JP2774546B2 - 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 beam from a light source is formed into a long linear image in a direction corresponding to the main scanning, and the light beam is equalized by a rotating polygon mirror having a reflecting surface near the linear image forming position. There is an apparatus of a system which deflects at an angular velocity, forms an image of a spot of this deflected light beam on a scanning surface by an imaging lens system, and optically scans 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 is configured such that “a substantially parallel light beam from the light source is formed into a long linear image in the main scanning corresponding direction, and the light beam is formed by a rotary polygon mirror having a reflecting surface near the linear image forming position. Is deflected at a uniform angular velocity, and the light beam deflected by the rotating polygon mirror is scanned by the scanning polygon in an optical scanning device that optically scans the scanning surface by imaging the deflected light beam into a spot on the scanning surface by an imaging lens system. Has a function of geometrically optically coupling the reflection position of the rotary polygonal mirror and the scanning plane in a substantially conjugate relationship with respect to the sub-scanning direction, and has an fθ function with respect to the main scanning direction. .

The fθ lens system has a two-group, two-lens configuration including first and second lenses provided in a first and second order from the side of the rotary polygon mirror toward the scanning surface. The first lens is an “anamorphic single lens having a negative refractive power in both the main and sub-scanning directions”, and the second lens is an “anamorphic single lens having a positive refractive power in both the main and sub-scanning directions”. is there.

The first lens has one surface formed of a spherical surface, the other surface formed of a cylinder surface or a toric surface, or a modified toric surface, and the second lens has one surface of a toric surface and the other surface of a toric surface or It is formed with a deformed 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)
4), the radius of curvature R _iX in the deflection plane, R _iY in the sub-scanning direction,
When the refractive indices of the first and second lenses are n ₁ and n ₂ , they are as follows: (I) −3.5 <[｛(1 / R _3X ) − (1 / R _4X )］ n ₂ ] / [ ｛(1 / R _1X ) − (1 / R _2X )｝ n ₁ ] <− 2.
0 (II) -2.5 <[{ (1 / R 3Y) - (1 / R 4Y)} n 2] / [{(1 / R 1Y) - (1 / R 2Y)} n 1] <- 1.
0 is satisfied.

Further, the deformed toric surface, when the radius of curvature in the sub-scanning direction on the optical axis is R _iY0 , and the distance from the optical axis in the main scanning direction is H _i , (However, the compound _sign is a curved surface that satisfies − when R _iX > 0, and + when R _iX <0).

In the following description, the “deflection surface” is a plane formed by sweeping the principal ray of an ideal deflection light beam by a rotating polygon mirror. A plane that includes the optical axis of the lens and that is orthogonal to the deflecting surface is hereinafter referred to as a “deflection orthogonal surface”.

Regarding the curvature of the lens surface, R _iX is a radius of curvature on the deflection surface, and R _iY is a radius of curvature in a plane parallel to the optical axis and orthogonal to the deflection surface. In addition, _RiO, which is one of the parameters for specifying the deformed toric surface, is the radius of curvature in the plane orthogonal to the deflection.

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

The condition (II) is a condition for favorably correcting the amount of field curvature in the sub-scanning direction and coma.

When the value exceeds the upper limit of the condition (II), the curvature of field in the sub-scanning direction becomes excessive, and outward coma occurs. If the lower limit is exceeded, the curvature of field in the sub-scanning direction becomes under, and inward coma occurs.

The deformed toric surface is employed to satisfactorily correct the curvature of field 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 substantially parallel luminous flux from a light source or a light source device 1 including a light source and a light condensing device is substantially parallel to a deflection surface near a reflection surface 4 of a rotary polygon mirror 3 by a cylinder lens 2 serving as a line image forming optical system. An image is formed as a line image.

