JP2877457B2 - 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.

Among such optical scanning devices, `` a parallel light beam from the light source device is imaged as a long line image in the main scanning corresponding direction, and the above-mentioned light is scanned by a rotating polygon mirror having a deflecting reflection surface near the image forming position of the line image. There is an apparatus of the type in which a light beam is deflected at a constant angular velocity, and the deflected light beam is imaged into a spot on the surface to be scanned by an imaging lens system to optically scan the surface to be scanned.

An optical scanning device using a rotating polygon mirror has a problem of "surface tilt", and the angular velocity of the deflected light beam is constant because the angular velocity of the rotating polygon mirror is constant. Scanning is not performed at a constant speed. Therefore, a device for scanning at a constant speed is required. The fθ lens system is a lens system that optically realizes constant-speed scanning of the surface to be scanned, and the image height of a light beam incident at an angle of θ with respect to the lens optical axis is fθ and fθ. Fθ
Function ".

In order to solve the problem of surface tilt, the lens system provided between the rotating polygon mirror and the surface to be scanned is made an anamorphic system, and the position of the deflecting reflection surface and the surface to be scanned are geometrically There is known a method of “establishing a conjugate relationship”.

[Problems to be Solved by the Invention] There are various known fθ lens systems that use an anamorphic lens to perform scanning at a constant speed and solve the problem of surface tilt. For example, Japanese Patent Application Laid-Open No. 63-19617 discloses a two-sheet configuration.

However, the fθ lens system does not always sufficiently correct the curvature of field, and the diameter of the image spot on the surface to be scanned fluctuates considerably depending on the scanning position, so that it is difficult to realize high-density optical scanning. Japanese Patent Application Laid-Open No. 61-120112 discloses a two-element fθ lens system using a so-called saddle-shaped toric surface in order to satisfactorily correct field curvature, but this fθ lens system has an aspherical surface. There is a problem that processing is difficult because two surfaces are used.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has a novel fθ that enables sufficient correction of curvature of field in the main and sub-scanning directions and a solution to the problem of surface tilt in a rotating polygon mirror. The purpose is to provide a lens system.

[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 parallel light beam from the light source device is formed as a long linear image in the main scanning corresponding direction, and the light beam is converted by a rotary polygon mirror having a deflecting / reflecting surface near the image forming position of the linear image. In an optical scanning device which deflects at a constant angular velocity, forms an image of the deflected light beam into a spot on the surface to be scanned by an imaging lens system, and optically scans the surface to be scanned at a substantially constant speed, the light is deflected by a rotating polygon mirror. Imaging lens system that forms the focused light beam on the surface to be scanned, and a function of making the position of the deflecting reflection surface and the surface to be scanned substantially geometrically conjugate with respect to the sub-scanning direction. "Fθ function" for main scanning direction
Having.

The plane formed by sweeping the principal ray of the deflected light beam ideally deflected by the rotating polygon mirror is referred to as a “deflection surface”. A plane parallel to the off-axis of the imaging lens system and orthogonal to the deflecting surface is referred to as a “deflection orthogonal surface”.

The fθ lens system of the present invention has a two-group, two-lens configuration composed of first and second lenses provided in the first and second order from the side of the rotary polygon mirror toward the surface to be scanned. When each lens surface is defined as the first to fourth surfaces counted from the side of the rotary polygon mirror, the shape of these lens surfaces within the deflection surface is the first.
From the surface to the fourth surface, the order is “straight line, arc, arc, arc”, and within the plane parallel to the deflecting surface, both the first and second lenses have positive refractive power.

The first surface is a “convex or concave cylinder surface having a refractive power only in a plane or a plane orthogonal to deflection”, the second surface is a “convex spherical surface”, and the third surface is “light having a radius of curvature in the plane orthogonal to deflection. Concave barrel-shaped toric surface that decreases with distance from the axis. "
The surface is a “convex toric surface having a strong curvature in a plane orthogonal to the deflection”.

