JP6406870B2 - Optical system and imaging apparatus having the same - Google Patents
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本発明は光学系及びそれを有する撮像装置に関し、たとえば、デジタルスチルカメラ・デジタルビデオカメラ、ＴＶカメラ、監視用カメラ、銀塩カメラ等の撮像装置に用いられる撮像光学系として好適なものである。 The present invention relates to an optical system and an image pickup apparatus having the same, and is suitable as an image pickup optical system used in an image pickup apparatus such as a digital still camera / digital video camera, a TV camera, a surveillance camera, and a silver salt camera.
近距離の撮影を主たる目的とした撮像光学系にマクロレンズがある。マクロレンズは一般の標準レンズや望遠レンズ等の撮像光学系に比べて、近距離の撮像時において高い光学性能が得られるように設計されている。又マクロレンズは多くの場合、近距離に限らず、無限遠から近距離に至る広範囲の距離の撮像に際しても使用される。 There is a macro lens as an imaging optical system whose main purpose is shooting at a short distance. The macro lens is designed so as to obtain high optical performance at the time of short-distance imaging as compared with an imaging optical system such as a general standard lens or a telephoto lens. In many cases, the macro lens is used not only for short distances but also for imaging a wide range of distances from infinity to short distances.
一般にマクロレンズにおいて、合焦可能な撮像距離範囲（撮像倍率範囲）の拡大を図ろうとすると、特に近接撮影である高倍率側においてフォーカシングに伴う収差変動が多く発生し、光学性能が低下してくる。そこでフォーカシングに伴う諸収差の変動を補正するために、フォーカシングに際して複数のレンズ群を移動するフローティング方式が用いられている。 In general, in a macro lens, when an attempt is made to expand the focusable imaging distance range (imaging magnification range), a large amount of aberration fluctuations occur due to focusing, particularly on the high magnification side, which is close-up photography, and optical performance deteriorates. . Therefore, in order to correct fluctuations in various aberrations accompanying focusing, a floating system that moves a plurality of lens groups during focusing is used.
マクロレンズでは高い撮影倍率の近接撮影において、深い被写界深度を確保するために開口絞りを絞り込んで撮影を行うことが多い。そのため、マクロレンズではシャッター速度が遅くなり、撮影時に手振れがあると像ブレが生じ、画質が低下しやすい。このため、一部のレンズを光軸に対して垂直方向に移動させることで、防振時における像ブレを補償するようにした撮影レンズが種々と提案されている（特許文献１）。 Macro lenses often perform close-up shooting at a high shooting magnification by narrowing the aperture stop to ensure a deep depth of field. For this reason, the shutter speed of the macro lens is slow, and if there is camera shake during shooting, image blurring occurs and the image quality is likely to deteriorate. For this reason, various photographic lenses have been proposed in which some lenses are moved in the direction perpendicular to the optical axis to compensate for image blur during image stabilization (Patent Document 1).
特許文献１は、物体側から像側へ順に、正、負、正、正、正の屈折力の第１レンズ群乃至第５レンズ群よりなり、フォーカシングに際して第２レンズ群と第４レンズ群が移動する撮影レンズを開示している。そして、第５レンズ群を負の屈折力の第５ａ群と正の屈折力の第５ｂ群より構成し、像ぶれ補正に際して第５ａ群を光軸に対して垂直方向へ移動させている。 Patent Document 1 includes first to fifth lens groups having positive, negative, positive, positive, and positive refractive powers in order from the object side to the image side. The second lens group and the fourth lens group are used for focusing. A moving photographic lens is disclosed. The fifth lens group includes a negative refractive power 5a group and a positive refractive power 5b group, and the 5a group is moved in the direction perpendicular to the optical axis during image blur correction.
近年、撮像装置に用いる撮像光学系には、最短撮像距離が短いこと、全物体距離にわたり高い光学性能を有すること、撮像光学系が振動したときの像ぶれの補正が容易で、しかも像ぶれ補正に際して光学性能の低下が少ないこと等が要望されている。全物体距離にわたり高い光学性能を得るには適切なフローティング方式を用いることが重要であり、像ぶれ補正の際の光学性能を良好に維持するには像ぶれ補正用の部分群のレンズ構成を適切に設定することが重要になってくる。 In recent years, the imaging optical system used in imaging devices has a short minimum imaging distance, high optical performance over the entire object distance, easy image blur correction when the imaging optical system vibrates, and image blur correction. At the time, there is a demand for a decrease in optical performance and the like. In order to obtain high optical performance over the entire object distance, it is important to use an appropriate floating system, and in order to maintain good optical performance during image blur correction, the lens configuration of the subgroup for image blur correction is appropriate. It becomes important to set to.
本発明は、最短撮像距離が短く、全物体距離にわたり高い光学性能を有し、防振時の光学性能を良好に維持することができる光学系を提供することを目的とする。 An object of the present invention is to provide an optical system that has a shortest imaging distance, high optical performance over the entire object distance, and can maintain good optical performance during image stabilization.
本発明の光学系は、物体側より像側へ順に配置された、正の屈折力の第１レンズ群、負の屈折力の第２レンズ群、開口絞り、正の屈折力の第３レンズ群、負の屈折力の第４レンズ群、正の屈折力の第５レンズ群より構成され、フォーカシングに際して隣り合うレンズ群の間隔が変化する光学系であって、
前記第３レンズ群は第１部分群及び第２部分群より構成されており、
無限遠から近距離へのフォーカシングに際して前記第２レンズ群及び前記第４レンズ群は像側へ移動し、
フォーカシングに際して、前記第１レンズ群と前記開口絞りと前記第３レンズ群は不動であり、
前記第１部分群及び前記第２部分群のいずれか一方は、像ぶれ補正に際して光軸に対して垂直方向の成分を含むように移動する防振群であり、
前記防振群の焦点距離をｆｓ、無限遠にフォーカスしているときの全系の焦点距離をｆｉｎｆ、無限遠にフォーカスしているときにおける前記第２レンズ群の横倍率をβ２ｉｎｆ、撮影倍率が等倍となる物体距離に合焦しているときにおける前記第２レンズ群の横倍率をβ２ｍｏｄとするとき、
０．５＜ｆｓ／ｆｉｎｆ＜１．５
１．０＜β２ｉｎｆ／β２ｍｏｄ＜１０．０
なる条件式を満足することを特徴としている。
The optical system of the present invention includes a first lens group having a positive refractive power, a second lens group having a negative refractive power, an aperture stop, and a third lens group having a positive refractive power, which are arranged in order from the object side to the image side. An optical system composed of a fourth lens group having a negative refractive power and a fifth lens group having a positive refractive power, wherein an interval between adjacent lens groups changes during focusing,
The third lens group is composed of a first partial group and a second partial group,
The second lens group and the fourth lens group move to the image side during focusing from infinity to a short distance,
During focusing, the first lens group, the aperture stop, and the third lens group are stationary,
Either one of the first partial group and the second partial group is an anti-vibration group that moves so as to include a component in a direction perpendicular to the optical axis during image blur correction,
The focal length of the anti-vibration group is fs, the focal length of the entire system when focusing at infinity is finf , the lateral magnification of the second lens group when focusing at infinity is β2inf, and the imaging magnification is When the lateral magnification of the second lens group is β2 mod when focusing on an object distance of equal magnification ,
0.5 <fs / finf <1.5
1.0 <β2inf / β2mod <10.0
It satisfies the following conditional expression.
