JPH11316350A - Optical scanning device - Google Patents

Optical scanning device

Info

Publication number
JPH11316350A
JPH11316350A JP12228298A JP12228298A JPH11316350A JP H11316350 A JPH11316350 A JP H11316350A JP 12228298 A JP12228298 A JP 12228298A JP 12228298 A JP12228298 A JP 12228298A JP H11316350 A JPH11316350 A JP H11316350A
Authority
JP
Japan
Prior art keywords
scanning
lens
sub
optical
scanned
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP12228298A
Other languages
Japanese (ja)
Other versions
JP3492911B2 (en
Inventor
Yoshiaki Hayashi
善紀 林
Seizo Suzuki
清三 鈴木
Koji Masuda
浩二 増田
Hiroyuki Suhara
浩之 須原
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Ricoh Co Ltd
Original Assignee
Ricoh Co Ltd
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Filing date
Publication date
Application filed by Ricoh Co Ltd filed Critical Ricoh Co Ltd
Priority to JP12228298A priority Critical patent/JP3492911B2/en
Publication of JPH11316350A publication Critical patent/JPH11316350A/en
Application granted granted Critical
Publication of JP3492911B2 publication Critical patent/JP3492911B2/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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Abstract

PROBLEM TO BE SOLVED: To expand an allowable degree of refraction index distribution while keeping a good light spot diameter when the refractive index has a distribution in a lens included in a scanning image-forming lens or a scanning image-forming lens system. SOLUTION: A 2nd image-forming optical system 18 is constituted of an anamorphic single scanning image-forming lens having a refractive index distribution in the direction corresponding to sub-scanning, and approximates the refractive index distribution by n(z)=n0 (0)+Δ(0).z<2> to a distance: (z) from the optical axis in the direction corresponding to the sub-scanning in a sub-scanning cross- section, herein a refractive index on an optical axis is expressed by n0 (0), and satisfies the condition: |1/[ 1/f(0)}-2Δn(0).d- 1/S0 (0)}]-SL(0)|<ω0 /2, wherein a lens thickness of each lens on the optical deflector side and the scanned surface side is expressed by f(0), a distance from an image-forming position of a line image up to a front side main point of the scanning image-forming lens in the direction corresponding to the sub-scanning is expressed by SL(0), and a spot diameter depth margin in the sub-scanning direction is expressed by ω(0).

Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【0001】[0001]

【発明の属する技術分野】この発明は光走査装置に関す
る。
The present invention relates to an optical scanning device.

【0002】[0002]

【従来の技術】光走査装置において、光偏向器で偏向さ
れる偏向光束を被走査面上に光スポットとして集光する
走査結像レンズ系は、従来、レンズ内部における屈折率
が一定であるものとして設計が行われている。近来、走
査結像レンズ系に、プラスチック成形によるプラスチッ
クレンズが使用されるようになってきている。プラスチ
ック成形でレンズを形成すると、成形型内での冷却の際
のレンズ内部の温度差の影響により、先に冷却するレン
ズ外周辺部に比してレンズ内部の密度が低くなる傾向が
あり、このため、作製されたレンズ内部に屈折率の分布
が生じてしまい、この屈折率の不均一が光学的に作用し
て、走査結像レンズ系の光学性能が設計通りにならない
という問題がある。この傾向は、冷却時間を短縮した場
合に特に顕著であり、冷却時間の短縮による生産効率の
向上と、それに伴うコストの低減化を困難にしている。
2. Description of the Related Art In an optical scanning apparatus, a scanning image forming lens system for condensing a deflecting light beam deflected by an optical deflector as a light spot on a surface to be scanned has conventionally been a lens having a constant refractive index inside the lens. The design has been made. In recent years, plastic lenses formed by plastic molding have been used for scanning imaging lens systems. When a lens is formed by plastic molding, the density inside the lens tends to be lower than that of the outer peripheral portion of the lens to be cooled first due to the effect of the temperature difference inside the lens when cooling in the mold. Therefore, there is a problem that a refractive index distribution occurs inside the manufactured lens, and the non-uniformity of the refractive index acts optically, so that the optical performance of the scanning imaging lens system is not as designed. This tendency is particularly remarkable when the cooling time is shortened, which makes it difficult to improve the production efficiency by shortening the cooling time and reduce the cost associated therewith.

【0003】また、光走査装置による画像記録の高密度
化の要請に伴い、光スポット径をより小さくすることが
求められ、このために、像面湾曲とともに球面収差を良
好に補正する必要が生じている。球面収差を良好に補正
するのに、レンズ内に「設計された所定の屈折率分布」
を持たせることが有効であるが、このような屈折率分布
を設計通りに実現することは難しい。
Further, with the demand for high-density image recording by an optical scanning device, it is required to reduce the diameter of a light spot, which necessitates good correction of spherical aberration as well as curvature of field. ing. In order to satisfactorily correct spherical aberration, a "designed predetermined refractive index distribution" in the lens
Is effective, but it is difficult to realize such a refractive index distribution as designed.

【0004】結局、プラスチック成形の際に発生するレ
ンズ内屈折率分布も、設計条件として与えられるレンズ
内屈折率分布も、屈折率の分布として一義的には決まら
ず、ある程度「バラつく」ことになる。このため、実使
用に耐える上記走査結像レンズの歩留まりの向上が困難
であり、走査結像レンズ系、ひいては光走査装置のコス
ト低減を困難にしている。
After all, neither the refractive index distribution in the lens generated during plastic molding nor the refractive index distribution in the lens given as a design condition is uniquely determined as a distribution of the refractive index. Become. For this reason, it is difficult to improve the yield of the scanning imaging lens that can be used in actual use, and it is difficult to reduce the cost of the scanning imaging lens system, and furthermore, the optical scanning device.

【0005】[0005]

【発明が解決しようとする課題】この発明は、走査結像
レンズや走査結像レンズ系に含まれるレンズ内に、屈折
率の分布がある場合に、良好な光スポット径を確保しつ
つ、屈折率の分布のバラツキの許容度を拡げることを課
題とする。
SUMMARY OF THE INVENTION According to the present invention, there is provided a lens for a scanning image forming lens or a lens included in a scanning image forming lens system, in which a refractive index distribution is ensured while securing a good light spot diameter. An object of the present invention is to increase the tolerance of variation in the distribution of the rate.

【0006】また、上記屈折率分布のバラツキによる結
像位置のバラツキを低減することをも課題とする。
Another object is to reduce the variation in the imaging position due to the variation in the refractive index distribution.

【0007】[0007]

【課題を解決するための手段】この発明の光走査装置は
「光源からの光束を、第1結像光学系により主走査対応
方向(光源から被走査面に至る光路上で、主走査方向に
対応する方向)に長い線像として結像させ、上記線像の
結像位置近傍に偏向反射面を持つ光偏向器により偏向さ
せ、偏向された光束を第2結像光学系により被走査面上
に光スポットとして集光させて光走査を行う光走査装
置」である。
According to an optical scanning apparatus of the present invention, a light beam from a light source is transmitted by a first imaging optical system in a main scanning direction (on an optical path from a light source to a surface to be scanned, in a main scanning direction). (A corresponding direction) is formed as a long line image, is deflected by an optical deflector having a deflecting reflection surface near the image forming position of the line image, and the deflected light beam is projected onto the surface to be scanned by the second imaging optical system. An optical scanning device that performs optical scanning by condensing light as a light spot on the optical scanning device.

【0008】請求項1記載の発明において、第2結像光
学系は「副走査対応方向(光源から被走査面に至る光路
上で副走査方向に対応する方向)に屈折率分布を有する
アナモフィックな単玉レンズである走査結像レンズ」で
構成される。この走査結像レンズにおける光軸上の屈折
率をn0(0)とするとき、副走査断面内で副走査対応方
向における光軸からの距離:zに対し、屈折率の分布を
「n(z)=n0(0)+Δn(0)・z2」で近似し、走査結
像レンズの、光偏向器側および被走査面側の各レンズ面
の、副走査断面内における曲率半径を、それぞれr
S1(0),rS2(0)、レンズ肉厚をd、これらrS1(0),
S2(0),d,n0(0)から算出される副走査対応方向
焦点距離をf(0)とし、線像の結像位置から「走査結像
レンズの副走査対応方向の前側主点」までの距離をS
0(0)、後側主点から被走査面までの距離をSL(0)、副
走査方向のスポット径深度余裕をω0とするとき、これ
らの量は、条件: (1) |1/[{1/f(0)}−2Δn(0)・d−{1/S0(0)}]−SL(0)| <ω0/2 を満足する。上記焦点距離:f(0)は、 f(0)=1/[{n0(0)−1}{(1/rS1(0))−(1/r
S2(0))}+{n0(0)−1}2・d/{n0(0)・rS1(0)・
S2(0)}] で与えられる。「副走査断面」は、単玉の走査結像レン
ズの光軸を含み、副走査対応方向に平行な平断面であ
る。「副走査方向のスポット径深度余裕:ω0」は、
「副走査対応方向のビームウエスト径(デフォーカスを
変化させたときの、副走査方向の光スポット径の最小
値)に対し、副走査方向の光スポット径の変動が10%
以下となるデフォーカス幅」として定義される。条件
(1)の上限を超えると、光スポットの副走査対応方向
の(被走査面からの)結像位置ずれが大きくなり、副走
査方向の光スポット径が設計値よりも顕著に大きくな
る。
According to the first aspect of the present invention, the second imaging optical system is an anamorphic having a refractive index distribution in a sub-scanning corresponding direction (a direction corresponding to the sub-scanning direction on an optical path from a light source to a surface to be scanned). The scanning imaging lens is a single lens. Assuming that the refractive index on the optical axis of the scanning imaging lens is n 0 (0), the distribution of the refractive index is “n ( z) = n 0 (0) + Δn (0) · z 2 ”, and the radius of curvature of each lens surface of the scanning imaging lens on the optical deflector side and the surface to be scanned in the sub-scanning cross section is Each r
S1 (0), rS2 (0), lens thickness d, these rS1 (0),
The focal length in the sub-scanning corresponding direction calculated from r S2 (0), d, n 0 (0) is f (0), and the position of the front image in the sub-scanning corresponding direction of the scanning image forming lens is determined from the image forming position of the line image. Distance to point
0 (0), the distance from the rear principal point to the surface to be scanned is S L (0), and the spot diameter depth margin in the sub-scanning direction is ω 0. / [{1 / f (0 )} - 2Δn (0) · d- {1 / S 0 (0)}] - S L (0) | satisfies <ω 0/2. The focal length: f (0) is expressed as f (0) = 1 / [{n 0 (0) −1} {(1 / r S1 (0)) − (1 / r
S2 (0))} + {n 0 (0) −1} 2 · d / {n 0 (0) · r S1 (0) ·
r S2 (0)}]. The “sub-scan section” is a plane section that includes the optical axis of the single-lens scanning imaging lens and is parallel to the sub-scan corresponding direction. “Spot diameter depth margin in the sub-scanning direction: ω 0
"The variation of the light spot diameter in the sub-scanning direction is 10% of the beam waist diameter in the sub-scanning corresponding direction (the minimum value of the light spot diameter in the sub-scanning direction when the defocus is changed).
It is defined as “the following defocus width”. When the value exceeds the upper limit of the condition (1), the imaging position deviation of the light spot in the direction corresponding to the sub-scanning (from the surface to be scanned) becomes large, and the light spot diameter in the sub-scanning direction becomes significantly larger than the designed value.

【0009】上記請求項1記載の光走査装置において、
第2結像光学系である走査結像レンズの光偏向器側の面
に入射する偏向光束の副走査対応方向の「光束半幅」を
Zとするとき、前記Δn(0)とZとは条件: (2) 0<Z2・Δn(0)≦1.1×10~4 を満足することが好ましい(請求項2)。
In the optical scanning device according to the first aspect,
When the “light beam half width” in the sub-scanning corresponding direction of the deflected light beam incident on the surface on the optical deflector side of the scanning image forming lens as the second image forming optical system is Z, the above-mentioned Δn (0) and Z are conditions. : (2) 0 <may satisfy Z 2 · Δn (0) ≦ 1.1 × 10 ~ 4 ( claim 2).

【0010】条件(2)の上限を超えると、副走査方向
の球面収差が大きくなり、副走査方向の光スポット径が
大きくなってしまう。
When the value exceeds the upper limit of the condition (2), the spherical aberration in the sub-scanning direction increases, and the light spot diameter in the sub-scanning direction increases.

【0011】また、下限を超えると、プラスチック成形
時の冷却時間短縮が難しく、成形時間が長くなってレン
ズの量産性が悪く、製造コストの低減化が困難である。
On the other hand, if the lower limit is exceeded, it is difficult to shorten the cooling time during plastic molding, and the molding time is prolonged, resulting in poor mass production of lenses and difficulty in reducing manufacturing costs.

【0012】上記請求項1または2記載の光走査装置に
おいて、第2結像光学系である走査結像レンズは「副走
査断面内において、光偏向器側に凹のメニスカス形状」
で、有効走査幅をW、光偏向器による偏向の起点から被
走査面に至る光軸上の距離をLとするとき、条件: (3) 0.2≦{rS2(0)/rS1(0)}×(W/L)2≦0.6 を満足することができる(請求項3)。
In the optical scanning device according to the first or second aspect, the scanning image forming lens as the second image forming optical system is “a meniscus shape concave on the optical deflector side in the sub-scan section”.
When the effective scanning width is W and the distance on the optical axis from the starting point of deflection by the optical deflector to the surface to be scanned is L, condition: (3) 0.2 ≦ {r S2 (0) / r S1 (0)} × (W / L) 2 ≦ 0.6 (claim 3).

【0013】条件(3)の上限を超えると、副走査方向
の球面収差が大きくなり、副走査方向の光スポット径が
大きくなってしまう。また条件(3)の下限を超える
と、副走査対応方向における走査結像レンズの横倍率が
大きくなり、走査結像レンズの組み付け誤差に対する許
容度が小さくなる。
When the value exceeds the upper limit of the condition (3), the spherical aberration in the sub-scanning direction increases, and the light spot diameter in the sub-scanning direction increases. When the value exceeds the lower limit of the condition (3), the lateral magnification of the scanning image forming lens in the sub-scanning corresponding direction increases, and the tolerance for the assembly error of the scanning image forming lens decreases.

【0014】上記請求項1または2または3記載の光走
査装置において、「主走査対応方向に長い線像の結像位
置と、第2結像光学系である走査結像レンズによる、上
記線像の被走査面近傍の結像位置との副走査対応方向の
横倍率」を、画角:θに関してβ(θ)とし、光走査の最
周辺画角をβ(θMAX),β(θMIN)とするとき、条件: (4−1) 0.95×β(0)≦β(θMAX)≦1.05×β(0) (4−2) 0.95×β(0)≦β(θMIN)≦1.05×β(0) を同時に満足することができる(請求項4)。
4. The optical scanning device according to claim 1, wherein the line image is formed by a scanning image forming lens which is a second image forming optical system, and a line image forming position of a long line image in a main scanning corresponding direction. The horizontal magnification in the direction corresponding to the sub-scan with respect to the image forming position near the surface to be scanned is β (θ) with respect to the angle of view: θ, and the most peripheral angle of view of the optical scanning is β (θ MAX ), β (θ MIN ), The condition is: (4-1) 0.95 × β (0) ≦ β (θ MAX ) ≦ 1.05 × β (0) (4-2) 0.95 × β (0) ≦ β (θ MIN ) ≦ 1.05 × β (0) can be satisfied at the same time (claim 4).

【0015】これら条件(4−1),(4−2)を満足
することにより、横倍率の変動に起因する光スポット径
の変動を有効に抑えることができる。
By satisfying these conditions (4-1) and (4-2), it is possible to effectively suppress the fluctuation of the light spot diameter caused by the fluctuation of the lateral magnification.

