JPH08320442A - Optical scanning device - Google Patents

Abstract

PURPOSE: To provide a small and inexpensive optical scanning device, specially a scanning lens, of high performance. CONSTITUTION: This device is provided with a light source transmitting a narrow luminous flux, a deflector 5 for deflecting/scanning the luminous flux in a prescribed direction and a scanning lens 1 forming the image of the luminous flux deflected by the deflector 5 on a scanning plane 7, the scanning lens 1 is composed of a single lens, the luminous flux deflected by the intrinsic rotating characteristic of the deflector 5 has a distortion characteristic moving at a constant speed on the plane to be scanned 7, the shape of both surfaces S1 , S2 in the meridional plane is formed as non-circular-arcuate shape independently determined so that the non-circular arcuate amount of both surfaces restricts two degrees of freedom of the scanning position and the image forming point for compensating the aberration of curvature of field in the meridional direction and the curvature, in the direction of spherical wane at the position along the non-circular-arcuate curve in the meridional plane of at least either of both surfaces S1 , S2 , is determined so as to be changed without correlating to the curvature in the meridional direction and compensate the curvature of field in the direction of spherical wane.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical scanning device used in a laser beam printer or the like. More particularly, it relates to a scanning lens system.

[0002]

2. Description of the Related Art A laser beam printer for recording image information by deflecting and scanning a laser beam or the like at a high speed has a high speed,
It has excellent features such as high resolution and low noise, and its demand is rapidly increasing as miniaturization and price reduction proceed. Therefore, as an optical writing head, which is an important component thereof, there is a great demand for downsizing and cost reduction of an optical scanning device. The optical scanning device is roughly divided into a light source, a deflector, and a scanning lens system. Among them, simplification of the scanning lens system is effective for downsizing and cost reduction.

The scanning lens system is distorted so that the light spot moves at a constant speed on the scanning surface in accordance with the turning characteristics of the deflector.
For example, when the deflector is a rotating polygon mirror and the light beam is deflected at a constant angular velocity, there is a distortion such that the deflection angle θ is proportional to the image height Y, and a light spot is desired everywhere on the scanning plane. Must have the function of forming an image uniformly on the diameter of Further, in the case of a rotary polygon mirror deflector, a face tilt correction function for compensating for variations in tilt (face tilt error) of each face of the polygon mirror is also required. Conventionally, a high-performance and high-resolution scanning lens having these functions has inevitably become large, complicated, and expensive.

Therefore, JP-A-54-98627 and JP-A-5-98627
As disclosed in JP-A-5-7727 and JP-A-58-5706, attempts have been made to make a single lens for scanning. However, in JP-A-54-98627, for a deflector having a sinusoidal vibration characteristic, it is possible to widely and satisfactorily correct aberrations for various values of parameters such as a shape by utilizing the rotation characteristic, but high speed operation is possible. In view of the above, the rotating polygon mirror deflector, which is still widely used today, has an aspherical surface in order to correspond to it, but it can be used only under extremely limited conditions as a special case. Therefore, it is impossible to flexibly meet various requirements such as the size of the optical system, the light source, and the required dot diameter.

Further, in Japanese Patent Application Laid-Open No. 55-7727, the fθ lens is constituted by a plano-convex lens, but it is difficult to say that it has good imaging performance in terms of field curvature and the like. Further, in Japanese Patent Application Laid-Open No. 58-5706, the fθ lens is constituted by a meniscus lens having a positive power. However, there is a problem in terms of spherical missing image field curvature. You must add a cylindrical lens that also serves as the lens. further,
In all of the above three examples, a lens must be newly added in order to provide the surface tilt correction function, and eventually the lens is not a single lens. It is possible to keep the aberration within an allowable range by increasing the optical axis length and narrowing the deflection angle, but this is not preferable because the entire optical system becomes large.

Incidentally, the material of the lens is also an important issue in considering miniaturization and cost reduction. Conventionally, glass is used as the material of the scanning lens, but since it is an optical system that requires diffraction-limited performance and has high required accuracy, manufacturing costs such as polishing are high. Therefore, if plastics such as polymethyl methacrylate (PMMA), polycarbonate, and polystyrene are used for the lens medium, mass production by injection molding becomes possible, so that production can be performed at extremely low cost.
However, there are few types of optical plastic materials, and none of them has a higher refractive index than glass. Therefore, it is more difficult to reduce the number of lenses and downsize the optical system than glass.

