0.000 Image plane
FFS2
X2: 4.2679E-04 Y2: -6.7326E-06 X2Y: -2.5337E-07
Y3: -5.5785E-06 X4: 4.6918E-09 X2Y2: 3.1150E-09
Y4: -7.1031E-09 X4Y: 1.2675E-11 X2Y3: 1.3406E-11
Y5: -1.8411E-10 X6: -2.8735E-14 X4Y2: -3.3803E-13
X2Y4: 4.6457E-14 Y6: -1.0449E-12 X6Y: -4.3111E-15
X4Y3: -3.0096E-16 X2Y5: -3.0692E-15 Y7: -9.3337E-15
X8: 4.2814E-18 X6Y2: -2.0280E-17 X4Y4: 3.2794E-18
X2Y6: -2.9687E-17 Y8: -1.7517E-16
FFS3
X2: 1.9184E-03 Y2: 2.6282E-03 X2Y: -4.6018E-07
Y3: -1.0651E-05 X4: 5.9470E-09 X2Y2: 1.9750E-08
Y4: -3.0035E-08 X4Y: -1.8519E-11 X2Y3: 1.0906E-10
Y5: -9.9070E-11 X6: 2.0163E-13 X4Y2: -5.1714E-13
X2Y4: 1.0605E-12 Y6: -9.1935E-13
FFS4
X2: 3.6035E-03 Y2: -1.5901E-03 X2Y: 3.6039E-06
Y3: -1.0138E-05 X4: -9.9592E-09 X2Y2: 6.6281E-08
Y4: -2.3389E-07 X4Y: -8.3471E-11 X2Y3: 7.1406E-10
Y5: -3.0766E-09 X6: 2.9222E-11 X4Y2: 2.3080E-11
X2Y4: 7.3342E-12 Y6: -3.6033E-11
FFS5
X2: 1.7546E-03 Y2: -7.1812E-03 Y3: -8.1649E-07
X4: 1.5257E-06 X2Y2: 2.7020E-06 Y4: 1.5931E-06
X4Y: -3.5981E-10 X3Y2: 2.8625E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
［数値実施例４］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 110.000 -25.0 -688.424 反射面
3* 0.000 58.986 60.505 -80.0 -391.293 反射面
4* 0.000 -82.630 8.961 -145.0 -137.979 反射面
5* 0.000 -82.630 70.979 -180.0 -86.344 1.60874 38.77 屈折面
6 0.000 -82.630 86.000 -180.0 25.514 1.73729 47.67 屈折面
7* 0.000 -82.630 88.500 -180.0 -69.734 屈折面
8 0.000 -82.630 98.500 -180.0 -50.974 1.55913 48.12 屈折面
9 0.000 -82.630 106.500 -180.0 67.810 屈折面
10* 0.000 -82.630 139.627 -180.0 -45.548 1.52318 63.65 屈折面
11 0.000 -82.630 149.627 -180.0 48.829 1.79062 25.86 屈折面
12* 0.000 -82.630 153.627 -180.0 196.696 屈折面
13 0.000 -82.630 168.627 -180.0 -102.400 1.61352 53.81 屈折面
14 0.000 -82.630 175.930 -180.0 68.458 屈折面
15 0.000 -82.630 206.197 -180.0 0.000 像面
FFS2
X2: 3.9767E-04 Y2: 2.7724E-06 X2Y: -4.7951E-07
Y3: -5.6245E-06 X4: -3.3108E-09 X2Y2: -8.5309E-09
Y4: -7.5945E-09 X4Y: 1.9416E-11 X2Y3: -5.0289E-11
Y5: -1.7118E-10 X6: -1.2982E-12 X4Y2: 2.4540E-12
X2Y4: 2.5322E-12 Y6: -1.1306E-12 X6Y: 7.8674E-16
X4Y3: -7.2791E-15 X2Y5: -9.1917E-15 Y7: -9.1214E-15
X8: -1.8117E-16 X6Y2: 1.0349E-15 X4Y4: 4.0021E-17
X2Y6: 2.5772E-16 Y8: -2.2069E-16
FFS3
X2: 1.9426E-03 Y2: 2.6291E-03 X2Y: -5.1668E-07
Y3: -1.0645E-05 X4: -1.7512E-09 X2Y2: -4.8102E-09
Y4: -2.8076E-08 X4Y: 4.2176E-11 X2Y3: -6.2639E-11
Y5: -4.4731E-11 X6: -7.0430E-13 X4Y2: 3.7544E-12
X2Y4: 9.0656E-12 Y6: -1.2052E-12
FFS4
X2: 3.7681E-03 Y2: -1.2002E-03 X2Y: 5.8023E-06
Y3: -6.3875E-06 X4: 2.4504E-07 X2Y2: 3.0318E-07
Y4: -7.6902E-08 X4Y: 3.6810E-09 X2Y3: 1.3741E-09
Y5: -1.1152E-09 X6: 1.2721E-10 X4Y2: -1.9031E-11
X2Y4: -1.0089E-10 Y6: -2.1456E-11
FFS5
X2: 7.0799E-03 Y2: -5.7102E-03 Y3: 3.8068E-06
X4: -1.0077E-05 X2Y2: -9.3304E-06 Y4: 1.1625E-06
X4Y: -6.5687E-10 X3Y2: 8.3270E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
FFS7
X2: -8.3243E-03 Y2: -1.9506E-02 Y3: 1.7368E-05
X4: 8.6124E-06 X2Y2: 2.3302E-05 Y4: 2.7192E-05
FFS10
X2: 7.2382E-03 Y2: 2.4486E-03 Y3: -2.5736E-06
X4: 3.4965E-06 X2Y2: 5.9459E-06 Y4: 1.7560E-06
FFS12
X2: -4.0192E-04 Y2: -3.0519E-03 Y3: -1.5234E-06
X4: 3.5239E-06 X2Y2: 9.2463E-06 Y4: 1.5987E-06
[Numerical Example 4]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 110.000 -25.0 -688.424 Reflective surface
3 * 0.000 58.986 60.505 -80.0 -391.293 Reflecting surface
4 * 0.000 -82.630 8.961 -145.0 -137.979 Reflective surface
5 * 0.000 -82.630 70.979 -180.0 -86.344 1.60874 38.77 Refractive surface