【0016】請求項5記載の光走査装置は、「第2結像
光学系が2枚以上のレンズを含む走査結像レンズ系で、
少なくとも1枚のレンズは副走査対応方向に屈折率分布
を有し、走査結像レンズ系における最も被走査面側にあ
るレンズが副走査対応方向に正のパワーを持つ」ことを
特徴とする。このようにすることにより、内部に屈折率
分布が存在しても、それに伴う像面湾曲の劣化を低減で
き、内部屈折率分布に「バラツキ」があっても、それに
伴う「像面湾曲のバラツキ」を小さく抑えることが可能
になる。
According to a fifth aspect of the present invention, there is provided an optical scanning device, wherein the second imaging optical system is a scanning imaging lens system including two or more lenses,
At least one lens has a refractive index distribution in the sub-scanning corresponding direction, and the lens closest to the surface to be scanned in the scanning image forming lens system has a positive power in the sub-scanning corresponding direction. " By doing so, even if there is a refractive index distribution inside, it is possible to reduce the deterioration of the curvature of field accompanying the refractive index distribution. Even if there is "variation" in the internal refractive index distribution, the "variation of the curvature of field" is reduced. ”Can be kept small.

【0017】上記請求項5記載の光走査装置において、
第2結像光学系である走査結像レンズ系を2枚のレンズ
で構成し、副走査対応方向のパワーを、光偏向器側のレ
ンズにつきP1、被走査面側のレンズにつきP2とすると
き、条件: (5) P2>P1 を満足することが好ましい(請求項6)。条件(5)を
満足することにより、上記請求項5の効果をより有効に
助長できる。この場合、第2結像光学系である走査結像
レンズ系の2枚のレンズのうち、被走査面側のレンズの
副走査断面内の形状は、「光偏向器側に凹のメニスカス
形状」とすることが好ましい(請求項7)。
[0017] In the optical scanning device according to the fifth aspect,
The scanning imaging lens system, which is the second imaging optical system, is composed of two lenses, and the power in the sub-scanning direction is P 1 for the lens on the optical deflector side and P 2 for the lens on the scanning surface side. It is preferable that the following condition is satisfied: (5) P 2 > P 1 (claim 6). By satisfying the condition (5), the effect of the fifth aspect can be more effectively promoted. In this case, of the two lenses of the scanning imaging lens system as the second imaging optical system, the shape of the lens on the surface to be scanned in the sub-scanning cross section is “a meniscus shape concave toward the optical deflector”. (Claim 7).

【0018】上記請求項5または6または7記載の光走
査装置において、第2結像光学系である走査結像レンズ
系を2枚のレンズで構成し、光偏向器側のレンズのみが
副走査対応方向に屈折率分布を有する場合、走査結像レ
ンズ系の光偏向器側レンズにおける光軸上の屈折率をn
0(0)、副走査断面(光偏向器側レンズの光軸を含み副
走査対応方向に平行な平断面)内で副走査対応方向にお
ける光軸からの距離:zに対して、同レンズ内の屈折率
の分布を「n(z)=n0(0)+Δn(0)・z2」で近似
し、光偏向器側レンズの、光偏向器側および被走査面側
の各レンズ面の副走査断面内の曲率半径をそれぞれrS1
(0),rS2(0)、レンズ肉厚をd1、これらrS1(0),
S2(0),d1,n0(0)から算出される副走査対応方向
焦点距離をf1(0)とし、線像の結像位置から「光偏向
器側レンズの副走査対応方向の前側主点」までの距離を
0(0) 、同レンズの副走査対応方向の後側主点から被
走査面側レンズの前側主点までの距離をS1(0) 、被走
査面側レンズの副走査対応方向の後側主点から被走査面
までの距離をSL(0) 、上記被走査面側レンズの副走査
対応方向焦点距離をf2(0)、副走査方向のスポット径
深度余裕をω0とし、「Λ={1/f1(0)}−2Δn(0)・
1−{1/S0(0)}」とするとき、条件: (6) |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・Λ)}]|<ω0/2 を満足することが好ましい(請求項8)。上記焦点距
離:f1(0)は、 f1(0)=1/[{n0(0)−1}{(1/rS1(0))−(1/
S2(0))}+{n0(0)−1}2・d1/{n0(0)・rS1(0)
・rS2(0)}] で与えられる。条件(6)の上限を超えると、光スポッ
トの副走査対応方向の(被走査面からの)結像位置ずれ
が大きくなり、副走査方向の光スポット径が設計値より
も顕著に大きくなる。
In the optical scanning device according to claim 5, the scanning image forming lens system as the second image forming optical system is composed of two lenses, and only the lens on the optical deflector side is sub-scanning. When the refractive index distribution is provided in the corresponding direction, the refractive index on the optical axis of the lens on the optical deflector side of the scanning imaging lens system is represented by n.
0 (0), the distance from the optical axis in the sub-scanning corresponding direction: z in the sub-scanning cross-section (the plane cross-section including the optical axis of the optical deflector side lens and parallel to the sub-scanning corresponding direction) is within the same lens. Is approximated by “n (z) = n 0 (0) + Δn (0) · z 2 ”, and the respective lens surfaces of the optical deflector-side lens on the optical deflector side and the scanning surface side are approximated. Let the radius of curvature in the sub-scan section be r S1
(0), r S2 (0), lens thickness d 1 , these r S1 (0),
The focal length in the sub-scanning corresponding direction calculated from r S2 (0), d 1 , and n 0 (0) is f 1 (0), and the position in the sub-scanning corresponding direction of the lens on the optical deflector side is defined as f 1 (0). S 0 the distance to the front principal point "in (0), S 1 (0 ) a distance from the rear principal point of the sub-scanning direction in the lens to the front principal point of the surface to be scanned side lens, the surface to be scanned The distance from the rear principal point of the side lens in the sub-scanning direction to the surface to be scanned is S L (0), the focal length of the lens to be scanned in the sub-scanning direction is f 2 (0), Assuming that the spot diameter depth margin is ω 0 , “Λ = {1 / f 1 (0)} − 2Δn (0) ·
d 1 − {1 / S 0 (0)} ”, the condition is: (6) | S L (0) −1 / [{1 / f 2 (0)} + {Λ / (1−S 1 (0) · Λ)}] | < it is preferable to satisfy the omega 0/2 (claim 8). The focal length: f 1 (0) is expressed as f 1 (0) = 1 / [{n 0 (0) −1} {(1 / r S1 (0)) − (1/1 /
r S2 (0))} + {n 0 (0) −1} 2 · d 1 / {n 0 (0) · r S1 (0)
R s2 (0)}]. When the value exceeds the upper limit of the condition (6), the imaging position shift of the light spot in the direction corresponding to the sub-scanning (from the surface to be scanned) becomes large, and the light spot diameter in the sub-scanning direction becomes significantly larger than the designed value.

【0019】上記請求項5または6または7記載の光走
査装置において、第2結像光学系である走査結像レンズ
系が2枚のレンズで構成され、被走査面側レンズのみが
副走査対応方向に屈折率分布を有する場合、走査結像レ
ンズ系の光偏向器側レンズの焦点距離をf1(0)とし、
第1結像光学系により結像する主走査対応方向に長い線
像の結像位置から光偏向器側レンズの副走査対応方向の
前側主点に至る距離をS0(0)、光偏向器側レンズの副
走査対応方向の後側主点から被走査面側レンズの副走査
対応方向の前側主点に至る距離をS1(0)、被走査面側
レンズの副走査対応方向の後側主点から被走査面に至る
距離をSL(0)とし、被走査面側レンズにおける光軸上
の屈折率をn0'(0)とするとき、副走査断面(被走査面
側レンズの光軸を含み副走査対応方向に平行な平断面)
内で副走査対応方向における光軸からの距離:zに対し
て、同レンズ内の屈折率の分布を「n'(z)=n0'(0)
+Δn'(0)・z2」で近似し、被走査面側レンズの、光
偏向器側および被走査面側の各レンズ面の、副走査断面
内における曲率半径をそれぞれ、rS3(0),rS4(0)、
レンズ肉厚をd3、これらrS3(0),rS4(0),d3,n
0'(0)から算出される副走査対応方向の焦点距離をf
2(0)、副走査方向のスポット径深度余裕をω0とし、
「Λ'={1/f1(0)}−{1/S0(0)}」とするとき、条
件: (7) |SL(0)−1/[{1/f2(0)}+{Λ'/(1−S1(0)・Λ')} −2Δn'(0)・d3]|<ω0/2 を満足することが好ましい(請求項9)。上記焦点距
離:f2(0)は、 f2(0)=1/[{n0'(0)−1}{(1/rS3(0))−(1/
S4(0))}+{n0'(0)−1}2・d3/{n0'(0)・r
S3(0)・rS4(0)}] で与えられる。条件(7)の上限を超えると、光スポッ
トの副走査対応方向の(被走査面からの)結像位置ずれ
が大きくなり、副走査方向の光スポット径が設計値より
も顕著に大きくなる。
In the optical scanning apparatus according to claim 5, the scanning image forming lens system as the second image forming optical system is composed of two lenses, and only the lens to be scanned corresponds to sub-scanning. When there is a refractive index distribution in the direction, the focal length of the optical deflector side lens of the scanning imaging lens system is f 1 (0),
The distance from the image forming position of the line image long in the main scanning corresponding direction formed by the first image forming optical system to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens is S 0 (0). The distance from the rear principal point in the sub-scanning corresponding direction of the side lens to the front principal point in the sub-scanning corresponding direction of the scanned surface side lens is S 1 (0), the rear side of the scanned surface side lens in the sub-scanning corresponding direction. When the distance from the principal point to the surface to be scanned is S L (0) and the refractive index on the optical axis of the lens on the surface to be scanned is n 0 ′ (0), the sub-scanning section (the lens of the lens on the surface to be scanned) (A cross section that includes the optical axis and is parallel to the sub-scanning direction.)
Within the lens, the distribution of the refractive index within the lens is represented by “n ′ (z) = n 0 ′ (0)” with respect to the distance z from the optical axis in the sub-scanning corresponding direction.
+ Δn ′ (0) · z 2 ”, and the radii of curvature in the sub-scanning section of the lens surface of the scanned surface side lens on the optical deflector side and the scanned surface side are respectively r S3 (0) , R S4 (0),
Let the lens thickness be d 3 , these r S3 (0), r S4 (0), d 3 , n
0 The focal length in the sub-scanning direction calculated from (0) is f
2 (0), the spot diameter depth margin in the sub-scanning direction is ω 0 ,
When “Λ ′ = {1 / f 1 (0)} − {1 / S 0 (0)}”, the condition: (7) | S L (0) −1 / [{1 / f 2 (0 )} + {Λ '/ ( 1-S 1 (0) · Λ')} -2Δn '(0) · d 3] | < it is preferable to satisfy the omega 0/2 (claim 9). The focal length: f 2 (0) is expressed as f 2 (0) = 1 / [{n 0 ′ (0) −1} {(1 / r S3 (0)) − (1 /
r S4 (0))} + {n 0 '(0) -1} 2 · d 3 / {n 0 ' (0) · r
S3 (0) .rS4 (0)}]. When the value exceeds the upper limit of the condition (7), the imaging position shift of the light spot in the direction corresponding to the sub-scan (from the surface to be scanned) becomes large, and the light spot diameter in the sub-scan direction becomes significantly larger than the design value.

【0020】上記請求項5または6または7記載の光走
査装置において、第2結像光学系である走査結像レンズ
系が2枚のレンズで構成され、これら2枚のレンズが共
に、副走査対応方向に屈折率分布を有する場合は、走査
結像レンズ系の光偏向器側レンズの光軸上の屈折率をn
0(0)とするとき、副走査断面(光偏向器側レンズの光
軸を含み副走査対応方向に平行な平断面)内で、副走査
対応方向における光軸からの距離:zに対して、同レン
ズ内の屈折率の分布を「n(z)=n0(0)+Δn(0)・
2」で近似し、光偏向器側レンズの、光偏向器側およ
び被走査面側の各レンズ面の副走査断面内における曲率
半径をそれぞれ、rS1(0),rS2(0)、レンズ肉厚をd
1、これらrS1(0),rS2(0),d1,n0(0)から算出
される副走査対応方向の焦点距離をf1(0)とし、走査
結像レンズ系の被走査面側レンズの光軸上の屈折率をn
0'(0)とするとき、副走査断面(被走査面側レンズの光
軸を含み副走査対応方向に平行な平断面)内で、副走査
対応方向における光軸からの距離:zに対して、同レン
ズ内の屈折率の分布を「n'(z)=n0'(0)+Δn'(0)
・z2」で近似し、被走査面側レンズの、光偏向器側お
よび被走査面側の各レンズ面の、副走査断面内における
曲率半径をそれぞれ、rS3(0),rS4(0)、レンズ肉厚
をd3、これらrS3(0),rS4(0),d3,n0'(0)から
算出される副走査対応方向の焦点距離をf2(0)とし、
第1結像光学系により結像する主走査対応方向に長い線
像の結像位置から光偏向器側レンズの副走査対応方向の
前側主点に至る距離をS0(0)、光偏向器側レンズの副
走査対応方向の後側主点から被走査面側レンズの副走査
対応方向の前側主点に至る距離をS1(0)、被走査面側
レンズの副走査対応方向の後側主点から被走査面に至る
距離をSL(0)、副走査方向のスポット径深度余裕をω0
とし、「Λ={1/f1(0)}−2Δn(0)・d1−{1/S
0(0)}」とするとき、条件: (8) |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・Λ)} −2Δn'(0)・d3]|<ω0/2 を満足することが好ましい(請求項10)。ここで、f
1(0)は、(6)式におけるものと同様であり、f2(0)
は(7)式におけるものと同様である。条件(8)の上
限を超えると、光スポットの副走査対応方向の(被走査
面からの)結像位置ずれが大きくなり、副走査方向の光
スポット径が設計値よりも顕著に大きくなる。
[0020] In the optical scanning device according to claim 5, the scanning image forming lens system as the second image forming optical system is composed of two lenses, and both of the two lenses are sub-scanning. When the refractive index distribution is provided in the corresponding direction, the refractive index on the optical axis of the lens on the optical deflector side of the scanning imaging lens system is set to n.
When 0 (0) is set, the distance from the optical axis in the sub-scanning corresponding direction: z in the sub-scanning cross section (a plane cross section including the optical axis of the optical deflector-side lens and parallel to the sub-scanning corresponding direction). , The distribution of the refractive index in the lens is expressed as “n (z) = n 0 (0) + Δn (0) ·
z 2 ”, and the radii of curvature of the lens on the optical deflector side and the lens surface on the scanned surface side in the sub-scanning cross section of the lens on the optical deflector side are respectively r S1 (0), r S2 (0), Lens thickness d
1 , the focal length in the sub-scanning corresponding direction calculated from these r S1 (0), r S2 (0), d 1 , n 0 (0) is f 1 (0), The refractive index on the optical axis of the surface side lens is n
When 0 ′ (0) is set, the distance from the optical axis in the sub-scanning corresponding direction: z in the sub-scanning section (a plane section including the optical axis of the scanned surface side lens and parallel to the sub-scanning corresponding direction) Then, the distribution of the refractive index in the lens is expressed as “n ′ (z) = n 0 ′ (0) + Δn ′ (0)
Z 2 ”, and the radii of curvature in the sub-scanning section of the lens surface of the scanning surface side lens on the optical deflector side and the lens surface of the scanning surface side are respectively r S3 (0) and r S4 (0 ), The lens thickness is d 3 , and the focal length in the sub-scanning corresponding direction calculated from these r S3 (0), r S4 (0), d 3 , n 0 ′ (0) is f 2 (0),
The distance from the image forming position of the line image long in the main scanning corresponding direction formed by the first image forming optical system to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens is S 0 (0). The distance from the rear principal point in the sub-scanning corresponding direction of the side lens to the front principal point in the sub-scanning corresponding direction of the scanned surface side lens is S 1 (0), the rear side of the scanned surface side lens in the sub-scanning corresponding direction. The distance from the principal point to the surface to be scanned is S L (0), and the spot diameter depth margin in the sub-scanning direction is ω 0
And Λ = {1 / f 1 (0)} − 2Δn (0) · d 1 − {1 / S
0 (0)} ”, the condition is: (8) | S L (0) −1 / [{1 / f 2 (0)} + {Λ / (1−S 1 (0) · Λ)} -2Δn '(0) · d 3 ] | < it is preferable to satisfy the omega 0/2 (claim 10). Where f
1 (0) is the same as that in equation (6), and f 2 (0)
Is the same as in equation (7). When the value exceeds the upper limit of the condition (8), the imaging position shift of the light spot in the sub-scanning corresponding direction (from the surface to be scanned) becomes large, and the light spot diameter in the sub-scanning direction becomes significantly larger than the designed value.