本発明によれば、最短撮像距離が短く、全物体距離にわたり高い光学性能を有し、防振時の光学性能を良好に維持することができる光学系が得られる。 According to the present invention, an optical system is obtained in which the shortest imaging distance is short, the optical performance is high over the entire object distance, and the optical performance during image stabilization can be maintained well.
以下に、本発明の光学系及びそれを有する撮像装置について説明する。本発明の光学系は、物体側より像側へ順に配置された、正の屈折力の第１レンズ群、負の屈折力の第２レンズ群、正の屈折力の第３レンズ群、負の屈折力の第４レンズ群、正の屈折力の第５レンズ群より構成されている。フォーカシングに際して隣り合うレンズ群の間隔が変化する。また第３レンズ群は第１部分群及び第２部分群より構成されている。無限遠から近距離へのフォーカシングに際して第２レンズ群及び第４レンズ群は像側へ移動する。フォーカシングに際して第１レンズ群と開口絞りと第３レンズ群は不動である。第１部分群及び第２部分群のいずれか一方は、像ぶれ補正に際して光軸に対して垂直方向の成分を含むように移動する防振群である。 The optical system of the present invention and the image pickup apparatus having the same will be described below. The optical system of the present invention includes a first lens group having a positive refractive power, a second lens group having a negative refractive power, a third lens group having a positive refractive power, and a negative lens disposed in order from the object side to the image side. The lens unit includes a fourth lens unit having a refractive power and a fifth lens unit having a positive refractive power. The distance between adjacent lens groups changes during focusing. The third lens group is composed of a first partial group and a second partial group. During focusing from infinity to a short distance, the second lens group and the fourth lens group move to the image side. During focusing, the first lens group, the aperture stop, and the third lens group do not move. One of the first partial group and the second partial group is a vibration-proof group that moves so as to include a component in a direction perpendicular to the optical axis during image blur correction.
本発明の光学系におけるレンズ群は、フォーカシングに伴うレンズ間隔の変化によって分けることができる。本発明の光学系を構成する各レンズ群は１以上のレンズで構成すれば良く、複数のレンズで構成されている場合に限られない。 The lens group in the optical system according to the present invention can be divided according to a change in the lens interval accompanying focusing. Each lens group constituting the optical system of the present invention may be composed of one or more lenses, and is not limited to being composed of a plurality of lenses.
図１（Ａ），（Ｂ）は、本発明の実施例１の光学系における無限遠と撮像倍率が等倍のときのレンズ断面図である。図２（Ａ），（Ｂ）は、実施例１の光学系における無限遠と撮像倍率が等倍のときの縦収差図である。図３（Ａ），（Ｂ）は、実施例１の光学系において光軸が０．４度傾いた状態で画像ブレを補正したとき（防振時）の無限遠と撮像倍率が等倍のときの横収差図である。実施例１はＦナンバー３．５０、撮像画角２８．５２度の光学系である。 FIGS. 1A and 1B are lens cross-sectional views when the infinite distance and the imaging magnification are equal in the optical system according to the first embodiment of the present invention. FIGS. 2A and 2B are longitudinal aberration diagrams when the optical system of Example 1 is at infinity and the imaging magnification is equal. FIGS. 3A and 3B show that the image magnification is equal to infinity when image blur is corrected with the optical axis tilted by 0.4 degrees in the optical system of Example 1 (during image stabilization). FIG. Example 1 is an optical system having an F number of 3.50 and an imaging field angle of 28.52 degrees.
図４（Ａ），（Ｂ）は、本発明の実施例２の光学系における無限遠と撮像倍率が等倍のときのレンズ断面図である。図５（Ａ），（Ｂ）は、実施例２の光学系における無限遠と撮像倍率が等倍のときの縦収差図である。図６（Ａ），（Ｂ）は、実施例２の光学系において光軸が０．４度傾いた状態で画像ブレを補正したとき（防振時）の無限遠と撮像倍率が等倍のときの横収差図である。実施例２はＦナンバー３．５０、撮像画角３１．０８度の光学系である。図７は本発明の撮像装置の要部概略図である。 4A and 4B are lens cross-sectional views when the infinite distance and the imaging magnification are equal in the optical system according to the second embodiment of the present invention. 5A and 5B are longitudinal aberration diagrams in the optical system of Example 2 when the infinity and the imaging magnification are equal. FIGS. 6A and 6B show that the image magnification is equal to infinity when image blur is corrected with the optical axis tilted by 0.4 degrees in the optical system of Example 2 (during image stabilization). FIG. Example 2 is an optical system having an F number of 3.50 and an imaging field angle of 31.08 degrees. FIG. 7 is a schematic view of the main part of the imaging apparatus of the present invention.
レンズ断面図において左側が物体側（前方、拡大側）、右側が像側（後方、縮小側）である。ＯＬは光学系であり、物体側から像側へ順に、正の屈折力の第１レンズ群Ｌ１、負の屈折力の第２レンズ群Ｌ２、開口絞りＳＰ、正の屈折力の第３レンズ群Ｌ３、負の屈折力の第４レンズ群Ｌ４、正の屈折力の第５レンズ群Ｌ５より成っている。 In the lens cross-sectional view, the left side is the object side (front, enlargement side), and the right side is the image side (rear, reduction side). OL is an optical system, and in order from the object side to the image side, a first lens unit L1 having a positive refractive power, a second lens unit L2 having a negative refractive power, an aperture stop SP, and a third lens unit having a positive refractive power. L3 includes a fourth lens unit L4 having a negative refractive power and a fifth lens unit L5 having a positive refractive power.
