JPH03132617A - Ftheta lens system in optical scanner - Google Patents

Abstract

PURPOSE:To sufficiently correct the curvature of an image surface in main and sub scanning directions and to solve a problem of surface collapse in a rotary polygonal mirror by satisfying a specific condition between a synthetic focal distance in a deflecting intersection surface and the radii of curvature of first and second surface in the deflecting intersection surface including an optical axis. CONSTITUTION:The first surface is a (convex or concave cylinder surface or flat provided with a refracting power only in the deflecting intersection surface), and the second surface is a (concave saddle type toric surface whose radius of curvature in the deflecting intersection surface is increased as being separated from the optical axis), and a third surface is a (convex spherical surface), and a fourth surface is a (convex toric surface with high radius of curvature in the deflecting intersection sur face). Assuming the synthetic focal distance in the deflecting intersection surface as fs, and the radii of curvature of the first and second surfaces in the deflecting intersection surface including the optical axis as r'1, r'2, a condition expressed in equation 0.3<1{(1/r'1)-(1/r'2)}.fs¦<2.7 can be satisfied. Thereby, it is possible to correct the curvature of the image surface in the main and sub scanning directions satisfacto rily as correction the surface collapse of the rotary polygonal mirror, and to perform optical scan with high density.

Description

【発明の詳細な説明】 ［産業上の利用分野］ 本発明は、光走査装置におけるｆθレンズ系に関する。[Detailed description of the invention] [Industrial application field] The present invention relates to an fθ lens system in an optical scanning device.

［従来の技術］ 光走査装置は、光束の走査により情報の書き込みや読み
取りを行う装置として知られ、レーザープリンターやフ
ァクシミリ等に使用されている。[Prior Art] Optical scanning devices are known as devices that write and read information by scanning a beam of light, and are used in laser printers, facsimile machines, and the like.

このような光走査装置のうちに、光源装置からの略平行
な光束を主走査対応方向に長い線像に結像させ、その線
像の結像位置の近傍に反射面を有する回転多面鏡により
上記光束を等角速度的に偏向させ、この偏向光束を結像
レンズ系により被走査面上にスポット状に結像させて被
走査面を光走査する方式の装置がある。Among such optical scanning devices, a substantially parallel light beam from a light source device is imaged into a long line image in the direction corresponding to the main scanning direction, and a rotating polygon mirror having a reflective surface near the imaging position of the line image is used. There is an apparatus that optically scans the surface to be scanned by deflecting the above-mentioned light beam at a constant angular velocity and forming a spot image of the deflected light beam on the surface to be scanned using an imaging lens system.

回転多面鏡を用いる光走査装置には所謂面倒れの問題が
あり、また偏向される光束は回転多面鏡の角速度が一定
であるため通常のｆ−ｔａｎθレンズを用いたのでは被
走査面の走査が等速的に行わわない。そこで等速走査す
るための工夫が必要となる。ｆθレンズ系は、この被走
査面の定速的な走査を光学的に実現する様にしたレンズ
系であり、レンズ光軸に対してθなる角をもって入射す
る光束の像高が焦点距離をｆとしてｆθとなるようにす
るｆθ機能を有する。Optical scanning devices that use a rotating polygon mirror have the problem of so-called surface tilt, and since the angular velocity of the rotating polygon mirror is constant for the deflected light beam, it is difficult to scan the surface to be scanned using a normal f-tanθ lens. is not performed uniformly. Therefore, it is necessary to devise a method for uniform speed scanning. The fθ lens system is a lens system that optically realizes constant-speed scanning of the surface to be scanned, and the image height of the light beam that enters at an angle of θ with respect to the lens optical axis has a focal length of f. It has an fθ function that makes fθ as fθ.

また面倒れの問題を解決する方法とじては、回転多面鏡
と被走査面との間に設けられるレンズ系をアナモフィッ
ク系とし、副走査方向に関して回転多面鏡の反射位置と
被走査面とを共役関係に結び付ける方法が知られている
。Another way to solve the surface tilt problem is to use an anamorphic lens system installed between the rotating polygon mirror and the scanned surface, so that the reflection position of the rotating polygon mirror and the scanned surface are conjugated in the sub-scanning direction. There are known ways to connect them to relationships.

［発明が解決しようとする課題］ ｆθレンズ系自体をアナモフィックとし、定速的な走査
と面倒れの問題の解決とを図ったものは種々知られてい
る。例えば、特開昭６３．−１９６１７号公報には２枚
構成のものが開示されている。[Problems to be Solved by the Invention] Various types of fθ lens systems are known in which the fθ lens system itself is anamorphic to achieve constant speed scanning and to solve the problem of surface tilt. For example, JP-A-63. -19617 publication discloses a two-sheet configuration.

しかしこのｆθレンズ系は像面湾曲の補正が必ずしも十
分ではなく、被走査面上に於ける結像スポットの径が走
査位置によりかなり大きく変動するので高密度の光走査
の実現が困難である。However, in this f-theta lens system, the correction of field curvature is not necessarily sufficient, and the diameter of the imaged spot on the scanned surface varies considerably depending on the scanning position, making it difficult to realize high-density optical scanning.

また特開昭６１−１２０１１２号公報には像面湾曲を良
好に補正するために鞍型トーリック面を使用した２枚構
成のｆθレンズ系が開示されているが、このｆθレンズ
系は非球面を２面用いているために加工が難しいという
問題がある。Furthermore, Japanese Patent Application Laid-open No. 120112/1983 discloses a two-element f-theta lens system that uses a saddle-shaped toric surface to satisfactorily correct field curvature, but this f-theta lens system has an aspherical surface. There is a problem that processing is difficult because two surfaces are used.