【0021】[0021]

【発明の実施の形態】以下、具体的な実施の形態を説明
する。請求項1記載の光走査装置の実施の1形態を示す
図1(a)において、発光源であるLD10から放射され
た発散性の光束は、LD10と共に「光源」を構成する
カップリングレンズ12により「以後の光学系」にカッ
プリングされる。光源からの光束は「第1結像光学系」
であるシリンダレンズ14により副走査対応方向(図面
に直交する方向)に収束され、「光偏向器」であるポリ
ゴンミラー16の偏向反射面近傍に主走査対応方向に長
い線像として結像し、ポリゴンミラー16の回転により
等角速度的に偏向する。偏向光束は「第2結像光学系」
を成す単玉の光走査用レンズ18に入射し、光走査用レ
ンズ18の作用により被走査面20(その位置に、光導
電性の感光体が配備される)上に光スポットとして集光
され、被走査面20を主走査方向(図の上下方向)に光
走査する。図中の距離:Wは「有効主走査幅」である。
DESCRIPTION OF THE PREFERRED EMBODIMENTS Specific embodiments will be described below. In FIG. 1A showing an embodiment of the optical scanning device according to the present invention, a divergent light beam emitted from an LD 10 as a light emitting source is coupled with a coupling lens 12 constituting a “light source” together with the LD 10. It is coupled to the “optical system after”. The light flux from the light source is "first imaging optical system"
Is converged in the sub-scanning corresponding direction (the direction orthogonal to the drawing) by the cylinder lens 14 and forms a linear image long in the main scanning corresponding direction near the deflecting and reflecting surface of the polygon mirror 16 which is an “optical deflector”. The light is deflected at a constant angular velocity by the rotation of the polygon mirror 16. Deflected light beam is "second imaging optical system"
And is condensed as a light spot on a scanned surface 20 (a photoconductive photoreceptor is provided at the position) by the action of the light scanning lens 18. Then, the scanned surface 20 is optically scanned in the main scanning direction (vertical direction in the figure). The distance W in the figure is the “effective main scanning width”.

【0022】即ち、図1の実施の形態は「光源10,1
2からの光束を、第1結像光学系14により主走査対応
方向に長い線像として結像させ、線像の結像位置近傍に
偏向反射面を持つ光偏向器16により偏向させ、偏向さ
れた光束を第2結像光学系18により被走査面20上に
光スポットとして集光させて光走査を行う光走査装置で
あって、第2結像光学系18はアナモフィックな単玉レ
ンズである走査結像レンズ」で構成されている(請求項
1)。なお、第1結像光学系であるシリンダレンズ14
は「凹のシリンダミラー」により代替することができ
る。「カップリングレンズ」は発光源からの光束を、シ
リンダレンズ以下の光学系にカップリングさせる光学素
子であり、発光源からの光束を「平行光束」または「弱
い集光性の光束」もしくは「弱い発散性の光束」にする
ことができる。
That is, the embodiment shown in FIG.
The light beam from 2 is formed as a long linear image in the main scanning corresponding direction by the first imaging optical system 14, and is deflected and deflected by an optical deflector 16 having a deflecting / reflecting surface near the image forming position of the line image. The light beam is focused on the surface to be scanned 20 by the second imaging optical system 18 as a light spot to perform optical scanning, and the second imaging optical system 18 is an anamorphic single lens. (Imaging lens). In addition, the cylinder lens 14 as the first imaging optical system
Can be replaced by a “concave cylinder mirror”. A "coupling lens" is an optical element that couples a light beam from a light emitting source to an optical system below a cylinder lens, and converts a light beam from a light emitting source into a "parallel light beam" or a "weak light-collecting light beam" or "weak light beam" Divergent light flux ".

【0023】図1(a)に示す実施の形態では、カップリ
ングレンズ12はLD10からの光束を「弱い集光光
束」とする機能を持ち、このため主走査対応方向に就い
てみると、偏向角:0の偏向光束は、光走査用レンズ1
8がなければ自然集光点:Qに集光する。「自然集光
点」は、カップリングレンズによりカップリングされた
光束が「光源から被走査面に到る光路を光軸に沿って直
線的に展開した仮想的な光路」において、この光路上に
線像結像光学系や走査結像レンズが無いとした場合に自
然に集光する位置である。偏向反射面による「偏向の起
点」から自然集光点:Qに到る距離を、図のように距
離:Sで表す。自然集光点Qが、光偏向器よりも被走査
面側にあるとき「S>0」であり、このときはカップリ
ングされた光束は弱い収束性である。また、自然集光点
Qが光偏向器よりも光源側にあるとき「S<0」で、こ
のときカップリングされた光束は弱い発散性である。カ
ップリングされた光束が平行光束であるときは「S=
∞」である。
In the embodiment shown in FIG. 1A, the coupling lens 12 has a function of converting the light beam from the LD 10 into a "weakly condensed light beam". The deflection light beam having an angle of 0 is transmitted to the optical scanning lens 1.
If there is no 8, the light is condensed on the natural light condensing point: Q. The “natural light condensing point” is defined as a light beam coupled by the coupling lens, which is a “virtual light path in which the light path from the light source to the surface to be scanned is linearly developed along the optical axis”. This is a position where light is naturally condensed when there is no line image forming optical system or scanning image forming lens. The distance from the “deflection start point” by the deflecting reflection surface to the natural focusing point: Q is represented by the distance: S as shown in the figure. When the natural light converging point Q is closer to the surface to be scanned than the optical deflector, “S> 0”. At this time, the coupled light flux has weak convergence. When the natural light converging point Q is closer to the light source than the optical deflector, “S <0”, and the light flux coupled at this time is weakly divergent. When the coupled light flux is a parallel light flux, “S =
∞ ”.

【0024】図2は、光走査用レンズ18の「副走査断
面」内の形状を示している。図のように副走査断面内の
形状は「偏向反射面側(図の左側)に凹のメニスカス形
状」で(請求項3)、副走査対応方向の前側主点:Hお
よび後側主点:H’は共に、レンズ本体よりも被走査面
側(図の右側)に位置する。従って、光走査用レンズ1
8の実際の位置よりも副走査対応方向の結像倍率を低減
化でき、組み付け誤差の結像性能への影響を軽減でき
る。図中のA点は「線像の結像位置」、B点は「上記線
像を物点とする光束が光走査用レンズ18により結像す
る結像点」である。上記A点と前側主点:Hの間の距
離:S0(0)、後側主点:H’とB点との距離:S0'
(0)を用いると、前述の|β(0)|は「S0'(0)/S
0(0)」である。また、図中のSL(0)は、後側主点:
H'から被走査面20に至る距離を表し、f(0)は、光
走査用レンズ18の、副走査対応方向の曲率半径:rS1
(0),rS2(0),肉厚:d,光軸上の屈折率n0(0) か
ら算出される副走査対応方向焦点距離であり、ω0は副
走査方向のスポット径深度余裕を表している。
FIG. 2 shows the shape of the optical scanning lens 18 in the “sub-scan section”. As shown in the figure, the shape in the sub-scanning cross section is “the meniscus shape concave on the deflecting reflection surface side (left side in the figure)” (Claim 3), and the front principal point: H and the rear principal point in the sub-scanning corresponding direction: H ′ are both located on the scanning surface side (right side in the figure) of the lens body. Therefore, the optical scanning lens 1
The imaging magnification in the sub-scanning corresponding direction can be reduced as compared with the actual position of No. 8 and the influence of the assembly error on the imaging performance can be reduced. Point A in the figure is a “image forming position of a line image”, and point B is “an image forming point at which a light beam having the line image as an object point is formed by the optical scanning lens 18”. Distance between point A and front principal point: H: S 0 (0), rear principal point: distance between H ′ and point B: S 0
(0), the above-mentioned | β (0) | is expressed as “S 0 '(0) / S
0 (0) ". S L (0) in the figure is a rear principal point:
F (0) is the radius of curvature of the optical scanning lens 18 in the sub-scanning corresponding direction: r S1.
(0), r S2 (0), thickness: d, focal length in the sub-scanning direction calculated from the refractive index n 0 (0) on the optical axis, and ω 0 is the spot diameter depth margin in the sub-scanning direction. Is represented.

【0025】図1(d)を参照すると、この図の左側の
図は、走査結像レンズ18における屈折率の分布を等高
線図的に示している。図1(d)の右側の図に示すよう
に、走査結像レンズ18における光軸上の屈折率をn
0(0)とするとき、副走査断面内で副走査対応方向にお
ける光軸からの距離:zに対して、屈折率の分布は、n
(z)=n0(0)+Δn(0)・z2で近似することができ
る。Δn(0)は「副走査断面内で副走査対応方向におけ
る単位距離(1mm)当りの、屈折率の変化」を表し、
屈折率分布:n(z)は、光軸の両側のz座標に関して対
称的である。走査結像レンズ18の、光偏向器側および
被走査面側の各レンズ面の、副走査断面内における曲率
半径をそれぞれrS1(0),rS2(0)、レンズ肉厚をd、
これらrS1(0),rS2(0),d,n0(0) から算出され
る副走査対応方向焦点距離をf(0)とする。
Referring to FIG. 1D, the figure on the left side of the figure shows the distribution of the refractive index in the scanning image forming lens 18 in a contour diagram. As shown in the diagram on the right side of FIG.
When 0 (0) is set, the distribution of the refractive index is n with respect to the distance z from the optical axis in the sub-scanning corresponding direction in the sub-scanning cross section.
(z) = n 0 (0) + Δn (0) · z 2 Δn (0) represents “change in refractive index per unit distance (1 mm) in the sub-scanning corresponding direction in the sub-scanning cross section”;
The refractive index distribution: n (z) is symmetric with respect to the z coordinate on both sides of the optical axis. The radii of curvature in the sub-scanning section of each lens surface of the scanning imaging lens 18 on the optical deflector side and the surface to be scanned side are r S1 (0) and r S2 (0), respectively, and the lens thickness is d.
The focal length in the sub-scanning corresponding direction calculated from these r S1 (0), r S2 (0), d, and n 0 (0) is f (0).

【0026】上記屈折率の分布:n(z)=n0(0)+Δ
n(0)・z2を「レンズ作用」に換算すると、焦点距
離:Δf=−1/{2Δn(0)・d}を持ったレンズに
相当し、Δn(0)>0のときは「負のレンズ」、Δn
(0)<0のときは「正のレンズ」のレンズ作用と等価で
ある。従って「屈折率の分布が無いときの走査結像レン
ズ18の焦点距離:f(0)と焦点距離:Δfを持つレン
ズの合成レンズ系」としての焦点距離は、1/[{1/
f(0)}+(1/Δf)]となる。屈折率分布による焦
点距離変化は結像点の変化をもたらす。上記屈折率分布
があるときの「後側主点:H’から結像点に至る距離」
をS’とすると、結像関係の式: (1/S’)+{1/S0(0)}={1/f(0)}+(1/
Δf) が成り立つことになるので、この式に上記Δf=−1/
{2Δn(0)・d}を代入すると、 S’=1/[{1/f(0)}−2Δn(0)・d−{1/S
0(0)}] が得られる。このとき、副走査対応方向における光スポ
ットの結像位置は、設計上の結像位置:SL(0)とのあ
いだに「ずれ:S’−SL(0)」を生じる。
Distribution of the refractive index: n (z) = n 0 (0) + Δ
When n (0) · z 2 is converted to “lens action”, it corresponds to a lens having a focal length: Δf = −1 / {2Δn (0) · d}, and when Δn (0)> 0, “ Negative lens ", Δn
When (0) <0, it is equivalent to the lens function of a “positive lens”. Accordingly, the focal length of the “synthetic lens system of the lens having the focal length: f (0) and the focal length: Δf of the scanning imaging lens 18 when there is no refractive index distribution” is 1 / [{1 /
f (0)} + (1 / Δf)]. A change in the focal length due to the refractive index distribution causes a change in the imaging point. "The distance from the rear principal point: H 'to the image point" when the above-mentioned refractive index distribution exists.
Is S ′, the expression of the imaging relationship is: (1 / S ′) + {1 / S 0 (0)} = {1 / f (0)} + (1 /
Δf) is satisfied, so that Δf = −1 /
By substituting {2Δn (0) · d}, S ′ = 1 / [{1 / f (0)} − 2Δn (0) · d− {1 / S
0 (0)}]. At this time, the image forming position of the light spot in the sub-scanning corresponding direction has a “deviation: S′−S L (0)” between the image forming position: S L (0) in design.

【0027】副走査方向のスポット径深度余裕:ω0
「副走査対応方向のビームウエスト径(デフォーカスを
変化させたときの副走査方向の光スポット径の最小値)
に対して、副走査方向の光スポット径が10%以下とな
るデフォーカス幅」として定義され、副走査方向の光ス
ポット径の許容領域を表す。この許容領域はビームウエ
ストの両側に存在するので、実際には結像位置ずれの絶
対値は「ω0/2」より小さくなくてはならない。従っ
て、副走査方向の光スポット径が、スポット径深度余裕
内に入る条件は、条件(1)が満足されることであるこ
とになる。
Spot diameter depth margin in the sub-scanning direction: ω 0 is “beam waist diameter in the sub-scanning corresponding direction (minimum value of the light spot diameter in the sub-scanning direction when defocus is changed)
Is defined as "a defocus width at which the light spot diameter in the sub-scanning direction is 10% or less", and represents an allowable area of the light spot diameter in the sub-scanning direction. This tolerance area is present on both sides of the beam waist, must without actually reducing the absolute value of the imaging position deviation than "omega 0/2" is. Therefore, the condition that the light spot diameter in the sub-scanning direction falls within the spot diameter depth margin is that the condition (1) is satisfied.

【0028】図14は、請求項5〜8記載の発明の実施
の1形態を説明に必要な部分のみ略示している。光源か
ら光偏向器に至る光学配置は図1(a)と同様で、符号A
は線像の結像位置を示している。
FIG. 14 schematically shows only a portion necessary for explanation of the first embodiment of the present invention. The optical arrangement from the light source to the optical deflector is the same as in FIG.
Indicates the imaging position of the line image.