6 0.000 -82.630 86.000 -180.0 25.514 1.73729 47.67 Refractive surface
7 * 0.000 -82.630 88.500 -180.0 -69.734 Refractive surface
8 0.000 -82.630 98.500 -180.0 -50.974 1.55913 48.12 Refractive surface
9 0.000 -82.630 106.500 -180.0 67.810 Refractive surface
10 * 0.000 -82.630 139.627 -180.0 -45.548 1.52318 63.65 Refractive surface
11 0.000 -82.630 149.627 -180.0 48.829 1.79062 25.86 Refractive surface
12 * 0.000 -82.630 153.627 -180.0 196.696 Refractive surface
13 0.000 -82.630 168.627 -180.0 -102.400 1.61352 53.81 Refractive surface
14 0.000 -82.630 175.930 -180.0 68.458 Refractive surface
15 0.000 -82.630 206.197 -180.0 0.000 Image plane
FFS2
X2: 3.9767E-04 Y2: 2.7724E-06 X2Y: -4.7951E-07
Y3: -5.6245E-06 X4: -3.3108E-09 X2Y2: -8.5309E-09
Y4: -7.5945E-09 X4Y: 1.9416E-11 X2Y3: -5.0289E-11
Y5: -1.7118E-10 X6: -1.2982E-12 X4Y2: 2.4540E-12
X2Y4: 2.5322E-12 Y6: -1.1306E-12 X6Y: 7.8674E-16
X4Y3: -7.2791E-15 X2Y5: -9.1917E-15 Y7: -9.1214E-15
X8: -1.8117E-16 X6Y2: 1.0349E-15 X4Y4: 4.0021E-17
X2Y6: 2.5772E-16 Y8: -2.2069E-16
FFS3
X2: 1.9426E-03 Y2: 2.6291E-03 X2Y: -5.1668E-07
Y3: -1.0645E-05 X4: -1.7512E-09 X2Y2: -4.8102E-09
Y4: -2.8076E-08 X4Y: 4.2176E-11 X2Y3: -6.2639E-11
Y5: -4.4731E-11 X6: -7.0430E-13 X4Y2: 3.7544E-12
X2Y4: 9.0656E-12 Y6: -1.2052E-12
FFS4
X2: 3.7681E-03 Y2: -1.2002E-03 X2Y: 5.8023E-06
Y3: -6.3875E-06 X4: 2.4504E-07 X2Y2: 3.0318E-07
Y4: -7.6902E-08 X4Y: 3.6810E-09 X2Y3: 1.3741E-09
Y5: -1.1152E-09 X6: 1.2721E-10 X4Y2: -1.9031E-11
X2Y4: -1.0089E-10 Y6: -2.1456E-11
FFS5
X2: 7.0799E-03 Y2: -5.7102E-03 Y3: 3.8068E-06
X4: -1.0077E-05 X2Y2: -9.3304E-06 Y4: 1.1625E-06
X4Y: -6.5687E-10 X3Y2: 8.3270E-09 X6: -1.1858E-09
X4Y2: -3.5575E-09 X2Y4: -3.5575E-09 Y6: -1.1858E-09
X8: -6.4505E-12 X6Y2: -2.5802E-11 X4Y4: -3.8703E-11
X2Y6: -2.5802E-11 Y8: -6.4505E-12
FFS7
X2: -8.3243E-03 Y2: -1.9506E-02 Y3: 1.7368E-05
X4: 8.6124E-06 X2Y2: 2.3302E-05 Y4: 2.7192E-05
FFS10
X2: 7.2382E-03 Y2: 2.4486E-03 Y3: -2.5736E-06
X4: 3.4965E-06 X2Y2: 5.9459E-06 Y4: 1.7560E-06
FFS12
X2: -4.0192E-04 Y2: -3.0519E-03 Y3: -1.5234E-06
X4: 3.5239E-06 X2Y2: 9.2463E-06 Y4: 1.5987E-06
［数値実施例５］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 150.000 -25.0 -1155.476 反射面
3* 0.000 76.604 85.721 -72.5 -1628.427 反射面
4* 0.000 -134.399 67.261 -72.5 412.879 反射面
5* 0.000 -80.776 22.266 -25.0 -253.657 反射面
6* 0.000 -80.776 112.266 0.0 72.707 1.51630 64.15 屈折面
7* 0.000 -80.776 118.266 0.0 66.731 屈折面
8* 0.000 -80.776 160.807 0.0 58.437 1.69680 55.50 屈折面
9 0.000 -80.776 176.985 0.0 -90.870 1.70238 29.80 屈折面
10* 0.000 -80.776 181.985 0.0 31761.437 屈折面
11 0.000 -80.776 220.129 0.0 0.000 像面
FFS2
X2: 1.4232E-04 Y2: 1.4713E-04 X2Y: 6.4387E-08
Y3: -6.8420E-08 X4: -1.8884E-09 X2Y2: -6.5784E-09
Y4: -1.1689E-08 X4Y: -5.0870E-11 X2Y3: -5.7432E-11
Y5: -5.8994E-11 X6: -6.3337E-14 X4Y2: -3.9371E-13
X2Y4: -8.3923E-14 Y6: -6.4291E-14
FFS3
X2: 6.7846E-04 Y2: 5.8629E-04 X2Y: 3.3943E-08
Y3: -4.8382E-08 X4: -3.4241E-09 X2Y2: -1.3263E-08
Y4: -2.5534E-08 X4Y: -9.4310E-11 X2Y3: -7.1581E-11
Y5: -3.0957E-11 X6: -3.0911E-13 X4Y2: -1.0020E-12
X2Y4: -4.1581E-13 Y6: -6.5496E-13
FFS4
X2: -9.1355E-04 Y2: -8.3423E-04 X2Y: 1.5854E-06
Y3: 2.6292E-06 X4: -5.5617E-10 X2Y2: -1.2707E-08
Y4: -1.0277E-07 X4Y: -9.0115E-10 X2Y3: -3.5999E-10
Y5: 7.5341E-10 X6: -1.8507E-11 X4Y2: -4.3779E-11
X2Y4: -1.5686E-11 Y6: -2.0567E-11
FFS5
X2: 1.5823E-03 Y2: 1.4634E-03 X2Y: 2.2592E-06
Y3: 3.2723E-06 X4: 4.9235E-08 X2Y2: 2.0798E-07