本発明は上述した事情に鑑みてなされたものであって、
主・副走査方向の像面湾曲の十分な補正と、回転多面鏡
における面倒れの問題の解決とを可能ならしめた新規な
ｆθレンズ系の提供を目的とする。The present invention was made in view of the above-mentioned circumstances, and
The object of the present invention is to provide a novel fθ lens system that makes it possible to sufficiently correct field curvature in the main and sub-scanning directions and solve the problem of surface tilt in a rotating polygon mirror.

［課題を解決するための手段］ 以下１本発明を説明する。[Means to solve the problem] One aspect of the present invention will be explained below.

本発明のｆθレンズ系は、「光源装置からの略平行な光
束を主走査対応方向に長い線像に結像させ、その線像の
結像位置の近傍に反射面を有する回転多面鏡により上記
光束を等角速度的に偏向させ、この偏向光束を結像レン
ズ系により被走査面上にスポット状に結像させて被走査
面を略等速的に光走査する光走査装置において、回転多
面鏡により偏向された光束を被走査面上に結像させる結
像レンズ系」であって、［副走査方向に関しては回転多
面鏡の反射位置と被走査面とを幾何光学的に略共役な関
係に結び付ける機能」を持ち、「主走査方向に関しては
ｆθ機能」を有する。The fθ lens system of the present invention focuses a substantially parallel light beam from a light source device into a long line image in a direction corresponding to the main scanning direction, and uses a rotating polygon mirror having a reflective surface near the imaging position of the line image to In an optical scanning device that deflects a light beam at a constant angular velocity and images the deflected light beam in a spot shape on the scanned surface using an imaging lens system to optically scan the scanned surface at approximately constant speed, a rotating polygon mirror is used. An imaging lens system that forms an image of the light beam deflected by It has an "fθ function in the main scanning direction."

また、このｆθレンズ系は、回転多面鏡の側から被走査
面側へ向かって第１、第２の順に配備される第１および
第２のレンズにより構成される２群・２枚構成である。Furthermore, this fθ lens system has a two-group, two-lens configuration consisting of a first lens and a second lens, which are arranged in the order of first and second from the rotating polygon mirror side toward the surface to be scanned. .

回転多面鏡により理想的に偏向された光束の主光線の掃
引により形成される面を「偏向面」と称し、結像レンズ
系の光軸に平行で偏向面に直交する面を「偏向直交面」
と言う。The surface formed by sweeping the principal ray of the light beam ideally deflected by the rotating polygon mirror is called the "deflection surface", and the surface parallel to the optical axis of the imaging lens system and perpendicular to the deflection surface is called the "deflection orthogonal surface". ”
Say.

回転多面鏡の側から数えて各レンズ面を第１乃至第４面
とするとき、これらのレンズ面の偏向面内での形状が第
１面から第４面に向かって順次「直線、円弧１円弧、円
弧」であり、偏向面に平行な面内では第１、第２のレン
ズとも正の屈折力を持つ。When each lens surface is counted from the side of the rotating polygon mirror as the first to fourth surfaces, the shapes of these lens surfaces within the deflection plane are sequentially "straight line, circular arc 1" from the first surface to the fourth surface. The first lens is a circular arc, a circular arc, and both the first and second lenses have positive refractive power in a plane parallel to the deflection plane.

上記第１面は［偏向直交面内にのみ屈折力を持つ凸もし
くは凹のシリンダー面または平面」、第２面は「偏向直
交面内の曲率半径が光軸から離れるに従い大きくなる凹
の鞍型トーリック面」、第３面は「凹の球面」、第４面
は「偏向直交面内に強い曲率を持つ凸のトーリック面」
である。The first surface is a convex or concave cylindrical surface or plane that has refractive power only in the plane orthogonal to deflection, and the second surface is a concave saddle shape in which the radius of curvature in the plane orthogonal to deflection increases as it moves away from the optical axis. The third surface is a "concave spherical surface" and the fourth surface is a "convex toric surface with strong curvature in the plane perpendicular to deflection."
It is.

偏向直交面内における合成焦点距離をｆｓ、光軸を含む
偏向直交面内に於ける上記第１．第２面の曲率半径をそ
れぞれｒｌｔｒ２とするとこれらは（Ｉ）　　　　０．
３　　＜Ｉ（（１／ｒ＋）−（１／ｒｚ））・ｆｓｌ＜
　　２．７なる条件を満足する。The resultant focal length in the plane orthogonal to deflection is fs, and the first point in the plane orthogonal to deflection including the optical axis is fs. Assuming that the radius of curvature of the second surface is rltr2, these are (I) 0.
3 <I((1/r+)-(1/rz))・fsl<
2.7 conditions are satisfied.

ここで第１図を参照して１本発明のｆθレンズ系の各レ
ンズ面を説明する。Here, each lens surface of the fθ lens system of the present invention will be explained with reference to FIG.