ＩＰは像面であり、本発明の光学系をビデオカメラやデジタルスチルカメラの撮像光学系として用いる際には、像面ＩＰはＣＣＤセンサやＣＭＯＳセンサ等の固体撮像素子（光電変換素子）の撮像面に相当する。また本発明の光学系を銀塩フィルムカメラ用の光学系として用いる際には、像面ＩＰはフィルム面に相当する。球面収差図において、ｄはｄ線、ＣはＣ線、ｇはｇ線、ＦはＦ線を表わしている。非点収差図において、ｄＭはｄ線のメリディオナル像面、ｄＳはｄ線のサジタル像面、ｇＭはｇ線のメリディオナル像面、ｇＳはｇ線のサジタル像面を表わす。また歪曲収差はｄ線によって表している。 IP is an image plane. When the optical system of the present invention is used as an imaging optical system of a video camera or a digital still camera, the image plane IP is an image of a solid-state imaging device (photoelectric conversion device) such as a CCD sensor or a CMOS sensor. It corresponds to a surface. When the optical system of the present invention is used as an optical system for a silver salt film camera, the image plane IP corresponds to a film surface. In the spherical aberration diagram, d represents the d line, C represents the C line, g represents the g line, and F represents the F line. In the graph showing astigmatism, dM represents a meridional image plane for d line, dS represents a sagittal image plane for d line, gM represents a meridional image plane for g line, and gS represents a sagittal image plane for g line. Distortion is represented by d-line.
倍率色収差図において、ＣはＣ線、ｇはｇ線、ＦはＦ線を表わしている。ＦｎｏはＦナンバーである。また、各横収差図におけるｄＭはｄ線のメリディオナル光線、ｄＳはｄ線のサジタル光線を表している。 In the lateral chromatic aberration diagram, C represents the C line, g represents the g line, and F represents the F line. Fno is an F number. In each lateral aberration diagram, dM represents a d-line meridional ray, and dS represents a d-line sagittal ray.
実施例１において、第３レンズ群Ｌ３は、物体側から像側へ順に配置された、部分群（第１部分群）Ｌ３ａ、部分群（第２部分群）Ｌ３ｂを有する。部分群Ｌ３ａは１枚の正レンズからなる。部分群Ｌ３ｂは正レンズと負レンズを接合した接合レンズからなり、像ぶれ補正に際して光軸に対し垂直方向の成分を含むように移動する防振群である。フォーカシングに際し、第１レンズ群Ｌ１、第３レンズ群Ｌ３、第５レンズ群Ｌ５は不動である。無限遠から近距離へのフォーカシングに際し、第２レンズ群Ｌ２と第４レンズ群Ｌ４が像側へ移動する。フォーカシングに際して、レンズ断面図及び後述する数値データに示すように開口絞りＳＰは不動である。 In Example 1, the third lens unit L3 includes a partial group (first partial group) L3a and a partial group (second partial group) L3b which are arranged in order from the object side to the image side. The subgroup L3a is composed of one positive lens. The sub-group L3b is a vibration-proof group that includes a cemented lens in which a positive lens and a negative lens are cemented, and moves so as to include a component in a direction perpendicular to the optical axis during image blur correction. During focusing, the first lens unit L1, the third lens unit L3, and the fifth lens unit L5 do not move. During focusing from infinity to a short distance, the second lens unit L2 and the fourth lens unit L4 move to the image side. At the time of focusing, the aperture stop SP does not move as shown in the lens cross-sectional view and numerical data described later.
実施例１において像ぶれ補正に際して第３レンズ群Ｌ３もしくは第４レンズ群Ｌ４を光軸に対して垂直方向の成分を持つように移動させても良い。 In the first embodiment, the third lens unit L3 or the fourth lens unit L4 may be moved so as to have a component in a direction perpendicular to the optical axis when correcting the image blur.
実施例２において、第３レンズ群Ｌ３は、物体側から像側へ順に配置された、部分群（第１部分群）Ｌ３ａ、部分群（第２部分群）Ｌ３ｂを有する。部分群Ｌ３ａは１枚の正レンズからなり、像ぶれ補正に際して光軸に対し垂直方向の成分を含むように移動する防振群である。部分系Ｌ３ｂは正レンズと負レンズを接合した接合レンズよりなる。フォーカシングに際し、第１レンズ群Ｌ１、第３レンズ群Ｌ３は不動である。無限遠から近距離へのフォーカシングに際して第２レンズ群Ｌ２、第４レンズ群Ｌ４は像側へ移動し、第５レンズ群Ｌ５は物体側に凸状の軌跡で移動する。 In Example 2, the third lens unit L3 includes a partial group (first partial group) L3a and a partial group (second partial group) L3b which are arranged in order from the object side to the image side. The partial group L3a is composed of one positive lens, and is a vibration-proof group that moves so as to include a component in a direction perpendicular to the optical axis when image blur correction is performed. The partial system L3b includes a cemented lens in which a positive lens and a negative lens are cemented. During focusing, the first lens unit L1 and the third lens unit L3 do not move. During focusing from infinity to short distance, the second lens unit L2 and the fourth lens unit L4 move toward the image side, and the fifth lens unit L5 moves along a convex locus toward the object side.
各実施例の光学系のレンズ構成の特徴について説明する。無限遠から近距離へのフォーカシングに際して負の屈折力の第２レンズ群Ｌ２と負の屈折力の第４レンズ群Ｌ４を像側へ移動させるフォーカスタイプを採用している。正の屈折力の第３レンズ群Ｌ３を開口絞りＳＰ近傍に配置することで、第３レンズ群Ｌ３の有効径を小型化している。さらに、第３レンズ群Ｌ３で光線を収斂させることで、第４レンズ群Ｌ４の有効径の小型化も図っている。そして、第３レンズ群Ｌ３の全部または一部の部分群を防振群とし、像ぶれ補正に際して光軸に対して垂直方向の成分を持つように移動させている。 The characteristics of the lens configuration of the optical system of each example will be described. A focusing type is employed in which the second lens unit L2 having a negative refractive power and the fourth lens unit L4 having a negative refractive power are moved to the image side during focusing from infinity to a short distance. By disposing the third lens unit L3 having a positive refractive power in the vicinity of the aperture stop SP, the effective diameter of the third lens unit L3 is reduced. Further, the effective diameter of the fourth lens unit L4 is reduced by converging the light rays with the third lens unit L3. Then, all or a part of the third lens unit L3 is set as an anti-vibration unit, and is moved so as to have a component in a direction perpendicular to the optical axis at the time of image blur correction.