Y4: 1.3285E-07 X4Y: -1.3703E-09 X2Y3: -7.2213E-10
Y5: 1.0142E-09 X6: -6.0312E-11 X4Y2: -1.6746E-10
X2Y4: -1.0664E-10 Y6: -1.1597E-10
FFS6
X2: -5.3034E-04 Y2: -3.4583E-04 X2Y: -1.3978E-05
Y3: 1.3281E-05 X4: -5.4032E-07 X2Y2: -7.9743E-07
Y4: -1.8640E-06 X6: 5.8290E-10 X4Y2: 1.7487E-09
X2Y4: 1.7487E-09 Y6: 5.8290E-10 X8: -5.1359E-14
X6Y2: -2.0544E-13 X4Y4: -3.0816E-13 X2Y6: -2.0544E-13
Y8: -5.1359E-14 X10: 1.5800E-15 X8Y2: 7.9002E-15
X6Y4: 1.5800E-14 X4Y6: 1.5800E-14 X2Y8: 7.9002E-15
Y10: 1.5800E-15
FFS7
X2: 2.3111E-03 Y2: -7.2233E-04 X2Y: -1.1065E-05
Y3: 1.6347E-05 X4: -2.4644E-07 X2Y2: -2.3027E-09
Y4: -5.9008E-07 X6: -2.2363E-10 X4Y2: -6.7089E-10
X2Y4: -6.7089E-10 Y6: -2.2363E-10 X8: 1.4984E-12
X6Y2: 5.9937E-12 X4Y4: 8.9905E-12 X2Y6: 5.9937E-12
Y8: 1.4984E-12 X10: 1.5881E-15 X8Y2: 7.9407E-15
X6Y4: 1.5881E-14 X4Y6: 1.5881E-14 X2Y8: 7.9407E-15
Y10: 1.5881E-15
FFS8
X2: -6.0588E-04 Y2: -1.8869E-04 X2Y: -3.0668E-06
Y3: 2.3356E-06 X4: -4.3367E-07 X2Y2: -1.7848E-06
Y4: -1.0144E-06
FFS10
X2: 8.1313E-04 Y2: 2.7076E-03 X2Y: -6.1991E-06
Y3: 4.2707E-06 X4: -4.5948E-08 X2Y2: -1.5567E-06
Y4: -1.8549E-06
[Numerical Example 5]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 150.000 -25.0 -1155.476 Reflective surface
3 * 0.000 76.604 85.721 -72.5 -1628.427 Reflecting surface
4 * 0.000 -134.399 67.261 -72.5 412.879 Reflective surface
5 * 0.000 -80.776 22.266 -25.0 -253.657 Reflecting surface
6 * 0.000 -80.776 112.266 0.0 72.707 1.51630 64.15 Refractive surface
7 * 0.000 -80.776 118.266 0.0 66.731 Refractive surface
8 * 0.000 -80.776 160.807 0.0 58.437 1.69680 55.50 Refractive surface
9 0.000 -80.776 176.985 0.0 -90.870 1.70238 29.80 Refractive surface
10 * 0.000 -80.776 181.985 0.0 31761.437 Refractive surface
11 0.000 -80.776 220.129 0.0 0.000 Image plane
FFS2
X2: 1.4232E-04 Y2: 1.4713E-04 X2Y: 6.4387E-08
Y3: -6.8420E-08 X4: -1.8884E-09 X2Y2: -6.5784E-09
Y4: -1.1689E-08 X4Y: -5.0870E-11 X2Y3: -5.7432E-11
Y5: -5.8994E-11 X6: -6.3337E-14 X4Y2: -3.9371E-13
X2Y4: -8.3923E-14 Y6: -6.4291E-14
FFS3
X2: 6.7846E-04 Y2: 5.8629E-04 X2Y: 3.3943E-08
Y3: -4.8382E-08 X4: -3.4241E-09 X2Y2: -1.3263E-08
Y4: -2.5534E-08 X4Y: -9.4310E-11 X2Y3: -7.1581E-11
Y5: -3.0957E-11 X6: -3.0911E-13 X4Y2: -1.0020E-12
X2Y4: -4.1581E-13 Y6: -6.5496E-13
FFS4
X2: -9.1355E-04 Y2: -8.3423E-04 X2Y: 1.5854E-06
Y3: 2.6292E-06 X4: -5.5617E-10 X2Y2: -1.2707E-08
Y4: -1.0277E-07 X4Y: -9.0115E-10 X2Y3: -3.5999E-10
Y5: 7.5341E-10 X6: -1.8507E-11 X4Y2: -4.3779E-11
X2Y4: -1.5686E-11 Y6: -2.0567E-11
FFS5
X2: 1.5823E-03 Y2: 1.4634E-03 X2Y: 2.2592E-06
Y3: 3.2723E-06 X4: 4.9235E-08 X2Y2: 2.0798E-07
Y4: 1.3285E-07 X4Y: -1.3703E-09 X2Y3: -7.2213E-10
Y5: 1.0142E-09 X6: -6.0312E-11 X4Y2: -1.6746E-10
X2Y4: -1.0664E-10 Y6: -1.1597E-10
FFS6
X2: -5.3034E-04 Y2: -3.4583E-04 X2Y: -1.3978E-05
Y3: 1.3281E-05 X4: -5.4032E-07 X2Y2: -7.9743E-07
Y4: -1.8640E-06 X6: 5.8290E-10 X4Y2: 1.7487E-09
X2Y4: 1.7487E-09 Y6: 5.8290E-10 X8: -5.1359E-14
X6Y2: -2.0544E-13 X4Y4: -3.0816E-13 X2Y6: -2.0544E-13
Y8: -5.1359E-14 X10: 1.5800E-15 X8Y2: 7.9002E-15
X6Y4: 1.5800E-14 X4Y6: 1.5800E-14 X2Y8: 7.9002E-15
Y10: 1.5800E-15
FFS7
X2: 2.3111E-03 Y2: -7.2233E-04 X2Y: -1.1065E-05
Y3: 1.6347E-05 X4: -2.4644E-07 X2Y2: -2.3027E-09
Y4: -5.9008E-07 X6: -2.2363E-10 X4Y2: -6.7089E-10
X2Y4: -6.7089E-10 Y6: -2.2363E-10 X8: 1.4984E-12
X6Y2: 5.9937E-12 X4Y4: 8.9905E-12 X2Y6: 5.9937E-12
Y8: 1.4984E-12 X10: 1.5881E-15 X8Y2: 7.9407E-15
X6Y4: 1.5881E-14 X4Y6: 1.5881E-14 X2Y8: 7.9407E-15
