JP6355414B2 - Optical system and image projection apparatus having the same - Google Patents

Optical system and image projection apparatus having the same Download PDF

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JP6355414B2
JP6355414B2 JP2014095056A JP2014095056A JP6355414B2 JP 6355414 B2 JP6355414 B2 JP 6355414B2 JP 2014095056 A JP2014095056 A JP 2014095056A JP 2014095056 A JP2014095056 A JP 2014095056A JP 6355414 B2 JP6355414 B2 JP 6355414B2
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高橋　真
真 高橋
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Description

本発明は光学系に関し、例えば画像表示素子に表示された画像を拡大投射する画像投射装置（プロジェクター）に用いる投射光学系やデジタルカメラ等に用い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 is suitable, for example, as a projection optical system used in an image projection apparatus (projector) that magnifies and projects an image displayed on an image display element, an imaging optical system used in a digital camera, or the like.

画像表示素子に表示された画像を大画面に投影する画像投射装置に用いられる投射光学系には画像表示素子に形成される画像全体をスクリーン面上に種々な投射距離から高解像度で投射できることが要望されている。更に近距離より広い画面にわたり投射できるように広画角であること等が要望されている。   The projection optical system used in the image projection apparatus that projects the image displayed on the image display element onto a large screen can project the entire image formed on the image display element from various projection distances with high resolution on the screen surface. It is requested. Further, there is a demand for a wide angle of view so that it can be projected over a screen wider than a short distance.

従来より、これらの要望を満足する画像投射装置用の投射光学系として、拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群と１以上のレンズ群を含む後群より構成されるレトロフォーカス型の投射光学系が知られている。またスクリーンが拡大共役側の無限遠にあったときから至近距離に変化したときの距離変化に対して複数のレンズ群を移動させて収差変動を軽減するようにした投射光学系が知られている（特許文献１）。   2. Description of the Related Art Conventionally, a projection optical system for an image projection apparatus that satisfies these demands is composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side. A retrofocus type projection optical system is known. There is also known a projection optical system that reduces aberration fluctuations by moving a plurality of lens groups in response to a change in distance when the screen is changed from infinity to an infinite distance on the magnification conjugate side. (Patent Document 1).

特許文献１では拡大共役側から縮小共役側に順に、負の屈折力の第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、正の屈折力の第４レンズ群よりなる単一の焦点距離の投射光学系を開示している。そしてスクリーンが拡大共役側で無限遠にあったときから至近距離にきたときの距離変化に対して第２レンズ群と第３レンズ群の間隔が拡がるように双方を縮小共役側へ移動してフォーカシングを行っている。   In Patent Document 1, in order from the magnification conjugate side to the reduction conjugate side, the first lens group having a negative refractive power, the second lens group having a negative refractive power, the third lens group having a positive refractive power, and the first lens group having a positive refractive power. A projection optical system having a single focal length composed of four lens groups is disclosed. Then, the screen is moved to the reduction conjugate side so that the distance between the second lens unit and the third lens unit is increased with respect to the change in distance when the screen is at infinity on the enlargement conjugate side, and focusing is performed. It is carried out.

更に特許文献１では拡大共役側から縮小共役側へ順に、負、負、正、正、正、負、正の屈折力の第１レンズ群乃至第７レンズ群よりなり、ズーミングに際して第３レンズ群乃至第６レンズ群を移動させるズームレンズを開示している。そしてスクリーンが拡大共役側で無限遠にあったときから至近距離にきたときの距離変化に対して第１レンズ群と第２レンズ群の間隔が拡がるように縮小共役側へ移動してフォーカシングを行っている。   Further, in Patent Document 1, the zoom lens includes first to seventh lens groups having negative, negative, positive, positive, positive, negative, and positive refractive powers in order from the enlargement conjugate side to the reduction conjugate side. A zoom lens for moving the sixth lens group is disclosed. Then, focusing is performed by moving to the reduction conjugate side so that the distance between the first lens group and the second lens group is widened with respect to the distance change when the screen is at infinity on the enlargement conjugate side. ing.

特開２０１１−７６０４０号公報JP 2011-76040 A

プロジェクターに用いられる投射光学系には、投射距離全般にわたり、投射画像が高画質で高い光学性能を有することが要望されている。前述の投射光学系においてこれらの要望を満足するには、全系のレンズ構成及びフォーカシングに際して移動するレンズ群の選択及びそれらのレンズ群の屈折力等を適切に設定することが重要になってくる。このときのレンズ群の選択や選択したレンズ群の屈折力やレンズ構成等が不適切であると、投射距離全般にわたり良好なる光学性能を得るのが困難になる。   A projection optical system used in a projector is required to have a high-quality optical image with high image quality over the entire projection distance. In order to satisfy these demands in the above-mentioned projection optical system, it is important to select the lens configuration of the entire system, the selection of lens groups that move during focusing, and the appropriate setting of the refractive power of those lens groups. . If the selection of the lens group at this time, the refractive power of the selected lens group, the lens configuration, etc. are inappropriate, it will be difficult to obtain good optical performance over the entire projection distance.

本発明は、投射距離全般にわたり良好なる光学性能が容易に得られる光学系及びそれを用いた画像投射装置の提供を目的とする。   An object of the present invention is to provide an optical system in which good optical performance can be easily obtained over the entire projection distance and an image projection apparatus using the same.

本発明の光学系は、拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
前記部分群Ｂ１ｃは前記部分群Ｂ１ｃが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動することを特徴としている。 この他、本発明の光学系は、拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、
前記部分群Ｂ１ｃが備えるレンズのうち最も前記拡大共役側に設けられた負レンズの屈折力をφＢ１ｃｎ、前記第１レンズ群の屈折力をφＢ１とするとき、
０．１＜φＢ１ｃｎ／φＢ１＜２．０
なる条件式を満足することを特徴としている。
この他、本発明の光学系は、拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、
前記部分群Ｂ１ａが備える前記１以上の正レンズのうち最も前記拡大共役側に設けられた正レンズの屈折力をφＢ１ａｐ、前記第１レンズ群の屈折力をφＢ１とするとき、
−０．１５＜φＢ１ａｐ／φＢ１＜−０．０１
なる条件式を満足することを特徴としている。 この他、本発明の光学系は、拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、
前記後群は前記拡大共役側から前記縮小共役側へ順に、正の屈折力の第２レンズ群、正の屈折力の第３レンズ群、正の屈折力の第４レンズ群、正の屈折力の第５レンズ群より構成され、広角端から望遠端へのズーミングに際して、前記第１レンズ群と前記第５レンズ群は不動で、前記第２レンズ群と前記第３レンズ群と前記第４レンズ群は互いに異なった軌跡で前記拡大共役側に移動することを特徴としている。 The optical system of the present invention is an optical system composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side.
The first lens group includes, in order from the enlargement conjugate side to the reduction conjugate side, negative refractive power of the subgroup B1a, negative refractive power of the subgroup B1b, is composed of subgroup B1c a positive refractive power,
The subgroup B1a has a negative lens which is most disposed on the enlargement conjugate side in the lens provided in the subgroup B1a, one or more positive lenses,
The subgroup B1c has a negative lens provided on the most magnification conjugate side among the lenses included in the subgroup B1c, and one or more positive lenses.
Infinity the subgroup B1c said partial group B1b during focusing to a close is to the reduction conjugate side, and thus being moved expanding both intervals. In addition, the optical system of the present invention, in order from the magnification conjugate side to the reduction conjugate side, in the optical system constituted by the first lens group having a negative refractive power and a rear group including one or more lens groups,
The first lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
When the refractive power of the negative lens provided closest to the magnification conjugate side among the lenses included in the partial group B1c is φB1cn, and the refractive power of the first lens group is φB1,
0.1 <φB1cn / φB1 <2.0
It satisfies the following conditional expression .
In addition, the optical system of the present invention, in order from the magnification conjugate side to the reduction conjugate side, in the optical system constituted by the first lens group having a negative refractive power and a rear group including one or more lens groups,
The first lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
When the refractive power of the positive lens provided closest to the magnification conjugate side among the one or more positive lenses included in the partial group B1a is φB1ap, and the refractive power of the first lens group is φB1,
−0.15 <φB1ap / φB1 <−0.01
It satisfies the following conditional expression. In addition, the optical system of the present invention is an optical system including a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side. The lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
The rear group includes, in order from the magnification conjugate side to the reduction conjugate side, a second lens group having a positive refractive power, a third lens group having a positive refractive power, a fourth lens group having a positive refractive power, and a positive refractive power. In the zooming from the wide-angle end to the telephoto end, the first lens group and the fifth lens group do not move, and the second lens group, the third lens group, and the fourth lens are not moved. The group is characterized by moving to the enlargement conjugate side along different trajectories.

本発明によれば、投射距離全般にわたり良好なる光学性能が容易に得られる光学系が得られる。   According to the present invention, it is possible to obtain an optical system that can easily obtain good optical performance over the entire projection distance.