【0029】即ち、図14の実施の形態において、光源
からの光束は、図示されない第1結像光学系により主走
査対応方向に長い線像として結像し、線像の結像位置:
A近傍に偏向反射面を持つ光偏向器により偏向され、偏
向された光束は第2結像光学系により被走査面20上に
光スポットとして集光して光走査を行う。第2結像光学
系は2枚以上のレンズ18’,19を含む走査結像レン
ズ系で、少なくとも1枚のレンズは副走査対応方向に屈
折率分布を有し、走査結像レンズ系における最も被走査
面側にあるレンズ19は「副走査対応方向に正のパワ
ー」を持つ(請求項5)。また、この実施の形態におい
て、第2結像光学系である走査結像レンズ系は2枚のレ
ンズ18’,19で構成され、副走査対応方向のパワー
を、光偏向器側のレンズ18’につきP1、被走査面2
0側のレンズ19につきP2とするとき「P2>P1」で
ある(請求項6)。第2結像光学系である走査結像レン
ズ系をなす2枚のレンズ18’,19のうち、被走査面
20側のレンズ19の「副走査断面内の形状」は、図1
4には示されていないが「光偏向器側に凹のメニスカス
形状」である(請求項7)。
That is, in the embodiment shown in FIG. 14, the light beam from the light source is imaged as a long line image in the main scanning corresponding direction by a first image forming optical system (not shown).
The light beam deflected by an optical deflector having a deflecting / reflecting surface in the vicinity of A is condensed as a light spot on the surface to be scanned 20 by the second imaging optical system to perform optical scanning. The second imaging optical system is a scanning imaging lens system including two or more lenses 18 ′ and 19, and at least one lens has a refractive index distribution in a sub-scanning corresponding direction. The lens 19 on the surface to be scanned has "positive power in the direction corresponding to sub-scanning" (claim 5). In this embodiment, the scanning image forming lens system as the second image forming optical system includes two lenses 18 'and 19, and the power in the sub-scanning corresponding direction is changed to the lens 18' on the optical deflector side. P 1 , scanned surface 2
A "P 2> P 1" when the P 2 per 0 side of the lens 19 (claim 6). The “shape in the sub-scanning section” of the lens 19 on the scanning surface 20 side among the two lenses 18 ′ and 19 forming the scanning imaging lens system as the second imaging optical system is shown in FIG.
Although not shown in FIG. 4, it has a "meniscus shape concave toward the optical deflector" (claim 7).

【0030】さらに、第2結像光学系を構成する2枚の
レンズ18’,19のうち光偏向器側のレンズ18’の
みが、副走査対応方向に屈折率分布を有し、レンズ1
8’における光軸上の屈折率をn0(0)とすると、副走
査断面内で副走査対応方向における光軸からの距離:z
に対して、同レンズ内の屈折率の分布は「n(z)=n
0(0)+Δn(0)・z2」で近似できる。光偏向器側レン
ズ18’の、光偏向器側および被走査面側の各レンズ面
の副走査断面内の曲率半径を、それぞれrS1(0),rS2
(0)、レンズ肉厚をd1、これらrS1(0),rS2(0),
1,n0(0)から算出される副走査対応方向焦点距離を
1(0) とし、線像の結像位置:Aから、光偏向器側レ
ンズ18’の副走査対応方向の前側主点までの距離をS
0(0) 、同レンズ18’の副走査対応方向の後側主点か
ら被走査面側レンズの前側主点までの距離をS1(0)、
被走査面側レンズ19の、副走査対応方向の後側主点か
ら被走査面までの距離をSL(0) 、同レンズ19の副走
査対応方向焦点距離をf2(0)、副走査方向のスポット
径深度余裕をω0とし、Λ={1/f1(0)}−2Δn(0)・
1−{1/S0(0)}とする。
Further, of the two lenses 18 'and 19 constituting the second imaging optical system, only the lens 18' on the optical deflector side has a refractive index distribution in the sub-scanning corresponding direction.
Assuming that the refractive index on the optical axis at 8 ′ is n 0 (0), the distance from the optical axis in the sub-scanning corresponding direction in the sub-scanning section: z
In contrast, the distribution of the refractive index in the lens is “n (z) = n
0 (0) + Δn (0) · z 2 ”. The radii of curvature of the lens surfaces of the optical deflector-side lens 18 'on the optical deflector side and the surface to be scanned side in the sub-scanning cross section are represented by r S1 (0) and r S2 respectively.
(0), the lens thickness is d 1 , these r S1 (0), r S2 (0),
The focal length in the sub-scanning direction calculated from d 1 and n 0 (0) is f 1 (0), and the front side of the optical deflector-side lens 18 ′ in the sub-scanning direction from the imaging position A of the line image. The distance to the principal point is S
0 (0), the distance from the rear principal point of the lens 18 ′ in the sub-scanning corresponding direction to the front principal point of the lens to be scanned is S 1 (0),
The distance from the rear principal point of the scanned surface side lens 19 in the sub-scanning corresponding direction to the surface to be scanned is S L (0), the focal length of the lens 19 in the sub-scanning direction is f 2 (0), Let the spot diameter depth margin in the direction be ω 0 and Λ = {1 / f 1 (0)} − 2Δn (0) ·
Let d 1 − {1 / S 0 (0)}.

【0031】レンズ18’に屈折率分布が存在すると、
レンズ18’の副走査対応方向の焦点距離がf1(0)か
らΔf1=−1/2Δn(0)・d1だけずれることは、上
述の説明から容易に理解されよう。従って、レンズ1
8’により結像される線像の副走査対応方向の像のでき
る位置をレンズ18’の後側焦点からの距離:S1
は、 S1’=1/[{1/f1(0)}−2Δn(0)・d1−{1
/S0(0)}] であり、この結像位置からレンズ19の前側主点までの
距離:S2は、 S2=S1’−S1(0) である。レンズ19(屈折率分布は無い)による(副走
査対応方向の)結像位置のレンズ19の後側主点からの
距離をS2’とすると、結像関係の式: (1/S2’)={1/f1(0)}+(1/S2)={1/f1
(0)}+1/(1/[1/{1/f1(0)}−2Δn(0)・d1
−{1/S0(0)}]−S1(0)) が成り立つので、これからS2’を求め、レンズ18’
に屈折率分布の無いときの結像位置:SL(0)との差:
|S2’−SL(0)|を求めると、前述の条件(1)の左辺
を導いたとのと同様の計算により、前記「Λ」を用いて
(6)式の左辺: |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・
Λ)}]| が得られるので、レンズ18’の屈折率分布の存在のも
とで、実用上良好な「副走査方向の光スポット径」で光走
査を行える条件は、条件(6)が満足されることである
ことが理解される。
If there is a refractive index distribution in the lens 18 ',
The fact that the focal length of the lens 18 'in the sub-scanning corresponding direction deviates from f 1 (0) by Δf 1 = − / Δn (0) · d 1 will be easily understood from the above description. Therefore, lens 1
Distance 8 'by a position that can sub-scanning direction of the image of the line image formed lens 18' from the rear focal point of: S 1 '
Is: S 1 ′ = 1 / [f1 / f 1 (0)} − 2Δn (0) · d 1 − {1
/ S 0 (0)}], and the distance from this imaging position to the front principal point of the lens 19: S 2 is S 2 = S 1 ′ −S 1 (0). Assuming that the distance from the rear principal point of the lens 19 at the imaging position (in the direction corresponding to the sub-scanning) by the lens 19 (having no refractive index distribution) is S 2 ′, the expression of the imaging relationship is: (1 / S 2 ′) ) = {1 / f 1 (0)} + (1 / S 2 ) = {1 / f 1
(0)} + 1 / (1 / [1 // 1 / f 1 (0)} − 2Δn (0) · d 1
− {1 / S 0 (0)}] − S 1 (0)), so S 2 ′ is obtained from this, and the lens 18 ′ is obtained.
Position when there is no refractive index distribution: Difference from S L (0):
When | S 2 ′ −S L (0) | is obtained, the left side of the equation (6) is calculated using the above “Λ” by the same calculation as that for deriving the left side of the above-mentioned condition (1): | S L (0) -1 / [{1 / f 2 (0)} + {Λ / (1-S 1 (0).
Λ)}] | can be obtained, and the condition (6) is that the optical scanning can be performed with the “light spot diameter in the sub-scanning direction” that is practically good in the presence of the refractive index distribution of the lens 18 ′. It is understood that this is to be satisfied.

【0032】逆に、第2結像光学系を構成する2枚のレ
ンズ18’,19のうち被走査面側レンズ19のみが、
副走査対応方向に屈折率分布を有する場合、レンズ19
における光軸上の屈折率をn0'(0)とすると、副走査断
面内で副走査対応方向における光軸からの距離:zに対
して、同レンズ内の屈折率の分布は「n'(z)=n0'(0)
+Δn'(0)・z2」で近似できる。図15に示すよう
に、光偏向器側レンズ18’の焦点距離をf1(0)と
し、第1結像光学系により結像する主走査対応方向に長
い線像の結像位置:Aから、光偏向器側レンズ18’の
副走査対応方向の前側主点に至る距離をS0(0)、光偏
向器側レンズ18’の副走査対応方向の後側主点から被
走査面側レンズ19の副走査対応方向の前側主点に至る
距離をS1(0)、被走査面側レンズ19の副走査対応方
向の後側主点から被走査面20に至る距離をSL(0)、
被走査面側レンズ19の、光偏向器側及び被走査面側の
各レンズ面の、副走査断面内における曲率半径をそれぞ
れrS3(0),rS4(0)、レンズ肉厚をd3とし、これら
S3(0),rS4(0),d3および上記n0'(0)から算出
される副走査対応方向の焦点距離をf2(0)、副走査方
向のスポット径深度余裕をω0とし、「Λ'={1/f
1(0)}−{1/S0(0)}」とする。この場合に、レンズ1
9の屈折率分布の存在のもとで実用上良好な「副走査方
向の光スポット径」で光走査を行える条件は、上記と同
様の考察により、条件: (7) |SL(0)−1/[{1/f2(0)}+{Λ'/(1−S1(0)・Λ')} −2Δn'(0)・d3]|<ω0/2 が満足されることであることが分かる。
Conversely, of the two lenses 18 'and 19 constituting the second imaging optical system, only the lens 19 on the scanning surface side is
If the lens has a refractive index distribution in the sub-scanning direction, the lens 19
Assuming that the refractive index on the optical axis at n is n 0 ′ (0), the distribution of the refractive index within the lens is “n ′” with respect to the distance z from the optical axis in the sub-scanning corresponding direction in the sub-scanning cross section. (z) = n 0 '(0)
+ Δn ′ (0) · z 2 ”. As shown in FIG. 15, the focal length of the optical deflector-side lens 18 ′ is f 1 (0), and the image forming position of the line image long in the main scanning corresponding direction formed by the first image forming optical system is from A. The distance from the rear principal point of the optical deflector-side lens 18 'to the sub-scanning corresponding direction in the sub-scanning direction is S 0 (0). the distance reaching the front principal point of the sub-scanning direction of 19 S 1 (0), a distance from a rear principal point of the sub-scanning direction of the scan surface side lens 19 on the scanned surface 20 S L (0) ,
The radii of curvature in the sub-scanning section of the lens surface of the scanned surface side lens 19 on the optical deflector side and the scanned surface side are r S3 (0) and r S4 (0), respectively, and the lens thickness is d 3. Where f 2 (0) is the focal length in the sub-scanning corresponding direction calculated from these r S3 (0), r S4 (0), d 3 and the above n 0 ′ (0), and the spot diameter depth in the sub-scanning direction The margin is ω 0, and “Λ ′ = {1 / f
1 (0)} − {1 / S 0 (0)} ”. In this case, the lens 1
The conditions under which the optical scanning can be performed with the “light spot diameter in the sub-scanning direction” that is practically favorable in the presence of the refractive index distribution of 9 are based on the same considerations as above, and are as follows: (7) | SL (0) -1 / [{1 / f 2 (0)} + {Λ '/ (1-S 1 (0) · Λ')} -2Δn '(0) · d 3] | <ω 0/2 is satisfied It is understood that it is.

【0033】さらに、第2結像光学系である走査結像レ
ンズ系を構成する光偏向器側レンズ18’、被走査面側
レンズ19が共に、副走査対応方向に屈折率分布を有す
る場合には、光偏向器側レンズ18’の光軸上の屈折率
をn0(0)とするとき、副走査断面内で副走査対応方向
における光軸からの距離:zに対して、同レンズ内の屈
折率の分布は「n(z)=n0(0)+Δn(0)・z2」で近
似でき、被走査面側レンズ19の光軸上の屈折率をn0'
(0)とするとき、副走査断面内で副走査対応方向におけ
る光軸からの距離:zに対し、同レンズ内の屈折率の分
布は「n'(z)=n0'(0)+Δn'(0)・z2」で近似で
きる。光偏向器側レンズ18’の、光偏向器側及び被走
査面側の各レンズ面の、副走査断面内における曲率半径
をそれぞれ、rS1(0),rS2(0)、レンズ肉厚をd1
これらrS1(0),rS2(0),d1,n0(0)から算出され
る副走査対応方向の焦点距離をf1(0)とし、被走査面
側レンズ19の、光偏向器側および被走査面側の各レン
ズ面の、副走査断面内における曲率半径をそれぞれ、r
S3(0),rS4(0)、レンズ肉厚をd3、これらr
S3(0),rS4(0),d3,n0'(0)から算出される副走
査対応方向の焦点距離をf2(0)とし、第1結像光学系
により結像する主走査対応方向に長い線像の結像位置か
ら光偏向器側レンズ18’の副走査対応方向の前側主点
に至る距離をS0(0)、光偏向器側レンズ18’の副走
査対応方向の後側主点から被走査面側レンズ19の副走
査対応方向の前側主点に至る距離をS1(0)、被走査面
側レンズ19の副走査対応方向の後側主点から被走査面
に至る距離をSL(0)、副走査方向のスポット径深度余
裕をω0とし、「Λ={1/f1(0)}−2Δn(0)・d1
{1/S0(0)}」とすると、この場合に、レンズ19の屈
折率分布の存在のもとで実用上良好な「副走査方向の光
スポット径」で光走査を行える条件は、上記と同様の考
察により、条件: (8) |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・Λ)} −2Δn'(0)・d3]|<ω0/2 を満足することであることが分かる。
Further, when both the optical deflector side lens 18 'and the scanned surface side lens 19 constituting the scanning image forming lens system as the second image forming optical system have a refractive index distribution in the sub-scanning corresponding direction. When the refractive index on the optical axis of the optical deflector-side lens 18 ′ is n 0 (0), the distance z from the optical axis in the sub-scanning corresponding direction in the sub-scanning section is within the lens. Can be approximated by “n (z) = n 0 (0) + Δn (0) · z 2 ”, and the refractive index on the optical axis of the scanning surface side lens 19 is n 0 ′.
When (0) is set, the distribution of the refractive index in the lens is “n ′ (z) = n 0 ′ (0) + Δn” with respect to the distance z from the optical axis in the sub-scanning corresponding direction in the sub-scanning cross section. '(0) .z 2 ". The radii of curvature of the lens surfaces of the optical deflector-side lens 18 ′ on the optical deflector side and the surface to be scanned side in the sub-scanning section are respectively r S1 (0), r S2 (0), and the lens thickness. d 1 ,
The focal length in the sub-scanning corresponding direction calculated from these r S1 (0), r S2 (0), d 1 , and n 0 (0) is f 1 (0), and the light deflection of the scanning surface side lens 19 is The radii of curvature of the respective lens surfaces on the device side and the surface to be scanned in the sub-scanning cross section are r
S3 (0), r S4 (0), lens thickness d 3 , r
S3 (0), r S4 ( 0), d 3, n 0 ' the focal length of the sub-scanning direction calculated from (0) and f 2 (0), the main for imaging by the first imaging optical system The distance from the image forming position of the line image long in the scanning corresponding direction to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens 18 ′ is S 0 (0), and the sub-scanning corresponding direction of the optical deflector-side lens 18 ′. The distance from the rear principal point to the front principal point in the sub-scanning corresponding direction of the scanned surface side lens 19 is S 1 (0), and scanning is performed from the rear principal point of the scanned surface side lens 19 in the sub-scanning corresponding direction. The distance to the surface is S L (0), the spot diameter depth margin in the sub-scanning direction is ω 0, and “Λ = {1 / f 1 (0)} − 2Δn (0) · d 1
{1 / S 0 (0)} ”, in this case, the conditions under which the optical scanning can be performed with the“ light spot diameter in the sub-scanning direction ”that is practically favorable in the presence of the refractive index distribution of the lens 19 are as follows: the same considerations as above, condition: (8) | S L ( 0) -1 / [{1 / f 2 (0)} + {Λ / (1-S 1 (0) · Λ)} -2Δn ' (0) · d 3] | it can be seen <is to satisfy the ω 0/2.