防振群の焦点距離をｆｓ、無限遠にフォーカスしているときの全系の焦点距離をｆｉｎｆとする。このとき、
０．５＜ｆｓ／ｆｉｎｆ＜１．５ ・・・（１）
なる条件式を満足している。
The focal length of the anti-vibration group is fs, and the focal length of the entire system when focusing at infinity is finf. At this time,
0.5 <fs / finf <1.5 (1)
The following conditional expression is satisfied.
条件式（１）は、像ぶれ補正用の部分群（以下「防振群」ともいう。）の焦点距離に関する式である。条件式（１）の上限を超えて防振群の正のパワーが弱くなると、防振敏感度が小さくなり、像ぶれ補正の際に必要な偏芯量が増大し、全系が大型化してくる。条件式（１）の下限を超えて防振群の正のパワーが強くなると像ぶれ補正に際して像面湾曲が増大し、この補正が困難となる。 Conditional expression (1) is an expression relating to the focal length of the image blur correction subgroup (hereinafter also referred to as “anti-vibration group”). If the positive power of the anti-vibration group becomes weaker than the upper limit of the conditional expression (1), the anti-vibration sensitivity decreases, the amount of eccentricity required for image blur correction increases, and the entire system increases in size. come. If the lower limit of the conditional expression (1) is exceeded and the positive power of the image stabilizing group becomes strong, the curvature of field increases at the time of image blur correction, and this correction becomes difficult.
以上のように、本発明によれば等倍付近までの撮影が可能で、手振れによる像ブレを光学的に補償することができ、防振時における光学性能を良好に維持することができる光学系が得られる。 As described above, according to the present invention, an optical system capable of photographing up to near the same magnification, optically compensating for image blur due to camera shake, and maintaining good optical performance during image stabilization. Is obtained.
各実施例において更に好ましくは次の条件式のうち１以上を満足するのが良い。ただし、第１レンズ群Ｌ１の焦点距離をｆ１、第２レンズ群Ｌ２の焦点距離をｆ２、第３レンズ群Ｌ３の焦点距離をｆ３、第４レンズ群Ｌ４の焦点距離をｆ４とする。また、無限遠にフォーカスしているときにおける第２レンズ群Ｌ２の横倍率をβ２ｉｎｆ、撮影倍率が等倍となる物体距離に合焦しているときにおける（撮影倍率が−１倍）（最至近距離）第２レンズ群Ｌ２の横倍率をβ２ｍｏｄとする。また、無限遠にフォーカスしているときにおける第４レンズ群Ｌ４の横倍率をβ４ｉｎｆ、撮影倍率が等倍となる物体距離に合焦しているときにおける第４レンズ群Ｌ４の横倍率をβ４ｍｏｄとする。 In each embodiment, it is more preferable to satisfy one or more of the following conditional expressions. However, the focal length of the first lens unit L1 is f1, the focal length of the second lens unit L2 is f2, the focal length of the third lens unit L3 is f3, and the focal length of the fourth lens unit L4 is f4. Further, when the focal length is infinity, the lateral magnification of the second lens unit L2 is β2inf, and when the focal length is an object distance where the photographing magnification is the same magnification (the photographing magnification is -1 times) (closest distance) Distance) The lateral magnification of the second lens unit L2 is β2 mod. Further, the lateral magnification of the fourth lens unit L4 when focused at infinity is β4inf, and the lateral magnification of the fourth lens unit L4 when focusing on the object distance at which the imaging magnification is equal is β4mod. To do.
また、無限遠から最至近距離へのフォーカシングに際しての第２レンズ群Ｌ２と第４レンズ群Ｌ４の移動量を各々ｍ２、ｍ４とする。移動量の符号は無限遠に合焦しているときと比較して至近距離に合焦しているときにレンズ群が像側へ移動する場合を正とする。このとき、次の条件式のうち１以上を満足するのが良い。 Further, the amounts of movement of the second lens unit L2 and the fourth lens unit L4 at the time of focusing from infinity to the closest distance are m2 and m4, respectively. The sign of the amount of movement is positive when the lens group moves to the image side when focusing on a close distance compared to when focusing on infinity. At this time, it is preferable to satisfy one or more of the following conditional expressions.
０．２＜ｆ３／ｆｉｎｆ＜２．０ ・・・（２）
−１．０＜ｆ２／ｆｉｎｆ＜−０．２ ・・・（３）
−１．０＜ｆ４／ｆｉｎｆ＜−０．２ ・・・（４）
１．０＜β２ｉｎｆ／β２ｍｏｄ＜１０．０ ・・・（５）
１．０＜β４ｉｎｆ／β４ｍｏｄ＜１０．０ ・・・（６）
０．１＜ｆ１／ｆｉｎｆ＜１．０ ・・・（７）
−０．８０＜ｍ２／ｆ２＜−０．２２ ・・・（８）
−０．８０＜ｍ４／ｆ４＜−０．２２ ・・・（９）
0.2 <f3 / finf <2.0 (2)
−1.0 <f2 / finf <−0.2 (3)
−1.0 <f4 / finf <−0.2 (4)
1.0 <β2inf / β2mod <10.0 (5)
1.0 <β4inf / β4mod <10.0 (6)
0.1 <f1 / finf <1.0 (7)
−0.80 <m2 / f2 <−0.22 (8)
−0.80 <m4 / f4 <−0.22 (9)
次に前述の各条件式の技術的意味について説明する。条件式（２）は第３レンズ群Ｌ３の焦点距離に関するものである。条件式（２）の上限を超えて第３レンズ群Ｌ３の正のパワーが弱くなると、光線を収斂させる力が弱くなり、全系が大型化してくる。条件式（２）の下限を超えて第３レンズ群Ｌ３の正のパワーが強くなると、諸収差を良好に保つことが困難となる。 Next, the technical meaning of each conditional expression described above will be described. Conditional expression (2) relates to the focal length of the third lens unit L3. If the positive power of the third lens unit L3 becomes weaker than the upper limit of the conditional expression (2), the force for converging light rays becomes weak, and the entire system becomes large. When the positive power of the third lens unit L3 increases beyond the lower limit of conditional expression (2), it becomes difficult to keep various aberrations in good condition.