第１図に於いて、図の左側は回転多面鏡の側、右側は被
走査面の側であり、従ってレンズは左側が第１のレンズ
、右側が第２のレンズを表しており、レンズ面は左から
右へ向かって原次第１乃至第４面である。第１図の上側
の図は、ｆθレンズ系の偏向面内でのレンズ形状を表し
、下側の図は光軸を含む偏向直交面内でのレンズ形状を
表している。偏向面内におけるレンズ面形状は、第１図
の上の図のように第１ないし第４レンズ面が、順に直線
、円弧１円弧、円弧である。偏向面に平行な面内での屈
折力は、第１．第２のレンズとも正である。第１図には
また。上記偏向面、偏向直交面内でのレンズ機能が「凸
」であるか「凹」であるかを表示しである。偏向面はそ
の被走査面との交線が理想的な主走査方向に対応するの
で、第１図の上の図は「主」と表示しである。同様に、
上記偏向直交面は副走査方向と対応するので第１図の下
の図は「副」と表示しである。第１図下図のように第１
面の偏向直交面内での形状は１円弧（実線および破線）
または直線（鎖線）であり、この形状が破線の円弧のと
きは第１面が凸のシリンダー面、実線の円弧のときは凹
のシリンダー面、鎖線で示す直線形状のときは平面であ
る。In Figure 1, the left side of the figure is the side of the rotating polygon mirror, and the right side is the side of the scanned surface.Therefore, the left side represents the first lens, the right side represents the second lens, and the lens surface From left to right, these are the first to fourth sides of Harajima. The upper diagram in FIG. 1 shows the lens shape in the deflection plane of the fθ lens system, and the lower diagram shows the lens shape in the plane orthogonal to the deflection plane that includes the optical axis. As shown in the upper diagram of FIG. 1, the shape of the lens surface within the deflection plane is such that the first to fourth lens surfaces are, in order, a straight line, one circular arc, and a circular arc. The refractive power in a plane parallel to the deflection plane is the first. The second lens is also positive. Also in Figure 1. This indicates whether the lens function in the deflection plane or plane orthogonal to the deflection plane is “convex” or “concave”. Since the line of intersection of the deflection surface with the surface to be scanned corresponds to the ideal main scanning direction, the upper diagram in FIG. 1 is indicated as "main". Similarly,
Since the plane orthogonal to the deflection plane corresponds to the sub-scanning direction, the lower part of FIG. 1 is labeled as "sub". As shown in Figure 1 below,
The shape in the plane perpendicular to the deflection of the surface is one circular arc (solid line and broken line)
Or it is a straight line (dashed line), and when this shape is a broken line arc, the first surface is a convex cylindrical surface, when it is a solid line arc, it is a concave cylindrical surface, and when it is a straight line shape shown by a chain line, it is a flat surface.

［作　　用］ 上記条件（１）に付き説明する。[For production] The above condition (1) will be explained.

上記の如きレンズ面構成でｆθレンズ系を構成すること
により主・副走査方向の像面湾曲の良好な補正が可能に
なる。By configuring the fθ lens system with the lens surface configuration as described above, it is possible to satisfactorily correct field curvature in the main and sub-scanning directions.

しかし主走査方向の像面湾曲を良好に補正した状態に於
いて、副走査方向の像面湾曲を有効に補正するには、さ
らに上記条件（Ｉ）の充足が必要となる。即ち上記の面
構成でレンズ構成して面倒れの補正を行った場合、副走
査方向の像面湾曲は、条件（１）の下限を越えるとアン
ダー側に、上限を越えるとオーバー側にそれぞれ顕著に
発生する。However, in a state where the curvature of field in the main scanning direction has been well corrected, in order to effectively correct the curvature of field in the sub-scanning direction, it is further necessary to satisfy the above condition (I). In other words, when the lens is configured with the above surface configuration and the surface tilt is corrected, the field curvature in the sub-scanning direction will be noticeable on the under side when the lower limit of condition (1) is exceeded, and on the over side when the upper limit is exceeded. occurs in

従って条件（１）を外れると結像性能が低下し、副走査
方向の光スポツト径の変動が大きくなり良好な光走査を
実現するのが困難となる。逆に、上記条件（Ｉ）を満足
する場合は、第２面の凹の鞍型トーリック面の［副走査
方向の像面湾曲補正機能」が良好に発揮される。Therefore, if condition (1) is not met, the imaging performance will deteriorate and the variation in the optical spot diameter in the sub-scanning direction will increase, making it difficult to achieve good optical scanning. Conversely, when the above condition (I) is satisfied, the ``field curvature correction function in the sub-scanning direction'' of the concave saddle-shaped toric surface of the second surface is well exhibited.

次に第２図を参照すると、この図はｆθレンズ系を用い
た光走査装置の１例を説明図的に略示している。また第
３図は、第２図の光学配置を副走査方向から見た状態、
即ち偏向面内での様子を示している。Next, referring to FIG. 2, this figure schematically illustrates an example of an optical scanning device using an fθ lens system. In addition, FIG. 3 shows the optical arrangement in FIG. 2 viewed from the sub-scanning direction.
That is, it shows the situation within the deflection plane.

第２図に於いて、光源もしくは光源と集光装置とからな
る光源装置１からの平行光束は線像結像光学系たるシリ
ンダーレンズ２により、回転多面鏡３の反射面３ａの近
傍に偏向面と略平行な線像ＬＩとして結像する。この線
像ＬＩの長手方向は主走査対応方向である。In FIG. 2, a parallel light beam from a light source device 1 consisting of a light source or a light source and a condensing device is directed to a deflection surface near the reflecting surface 3a of a rotating polygon mirror 3 by a cylinder lens 2 which is a line image forming optical system. The image is formed as a line image LI that is approximately parallel to the line image LI. The longitudinal direction of this line image LI corresponds to the main scanning direction.

回転多面鏡３により反射された光束は、ｆθレンズ系に
より被走査面６上にスポット状に結像され１回転多面鏡
３の矢印方向への等速回転に従い被走査面６を等速的に
走査する。The light beam reflected by the rotating polygon mirror 3 is imaged into a spot on the scanned surface 6 by the fθ lens system, and is uniformly scanned across the scanned surface 6 as the single-rotation polygon mirror 3 rotates at a constant speed in the direction of the arrow. scan.