【0034】[0034]

【実施例】以下、具体的な実施例と比較例とを挙げる。
実施例1〜3は請求項1〜3記載の光走査装置の実施例
であり、比較例1〜3は実施例1〜3に対する比較例で
ある。上記実施例3は請求項4記載の発明の実施例でも
ある。実施例4は、請求項5〜8記載の発明の実施例で
ある。また、実施例5は請求項9記載の光走査装置の実
施例であり、実施例6は請求項10記載の光走査装置の
実施例である。
EXAMPLES Specific examples and comparative examples will be described below.
Examples 1 to 3 are examples of the optical scanning device according to claims 1 to 3, and Comparative Examples 1 to 3 are comparative examples with respect to Examples 1 to 3. The third embodiment is also an embodiment of the fourth aspect of the present invention. Embodiment 4 is an embodiment of the invention described in claims 5 to 8. A fifth embodiment is an embodiment of the optical scanning device according to the ninth aspect, and a sixth embodiment is an embodiment of the optical scanning device according to the tenth aspect.

【0035】実施例1〜3・比較例1〜3は、図1(a)
に示すごとき実施の形態を利用して実施した。但し、こ
れら実施例および比較例で、光偏向器としては図1(a)
の、回転多面鏡16に代えて「回転単面鏡」を用い、偏
向反射面の回転軸が偏向反射面と一致するようにして
「サグ」が発生しないようにした。また、実施例1〜3
・比較例1〜3を通じ、光源のカップリングレンズでカ
ップリングされた光束は「平行光束」となり、シリンダ
レンズにより主走査対応方向に長い線像として、光偏向
器の偏向反射面の回転軸位置に結像するので、光偏向器
による偏向光束の偏向の起点は変動しない。
Examples 1 to 3 and Comparative Examples 1 to 3 are shown in FIG.
This was implemented using the embodiment shown in FIG. However, in these examples and comparative examples, the optical deflector is shown in FIG.
Instead of the rotating polygon mirror 16, a "rotating single mirror" is used, and the rotation axis of the deflecting reflecting surface is made coincident with the deflecting reflecting surface so that "sag" does not occur. Examples 1 to 3
Throughout Comparative Examples 1 to 3, the light beam coupled by the coupling lens of the light source becomes a “parallel light beam”, and the rotational axis position of the deflecting / reflecting surface of the optical deflector is converted into a long line image in the main scanning corresponding direction by the cylinder lens. Therefore, the starting point of the deflection of the deflected light beam by the optical deflector does not change.

【0036】光偏向器以後の光路において、図1(a)に
示すように、距離:d0,d1,d2を定める。距離:d1
は「単玉の走査結像レンズの肉厚」であり、条件(1)
の左辺における「d」である。また、走査結像レンズに
おける面形状を、光偏向器側の面に就きX1(Y) および
1(Y) で表し、被走査面側の面形状に就きX2(Y) お
よびx2(Y) で表す。X1(Y)およびX2(Y)は「光軸を
含み主走査対応方向に平行な面」内におけるレンズ面形
状で、非球面形状に関連して周知の式、即ち、光軸方向
にX軸、主走査対応方向にY軸を取るとき、Riを近軸
曲率半径、Ki,Ai,Bi,Ci,Di,...を定数と
して、 Xi(Y)=Y2/[Ri+Ri√{1−(1+Ki)(Y/
i)2}]+Ai・Y4+Bi・Y6+Ci・Y8+Di・Y10
+... で表され、近軸曲率半径:Ri及び定数:Ki,Ai
i,Ci,Di,.(光偏向器側面に就きi=1、被走
査面側面に就きi=2)を与えて特定される「非円弧形
状」である。
In the optical path after the optical deflector, distances d 0 , d 1 and d 2 are determined as shown in FIG. Distance: d 1
Is the "thickness of the single-lens scanning imaging lens", and the condition (1)
Is "d" on the left side of. Further, the surface shape of the scanning image forming lens is represented by X 1 (Y) and x 1 (Y) on the surface on the optical deflector side, and X 2 (Y) and x 2 on the surface shape on the scanned surface side. (Y). X 1 (Y) and X 2 (Y) are lens surface shapes in the “plane including the optical axis and parallel to the main scanning direction”, and are well-known formulas related to the aspherical shape, that is, in the optical axis direction. When taking the X-axis and the Y-axis in the main scanning corresponding direction, R i is the paraxial radius of curvature, K i , A i , B i , C i , D i,. . . Let X i (Y) = Y 2 / [R i + R i √ {1- (1 + K i ) (Y /
R i ) 2 }] + A i · Y 4 + B i · Y 6 + C i · Y 8 + D i · Y 10
+. . . Where the paraxial radius of curvature: R i and the constants: K i , A i ,
B i , C i , D i,. (I = 1 for the side of the optical deflector and i = 2 for the side of the surface to be scanned).

【0037】実施例1〜3・比較例1〜3とも「光軸を
含み主走査対応方向に平行な面内での光学配置」は共通
で、上記Ri,Ki,Ai,Bi,Ci,Di,.(i=1,
2),di(i=0〜3)および走査結像レンズ18の
材質の屈折率として光軸位置における屈折率:n0(0)
を与える。
In all of Examples 1 to 3 and Comparative Examples 1 to 3, the “optical arrangement in a plane including the optical axis and parallel to the main scanning direction” is common, and the above R i , K i , A i , and B i are used. , C i , D i,. (I = 1,
2), d i (i = 0 to 3) and the refractive index of the material of the scanning imaging lens 18 at the optical axis position: n 0 (0)
give.

【0038】「光軸を含み、主走査対応方向に平行な
面」内のデータ(実施例1〜3・比較例1〜3に共通) S=∞(カップリングされた光束は平行光束である) W=216mm、L=175mm i Rii0(0) 0 29.887 1 137.503 12.364 1.53664 2 −154.248 132.649 X1(Y): R1= 137.503,K1=−92.438, A1=−1.11822E−6,B1= 7.28745E−10, C1=−3.20311E−13,D1= 9.55204E−17 X2(Y): R2=−154.248,K2= 5.36873, A2=−2.51300E−6,B2= 1.95625E−9, C2=−1.18490E−12,D2= 3.38372E−16 。
Data in "plane including optical axis and parallel to main scanning direction" (common to Examples 1 to 3 and Comparative Examples 1 to 3) S = ∞ (Coupled light flux is parallel light flux) ) W = 216mm, L = 175mm i R i d i n 0 (0) 0 29.887 1 137.503 12.364 1.53664 2 -154.248 132.649 X 1 (Y): R 1 = 137 .503, K 1 = -92.438, A 1 = -1.11822E-6, B 1 = 7.28745E-10, C 1 = -3.20311E-13, D 1 = 9.55204E-17 X 2 (Y): R 2 = -154.248 , K 2 = 5.36873, A 2 = -2.51300E-6, B 2 = 1.95625E-9, C 2 = -1.18490E-12, D 2 = 3.38372E-16.

【0039】なお、長さの次元を持つ数値の単位は「m
m」である。上記数値中「Eとそれに続く数値」は「1
0のべき乗」を表す。例えば「E−9」は10~9を意味
し、この数値がその直前にある数値にかけられるのであ
る。以下の説明においても同様である。上記のデータに
より実現される「主走査方向の像面湾曲と歪曲収差」を
図3に示す。図3に示す歪曲収差は、偏向光束の偏向角
(画角):θに対応する光スポットの実際の像高:H
(θ)、偏向角:θに対する理想像高:H0(θ)(=k0
θ:k0;比例定数)を用いて、 [{{H(θ)−H0(θ)}/H0(θ)]×100(%)=[{{H
(θ)−k0・θ}/(k0・θ)]×100(%) により定義されるもので、周知のfθ特性に類する特性
である。
The unit of the numerical value having the length dimension is “m”.
m ”. In the above numerical values, "E and subsequent numerical values" are "1
Power of 0 ". For example, "E-9" means 10 to 9 , and this numerical value is multiplied by the numerical value immediately before it. The same applies to the following description. FIG. 3 shows “field curvature and distortion in the main scanning direction” realized by the above data. The distortion shown in FIG. 3 is the actual image height of the light spot corresponding to the deflection angle (angle of view) of the deflected light beam: H.
(θ), deflection angle: ideal image height with respect to θ: H 0 (θ) (= k 0.
θ: k 0 ; proportional constant), [{{H (θ) −H 0 (θ)} / H 0 (θ)] × 100 (%) = [{{H
(θ) −k 0 · θ} / (k 0 · θ)] × 100 (%), which is a characteristic similar to the well-known fθ characteristic.

【0040】以下に挙げる実施例1〜6・比較例1〜3
において、第1結像光学系であるシリンダレンズの中心
肉厚:D0、副走査断面内の曲率半径:Rs1(光源側),
s2(光偏向器側)、光偏向器側面から偏向反射面に至る
距離:D1、材質の屈折率:Nとする。実施例1〜3・
比較例1〜3に就き、上記D0、Rs1,Rs2、D1、Nお
よび前記n0(0)、Δn(0)、rS1(0),rS2(0)、S0
(0)、SL(0)、ω0、W、L、Z(走査結像レンズの光
偏向器側の面に入射する偏向光束の副走査対応方向の強
度半値幅)および条件(1)の左辺、条件(2)のパラ
メータ:Z・Δn(0)、条件(3)のパラメータ:{rS2
(0)/rS1(0)}×(W/L)2、β(0)を挙げる。まず、
実施例1〜3のデータを挙げる。 実施例1 実施例2 実施例3 D0 3 3 3 Rs1 30.0 30.0 30.0 Rs2 ∞ ∞ ∞ D1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 rS1(0) -60 -60 -35 rS2(0) -13.54 -14.15 -11.96 n0(0) 1.53664 1.53664 1.53664 Δn(0) 2.70E-5 -5.0E-5 1.0E-4 W 216 216 216 L 175 175 175 S0(0) 39.39 39.51 40.18 SL(0) 130.50 130.38 129.13 Z 1.02 1.02 1.02 ω0 6.7 6.7 7.8 条件(1)の左辺 3.01 0.57 0.53 Z2・Δn(0) 2.81E-5 -5.20E-5 1.04E-4 {rS2(0)/rS1(0)}×(W/L)2 0.279 0.291 0.422 β(0) 3.39 3.31 3.23 。
The following Examples 1 to 6 and Comparative Examples 1 to 3
, The center thickness of the cylinder lens as the first imaging optical system: D 0 , the radius of curvature in the sub-scanning section: R s1 (light source side),
R s2 (on the side of the light deflector), the distance from the side of the light deflector to the deflecting reflection surface: D 1 , and the refractive index of the material: N. Examples 1-3
In Comparative Examples 1 to 3, D 0 , R s1 , R s2 , D 1 , N and the above n 0 (0), Δn (0), r S1 (0), r S2 (0), S 0
(0), S L (0), ω 0 , W, L, Z (half-width of intensity of the deflected light beam incident on the surface of the scanning imaging lens on the optical deflector side in the sub-scanning corresponding direction) and condition (1) , Parameter of condition (2): Z · Δn (0), parameter of condition (3): {r S2
(0) / r S1 (0)} × (W / L) 2 and β (0). First,
Data of Examples 1 to 3 will be described. Example 1 Example 2 Example 3 D 0 3 3 3 R s1 30.0 30.0 30.0 R s2 ∞ ∞ 1 D 1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 r S1 (0) -60 -60 -35 r S2 (0)- 13.54 -14.15 -11.96 n 0 (0) 1.53664 1.53664 1.53664 Δn (0) 2.70E-5 -5.0E-5 1.0E-4 W 216 216 216 L 175 175 175 S 0 (0) 39.39 39.51 40.18 S L (0 ) 130.50 130.38 129.13 Z 1.02 1.02 1.02 ω 0 6.7 6.7 7.8 Left side of condition (1) 3.01 0.57 0.53 Z 2 · Δn (0) 2.81E-5 -5.20E-5 1.04E-4 (r S2 (0) / r S1 (0)} × (W / L) 2 0.279 0.291 0.422 β (0) 3.39 3.31 3.23.

【0041】実施例1〜3に関する「球面収差」の図を
図4〜図6に順次示す。実施例1〜3は条件(1)〜
(3)を満足し、図4〜6のように球面収差は良好であ
る。特に、実施例2ではΔn(0)<0であり、球面収差
はより良好に補正されている。実施例1,2において、
副走査断面内および副走査断面に平行な断面内における
走査結像レンズ面形状は両面ともに「円弧形状」であ
り、上記rS1(0),rS2(0)が曲率半径である。即ち、
実施例1,2において、前述の形状:x1(Y) 、x
2(Y)は、それぞれ、前述のX1(Y),X2(Y)を「光軸
上で各レンズ面から距離:rS1(0),rS2(0)だけ離
れ、主走査方向に平行で光軸に直交する軸」の回りに回
転して得られる形状である。
FIGS. 4 to 6 show diagrams of “spherical aberration” in Examples 1 to 3. In Examples 1 to 3, conditions (1) to
(3) is satisfied, and the spherical aberration is good as shown in FIGS. In particular, in Example 2, Δn (0) <0, and the spherical aberration is more favorably corrected. In Examples 1 and 2,
The scanning image forming lens surface shape in the sub-scanning cross section and in the cross section parallel to the sub-scanning cross section is "arc-shaped" on both surfaces, and the above-mentioned r S1 (0) and r S2 (0) are the radii of curvature. That is,
In the first and second embodiments, the aforementioned shapes: x 1 (Y), x
2 (Y) respectively deviates the aforementioned X 1 (Y) and X 2 (Y) from the respective lens surfaces on the optical axis by distances r S1 (0) and r S2 (0) in the main scanning direction. And a shape obtained by rotating around an axis "parallel to the optical axis and orthogonal to the optical axis."