条件式（３）は第２レンズ群Ｌ２の焦点距離に関するものである。条件式（３）の上限を超えて第２レンズ群Ｌ２の負のパワーが強くなると（負の屈折力の絶対値が大きくなると）、諸収差を良好に保つことが困難となる。条件式（３）の下限を超えて第２レンズ群Ｌ２の負のパワーが弱くなると（負の屈折力の絶対値が小さくなると）、フォーカシングに際しての移動量が増え、レンズ全長が増大してくる。 Conditional expression (3) relates to the focal length of the second lens unit L2. When the negative power of the second lens unit L2 increases beyond the upper limit of conditional expression (3) (when the absolute value of the negative refractive power increases), it becomes difficult to maintain various aberrations satisfactorily. If the lower power of the conditional expression (3) is exceeded and the negative power of the second lens unit L2 becomes weak (the absolute value of the negative refractive power decreases), the amount of movement during focusing increases and the total lens length increases. .
条件式（４）は第４レンズ群Ｌ４の焦点距離に関するものである。条件式（４）の上限を超えて第４レンズ群Ｌ４の負のパワーが強くなると、諸収差を良好に保つことが困難となる。条件式（４）の下限を超えて第４レンズ群Ｌ４の負のパワーが弱くなると、フォーカシングに際しての移動量が増え、レンズ全長が増大してくる。 Conditional expression (4) relates to the focal length of the fourth lens unit L4. When the negative power of the fourth lens unit L4 is increased beyond the upper limit of conditional expression (4), it becomes difficult to keep various aberrations in good condition. When the negative power of the fourth lens unit L4 becomes weaker beyond the lower limit of conditional expression (4), the amount of movement during focusing increases and the total lens length increases.
この条件式（５）は、フォーカス用の第２レンズ群Ｌ２の横倍率に関するものである。条件式（５）の上限を超えて横倍率の変化が大きくなると、諸収差を良好に保つことが困難となる。条件式（５）の下限を超えて横倍率の変化が小さくなるとフォーカシングに際しての第２レンズ群Ｌ２の移動量が増大し、全系が大型化してくる。 Conditional expression (5) relates to the lateral magnification of the second lens unit L2 for focusing. If the change in the lateral magnification increases beyond the upper limit of conditional expression (5), it becomes difficult to maintain various aberrations satisfactorily. If the change in the lateral magnification becomes smaller than the lower limit of conditional expression (5), the amount of movement of the second lens unit L2 during focusing increases, and the entire system becomes larger.
条件式（６）は、フォーカス用の第４レンズ群Ｌ４の横倍率に関するものである。条件式（６）の上限を超えて横倍率の変化が大きくなると、諸収差を良好に保つことが困難となる。条件式（６）の下限を超えて横倍率が小さくなるとフォーカシングに際しての第４レンズ群Ｌ４の移動量が増加し、全系が大型化してくる。 Conditional expression (6) relates to the lateral magnification of the fourth lens unit L4 for focusing. If the change in lateral magnification increases beyond the upper limit of conditional expression (6), it becomes difficult to keep various aberrations in good condition. When the lateral magnification is reduced beyond the lower limit of conditional expression (6), the amount of movement of the fourth lens unit L4 during focusing increases, and the entire system becomes larger.
条件式（７）は、最も物体側に配置される正の屈折力のレンズ群（第１レンズ群Ｌ１）の焦点距離に関するものである。条件式（７）の上限を超えると光線を収斂させる力が弱くなり、レンズ全長が増大してくる。条件式（７）の下限を超えて第１レンズ群Ｌ１の正の屈折力が強くなりすぎると諸収差が増加し、全系が大型化してくる。 Conditional expression (7) relates to the focal length of the lens unit (first lens unit L1) having a positive refractive power arranged on the most object side. When the upper limit of conditional expression (7) is exceeded, the force for converging the light beam becomes weak, and the total lens length increases. If the lower limit of conditional expression (7) is exceeded and the positive refractive power of the first lens unit L1 becomes too strong, various aberrations increase and the entire system becomes large.
条件式（８）は第２レンズ群Ｌ２のフォーカシングに際しての移動量と焦点距離に関するものである。条件式（８）の上限を超えて第２レンズ群Ｌ２の負の屈折力の絶対値が小さくなると（負の屈折力が小さくなると）フォーカシングに際してのレンズ群の移動量が増え、レンズ全長が大型化してくる。また、条件式（８）の下限を超えて第２レンズ群Ｌ２の負の屈折力の絶対値が大きくなると（負の屈折力が大きくなると）諸収差の変動が大きくなり、光学性能を良好に保つことが困難となる。 Conditional expression (8) relates to the amount of movement and the focal length during focusing of the second lens unit L2. When the absolute value of the negative refractive power of the second lens unit L2 becomes smaller than the upper limit of conditional expression (8) (when the negative refractive power becomes smaller), the amount of movement of the lens unit during focusing increases, and the total lens length increases. It will turn. Further, when the absolute value of the negative refractive power of the second lens unit L2 exceeds the lower limit of conditional expression (8) (when the negative refractive power increases), the variation of various aberrations increases, and the optical performance is improved. It becomes difficult to keep.
条件式（９）は第４レンズ群Ｌ４のフォーカシングに際しての移動量と焦点距離に関するものである。条件式（９）の上限を超えて第４レンズ群Ｌ４の負の屈折力の絶対値が小さくなると（負の屈折力が小さくなると）フォーカシングに際してのレンズ群の移動量が増え、レンズ全長が大型化してくる。また、条件式（９）の下限を超えて第４レンズ群Ｌ４の負の屈折力の絶対値が大きくなると（負の屈折力が大きくなると）諸収差の変動が大きくなり、光学性能を良好に保つことが困難となる。 更に、好ましくは条件式（１）乃至（７）の数値範囲を次の如く設定するのが良い。 Conditional expression (9) relates to the amount of movement and the focal length during focusing of the fourth lens unit L4. When the absolute value of the negative refracting power of the fourth lens unit L4 becomes smaller than the upper limit of the conditional expression (9) (when the negative refracting power becomes smaller), the amount of movement of the lens unit during focusing increases, and the total lens length becomes large. It will turn. Further, when the absolute value of the negative refractive power of the fourth lens unit L4 exceeds the lower limit of conditional expression (9) (when the negative refractive power increases), various aberrations increase, and the optical performance is improved. It becomes difficult to keep. Furthermore, it is preferable to set the numerical ranges of the conditional expressions (1) to (7) as follows.