Y10: 1.5881E-15
FFS8
X2: -6.0588E-04 Y2: -1.8869E-04 X2Y: -3.0668E-06
Y3: 2.3356E-06 X4: -4.3367E-07 X2Y2: -1.7848E-06
Y4: -1.0144E-06
FFS10
X2: 8.1313E-04 Y2: 2.7076E-03 X2Y: -6.1991E-06
Y3: 4.2707E-06 X4: -4.5948E-08 X2Y2: -1.5567E-06
Y4: -1.8549E-06
［数値実施例６］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 150.000 -25.0 -1150.392 反射面
3* 0.000 61.284 98.577 -72.5 -1622.568 反射面
4* 0.000 -137.955 81.146 -72.5 398.910 反射面
5* 0.000 -84.332 36.151 -25.0 -267.962 反射面
6* 0.000 -84.332 126.151 0.0 52.036 1.52627 59.27 屈折面
7* 0.000 -84.332 133.162 0.0 150.000 屈折面
8 0.000 -84.332 138.162 0.0 44.395 1.52657 63.41 屈折面
9 0.000 -84.332 144.162 0.0 31.540 屈折面
10* 0.000 -84.332 188.518 0.0 54.799 1.69680 55.50 屈折面
11 0.000 -84.332 205.588 0.0 -43.656 1.72408 40.83 屈折面
12* 0.000 -84.332 210.588 0.0 149.164 屈折面
13 0.000 -84.332 261.942 0.0 0.000 像面
FFS2
X2: 1.4374E-04 Y2: 1.4033E-04 X2Y: 7.0116E-07
Y3: 5.7882E-08 X4: 6.3755E-10 X2Y2: -1.9048E-09
Y4: -8.0876E-09 X4Y: -6.9405E-11 X2Y3: -9.9520E-11
Y5: -5.5780E-11 X6: -2.2852E-13 X4Y2: -1.1292E-13
X2Y4: 5.5816E-13 Y6: 8.6818E-14
FFS3
X2: 6.9267E-04 Y2: 5.7311E-04 X2Y: 1.2531E-06
Y3: 2.4501E-07 X4: 2.0570E-09 X2Y2: -4.4968E-09
Y4: -1.6375E-08 X4Y: -1.4129E-10 X2Y3: -2.1626E-10
Y5: -6.6734E-11 X6: -6.1971E-13 X4Y2: 3.1163E-13
X2Y4: 3.3182E-12 Y6: 9.4897E-13
FFS4
X2: -9.3809E-04 Y2: -7.2834E-04 X2Y: 7.6188E-06
Y3: 2.7736E-06 X4: 4.2136E-08 X2Y2: 5.8812E-08
Y4: -4.0527E-08 X4Y: -1.5199E-09 X2Y3: -3.2381E-09
Y5: -7.1949E-10 X6: -2.2977E-11 X4Y2: -1.3904E-11
X2Y4: 1.7619E-10 Y6: 7.2474E-11
FFS5
X2: 1.5087E-03 Y2: 1.7066E-03 X2Y: 9.1236E-06
Y3: 2.7980E-06 X4: 2.6542E-08 X2Y2: 1.1581E-07
Y4: 1.8710E-08 X4Y: -2.3243E-09 X2Y3: -4.6565E-09
Y5: -9.5117E-10 X6: -6.5277E-11 X4Y2: -9.7312E-11
X2Y4: 2.6641E-10 Y6: 9.3540E-11
FFS6
X2: -9.2839E-04 Y2: -2.0928E-03 X2Y: -3.2653E-07
Y3: 1.1996E-05 X4: 2.4985E-06 X2Y2: 8.9441E-06
Y4: 1.8610E-06 X6: 5.8290E-10 X4Y2: 1.7487E-09
X2Y4: 1.7487E-09 Y6: 5.8290E-10 X8: -5.1359E-14
X6Y2: -2.0544E-13 X4Y4: -3.0816E-13 X2Y6: -2.0544E-13
Y8: -5.1359E-14 X10: 1.5800E-15 X8Y2: 7.9002E-15
X6Y4: 1.5800E-14 X4Y6: 1.5800E-14 X2Y8: 7.9002E-15
Y10: 1.5800E-15
FFS7
X2: 7.9420E-03 Y2: 1.8737E-03 X2Y: 9.8743E-06
Y3: 1.6920E-05 X4: 2.6222E-06 X2Y2: 1.0180E-05
Y4: 2.1822E-06 X6: -2.2363E-10 X4Y2: -6.7089E-10
X2Y4: -6.7089E-10 Y6: -2.2363E-10 X8: 1.4984E-12
X6Y2: 5.9937E-12 X4Y4: 8.9905E-12 X2Y6: 5.9937E-12
Y8: 1.4984E-12 X10: 1.5881E-15 X8Y2: 7.9407E-15
X6Y4: 1.5881E-14 X4Y6: 1.5881E-14 X2Y8: 7.9407E-15
Y10: 1.5881E-15
FFS10
X2: 1.3392E-03 Y2: 1.4219E-03
FFS12
X2: -8.8303E-04 Y2: 3.0294E-03
[Numerical Example 6]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 150.000 -25.0 -1150.392 Reflecting surface
3 * 0.000 61.284 98.577 -72.5 -1622.568 Reflecting surface
4 * 0.000 -137.955 81.146 -72.5 398.910 Reflective surface
5 * 0.000 -84.332 36.151 -25.0 -267.962 Reflecting surface
6 * 0.000 -84.332 126.151 0.0 52.036 1.52627 59.27 Refractive surface
7 * 0.000 -84.332 133.162 0.0 150.000 Refractive surface
8 0.000 -84.332 138.162 0.0 44.395 1.52657 63.41 Refractive surface
9 0.000 -84.332 144.162 0.0 31.540 Refractive surface
10 * 0.000 -84.332 188.518 0.0 54.799 1.69680 55.50 Refractive surface
11 0.000 -84.332 205.588 0.0 -43.656 1.72408 40.83 Refractive surface
12 * 0.000 -84.332 210.588 0.0 149.164 Refractive surface
13 0.000 -84.332 261.942 0.0 0.000 Image plane
FFS2
X2: 1.4374E-04 Y2: 1.4033E-04 X2Y: 7.0116E-07