ｆ＆レンズ系は第１のレンズ４と第２のレンズ５とによ
り構成され、レンズ４は回転多面鏡３の鍔、レンズ５は
被走査面６の側にそれぞれ配設される。偏向面内で見る
と第３図に示すように、レンズ４，５によるｆθレンズ
系は光源装置１側の無限遠と被走査面６の位置とを幾何
光学的な共役関係に結び付けている。The f& lens system is composed of a first lens 4 and a second lens 5, with the lens 4 being disposed on the flange of the rotating polygon mirror 3, and the lens 5 being disposed on the side of the surface to be scanned 6, respectively. When viewed in the deflection plane, as shown in FIG. 3, the fθ lens system including lenses 4 and 5 connects infinity on the light source device 1 side and the position of the scanned surface 6 in a geometrically optical conjugate relationship.

これに対し偏向直交面内で見ると、即ち副走査方向に関
してはｆθレンズ系は回転多面鏡３の反射位置と被走査
面６とを幾何光学的に略共役な関係に結び付けている。On the other hand, when viewed in the plane perpendicular to the deflection, that is, in the sub-scanning direction, the fθ lens system connects the reflection position of the rotating polygon mirror 3 and the surface to be scanned 6 in a geometrically optically substantially conjugate relationship.

従って、第４図に示すように反射面３ａが符号３ａ’　
で示すように面倒れを生じてもｆθレンズ系による被走
査面６上の結像位置は、副走査方向（第４図上下方向）
には殆ど移動しない。従って面倒れは補正される。Therefore, as shown in FIG.
As shown in , even if the surface is tilted, the image formation position on the scanned surface 6 by the fθ lens system remains in the sub-scanning direction (vertical direction in Fig. 4).
It hardly moves. Therefore, the surface inclination is corrected.

さて、回転多面鏡３が回転すると反射面３ａは軸３Ａを
中心として回転するため、第５図に示すように反射面の
回転に伴い線像の結像位置Ｐと反射面３ａとの間に位置
ずれΔＸが生じ、ｆθレンズ系による線像の共役像の位
置Ｐ′は被走査面６からΔＸ′だけずれる。このずれ量
ΔＸ′はｆθレンズ系の副走査方向の横倍率をβとして
、周知の如くΔｘ′：β２・ΔＸで与えられる。Now, when the rotating polygon mirror 3 rotates, the reflective surface 3a rotates around the axis 3A, so as shown in FIG. A positional shift ΔX occurs, and the position P' of the conjugate image of the line image by the fθ lens system is shifted from the scanned surface 6 by ΔX'. This shift amount ΔX' is given by Δx':β2·ΔX, where β is the lateral magnification of the fθ lens system in the sub-scanning direction.

偏向面内で、ｆθレンズ系のレンズ光軸と偏向光束の主
光線とのなす角をθとする時、０と上記ΔＸとの関係を
示したのが第６図及び第７図である。第６図は固有入射
角α（第８図参照）を９０度とし、回転多面鏡３の内接
円半径Ｒ′をパラメーターとして描いている。また、第
７図では上記内接円半径Ｒ′を４０ｍｍとし、固有入射
角αをパラメーターとして描いている。第６，７図から
分かるように、ΔＸは内接円半径Ｒ′が大きいほど、ま
た固有入射角αが小さいほど大きくなる。FIGS. 6 and 7 show the relationship between 0 and ΔX, where θ is the angle between the lens optical axis of the fθ lens system and the principal ray of the deflected light beam in the deflection plane. In FIG. 6, the characteristic angle of incidence α (see FIG. 8) is 90 degrees, and the radius R' of the inscribed circle of the rotating polygon mirror 3 is used as a parameter. Further, in FIG. 7, the radius R' of the inscribed circle is 40 mm, and the characteristic angle of incidence α is drawn as a parameter. As can be seen from FIGS. 6 and 7, ΔX increases as the radius R' of the inscribed circle increases and as the specific angle of incidence α decreases.

また、反射面の回転に伴う線像の位置と反射面との相対
的な位置ずれは、偏向面内で２次元的に生じ、且つレン
ズ光軸に対しても非対象に移動する。従って、第２図の
如き光走査装置ではｆθレンズ系の主、副走査方向の像
面湾曲を主走査領域全域にわたって良好に補正する必要
がある。また、主走査方向に関してはｆθ特性が良好に
補正されねばならないことは言うまでもない。Moreover, the relative positional shift between the position of the line image and the reflecting surface due to the rotation of the reflecting surface occurs two-dimensionally within the deflection plane, and also moves asymmetrically with respect to the lens optical axis. Therefore, in the optical scanning device as shown in FIG. 2, it is necessary to satisfactorily correct the field curvature of the f.theta. lens system in the main and sub-scanning directions over the entire main-scanning region. Furthermore, it goes without saying that the fθ characteristic must be well corrected in the main scanning direction.

ここで前述の固有入射角αにつき説明すると、第８図に
おいて、符号ａは回転多面鏡に入射する光束の主光線を
示し、符号すはｆθレンズ系の光軸を示している。固有
入射角αは、図の如く主光線ａと光軸すの交角として定
義される。Now, to explain the above-mentioned specific angle of incidence α, in FIG. 8, the symbol a indicates the chief ray of the light beam incident on the rotating polygon mirror, and the symbol s indicates the optical axis of the fθ lens system. The unique angle of incidence α is defined as the intersection angle between the principal ray a and the optical axis S as shown in the figure.

主光線ａと光軸すの交点の位置を原点として図のとと＜
　Ｘ、Ｙ軸を定め１回転釜面鏡３の回転軸位置の座標を
Ｘｃ、Ｙｃとする。In the figure, the origin is the intersection of principal ray a and optical axis S.
The X and Y axes are determined, and the coordinates of the rotational axis positions of the single-rotation hook mirror 3 are defined as Xc and Yc.