０．８＜ｆｓ／ｆｉｎｆ＜１．３ ・・・（１ａ）
０．２＜ｆ３／ｆｉｎｆ＜０．５ ・・・（２ａ）
−０．４０＜ｆ２／ｆｉｎｆ＜−０．２５ ・・・（３ａ）
−０．８＜ｆ４／ｆｉｎｆ＜−０．４ ・・・（４ａ）
１．０＜β２ｉｎｆ／β２ｍｏｄ＜３．９ ・・・（５ａ）
１．０＜β４ｉｎｆ／β４ｍｏｄ＜３．９ ・・・（６ａ）
０．４０＜ｆ１／ｆｉｎｆ＜０．６３ ・・・（７ａ）
−０．６０＜ｍ２／ｆ２＜−０．３０ ・・・（８ａ）
−０．６０＜ｍ４／ｆ４＜−０．３０ ・・・（９ａ）
0.8 <fs / finf <1.3 (1a)
0.2 <f3 / finf <0.5 (2a)
−0.40 <f2 / finf <−0.25 (3a)
−0.8 <f4 / finf <−0.4 (4a)
1.0 <β2inf / β2mod <3.9 (5a)
1.0 <β4inf / β4mod <3.9 (6a)
0.40 <f1 / finf <0.63 (7a)
−0.60 <m2 / f2 <−0.30 (8a)
−0.60 <m4 / f4 <−0.30 (9a)
以上のように各実施例によれば、撮影倍率が等倍程度の近距離撮影（マクロ撮影）が容易で、しかも手振れなどによる像ブレを光学的に良好に補償する防振機能を有する光学系が得られる。 As described above, according to each embodiment, an optical system having an image stabilization function that can easily perform short-distance shooting (macro shooting) with a shooting magnification of approximately the same magnification and that optically compensates for image blur due to camera shake or the like. Is obtained.
次に、本発明の光学系を用いた一眼レフカメラシステムの実施形態を、図７を用いて説明する。図７において、１０は一眼レフカメラ本体、１１は本発明による光学系を搭載した交換レンズである。１２は交換レンズ１１を通して得られる被写体像を記録するフィルムや撮像素子（光電変換素子）などの記録手段である。１３は交換レンズ１１からの被写体像を観察するファインダー光学系、１４は交換レンズ１１からの光を記録手段１２とファインダー光学系１３に選択的に導くために回動するクイックリターンミラーである。 Next, an embodiment of a single-lens reflex camera system using the optical system of the present invention will be described with reference to FIG. In FIG. 7, reference numeral 10 denotes a single-lens reflex camera body, and 11 denotes an interchangeable lens equipped with an optical system according to the present invention. Reference numeral 12 denotes recording means such as a film for recording a subject image obtained through the interchangeable lens 11 and an imaging element (photoelectric conversion element). Reference numeral 13 denotes a finder optical system for observing the subject image from the interchangeable lens 11, and reference numeral 14 denotes a quick return mirror that rotates to selectively guide the light from the interchangeable lens 11 to the recording means 12 and the finder optical system 13.
ファインダーで被写体像を観察する場合は、クイックリターンミラー１４を介してピント板１５に結像した被写体像をペンタプリズム１６で正立像としたのち、接眼光学系１７で拡大して観察する。撮影時にはクイックリターンミラー１４が矢印方向に回動して被写体像は記録手段１２に結像して記録される。１８はサブミラー、１９は焦点検出装置である。このように本発明の光学系を一眼レフカメラ交換レンズに適用することにより、高い光学性能を有した撮像装置が実現できる。 When observing the subject image with the finder, the subject image formed on the focusing plate 15 via the quick return mirror 14 is made into an erect image with the pentaprism 16 and then magnified and observed with the eyepiece optical system 17. At the time of shooting, the quick return mirror 14 rotates in the direction of the arrow, and the subject image is formed and recorded on the recording means 12. Reference numeral 18 denotes a submirror, and 19 denotes a focus detection device. Thus, by applying the optical system of the present invention to a single-lens reflex camera interchangeable lens, an imaging apparatus having high optical performance can be realized.
なお、本発明はクイックリターンミラーのないミラーレンズの一眼カメラにも同様に適用することができ、上記に限ったものではない。 The present invention can be similarly applied to a single-lens camera with a mirror lens without a quick return mirror, and is not limited to the above.
次に、各実施例に対応する数値実施例を示す。各実施例の数値実施例において、ｊは物体側から数えた面番号を表し、ｒｊは第ｊ番目の面番号の曲率半径である。ｄｊは第ｊ番目と第（ｊ＋１）番目の面との光軸上の面間隔、ｎｄｊ，νｄｊは第ｊ番目の光学材料のｄ線に対する屈折率、アッベ数を表している。光学系の焦点距離、Ｆナンバー、半画角（度）、像高を示す。また、レンズ全長は第１レンズ面から像面までの距離である。ＢＦはバックフォーカスであり最終レンズ面から像面までの距離である。 Next, numerical examples corresponding to the respective examples will be shown. In the numerical example of each embodiment, j represents a surface number counted from the object side, and rj is a radius of curvature of the jth surface number. dj represents the distance between the j-th surface and the (j + 1) -th surface on the optical axis, and ndj and νdj represent the refractive index and Abbe number of the j-th optical material with respect to the d-line. Indicates the focal length, F number, half angle of view (degrees), and image height of the optical system. The total lens length is the distance from the first lens surface to the image plane. BF is a back focus, which is a distance from the final lens surface to the image plane.