Y3: 5.7882E-08 X4: 6.3755E-10 X2Y2: -1.9048E-09
Y4: -8.0876E-09 X4Y: -6.9405E-11 X2Y3: -9.9520E-11
Y5: -5.5780E-11 X6: -2.2852E-13 X4Y2: -1.1292E-13
X2Y4: 5.5816E-13 Y6: 8.6818E-14
FFS3
X2: 6.9267E-04 Y2: 5.7311E-04 X2Y: 1.2531E-06
Y3: 2.4501E-07 X4: 2.0570E-09 X2Y2: -4.4968E-09
Y4: -1.6375E-08 X4Y: -1.4129E-10 X2Y3: -2.1626E-10
Y5: -6.6734E-11 X6: -6.1971E-13 X4Y2: 3.1163E-13
X2Y4: 3.3182E-12 Y6: 9.4897E-13
FFS4
X2: -9.3809E-04 Y2: -7.2834E-04 X2Y: 7.6188E-06
Y3: 2.7736E-06 X4: 4.2136E-08 X2Y2: 5.8812E-08
Y4: -4.0527E-08 X4Y: -1.5199E-09 X2Y3: -3.2381E-09
Y5: -7.1949E-10 X6: -2.2977E-11 X4Y2: -1.3904E-11
X2Y4: 1.7619E-10 Y6: 7.2474E-11
FFS5
X2: 1.5087E-03 Y2: 1.7066E-03 X2Y: 9.1236E-06
Y3: 2.7980E-06 X4: 2.6542E-08 X2Y2: 1.1581E-07
Y4: 1.8710E-08 X4Y: -2.3243E-09 X2Y3: -4.6565E-09
Y5: -9.5117E-10 X6: -6.5277E-11 X4Y2: -9.7312E-11
X2Y4: 2.6641E-10 Y6: 9.3540E-11
FFS6
X2: -9.2839E-04 Y2: -2.0928E-03 X2Y: -3.2653E-07
Y3: 1.1996E-05 X4: 2.4985E-06 X2Y2: 8.9441E-06
Y4: 1.8610E-06 X6: 5.8290E-10 X4Y2: 1.7487E-09
X2Y4: 1.7487E-09 Y6: 5.8290E-10 X8: -5.1359E-14
X6Y2: -2.0544E-13 X4Y4: -3.0816E-13 X2Y6: -2.0544E-13
Y8: -5.1359E-14 X10: 1.5800E-15 X8Y2: 7.9002E-15
X6Y4: 1.5800E-14 X4Y6: 1.5800E-14 X2Y8: 7.9002E-15
Y10: 1.5800E-15
FFS7
X2: 7.9420E-03 Y2: 1.8737E-03 X2Y: 9.8743E-06
Y3: 1.6920E-05 X4: 2.6222E-06 X2Y2: 1.0180E-05
Y4: 2.1822E-06 X6: -2.2363E-10 X4Y2: -6.7089E-10
X2Y4: -6.7089E-10 Y6: -2.2363E-10 X8: 1.4984E-12
X6Y2: 5.9937E-12 X4Y4: 8.9905E-12 X2Y6: 5.9937E-12
Y8: 1.4984E-12 X10: 1.5881E-15 X8Y2: 7.9407E-15
X6Y4: 1.5881E-14 X4Y6: 1.5881E-14 X2Y8: 7.9407E-15
Y10: 1.5881E-15
FFS10
X2: 1.3392E-03 Y2: 1.4219E-03
FFS12
X2: -8.8303E-04 Y2: 3.0294E-03
［数値実施例７］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 150.000 -25.0 -1861.062 反射面
3* 0.000 99.586 66.438 -72.5 -1242.658 反射面
4* 0.000 -219.197 38.548 -72.5 511.020 反射面
5* 0.000 -142.592 -25.731 -25.0 -371.084 反射面
6* 0.000 -142.592 94.269 0.0 70.023 1.55163 50.17 屈折面
7 0.000 -142.592 102.562 0.0 150.000 屈折面
8 0.000 -142.592 107.643 0.0 -323.769 1.62742 57.97 屈折面
9* 0.000 -142.592 115.643 0.0 96.083 屈折面
10 0.000 -142.592 195.643 0.0 74.395 1.83852 30.65 屈折面
11 0.000 -142.592 207.643 0.0 -125.616 1.66859 32.22 屈折面
12 0.000 -142.592 212.643 0.0 55.367 屈折面
13 0.000 -142.592 292.643 0.0 0.000 像面
FFS2
X2: 4.0282E-04 Y2: 2.3452E-04 X2Y: 1.6035E-06
Y3: 7.2071E-07 X4: 1.0679E-08 X2Y2: 3.6504E-08
Y4: 1.2466E-08 X4Y: 1.0531E-10 X2Y3: 2.6311E-10
Y5: 7.4158E-11 X6: 1.0989E-13 X4Y2: 7.0591E-13
X2Y4: 2.3931E-12 Y6: 1.5257E-13
FFS3
X2: 5.9623E-04 Y2: 4.4511E-04 X2Y: 2.4785E-06
Y3: 1.3762E-06 X4: 1.0812E-08 X2Y2: 4.7335E-08
Y4: 1.8156E-08 X4Y: 9.2616E-12 X2Y3: 9.1309E-11
Y5: 3.9265E-11 X6: 1.7592E-15 X4Y2: -1.4104E-12
X2Y4: -7.3582E-13 Y6: -1.0188E-12
FFS4
X2: -1.3077E-03 Y2: -8.9054E-04 X2Y: 2.5233E-06
Y3: 5.1963E-07 X4: 9.8944E-10 X2Y2: 3.5798E-08
Y4: 2.8619E-08 X4Y: 7.1953E-12 X2Y3: -4.1219E-11
Y5: -5.9845E-11 X6: 1.1242E-12 X4Y2: -3.5582E-14
X2Y4: -4.6165E-12 Y6: -5.5678E-12
FFS5
X2: 2.0494E-03 Y2: 2.2413E-03 X2Y: 2.6489E-06
Y3: 4.5587E-07 X4: -1.9154E-09 X2Y2: 3.1063E-08
Y4: 2.4638E-08 X4Y: -2.5873E-11 X2Y3: -8.6741E-11
Y5: -3.8680E-11 X6: 2.0390E-12 X4Y2: 5.9805E-15
X2Y4: -3.8795E-12 Y6: -3.2445E-12
FFS6
X2: -1.0640E-03 Y2: 5.1091E-04
FFS9
X2: 1.5628E-03 Y2: 1.8917E-03
[Numerical Example 7]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 150.000 -25.0 -1861.062 Reflecting surface