前述した。線像位置と反射面との位置ずれ量のΔＸの変
動をなるべく少なくする為には周知のごとく、Ｒを回転
多面鏡の外接円半径として０　＜Ｘｃ＜Ｒｃｏｓ（ａ　
／　２　）０　＜Ｙｐ＜Ｒ５１ｎ（ａ／２） なる条件をＸｃ、Ｙｃに課せばよい。As mentioned above. As is well known, in order to minimize the variation in ΔX of the positional deviation between the line image position and the reflecting surface, 0 < Xc < Rcos (a
/2)0<Yp<R51n(a/2) The following condition may be imposed on Xc and Yc.

また、入射光束の主光線ａが有効主走査領域外に存在し
、被走査面６からの戻り光がゴースト光として被走査面
の主走査領域に再入射しないようにするには、回転多面
鏡３の面数をＮ、偏向角をθとして、上記αに対し、 θくα〈（４π／Ｎ）−〇 なる条件を課すれば良い。In addition, in order to prevent the principal ray a of the incident light beam from existing outside the effective main scanning area and the return light from the scanned surface 6 to re-enter the main scanning area of the scanned surface as ghost light, a rotating polygon mirror is used. If the number of surfaces of 3 is N and the deflection angle is θ, the following condition may be imposed on the above α: θ×α<(4π/N)−〇.

次に、本発明の特徴の一端をなす鞍型トーリック面に付
き説明する。Next, the saddle-shaped toric surface, which is one of the features of the present invention, will be explained.

良く知られているようにトーリック面とは、円弧を「こ
の円弧を含む平面内にあって円弧の曲率中心を通らない
直線」の回りに回転して得られる面である。As is well known, a toric surface is a surface obtained by rotating a circular arc around "a straight line that is within the plane containing this circular arc and does not pass through the center of curvature of the circular arc."

第９図を参照すると、ＡＶＢを通る曲線は位置ＣＩを曲
率中心とする円弧である。この円弧を、「円弧と同一面
内にあって、且つ円弧を介して位置Ｃ１と反対側にある
直線Ｘ、Ｙ、Ｊを軸として回転させると第ｆθ図に示す
ような鞍型の曲面ＳＴが得られる。Referring to FIG. 9, the curve passing through AVB is a circular arc having the center of curvature at position CI. When this circular arc is rotated around straight lines X, Y, and J that are in the same plane as the circular arc and on the opposite side of the circular arc from position C1, a saddle-shaped curved surface ST as shown in Fig. is obtained.

この面ＳＴが鞍型トーリック面である、この面ＳＴをレ
ンズ面として使用する際に凸面として使用する場合と凹
面として使用する場合とが可能であり、本発明では第２
面に凹の鞍型トーリック面を使用するのである。This surface ST is a saddle-shaped toric surface. When this surface ST is used as a lens surface, it can be used as a convex surface or as a concave surface.
A concave saddle-shaped toric surface is used.

なお、第４面の凸のトーリック面では円弧が光軸を含む
偏向直交面内にあり、回転軸はこの面内で副走査方向に
平行で、円弧の曲率中心に関して円弧と反対側にある。In addition, in the convex toric surface of the fourth surface, the circular arc is in a deflection orthogonal plane that includes the optical axis, and the rotation axis is parallel to the sub-scanning direction within this plane and is on the opposite side of the circular arc with respect to the center of curvature of the circular arc.

従って、このトーリック面は光軸を含む偏向直交面内に
強い曲率を持つ。Therefore, this toric surface has a strong curvature in the plane orthogonal to the deflection including the optical axis.

ＸｒＹｒ軸に直交する面内における鞍型トーリック面の
曲率半径を見ると、これは０２点を軸方向にばれるに従
って大きくなっており、この曲率半径は軸Ｘ、Ｙ、と円
弧ＡＶＢとの距離に等しい。Looking at the radius of curvature of the saddle-shaped toric surface in the plane orthogonal to the XrYr axis, it becomes larger as the 02 point is deviated in the axial direction, and this radius of curvature increases with the distance between the axes X, Y and the arc AVB. equal.

本発明では、第２面の凸の鞍型トーリック面に於いて、
軸Ｘ、Ｙ、の方向を偏向面内で主走査方向と平行にする
のである。In the present invention, in the convex saddle-shaped toric surface of the second surface,
The directions of the axes X and Y are made parallel to the main scanning direction within the deflection plane.

［実施例］ 以下、具体的な実施例を６例挙げる。[Example] Six specific examples are listed below.

各実施例においてｆＭはｆθレンズ系の主走査方向に関
する合成焦点距離、即ち偏向面に平行な面内における合
成焦点距離を表し、この値はｆθ０に規格化される。ま
たｆ３は偏向直交面内での合成焦点距離即ち副走査方向
に関する合成焦点距離を表す。２θは偏向角（単位二度
）、αは固有入射角（単位：度）、βは偏向直交面内の
横倍率を表す。In each embodiment, fM represents the composite focal length of the fθ lens system in the main scanning direction, that is, the composite focal length in a plane parallel to the deflection plane, and this value is normalized to fθ0. Further, f3 represents a composite focal length in a plane perpendicular to the deflection, that is, a composite focal length in the sub-scanning direction. 2θ represents the deflection angle (unit: twice), α represents the specific angle of incidence (unit: degree), and β represents the lateral magnification in the plane orthogonal to the deflection.