また、非球面は面番号の後に＊の符号を付加している。非球面形状は、Ｘを光軸方向の面頂点からの変位量、ｈを光軸と垂直な方向の光軸からの高さ、Ｒを近軸曲率半径、ｋを円錐定数、Ａ４，Ａ６，Ａ８を各々各次数の非球面係数とするとき、
ｘ＝（ｈ2／Ｒ）／［１＋｛１−（１＋ｋ）（ｈ／Ｒ）2｝］1/2＋Ａ４・Ｈ4＋＋Ａ６・Ｈ6＋Ａ８・Ｈ8
で表す。なお、各非球面係数における「Ｅ±ＸＸ」は「×１０±ＸＸ」を意味している。
また、各数値実施例における前記の条件式の値を表１に示す。
In addition, the aspherical surface is provided with a symbol * after the surface number. In the aspherical shape, X is the amount of displacement from the surface apex in the optical axis direction, h is the height from the optical axis in the direction perpendicular to the optical axis, R is the paraxial radius of curvature, k is the conic constant, A4, A6, When A8 is an aspheric coefficient of each order,
x = (h 2 / R) / [1+ {1− (1 + k) (h / R) 2 }] 1/2 + A4 · H 4 ++ A6 · H 6 + A8 · H 8
Represented by Note that “E ± XX” in each aspheric coefficient means “× 10 ± XX ”.
Table 1 shows the values of the conditional expressions in each numerical example.
（数値実施例１）
単位 mm
面データ
面番号 r d nd νd
1 32.481 3.23 1.65160 58.5
2 -79.222 0.15
3 21.104 3.68 1.62299 58.2
4 -34.926 1.30 1.84666 23.8
5 71.129 (可変)
6 98.063 1.00 1.83400 37.2
7 13.481 2.53
8 -17.717 1.10 1.76200 40.1
9 19.466 2.94 1.84666 23.8
10 -34.587 (可変)
11 ∞ 1.20
12 -233.884 1.94 1.78800 47.4
13 -25.391 1.09
14 40.302 2.74 1.69680 55.5
15 -18.763 1.20 1.67270 32.1
16 -1222.568 (可変)
17 -38.346 1.22 1.84666 23.8
18 -20.374 1.00 1.69100 54.8
19* 57.221 (可変)
20 34.413 5.15 1.60311 60.6
21 -25.255 2.05
22 -20.820 1.24 1.84666 23.8
23 483.717 17.69
像面 ∞
(Numerical example 1)
Unit mm
Surface data surface number rd nd νd
1 32.481 3.23 1.65 160 58.5
2 -79.222 0.15
3 21.104 3.68 1.62299 58.2
4 -34.926 1.30 1.84666 23.8
5 71.129 (variable)
6 98.063 1.00 1.83400 37.2
7 13.481 2.53
8 -17.717 1.10 1.76200 40.1
9 19.466 2.94 1.84666 23.8
10 -34.587 (variable)
11 ∞ 1.20
12 -233.884 1.94 1.78800 47.4
13 -25.391 1.09
14 40.302 2.74 1.69680 55.5
15 -18.763 1.20 1.67270 32.1
16 -1222.568 (variable)
17 -38.346 1.22 1.84666 23.8
18 -20.374 1.00 1.69 100 54.8
19 * 57.221 (variable)
20 34.413 5.15 1.60311 60.6
21 -25.255 2.05
22 -20.820 1.24 1.84666 23.8
23 483.717 17.69
Image plane ∞
非球面データ
第19面
K = 0.00000e+000 A 4=-7.30784e-006 A 6= 1.17385e-008 A 8=-1.90930e-010
焦点距離 53.73
Fナンバー 3.50
半画角（度） 14.26
像高 13.66
レンズ全長 76.39
BF 17.69
倍率 ∞ -0.5 -1
d 5 0.93 4.19 8.29
d10 8.52 5.25 1.16
d16 1.53 7.18 13.34
d19 12.97 7.32 1.15
群データ
群 始面 焦点距離
1 1 24.13
2 6 -15.75
3 11 21.63
4 17 -37.48
5 20 284.09
Aspheric data 19th surface
K = 0.00000e + 000 A 4 = -7.30784e-006 A 6 = 1.17385e-008 A 8 = -1.90930e-010
Focal length 53.73
F number 3.50
Half angle of view (degrees) 14.26
Statue height 13.66
Total lens length 76.39
BF 17.69
Magnification ∞ -0.5 -1
d 5 0.93 4.19 8.29
d10 8.52 5.25 1.16
d16 1.53 7.18 13.34
d19 12.97 7.32 1.15
Group data group Start surface Focal length
1 1 24.13
2 6 -15.75
3 11 21.63
4 17 -37.48
5 20 284.09
（数値実施例２）
単位 mm
面データ
面番号 r d nd νd
1 28.805 2.99 1.81600 46.6
2 -157.289 0.15
3 23.902 3.30 1.58913 61.1
4 -36.290 1.30 1.84666 23.8
5 49.940 (可変)
6 50.781 0.80 1.83481 42.7
7 12.747 2.04
8 -25.722 0.80 1.83400 37.2
9 9.616 3.00 1.84666 23.8
10 -109.053 (可変)
11(絞り) ∞ 1.19
12 118.672 1.81 1.69680 55.5
13 -51.169 1.19
14 43.271 3.38 1.78800 47.4
15 -13.825 1.20 1.84666 23.8
16 -36.999 (可変)
17 -31.839 1.18 1.84666 23.8
18 -19.553 1.00 1.69100 54.8
19* 40.901 (可変)
20 76.091 4.02 1.81600 46.6
21 -25.398 3.87
22 -18.468 1.24 1.84666 23.8
23 -53.565 (可変)
像面 ∞
(Numerical example 2)
Unit mm
Surface data surface number rd nd νd
1 28.805 2.99 1.81600 46.6
2 -157.289 0.15
3 23.902 3.30 1.58913 61.1
4 -36.290 1.30 1.84666 23.8
5 49.940 (variable)
6 50.781 0.80 1.83481 42.7
7 12.747 2.04
8 -25.722 0.80 1.83400 37.2
9 9.616 3.00 1.84666 23.8
10 -109.053 (variable)
11 (Aperture) ∞ 1.19
12 118.672 1.81 1.69680 55.5
13 -51.169 1.19
14 43.271 3.38 1.78800 47.4
15 -13.825 1.20 1.84666 23.8
16 -36.999 (variable)
17 -31.839 1.18 1.84666 23.8
18 -19.553 1.00 1.69 100 54.8
19 * 40.901 (variable)
20 76.091 4.02 1.81600 46.6
21 -25.398 3.87
22 -18.468 1.24 1.84666 23.8
23 -53.565 (variable)
Image plane ∞
非球面データ
第19面
K = 0.00000e+000 A 4=-3.47975e-006 A 6=-1.28602e-007 A 8= 1.52010e-009
焦点距離 49.11
Fナンバー 3.50
半画角（度） 15.54
像高 13.66
レンズ全長 85.40
BF 26.90
倍率 ∞ -0.5 -1
d 5 0.97 4.09 8.32
d10 8.70 5.55 1.35
d16 1.23 7.79 14.23
d19 13.14 7.56 1.25
d23 26.90 25.93 25.80
群データ
群 始面 焦点距離
1 1 26.83
2 6 -13.75
3 11 18.74
4 17 -27.88
5 20 56.82
Aspheric data 19th surface
K = 0.00000e + 000 A 4 = -3.47975e-006 A 6 = -1.28602e-007 A 8 = 1.52010e-009
Focal length 49.11
F number 3.50
Half angle of view (degrees) 15.54
Statue height 13.66
Total lens length 85.40
BF 26.90
Magnification ∞ -0.5 -1
d 5 0.97 4.09 8.32
d10 8.70 5.55 1.35
d16 1.23 7.79 14.23
d19 13.14 7.56 1.25