【0042】実施例3においては、走査結像レンズ18
の両面は、図1(b)もしくは(c)で示すような「特殊な
トーリック面」となっている。前述のように、副走査断
面に平行な面内に関する形状を、図1(a)のように記
号的にx1(Y),x2(Y)で表す。Yは上記副走査断面に
平行な面の主走査対応方向における座標である。図1
(b),(c)において、曲線:X(Y)は前記「非円弧形状
(Rは上式における近軸曲率半径)」を表わす。特殊な
トーリック面は、図1(b),(c)に示すように「非円弧
形状の各Y座標位置(主走査対応方向における光軸から
の距離)に応じ、副走査断面に平行な平断面(図のXZ
面)内の曲率円の曲率半径:r(Y)が連続的に変化する
形状である。このとき、曲率半径:r(Y)における曲率
中心を連ねたものは、図1(b),(c)に鎖線で示すよう
に一般に「非直線」である。これら、rs1(Y),r
s2(Y)を特定するのに、これらが光軸対称であるときに
は、偶数次の多項式: rsk(Y)=rsk(0)+Σakj・Y**2j で表す。iは、偏向反射面側の面に就き「k=1」、被
走査面側の面に就き「k=2」であり、jは自然数:
1,2,3,...である。「Y**2j」は「Yの2
j乗」を表す。また、rs1(Y),rs2(Y)が光軸非対称
である場合には、多項式: rsk(Y)=rsk(0)+Σbkj・Y**j (j=
1,2,3,,,) で表される。前述のように各実施例1〜3とも、光偏向
器として「回転単面鏡」を用い、偏向反射面の回転軸が
偏向反射面と一致するようにしたので、偏向光束の偏向
は走査結像レンズの光軸に関して対称的であるので、上
記偶数次の多項式を用いる。
In the third embodiment, the scanning image forming lens 18
Are "special toric surfaces" as shown in FIG. 1 (b) or (c). As described above, the shape in the plane parallel to the sub-scanning section is symbolically represented by x 1 (Y) and x 2 (Y) as shown in FIG. Y is a coordinate of a plane parallel to the sub-scanning section in the main scanning corresponding direction. FIG.
In (b) and (c), the curve: X (Y) represents the aforementioned “non-arc shape (R is the paraxial radius of curvature in the above equation)”. As shown in FIGS. 1 (b) and 1 (c), the special toric surface corresponds to a flat plane parallel to the sub-scanning section according to each non-circular Y coordinate position (distance from the optical axis in the main scanning corresponding direction). Cross section (XZ in the figure)
This is a shape in which the radius of curvature: r (Y) of the curvature circle in the plane) changes continuously. At this time, a series of centers of curvature at a radius of curvature: r (Y) is generally "non-linear" as shown by a chain line in FIGS. 1 (b) and 1 (c). These r s1 (Y), r
to identify the s2 (Y), but when they are optical axis symmetry, the even-order polynomial: represented by r sk (Y) = r sk (0) + Σa kj · Y ** 2j. i is “k = 1” for the surface on the deflecting reflection surface side and “k = 2” for the surface on the scanned surface side, and j is a natural number:
1, 2, 3,. . . It is. "Y ** 2j" is "Y2
j ”. When r s1 (Y) and r s2 (Y) are asymmetrical along the optical axis, the polynomial: r sk (Y) = r sk (0) +) b kj · Y ** j (j =
1, 2, 3, ...). As described above, in each of the first to third embodiments, a “rotating single-sided mirror” is used as an optical deflector, and the rotation axis of the deflecting / reflecting surface coincides with the deflecting / reflecting surface. Since it is symmetric with respect to the optical axis of the image lens, the above-mentioned even-order polynomial is used.

【0043】実施例3において、 x1(Y):rs1(Y)=rs1(0)+Σa1j・Y**2j rs1(0)=−35,a11=2.78772E−2,a
12=−1.11838E−4,a13= 1.24795
E−7,a14=−2.06364E−11,a15=−
6.94829E−14,a16= 3.9456E−1
7 x2(Y):rs2(Y)=rs2(0)+Σa2j・Y**2j rs2(0)=−11.96 a21=−5.58E−4,a22=a23=a24=a25=a
26=..=0.0 である。
In the third embodiment, x 1 (Y): r s1 (Y) = r s1 (0) + Σa 1j · Y ** 2j r s1 (0) = − 35, a 11 = 2.77872E-2, a
12 = -1.11838E-4, a 13 = 1.24795
E-7, a 14 = -2.06364E -11, a 15 = -
6.94829E-14, a 16 = 3.9456E -1
7 x 2 (Y): r s2 (Y) = r s2 (0) + Σa 2j · Y ** 2j r s2 (0) = - 11.96 a 21 = -5.58E-4, a 22 = a 23 = A 24 = a 25 = a
26 =. . = 0.0.

【0044】実施例3では、β(θMAX)=β(θMIN)=β
(±45度)=3.13、β(0)=3.23であって、β
MAX)/β(0)=β(θMIN)/β(0)=0.97となる
から条件(4)を満足し、副走査方向の光スポット径の像
高による変動が小さい(請求項4)。なお、実施例3の
走査結像レンズでは、θMAXおよびθMINにおいてはレン
ズ内に屈折率の不均一は存在しないものとしている。
In the third embodiment, β (θ MAX ) = β (θ MIN ) = β
(± 45 degrees) = 3.13, β (0) = 3.23, and β
Since (θ MAX ) / β (0) = β (θ MIN ) / β (0) = 0.97, the condition (4) is satisfied, and the fluctuation of the light spot diameter in the sub-scanning direction due to the image height is small ( Claim 4). In the scanning imaging lens of the third embodiment, it is assumed that there is no nonuniform refractive index in the lens at θ MAX and θ MIN .

【0045】比較例1〜3のデータは次の通りである。 比較例1 比較例2 比較例3 D0 3 3 3 Rs1 30.0 30.0 30.0 Rs2 ∞ ∞ ∞ D1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 rS1(0) -14 -35 -35 rS2(0) -10.04 -11.38 -12.00 n0(0) 1.53664 1.53664 1.53664 Δn(0) 2.70E-5 2.0E-4 1.0E-4 W 216 216 216 L 175 175 175 S0(0) 43.50 39.97 40.20 SL(0) 122.89 129.37 129.11 Z 1.02 1.02 1.43 ω0 − − − 条件(1)の左辺 2.97 0.92 3.28 Z2・Δn(0) 2.81E-5 2.08E-4 2.04E-4 {rS2(0)/rS1(0)}×(W/L)2 0.885 0.401 0.423 β(0) 2.89 3.26 3.29 。The data of Comparative Examples 1 to 3 are as follows. Comparative Example 1 Comparative Example 2 Comparative Example 3 D 0 3 3 3 R s1 30.0 30.0 30.0 R s2 ∞ ∞ 1 D 1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 r S1 (0) -14 -35 -35 r S2 (0)- 10.04 -11.38 -12.00 n 0 (0) 1.53664 1.53664 1.53664 Δn (0) 2.70E-5 2.0E-4 1.0E-4 W 216 216 216 L 175 175 175 S 0 (0) 43.50 39.97 40.20 S L (0) 122.89 129.37 129.11 Z 1.02 1.02 1.43 ω 0 − − − Left side of condition (1) 2.97 0.92 3.28 Z 2・ Δn (0) 2.81E-5 2.08E-4 2.04E-4 {r S2 (0) / r S1 ( 0)} × (W / L) 2 0.885 0.401 0.423 β (0) 2.89 3.26 3.29

【0046】比較例1〜3に関する「球面収差」の図を
図7〜図9に順次示す。比較例1〜3と実施例1〜3の
球面収差を比較すると明らかなように、実施例1〜3は
比較例1〜3に比して球面収差が良好であり、その分、
副走査方向の光スポット径を小径化できることがわか
る。比較例1では条件(3)の上限を越えており、比較
例2,3では条件(2)の上限を越えており、いずれも
球面収差が実施例1〜3より劣化している。
FIGS. 7 to 9 sequentially show diagrams of “spherical aberration” in Comparative Examples 1 to 3. As is clear from comparison of the spherical aberrations of Comparative Examples 1 to 3 and Examples 1 to 3, Examples 1 to 3 have better spherical aberration than Comparative Examples 1 to 3, and
It can be seen that the diameter of the light spot in the sub-scanning direction can be reduced. In Comparative Example 1, the value exceeds the upper limit of the condition (3), and in Comparative Examples 2 and 3, the value exceeds the upper limit of the condition (2).

【0047】「実施例4〜6」は、図14に示すごとき
実施の形態を利用して実施した。光偏向器としては「回
転単面鏡」を用い、偏向反射面の回転軸が偏向反射面と
一致するようにして「サグ」が発生しないようにした。
光源のカップリングレンズでカップリングされた光束は
「平行光束」となり、シリンダレンズにより主走査対応
方向に長い線像として、光偏向器の偏向反射面の回転軸
位置に結像するので、光偏向器による偏向光束の偏向の
起点は変動しない。図14に示すように、光偏向器以後
の光路において、距離:d0,d1,d2,d3,d4を定
める。距離:d1は「光偏向器側レンズの肉厚」であ
り、条件(6),(8)の「Λ」における「d1」であ
る。また、距離:d3は「被走査面側レンズの肉厚であ
り、であり、条件(7),(8)の「Λ'」における
「d3」である。走査結像レンズ系の光軸を含み、主走
査対応方向に平行な面内における曲率半径もしくは近軸
曲率半径をRi(i=1〜4)で表し、レンズ18’,1
9の材質の屈折率(屈折率に分布のない設計上の屈折
率)をNj(j=1,2)で表すことにする。
"Examples 4 to 6" were implemented using the embodiment as shown in FIG. A "rotating single-sided mirror" was used as the optical deflector, and the rotation axis of the deflecting / reflecting surface coincided with the deflecting / reflecting surface so that "sag" did not occur.
The light beam coupled by the coupling lens of the light source becomes a “parallel light beam” and is imaged as a long linear image in the main scanning direction by the cylinder lens at the rotation axis position of the deflecting / reflecting surface of the optical deflector. The starting point of the deflection of the deflected light beam by the detector does not change. As shown in FIG. 14, distances d 0 , d 1 , d 2 , d 3 and d 4 are determined in the optical path after the optical deflector. The distance: d 1 is “the thickness of the lens on the optical deflector side”, which is “d 1 ” in “Λ” in the conditions (6) and (8). Further, the distance: d 3 is “the thickness of the scanned surface side lens, and is d 3 in“ に お け る ′ ”in the conditions (7) and (8). A radius of curvature or a paraxial radius of curvature in a plane including the optical axis of the scanning imaging lens system and parallel to the main scanning corresponding direction is represented by R i (i = 1 to 4).
The refractive index of the material No. 9 (designed refractive index having no refractive index distribution) is represented by N j (j = 1, 2).

【0048】走査結像レンズ系における光偏向器側レン
ズ18’の両面は上記面内で「非円弧形状」であるの
で、前述のX1(Y) およびX2(Y)) で表す。
Since both surfaces of the optical deflector-side lens 18 'in the scanning image forming lens system are "non-circular" in the above-mentioned plane, they are represented by X 1 (Y) and X 2 (Y) described above.

【0049】「光軸を含み、主走査対応方向に平行な
面」内のデータは、実施例4〜6において共通であり、
以下のように与えられる。
The data in the “plane including the optical axis and parallel to the main scanning corresponding direction” is common to the fourth to sixth embodiments.
It is given as follows.

【0050】 S=∞(カップリングされた光束は平行光束である) W=216mm、L=175mm i Rii j Nj 0 29.887 1 137.503 12.364 1 1.53664 2 −154.248 20.000 3 −700.0 3.0 2 1.53664 4 −700.0 111.649 X1(Y): R1= 137.503,K1=−92.438, A1=−1.11822E−6,B1= 7.28745E−10, C1=−3.20311E−13,D1= 9.55204E−17 X2(Y): R2=−154.248,K2= 5.36873, A2=−2.51300E−6,B2= 1.95625E−9, C2=−1.18490E−12,D2= 3.38372E−16 。[0050] S = ∞ (the coupled light beams are parallel light fluxes) W = 216mm, L = 175mm i R i d i j N j 0 29.887 1 137.503 12.364 1 1.53664 2 - 154.248 20.0000 3 -700.0 3.0 2 1.53664 4 -700.0 111.649 X 1 (Y): R 1 = 137.503, K 1 = −92.438, A 1 = -1.11822E-6, B 1 = 7.28745E -10, C 1 = -3.20311E-13, D 1 = 9.55204E-17 X 2 (Y): R 2 = -154.248, K 2 = 5.36873, A 2 = -2.51300E- 6, B 2 = 1.95625E-9, C 2 = -1.18490E-12, D 2 = 3.38372E-16.

【0051】レンズ19は両面とも「光軸を含み、主走
査対応方向に平行な面内」で上記曲率半径:R3,R4
「円弧形状」である。上記データに基づく、主走査方向
の像面湾曲と歪曲収差(前記実施例1〜3の場合と同様
に定義されたもの)を図10に示す。
Both surfaces of the lens 19 are "in the plane including the optical axis and parallel to the main scanning direction" and have an "arc shape" with the above-mentioned radii of curvature: R 3 and R 4 . FIG. 10 shows field curvature and distortion in the main scanning direction (defined in the same manner as in the first to third embodiments) based on the above data.

【0052】実施例4〜6のデータは次の通りである。 実施例4 実施例5 実施例6 D0 3 3 3 Rs1 30.0 30.0 30.0 Rs2 ∞ ∞ ∞ D1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 rS1(0) -500 -500 -500 rS2(0) -450 -450 -450 n0(0) 1.53664 1.53664 1.53664 Δn(0) 2.70E-5 0 2.0E-05 rS3(0) -31 -31 -31 rS4(0) -12.45 -13.03 -12.6 Δn'(0) − 1.0E-05 1.0E-05 W 216 216 216 L 175 175 175 S0(0) 103.95 103.95 103.95 S1(0) -43.57 -43.48 -43.55 SL(0) 110.41 110.31 110.38 f1(0) 7718.923 7718.923 7718.923 f2(0) 36.698 39.579 37.427 Λ -0.0102 − -0.0100 Λ' − -0.0095 − 条件(6)の左辺 0.38 − − 条件(7)の左辺 − 0.2 − 条件(8)の左辺 − − 0.8 ω0 8.2 8.2 8.2 β(0) 1.82 1.81 1.83 。The data of Examples 4 to 6 are as follows. Example 4 Example 5 Example 6 D 0 3 3 3 R s1 30.0 30.0 30.0 R s2 ∞ ∞ 1 D 1 56.703 56.703 56.703 N 1.51118 1.51118 1.51118 r S1 (0) -500 -500 -500 r S2 (0)- 450 -450 -450 n 0 (0) 1.53664 1.53664 1.53664 Δn (0) 2.70E-5 0 2.0E-05 r S3 (0) -31 -31 -31 r S4 (0) -12.45 -13.03 -12.6 Δn ' (0)-1.0E-05 1.0E-05 W 216 216 216 L L 175 175 175 S 0 (0) 103.95 103.95 103.95 S 1 (0) -43.57 -43.48 -43.55 S L (0) 110.41 110.31 110.38 f 1 ( 0) 7718.923 7718.923 7718.923 f 2 (0) 36.698 39.579 37.427 Λ -0.0102--0.0100 Λ '--0.0095-Left side of condition (6) 0.38--Left side of condition (7)-0.2-Left side of condition (8)- −0.8 ω 0 8.2 8.2 8.2 β (0) 1.82 1.81 1.83.