3 * 0.000 99.586 66.438 -72.5 -1242.658 Reflecting surface
4 * 0.000 -219.197 38.548 -72.5 511.020 Reflective surface
5 * 0.000 -142.592 -25.731 -25.0 -371.084 Reflecting surface
6 * 0.000 -142.592 94.269 0.0 70.023 1.55163 50.17 Refractive surface
7 0.000 -142.592 102.562 0.0 150.000 Refractive surface
8 0.000 -142.592 107.643 0.0 -323.769 1.62742 57.97 Refractive surface
9 * 0.000 -142.592 115.643 0.0 96.083 Refractive surface
10 0.000 -142.592 195.643 0.0 74.395 1.83852 30.65 Refractive surface
11 0.000 -142.592 207.643 0.0 -125.616 1.66859 32.22 Refractive surface
12 0.000 -142.592 212.643 0.0 55.367 Refractive surface
13 0.000 -142.592 292.643 0.0 0.000 Image plane
FFS2
X2: 4.0282E-04 Y2: 2.3452E-04 X2Y: 1.6035E-06
Y3: 7.2071E-07 X4: 1.0679E-08 X2Y2: 3.6504E-08
Y4: 1.2466E-08 X4Y: 1.0531E-10 X2Y3: 2.6311E-10
Y5: 7.4158E-11 X6: 1.0989E-13 X4Y2: 7.0591E-13
X2Y4: 2.3931E-12 Y6: 1.5257E-13
FFS3
X2: 5.9623E-04 Y2: 4.4511E-04 X2Y: 2.4785E-06
Y3: 1.3762E-06 X4: 1.0812E-08 X2Y2: 4.7335E-08
Y4: 1.8156E-08 X4Y: 9.2616E-12 X2Y3: 9.1309E-11
Y5: 3.9265E-11 X6: 1.7592E-15 X4Y2: -1.4104E-12
X2Y4: -7.3582E-13 Y6: -1.0188E-12
FFS4
X2: -1.3077E-03 Y2: -8.9054E-04 X2Y: 2.5233E-06
Y3: 5.1963E-07 X4: 9.8944E-10 X2Y2: 3.5798E-08
Y4: 2.8619E-08 X4Y: 7.1953E-12 X2Y3: -4.1219E-11
Y5: -5.9845E-11 X6: 1.1242E-12 X4Y2: -3.5582E-14
X2Y4: -4.6165E-12 Y6: -5.5678E-12
FFS5
X2: 2.0494E-03 Y2: 2.2413E-03 X2Y: 2.6489E-06
Y3: 4.5587E-07 X4: -1.9154E-09 X2Y2: 3.1063E-08
Y4: 2.4638E-08 X4Y: -2.5873E-11 X2Y3: -8.6741E-11
Y5: -3.8680E-11 X6: 2.0390E-12 X4Y2: 5.9805E-15
X2Y4: -3.8795E-12 Y6: -3.2445E-12
FFS6
X2: -1.0640E-03 Y2: 5.1091E-04
FFS9
X2: 1.5628E-03 Y2: 1.8917E-03
［数値実施例８］
面データ（単位 mm）
面番号 Ｘ Ｙ Ｚ Ａ Ｒｙ Ｎｄ νｄ 備考
1 0.000 0.000 0.000 0.0 0.000 絞り面
2* 0.000 0.000 150.000 -25.0 -2531.611 反射面
3* 0.000 99.580 66.442 -72.5 -1226.838 反射面
4* 0.000 -219.202 38.552 -72.5 508.195 反射面
5* 0.000 -127.277 -38.582 -25.0 -358.378 反射面
6* 0.000 -127.277 111.452 0.0 80.525 1.56557 52.17 屈折面
7 0.000 -127.277 120.026 0.0 150.000 屈折面
8 0.000 -127.277 124.148 0.0 361.180 1.69149 44.56 屈折面
9* 0.000 -127.277 132.148 0.0 89.013 屈折面
10* 0.000 -127.277 190.867 0.0 292.483 1.73068 28.32 屈折面
11 0.000 -127.277 195.867 0.0 112.229 1.77656 42.31 屈折面
12 0.000 -127.277 203.867 0.0 -533.791 屈折面
13 0.000 -127.277 277.866 0.0 0.000 像面
FFS2
X2: 4.8193E-04 Y2: 2.7620E-04 X2Y: 1.2721E-06
Y3: 6.8102E-07 X4: 1.2998E-08 X2Y2: 3.4126E-08
Y4: 2.7662E-08 X4Y: 1.6033E-10 X2Y3: 3.7334E-10
Y5: 1.7210E-10 X6: -1.0227E-13 X4Y2: 8.5564E-12
X2Y4: 5.0931E-12 Y6: -2.6279E-13
FFS3
X2: 5.6652E-04 Y2: 4.7233E-04 X2Y: 2.0137E-06
Y3: 1.3571E-06 X4: 2.2155E-08 X2Y2: 4.6367E-08
Y4: 3.5025E-08 X4Y: -8.0998E-13 X2Y3: 1.4580E-10
Y5: 8.0239E-11 X6: -1.8638E-12 X4Y2: -2.6555E-12
X2Y4: -2.6708E-12 Y6: -1.5201E-12
FFS4
X2: -1.2785E-03 Y2: -9.0330E-04 X2Y: 1.6820E-06
Y3: 7.9994E-07 X4: 2.9723E-08 X2Y2: 4.5942E-08
Y4: 2.6124E-08 X4Y: -5.8611E-11 X2Y3: -7.9934E-11
Y5: -2.8896E-11 X6: -3.9612E-12 X4Y2: -7.3306E-12
X2Y4: -4.3709E-12 Y6: 7.4177E-13
FFS5
X2: 2.0180E-03 Y2: 2.1860E-03 X2Y: 1.6252E-06
Y3: 5.7115E-07 X4: 3.1735E-08 X2Y2: 3.4058E-08
Y4: 1.4607E-08 X4Y: -7.8340E-11 X2Y3: -9.5428E-11
Y5: -5.2447E-11 X6: -4.2756E-12 X4Y2: -5.4464E-12
X2Y4: -2.3406E-12 Y6: 1.1531E-13
FFS6
X2: 2.6936E-04 Y2: 3.9444E-04 X2Y: -3.6229E-06
Y3: -2.1782E-06 X4: -5.5526E-08 X2Y2: 3.5721E-09
X4Y: 1.3713E-09
FFS9
X2: 6.9077E-05 Y2: 1.3778E-04 X2Y: -5.5222E-06
Y3: -2.1507E-06 X2Y2: 4.9548E-08 X4Y: -7.7738E-10