d23 26.90 25.93 25.80
Group data group Start surface Focal length
1 1 26.83
2 6 -13.75
3 11 18.74
4 17 -27.88
5 20 56.82
Ｌ１ 第１レンズ群 Ｌ２ 第２レンズ群 Ｌ３ 第３レンズ群
Ｌ３ａ 部分群 Ｌ３ｂ 部分群 Ｌ４ 第４レンズ群 Ｌ５ 第５レンズ群
L1 1st lens group L2 2nd lens group L3 3rd lens group L3a Partial group L3b Partial group L4 4th lens group L5 5th lens group
Claims (10)
前記第３レンズ群は第１部分群及び第２部分群より構成されており、
無限遠から近距離へのフォーカシングに際して前記第２レンズ群及び前記第４レンズ群は像側へ移動し、
フォーカシングに際して、前記第１レンズ群と前記開口絞りと前記第３レンズ群は不動であり、
前記第１部分群及び前記第２部分群のいずれか一方は、像ぶれ補正に際して光軸に対して垂直方向の成分を含むように移動する防振群であり、
前記防振群の焦点距離をｆｓ、無限遠にフォーカスしているときの全系の焦点距離をｆｉｎｆ、無限遠にフォーカスしているときにおける前記第２レンズ群の横倍率をβ２ｉｎｆ、撮影倍率が等倍となる物体距離に合焦しているときにおける前記第２レンズ群の横倍率をβ２ｍｏｄとするとき、
０．５＜ｆｓ／ｆｉｎｆ＜１．５
１．０＜β２ｉｎｆ／β２ｍｏｄ＜１０．０
なる条件式を満足することを特徴とする光学系。 A first lens group having a positive refractive power, a second lens group having a negative refractive power, an aperture stop, a third lens group having a positive refractive power, and a first lens group having a negative refractive power, which are arranged in order from the object side to the image side. An optical system composed of four lens groups and a fifth lens group having a positive refractive power, wherein the distance between adjacent lens groups changes during focusing;
The third lens group is composed of a first partial group and a second partial group,
The second lens group and the fourth lens group move to the image side during focusing from infinity to a short distance,
During focusing, the first lens group, the aperture stop, and the third lens group are stationary,
Either one of the first partial group and the second partial group is an anti-vibration group that moves so as to include a component in a direction perpendicular to the optical axis during image blur correction,
The focal length of the anti-vibration group is fs, the focal length of the entire system when focusing at infinity is finf , the lateral magnification of the second lens group when focusing at infinity is β2inf, and the imaging magnification is When the lateral magnification of the second lens group is β2 mod when focusing on an object distance of equal magnification ,
0.5 <fs / finf <1.5
1.0 <β2inf / β2mod <10.0
An optical system that satisfies the following conditional expression:
０．２＜ｆ３／ｆｉｎｆ＜２．０
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。 When the focal length of the third lens group is f3,
0.2 <f3 / finf <2.0
The optical system according to claim 1, wherein the following conditional expression is satisfied.
−１．０＜ｆ２／ｆｉｎｆ＜−０．２
なる条件式を満足することを特徴とする請求項１または２に記載の光学系。 When the focal length of the second lens group is f2,
−1.0 <f2 / finf <−0.2
The optical system according to claim 1, wherein the following conditional expression is satisfied.
−１．０＜ｆ４／ｆｉｎｆ＜−０．２
なる条件式を満足することを特徴とする請求項１乃至３のいずれか１項に記載の光学系。 When the focal length of the fourth lens group is f4,
−1.0 <f4 / finf <−0.2
The optical system according to claim 1, wherein the following conditional expression is satisfied.
１．０＜β４ｉｎｆ／β４ｍｏｄ＜１０．０
なる条件式を満足することを特徴とする請求項１乃至４のいずれか１項に記載の光学系。 When the lateral magnification of the fourth lens group when focused at infinity is β4inf, and when the lateral magnification of the fourth lens group is focused at an object distance at which the photographing magnification is equal, β4mod ,
1.0 <β4inf / β4mod <10.0
Optical system according to any one of claims 1 to 4, characterized by satisfying the conditional expression.
０．１＜ｆ１／ｆｉｎｆ＜１．０
なる条件式を満足することを特徴とする請求項１乃至５のいずれか１項に記載の光学系。 When the focal length of the first lens group is f1,
0.1 <f1 / finf <1.0
Optical system according to any one of claims 1 to 5, characterized by satisfying the conditional expression.
−０．８０＜ｍ２／ｆ２＜−０．２２
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１項に記載の光学系。 The focal length of the second lens group is f2, and the amount of movement of the second lens group when focusing from infinity to the closest distance is m2. When the sign of the amount of movement when the second lens group moves to the image side when in focus is positive,
−0.80 <m2 / f2 <−0.22
Optical system according to any one of claims 1 to 6, characterized by satisfying the conditional expression.
−０．８０＜ｍ４／ｆ４＜−０．２２
なる条件式を満足することを特徴とする請求項１乃至７のいずれか１項に記載の光学系。 The focal length of the fourth lens group is f4, and the amount of movement of the fourth lens group during focusing from infinity to the closest distance is m4, which is closer to the closest distance than when focusing on infinity. When the sign of the amount of movement when the fourth lens group moves to the image side when in focus is positive,
−0.80 <m4 / f4 <−0.22
Optical system according to any one of claims 1 to 7, characterized by satisfying the conditional expression.
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