Assuming that the combined focal length in the plane orthogonal to the deflection plane is f _S , and the radii of curvature of the third and fourth planes in the plane orthogonal to the deflection plane including the optical axis are r ′ ₃ and r ′ ₄ , respectively. | {(1 / r ′ ₃ ) − (1 / r ′ ₄ )} · f _S | <1.4.

Here, each lens surface of the fθ lens system of the present invention will be described with reference to FIG.

In FIG. 1, the left side of the figure is the side of the rotating polygon mirror, and the right side is the side of the surface to be scanned. Therefore, the left side of the figure shows the first lens and the right side shows the second lens. Are the first to fourth surfaces sequentially from left to right.

1 shows the lens shape in the deflection plane of the fθ lens system, and the lower figure shows the lens shape in the deflection orthogonal plane including the optical axis.

Since the intersection of the deflection surface with the surface to be scanned corresponds to the ideal main scanning direction, the upper drawing of FIG. 1 is indicated as "main". Similarly, since the plane orthogonal to the deflection corresponds to the sub-scanning direction, the drawing below FIG. 1 is indicated as "sub".

As for the lens surface shape in the deflecting surface, the first to fourth lens surfaces are a straight line, an arc, an arc, and an arc in this order as shown in the upper part of FIG. The refractive power in a plane parallel to the deflection surface is
1, Both the second lens is “positive”.

[Operation] The condition (I) will be described.

By configuring the fθ lens system with the above-described lens surface configuration, it is possible to favorably correct the curvature of field in the main and sub scanning directions.

However, in a state where the curvature of field in the main scanning direction is well corrected, in order to effectively correct the curvature of field in the sub-scanning direction, the above condition (I) must be further satisfied. That is, in the case where the lens is formed with the above-described surface configuration and the surface tilt is corrected, the curvature of field in the sub-scanning direction occurs on the over side when the lower limit of the condition (I) is exceeded, and on the under side when the upper limit is exceeded. I do. Therefore, if the condition (I) is not satisfied, the imaging performance is reduced, the fluctuation of the light spot diameter in the sub-scanning direction becomes large, and it becomes difficult to realize good optical scanning. Conversely, when the above condition (I) is satisfied, the "field curvature correcting function in the sub-scanning direction" of the concave barrel-shaped toric surface on the third surface is favorably exhibited.

Next, referring to FIG. 2, this figure schematically illustrates an example of an optical scanning apparatus using an fθ lens system. FIG. 3 shows the optical arrangement of FIG. 2 viewed from the sub-scanning direction, that is, the state in the deflection plane.

In FIG. 2, a parallel light beam from a light source device 1 comprising a light source or a light source and a condensing device is converted by a cylinder lens 2 as a line image forming optical system into a deflecting and reflecting surface 3a of a rotary polygon mirror 3.
Is formed as a line image LI substantially parallel to the deflection surface. The longitudinal direction of the line image LI is a main scanning corresponding direction.

The light beam reflected by the rotating polygon mirror 3 is formed into an image of a spot on the surface 6 to be scanned by the fθ lens system. Scan.

The fθ lens system includes a first lens 4 and a second lens 5, and the lens 4 is located on the side of the rotary polygon mirror 3 and the lens 5.
Are disposed on the side of the surface 6 to be scanned. As viewed in the deflection plane, as shown in FIG. 3, the fθ lens system including the lenses 4 and 5 links the infinity on the light source device 1 side and the position of the surface 6 to be scanned to a geometrical 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 deflection reflection surface 3a and the surface 6 to be scanned in a geometrically optically conjugate relationship. Therefore, as shown in FIG.
As shown in the figure, even if the surface tilts, the image formation position on the scanned surface 6 by the fθ lens system hardly moves in the sub-scanning direction (vertical direction in FIG. 4). Therefore, the tilting is corrected.