FFS10
X2: -2.0921E-04 Y2: -1.1770E-04 Y3: -2.2041E-07
X4: -9.0295E-08 X2Y2: -1.7689E-08
[Numerical Example 8]
Surface data (unit: mm)
Surface number X Y Z A Ry Nd νd Remarks
1 0.000 0.000 0.000 0.0 0.000 Aperture surface
2 * 0.000 0.000 150.000 -25.0 -2531.611 Reflecting surface
3 * 0.000 99.580 66.442 -72.5 -1226.838 Reflecting surface
4 * 0.000 -219.202 38.552 -72.5 508.195 Reflective surface
5 * 0.000 -127.277 -38.582 -25.0 -358.378 Reflective surface
6 * 0.000 -127.277 111.452 0.0 80.525 1.56557 52.17 Refractive surface
7 0.000 -127.277 120.026 0.0 150.000 Refractive surface
8 0.000 -127.277 124.148 0.0 361.180 1.69149 44.56 Refractive surface
9 * 0.000 -127.277 132.148 0.0 89.013 Refractive surface
10 * 0.000 -127.277 190.867 0.0 292.483 1.73068 28.32 Refractive surface
11 0.000 -127.277 195.867 0.0 112.229 1.77656 42.31 Refractive surface
12 0.000 -127.277 203.867 0.0 -533.791 Refractive surface
13 0.000 -127.277 277.866 0.0 0.000 Image plane
FFS2
X2: 4.8193E-04 Y2: 2.7620E-04 X2Y: 1.2721E-06
Y3: 6.8102E-07 X4: 1.2998E-08 X2Y2: 3.4126E-08
Y4: 2.7662E-08 X4Y: 1.6033E-10 X2Y3: 3.7334E-10
Y5: 1.7210E-10 X6: -1.0227E-13 X4Y2: 8.5564E-12
X2Y4: 5.0931E-12 Y6: -2.6279E-13
FFS3
X2: 5.6652E-04 Y2: 4.7233E-04 X2Y: 2.0137E-06
Y3: 1.3571E-06 X4: 2.2155E-08 X2Y2: 4.6367E-08
Y4: 3.5025E-08 X4Y: -8.0998E-13 X2Y3: 1.4580E-10
Y5: 8.0239E-11 X6: -1.8638E-12 X4Y2: -2.6555E-12
X2Y4: -2.6708E-12 Y6: -1.5201E-12
FFS4
X2: -1.2785E-03 Y2: -9.0330E-04 X2Y: 1.6820E-06
Y3: 7.9994E-07 X4: 2.9723E-08 X2Y2: 4.5942E-08
Y4: 2.6124E-08 X4Y: -5.8611E-11 X2Y3: -7.9934E-11
Y5: -2.8896E-11 X6: -3.9612E-12 X4Y2: -7.3306E-12
X2Y4: -4.3709E-12 Y6: 7.4177E-13
FFS5
X2: 2.0180E-03 Y2: 2.1860E-03 X2Y: 1.6252E-06
Y3: 5.7115E-07 X4: 3.1735E-08 X2Y2: 3.4058E-08
Y4: 1.4607E-08 X4Y: -7.8340E-11 X2Y3: -9.5428E-11
Y5: -5.2447E-11 X6: -4.2756E-12 X4Y2: -5.4464E-12
X2Y4: -2.3406E-12 Y6: 1.1531E-13
FFS6
X2: 2.6936E-04 Y2: 3.9444E-04 X2Y: -3.6229E-06
Y3: -2.1782E-06 X4: -5.5526E-08 X2Y2: 3.5721E-09
X4Y: 1.3713E-09
FFS9
X2: 6.9077E-05 Y2: 1.3778E-04 X2Y: -5.5222E-06
Y3: -2.1507E-06 X2Y2: 4.9548E-08 X4Y: -7.7738E-10
FFS10
X2: -2.0921E-04 Y2: -1.1770E-04 Y3: -2.2041E-07
X4: -9.0295E-08 X2Y2: -1.7689E-08
また、数値実施例１乃至８における種々の値を表１にまとめて示す。 Various values in Numerical Examples 1 to 8 are collectively shown in Table 1.
［撮像装置］
次に、本発明の光学系を撮像光学系として用いたデジタルスチルカメラ（撮像装置）の実施例について、図１７を用いて説明する。図１７において、１０はカメラ本体、１１は実施例１乃至８で説明したいずれかの光学系によって構成された撮影光学系である。１２はカメラ本体に内蔵され、撮影光学系１１によって形成された光学像を受光して光電変換するＣＣＤセンサやＣＭＯＳセンサ等の固体撮像素子（光電変換素子）である。カメラ本体１０はクイックターンミラーを有する所謂一眼レフカメラでも良いし、クイックターンミラーを有さない所謂ミラーレスカメラでも良い。
[Imaging device]
Next, an embodiment of a digital still camera (imaging device) using the optical system of the present invention as an imaging optical system will be described with reference to FIG. In FIG. 17,
このように本発明の光学系をデジタルスチルカメラ等の撮像装置に適用することにより、各物体距離で良好な光学性能を有する撮像装置を得ることができる。 Thus, by applying the optical system of the present invention to an imaging apparatus such as a digital still camera, an imaging apparatus having good optical performance at each object distance can be obtained.
以上、本発明の好ましい実施形態及び実施例について説明したが、本発明はこれらの実施形態及び実施例に限定されず、その要旨の範囲内で種々の組合せ、変形及び変更が可能である。 The preferred embodiments and examples of the present invention have been described above, but the present invention is not limited to these embodiments and examples, and various combinations, modifications, and changes can be made within the scope of the gist.
