JP2695208B2 - Fθ lens system in optical scanning device - Google Patents

Description

The present invention relates to an fθ lens system in an optical scanning device.

2. Description of the Related Art An optical scanning device is known as a device for writing and reading information by scanning a light beam, and is used for a laser printer, a facsimile, and the like. In such an optical scanning device, a light flux from a light source is linearly imaged, and the light flux is deflected at a constant angular velocity by a rotary polygon mirror having a reflecting surface in the vicinity of the linear imaging position, There is an apparatus of a type in which this deflected light beam is imaged in a spot shape on a scanning surface by an imaging lens system to optically scan the scanning surface.

An optical scanning device using a rotary polygon mirror has a problem of surface tilt, and the angular velocity of the deflected light beam is constant. Therefore, it is necessary to devise a method to scan the scanning surface at a constant speed. . The fθ lens system is a lens system that optically realizes the constant-speed scanning of the scanning surface, and the incident angle θ
The image height of the luminous flux incident with f is fθ where f is the focal length.
Fθ function to make

As a method for solving the problem of surface tilt, an anamorphic lens system provided between the rotating polygon mirror and the scanning plane is used, and the reflection position of the rotating polygon mirror and the scanning plane are conjugated in the sub-scanning direction. There is a known way to link them.

[Problems to be Solved by the Invention] The f-theta lens system itself is made anamorphic, and a technique for solving the problem of constant-speed scanning and tilting is disclosed in Japanese Patent Application Laid-Open No. Sho 59-147316. It has been known.
Although this lens system has a large deflection angle, the effect of the change in the position of the entrance pupil by the rotating polygon mirror has not been studied with respect to the field curvature.

Further, the one disclosed in Japanese Patent Application Laid-Open No. 61-245129 does not sufficiently examine the problem of the above-mentioned fluctuation of the entrance pupil position due to the curvature of field, nor the removal of the scanning line pitch unevenness due to the surface tilt.

The present invention has been made in view of the above-described circumstances, and has been made in view of the above-described circumstances, and has been made in view of the above circumstances. It is an object of the present invention to provide a novel fθ lens system which can solve these problems.

[Means for Solving the Problems] Hereinafter, the present invention will be described.

The fθ lens system according to the present invention "forms a light beam from a light source into a linear image and deflects the light beam at a constant angular velocity by a rotary polygon mirror having a reflecting surface in the vicinity of the linear image forming position. In a light scanning device that forms an image of a deflected light beam on the scanning surface by a focusing lens system and optically scans the scanning surface, a lens system that images the light beam deflected by the rotating polygon mirror on the scanning surface " Therefore, with respect to the sub-scanning direction, the function of connecting the reflection position of the rotary polygon mirror and the scanning surface in a conjugate relationship,
fθ function.

The fθ lens system has a two-group / two-lens configuration composed of first and second lenses arranged in a first and second order from the rotary polygon mirror side toward the scanning surface side. The first lens is an "anamorphic single lens that has negative refracting power in both the main and sub scanning directions," and the second lens is "an anamorphic single lens that has positive refracting power in both the main and sub scanning directions." is there.

The first lens is “the lens surface on the side of the rotary polygon mirror is a spherical surface, and the lens surface on the scanning surface side is a cylinder surface or a modified cylinder surface”, and the second lens is “the side of the rotary polygon mirror. Is a flat surface, a cylinder surface, or a deformed cylinder surface, and the lens surface on the scanning surface side is a toric surface ".

The lens surfaces are sequentially referred to as first to fourth lens surfaces from the side of the rotary polygon mirror toward the scanning surface, and the i-th lens surface (i = 1)
When the radius of curvature of ~ 4) is R _iX in the deflection plane and R _{iY in} the sub-scanning direction, these are (I) 1.5 <R _1X / R _4X <2.5 (II) −2.5 <[(1 / R _4Y ) / {(1 / R _2Y ) − (1 /
R _3Y }] <-1 is satisfied.

Regarding the curvature of the lens surface, R _iX is a component of the radius of curvature on the cross section by the deflecting surface, and R _iY is a radius of curvature component of the section parallel to the optical axis and orthogonal to the deflecting surface.

The "deflecting surface" is a plane formed by sweeping the principal ray of an ideal deflected light beam by a rotating polygon mirror. Hereinafter, a plane that includes the optical axis of the lens and is orthogonal to the deflection plane is referred to as a "deflection orthogonal plane".