（Ａ），（Ｂ）は本発明の実施例１の光学系の広角端と望遠端におけるレンズ断面図(A), (B) is a lens cross-sectional view at the wide-angle end and the telephoto end of the optical system according to the first embodiment of the present invention. （Ａ），（Ｂ）は実施例１の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図(A), (B) is lens sectional drawing in projection distance 1210mm and 690mm in the wide angle end of Example 1. FIG. （Ａ），（Ｂ），（Ｃ）は実施例１の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図(A), (B), and (C) are aberration diagrams at the wide-angle end and the telephoto end at the projection distance of 1210 mm and aberration diagrams at the wide-angle end at the projection distance of 690 mm. （Ａ），（Ｂ），（Ｃ）は実施例１の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差と投射距離６９０ｍｍにおける広角端における倍率色収差図(A), (B), and (C) are chromatic aberration of magnification at the wide angle end and the telephoto end at the projection distance of 1210 mm and the lateral chromatic aberration at the wide angle end of the projection distance of 690 mm. （Ａ），（Ｂ）は本発明の実施例２の光学系の広角端と望遠端におけるレンズ断面図FIGS. 4A and 4B are sectional views of lenses at the wide-angle end and the telephoto end of the optical system according to Example 2 of the present invention. （Ａ），（Ｂ）は実施例２の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図(A), (B) is lens sectional drawing in projection distance 1210mm and 690mm in the wide angle end of Example 2. FIG. （Ａ），（Ｂ），（Ｃ）は実施例２の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図(A), (B), (C) are aberration diagrams at the wide-angle end and telephoto end of the optical system of Example 2 at a projection distance of 1210 mm, and aberration diagrams at a wide-angle end at a projection distance of 690 mm. （Ａ），（Ｂ），（Ｃ）は実施例２の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差と投射距離６９０ｍｍにおける広角端における倍率色収差図(A), (B), (C) are chromatic aberration of magnification at the wide-angle end and telephoto end at the projection distance of 1210 mm and the lateral chromatic aberration at the wide-angle end at the projection distance of 690 mm. （Ａ），（Ｂ）は本発明の実施例３の光学系の広角端と望遠端におけるレンズ断面図FIGS. 4A and 4B are lens cross-sectional views at the wide-angle end and the telephoto end of the optical system according to Embodiment 3 of the present invention. （Ａ），（Ｂ）は実施例３の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図(A), (B) is lens sectional drawing in projection distance 1210mm and 690mm in the wide angle end of Example 3. FIG. （Ａ），（Ｂ），（Ｃ）は実施例３の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図(A), (B), and (C) are aberration diagrams at the wide-angle end and telephoto end of the optical system of Example 3 at a projection distance of 1210 mm, and aberration diagrams at the wide-angle end at a projection distance of 690 mm. （Ａ），（Ｂ），（Ｃ）は実施例３の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差と投射距離６９０ｍｍにおける広角端における倍率色収差図(A), (B), and (C) are chromatic aberration of magnification at the wide-angle end and telephoto end at the projection distance of 1210 mm and the lateral chromatic aberration at the wide-angle end at the projection distance of 690 mm. （Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおけるレンズ断面図(A), (B) is lens sectional drawing in the projection distance 1210mm of the optical system of Example 4, and the projection distance 690mm. （Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおける収差図(A) and (B) are aberration diagrams of the optical system of Example 4 at a projection distance of 1210 mm and a projection distance of 690 mm. （Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおける倍率色収差図(A), (B) is a chromatic aberration diagram of magnification at a projection distance of 1210 mm and a projection distance of 690 mm of the optical system of Example 4. 本発明の画像投射装置の要部概略図Schematic diagram of main parts of the image projection apparatus of the present invention

以下に、本発明の好ましい実施の形態を添付の図面に基づいて詳細に説明する。本発明の光学系は、拡大共役側（物体側）から縮小共役側（像側）へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される単一焦点距離の投射レンズ又はズームレンズである。第１レンズ群は拡大共役側から縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成される。   Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The optical system of the present invention is a single lens composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side (object side) to the reduction conjugate side (image side). A focal length projection lens or zoom lens. The first lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.

部分群Ｂ１ａは部分群Ｂ１ａが備えるレンズのうち最も拡大共役側に負レンズと、１以上の正レンズを有している。無限遠から至近へのフォーカシングに際して部分群Ｂ１ｂと部分群Ｂ１ｃは縮小共役側へ、双方の間隔を拡大しつつ移動する。部分群Ｂ１ｃは部分群Ｂ１ｃが備えるレンズのうち最も拡大共役側に負レンズと１以上の正レンズを有する。尚、本発明の光学系はデジタルカメラ等の撮像装置用の撮像光学系としても適用できる。 The subgroup B1a has a negative lens and one or more positive lenses on the most magnification conjugate side among the lenses included in the subgroup B1a . At the time of focusing from infinity to the closest position, the subgroup B1b and the subgroup B1c move toward the reduction conjugate side while increasing the distance between them. The subgroup B1c has a negative lens and one or more positive lenses on the most magnification conjugate side among the lenses included in the subgroup B1c . The optical system of the present invention can also be applied as an imaging optical system for an imaging apparatus such as a digital camera.

図１（Ａ），（Ｂ）は本発明の実施例１の光学系の広角端と望遠端におけるレンズ断面図である。図２（Ａ），（Ｂ）は実施例１の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図である。図３（Ａ），（Ｂ），（Ｃ）は実施例１の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図である。図４（Ａ），（Ｂ），（Ｃ）は実施例１の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差図と投射距離６９０ｍｍにおける広角端における倍率色収差図である。 FIGS. 1A and 1B are lens cross-sectional views at the wide-angle end and the telephoto end of the optical system according to Example 1 of the present invention. 2A and 2B are lens cross-sectional views at a projection distance of 1210 mm and 690 mm at the wide angle end of the first embodiment. 3A, 3B, and 3C are aberration diagrams at the wide-angle end and the telephoto end at the projection distance of 1210 mm and aberration diagrams at the wide-angle end at the projection distance of 690 mm. 4A, 4B, and 4C are chromatic aberration diagrams at the wide angle end and the telephoto end at the projection distance of 1210 mm of the optical system of the first embodiment, and chromatic aberration diagrams at the wide angle end at the projection distance of 690 mm.

図５（Ａ），（Ｂ）は本発明の実施例２の光学系の広角端と望遠端におけるレンズ断面図である。図６（Ａ），（Ｂ）は実施例２の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図である。図７（Ａ），（Ｂ），（Ｃ）は実施例２の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図である。図８（Ａ），（Ｂ），（Ｃ）は実施例２の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差図と投射距離６９０ｍｍにおける広角端における倍率色収差図である。 5A and 5B are lens cross-sectional views at the wide-angle end and the telephoto end of the optical system according to Example 2 of the present invention. 6A and 6B are lens cross-sectional views at a projection distance of 1210 mm and 690 mm at the wide angle end of the second embodiment. 7A, 7B, and 7C are aberration diagrams at the wide-angle end and the telephoto end at the projection distance of 1210 mm and aberration diagrams at the wide-angle end at the projection distance of 690 mm. 8A, 8B, and 8C are chromatic aberration diagrams at the wide angle end and the telephoto end at the projection distance of 1210 mm of the optical system of Example 2, and chromatic aberration diagrams at the wide angle end at the projection distance of 690 mm.

図９（Ａ），（Ｂ）は本発明の実施例３の光学系の広角端と望遠端におけるレンズ断面図である。図１０（Ａ），（Ｂ）は実施例３の広角端において投射距離１２１０ｍｍ，６９０ｍｍにおけるレンズ断面図である。図１１（Ａ），（Ｂ），（Ｃ）は実施例３の光学系の投射距離１２１０ｍｍでの広角端と望遠端における収差図と投射距離６９０ｍｍにおける広角端における収差図である。図１２（Ａ），（Ｂ），（Ｃ）は実施例３の光学系の投射距離１２１０ｍｍでの広角端と望遠端における倍率色収差図と投射距離６９０ｍｍにおける広角端における倍率色収差図である。 9A and 9B are lens cross-sectional views at the wide-angle end and the telephoto end of the optical system according to Example 3 of the present invention. 10A and 10B are lens cross-sectional views at the projection distances of 1210 mm and 690 mm at the wide angle end of the third embodiment. 11A, 11B, and 11C are aberration diagrams at the wide-angle end and the telephoto end of the optical system of Example 3 at a projection distance of 1210 mm and aberration diagrams at a wide-angle end at a projection distance of 690 mm. 12A, 12B, and 12C are chromatic aberration diagrams at the wide angle end and the telephoto end at the projection distance of 1210 mm of the optical system of the third embodiment, and chromatic aberration diagrams at the wide angle end at the projection distance of 690 mm.

図１３（Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおけるレンズ断面図である。図１４（Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおける収差図である。図１５（Ａ），（Ｂ）は実施例４の光学系の投射距離１２１０ｍｍと投射距離６９０ｍｍにおける倍率色収差図である。   13A and 13B are lens cross-sectional views of the optical system of Example 4 at a projection distance of 1210 mm and a projection distance of 690 mm. 14A and 14B are aberration diagrams of the optical system of Example 4 at a projection distance of 1210 mm and a projection distance of 690 mm. FIGS. 15A and 15B are chromatic aberration diagrams of magnification at the projection distance of 1210 mm and the projection distance of 690 mm of the optical system of the fourth embodiment.

図１６は本発明の光学系を有する画像投射装置（プロジェクター）の要部概略図である。各実施例の光学系は画像投射装置（プロジェクター）に用いられる投射レンズ（投射光学系）である。レンズ断面図において、左方がスクリーン（拡大共役側），（物体側）、右方が被投射画像側（画像表示素子側），（縮小共役側），（像側）である。レンズ断面図において、ＬＡは光学系である。 FIG. 16 is a schematic diagram of a main part of an image projection apparatus (projector) having the optical system of the present invention. The optical system of each embodiment is a projection lens (projection optical system) used in an image projection apparatus (projector). In the lens cross-sectional view, the left side is the screen (enlarged conjugate side), (object side), and the right side is the projected image side (image display element side), (reduced conjugate side), (image side) . In the lens cross-sectional view, LA is an optical system.

実施例１乃至３の光学系はズームレンズより構成され、実施例４の光学系は単一焦点距離の投射レンズである。ｉは拡大共役側からのレンズ群の順番を示し、Ｂｉは第ｉレンズ群である。ＬＲは１以上のレンズ群よりなる後群である。Ｂ１ａ，Ｂ１ｂ，Ｂ１ｃは各々第１レンズ群Ｂ１を構成する部分群である。ＳＴは開口絞りである。ＩＰは液晶パネル（画像表示素子）等の原画像（被投射画像）に相当している。   The optical systems of Examples 1 to 3 are configured by a zoom lens, and the optical system of Example 4 is a single focal length projection lens. i indicates the order of the lens groups from the magnification conjugate side, and Bi is the i-th lens group. LR is a rear group composed of one or more lens groups. B1a, B1b, and B1c are partial groups constituting the first lens group B1. ST is an aperture stop. IP corresponds to an original image (projected image) such as a liquid crystal panel (image display element).

本実施例では原画を形成する画像表示素子が配置される。Ｓはスクリーン面である。ＰＲは色分解、色合成用のプリズム、光学フィルター、フェースプレート（平行平板ガラス）、水晶ローパスフィルター、赤外カットフィルター等に相当する光学ブロックである。 In this embodiment, an image display element for forming an original image is arranged. S is the screen surface . PR is an optical block corresponding to a prism for color separation and color synthesis, an optical filter, a face plate (parallel plate glass), a quartz low-pass filter, an infrared cut filter, and the like.

図１，図５，図９において矢印は広角端から望遠端へのズーミングの際のレンズ群の移動方向（移動軌跡）を示している。図２，図６，図１０において矢印は広角端において無限遠から至近へのフォーカシングに際しての部分群の移動方向を示している。図１３において矢印は無限遠から至近へのフォーカシングに際しての部分群の移動方向を示している。 1, 5, and 9, arrows indicate the moving direction (movement locus) of the lens unit during zooming from the wide-angle end to the telephoto end. 2, 6, Oite arrows in FIG. 1 0 shows the movement direction of the subgroup of during focusing from infinity to a close at the wide-angle end. In FIG. 13, the arrows indicate the moving directions of the subgroups during focusing from infinity to close.