Now, when the rotating polygon mirror 3 rotates, the deflecting / reflecting surface 3a becomes the axis 3A.
5, a displacement ΔX occurs between the imaging position P of the line image and the deflecting reflecting surface 3a due to the rotation of the deflecting reflecting surface as shown in FIG. The position P ′ of the conjugate image is shifted from the scanned surface 6 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. 6 and 7 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. 6 depicts the specific incident angle α (see FIG. 8) as 90 degrees and the radius R ′ of the inscribed circle of the rotating polygon mirror 3 as a parameter. In FIG. 7, the radius R 'of the inscribed circle is 40 mm, and the specific incident angle α
Is drawn as a parameter. As can be seen from FIGS. 6 and 7, ΔX increases as the radius of the inscribed circle R ′ increases and as the specific incident angle α decreases.

Also, the relative displacement between the position of the line image and the deflection reflecting surface due to the rotation of the deflection reflecting surface occurs two-dimensionally in the deflection surface,
In addition, it moves asymmetrically with respect to the lens optical axis. Therefore, in the non-scanning device as shown in FIG. 2, 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 well corrected in the main scanning direction.

Here, a description will be given of the above-mentioned specific incident angle α. In FIG. 8, reference symbol a indicates a principal ray of a light beam incident on the rotary polygon mirror, and reference symbol b indicates an optical axis of the fθ lens system. The specific incident angle α is defined as the intersection angle between the principal ray a and the optical axis b as shown in the figure.

The X and Y axes are determined as shown in the figure with the position of the intersection of the principal ray a and the optical axis b as the origin, and the coordinates of the rotation axis position 3A of the rotary polygon mirror 3 are X
c and Yc.

As described above, Δ of the positional deviation amount between the line image position and the deflecting reflection surface
In order to minimize the fluctuation of X, as is well known, R
Is defined as 0 <Xc <Rcos (α / 2), 0 <Yp <Rsin (α / 2), and Xc, Yc.

In order to prevent the principal ray a of the incident light beam from existing outside the effective main scanning area and prevent the return light from the scanned surface 6 from re-entering the main scanning area on the scanned surface as ghost light, the rotating polygon mirror 3 must be used. Is the number of surfaces and the deflection angle is θ, and the above α may be subject to the condition θ <α <(4π / N) −θ.

Next, the barrel-shaped toric surface forming one end of the features of the present invention will be described.

Curve passing through AVB Referring to FIG. 9 is a circular arc whose center of curvature position C _1. When this arc is rotated about the straight line X ₁ Y ₁ on the arc AVB side from the center of curvature C ₁ in the same plane as the arc, a barrel-shaped curved surface TT as shown in FIG. 10 is obtained.
This surface TT is a barrel-shaped toric surface. When this surface TT is used as a lens surface, it can be used as a convex surface or as a concave surface. Use the toric surface.

In the convex toric surface of the fourth surface, the arc is in the plane orthogonal to the deflection including the optical axis, and the rotation axis is parallel to the sub-scanning direction in this surface, and is on the opposite side to the arc with respect to the center of curvature of the arc.
Therefore, this toric surface has a strong curvature in a plane orthogonal to the deflection including the optical axis.

Looking at the radius of curvature of the barrel-shaped toric surface in X ₁ Y ₁ perpendicular to the axis to the plane, which is smaller with increasing distance to C ₂ points in the axial direction, the radius of curvature the axis X ₁ Y ₁ and arc AVB Equal to the distance to

In the present invention, the direction of the axis X ₁ Y ₁ on the concave barrel-shaped toric surface of the third surface is made parallel to the main scanning direction within the deflection surface.