The deformed cylinder surface has a linear shape whose intersection with the deflection surface is parallel to the main scanning direction, and a lens surface curvature radius (curvature radius in the sub-scanning direction) within a “plane” parallel to the deflection orthogonal surface. Is a deformed cylinder surface given by the polynomial C ₀ + C ₁ H + C ₂ H ² + C ₃ H ³ + ... + C _n H ⁿ of the distance H between the “plane” and the optical axis in the main scanning direction, and the coefficient C ₀ , C ₁ ,
..., specified by specifying C _n .

In the above condition (II), the radius of curvature of the lens surface in the sub-scanning direction
Although R _2Y and R _3Y are included, as described above, any lens surface having these radii of curvature can be a deformed cylinder surface. In that case, the values of these radii of curvature R _2Y and R _3Y are assumed to be the values of the first term C ₀ of the above polynomial with respect to the condition (II).

[Operation] The above conditions (I) and (II) have the following meanings.
That is, the condition (I) is a condition for keeping the field curvature in the main scanning direction and the linearity, that is, the fθ characteristic in good condition. If the upper limit is exceeded, the field curvature in the main scanning direction becomes under,
The fθ characteristic becomes over. If the lower limit is exceeded, the curvature of field will be over, and the fθ characteristic will be under.

The condition (II) is a condition for favorably correcting the off-axis coma aberration generated in the anamorphic lens.

If the upper limit of condition (II) is exceeded, outward coma will occur, and if the lower limit is exceeded, inward coma will occur.

The deformed cylinder surface is adopted to favorably correct the field curvature in the sub-scanning direction.

 This will be described below with reference to the drawings.

FIG. 1 schematically illustrates an example of an optical scanning device using the fθ lens system of the present invention. FIG. 2 shows a state of the optical arrangement of FIG. 1 viewed from the sub-scanning direction, that is, a state in a deflection plane.

A parallel light flux from a light source or a light source device 1 including a light source and a condenser is a cylinder lens 2 which is a line image forming optical system.
Thereby, an image is formed in the vicinity of the reflecting surface 4 of the rotary polygon mirror 3 as a line image substantially parallel to the deflecting surface.

The light beam reflected by the rotating polygon mirror 3 is fθ of the present invention.
The lens system forms a spot-like image on the scanning surface 7,
The scanning surface 7 follows the rotation of the rotary polygon mirror 3 at a constant speed in the direction of the arrow.
Are scanned at a constant speed.

The fθ lens system includes a first lens 5 and a second lens 6, and the lens 5 is located on the side of the rotary polygon mirror 3 and the lens 6
Are disposed on the scanning surface 7 side, respectively. As seen in the deflection plane, as shown in FIG. 2, the fθ lens system including the lenses 5 and 6 links the infinity on the light source side and the position of the scanning plane 7 in a conjugate relationship.

On the other hand, when viewed in the plane orthogonal to the deflection, that is, in the sub-scanning direction, the fθ lens system connects the reflection position of the rotary polygon mirror 3 and the scanning surface 7 in a substantially conjugate relationship. Therefore, the third
As shown in the figure, even if the reflecting surface 4 is tilted as shown by reference numeral 4 ', the image forming position on the scanning surface 7 by the fθ lens system is almost in the sub-scanning direction (up and down direction in FIG. 3). Do not move. Therefore, the tilting is corrected.

Now, when the rotary polygon mirror 3 rotates, the reflecting surface 4 rotates about the axis 3A. Therefore, as shown in FIG. 4, along with the rotation of the reflecting surface, the image forming position P of the line image and the reflecting surface 4 are A positional deviation ΔX occurs between the two, and the position P ′ of the conjugate image of the line image by the fθ lens system is deviated from the scanning surface 7 by ΔX ′.

The shift amount ΔX ′ is given by ΔX ′ = β ² ΔX, as is well known, where β is the lateral magnification of the fθ lens system in the sub-scanning direction.

FIGS. 5 and 6 show the relationship between θ and ΔX, where θ is the angle formed between the lens optical axis of the fθ lens system and the principal ray of the deflected light beam in the deflection plane. In FIG. 5, the angle of incidence α (the angle between the principal ray of the light beam incident on the rotary polygon mirror and the optical axis of the fθ lens system: see FIG. 7) is 90 degrees, and the rotary polygon mirror 3
The inscribed circle radius R of is drawn as a parameter. In FIG. 6, the radius R of the inscribed circle is set to 40 mm, and the incident angle α is used as a parameter.

As can be seen from FIGS. 5 and 6, ΔX increases as the radius R of the inscribed circle increases and as the incident angle α decreases.