実施例１乃至３のズームレンズよりなる光学系について説明する。実施例１乃至３のズームレンズにおいて広角端と望遠端は変倍用のレンズ群が機構上光軸上を移動可能な範囲の両端に位置したときのズーム位置をいう。実施例１乃至３のズームレンズは拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群Ｂ１、後群ＬＲよりなっている。後群ＬＲは正の屈折力の第２レンズ群Ｂ２、正の屈折力の第３レンズ群Ｂ３、正の屈折力の第４レンズ群Ｂ４、正の屈折力の第５レンズ群Ｂ５より成る。   An optical system including the zoom lenses of Examples 1 to 3 will be described. In the zoom lenses of Embodiments 1 to 3, the wide-angle end and the telephoto end are zoom positions when the lens groups for zooming are positioned at both ends of the range in which the mechanism can move on the optical axis. The zoom lenses according to the first to third embodiments include, in order from the magnification conjugate side to the reduction conjugate side, a first lens unit B1 having a negative refractive power and a rear unit LR. The rear group LR includes a second lens group B2 having a positive refractive power, a third lens group B3 having a positive refractive power, a fourth lens group B4 having a positive refractive power, and a fifth lens group B5 having a positive refractive power.

そしてズーミングに際して第１レンズ群Ｂ１と、第５レンズ群Ｂ５は不動である。広角端から望遠端へのズーミングに際して第２レンズ群Ｂ２と、第３レンズ群Ｂ３、第４レンズ群Ｂ４が互いに異なった軌跡で拡大共役側へ移動する。第１レンズ群Ｂ１は拡大共役側から縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成される。無限遠から至近へのフォーカシングに際して（投射距離が遠方から近距離になるに従って）部分群Ｂ１ｂと部分群Ｂ１ｃは縮小共役側へ双方の間隔を拡大しつつ移動する。   During zooming, the first lens unit B1 and the fifth lens unit B5 do not move. During zooming from the wide-angle end to the telephoto end, the second lens unit B2, the third lens unit B3, and the fourth lens unit B4 move toward the magnification conjugate side along different paths. The first lens unit B1 includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c. At the time of focusing from infinity to the close distance (as the projection distance is changed from the far distance to the short distance), the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between the two.

実施例４の光学系は拡大共役側から縮小共役側へ順に負の屈折力の第１レンズ群Ｂ１、後群ＬＲよりなっている。後群ＬＲは正の屈折力のレンズ群よりなっている。第１レンズ群Ｂ１は拡大共役側から縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成される。無限遠から至近へのフォーカシングに際して（投射距離が遠方から近距離になるに従って）部分群Ｂ１ｂと部分群Ｂ１ｃは縮小共役側へ双方の間隔を拡大しつつ移動する。   The optical system of Example 4 includes a first lens unit B1 having a negative refractive power and a rear unit LR in order from the magnification conjugate side to the reduction conjugate side. The rear group LR includes a lens group having a positive refractive power. The first lens unit B1 includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c. At the time of focusing from infinity to the close distance (as the projection distance is changed from the far distance to the short distance), the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between the two.

球面収差図において実線は波長５５０ｎｍを示している。非点収差図において点線はメリディオナル像面、実線はサジタル像面を示す。ＦｎｏはＦナンバー、ωは半画角（度）である。また、収差図において球面収差は０．１ｍｍ、非点収差は０．１ｍｍ、歪曲は０．５％のスケールで描いている。球面収差図と非点収差図においてFOCUS,0.0とは近軸像点ではなく、各像高の収差量を加味してバランスをとった像面位置としている。図４，図８，図１２，図１５の倍率色収差図においては、基準波長（５５０ｎｍ）に対する各色（波長６２０ｎｍ，波長５７０ｎｍ，波長４４０ｎｍ）を表わしている。 In the spherical aberration diagram, the solid line indicates the wavelength of 550 nm . In the astigmatism diagram, the dotted line indicates the meridional image plane, and the solid line indicates the sagittal image plane. Fno is an F number, and ω is a half angle of view (degrees). In the aberration diagrams, spherical aberration is drawn at a scale of 0.1 mm, astigmatism is drawn at a scale of 0.1 mm, and distortion is drawn at a scale of 0.5%. In the spherical aberration diagram and the astigmatism diagram, FOCUS, 0.0 is not a paraxial image point, but a balanced image plane position in consideration of the amount of aberration at each image height. In the lateral chromatic aberration diagrams of FIGS. 4, 8, 12, and 15, each color (wavelength 620 nm, wavelength 570 nm, wavelength 440 nm) with respect to the reference wavelength (550 nm) is shown.

次に本発明の光学系より好ましい構成について説明する。各実施例では被投射画像をスクリーンに投射するものであるが、説明を簡単にするために光束の通過順として拡大共役側のスクリーン（物体）からの光束が縮小共役側の被投射画像（像面）に入射して結像するものとして説明する。各実施例において、部分群Ｂ１ｂの屈折力をφＢ１ｂ、部分群Ｂ１ｃの屈折力をφＢ１ｃ、第１レンズ群の屈折力をφＢ１、第１レンズ群に含まれる正レンズの屈折力の総和をφＬ１ｐとする。   Next, a more preferable configuration than the optical system of the present invention will be described. In each embodiment, the projected image is projected onto the screen. However, in order to simplify the explanation, the light flux from the screen (object) on the enlargement conjugate side is projected on the reduction conjugate side (image) as the order of passage of the light flux. In the following description, it is assumed that an image is formed by being incident on the surface. In each embodiment, the refractive power of the subgroup B1b is φB1b, the refractive power of the subgroup B1c is φB1c, the refractive power of the first lens group is φB1, and the total refractive power of the positive lenses included in the first lens group is φL1p. To do.

部分群Ｂ１ｃの最も拡大共役側の負レンズの屈折力をφＢ１ｃｎとする。部分群Ｂ１ａの最も拡大共役側の正レンズの屈折力をφＢ１ａｐ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。
−１．０００＜φＢ１ｃ／φＢ１＜−０．００５ ・・・（１）
０．６＜φＢ１ｂ／φＢ１＜３．０ ・・・（２）
−２．５＜φＬ１ｐ／φＢ１＜−１．０ ・・・（３）
０．１＜φＢ１ｃｎ／φＢ１＜２．０ ・・・（４）
−０．１５＜φＢ１ａｐ／φＢ１＜−０．０１ ・・・（５） Let the refractive power of the negative lens closest to the magnification conjugate in the subgroup B1c be φB1cn. The refractive power of the positive lens closest to the magnification conjugate in the subgroup B1a is denoted by φB1ap. At this time, one or more of the following conditional expressions should be satisfied.
-1,000 <φB1c / φB1 <−0.005 (1)
0.6 <φB1b / φB1 <3.0 (2)
-2.5 <φL1p / φB1 <−1.0 (3)
0.1 <φB1cn / φB1 <2.0 (4)
−0.15 <φB1ap / φB1 <−0.01 (5)

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（１）は部分群Ｂ１ｃの正のパワー（屈折力）に関する。条件式（１）の下限を超えて部分群Ｂ１ｃの正のパワーが弱くなりすぎると、フォーカシングの際の移動量が増大し、全系が大型化してくる。条件式（１）の上限を超えて部分群Ｂ１ｃのパワーが強くなりすぎると、フォーカシングに際して像面湾曲等の収差変動が大きくなり全物体距離にわたり光学性能を良好に維持するのが困難になる。また、部分群Ｂ１ｃは最も拡大共役側に少なくとも１つの負レンズと、負レンズの縮小共役側に少なくとも１つの正レンズをもつ構成とするのが良い。   Next, the technical meaning of each conditional expression described above will be described. Conditional expression (1) relates to the positive power (refractive power) of the subgroup B1c. If the lower limit of conditional expression (1) is exceeded and the positive power of the subgroup B1c becomes too weak, the amount of movement during focusing increases and the entire system becomes larger. If the power of the subgroup B1c becomes too strong beyond the upper limit of the conditional expression (1), aberration fluctuations such as field curvature become large during focusing, and it becomes difficult to maintain good optical performance over the entire object distance. Further, it is preferable that the subgroup B1c has at least one negative lens on the most magnification conjugate side and at least one positive lens on the reduction conjugate side of the negative lens.

このとき拡大共役側の負レンズは倍率色収差をアンダー側へ発生させる事でレンズ全体の倍率色収差を補正する機能を持つ。更に、軸外主光線を光軸から離れる方向に曲げる（屈折させる）事で縮小共役側に配置した正レンズに入射する軸上光線の入射高を大きくする事で正レンズの倍率色収差の補正効果を高めるのが容易になる。部分群Ｂ１ｂは主に部分群Ｂ１ｃのフォーカシングの際に生じる像面湾曲等の収差変動を補正する。部分群Ｂ１ｂは強い負のパワーを持ち、フォーカシングに際して像面湾曲等の収差変動を補正している。また部分群Ｂ１ｂは、複数の負レンズで負のパワーを分散させている。   At this time, the negative lens on the magnification conjugate side has a function of correcting the chromatic aberration of magnification of the entire lens by generating chromatic aberration of magnification to the under side. Furthermore, by correcting (refracting) the off-axis principal ray away from the optical axis, the incident height of the on-axis ray incident on the positive lens placed on the reduction conjugate side is increased, thereby correcting the lateral chromatic aberration of the positive lens. It becomes easy to increase. The subgroup B1b mainly corrects aberration fluctuations such as field curvature that occur during focusing of the subgroup B1c. The subgroup B1b has a strong negative power and corrects aberration fluctuations such as field curvature during focusing. In the subgroup B1b, negative power is dispersed by a plurality of negative lenses.

条件式（２）は部分群Ｂ１ｂの負の屈折力を適切に設定し、全ズーム域で良好な光学性能を確保しつつフォーカシングの際の収差変動をより低減させるためのものである。条件式（２）の下限を超えて、部分群Ｂ１ｂ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像面湾曲の変動の補正が困難になる。条件式（２）の上限を超えて、部分群Ｂ１ｂ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）負の像面湾曲が大きく発生してくる。また、部分群Ｂ１ａは最も拡大共役側は負レンズが配置され、１以上の正レンズを有するのが良い。これによれば歪曲収差の補正が容易になる。   Conditional expression (2) is for appropriately setting the negative refractive power of the subgroup B1b and further reducing aberration fluctuations during focusing while ensuring good optical performance in the entire zoom range. If the lower limit of conditional expression (2) is exceeded and the negative power of the subgroup B1b is weakened (if the absolute value of the negative refractive power is reduced), it becomes difficult to correct fluctuations in field curvature during focusing. If the upper limit of the conditional expression (2) is exceeded and the negative power of the subgroup B1b is increased (when the absolute value of the negative refractive power is increased), negative field curvature is greatly generated. Further, it is preferable that the subgroup B1a has a negative lens on the most conjugated side and has one or more positive lenses. This facilitates correction of distortion.