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 viewed 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 surface 7 to a geometric optic 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 links the reflection position of the rotary polygon mirror 3 and the scanning surface 7 to a substantially geometrical optically conjugate relationship.
Therefore, even if the reflecting surface 4 is tilted as shown by reference numeral 4 'as shown in FIG.
The upper imaging position hardly moves in the sub-scanning direction (vertical direction in FIG. 3). Therefore, the tilting is corrected.

Now, when the rotating polygon mirror 3 rotates, the reflecting surface 4 rotates about the axis 3A, and as shown in FIG. A displacement ΔX occurs between them. At this time, the shift amount ΔX ′ between the position P ′ of the conjugate image of the line image by the fθ lens system and the scanning surface 7 is represented by ΔX ′ = β ² ΔX as is known, where β is the lateral magnification of the fθ lens system in the sub-scanning direction. Given.

FIGS. 5 and 6 show the relationship between θ and ΔX when the angle between the lens optical axis of the fθ lens system and the principal ray of the deflected light beam is θ in the deflection plane. FIG. 5 shows that the specific incident angle α (the angle between the principal ray of the light beam incident on the rotating polygon mirror and the optical axis of the fθ lens system: see FIG. 7) is 90 degrees, and the inscribed circle radius R of the rotating polygon mirror 3 is R. 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 specific incident angle α decreases.

Further, the relative displacement between the position of the line image and the reflection surface due to the rotation of the reflection surface occurs two-dimensionally in the deflection surface and 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 above-described specific incident angle α will be described.
In the figure, the symbol a indicates the principal ray of the light beam incident on the rotating polygon mirror, and the symbol b indicates the light beam reflected by the rotating polygon mirror 3 is fθ.
It shows the principal ray when it is parallel to the optical axis of the lens system. 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, and the coordinates of the rotation axis position of the rotary polygon mirror 3 are Xp and Yp.

The specific incident angle α is generally 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.

FIG. 8 is an explanatory diagram showing a deformed toric surface forming one end of the feature of the present invention.

The deformed toric surface is such that the radius of curvature in the sub-scanning direction is small at the optical axis portion as shown in FIG. 8, and the radius of curvature in the sub-scanning direction gradually increases as the optical axis moves away from the main scanning direction. It satisfies the above-mentioned equation (III) analytically. Therefore, the deformed toric surface is uniquely determined if R _iX and R _iY0 are given.

[Examples] Hereinafter, five 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 the composite focal length of the synthesis focal distance or the sub-scanning direction in the deflection plane perpendicular. 2θ indicates the deflection angle, and α indicates the specific 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.

Further, K ₁ = [｛(1 / R _3X ) − (1 / R _4X )｝ n ₂ ] /
[｛(1 / R _1X ) − (1 / R _2X )｝ n ₁ ], K ₂ = [｛(1 / R _3Y ) −
(1 / R _4Y )｝ n ₂ ] / [｛(1 / R _1Y ) − (1 / R _2Y )｝ n ₁ ].

Example 1 f _M = 100, f _S = 24.254, 2θ = 65.6 °, α = 60 °, R = 14.085, K1 = −3.261, K2 = −1.034, d ₀ = 7.027 In this embodiment, the first surface is a toric surface,
The surface is a spherical surface, and the third and fourth surfaces are toric surfaces.

Example 2 f _M = 100, f _S = 23.35, 2θ = 65.6 °, α = 60 °, R = 14.085, K1 = −3.261, K2 = −1.236, d ₀ = 7.027 In this embodiment, the first surface is a spherical surface, the second and fourth surfaces are toric surfaces, and the third surface marked * is a deformed toric surface. R on the deformed toric surface of the third surface
Needless to say, _3Y is R _3Y0 in the general formula (III).

Example 3 f _M = 100, f _S = 23.00, 2θ = 65.6 °, α = 60 °, R = 14.085, K1 = −2.901, K2 = −1.25, d ₀ = 7.317 In this embodiment, the first surface is a cylinder surface and the second surface is a second surface.
The surface is a spherical surface, and the third and fourth surfaces are toric surfaces.