【0053】レンズ19の両面は、副走査断面とこれに
平行な平面内で、上記rS3(0)およびrS4(0)を半径と
する円弧形状である。実施例4は条件(6)を満足し、
β(0)は実施例1〜3に比して低減している(副走査方
向の光スポット径が実施例1〜3より小さい)。また、
光偏向器側のレンズ18’の副走査対応方向のパワー:
1 =1.3E−4、被走査面側のレンズ19の副走査
対応方向のパワー:P2 =2.6E−2で、条件(5)の
「P2>P1」を満足し(請求項6)、被走査面側のレン
ズ19の副走査断面内の形状は「光偏向器側に凹のメニ
スカス形状」であり、前・後側主点位置が実際のレンズ
配置よりも被走査面側に位置するので、組み付け誤差に
対する許容度が大きい請求項7)。実施例5は条件
(7)を、実施例6は条件(8)をそれぞれ満足し、こ
れら実施例5,6において、β(0)は実施例1〜3に比
して低減している。また、光偏向器側のレンズ18’の
副走査対応方向のパワー:P1 は、実施例5,6ともP
1=1.3E−4、被走査面側のレンズ19の副走査対
応方向のパワー:P2は、実施例5においてP2 =2.
5E−2、実施例6においてP2 =2.7E−2であっ
て、実施例5,6とも、条件(5)の「P2>P1」を満足
し(請求項6)、被走査面側のレンズ19の副走査断面
内の形状は、実施例5,6とも「光偏向器側に凹のメニ
スカス形状」であり、前・後側主点位置が実際のレンズ
配置よりも被走査面側に位置するので、組み付け誤差に
対する許容度が大きい請求項7)。図11〜13に実施
例1〜6に関する「副走査方向のデフォーカス量(副走
査方向のビームウエストからのずれ量)」に対する副走
査方向のビームスポット径(副走査方向の光束系)の変
化を示している。図11は実施例1,2に関する図、図
12は実施例3に関する図、図13は実施例4,5,6
に関する図である。これらの図における「横線」はビー
ムスポット径が「ビームウエスト(ビームスポット径の
最小値)の10%増」の値を示し、この「横線」が、ビ
ームスポット径変化の曲線により切り取られる長さに対
応するデフォーカス領域が「スポット径深度余裕:
ω0」である。なお、各実施例および比較例において、
主走査対応方向における屈折率の分布および光軸に平行
な方向の屈折率の分布については、微小変化であるとし
てこれらを無視した。光軸に平行な方向の屈折率は、偏
向光束の光路長に影響するが、屈折率の変化量が小さい
こと、および光路長の変化には屈折率の平均が影響する
ことにより、上記屈折率分布を無視しても、実測上、光
軸に平行な方向の屈折率分布の影響はなかった。また、
上記説明において、主点位置には屈折率の分布を考慮し
ていないが、実質的な問題はない。
Both surfaces of the lens 19 have an arc shape having a radius of r S3 (0) and r S4 (0) in a sub-scanning cross section and a plane parallel thereto. Example 4 satisfies the condition (6),
β (0) is smaller than in Examples 1 to 3 (the light spot diameter in the sub-scanning direction is smaller than Examples 1 to 3). Also,
Power of lens 18 'on the optical deflector side in the sub-scanning direction:
When P 1 = 1.3E-4 and the power of the lens 19 on the scanned surface side in the sub-scanning direction: P 2 = 2.6E-2, the condition (5) “P 2 > P 1 ” is satisfied ( The shape of the lens 19 on the scanning surface side in the sub-scanning cross section is “a meniscus shape concave on the optical deflector side”, and the front and rear principal points are scanned more than the actual lens arrangement. Since it is located on the surface side, the tolerance for an assembly error is large. The fifth embodiment satisfies the condition (7), and the sixth embodiment satisfies the condition (8). In the fifth and sixth embodiments, β (0) is reduced as compared with the first to third embodiments. Further, sub-scanning direction of the power of the optical deflector side lens 18 ': P 1 is the fifth and sixth embodiments both P
1 = 1.3E-4, the power in the sub-scanning corresponding direction of the lens 19 on the scanning surface side: P 2 is P 2 = 2.
5E-2, P 2 = 2.7E-2 in the sixth embodiment, and both the fifth and sixth embodiments satisfy the condition (5) “P 2 > P 1 ” (claim 6), and are scanned. The shape of the lens 19 on the surface side in the sub-scanning cross section is “the meniscus shape concave on the optical deflector side” in each of the fifth and sixth embodiments, and the front and rear principal points are scanned more than the actual lens arrangement. Since it is located on the surface side, the tolerance for an assembly error is large. FIGS. 11 to 13 show changes in the beam spot diameter (light beam system in the sub-scanning direction) in the sub-scanning direction with respect to the “defocus amount in the sub-scanning direction (the amount of deviation from the beam waist in the sub-scanning direction)” in Examples 1 to 6. Is shown. 11 is a diagram related to the first and second embodiments, FIG. 12 is a diagram related to the third embodiment, and FIG. 13 is a diagram related to the fourth, fifth, and sixth embodiments.
FIG. The “horizontal line” in these figures indicates the value of the beam spot diameter “increased by 10% of the beam waist (the minimum value of the beam spot diameter)”, and the “horizontal line” is the length cut off by the curve of the beam spot diameter change. The defocus area corresponding to “Spot diameter depth margin:
ω 0 ”. In each example and comparative example,
Regarding the distribution of the refractive index in the main scanning corresponding direction and the distribution of the refractive index in the direction parallel to the optical axis, these were ignored because they were minute changes. Although the refractive index in the direction parallel to the optical axis affects the optical path length of the deflected light beam, the refractive index change is small, and the change in the optical path length is affected by the average refractive index. Even if the distribution was neglected, there was no influence of the refractive index distribution in the direction parallel to the optical axis on the actual measurement. Also,
In the above description, the distribution of the refractive index is not considered in the position of the principal point, but there is no substantial problem.

【0054】[0054]

【発明の効果】以上に説明したように、この発明によれ
ば新規な光走査装置を実現できる。請求項1〜4記載の
発明は、光スポットの小径化に必要な「良好な球面収
差」を、走査結像レンズ内部の屈折率の不均一にも拘ら
ず実現できる。また、請求項2記載の発明は、副走査方
向の球面収差のより有効な補正を可能とし、副走査方向
の光スポット径のより有効な小径化を可能とする。請求
項3記載の発明では、副走査方向の球面収差を有効に補
正して、副走査方向の光スポット径を有効に小径化し、
副走査対応方向における走査結像レンズの横倍率の増大
を抑えて、走査結像レンズの組み付け誤差に対する許容
度を大きくできる。さらに、請求項4記載の発明では、
横倍率の変動に起因する副走査方向の光スポット径の像
高による変動を有効に抑えることができる。請求項5記
載の発明では、走査結像レンズ系に内部屈折率分布を持
つレンズが存在しても、それに伴う像面湾曲の劣化を低
減でき、内部屈折率分布に「バラツキ」があっても、そ
れに伴う「像面湾曲のバラツキ」を小さく抑えることが
可能になる。請求項6,7記載の発明では、上記請求項
5記載の発明の効果をより有効に助長できる。また、請
求項8〜10記載の発明では、走査結像レンズ内部の屈
折率の不均一にも拘らず「設計上の光スポット径との差
が許容範囲内である光スポット径」を実現できる。この
発明によれば、上記のように、走査結像レンズや走査結
像レンズ系内のレンズに屈折率の不均一が存在しても、
その不均一の範囲がある範囲内に収まるものは実使用が
できるので、走査結像レンズや走査結像レンズ系の歩留
まりが向上し、プラスチック成形の差異の冷却時間の短
縮を図ることができ、走査結像レンズや走査結像レンズ
系の製造効率を向上させ、これらのコストひいては光走
査装置のコストの低減化が可能になる。
As described above, according to the present invention, a novel optical scanning device can be realized. According to the first to fourth aspects of the present invention, "good spherical aberration" required for reducing the diameter of the light spot can be realized irrespective of the nonuniform refractive index inside the scanning imaging lens. Further, the invention described in claim 2 enables more effective correction of spherical aberration in the sub-scanning direction, and enables more effective reduction of the light spot diameter in the sub-scanning direction. According to the third aspect of the present invention, the spherical aberration in the sub-scanning direction is effectively corrected, and the light spot diameter in the sub-scanning direction is effectively reduced,
An increase in the lateral magnification of the scanning imaging lens in the sub-scanning corresponding direction can be suppressed, and the tolerance for the assembly error of the scanning imaging lens can be increased. Further, in the invention according to claim 4,
It is possible to effectively suppress the variation of the light spot diameter in the sub-scanning direction due to the variation in the lateral magnification due to the image height. According to the fifth aspect of the present invention, even if a lens having an internal refractive index distribution exists in the scanning image forming lens system, the deterioration of the field curvature associated therewith can be reduced, and even if the internal refractive index distribution has "variation". Accordingly, it is possible to suppress the "variation in the curvature of field" associated therewith. According to the sixth and seventh aspects of the invention, the effects of the fifth aspect of the invention can be more effectively promoted. Further, in the invention according to claims 8 to 10, "a light spot diameter whose difference from a designed light spot diameter is within an allowable range" can be realized irrespective of uneven refractive index inside the scanning image forming lens. . According to the present invention, as described above, even if there is uneven refractive index in the scanning image forming lens or the lens in the scanning image forming lens system,
Since the non-uniform range falls within a certain range, it can be actually used, so that the yield of the scanning imaging lens and the scanning imaging lens system is improved, and the cooling time for the difference in plastic molding can be shortened. It is possible to improve the manufacturing efficiency of the scanning imaging lens and the scanning imaging lens system, and to reduce the cost of the scanning imaging lens and the cost of the optical scanning device.

【図面の簡単な説明】[Brief description of the drawings]

【図1】請求項1〜4記載の発明の実施の形態を説明す
るための図である。
FIG. 1 is a diagram for explaining an embodiment of the invention described in claims 1 to 4;

【図2】請求項1記載の発明における条件(1)を説明
するための図である。
FIG. 2 is a diagram for explaining a condition (1) in the invention described in claim 1;

【図3】実施例1〜3・比較例1〜3の主走査方向の像
面湾曲と歪曲収差を示す図である。
FIG. 3 is a diagram illustrating curvature of field and distortion in the main scanning direction of Examples 1 to 3 and Comparative Examples 1 to 3.

【図4】実施例1の副走査方向の球面収差を示す図であ
る。
FIG. 4 is a diagram illustrating spherical aberration in the sub-scanning direction according to the first embodiment.

【図5】実施例2の副走査方向の球面収差を示す図であ
る。
FIG. 5 is a diagram illustrating spherical aberration in a sub-scanning direction according to a second embodiment.

【図6】実施例3の副走査方向の球面収差を示す図であ
る。
FIG. 6 is a diagram illustrating spherical aberration in a sub-scanning direction according to a third embodiment.

【図7】比較例1の副走査方向の球面収差を示す図であ
る。
FIG. 7 is a diagram illustrating spherical aberration in the sub-scanning direction of Comparative Example 1.

【図8】比較例2の副走査方向の球面収差を示す図であ
る。
FIG. 8 is a diagram illustrating spherical aberration in a sub-scanning direction of Comparative Example 2.

【図9】比較例3の副走査方向の球面収差を示す図であ
る。
FIG. 9 is a diagram illustrating spherical aberration in the sub-scanning direction of Comparative Example 3.

【図10】実施例4,5および6の主走査方向の像面湾
曲と歪曲収差を示す図である。
FIG. 10 is a diagram illustrating curvature of field and distortion in the main scanning direction of Examples 4, 5, and 6.

【図11】実施例1,2におけるデフォーカス量とビー
ムスポット径の関係を示す図である。
FIG. 11 is a diagram illustrating a relationship between a defocus amount and a beam spot diameter in Examples 1 and 2.

【図12】実施例3におけるデフォーカス量とビームス
ポット径の関係を示す図である。
FIG. 12 is a diagram illustrating a relationship between a defocus amount and a beam spot diameter according to a third embodiment.

【図13】実施例4,5および6におけるデフォーカス
量とビームスポット径の関係を示す図である。
FIG. 13 is a diagram illustrating a relationship between a defocus amount and a beam spot diameter in Examples 4, 5, and 6.

【図14】請求項5〜8記載の発明の実施の形態を説明
するための図である。
FIG. 14 is a view for explaining an embodiment of the invention described in claims 5 to 8;

【図15】請求項5〜8記載の発明における条件(7)
を説明するための図である。
FIG. 15 is a condition (7) according to the invention as set forth in claims 5 to 8;
FIG.

【符号の説明】[Explanation of symbols]

10 半導体レーザ 12 カップリングレンズ 14 第1結像光学系(シリンダレンズ) 16 光偏向器 18 第2結像光学系(走査結像レンズ) 18’ 光偏向器側レンズ 19 被走査面側レンズ 20 被走査面 Reference Signs List 10 semiconductor laser 12 coupling lens 14 first imaging optical system (cylinder lens) 16 optical deflector 18 second imaging optical system (scanning imaging lens) 18 ′ optical deflector side lens 19 scanned surface side lens 20 Scanning plane

フロントページの続き (72)発明者 須原 浩之 東京都大田区中馬込1丁目3番6号・株式 会社リコー内Continued on the front page (72) Inventor Hiroyuki Suhara 1-3-6 Nakamagome, Ota-ku, Tokyo, Ricoh Co., Ltd.

Claims (10)