条件式（３）は第１レンズ群Ｂ１に含まれる正レンズの屈折力の総和に関し、全ズーム領域で良好な光学性能を確保しつつフォーカシングに際しての収差変動をより低減させるためのものである。条件式（３）の上限を超えて、正レンズの正のパワーの総和が小さくなりすぎると、歪曲収差の補正が過剰になるので良くない。条件式（３）の下限を超えて、正レンズの正のパワーの総和が大きくなりすぎると、歪曲収差の補正が困難になる。   Conditional expression (3) relates to the sum of the refractive powers of the positive lenses included in the first lens unit B1, and is intended to further reduce aberration fluctuations during focusing while ensuring good optical performance in the entire zoom range. If the upper limit of conditional expression (3) is exceeded and the sum of the positive powers of the positive lens becomes too small, correction of distortion will be excessive, which is not good. If the total of the positive powers of the positive lens becomes too large beyond the lower limit of conditional expression (3), it becomes difficult to correct distortion.

条件式（４）は部分群Ｂ１ｃの最も拡大共役側の負レンズの屈折力を適切に設定し、主に倍率色収差を良好に補正するためのものである。条件式（４）の上限を超えると倍率色収差が補正不足となり、また下限値を超えると倍率色収差が補正過剰になってくる。   Conditional expression (4) is for appropriately setting the refractive power of the negative lens closest to the magnification conjugate in the subgroup B1c and mainly correcting the lateral chromatic aberration favorably. If the upper limit of conditional expression (4) is exceeded, lateral chromatic aberration will be undercorrected, and if the lower limit is exceeded, lateral chromatic aberration will be overcorrected.

条件式（５）は部分群Ｂ１ａの正レンズのうち最も拡大共役側の正レンズの屈折力を適切に設定し、主に歪曲収差を良好に補正するためのものである。条件式（５）の上限値を超えると歪曲収差が補正不足となり、また下限値を超えると歪曲収差が補正過剰になってくる。   Conditional expression (5) is for appropriately setting the refractive power of the positive lens closest to the magnification conjugate among the positive lenses in the subgroup B1a, and mainly correcting distortion well. If the upper limit value of conditional expression (5) is exceeded, distortion will be undercorrected, and if the lower limit value is exceeded, distortion will be overcorrected.

更に好ましくは条件式（１）乃至（５）の数値範囲を次の如く設定するのが良い。
−０．９００＜φＢ１ｃ／φＢ１＜−０．００７ ・・・（１ａ）
０．７＜φＢ１ｂ／φＢ１＜２．６ ・・・（２ａ）
−２．２＜φＬ１ｐ／φＢ１＜−１．２ ・・・（３ａ）
０．２＜φＢ１ｃｎ／φＢ１＜１．９ ・・・（４ａ）
−０．１３＜φＢ１ａｐ／φＢ１＜−０．０３ ・・・（５ａ） More preferably, the numerical ranges of the conditional expressions (1) to (5) are set as follows.
−0.900 <φB1c / φB1 <−0.007 (1a)
0.7 <φB1b / φB1 <2.6 (2a)
−2.2 <φL1p / φB1 <−1.2 (3a)
0.2 <φB1cn / φB1 <1.9 (4a)
−0.13 <φB1ap / φB1 <−0.03 (5a)

尚、本発明の光学系と、原画を形成する画像表示素子とを有し、画像表示素子によって形成された原画を光学系によって投射する画像投射装置に用いたときは、投射半画角をω（度）とする。このとき、
３７°＜ω＜５０° ・・・（６）
なる条件式を満足するのが良い。条件式（６）の下限値を超えると倍率色収差が補正過剰となる。また上限値を超えると倍率色収差が補正不足になるとともに歪曲収差が増大してくる。 When the optical system of the present invention and an image display element that forms an original image are used in an image projection apparatus that projects the original image formed by the image display element by the optical system, the projection half angle of view is ω. (Degrees). At this time,
37 ° <ω <50 ° (6)
It is good to satisfy the following conditional expression. If the lower limit of conditional expression (6) is exceeded, the lateral chromatic aberration will be overcorrected. If the upper limit is exceeded, lateral chromatic aberration will be undercorrected and distortion will increase.

次に各実施例のレンズ構成について説明する。実施例１の光学系は画像投射装置に用いるズームレンズである。実施例１は拡大共役側から縮小共役側へ順に、負、正、正、正、正の屈折力の第１レンズ群Ｂ１乃至第５レンズ群Ｂ５より構成されている。後群ＬＲは第２レンズ群Ｂ２乃至第５レンズ群Ｂ５より構成されている。ズーミングに際して第２レンズ群Ｂ２乃至第４レンズ群Ｂ４が移動する。第１レンズ群Ｂ１と第５レンズ群Ｂ５はズーミングに際して不動である。ズーミングに際して不動の第１レンズ群Ｂ１は拡大共役側から縮小共役側に部分群Ｂ１ａ、部分Ｂ１ｂ、部分群Ｂ１ｃより構成されている。 Next, the lens configuration of each example will be described. The optical system of Example 1 is a zoom lens used in an image projection apparatus . The first exemplary embodiment includes, in order from the magnification conjugate side to the reduction conjugate side, the first lens unit B1 to the fifth lens unit B5 having negative, positive, positive, positive, and positive refractive powers. The rear group LR is composed of a second lens group B2 to a fifth lens group B5. During zooming, the second lens unit B2 to the fourth lens unit B4 move. The first lens unit B1 and the fifth lens unit B5 do not move during zooming. The first lens unit B1 that does not move during zooming includes a partial group B1a, a partial B1b, and a partial group B1c from the magnification conjugate side to the reduction conjugate side.

遠方から至近へのフォーカシングに際して部分群Ｂ１ｂと部分群Ｂ１ｃが縮小共役側に双方のレンズ系の間隔を広げながら移動する。部分群Ｂ１ａが不動であるためレンズ全長が一定となり、フォーカシングの際のレンズ重心の変化を軽減してメカ機構の簡易化を容易にしている。またレンズ全長の変化がないため外観上の品位を向上させる事が容易になる。ここでレンズ全長とは拡大共役側の第１レンズ面から縮小共役側の最終レンズ面までの距離（光学全長）に空気換算値のバックフォーカスの値を加えたものである。   During focusing from a distant place to a close place, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between both lens systems. Since the subgroup B1a is stationary, the total lens length is constant, and the change in the center of gravity of the lens during focusing is reduced to facilitate the mechanical mechanism. Further, since there is no change in the total lens length, it is easy to improve the appearance quality. Here, the total lens length is a distance (optical total length) from the first lens surface on the magnification conjugate side to the final lens surface on the reduction conjugate side plus the back focus value in terms of air.

遠方から至近へのフォーカシングの際に部分群Ｂ１ｂの移動量に対して部分群Ｂ１ｃの移動量の方が大きい部分群Ｂ１ｃにおいて軸外主光線の光軸からの入射高が小さくなるように構成している。これにより部分群Ｂ１ｃで主たるフォーカシングを行うときのフォーカシングに際して軸外収差の変動が少なくなるようにしている。   At the time of focusing from far to close, the incident height of the off-axis principal ray from the optical axis becomes smaller in the subgroup B1c where the movement amount of the subgroup B1c is larger than the movement amount of the subgroup B1b. ing. As a result, fluctuations in off-axis aberrations are reduced during focusing when main focusing is performed in the subgroup B1c.

各レンズ群及び各部分群のレンズ構成は、以下、拡大共役側から縮小共役側へ順に、次のとおりである。部分群Ｂ１ａは負レンズ、正レンズより構成され、部分群Ｂ１ｂは負レンズ、負レンズより構成され、部分群Ｂ１ｃは負レンズ、負レンズと正レンズを接合した接合レンズより構成されている。   The lens configuration of each lens group and each partial group is as follows in order from the magnification conjugate side to the reduction conjugate side. The subgroup B1a is composed of a negative lens and a positive lens, the subgroup B1b is composed of a negative lens and a negative lens, and the subgroup B1c is composed of a negative lens and a cemented lens obtained by cementing the negative lens and the positive lens.

第２レンズ群Ｂ２は１つの正レンズより構成されている。第３レンズ群Ｂ３は正レンズと負レンズを接合した接合レンズより構成されている。第４レンズ群Ｂ４は負レンズと正レンズを接合した接合レンズ、負レンズと正レンズを接合した接合レンズ、正レンズより構成されている。第５レンズ群Ｂ５は正レンズと負レンズを接合した接合レンズより構成されている。   The second lens group B2 is composed of one positive lens. The third lens unit B3 includes a cemented lens in which a positive lens and a negative lens are cemented. The fourth lens unit B4 includes a cemented lens in which a negative lens and a positive lens are cemented, a cemented lens in which a negative lens and a positive lens are cemented, and a positive lens. The fifth lens unit B5 includes a cemented lens in which a positive lens and a negative lens are cemented.

実施例２の光学系は、実施例１と同様のズームタイプよりなるズームレンズである。第１レンズ群Ｂ１のレンズ構成、フォーカシングに際してのレンズ系の移動条件は実施例１と同じである。第２レンズ群Ｂ２、第３レンズ群Ｂ３、第４レンズ群Ｂ４、第５レンズ群Ｂ５のレンズ構成も実施例１と同じである。   The optical system according to the second embodiment is a zoom lens having the same zoom type as that according to the first embodiment. The lens configuration of the first lens unit B1 and the moving conditions of the lens system during focusing are the same as in the first embodiment. The lens configurations of the second lens group B2, the third lens group B3, the fourth lens group B4, and the fifth lens group B5 are the same as those in the first embodiment.

実施例３の光学系は実施例１と同様のズームタイプよりなるズームレンズである。第１レンズ群Ｂ１が３つの部分群よりなり、フォーカシングに際しての部分群の移動条件は実施例１と同じである。各レンズ群及び各部分群のレンズ構成は以下、拡大共役側から縮小共役側へ順に次のとおりである。   The optical system of Example 3 is a zoom lens of the same zoom type as that of Example 1. The first lens unit B1 includes three subgroups, and the movement conditions of the subgroups during focusing are the same as those in the first embodiment. The lens configuration of each lens group and each partial group is as follows in order from the magnification conjugate side to the reduction conjugate side.