ｒｌｘは回転多面鏡の側から数えてｉ番目のレンズ面の
偏向面内の曲率半径、即ち第１回答図で「主」と表示さ
れた図に現れたレンズ面形状の曲率半径、　ｒａｙはｉ
番目のレンズ面の偏向直交面内の曲率半径、即ち第１回
答図で「副」と表示された図に現れたレンズ面形状の曲
率半径であり、特にｒｌＶｔｒ２Ｖは条件（Ｉ）に関連
してｒＩｖｒ２として説明したものである。また第２面
に関し、ｒ　２３１は第９図の７０１間の距離、ｒ２Ｖ
はＶＯ２間の距離を表す。rlx is the radius of curvature in the deflection plane of the i-th lens surface counting from the side of the rotating polygon mirror, that is, the radius of curvature of the lens surface shape that appears in the diagram labeled "main" in the first answer diagram, and ray is i
The radius of curvature of the second lens surface in the plane perpendicular to the deflection, that is, the radius of curvature of the lens surface shape that appears in the figure labeled "sub" in the first answer figure, and especially rlVtr2V is related to condition (I). This is explained as rIvr2. Regarding the second surface, r231 is the distance between 701 in FIG. 9, r2V
represents the distance between VO2.

ｄｉはｉ番目のレンズ面間距離、ｄｏは回転多面鏡の反
射面から第ルンズ面までの距離、　ｎｊはｊ番目のレン
ズの屈折率を表す。di is the distance between the i-th lens surfaces, do is the distance from the reflecting surface of the rotating polygon mirror to the lens surface, and nj is the refractive index of the j-th lens.

さらに、Ｋをもって上記条件（１）における１（（１／
ｒ′１）−（１／ｒＭ））・ｆａｌを表す。Furthermore, with K, 1((1/
r′1)−(1/rM))・fal.

実施例　１ ｆＭ＝ｌＯＯ，ｆ、＝１５．８４７　　、βニー４．２
５４．α＝５４，２θ＝６０Ｋ”２．６４．ｄｏ”５．
４１１ １　　　ｒｔｘ　　　　　ｒｓｖ　　　　ｄｔ　　　ｊ
　　　ｎ１１　　　００　　　−１２．０２５　１．５
０９　１１．７１２２１２　−９５４．９２６　　１２
．０２５　７．２４５３　−３６．５２８　　−３８．
５２８　１１．８８３　２１．６７５４　−２５．４８
８　　−７．２５４ 第１１図に、実施例１に関する収差図・ｆｉｌｌ特性図
を示す。像面湾曲図は回転多面鏡の回転に伴うものであ
り、破線は主走査方向のもの、実線が副走査方向のもの
を表している。Example 1 fM=lOO,f,=15.847, β knee 4.2
54. α=54, 2θ=60K”2.64.do”5.
411 1 rtx rsv dt j
n11 00 -12.025 1.5
09 11.712212 -954.926 12
．． 025 7.2453 -36.528 -38.
528 11.883 21.6754 -25.48
8-7.254 FIG. 11 shows an aberration diagram and a fill characteristic diagram regarding Example 1. The field curvature diagram is associated with the rotation of the rotating polygon mirror, and the broken line represents the main scanning direction, and the solid line represents the sub-scanning direction.

また　ｆθ特性は理想像高をｆＭ・θ、実際の像高をｈ
とするとき、（ｈ−ｆＭ−ｅ　）−ｆθ０／（ｆＭ−８
）　テ定義される。In addition, fθ characteristics are as follows: ideal image height is fM・θ, and actual image height is h.
When (h-fM-e)-fθ0/(fM-8
) is defined.

実施例　２ ｆＭ＝ｆθ０．ｆｓ＝１５．４６２　、β＝−６，０”
１１．　ａ　＝５４．２　ｆ）　：６０．４に＝０．４
８．ｄ、＝９．０１９ １　　　　　　ｒｉｘ　　　　　　　　　　　　ｒＢ　
　　　　　　　　　ｄｉ　　　　　　ｊ　　　　　　ｎ
１１　　　　ｏｏ８．４１７　　３．７１６　　１１．
７１２２１２　−６２３．５５　　　　　６．６７４　
　０．６０２３　　−４０．６５５　　−４０．６５５
　８．７７９　　２１．６７５４　　−２６．３３５　
　　−７．５４第１２図に、実施例２に関する収差図・
ｆθ特性図を示す。Example 2 fM=fθ0. fs=15.462, β=-6,0"
11. a = 54.2 f): 60.4 = 0.4
8. d,=9.019 1 rix rB
di j n
11 oo8.417 3.716 11.
712212 -623.55 6.674
0.6023 -40.655 -40.655
8.779 21.6754 -26.335
-7.54 Figure 12 shows the aberration diagram for Example 2.
The fθ characteristic diagram is shown.

実施例　３ ｆ、＝ｆθ０．ｆｓ＝１３．５１５　、β＝−７，６９
５，ａ　＝５４，２θ＝６０．８に＝０．８６．ｄ、＝
７．８１６ １　　　ｒＩｚ　　　　　ｒｌｙ　　　　ｄｉ　　　Ｊ
　　　ｎ１１　　　■　　　　　５．４１１　３．３６
７　１１．７１２２１２　−４７８．０３５　　　４．
０２８　１．２０２３　−３６．７９６　　−３６．７
９６　６．０１２　２１．６７５４　−２８．９９８　
　−６．０４２ 第１３図に、実施例３に関する収差図・ｆθ特性図を示
す。Example 3 f,=fθ0. fs=13.515, β=-7,69
5, a = 54, 2θ = 60.8 = 0.86. d,=
7.816 1 rIz rly di J
n11 ■ 5.411 3.36
7 11.712212 -478.035 4.
028 1.2023 -36.796 -36.7
96 6.012 21.6754 -28.998
-6.042 FIG. 13 shows an aberration diagram and an fθ characteristic diagram regarding Example 3.