Ｌ 光学系
Ｍ０ 反射光学系
Ｌ０ 屈折光学系
ＬＦ フォーカスレンズ群
L optical system M0 reflective optical system L0 refractive optical system LF focus lens group
Claims (15)
前記反射光学系は自由曲面ミラーを備え、
前記屈折光学系は無限遠から至近距離へのフォーカシングに際して物体側に移動するフォーカスレンズ群を含み、
前記屈折光学系の光軸に直交し前記反射光学系の焦点距離が最も小さい方向を第１の方向、前記光軸および前記第１の方向に直交する方向を第２の方向とし、前記第１の方向における前記フォーカスレンズ群の焦点距離をｆｙ、前記第２の方向における前記フォーカスレンズ群の焦点距離をｆｘとしたとき、
ｆｘ＞ｆｙ
なる条件式を満足することを特徴とする光学系。 In order from the object side to the image side, a reflective optical system that reflects incident light, and a refractive optical system that refracts the light reflected by the reflective optical system,
The reflective optical system includes a free-form surface mirror,
The refractive optical system includes a focus lens group that moves to the object side during focusing from infinity to a close distance,
A direction perpendicular to the optical axis of the refractive optical system and having the smallest focal length of the reflective optical system is defined as a first direction, and a direction perpendicular to the optical axis and the first direction is defined as a second direction. When the focal length of the focus lens group in the direction is fy and the focal length of the focus lens group in the second direction is fx,
fx> fy
An optical system that satisfies the following conditional expression:
１．００＜ｆｘ／ｆｙ＜２．８０
なる条件式を満足することを特徴とする請求項１に記載の光学系。 0 <fy
1.00 <fx / fy <2.80
The optical system according to claim 1, wherein the following conditional expression is satisfied.
０．３００＜ｆｘ／ｆｙ＜１．００
なる条件式を満足することを特徴とする請求項１に記載の光学系。 fx <0
0.300 <fx / fy <1.00
The optical system according to claim 1, wherein the following conditional expression is satisfied.
前記反射光学系は自由曲面ミラーを備え、
前記屈折光学系は無限遠から至近距離へのフォーカシングに際して像側に移動するフォーカスレンズ群を含み、
前記屈折光学系の光軸に直交し前記反射光学系の焦点距離が最も小さい方向を第１の方向、前記光軸および前記第１の方向に直交する方向を第２の方向とし、前記第１の方向における前記フォーカスレンズ群の焦点距離をｆｙ、前記第２の方向における前記フォーカスレンズ群の焦点距離をｆｘとしたとき、
ｆｙ＞ｆｘ
なる条件式を満足することを特徴とする光学系。 In order from the object side to the image side, a reflective optical system that reflects incident light, and a refractive optical system that refracts the light reflected by the reflective optical system,
The reflective optical system includes a free-form surface mirror,
The refractive optical system includes a focus lens group that moves to the image side during focusing from infinity to a close range,
A direction perpendicular to the optical axis of the refractive optical system and having the smallest focal length of the reflective optical system is defined as a first direction, and a direction perpendicular to the optical axis and the first direction is defined as a second direction. When the focal length of the focus lens group in the direction is fy and the focal length of the focus lens group in the second direction is fx,
fy> fx
An optical system that satisfies the following conditional expression:
１．００＜ｆｘ／ｆｙ＜２．８０
なる条件式を満足することを特徴とする請求項４に記載の光学系。 fy <0
1.00 <fx / fy <2.80
The optical system according to claim 4, wherein the following conditional expression is satisfied.
０．３００＜ｆｘ／ｆｙ＜１．００
なる条件式を満足することを特徴とする請求項４に記載の光学系。 0 <fx
0.300 <fx / fy <1.00
The optical system according to claim 4, wherein the following conditional expression is satisfied.
１．０１＜｜Ｆｘ｜／｜Ｆｙ｜＜１．５０
なる条件式を満足することを特徴とする請求項１乃至６のいずれか一項に記載の光学系。 When the focal length of the reflective optical system in the first direction is Fy, and the focal length of the reflective optical system in the second direction is Fx,
1.01 <| Fx | / | Fy | <1.50
The optical system according to claim 1, wherein the following conditional expression is satisfied.
１．０５＜｜Ｆｕ１｜／｜Ｆｖ１｜＜５．００
なる条件式を満足することを特徴とする請求項８に記載の光学系。 The focal length of the first reflecting surface in the direction orthogonal to the optical axis and having the smallest focal length of the first reflecting surface is Fv1, and the direction orthogonal to the direction in which the focal length of the first reflecting surface is minimized. When the focal length of the first reflecting surface at is Fu1,
1.05 <| Fu1 | / | Fv1 | <5.00
The optical system according to claim 8, wherein the following conditional expression is satisfied.
１．０５＜｜Ｆｕ２｜／｜Ｆｖ２｜＜５．００
なる条件式を満足することを特徴とする請求項８または９に記載の光学系。 The focal length of the second reflecting surface in the direction orthogonal to the optical axis and having the smallest focal length of the second reflecting surface is Fv2, and the direction orthogonal to the direction in which the focal length of the second reflecting surface is minimized. When the focal length of the second reflecting surface at is Fu1,
1.05 <| Fu2 | / | Fv2 | <5.00
The optical system according to claim 8 or 9, wherein the following conditional expression is satisfied.
１．２０＜｜Ｆｕ３｜／｜Ｆｖ３｜＜６０．０
なる条件式を満足することを特徴とする請求項８乃至１０のいずれか一項に記載の光学系。 The focal length of the third reflecting surface in the direction orthogonal to the optical axis and having the smallest focal length of the third reflecting surface is Fv3, and the direction orthogonal to the direction in which the focal length of the third reflecting surface is minimized. When the focal length of the third reflecting surface at is Fu3,
1.20 <| Fu3 | / | Fv3 | <60.0
The optical system according to claim 8, wherein the following conditional expression is satisfied.
光軸に直交し前記第４の反射面の焦点距離が最も小さくなる方向における前記第４の反射面の焦点距離をＦｖ４、前記第４の反射面の焦点距離が最も小さくなる方向に直交する方向における前記第４の反射面の焦点距離をＦｕ４としたとき、
１．２０＜｜Ｆｕ４｜／｜Ｆｖ４｜＜３．００
なる条件式を満足することを特徴とする請求項８乃至１１のいずれか一項に記載の光学系。 The reflective optical system further includes a fourth reflecting surface that reflects light reflected by the third reflecting surface;
The focal length of the fourth reflecting surface in a direction orthogonal to the optical axis and having the smallest focal length of the fourth reflecting surface is Fv4, and the direction orthogonal to the direction in which the focal length of the fourth reflecting surface is smallest. When the focal length of the fourth reflecting surface at is Fu4,
1.20 <| Fu4 | / | Fv4 | <3.00
The optical system according to claim 8, wherein the following conditional expression is satisfied.
３．００＜Ｄ／ｙ０＜２０．０
なる条件式を満足することを特徴とする請求項１乃至１３のいずれか一項に記載の光学系。 When the entrance pupil diameter is D and the maximum image height is y0,
3.00 <D / y0 <20.0
The optical system according to claim 1, wherein the following conditional expression is satisfied.
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