部分群Ｂ１ａは負レンズと正レンズより構成され、部分群Ｂ１ｂは負レンズより構成され、部分群Ｂ１ｃは負レンズ、負レンズと正レンズを接合した接合レンズより構成されてるい。第２レンズ群Ｂ２、第３レンズ群Ｂ３、第４レンズ群Ｂ４、第５レンズ群Ｂ５のレンズ構成は実施例１と同じである。   The subgroup B1a is composed of a negative lens and a positive lens, the subgroup B1b is composed of a negative lens, and the subgroup B1c is composed of a negative lens and a cemented lens obtained by cementing the negative lens and the positive lens. The lens configurations of the second lens group B2, the third lens group B3, the fourth lens group B4, and the fifth lens group B5 are the same as those in the first embodiment.

実施例４の光学系は単一の焦点距離よりなる投射レンズである。第１レンズ群Ｂ１が拡大共役側から縮小共役側へ順に、部分群Ｂ１ａ、部分群Ｂ１ｂ、部分群Ｂ１ｃより構成されている。遠方から至近へのフォーカシングに際して部分群Ｂ１ｂと部分群Ｂ１ｃが縮小共役側へ双方の間隔を広げながら移動する。部分群Ｂ１ａは不動である。部分群Ｂ１ａ、部分群Ｂ１ｂ、部分群Ｂ１ｃのレンズ構成は実施例１と同じである。   The optical system of Example 4 is a projection lens having a single focal length. The first lens unit B1 includes a partial group B1a, a partial group B1b, and a partial group B1c in order from the magnification conjugate side to the reduction conjugate side. In focusing from a distant place to a close place, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while widening both intervals. The subgroup B1a is immobile. The lens configurations of the subgroup B1a, the subgroup B1b, and the subgroup B1c are the same as those in the first embodiment.

後群ＬＲは拡大共役側から縮小共役側へ順に正レンズ、正レンズと負レンズの接合レンズ、負レンズと正レンズの接合レンズ、負レンズと正レンズの接合レンズ、正レンズと正レンズと負レンズの接合レンズより構成されている。   The rear group LR is in order from the magnification conjugate side to the reduction conjugate side, a positive lens, a cemented lens of a positive lens and a negative lens, a cemented lens of a negative lens and a positive lens, a cemented lens of a negative lens and a positive lens, a positive lens, a positive lens, and a negative lens. It consists of a cemented lens.

本発明の画像投射装置では光学系と、原画を形成する画像表示素子とを有し前記画像表示素子によって形成された原画を光学系によって投射する。   The image projection apparatus of the present invention has an optical system and an image display element for forming an original image, and projects the original image formed by the image display element by the optical system.

次に本発明の画像投射装置を図１６を用いて説明する。図１６において４１は光源である。４２は画像表示素子に対してむらの少ない照明を実現し、出射される光の偏光方向をＰ偏光またはＳ偏光の任意の方向にそろえる機能を有する照明光学系である。４３は照明光学系４２からの光を画像表示素子に対応した任意の色に分解する色分離光学系である。 Next, the image projection apparatus of the present invention will be described with reference to FIG. In FIG. 16, reference numeral 41 denotes a light source. Reference numeral 42 denotes an illumination optical system that realizes illumination with less unevenness on the image display element and has a function of aligning the polarization direction of emitted light to an arbitrary direction of P-polarized light or S-polarized light . A color separation optical system 43 separates light from the illumination optical system 42 into an arbitrary color corresponding to the image display element.

４７，４８，４９は入射した偏光を電気信号に応じて変調する反射型の液晶よりなる画像表示素子である。４４，４５は画像表示素子４７，４８，４９で変調に応じて、光を透過または反射させる偏光ビームスプリッタである。４６は各画像表示素子４７，４８，４９からの光を１つに合成する色合成光学系である。５０は色合成光学系４６で合成された光をスクリーン５１などの被投射物に投射する投射光学系である。５０に本発明の光学系を用いている。これにより、フォーカシングに際して諸収差の変化が良好に補正され、画面全体にわたり光学性能が良好な画像投射装置を得ている。 Reference numerals 47, 48, and 49 denote image display elements made of reflective liquid crystal that modulates incident polarized light according to an electric signal. Reference numerals 44 and 45 denote polarization beam splitters that transmit or reflect light according to modulation by the image display elements 47, 48, and 49. A color combining optical system 46 combines the light from the image display elements 47, 48, and 49 into one. Reference numeral 50 denotes a projection optical system that projects light synthesized by the color synthesis optical system 46 onto a projection object such as a screen 51. 50 uses the optical system of the present invention. Thereby, changes in various aberrations are favorably corrected during focusing, and an image projection apparatus having good optical performance over the entire screen is obtained.

以上、本発明の好ましい実施形態について説明したが、本発明はこれらの実施形態に限定されず、その要旨の範囲内で種々の変形及び変更が可能である。   As mentioned above, although preferable embodiment of this invention was described, this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

次に各実施例の光学系の数値実施例を示す。数値実施例（表Ａ）のレンズ構成中の面番号は、拡大共役側から縮小共役側に順に各レンズ面に付した番号である。ｒは各レンズ面の曲率半径、ｄはレンズ面ｉとレンズ面（ｉ＋１）との間の光軸上での間隔（物理的間隔）を示す。像側の４つの面はガラスブロックに相当する。   Next, numerical examples of the optical system of each embodiment will be shown. The surface number in the lens configuration of the numerical example (Table A) is a number assigned to each lens surface in order from the enlargement conjugate side to the reduction conjugate side. r represents the radius of curvature of each lens surface, and d represents the distance (physical distance) on the optical axis between the lens surface i and the lens surface (i + 1). The four surfaces on the image side correspond to glass blocks.

表中に可変と記載されている間隔は、フォーカシング又はズーミングに伴って変化する。また、ｎｄ，νｄはそれぞれ、各レンズを構成する材料のｄ線に対する屈折率とアッベ数を示している。また表Ａに数値実施例の光学系の焦点距離、開口比（Ｆナンバー）、半画角、レンズ光学全長（第１レンズ面から最終レンズ面までの距離）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（被投射面）までの空気換算長である。ズーム比、フォーカシング又はズーミング時の各レンズ群の間隔を示す。（表Ｂ）に、非球面形状を示すための非球面係数Ａ〜Ｆを示している。   The interval described as variable in the table changes with focusing or zooming. Further, nd and νd indicate the refractive index and the Abbe number for the d-line of the material constituting each lens, respectively. Table A shows the focal length, the aperture ratio (F number), the half angle of view, and the total lens optical length (distance from the first lens surface to the final lens surface) of the optical system of the numerical example. BF is a back focus, and is an air conversion length from the final lens surface to the image surface (projected surface). This indicates the distance between the lens groups during zoom ratio, focusing, or zooming. (Table B) shows aspherical coefficients A to F for indicating the aspherical shape.

ｙはレンズ面の径方向での座標を、ｘは光軸方向での座標を示す。また、Ｅ−Ｘは１０−Ｘを示す。このとき、非球面形状は次のとおりである。 y represents the coordinate in the radial direction of the lens surface, and x represents the coordinate in the optical axis direction. Furthermore, E-X indicates a 10 -X. At this time, the aspherical shape is as follows.

ｘ＝（ｙ２/Ｒ）/[１＋｛１−（１＋Ｋ）（ｙ２/Ｒ２）｝１/２]＋Ａｙ４＋Ｂｙ６＋Ｃｙ８＋Ｄｙ１０＋Ｅｙ１２＋Ｆｙ１４
また前述の各実施例と数値との関係を（表１）に示す。 x = (y 2 / R) / [1+ {1− (1 + K) (y 2 / R 2 )} 1/2 ] + Ay 4 + By 6 + Cy 8 + Dy 10 + Ey 12 + Fy 14
Table 1 shows the relationship between the above-described embodiments and numerical values.

数値実施例１

（Ａ） レンズ構成

広角 望遠
f（焦点距離） 12.65 15.18
F（開口比） 2.75 2.88
半画角（度） 45.8 40.6
光学全長 175.9
BF 40.3
ズーム比 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 10.89
r3 = 263.90 d3 = 2.85 n2 = 1.489 ν2 = 70.2
r4 = 1475.29 d4 =可変
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 9.72
r7 = -178.67 d7 = 1.50 n4 = 1.748 ν4 = 44.8
r8 = 41.53 d8 =可変
r9 = -93.95 d9 = 1.50 n5 = 1.623 ν5 = 60.3
r10 = 82.18 d10 = 1.97
r11 = 57.66 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 34.42 d12 =11.00 n7 = 1.746 ν7 = 28.3 ST
r13 = -59.35 d13 = 可変
r14 = 58.01 d14 = 3.39 n8 = 1.704 ν8 = 30.1
r15 = 287.08 d15 = 可変
r16 = 430.63 d16 = 2.77 n9 = 1.518 ν9 = 64.1
r17 = -30.81 d17 = 1.50 n10 =1.748 ν10 = 44.8
r18 = -67.44 d18 = 可変
r19 = ∞ d19 = 可変
r20 =-258.76 d20 = 1.00 n11 =1.746 ν11 = 28.3
r21 = 21.14 d21 = 6.43 n12 =1.518 ν12 = 64.1
r22 = -24.21 d22 = 1.20
r23 = -19.03 d23 = 1.00 n13 =1.856 ν13 = 32.3
r24 = 78.89 d24 = 4.13 n14 =1.518 ν14 = 64.1
r25 = -42.91 d25 = 0.50
r26 = 200.43 d26 = 7.21 n15 =1.498 ν15 = 81.5
r27 = -24.10 d27 = 可変
r28 = 97.24 d28 = 6.46 n16 =1.816 ν16 = 22.8
r29 = -38.83 d29 = 1.00 n17 =1.754 ν17 = 35.3
r30 =-162.87 d30 = 2.30
r31 = ∞ d31 =32.3 n18 =1.516 ν18 = 64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 =17.7 n19 =1.805 ν19 = 25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0
Numerical example 1