[0007] In view of these points, it is understood that a lens having a large degree of freedom is desired, which is a single lens regardless of the refractive index of the material and which can favorably correct aberrations even if the optical axis length is short. .

[0008]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems, and has as its object to provide a small, low-cost, and high-performance optical scanning device, particularly a scanning lens. It is.

[0009]

An optical scanning device of the present invention which achieves the above object, comprises a light source for emitting a thin light beam, a deflector for deflecting and scanning the light beam in a predetermined direction, and a deflector deflected by the deflector. And a scanning lens for forming an image of the light flux on the scanned plane, the scanning lens is configured by a single lens, and the light flux deflected by the unique rotation characteristic of the deflector is on the scanned plane. It has a distortion characteristic of moving at a constant speed, and the shapes of both surfaces in the meridional plane are non-circular so that the curvature of field in the meridional direction of the light flux at any position on the scanned plane is corrected. Is formed in a non-arcuate shape that is independently determined so as to constrain the two degrees of freedom between the scanning position and the image formation point, and further, in order to correct the field curvature aberration in the sagittal direction, A sphere located along a non-circular curve in at least one meridian plane It is characterized in that the direction of curvature are thus determined so as to vary without correlation between the meridional direction of the curvature.

[0010]

BEST MODE FOR CARRYING OUT THE INVENTION The principle of the present invention will be described below with reference to FIGS. 1, 2, 3, and 4. As described above, the scanning lens forms a light beam deflected by the deflector with a rotation characteristic such as constant angular velocity or sinusoidal vibration on the scanned plane without curvature of field, and an image point on the scanned plane is formed. It has a function of giving distortion such that scanning is performed at a constant speed. For example, if the deflector is rotating polygonal mirror, the light beam emitted from the light source as shown in FIG. 1 is reflected by the deflection angle θ in accordance with the rotation of the polygon mirror 5 by the mirror S _M. The scanning lens 1 transmits this light beam to a point T where the coordinate value Y is proportional to the deflection angle θ on the plane to be scanned.
Set to image at _I. The scanning lens of the present invention is a single-lens lens that has a high degree of use of the aspherical features on both surfaces S ₁ and S ₂ shown in FIG. 1 based on the principle described below, has little aberration, and can perform wide-angle deflection. is there.

The first constitutional principle of the lens surface shape according to the present invention is that, assuming that the light beam to be scanned is very thin, the light beam is expressed only by the parameters of the position and direction of the chief ray and the image forming distance, and One point on the surface is that the inclination and curvature are determined so that the direction or the imaging distance is changed only for the chief ray passing therethrough. In terms of the aberration correction, this means that spherical curvature and coma are ignored and field curvature aberration and distortion are completely corrected including higher-order terms. The above assumption is generally sufficient for a scanning optical system such as a laser beam printer.

Further, in the scanning lens system, since the principal ray of the light beam deflected at an arbitrary deflection angle is always on the same plane (this is called a meridian plane), the light beam is very thin, and the surface is also on the surface. It can be seen that the point where the inclination and the curvature are specified is only on the curve where the meridional surface and the lens surface intersect. Therefore, the second construction principle of the present invention is to create a curve on the meridian plane,
The inclination and curvature in the meridional plane at any point on the curve achieve the purpose of the scanning lens described above, and at any point on the curve, a cross section including the chief ray and perpendicular to the meridional plane (spherical section). It is assumed that a surface can be formed if a curvature (referred to as a cross section) is given.

However, since the inclination and the curvature in the meridional direction are continuously connected to each other to form the lens surface position in the meridian plane, they cannot be determined independently, but the spherical section curvature is independent of them. Can handle. Therefore, it is obvious that an optical system to which the first and second constitutional principles are applied only to the lens surface shape in the meridional plane is also included in the scope of the present invention.