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

In each embodiment, f _M represents a combined focal length in the main scanning direction of the fθ lens system, that is, a combined focal length in a plane parallel to the deflection surface, and this value is normalized to 100. Also 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 is the deflection angle (unit: degree),
α represents a specific incident angle (unit: degree), and β represents a lateral magnification in the sub-scanning direction.

r _ix is the radius of curvature in the deflection plane of the i-th lens surface counted from the side of the rotating polygon mirror, that is, the radius of curvature of the lens surface shape appearing in the figures indicated as “main” in each of FIGS. _iY is the radius of curvature of the i-th lens surface in the plane orthogonal to the deflection, that is, the radius of curvature of the lens surface shape that appears in the figure indicated as “sub” in each of FIGS. 1A and 1B, and r _3Y and r _4Y are the conditions. R ′ ₃ , r ′ ₄ in relation to (I)
It is explained as. Regarding the third surface, r _3X represents the distance between VC ₁ and _3Y represents the distance between VC _{2 in} FIG.

d ₁ is the distance between the i-th lens surfaces, d _O is the distance from the deflecting reflection surface of the rotary polygon mirror to the first lens surface, and n _j is the refractive index of the j-th lens.

Further, K represents | {(1 / r ′ ₃ ) − (1 / r ′ ₄ )} · f _S | in the above condition (I).

Example 1 f _M = 100, f _S = 14.945, β = −5.91, α = 54, 2θ = 63.4, K =
_{1.25, d O = 5.411 i r} iX r iY d i j n i 1 ∞ ∞ 1.5091 1.71221 2 -954.926 -954.926 7.245 3 -36.528 -17.196 4.6382 1.675 4 -25.488 -7.062 Example 2 f _M = 100, f _S = 14.052, β = −6.39, α = 54, 2θ = 63.4, K =
_{1.04, d O = 7.816 i r} iX r iY d i j n i 1 ∞ ∞ 3.3671 1.71221 2 -623.550 -623.550 1.202 3 -36.796 -12.386 6.0122 1.675 4 -26.335 -6.454 Example 3 f _M = 100, f _S = 16.175, β = -5.45, α = 54, 2θ = 63.4, K =
0.95, d _O = 9.019 i r _iX r _iY d _i j n _i 1 ∞ ∞ 3.7161 1.71221 2 −478.035 −478.035 0.602 3 −40.655 −14.310 8.7792 1.675 4 −28.998 −7.778 Example 4 f _M = 100, f _S = 15.123, β = -5.69, α = 54, 2θ = 63.4, K =
_{1.31, d O = 5.411 i r} iX r iY d i j n i 1 ∞ -57.720 1.5091 1.71221 2 -954.926 -954.926 7.245 3 -36.528 -18.398 4.6382 1.675 4 -25.488 -7.090 Example 5 f _M = 100, _{f S = 13.106, β = -7.77} , α = 54,2θ = 63.4, K =
_{0.68, d O = 5.411 i r} iX r iY d i j n i 1 ∞ 9.019 1.5091 1.71221 2 -954.926 -954.926 7.245 3 -36.528 -10.231 4.6382 1.675 4 -25.488 -6.675 Example 6 f _M = 100, f _S = 13.946, β = -6.5, α = 54, 2θ = 63.4, K =
_{0.9, d O = 7.816 i r} iX r iY d i j n i 1 ∞ 72.149 3.3671 1.71221 2 -623.550 -623.550 1.202 3 -36.796 -10.822 6.0122 1.675 4 -26.335 -6.382 Example 7 f _M = 100, f _S = 14.201, β = -6.25, α = 54, 2θ = 63.4, K =
_{1.34, d O = 7.816 i r} iX r iY d i j n i 1 ∞ -36.676 3.3671 1.71221 2 -623.550 -623.550 1.202 3 -36.796 -18.037 6.0122 1.675 4 -26.335 -6.670 Example 8 f _M = 100, _{f S = 16.184, β = -5.44} , α = 54,2θ = 63.4, K =
_{1.0, d O = 9.019 i r} iX r iY d i j n i 1 ∞ -300.623 3.7161 1.71221 2 -478.035 -478.035 0.602 3 -40.655 -15.031 8.7792 1.675 4 -28.998 -7.806 Example 9 f _M = 100, f _S = 16.012, β = -5.62, α = 54, 2θ = 63.4, K =
0.46, d _O = 9.019 i r _iX r _iY d _i j n _i 1 ∞ 28.619 3.7161 1.71221 2 −478.035 −478.035 0.602 3 −40.655 −9.620 8.7792 1.675 4 −28.998 −7.550 Implemented in FIGS. 11 to 19 Aberration diagram for Examples 1 to 9
A θ characteristic diagram is shown. The curvature of field diagram is associated with the rotation of the rotary polygon mirror. The broken line indicates the one in the main scanning direction, and the solid line indicates the one in the sub-scanning direction.