(A) Lens configuration

Wide angle telephoto
f (focal length) 12.65 15.18
F (aperture ratio) 2.75 2.88
Half angle of view (degrees) 45.8 40.6
Optical total length 175.9
BF 40.3
Zoom ratio 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 10.89
r3 = 263.90 d3 = 2.85 n2 = 1.489 ν2 = 70.2
r4 = 1475.29 d4 = variable
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 9.72
r7 = -178.67 d7 = 1.50 n4 = 1.748 ν4 = 44.8
r8 = 41.53 d8 = variable
r9 = -93.95 d9 = 1.50 n5 = 1.623 ν5 = 60.3
r10 = 82.18 d10 = 1.97
r11 = 57.66 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 34.42 d12 = 11.00 n7 = 1.746 ν7 = 28.3 ST
r13 = -59.35 d13 = variable
r14 = 58.01 d14 = 3.39 n8 = 1.704 ν8 = 30.1
r15 = 287.08 d15 = variable
r16 = 430.63 d16 = 2.77 n9 = 1.518 ν9 = 64.1
r17 = -30.81 d17 = 1.50 n10 = 1.748 ν10 = 44.8
r18 = -67.44 d18 = variable
r19 = ∞ d19 = variable
r20 = -258.76 d20 = 1.00 n11 = 1.746 ν11 = 28.3
r21 = 21.14 d21 = 6.43 n12 = 1.518 ν12 = 64.1
r22 = -24.21 d22 = 1.20
r23 = -19.03 d23 = 1.00 n13 = 1.856 ν13 = 32.3
r24 = 78.89 d24 = 4.13 n14 = 1.518 ν14 = 64.1
r25 = -42.91 d25 = 0.50
r26 = 200.43 d26 = 7.21 n15 = 1.498 ν15 = 81.5
r27 = -24.10 d27 = variable
r28 = 97.24 d28 = 6.46 n16 = 1.816 ν16 = 22.8
r29 = -38.83 d29 = 1.00 n17 = 1.754 ν17 = 35.3
r30 = -162.87 d30 = 2.30
r31 = ∞ d31 = 32.3 n18 = 1.516 ν18 = 64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 = 17.7 n19 = 1.805 ν19 = 25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0

変倍時 （2100mm） フォーカス時 （広角端）
群間隔 広角 望遠 群間隔 690mm 1210mm 5200mm
d13 34.75 17.43 d4 1.69 1.50 1.35
d15 14.81 20.70 d8 19.38 18.92 18.49
d18 1.50 4.94 d13(広角) 34.10 34.75 35.33
d19 21.39 20.14 d13(望遠） 16.78 17.43 18.01
d27 0.50 9.74
When zoomed (2100mm) When focused (wide-angle end)
Group spacing Wide angle Telephoto Group spacing 690mm 1210mm 5200mm
d13 34.75 17.43 d4 1.69 1.50 1.35
d15 14.81 20.70 d8 19.38 18.92 18.49
d18 1.50 4.94 d13 (wide angle) 34.10 34.75 35.33
d19 21.39 20.14 d13 (Telephoto) 16.78 17.43 18.01
d27 0.50 9.74

（Ｂ） 非球面係数

r1 K= 0 A=8.97E-06 B=-7.64E-09 C= 7.09E-12 D=-3.76E-15
E= 9.53E-19
r5 K= 0 A=5.18E-06 B=-6.56E-11 C=-2.41E-12 D=-3.30E-15
E= 3.40E-18
r6 K= 0 A=2.16E-05 B= 2.43E-09 C= 8.87E-12 D= 1.08E-13
E=-1.16E-16
(B) Aspheric coefficient

r1 K = 0 A = 8.97E-06 B = -7.64E-09 C = 7.09E-12 D = -3.76E-15
E = 9.53E-19
r5 K = 0 A = 5.18E-06 B = -6.56E-11 C = -2.41E-12 D = -3.30E-15
E = 3.40E-18
r6 K = 0 A = 2.16E-05 B = 2.43E-09 C = 8.87E-12 D = 1.08E-13
E = -1.16E-16

数値実施例２

（Ａ） レンズ構成

広角 望遠
f（焦点距離） 12.64 15.17
F（開口比） 2.75 2.88
半画角（度） 45.8 40.6
光学全長 165.8
BF 40.3
ズーム比 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 8.92
r3 = 120.51 d3 = 3.93 n2 = 1.489 ν2 = 70.4
r4 = 338.53 d4 = 可変
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 11.48
r7 = -64.32 d7 = 2.50 n4 = 1.748 ν4 = 44.8
r8 = 35.71 d8 = 可変
r9 = -869.50 d9 = 1.90 n5 = 1.623 ν5 = 60.3
r10 = 99.15 d10 = 0.50
r11 = 55.12 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 32.68 d12 =11.00 n7 = 1.761 ν7 = 27.6 ST
r13 = -65.45 d13 = 可変
r14 = 61.79 d14 = 3.39 n8 = 1.671 ν8 = 32.4
r15 = 572.05 d15 = 可変
r16 =-5554.56 d16 = 2.76 n9 = 1.518 ν9 = 64.1
r17 = -25.47 d17 = 0.75 n10 =1.675 ν10 = 52.0
r18 = -63.26 d18 = 可変
r19 = ∞ d19 = 可変
r20 = -376.24 d20 = 1.00 n11 =1.756 ν11 = 31.9
r21 = 20.69 d21 = 6.71 n12 =1.518 ν12 = 64.1
r22 = -22.83 d22 = 1.09
r23 = -18.86 d23 = 1.00 n13 =1.856 ν13 = 32.3
r24 = 73.85 d24 = 4.18 n14 =1.518 ν14 = 64.1
r25 = -43.52 d25 = 0.50
r26 = 156.35 d26 = 7.45 n15 =1.498 ν15 = 81.5
r27 = -24.34 d27 = 可変
r28 = 102.64 d28 = 5.54 n16 =1.816 ν16 = 22.8
r29 = -54.17 d29 = 1.00 n17 =1.754 ν17 = 35.3
r30 = -135.38 d30 = 2.30
r31 = ∞ d31 =32.3 n18 =1.516 ν18 = 64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 =17.7 n19 =1.805 ν19 = 25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0
Numerical example 2

(A) Lens configuration

Wide angle telephoto
f (focal length) 12.64 15.17
F (aperture ratio) 2.75 2.88
Half angle of view (degrees) 45.8 40.6
Optical total length 165.8
BF 40.3
Zoom ratio 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 8.92
r3 = 120.51 d3 = 3.93 n2 = 1.489 ν2 = 70.4
r4 = 338.53 d4 = variable
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 11.48
r7 = -64.32 d7 = 2.50 n4 = 1.748 ν4 = 44.8
r8 = 35.71 d8 = variable
r9 = -869.50 d9 = 1.90 n5 = 1.623 ν5 = 60.3
r10 = 99.15 d10 = 0.50
r11 = 55.12 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 32.68 d12 = 11.00 n7 = 1.761 ν7 = 27.6 ST
r13 = -65.45 d13 = variable
r14 = 61.79 d14 = 3.39 n8 = 1.671 ν8 = 32.4
r15 = 572.05 d15 = variable
r16 = -5554.56 d16 = 2.76 n9 = 1.518 ν9 = 64.1
r17 = -25.47 d17 = 0.75 n10 = 1.675 ν10 = 52.0
r18 = -63.26 d18 = variable
r19 = ∞ d19 = variable
r20 = -376.24 d20 = 1.00 n11 = 1.756 ν11 = 31.9
r21 = 20.69 d21 = 6.71 n12 = 1.518 ν12 = 64.1
r22 = -22.83 d22 = 1.09
r23 = -18.86 d23 = 1.00 n13 = 1.856 ν13 = 32.3
r24 = 73.85 d24 = 4.18 n14 = 1.518 ν14 = 64.1
r25 = -43.52 d25 = 0.50
r26 = 156.35 d26 = 7.45 n15 = 1.498 ν15 = 81.5
r27 = -24.34 d27 = variable
r28 = 102.64 d28 = 5.54 n16 = 1.816 ν16 = 22.8
r29 = -54.17 d29 = 1.00 n17 = 1.754 ν17 = 35.3
r30 = -135.38 d30 = 2.30
r31 = ∞ d31 = 32.3 n18 = 1.516 ν18 = 64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 = 17.7 n19 = 1.805 ν19 = 25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0

変倍時 （2100mm） フォーカス時 （広角端）
群間隔 広角 望遠 群間隔 690mm 1210mm 5200mm
d13 30.55 12.36 d4 1.66 1.50 1.36
d15 15.61 23.74 d8 16.10 15.89 15.59
d18 0.93 3.14 d13(広角) 30.18 30.55 30.99
d19 18.75 16.86 d13(望遠) 11.99 12.36 12.8
d27 0.50 10.23
When zoomed (2100mm) When focused (wide-angle end)
Group spacing Wide angle Telephoto Group spacing 690mm 1210mm 5200mm
d13 30.55 12.36 d4 1.66 1.50 1.36
d15 15.61 23.74 d8 16.10 15.89 15.59
d18 0.93 3.14 d13 (wide angle) 30.18 30.55 30.99
d19 18.75 16.86 d13 (Telephoto) 11.99 12.36 12.8
d27 0.50 10.23

（Ｂ） 非球面係数

r1 K= 0 A= 9.27E-06 B=-8.22E-09 C= 7.56E-12 D=-3.98E-15
E= 1.01E-18
r5 K= 0 A= 7.52E-06 B=-2.57E-09 C=-2.80E-12 D= 1.48E-15
E= 1.04E-19
r6 K= 0 A= 2.19E-05 B= 1.44E-09 C=-3.04E-12 D= 1.16E-13
E=-1.09E-16
(B) Aspheric coefficient

r1 K = 0 A = 9.27E-06 B = -8.22E-09 C = 7.56E-12 D = -3.98E-15
E = 1.01E-18
r5 K = 0 A = 7.52E-06 B = -2.57E-09 C = -2.80E-12 D = 1.48E-15
E = 1.04E-19
r6 K = 0 A = 2.19E-05 B = 1.44E-09 C = -3.04E-12 D = 1.16E-13
E = -1.09E-16