The construction principle of the lens according to the present invention will be specifically described below with reference to the perspective view of FIG. Light flux {L _i-1} 2 is converted into the light flux {L _i} by the surface S _i. The imaging distance measured from T _{i of the} luminous flux {L _i } is g _mi for meridional luminous flux and g _{si for} aspherical luminous flux. In general, g _mi and g _si are not equal. As described above, since the light beam is very thin, when the light beam {L _i } is handled, only the chief ray L _ci and the image forming distances g _mi and g _{si of the} meridian and the sphere missing need to be considered. Now, surface S
The direction of the chief ray L _ci after passing _i can be controlled by the normal direction e _i of the surface S _i at T _i . The image formation distance g _mi after passing through the surface S _i, g _si can be controlled by the surface S meridional section curvature at T _i of _i radius R _mi and sagittal section curvature radius R _si. Accordingly, the function of forming an image of one light beam deflected at a certain angle on the scanning plane at a position where uniform scanning can be realized is provided by the position of one point on the lens surface and its differential amount (normal direction and curvature). Thus, if the above-mentioned functions are provided at each point on the lens surface corresponding to the light beam deflected at an arbitrary angle by linking them and the desired function of the scanning lens is determined. This is the above-mentioned first configuration principle.

As described above, since the chief rays L _{ci and the} like do not leave the meridian plane, the normal direction vector e _i of the surface S _i is also in the meridian plane and the degree of freedom representing the inclination of the surface is shown in FIG. One degree of freedom of the angle α _i formed by the optical axis shown and the normal vector is sufficient. The meridional section curvature of the surface S _i is the derivative of the inclination alpha _i of the surface, because the inclination alpha _i surface is a differential quantity of positions on the meridian plane of the surface S _i, in the direction of the surface of Kekkyokuko meridional It can be seen that specifying the slope and the curvature has the same meaning as solving the differential equation and creating a two-dimensional curve on the meridional plane. Further, since the curvature of the spherical section is determined without affecting the curve, it is determined for each point on the curve after the curve is created. This is the second configuration principle.

The scanning lens can be realized by the above-described constitutional principle, and it will be explained using a principle diagram of FIG. 3 that it can be realized by a single lens having both aspherical surfaces. In FIG. 3, the paper surface represents the meridian surface.

First, consider the meridian plane. What I want to constrain is the two degrees of freedom that the coordinate values Y _I and T _I of the intersection T _I of the principal ray L _ci and the plane S _I to be scanned are imaging points. For example, to constrain the scanning position Y _I of the light beam deflected at an arbitrary angle θ, the inclination α ₁ of the surface is specified at all positions on the surface,
Accordingly, the shape in which the surfaces are smoothly connected is determined by the boundary condition (for example, the coordinate value X ₁ of the intersection P ₁ with the optical axis and the inclination at that point are 0).
) Is determined in one way as in S ₁ , and the radius of curvature R _m1 on that surface cannot be specified,
The light beam forms an image at a point T _I ′ that is not on the plane to be scanned.
Conversely, it is impossible to specify the gradient alpha ₁ in the same way the surface by specifying the radius of curvature R _m1 of the surface at all positions on the surface to restrain the imaging point. As described above, one surface is required to constrain one degree of freedom among the parameters of the light ray with an arbitrary value of the deflection angle θ. Therefore, in order to restrict the above two degrees of freedom, At least two lens surfaces are required.

Next, considering the spherical ray bundle, what is desired to be constrained is one degree of freedom of the image forming position g _{si in} the sagittal direction, which is in the constrained state in the meridian plane, that is, while keeping the shape of the curve, Since it can be controlled by giving a curvature to the curve on the meridian surface in a direction perpendicular to the curve, it is not necessary to add a new surface to the above-mentioned two surfaces.

Therefore, it is understood that the required lens surfaces are two and a single lens is sufficient. Also, since both surfaces are inclined at all positions of the lens surface and the curvature is designated, the single lens must have both aspheric surfaces.

Now, let us consider the symmetry of the surfaces of the single-lens aspherical lens having the above-mentioned structure. If the two curves created in the meridian plane are rotated around some axis such as the optical axis, the degree of freedom of the radius of curvature in the direction of the sphere is lost. Therefore, if the rotation symmetry is provided, the imaging of the missing light beam cannot be controlled, and the missing curvature of the spherical image surface occurs. Regarding the plane symmetry, since the light flux is always on the meridian plane, it is clearly symmetric about the meridian plane, and the light flux having a deflection angle of θ and the light flux of −θ are the same assuming that the light flux passing through the optical axis has a deflection angle of 0. Because of the condition, it is also symmetric about a plane that includes the optical axis and is perpendicular to the meridian plane. As described above, the scanning lens of the present invention has no symmetry except that it has two planes of symmetry, so that it is possible to completely correct spherical-defective field curvature aberration, meridional field curvature aberration, and distortion characteristic aberration. .