Further, the relative positional deviation between the position of the line image and the reflecting surface due to the rotation of the reflecting surface occurs two-dimensionally within the deflecting surface and also moves asymmetrically with respect to the lens optical axis.

Therefore, in the optical scanning device as shown in FIG. 1, it is necessary to satisfactorily correct the field curvature of the fθ lens system in the main and sub scanning directions. Needless to say, the fθ characteristic must be corrected well in the main scanning direction.

Here, the incident angle α will be described. In FIG. 7, reference numeral a denotes a principal ray of a light beam incident on the rotating polygonal mirror, and reference numeral b denotes a light beam reflected by the rotating polygonal mirror 3 when an optical axis of the fθ lens system is changed. 3 shows the principal ray when it is parallel to.
The X and Y axes are determined as shown in the figure with the intersection of the principal rays a and b as the origin,
The coordinates of the rotation axis position of the rotary polygon mirror 3 are defined as Xp and Yp.

The incident angle α is defined as the angle of intersection of the principal rays a and b as shown in the figure.

In order to minimize the variation of ΔX of the displacement between the line image position and the reflecting surface as described above, 0 <Xp <Rcos (α / 2) 0 <Yp <Rsin (α / 2) Conditions may be imposed on Xp and Yp.

Further, FIG. 8 is an explanatory view showing a deformed cylinder surface which is one of the features of the present invention.

When this deformed cylinder surface is adopted as the i-th lens surface, as shown in the figure, the radius of curvature R _iX in the deflection surface is
Is ∞, but the radius of curvature R _{iY in the} sub-scanning direction is C on the optical axis.
Analytical expression of the radius of curvature in the sub-scanning direction at a portion that is ₀ and deviates from the optical axis in the main scanning direction is the polynomial R _iY (H) = C ₀ + C ₁ H + C ₂ H ² + C as described above. It is given by ₃ H ³ ＋ …… ＋ C _n H ⁿ .

[Examples] Hereinafter, four specific examples will be given.

In each embodiment, f _M represents a combined focal length of the fθ lens system in the main scanning direction, that is, a combined focal length in a plane parallel to the deflection surface, and this value is normalized to 100. Further, f _S represents a combined focal length in the plane orthogonal to the deflection, that is, a combined focal length in the sub-scanning direction. 2θ indicates a deflection angle, and α indicates an incident angle.

R _iX is the radius of curvature of the i-th lens surface in the deflection plane counted from the side of the rotating polygon mirror, R _iY is the radius of curvature of the i-th lens surface in the plane orthogonal to the deflection, and d _i is the distance between the i-th lens surfaces. The distance, d ₀ is the distance from the reflecting surface of the rotating polygon mirror to the first lens surface, n _j is the refractive index of the j-th lens, and R is the radius of the inscribed circle of the rotating polygon mirror.

Furthermore, K ₁ = R _1X / R _4X , K ₂ = [(1 / R _4Y ) / {(1 / R _2Y )
-(1 / R _3Y }] is represented.

Example 1 f _M = 100, f _S = 21.3685,2 θ = 65.8 °, α = 60 °, R = 14.0845, K1 = 2.0199, K2 = −1.3194, d ₀ = 7.4343 In this example, the second surface marked with * is the deformed cylinder surface and the coefficients of the polynomial that characterize this surface are as follows:

C ₀ = 17.9982, C ₁ = −4.2013 ・ 10 ^-1 C ₂ ＝ −2.3145 ・ 10 ^-1 ,, C ₃ ＝ 1.4346 ・ 10 ^-2 C ₄ ＝ 1.8275 ・ 10 ^-3 , C ₅ ＝ −2.0887 ・ 10 ^-4 C ₆ = −1.0331 · 10 ⁻⁵ Example 2 f _M = 100, f _S = 21.1663,2 θ = 65.6 °, α = 60 °, R = 14.0845, K1 = 2.0199, K2 = −2.2916, d ₀ = 7.4343 In this embodiment, the second surface marked with * is the deformed cylinder surface, and each coefficient of the polynomial is as follows.

C ₀ = 44.9167, C ₁ = -1.1896 C ₂ = -6.265 ・ 10 ^-1 ,, C ₃ = 5.3039 ・ 10 ^-2 C ₄ = 7.7804 ・ 10 ^-3 , C ₅ = -9.7627 ・ 10 ^-5 C ₆ =- 5.1653 · 10 ⁻⁵ , C ₇ = 1.1369 · 10 ⁻⁵ Example 3 f _M = 100, f _S = 21.3153,2 θ = 65.6 °, α = 60 °, R = 14.0845, K1 = 2.0199, K2 = −2.0581, d ₀ = 7.4343 In this embodiment, the third surface marked with * is the deformed cylinder surface, and each coefficient of the polynomial is as follows.