数値実施例３

（Ａ） レンズ構成

広角 望遠
f（焦点距離） 12.65 15.18
F（開口比） 2.75 2.88
半画角（度） 45.8 40.6
光学全長 165.8
BF 40.3
ズーム比 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.646 ν1 = 56.1
r2 = 47.00 d2 = 12.31
r3 =-2857.69 d3 = 2.22 n2 = 1.489 ν2 = 70.4
r4 = -451.23 d4 = 可変
r5 = 500.00 d5 = 2.00 n3 = 1.748 ν3 = 44.8
r6 = 45.00 d6 = 可変
r7 = -49.71 d7 = 2.50 n4 = 1.734 ν4 = 46.0
r8 = 45.12 d8 = 14.25
r9 = 71.91 d9 = 1.50 n5 = 1.933 ν5 = 18.9
r10 = 39.02 d10 =11.00 n6 = 1.761 ν6 = 27.6
r11 = -63.74 d11 = 可変
r12 = 82.46 d12 = 3.26 n7 = 1.507 ν7 = 60.9 ST
r13 =-505.79 d13 = 可変
r14 = 54.53 d14 = 4.15 n8 = 1.657 ν8 = 33.4
r15 = -50.50 d15 = 0.75 n9 = 1.748 ν9 = 44.8
r16 = 86.80 d16 = 可変
r17 = ∞ d17 = 可変
r18 = 344.04 d18 = 2.00 n10 =1.761 ν10 = 27.6
r19 = 21.20 d19 = 6.18 n11 =1.518 ν11 = 64.1
r20 = -27.67 d20 = 1.33
r21 = -20.04 d21 = 1.00 n12 =1.856 ν12 = 32.3
r22 = 95.16 d22 = 4.35 n13 =1.489 ν13 = 70.4
r23 = -35.04 d23 = 0.50
r24 = 157.61 d24 = 7.20 n14 =1.498 ν14 = 81.5
r25 = -26.02 d25 = 可変
r26 = 120.83 d26 = 6.22 n15 =1.816 ν15 = 22.8
r27 = -41.28 d27 = 1.00 n16 =1.761 ν16 = 27.6
r28 =-111.29 d28 = 2.30
r29 = ∞ d29 =32.3 n17 =1.516 ν18 = 64.1
r30 = ∞ d30 = 1.9
r31 = ∞ d31 =17.7 n18 =1.805 ν19 = 25.4
r32 = ∞ d32 = 5.0
r33 = ∞ d33 = 0.0
Numerical Example 3

(A) Lens configuration

Wide angle telephoto
f (focal length) 12.65 15.18
F (aperture ratio) 2.75 2.88
Half angle of view (degrees) 45.8 40.6
Optical total length 165.8
BF 40.3
Zoom ratio 1.20

r1 = 350.00 d1 = 3.00 n1 = 1.646 ν1 = 56.1
r2 = 47.00 d2 = 12.31
r3 = -2857.69 d3 = 2.22 n2 = 1.489 ν2 = 70.4
r4 = -451.23 d4 = variable
r5 = 500.00 d5 = 2.00 n3 = 1.748 ν3 = 44.8
r6 = 45.00 d6 = variable
r7 = -49.71 d7 = 2.50 n4 = 1.734 ν4 = 46.0
r8 = 45.12 d8 = 14.25
r9 = 71.91 d9 = 1.50 n5 = 1.933 ν5 = 18.9
r10 = 39.02 d10 = 11.00 n6 = 1.761 ν6 = 27.6
r11 = -63.74 d11 = variable
r12 = 82.46 d12 = 3.26 n7 = 1.507 ν7 = 60.9 ST
r13 = -505.79 d13 = variable
r14 = 54.53 d14 = 4.15 n8 = 1.657 ν8 = 33.4
r15 = -50.50 d15 = 0.75 n9 = 1.748 ν9 = 44.8
r16 = 86.80 d16 = variable
r17 = ∞ d17 = variable
r18 = 344.04 d18 = 2.00 n10 = 1.761 ν10 = 27.6
r19 = 21.20 d19 = 6.18 n11 = 1.518 ν11 = 64.1
r20 = -27.67 d20 = 1.33
r21 = -20.04 d21 = 1.00 n12 = 1.856 ν12 = 32.3
r22 = 95.16 d22 = 4.35 n13 = 1.489 ν13 = 70.4
r23 = -35.04 d23 = 0.50
r24 = 157.61 d24 = 7.20 n14 = 1.498 ν14 = 81.5
r25 = -26.02 d25 = variable
r26 = 120.83 d26 = 6.22 n15 = 1.816 ν15 = 22.8
r27 = -41.28 d27 = 1.00 n16 = 1.761 ν16 = 27.6
r28 = -111.29 d28 = 2.30
r29 = ∞ d29 = 32.3 n17 = 1.516 ν18 = 64.1
r30 = ∞ d30 = 1.9
r31 = ∞ d31 = 17.7 n18 = 1.805 ν19 = 25.4
r32 = ∞ d32 = 5.0
r33 = ∞ d33 = 0.0

変倍時 （2100mm） フォーカス時 （広角端）
群間隔 広角 望遠 群間隔 690mm 1210mm 5200mm
d11 30.40 7.30 d4 1.64 1.50 1.43
d13 0.50 13.25 d6 13.42 12.80 12.01
d16 13.38 16.76 d11(広角) 29.64 30.4 31.26
d17 18.80 16.85 d11(望遠) 6.54 7.3 8.16
d25 0.50 9.42
When zoomed (2100mm) When focused (wide-angle end)
Group spacing Wide angle Telephoto Group spacing 690mm 1210mm 5200mm
d11 30.40 7.30 d4 1.64 1.50 1.43
d13 0.50 13.25 d6 13.42 12.80 12.01
d16 13.38 16.76 d11 (wide angle) 29.64 30.4 31.26
d17 18.80 16.85 d11 (Telephoto) 6.54 7.3 8.16
d25 0.50 9.42

（Ｂ） 非球面係数

r1 K= 0 A= 7.73E-06 B=-6.68E-09 C= 6.52E-12 D=-3.62E-15
E= 1.02E-18
r5 K= 0 A= 3.81E-06 B=-2.51E-09 C=-2.04E-12 D= 1.47E-15
E= 9.76E-19
r6 K= 0 A= 1.43E-05 B=-1.29E-08 C= 4.28E-11 D=-7.85E-14
E= 5.18E-17
(B) Aspheric coefficient

r1 K = 0 A = 7.73E-06 B = -6.68E-09 C = 6.52E-12 D = -3.62E-15
E = 1.02E-18
r5 K = 0 A = 3.81E-06 B = -2.51E-09 C = -2.04E-12 D = 1.47E-15
E = 9.76E-19
r6 K = 0 A = 1.43E-05 B = -1.29E-08 C = 4.28E-11 D = -7.85E-14
E = 5.18E-17

数値実施例４

（Ａ） レンズ構成


f（焦点距離） 12.65
F（開口比） 2.75
半画角（度） 45.8
光学全長 178.7
BF 40.3


r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 10.80
r3 = 259.63 d3 = 3.23 n2 = 1.489 ν2 = 70.2
r4 = -4174.21 d4 = 可変
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 8.66
r7 = -467.15 d7 = 2.25 n4 = 1.746 ν4 = 49.3
r8 = 35.65 d8 = 可変
r9 = -113.94 d9 = 1.90 n5 = 1.623 ν5 = 60.3
r10 = 74.27 d10 = 3.93
r11 = 59.71 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 34.48 d12 =11 n7 = 1.761 ν7 = 27.5
r13 = -59.12 d13 = 可変
r14 = 79.53 d14 = 3.99 n8 = 1.704 ν8 = 30.1
r15 = 238.10 d15 =21.45
r16 =-1576.22 d16 = 4.02 n9 = 1.518 ν9 = 64.1
r17 = -26.86 d17 = 1.22 n10 =1.748 ν10 =44.8
r18 = -52.36 d18 = 0.5 ST
r19 = ∞ d19 =23.97
r20 = 1044.81 d20 = 1.00 n11 =1.746 ν11 =28.3
r21 = 21.37 d21 = 7.34 n12 =1.518 ν12 =64.1
r22 = -23.23 d22 = 1.17
r23 = -19.24 d23 = 1.00 n13 =1.856 ν13 =32.3
r24 = 78.21 d24 = 4.69 n14 =1.518 ν14 =64.1
r25 = -41.73 d25 = 0.50
r26 = 217.67 d26 = 8.29 n15 =1.498 ν15 =81.5
r27 = -25.00 d27 = 0.5
r28 = 101.92 d28 = 8.08 n16 =1.816 ν16 =22.8
r29 = -33.55 d29 = 1.00 n17 =1.754 ν17 =35.3
r30 = -228.67 d30 = 2.30
r31 = ∞ d31 = 32.3 n18 =1.516 ν18 =64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 = 17.7 n19 =1.805 ν19 =25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0
Numerical Example 4

(A) Lens configuration


f (focal length) 12.65
F (aperture ratio) 2.75
Half angle of view (degrees) 45.8
Optical total length 178.7
BF 40.3


r1 = 350.00 d1 = 3.00 n1 = 1.623 ν1 = 60.3
r2 = 47.00 d2 = 10.80
r3 = 259.63 d3 = 3.23 n2 = 1.489 ν2 = 70.2
r4 = -4174.21 d4 = variable
r5 = 500.00 d5 = 2.00 n3 = 1.696 ν3 = 53.2
r6 = 45.00 d6 = 8.66
r7 = -467.15 d7 = 2.25 n4 = 1.746 ν4 = 49.3
r8 = 35.65 d8 = variable
r9 = -113.94 d9 = 1.90 n5 = 1.623 ν5 = 60.3
r10 = 74.27 d10 = 3.93
r11 = 59.71 d11 = 1.50 n6 = 1.933 ν6 = 18.9
r12 = 34.48 d12 = 11 n7 = 1.761 ν7 = 27.5
r13 = -59.12 d13 = variable
r14 = 79.53 d14 = 3.99 n8 = 1.704 ν8 = 30.1
r15 = 238.10 d15 = 21.45
r16 = -1576.22 d16 = 4.02 n9 = 1.518 ν9 = 64.1
r17 = -26.86 d17 = 1.22 n10 = 1.748 ν10 = 44.8
r18 = -52.36 d18 = 0.5 ST
r19 = ∞ d19 = 23.97
r20 = 1044.81 d20 = 1.00 n11 = 1.746 ν11 = 28.3
r21 = 21.37 d21 = 7.34 n12 = 1.518 ν12 = 64.1
r22 = -23.23 d22 = 1.17
r23 = -19.24 d23 = 1.00 n13 = 1.856 ν13 = 32.3
r24 = 78.21 d24 = 4.69 n14 = 1.518 ν14 = 64.1
r25 = -41.73 d25 = 0.50
r26 = 217.67 d26 = 8.29 n15 = 1.498 ν15 = 81.5
r27 = -25.00 d27 = 0.5
r28 = 101.92 d28 = 8.08 n16 = 1.816 ν16 = 22.8
r29 = -33.55 d29 = 1.00 n17 = 1.754 ν17 = 35.3
r30 = -228.67 d30 = 2.30
r31 = ∞ d31 = 32.3 n18 = 1.516 ν18 = 64.1
r32 = ∞ d32 = 1.9
r33 = ∞ d33 = 17.7 n19 = 1.805 ν19 = 25.4
r34 = ∞ d34 = 5.0
r35 = ∞ d35 = 0.0