実施例　４ ｆＭ＝ｆθ０．ｆｇ＝１５．５７８　、βニー５．９２
８．　ａ　＝５４．２　Ｂ　＝６０．４に＝０．３２．
ｄ、＝９．０１９ １　　　ｒｉｘ　　　　　ｒｓｖ　　　　ｄｉ　　　ｊ
　　　ｎ１１　　　　ω　　　　　　１４．４３　　　
３．７１６　　１　１．７１２２１２　−６２３．５５
　　　　１１．０９９　　０．６０２３　　−４０．６
５５　　−４０．６５５　　８．７７９　　２１．６７
５４　　−２６．３３５　　　−７．８９第１４図に、
実施例４に関する収差図・ｆθ特性図を示す。Example 4 fM=fθ0. fg=15.578, β knee 5.92
8. a = 54.2 B = 60.4 = 0.32.
d,=9.019 1 rix rsv di j
n11 ω 14.43
3.716 1 1.712212 -623.55
11.099 0.6023 -40.6
55 -40.655 8.779 21.67
54 -26.335 -7.89 In Figure 14,
The aberration diagram and fθ characteristic diagram regarding Example 4 are shown.

実施例　５ ｆ、＝ｆθ０．ｆｓ＝１６．０５８　　、β＝−４，３
６６、α＝５４，２θ＝６０．０Ｋ＝２．４３．ｄ、＝
５．４１１ １　　　ｒ＋ｘ　　　　　ｒｔｖ　　　　ｄｔ　　　ｊ
　　　ｎｔｌ　　　　ｏｏω１．５０９　１１．７１２
２１２　−９５４．９２８　　　６．６１４　７．２４
５・３　−３６．５２８　　−３６．５２８　１１．８
８３　２１．６７５４　−２５．４８８　　−７．２１
９ 第１５図に、実施例５に関する収差図・ｆＯ特性図を示
す。Example 5 f,=fθ0. fs=16.058, β=-4,3
66, α=54, 2θ=60.0K=2.43. d, =
5.411 1 r+x rtv dt j
ntl ooω1.509 11.712
212 -954.928 6.614 7.24
5・3 -36.528 -36.528 11.8
83 21.6754 -25.488 -7.21
9 FIG. 15 shows an aberration diagram and an fO characteristic diagram regarding Example 5.

実施例　６ ｆ、ｔ”ｆθ０．ｆｓ”１３．９５　　　、β＝−６，
４５２，ａ　＝５４．２０　二６０．８に＝０．５　、
ｄ、＝７．８１６ １　　　ｒｉｘ　　　　　ｒＩｖ　　　　ｄｔ　　　ｊ
　　　ｎ＋１　　　　　ｏｏ　　　　　　　　　ｏｏ　
　　　　３．３６７　　１　１−７１２２１２　　−４
７８．０３５　　　　２７．６５７　　１．２０２３　
　　−３６．７９６　　　−３６．７９６　　６．０１
２　　２　１．６７５４　　　−２８．９９８　　　　
−６．９１１第１６図に、実施例６に関する収差図・ｆ
θ特性図を示す。Example 6 f, t”fθ0.fs”13.95, β=-6,
452, a = 54.20 260.8 = 0.5,
d, =7.816 1 rix rIv dt j
n+1 oo oo
3.367 1 1-712212 -4
78.035 27.657 1.2023
-36.796 -36.796 6.01
2 2 1.6754 -28.998
-6.911 Figure 16 shows the aberration diagram for Example 6.
The θ characteristic diagram is shown.

各実施例とも、収差が良好であり特に、像面湾曲は主・
副走査方向とも極めて良好に補正されている。またｆθ
特性も良好である。In each example, aberrations are good, especially field curvature is
The correction is extremely good in both the sub-scanning direction. Also fθ
The characteristics are also good.

［発明の効果］ 以上、本発明によれば新規なｆθレンズ系を提供できる
。このｆθレンズ系は、上述の如き構成となっているの
で、回転多面鏡の面倒れを良好に補正しつつ、主・副走
査方向の像面湾曲を良好に補正して光走査を実現でき、
従って高密度の光走査が可能になる。[Effects of the Invention] As described above, according to the present invention, a novel fθ lens system can be provided. Since this f-theta lens system has the above-described configuration, it is possible to achieve optical scanning by properly correcting the surface tilt of the rotating polygon mirror and the field curvature in the main and sub-scanning directions.
Therefore, high-density optical scanning becomes possible.

【図面の簡単な説明】[Brief explanation of the drawing]