The fθ characteristics an ideal image height f _M · θ, when the actual image height is h, as defined in _{(h-f M · θ)} · 100 / (f M · θ).

Each of the embodiments has good aberration.
It is corrected very well in the sub-scanning direction. Fθ
The characteristics are also good.

[Effects of the Invention] As described above, according to the present invention, a novel fθ lens system can be provided. Since the fθ lens system has the above-described configuration, it is possible to satisfactorily correct the surface tilt of the rotating polygon mirror and satisfactorily correct the field curvature in the main and sub-scanning directions to realize optical scanning. Optical scanning of the density becomes possible.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining the shape of the fθ lens system of the present invention, FIGS. 2 to 8 are diagrams for explaining an optical scanning device, and FIGS. 9 and 10 are barrel-shaped toric surfaces. FIGS. 11 to 19 are diagrams illustrating aberrations and fθ characteristics relating to each example. DESCRIPTION OF SYMBOLS 1 ... Light source device, 2 ... Cylinder lens, 3 ... Rotating polygon mirror, 4, 5 ... 1st and 2nd lens which comprises ftheta lens system

Claims (1)

(57) [Claims] A parallel light beam from a light source device is formed as a long linear image in a direction corresponding to the main scanning, and the light beam is converted into a uniform angular velocity by a rotary polygon mirror having a deflecting reflection surface near an image forming position of the linear image. In a light scanning device that forms a spot on the surface to be scanned by the imaging lens system and optically scans the surface to be scanned at a substantially constant speed, the light is deflected by the rotating polygon mirror. An imaging lens system for forming an image of a light beam on a surface to be scanned. The imaging lens system has a function of making the position of the deflecting reflection surface and the surface to be scanned substantially geometrically conjugate with respect to the sub-scanning direction, and also has a function in the main scanning direction. Has a fθ function, and is a two-group, two-element configuration including first and second lenses arranged in first and second order from the side of the rotary polygon mirror toward the surface to be scanned, The principal ray of the deflected light beam ideally deflected by the rotating polygon mirror is When a plane swept with the deflection is called a deflecting surface, and a surface parallel to the optical axis of the imaging lens system and orthogonal to the deflecting surface is called a deflecting orthogonal surface, the first to fourth surfaces are counted from the rotating polygon mirror side. The shape of the surface within the deflection plane is sequentially linear from the first surface to the fourth surface,
An arc, an arc, or an arc, wherein the first and second lenses both have a positive refractive power in a plane parallel to the deflecting surface, and the first surface has a convex power having a refractive power only in a plane or a plane orthogonal to the deflection. The concave cylinder surface, the second surface is a convex spherical surface, the third surface is a concave barrel-shaped toric surface in which the radius of curvature in the plane perpendicular to the deflection decreases as the distance from the optical axis increases, and the fourth surface is a strong curvature in the plane orthogonal to the deflection. A composite focal length in the orthogonal plane of deflection, f _s , and the radii of curvature of the third and fourth surfaces in the orthogonal plane including the optical axis are r ′ ₃ , r ′ ₄ , respectively. when the, they 0.4 <| {(1 / r '3) - (1 / r' 4)} · f S | <fθ lens system and satisfies 1.4 following condition.