フォーカス時 （広角端）
群間隔 690mm 1210mm 5200mm
d4 1.75 1.50 1.39
d8 19.76 19.50 19.14
d13 19.69 20.67 22.51
During focus (wide-angle end)
Group spacing 690mm 1210mm 5200mm
d4 1.75 1.50 1.39
d8 19.76 19.50 19.14
d13 19.69 20.67 22.51

（Ｂ） 非球面係数

r1 K= 0 A= 8.60E-06 B=-7.20E-09 C= 6.55E-12 D=-3.25E-15
E= 7.67E-19
r5 K= 0 A= 2.50E-06 B= 1.41E-10 C=-7.20E-13 D=-2.16E-15
E= 1.59E-18
r6 K= 0 A= 1.78E-05 B=-1.73E-09 C=-5.56E-13 D= 1.15E-13
E=-1.55E-16
(B) Aspheric coefficient

r1 K = 0 A = 8.60E-06 B = -7.20E-09 C = 6.55E-12 D = -3.25E-15
E = 7.67E-19
r5 K = 0 A = 2.50E-06 B = 1.41E-10 C = -7.20E-13 D = -2.16E-15
E = 1.59E-18
r6 K = 0 A = 1.78E-05 B = -1.73E-09 C = -5.56E-13 D = 1.15E-13
E = -1.55E-16


Ｌ１ 第１レンズ群 Ｌ２ 第２レンズ群 Ｌ３ 第３レンズ群
Ｌ４ 第４レンズ群 Ｌ５ 第５レンズ群 ＬＲ 後群 L1 First lens group L2 Second lens group L3 Third lens group L4 Fourth lens group L5 Fifth lens group LR Rear group

Claims (12)

拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
前記部分群Ｂ１ｃは前記部分群Ｂ１ｃが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動することを特徴とする光学系。 In an optical system composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side,
The first lens group includes, in order from the enlargement conjugate side to the reduction conjugate side, negative refractive power of the subgroup B1a, negative refractive power of the subgroup B1b, is composed of subgroup B1c a positive refractive power,
The subgroup B1a has a negative lens which is most disposed on the enlargement conjugate side in the lens provided in the subgroup B1a, one or more positive lenses,
The subgroup B1c has a negative lens provided on the most magnification conjugate side among the lenses included in the subgroup B1c, and one or more positive lenses.
Infinity the subgroup B1c said partial group B1b during focusing to a close is to the reduction conjugate side, an optical system, characterized in that to move expanding both intervals. 前記部分群Ｂ１ｂの屈折力をφＢ１ｂ、前記部分群Ｂ１ｃの屈折力をφＢ１ｃ、前記第１レンズ群の屈折力をφＢ１、前記第１レンズ群に含まれる正レンズの屈折力の総和をφＬ１ｐとするとき、
−１．０００＜φＢ１ｃ／φＢ１＜−０．００５
０．６＜φＢ１ｂ／φＢ１＜３．０
−２．５＜φＬ１ｐ／φＢ１＜−１．０
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。 The refractive power of the partial group B1b is φB1b, the refractive power of the partial group B1c is φB1c, the refractive power of the first lens group is φB1, and the total refractive power of the positive lenses included in the first lens group is φL1p. When
-1,000 <φB1c / φB1 <−0.005
0.6 <φB1b / φB1 <3.0
−2.5 <φL1p / φB1 <−1.0
The optical system according to claim 1, wherein the following conditional expression is satisfied. 前記部分群Ｂ１ｃが備えるレンズのうち最も前記拡大共役側に設けられた負レンズの屈折力をφＢ１ｃｎ、前記第１レンズ群の屈折力をφＢ１とするとき、
０．１＜φＢ１ｃｎ／φＢ１＜２．０
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 Faibi1cn, the refractive power of the first lens group and φB1 most refractive power of the negative lens disposed on the enlargement conjugate side of the lens that the subgroup B1c comprises,
0.1 <φB1cn / φB1 <2.0
Optical system according to claim 1 or 2, characterized by satisfying the conditional expression. 前記部分群Ｂ１ａが備える前記１以上の正レンズのうち最も前記拡大共役側に設けられた正レンズの屈折力をφＢ１ａｐ、前記第１レンズ群の屈折力をφＢ１とするとき、
−０．１５＜φＢ１ａｐ／φＢ１＜−０．０１
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 said one or more φB1ap the refractive power of the positive lens disposed on the most the enlargement conjugation side of the positive lens, the refractive power of the first lens group φB1 of the subgroup B1a comprises,
−0.15 <φB1ap / φB1 <−0.01
Optical system according to any one of claims 1 to 3, characterized by satisfying the conditional expression. 前記拡大共役側から前記縮小共役側へ順に、前記部分群Ｂ１ａは負レンズ、正レンズより構成され、前記部分群Ｂ１ｂは負レンズ、負レンズより構成され、又は負レンズより構成され、前記部分群Ｂ１ｃは負レンズ、負レンズと正レンズの接合レンズより構成され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。 In order from the enlargement conjugate side to the reduction conjugate side, the subgroup B1a is composed of a negative lens, a positive lens, the partial group B1b negative lens, a negative lens, or is composed of a negative lens, the partial group The optical system according to any one of claims 1 to 4 , wherein B1c includes a negative lens and a cemented lens of a negative lens and a positive lens. 前記後群は前記拡大共役側から前記縮小共役側へ順に、正の屈折力の第２レンズ群、正の屈折力の第３レンズ群、正の屈折力の第４レンズ群、正の屈折力の第５レンズ群より構成され、広角端から望遠端へのズーミングに際して、前記第１レンズ群と前記第５レンズ群は不動で、前記第２レンズ群と前記第３レンズ群と前記第４レンズ群は互いに異なった軌跡で前記拡大共役側に移動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。 In order to the reduction conjugate side the rear group from the enlargement conjugate side, a second lens unit having positive refractive power, a third lens unit having positive refractive power, a fourth lens unit having a positive refractive power, positive refractive power In the zooming from the wide-angle end to the telephoto end, the first lens group and the fifth lens group do not move, and the second lens group, the third lens group, and the fourth lens are not moved. optical system according to any one of claims 1 to 5 group is characterized in that to move the enlargement conjugate side in mutually different trajectory. 拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、
前記部分群Ｂ１ｃが備えるレンズのうち最も前記拡大共役側に設けられた負レンズの屈折力をφＢ１ｃｎ、前記第１レンズ群の屈折力をφＢ１とするとき、
０．１＜φＢ１ｃｎ／φＢ１＜２．０
なる条件式を満足することを特徴とする光学系。 In an optical system composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side,
The first lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
When the refractive power of the negative lens provided closest to the magnification conjugate side among the lenses included in the partial group B1c is φB1cn, and the refractive power of the first lens group is φB1,
0.1 <φB1cn / φB1 <2.0
An optical system that satisfies the following conditional expression: 拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、In an optical system composed of a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side,
前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、The first lens group includes, in order from the magnification conjugate side to the reduction conjugate side, a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
前記部分群Ｂ１ａが備える前記１以上の正レンズのうち最も前記拡大共役側に設けられた正レンズの屈折力をφＢ１ａｐ、前記第１レンズ群の屈折力をφＢ１とするとき、When the refractive power of the positive lens provided closest to the magnification conjugate side among the one or more positive lenses included in the partial group B1a is φB1ap, and the refractive power of the first lens group is φB1,
−０．１５＜φＢ１ａｐ／φＢ１＜−０．０１−0.15 <φB1ap / φB1 <−0.01
なる条件式を満足することを特徴とする光学系。An optical system that satisfies the following conditional expression: 前記後群は正の屈折力のレンズ群より構成されることを特徴とする請求項１乃至８のいずれか１項に記載の光学系。 Optical system according to any one of claims 1 to 8 wherein the rear group is characterized in that it is composed of a lens unit having a positive refractive power. 拡大共役側から縮小共役側へ順に、負の屈折力の第１レンズ群、１以上のレンズ群を含む後群より構成される光学系において、前記第１レンズ群は前記拡大共役側から前記縮小共役側へ順に、負の屈折力の部分群Ｂ１ａ、負の屈折力の部分群Ｂ１ｂ、正の屈折力の部分群Ｂ１ｃより構成され、In an optical system including a first lens group having a negative refractive power and a rear group including one or more lens groups in order from the magnification conjugate side to the reduction conjugate side, the first lens group is reduced from the magnification conjugate side. In order to the conjugate side, it is composed of a negative refractive power subgroup B1a, a negative refractive power subgroup B1b, and a positive refractive power subgroup B1c.
前記部分群Ｂ１ａは前記部分群Ｂ１ａが備えるレンズのうち最も前記拡大共役側に設けられた負レンズと、１以上の正レンズを有し、The subgroup B1a includes a negative lens provided on the most magnifying conjugate side among lenses included in the subgroup B1a, and one or more positive lenses.
無限遠から至近へのフォーカシングに際して前記部分群Ｂ１ｂと前記部分群Ｂ１ｃは前記縮小共役側へ、双方の間隔を拡大しつつ移動し、During focusing from infinity to close, the subgroup B1b and the subgroup B1c move to the reduction conjugate side while increasing the distance between them,
前記後群は前記拡大共役側から前記縮小共役側へ順に、正の屈折力の第２レンズ群、正の屈折力の第３レンズ群、正の屈折力の第４レンズ群、正の屈折力の第５レンズ群より構成され、広角端から望遠端へのズーミングに際して、前記第１レンズ群と前記第５レンズ群は不動で、前記第２レンズ群と前記第３レンズ群と前記第４レンズ群は互いに異なった軌跡で前記拡大共役側に移動することを特徴とする光学系。The rear group includes, in order from the magnification conjugate side to the reduction conjugate side, a second lens group having a positive refractive power, a third lens group having a positive refractive power, a fourth lens group having a positive refractive power, and a positive refractive power. In the zooming from the wide-angle end to the telephoto end, the first lens group and the fifth lens group do not move, and the second lens group, the third lens group, and the fourth lens are not moved. The optical system is characterized in that the group moves to the enlargement conjugate side along different trajectories. 請求項１乃至１０のいずれか１項に記載の光学系と、原画を形成する画像表示素子とを有し、前記画像表示素子によって形成された原画を前記光学系によって投射することを特徴とする画像投射装置。 It has the optical system of any one of Claims 1 thru | or 10 , and the image display element which forms an original image, The original image formed of the said image display element is projected by the said optical system, It is characterized by the above-mentioned. Image projection device. 前記光学系の投射半画角をω（度）とするとき、
３７°＜ω＜５０°
なる条件式を満足することを特徴とする請求項１１に記載の画像投射装置。 When the projection half angle of view of the optical system is ω (degrees),
37 ° <ω <50 °
The image projection apparatus according to claim 11, wherein the following conditional expression is satisfied.
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