A specific method for realizing the shape of the single-lens double aspherical lens for scanning of the present invention will be described below with reference to the principle diagram of FIG. First, a method of creating two curves on the meridian plane will be described.
As shown in FIG. 4, the lens surfaces S ₁ and S ₂ are the distances s ₁ and s ₂ along the curve from the intersections P ₁ and P ₂ with the optical axis and the inclinations from the direction perpendicular to the optical axis at that point. It is specified in relation to the angles α ₁ and α ₂ . If this is expressed in rectangular coordinates again, for the surfaces S ₁ and S ₂ , if the optical axis is the x axis and the height direction of the lens is the y axis with the origins at P ₁ and P ₂ respectively,
Coordinate values (x ₁ , y ₁ ), (x ₂ , y ₂ ) of points T ₁ and T ₂
Is Becomes

Now, as shown in FIG. 4, the emission point on the optical axis
P_MTo deflection angle θ, meridional imaging distance g _m0Light flux L emitted at
_i(I = 0, 1, 2) is the surface S₁, S₂And T respectively₁,
T₂And the image plane S_IAnd T_IAnd then light as follows
The output position and the output direction of the bundle are shown. That is, the vector P_MT₁= (A₀cos θ, a₀sin θ) Vector T₁T₂= (A₁cos θ₁, A₁sin θ₁) (2) Vector T₂T_I= (A₂cos θ₂, A₂sin θ₂). Further surface S₁, S₂Of T₁, T₂Meridian section at
R is the radius of curvature_m1, R_m2And the luminous flux L₁,
L₂The meridian imaging distance of g_m1, G_m2And

In accordance with the above description method, the above-mentioned lens shape forming principle can be formulated. The formulation will be described by dividing it into the following six items. The direction of the light beam is controlled by the inclination of the surface at the intersection of the light beams with the surfaces S ₁ and S ₂ . The image forming distance of the light beam is controlled by the curvature of the surface at the intersection of the light beams with the surfaces S ₁ and S ₂ . The coordinates of the intersections of the light fluxes on the surface are equal. The points on the surface are smoothly continuous. The light beam forms an image on the scanning plane. The imaging point is scanned at a constant speed on the scanning plane.

The relationship between the inclination of the refracting surface and the direction of the light beam is
By applying the well-known law of refraction to the intersections of the S ₁ and S ₂ surfaces with L ₁ and L ₂ , sin (α ₁ −θ) = nsin (α ₁ −θ ₁ ): S ₁ surface (3) It can be expressed as nsin (α ₂ −θ ₁ ) = sin (α ₂ −θ ₂ ): S ₂ surface (4). However, n is the refractive index of the lens medium.

The relationship between the curvature of the surface and the image forming distance of the light beam is
Applying the relational expression of the meridional imaging distance when a thin light beam is obliquely incident on a surface having a certain curvature to the S ₁ surface and the S ₂ surface, ncos ² (α ₁ −θ ₁ ) / g _m1 = cos ² ( α ₁ −θ) / (g _m0 −a ₀ ) + {ncos (α ₁ −θ ₁ ) −cos (α ₁ −θ)} / R _m1 (5) S ₁ surface cos ² (α ₂ −θ ₂ ). / G _m2 = ncos ² (α ₂ −θ ₁ ) / (g _m1 −a ₁ ) + {cos (α ₂ −θ ₂ ) −ncos (α ₂ −θ ₁ )} / R _m2 (6) S ₂ surface Is obtained.

As for the above, it is assumed that the orthogonal coordinate value of the surface position calculated by the above equation (1) is equal to the orthogonal coordinate value of the refraction point of the ray calculated based on the above equation (2). , There is a relationship. However, X ₁ is the x coordinate value of the intersection of the surface S ₁ and the optical axis, and X ₂ is the x coordinate value of the intersection of the surface S ₂ and the optical axis.