C ₀ = -49.3808, C ₁ = 4.9362 / 10 ^-2 C ₂ = 1.2311 / 10 ^-2 , C ₃ = -7.9496 / 10 ^-4 C ₄ = -8.7432 / 10 ^-5 , C ₅ = 2.3468 / 10 ^-6 Example 4 f _M = 100, f _S = 21.3340,2θ = 65.6 °, α = 60 °, R = 14.0845, K1 = 2.0199, K2 = −2.0243, d ₀ = 7.4343 In this embodiment, the second surface marked with * is the deformed cylinder surface, and each coefficient of the polynomial is as follows.

C ₀ = 49.5804, C ₁ = -5.9315 ・ 10 ^-1 C ₂ = -1.8883 ・ 10 ^-1 ,, C ₃ = 3.3999 ・ 10 ^-2 C ₄ = 3.8801 ・ 10 ^-3 , C ₅ = -4.3651 ・ 10 ^-4 C ₆ = 1.0331 · 10 ^-5 the specific numeric value of f _M is a f _M = 220.1 through the fourth embodiments.

FIG. 9 shows an aberration diagram relating to the first embodiment. 10 to 12 are aberration diagrams related to Examples 2 to 4. The solid line in the figure of curvature of field indicates the image forming position in the sub-scanning direction, and the broken line indicates the image forming position in the main scanning direction. Since the field curvature is asymmetric due to the change in the position of the entrance pupil due to the rotation of the rotary polygon mirror, it is shown over the entire deflection region.

Further, FIGS. 13 to 16 show spot diagrams showing the image forming performance in each example. The effective scanning angles ± 32.8 °, ± 23.43 °, and 0 ° image height around the optical axis are shown.

[Effects of the Invention] As described above, according to the present invention, a novel fθ in the optical scanning device
A lens system can be provided. As described above, this lens system has a small curvature of field, so that high-density writing is possible, and since a long cylinder lens is not required for correcting surface tilt, it is possible to make the optical scanning device compact. Become.

[Brief description of the drawings]

FIG. 1 is a schematic perspective view showing an outline of an optical scanning device using the fθ lens system of the present invention, and FIGS. 2 to 3 are views for explaining the fθ lens system of the present invention. 7 to FIG. 7 are diagrams for explaining the variation of the entrance pupil position based on the rotation of the rotary polygon mirror and its countermeasures, FIG. 8 is a diagram for explaining the deformed cylinder surface, and FIGS. Is the aberration diagram,
13 to 16 are diagrams showing spot diagrams. 5 ... first lens, 6 ... second lens

Claims (1)

(57) [Claims] 1. A light beam from a light source is linearly imaged, and the light beam is deflected at a constant angular velocity by a rotary polygon mirror having a reflecting surface in the vicinity of the linear image formation position, and the deflected light beam is formed. An optical scanning device for forming an image in a spot shape on a scanning surface by an image lens system and optically scanning the scanning surface. A lens system for forming an image of a light beam deflected by a rotary polygon mirror on the scanning surface. Regarding the direction, it has a function of connecting the reflection position of the rotary polygon mirror and the scanning surface in a substantially conjugate relationship, and an fθ function, and is arranged in the first and second order from the rotary polygon mirror side toward the scanning surface side. The first lens is an anamorphic single lens having a negative refracting power in both the main and sub-scanning directions. The second lens has a positive refractive power in both the main and sub scanning directions. An anamorphic single lens, the first lens has a spherical lens surface on the side of the rotary polygonal mirror, the lens surface on the scanning surface side is a cylinder surface or a deformed cylinder surface, and the second lens has the rotation surface. The lens surface on the polygonal mirror side is a flat surface or a cylinder surface or a deformed cylinder surface, the lens surface on the scanning surface side is a toric surface, and the lens surfaces are sequentially arranged from the rotary polygonal mirror side toward the scanning surface,
The first to fourth lens surfaces and the i-th lens surface (i = 1 to
When the radius of curvature of 4) is R _iX in the deflection plane and R _{iY in} the sub-scanning direction, these are (I) 1.5 <R _1X / R _4X <2.5 (II) −2.5 <[(1 / R _4Y ) / {(1 / R _2Y ) − (1 /
R _3Y }] <− 1, the fθ lens system.