【特許請求の範囲】[Claims] 【請求項1】光源からの光束を、第1結像光学系により
主走査対応方向に長い線像として結像させ、上記線像の
結像位置近傍に偏向反射面を持つ光偏向器により偏向さ
せ、偏向された光束を第2結像光学系により被走査面上
に光スポットとして集光させて光走査を行う光走査装置
において、 上記第2結像光学系は、副走査対応方向に屈折率分布を
有するアナモフィックな単玉レンズである走査結像レン
ズで構成され、 上記走査結像レンズにおける光軸上の屈折率をn0(0)
とするとき、副走査断面内で副走査対応方向における光
軸からの距離:zに対して、屈折率の分布を、n(z)=
0(0)+Δn(0)・z2で近似し、 上記走査結像レンズの、光偏向器側および被走査面側の
各レンズ面の、上記副走査断面内における曲率半径をそ
れぞれrS1(0),rS2(0)、レンズ肉厚をd、これらr
S1(0),rS2(0),d,n0(0) から算出される副走査
対応方向焦点距離をf(0)とし、 上記線像の結像位置から、上記走査結像レンズの副走査
対応方向の前側主点までの距離をS0(0)、後側主点か
ら被走査面までの距離をSL(0)、副走査方向のスポッ
ト径深度余裕をω0とするとき、条件: (1) |1/[{1/f(0)}−2Δn(0)・d−{1/S0(0)}]−SL(0)| <ω0/2 を満足することを特徴とする光走査装置。
A light beam from a light source is formed by a first image forming optical system as a long line image in a direction corresponding to main scanning, and is deflected by an optical deflector having a deflective reflection surface near an image forming position of the line image. An optical scanning device that performs optical scanning by converging the deflected light beam as a light spot on the surface to be scanned by the second imaging optical system, wherein the second imaging optical system is refracted in the sub-scanning corresponding direction. A scanning imaging lens which is an anamorphic single lens having a refractive index distribution, wherein the refractive index on the optical axis of the scanning imaging lens is n 0 (0)
In the sub-scanning section, the distribution of the refractive index is expressed as n (z) =
n 0 (0) + Δn (0) · z 2 , and the radii of curvature of the respective lens surfaces of the scanning imaging lens on the optical deflector side and the surface to be scanned in the sub-scanning section are r S1. (0), r S2 (0), lens thickness d, these r
S1 (0), r S2 (0), d, n 0 in the sub-scanning corresponding direction focal distance calculated from (0) and f (0), the imaging position of the line image, the scanning imaging lens When the distance from the front principal point in the sub-scanning direction is S 0 (0), the distance from the rear principal point to the surface to be scanned is S L (0), and the spot diameter depth margin in the sub-scanning direction is ω 0 conditions: (1) | 1 / [ {1 / f (0)} - 2Δn (0) · d- {1 / S 0 (0)}] - S L (0) | < satisfy omega 0/2 An optical scanning device, comprising:
【請求項2】請求項1記載の光走査装置において、 第2結像光学系である走査結像レンズの光偏向器側の面
に入射する偏向光束の副走査対応方向の光束半幅をZと
するとき、条件: (2) 0<Z2・Δn(0)≦1.1×10~4 を満足することを特徴とする光走査装置。
2. The optical scanning device according to claim 1, wherein the half width of the deflecting light beam incident on the surface on the optical deflector side of the scanning image forming lens as the second image forming optical system in the sub-scanning corresponding direction is Z. (2) An optical scanning device characterized by satisfying 0 <Z 2 · Δn (0) ≦ 1.1 × 10 ~ 4 .
【請求項3】請求項1または2記載の光走査装置におい
て、 第2結像光学系である走査結像レンズが、副走査断面内
において、光偏向器側に凹のメニスカス形状であり、有
効走査幅をW、光偏向器による偏向の起点から被走査面
に至る光軸上の距離をLとするとき、条件: (3) 0.2≦{rS2(0)/rS1(0)}×(W/L)2≦0.6 を満足することを特徴とする光走査装置。
3. The optical scanning device according to claim 1, wherein the scanning imaging lens serving as the second imaging optical system has a meniscus shape concave toward the optical deflector in the sub-scanning cross section. When the scanning width is W and the distance on the optical axis from the starting point of deflection by the optical deflector to the surface to be scanned is L, the condition: (3) 0.2 ≦ {r S2 (0) / r S1 (0) } × (W / L) 2 ≦ 0.6.
【請求項4】請求項1または2または3記載の光走査装
置において、 主走査対応方向に長い線像の結像位置と、第2結像光学
系である走査結像レンズによる上記線像の被走査面近傍
の結像位置との副走査対応方向の横倍率を、画角:θに
関してβ(θ)とし、光走査の最周辺画角をβ(θMAX),
β(θMIN)とするとき、条件: (4−1) 0.95×β(0)≦β(θMAX)≦1.05×β(0) (4−2) 0.95×β(0)≦β(θMIN)≦1.05×β(0) を同時に満足することを特徴とする光走査装置。
4. The optical scanning device according to claim 1, wherein an image forming position of a line image which is long in a main scanning corresponding direction, and the line image formed by a scanning image forming lens which is a second image forming optical system. The lateral magnification in the direction corresponding to the sub-scan with respect to the imaging position near the surface to be scanned is β (θ) with respect to the angle of view: θ, and the most peripheral angle of view of the optical scanning is β (θ MAX ).
When β (θ MIN ) is satisfied , the condition is: (4-1) 0.95 × β (0) ≦ β (θ MAX ) ≦ 1.05 × β (0) (4-2) 0.95 × β ( 0) ≦ β (θ MIN ) ≦ 1.05 × β (0) at the same time.
【請求項5】光源からの光束を、第1結像光学系により
主走査対応方向に長い線像として結像させ、上記線像の
結像位置近傍に偏向反射面を持つ光偏向器により偏向さ
せ、偏向された光束を第2結像光学系により被走査面上
に光スポットとして集光させて光走査を行う光走査装置
において、 上記第2結像光学系は、2枚以上のレンズを含む走査結
像レンズ系で、少なくとも1枚のレンズは副走査対応方
向に屈折率分布を有し、 上記走査結像レンズ系における最も被走査面側にあるレ
ンズが副走査対応方向に正のパワーを持つことを特徴と
する光走査装置。
5. A light beam from a light source is formed by a first image forming optical system as a long line image in a direction corresponding to main scanning, and is deflected by an optical deflector having a deflective reflection surface near an image forming position of the line image. In the optical scanning device that performs optical scanning by converging the deflected light beam as a light spot on the surface to be scanned by the second imaging optical system, the second imaging optical system includes two or more lenses. In the scanning imaging lens system, at least one lens has a refractive index distribution in the sub-scanning corresponding direction, and the lens closest to the surface to be scanned in the scanning imaging lens system has a positive power in the sub-scanning corresponding direction. An optical scanning device, comprising:
【請求項6】請求項5記載の光走査装置において、 第2結像光学系である走査結像レンズ系は2枚のレンズ
で構成され、 副走査対応方向のパワーを、光偏向器側のレンズにつき
1、被走査面側のレンズにつきP2とするとき、条件: (5) P2>P1 を満足することを特徴とする光走査装置。
6. The optical scanning device according to claim 5, wherein the scanning image forming lens system serving as the second image forming optical system is constituted by two lenses, and the power in the sub-scanning corresponding direction is supplied to the optical deflector side. lens per P 1, when the P 2 per lens surface to be scanned side, conditions: (5) P 2> optical scanning apparatus which satisfies the P 1.
【請求項7】請求項6記載の光走査装置において、 第2結像光学系である走査結像レンズ系の2枚のレンズ
のうち、被走査面側のレンズの副走査断面内の形状が、
光偏向器側に凹のメニスカス形状であることを特徴とす
る光走査装置。
7. The optical scanning device according to claim 6, wherein, of the two lenses of the scanning image forming lens system as the second image forming optical system, the shape of the lens on the scanning surface side in the sub-scanning cross section is set. ,
An optical scanning device having a meniscus shape concave toward the optical deflector.
【請求項8】請求項5または6または7記載の光走査装
置において、 第2結像光学系である走査結像レンズ系が2枚のレンズ
で構成され、光偏向器側のレンズのみが副走査対応方向
に屈折率分布を有し、 上記走査結像レンズ系の光偏向器側レンズにおける光軸
上の屈折率をn0(0)とするとき、副走査断面内で副走
査対応方向における光軸からの距離:zに対して、同レ
ンズ内の屈折率の分布をn(z)=n0(0)+Δn(0)・
2で近似し、 上記光偏向器側レンズの、光偏向器側および被走査面側
の各レンズ面の、上記副走査断面内における曲率半径を
それぞれ、rS1(0),rS2(0)、レンズ肉厚をd1、こ
れらrS1(0),rS2(0),d1,n0(0) から算出され
る副走査対応方向焦点距離をf1(0)とし、 上記線像の結像位置から、上記光偏向器側レンズの副走
査対応方向の前側主点までの距離をS0(0) 、同レンズ
の副走査対応方向の後側主点から被走査面側レンズの前
側主点までの距離をS1(0) 、被走査面側レンズの副走
査対応方向の後側主点から被走査面までの距離をS
L(0) 、上記被走査面側レンズの副走査対応方向焦点距
離をf2(0)、副走査方向のスポット径深度余裕をω0
し、 Λ={1/f1(0)}−2Δn(0)・d1−{1/S0(0)} とするとき、条件: (6) |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・Λ)}]|<ω0/2 を満足することを特徴とする光走査装置。
8. The optical scanning device according to claim 5, wherein the scanning image forming lens system as the second image forming optical system is composed of two lenses, and only the lens on the optical deflector side is an auxiliary lens. It has a refractive index distribution in the scanning-corresponding direction, and when the refractive index on the optical axis of the optical deflector-side lens of the scanning image forming lens system is n 0 (0), in the sub-scanning section, For a distance from the optical axis: z, the distribution of the refractive index in the lens is expressed as n (z) = n 0 (0) + Δn (0) ·
z 2 , and the radii of curvature of the lens surfaces of the optical deflector side lens on the optical deflector side and the surface to be scanned side in the sub-scanning section are r S1 (0) and r S2 (0 ), The lens thickness is d 1 , and the focal length in the sub-scanning corresponding direction calculated from these r S1 (0), r S2 (0), d 1 , and n 0 (0) is f 1 (0). The distance from the image formation position to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens is S 0 (0), and the distance from the rear principal point in the sub-scanning corresponding direction of the lens to the scanning surface side lens is Is the distance from the front principal point to S 1 (0), and the distance from the rear principal point in the sub-scanning direction of the lens to be scanned to the surface to be scanned is S.
L (0), f 2 ( 0) of the sub-scanning direction focal length of the surface to be scanned side lens in the sub-scanning direction of the spot hydraulic radius of allowance and ω 0, Λ = {1 / f 1 (0)} - When 2Δn (0) · d 1 − {1 / S 0 (0)}, the condition is: (6) | S L (0) −1 / [{1 / f 2 (0)} + {Λ / ( 1-S 1 (0) · Λ)}] | < optical scanning apparatus which satisfies the omega 0/2.
【請求項9】請求項5または6または7記載の光走査装
置において、 第2結像光学系である走査結像レンズ系が2枚のレンズ
で構成され、被走査面側レンズのみが副走査対応方向に
屈折率分布を有し、 上記走査結像レンズ系の光偏向器側レンズの焦点距離を
1(0)とし、 第1結像光学系により結像する主走査対応方向に長い線
像の結像位置から上記光偏向器側レンズの副走査対応方
向の前側主点に至る距離をS0(0)、上記光偏向器側レ
ンズの副走査対応方向の後側主点から上記被走査面側レ
ンズの副走査対応方向の前側主点に至る距離をS
1(0)、上記被走査面側レンズの副走査対応方向の後側
主点から被走査面に至る距離をSL(0)、 上記被走査面側レンズにおける光軸上の屈折率をn0'
(0)とするとき、副走査断面内で副走査対応方向におけ
る光軸からの距離:zに対して、同レンズ内の屈折率の
分布をn'(z)=n0'(0)+Δn'(0)・z2で近似し、 上記被走査面側レンズの、光偏向器側および被走査面側
の各レンズ面の、上記副走査断面内における曲率半径を
それぞれ、rS3(0),rS4(0)、レンズ肉厚をd3、こ
れらrS3(0),rS4(0),d3,n0'(0)から算出され
る副走査対応方向の焦点距離をf2(0)、副走査方向の
スポット径深度余裕をω0とし、 Λ'={1/f1(0)}−{1/S0(0)} とするとき、条件: (7) |SL(0)−1/[{1/f2(0)}+{Λ'/(1−S1(0)・Λ')} −2Δn'(0)・d3]|<ω0/2 を満足することを特徴とする光走査装置。
9. The optical scanning device according to claim 5, wherein the scanning image forming lens system as the second image forming optical system is composed of two lenses, and only the lens to be scanned is sub-scanned. A line having a refractive index distribution in a corresponding direction, a focal length of the optical deflector-side lens of the scanning image forming lens system being f 1 (0), and a long line in the main scanning corresponding direction formed by the first image forming optical system. The distance from the image formation position to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens is S 0 (0), and the distance from the rear principal point in the sub-scanning corresponding direction of the optical deflector-side lens is The distance from the scanning plane side lens to the front principal point in the sub-scanning corresponding direction is S
1 (0), the distance from the rear principal point in the sub-scanning corresponding direction of the scanned surface side lens to the scanned surface is S L (0), and the refractive index on the optical axis of the scanned surface side lens is n. 0 '
When (0) is set, the distribution of the refractive index in the lens is represented by n ′ (z) = n 0 ′ (0) + Δn with respect to the distance z from the optical axis in the sub-scanning direction in the sub-scanning cross section. '(0) · z 2 , and the radii of curvature in the sub-scan section of each lens surface of the lens to be scanned and the optical deflector side and the surface to be scanned are r s3 (0) , R S4 (0), the lens thickness d 3 , and the focal length in the sub-scanning corresponding direction calculated from these r S3 (0), r S4 (0), d 3 , n 0 ′ (0) is f 2. (0), when the spot diameter depth margin in the sub-scanning direction is ω 0 and Λ ′ = {1 / f 1 (0)} − {1 / S 0 (0)}, the condition is: (7) | S L (0) −1 / [{1 / f 2 (0)} + {Λ ′ / (1−S 1 (0) · Λ ′)} − 2Δn ′ (0) · d 3 ] | <ω 0 / 2. An optical scanning device, which satisfies 2.
【請求項10】請求項5または6または7記載の光走査
装置において、 第2結像光学系である走査結像レンズ系が2枚のレンズ
で構成され、これら2枚のレンズが共に、副走査対応方
向に屈折率分布を有し、 上記走査結像レンズ系の光偏向器側レンズの光軸上の屈
折率をn0(0)とするとき、副走査断面内で副走査対応
方向における光軸からの距離:zに対して、同レンズ内
の屈折率の分布をn(z)=n0(0)+Δn(0)・z2で近
似し、 上記光偏向器側レンズの、光偏向器側および被走査面側
の各レンズ面の、上記副走査断面内における曲率半径を
それぞれ、rS1(0),rS2(0)、レンズ肉厚をd1、こ
れらrS1(0),rS2(0),d1,n0(0)から算出される
副走査対応方向の焦点距離をf1(0)とし、 上記走査結像レンズ系の被走査面側レンズの光軸上の屈
折率をn0'(0)とするとき、副走査断面内で副走査対応
方向における光軸からの距離:zに対して、同レンズ内
の屈折率の分布をn'(z)=n0'(0)+Δn'(0)・z2
で近似し、 上記被走査面側レンズの、光偏向器側および被走査面側
の各レンズ面の、上記副走査断面内における曲率半径を
それぞれ、rS3(0),rS4(0)、レンズ肉厚をd3、こ
れらrS3(0),rS4(0),d3,n0'(0)から算出され
る副走査対応方向の焦点距離をf2(0)、 第1結像光学系により結像する主走査対応方向に長い線
像の結像位置から上記光偏向器側レンズの副走査対応方
向の前側主点に至る距離をS0(0)、上記光偏向器側レ
ンズの副走査対応方向の後側主点から上記被走査面側レ
ンズの副走査対応方向の前側主点に至る距離をS
1(0)、上記被走査面側レンズの副走査対応方向の後側
主点から被走査面に至る距離をSL(0)、副走査方向の
スポット径深度余裕をω0とし、 Λ={1/f1(0)}−2Δn(0)・d1−{1/S0(0)} とするとき、条件: (8) |SL(0)−1/[{1/f2(0)}+{Λ/(1−S1(0)・Λ)} −2Δn'(0)・d3]|<ω0/2 を満足することを特徴とする光走査装置。
10. The optical scanning device according to claim 5, wherein the scanning image forming lens system as the second image forming optical system is composed of two lenses, and both of the two lenses are auxiliary lenses. It has a refractive index distribution in the scanning corresponding direction, and when the refractive index on the optical axis of the optical deflector-side lens of the scanning image forming lens system is n 0 (0), in the sub-scanning cross section, With respect to the distance from the optical axis: z, the distribution of the refractive index in the lens is approximated by n (z) = n 0 (0) + Δn (0) · z 2. The radii of curvature of the lens surfaces on the deflector side and the surface to be scanned side in the sub-scanning section are respectively r S1 (0) and r S2 (0), the lens thickness is d 1 , and these r S1 (0) , r S2 (0), d 1, n 0 (0) the focal length of the sub-scanning direction is calculated as f 1 (0) from the scanned surface side of the scanning and imaging lens system When the refractive index on the optical axis of the lens n 0 'and (0), the distance from the optical axis in the sub-scanning direction in the sub-scan section: For z, the distribution of the refractive index in the lens n '(z) = n 0 ' (0) + Δn '(0) · z 2
Where r S3 (0), r S4 (0), and r S3 (0), the radius of curvature of each lens surface of the scanned surface side lens on the optical deflector side and the scanned surface side in the sub-scanning section, respectively. The lens thickness is d 3 , the focal length in the sub-scanning corresponding direction calculated from these r S3 (0), r S4 (0), d 3 , and n 0 ′ (0) is f 2 (0). The distance from the image forming position of the line image long in the main scanning direction formed by the image optical system to the front principal point in the sub-scanning corresponding direction of the optical deflector-side lens is S 0 (0). The distance from the rear principal point in the sub-scanning corresponding direction of the lens to the front principal point in the sub-scanning corresponding direction of the scanned surface side lens is S
1 (0), the distance from the rear principal point of the scanned surface side lens in the sub-scanning corresponding direction to the scanned surface is S L (0), the spot diameter depth margin in the sub-scanning direction is ω 0, and Λ = {1 / f 1 (0)} − 2Δn (0) · d 1 − {1 / S 0 (0)}, the condition: (8) | S L (0) −1 / [{1 / f 2 (0)} + {Λ / (1-S 1 (0) · Λ)} -2Δn '(0) · d 3] | < optical scanning apparatus which satisfies the omega 0/2.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100485315B1 (en) * 2001-08-24 2005-04-27 캐논 가부시끼가이샤 Scanning optical device and image forming apparatus using the same
US7170662B2 (en) 2003-10-14 2007-01-30 Brother Kogyo Kabushiki Kaisha Optical lens system, optical scanning apparatus, and image forming apparatus

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100485315B1 (en) * 2001-08-24 2005-04-27 캐논 가부시끼가이샤 Scanning optical device and image forming apparatus using the same
US7170662B2 (en) 2003-10-14 2007-01-30 Brother Kogyo Kabushiki Kaisha Optical lens system, optical scanning apparatus, and image forming apparatus

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