As for the condition that the surfaces are continuous,
That is, the integration in the equations (7) to (10) is possible. The condition that the surface is smooth is that the surface inclinations α ₁ , α
₂ is differentiable and dα ₁ / ds ₁ = −1 / R _m1 (11) dα ₂ / ds ₂ = −1 / R _m2 (12)

The condition that the image points are scanned at a constant speed on the scanning plane is that the intersection point (X _I , Y _I ) of the image plane and the light beam is X _I = a ₂ cos θ ₂ + a ₁ cos θ ₁ + a ₀ cos θ (13) Y there is relationship _{I = a 2 sinθ 2 + a} 1 sinθ 1 + a 0 sinθ (14), and the scan point position Y _I, using the deflector rotation characteristic θ = F (τ) (15 ) Y I = K · F ⁻¹ (θ) (16) However, F ⁻¹ is an inverse function of F, τ is a time parameter, and K is an appropriate proportional constant. For example now, when turning characteristics were uniform angular velocity deflection, F (τ) = ωτ ω : Since an angular velocity _{(17) Y I = K ·} θ / ω = f · θ f = K / ω: constants ( 18) can be written. Further, X _{I in the} equation (13) represents the optical axis length in the x coordinate of the scanning surface.

The conditions for forming an image on the scanning plane of (6) are as follows:
It is satisfied if the meridional luminous flux imaging distance g _{m2 in the} formula is equal to a ₂ expressed by the formulas (13) and (14). That is, g _m2 = a ₂ (19) As described above, the construction principle of the lens shape according to the present invention is (3), (4), (5), (6), (7), (8),
(9), (10), (11), (12), (13),
It was formulated by the equations (14), (16), and (19), but it is described below that the lens surface shape can be directly expressed in some form by calculating these. Of the variables appearing in the equation, the deflection angle θ and the initial meridional imaging distance g _m0 are given at the time of emission and are known. The optical axis length X _I, surface S _1, the intersection position X ₁ of the optical axis of the S _2, X _2,
The constant velocity scanning constant K is a constant value that does not depend on the deflection angle θ.
Therefore, the unknowns are the remaining θ ₁ , θ ₂ , α ₁ , α ₂ , s ₁ ,
_{s 2, g m1, g m2} , a 0, a 1, a 2, R m1, R m2, Y
_Since there are 14 of _I , and the above 14 equations are all independent, the simultaneous equations can be solved and the 14 variables can be expressed as a function of the deflection angle θ, for example. Therefore, for example, when expressing the surface S ₁ , the relationship between the inclination α ₁ and the distance s ₁ along the surface from the optical axis may be associated with the deflection angle θ as a parameter.

By the way, since the above-described simultaneous equations of 14 elements are non-linear and include a differential term and an integral term, they cannot be directly solved and a numerical solution method must be used. Although various numerical solutions are conceivable and the present invention is not limited thereto, here, as an example, it is shown that this equation can be actually solved by numerical calculation by the method of numerical integration in the differential vector field to determine the lens shape. I will show you.

Solving with a differential vector field means that all equations are expressed in differential form, all current variable values are known, and increments (differential variables) of each variable are calculated to obtain the value of the next variable. Is. Expressed in differential form to organize supra 14 Equation (3), (4) expression _{(dα 1 -dθ) cos (α} 1 -θ) = n (dα 1 -dθ 1) cos (α 1 - _{θ 1) (20) n (} dα 2 -dθ 1) cos (α 2 -θ 1) = (dα 2 -dθ 2) cos (α 2 -θ 2) (21) (5), and (6) By combining the equations (11) and (12), {ncos ² (α ₁ −θ ₁ ) / g _m1 } ds ₁ = {cos ² (α ₁ −θ) / (g _m0 −a ₀ )} ds ₁ − ｛ ncos (α ₁ −θ ₁ ) −cos (α ₁ −θ)｝ dα ₁ (22) ｛cos ² (α ₂ −θ ₂ ) / a ₂ ｝ ds ₂ = ｛ncos ² (α ₂ −θ ₁ ) / (G _m1 −a ₁ )｝ ds ₂ − ｛cos (α ₂ −θ ₂ ) −ncos (α ₂ −θ ₁ )｝ dα ₂ (23) where g _m1 is a combination of equations (22) and (23). And erase it.