Example 4 f _M = 100, f _S = 24.615, 2θ = 65.6 °, α = 60 °, R = 14.085, K1 = −3.261, K2 = −1.689, d ₀ = 7.027 In this embodiment, the first surface is a spherical surface, the third and fourth surfaces are toric surfaces, the second surface marked with * is a deformed toric surface, and R _2Y is represented by the general formula (III). _R2Y0 in

Example 5 f _M = 100, f _S = 23.338, 2θ = 65.6 °, α = 60 °, R = 14.085, K1 = −3.261, K2 = −1.147, d ₀ = 7.027 In this embodiment, the second surface is a spherical surface, the third and fourth surfaces are toric surfaces, the first surface marked with * is a deformed toric surface, and R _1Y is represented by the general formula (III). R _1Y0 in

The specific numeric value of f _M is a f _M = 220.1mm through the fifth embodiments.

FIG. 9 shows an aberration diagram relating to the first embodiment. 10 to 13 show aberration diagrams for Examples 2 to 5. 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. The field curvature is shown over the entire deflection region since it is asymmetrical due to the variation of the entrance pupil position with the rotation of the rotating polygon mirror.

FIG. 14 to FIG. 18 show spot diagrams representing the imaging performance in each embodiment. Assuming that the maximum deflection angle is 1 around the optical axis, the deflection angles are 0, ± 0.7, ± 1.

[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, FIGS. 2 to 3 are diagrams for explaining the fθ lens of the present invention, and FIGS. FIG. 7 is a diagram for explaining the change of the entrance pupil position based on the rotation of the rotary polygon mirror and a countermeasure thereof, FIG. 8 is a diagram for explaining the deformed toric surface, and FIGS. Aberration diagram, No.
FIG. 14 to FIG. 18 are diagrams showing spot diagrams. 5 ... first lens, 6 ... second lens

Claims (1)

(57) [Claims] A substantially parallel light beam from a light source is formed into a long linear image in a direction corresponding to main scanning, and the light beam is subjected to uniform angular velocity by a rotary polygon mirror having a reflecting surface near the linear image forming position. In a light scanning device that optically scans the scanning surface by forming an image of the deflected light beam in a spot shape on the scanning surface by the imaging lens system, the light beam deflected by the rotary polygon mirror is imaged on the scanning surface. A lens system that has a function of linking the reflection position of the rotating polygonal mirror and the scanning plane in a substantially conjugate relationship with respect to the sub-scanning direction, has an fθ function with respect to the main scanning direction, and has a function from the side of the rotating polygonal mirror. A two-group, two-lens configuration including first and second lenses arranged in a first and second order toward the scanning surface side, wherein the first lens is used in both the main and sub-scanning directions. Anamorphic single lens with negative refractive power, The second lens is an anamorphic single lens having a positive refractive power in both the main and sub-scanning directions. The first lens has a spherical surface on one surface and a cylinder surface or toric surface or a deformed toric on the other surface. The second lens has one surface formed of a toric surface and the other surface formed of a toric surface or a deformed toric surface, and sequentially forms a lens surface from a rotating polygon mirror toward a 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 deflecting plane, R _iY in the sub-scanning direction, and the refractive indices of the first and second lenses are n ₁ and n ₂ , these are represented by (I) −3.5 <[ _{{(1 / R 3X) -} (1 / R 4X)} n 2] / [{(1 / R 1X) - (1 / R 2X)} n 1] <- 2.0 (II) -2.5 <[{( 1 / R _3Y ) − (1 / R _4Y )｝ n ₂ ] / [｛(1 / R _1Y ) − (1 / R _2Y )｝ n ₁ ] <− 1.0 Satisfies the condition: When the radius of curvature in the sub-scanning direction on the optical axis is R _iY0 , and the distance from the optical axis in the main scanning direction is H _i , (However, the compound _sign is a curved surface that satisfies − if R _iX > 0, and + if R _iX <0).