第１図は、本発明のｆθレンズ系の形状を説明するため
の図、第２図乃至第８図は光走査装置を説明するための
図、第９図および第ｆθ図は鞍型トーリック面を説明す
るための図、第１１図乃至第１６図は、各実施例に関す
る収差図・ｆθ特性図であ■ｆθ．光源装置、２００．
シリンダーレンズ、３０．。 回転多面鏡、４，５．、、ｆθレンズ系を構成する第１
％ （ 図 （凸） （凸） （凹〕 （凸） 第 ６ 図 第 図 気 図 第 （Ｏ 図 第 ワ 図 θ（ｉｅρ 俤　（（図 （突死例り Ｆｔｖｏ　−５４１ θ−３１７゛ θ−３７．７゜ □上！？■Ｒ差 一−−−−　正弦＋住 津山消印 Ｔτ性（幻 領（２図 （実力七個２） Ｆｓｏ−５４，１ θ−３７．７゜ θ＝ｊ／、７” 正ＰＩｆ、冬件 俤（４図 （突充例４） Ｆｈｏ−５４，７ θ＝ｊ１７゜ θ−ｊ／　７’ 正ダゑ条件 俤（づ図 （芙光例ｂ） Ｆｓｏ＝５４．’１ θ−３！’／。 正戟釡作 第（５図 （芙杷例５） ＮＯ ４７ θ＝づイア。 θ−ｊ１．ワ゛ θ−ｊ１７′ 第１Ｇ図 （突杷Ｏ１釦 ＦＮｏ＝５４７ θ−づＪ、７゛ θ−６１．７゜ イ嚢面清［日３ チθｊ寺＋生（幻 ＋Ｅ弦斎件Figure 1 is a diagram for explaining the shape of the fθ lens system of the present invention, Figures 2 to 8 are diagrams for explaining the optical scanning device, and Figures 9 and fθ are for a saddle-shaped toric surface. Figures 11 to 16 are aberration diagrams and fθ characteristic diagrams for each example. Light source device, 200.
Cylinder lens, 30. . Rotating polygon mirror, 4,5. ,, the first lens constituting the fθ lens system
% (Figure (Convex) (Convex) (Concave) (Convex) 37.7゜□Up!? ■R difference 1 ---- Sine + Sumitsuyama postmark Tτ property (phantom territory (2 figures (7 ability 2) Fso - 54, 1 θ - 37.7 ° θ = j / , 7'' Positive PIf, winter condition (Figure 4 (Full example 4) Fho-54,7 θ=j17゜θ-j/ 7' Positive PIf, Winter condition (Figure 4 (Fu light example b) Fso=54 .'1 θ-3!'/.Shogekibutsu No. 5 (Loquat Example 5) NO 47 θ=Zia. θ-j1.W θ-j17' Figure 1G (Loquat O1 button FNo= 547 θ-zuJ, 7゛θ-61.7゜I bag face clear [day 3 Chi θj temple + life (phantom + E string service)

Claims (1)

【特許請求の範囲】 光源装置からの略平行な光束を主走査対応方向に長い線
像に結像させ、その線像の結像位置の近傍に反射面を有
する回転多面鏡により上記光束を等角速度的に偏向させ
、この偏向光束を結像レンズ系により被走査面上にスポ
ット状に結像させて被走査面を略等速的に光走査する光
走査装置において、回転多面鏡により偏向された光束を
被走査面上に結像させる結像レンズ系であって、 副走査方向に関して回転多面鏡の反射位置と被走査面と
を幾何光学的に略共役な関係に結び付ける機能を持つと
ともに、主走査方向に関してｆθ機能を有し、 回転多面鏡の側から被走査面側へ向かって第１、第２の
順に配備される、第１および第２のレンズにより構成さ
れる２群・２枚構成であり、 回転多面鏡により理想的に偏向された光束の主光線の掃
引により形成される面を偏向面、結像レンズ系の光軸に
平行で偏向面に直交する面を偏向直交面とするとき、 上記回転多面鏡の側から数えて各レンズ面を第１乃至第
４面とすると、これらのレンズ面の偏向面内での形状が
第１面から第４面に向かって順次、直線、円弧、円弧、
円弧であり、 偏向面に平行な面内では第１、第２のレンズとも正の屈
折力を持ち、 上記第１面は偏向直交面内にのみ屈折力を持つ凸もしく
は凹のシリンダー面または平面、第２面は偏向直交面内
の曲率半径が光軸から離れるに従い大きくなる凹の鞍型
トーリック面、第３面は凹の球面、第４面は偏向直交面
内に強い曲率を持つ凸のトーリック面であり、 偏向直交面内における合成焦点距離をｆ＿ｓ、光軸を含
む偏向直交面内に於ける第１、第２面の曲率半径をそれ
ぞれｒ′＿１、ｒ′＿２とするとき、これらが−０．３
＜｜｛（１／ｒ′＿１）−（１／ｒ′＿２）｝・ｆ＿ｓ
｜＜２．７なる条件を満足することを特徴とするｆθレ
ンズ系。[Scope of Claims] A substantially parallel light beam from a light source device is formed into a long line image in a direction corresponding to the main scanning direction, and the light beam is equally divided by a rotating polygon mirror having a reflective surface near the imaging position of the line image. In an optical scanning device, the deflected light beam is deflected at an angular velocity, and the deflected light beam is imaged as a spot on the scanned surface by an imaging lens system, and the scanned surface is optically scanned at approximately constant velocity. This is an imaging lens system that forms an image of a light beam on a surface to be scanned, and has a function of connecting the reflection position of the rotating polygon mirror and the surface to be scanned in a geometrically optically substantially conjugate relationship in the sub-scanning direction. It has an fθ function in the main scanning direction, and is arranged in the order of first and second from the rotating polygon mirror side toward the surface to be scanned, and is composed of two groups and two lenses, each consisting of a first and a second lens. The surface formed by sweeping the principal ray of the light beam ideally deflected by a rotating polygon mirror is called the deflection surface, and the surface parallel to the optical axis of the imaging lens system and orthogonal to the deflection surface is called the orthogonal deflection surface. When counting from the side of the rotating polygon mirror, each lens surface is defined as the first to fourth surfaces, and the shapes of these lens surfaces within the deflection plane are sequentially linear from the first surface to the fourth surface. , arc, arc,
It is a circular arc, and both the first and second lenses have positive refractive power in a plane parallel to the deflection plane, and the first surface is a convex or concave cylindrical surface or plane that has refractive power only in the plane perpendicular to the deflection plane. , the second surface is a concave saddle-shaped toric surface in which the radius of curvature in the plane orthogonal to deflection increases as it moves away from the optical axis, the third surface is a concave spherical surface, and the fourth surface is a convex toric surface with a strong curvature in the plane orthogonal to deflection. It is a toric surface, and when the synthetic focal length in the plane orthogonal to deflection is f_s, and the radii of curvature of the first and second surfaces in the plane orthogonal to deflection including the optical axis are r'_1 and r'_2, respectively, these is -0.3
<|{(1/r'_1)-(1/r'_2)}・f_s
An fθ lens system characterized by satisfying the condition |<2.7.