The equations (7) to (10) are expressed as da ₀ cos θ-a ₀ sin θd θ = -sin α ₁ ds ₁ (24) da ₀ sin θ + a ₀ cos θ dθ = cos α ₁ ds ₁ (25) da ₁ cos θ ₁ -a ₁ sin θ ₁ dθ ₁ + da ₀ cos θ −a ₀ sin θ dθ = −sin α ₂ ds ₂ (26) da ₁ sin θ ₁ + a ₁ cos θ ₁ dθ ₁ + da ₀ sin θ + a ₀ cos θ dθ = cos α ₂ ds ₂ (27) (13), (14). equation _{0 = da 2 cosθ 2 -a 2} sinθ 2 dθ 2 + da 1 cosθ 1 - a 1 sinθ 1 dθ 1 + da 0 cosθ-a 0 sinθdθ (28) dY I = da 2 sinθ 2 + a 2 cosθ 2 dθ 2 + da ₁ sin θ ₁ + a ₁ cos θ ₁ dθ ₁ + da ₀ sin θ + a ₀ cos θdθ (29) The expression (16) is dY _I = K {F ⁻¹ (θ)} dθ (30). Expression (19) may simply be substituted. (20)-
The unknown differential variables in equation (30) are dθ ₁ , d
θ ₂ , dα ₁ , dα ₂ , ds ₁ , ds ₂ , da ₀ , da
₁ , da ₂ , dY _I , and the above (20) to (30)
Expression (22), (23) the melts easily because except those in one expression by simultaneous is second order equations are all first-order equation, for example, by known differential variables d [theta] d [theta] ₁ = Fθ ₁ (θ ₁ , θ ₂ , α ₁ , α ₂ , s ₁ , s ₂ , a ₀ , a ₁ , a ₂ ) dθ (31) Thus, for example, θ ₁ is The deflection angle θ can be expressed as a parameter by integrating
However, θ ⁰ ₁ is an initial value. In the actual calculation, initial values are 0, a for θ ₁ , θ ₂ , α ₁ , α ₂ , s ₁ , and s _{2.
^{0, a 1, a 0 0}} = X 1 a 0 1 = X 2 -X 1 (33) for a ₂ by using the value of X _1, X _2, X _I, supra a ⁰ ₂ = X _I - X ₂ can be calculated by numerical integration.

[0033] Now, more meridional on surface curve of the lens shape of the present invention as is, but it necessarily embodied, constant n appearing in the process of _{embodying, X 1, X 2, X} I, g m0, K is the degree of freedom that the lens shape of the present invention can have. That is, a set of appropriate constants {X ₁ ^* , X ₂ ^* ,
X _I ^*, g _m0 ^*, it is not there is one lens shape for one of the K ^*}, naturally present invention includes those of all these.

If the meridional initial image forming position g _m0 ^* is set to infinity, that is, if the meridional light beam before entering the scanning lens is a parallel light beam, the optical system is easy to control and easy to handle. Become. The scanning lens of the present invention is naturally applicable to a parallel light beam as described above.

Next, a method of determining the radius of curvature R _s1 and R _s2 of the spherical section for controlling the spherical image forming distance will be described. (5),
Although narrow light beam to (6) showed a relational expression meridional imaging distance when incident obliquely, for Tamaketsuyuizo _{distance, n / g s1 = 1 /} (g s0 -a 0) + { _{ncos (α 1 -θ 1) -cos} (α 1 -θ)} / R s1: S 1 side _{(34) 1 / g s2 =} n / (g s1 -a 1) + {cos (α 2 -θ 2 ) −ncos (α ₂ −θ ₁ )｝ / R _s2 : S ₂ plane (35) The condition that there is an image point in the missing direction on the plane to be scanned is g _s2 = a ₂ (36). The radii of curvature R _s1 and R _{s2 of the} spherical section are determined by the equations (34), (35) and (36). In the equations, a ₀ , a ₁ , a ₂ , α ₁ , α ₂ , θ, θ ₁ , and θ ₂ are known because the meridional curve has already been determined by the above-described method, and g _s0 is given, so the unknown is g.
_s1 , _gs2 , _Rs1 , and _Rs2 . Accordingly, there are redundant degrees of freedom for the three equations, and it is understood that one of the unknowns may be appropriately determined. For example, in order to simplify the surface shape, if R _s1 is always infinite and the second term on the right side of the equation (34) is set to 0, the first surface has no curvature in the sagittal direction.

It should be noted that the initial spherical absent image forming distance g _s0 may be arbitrarily given, but when the deflector is a rotary polygon mirror, if g _s0 = 0, the reflection point of the mirror surface and the scanning point become a conjugate image point. A trouble correction function can be provided.

[0037]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Tables 1 to 9 and FIGS. 5 to 12 show examples of calculating the lens surface shape based on the principle of the lens shape according to the present invention.

As described above, the lens shape of the present invention has the refractive index n of the lens medium, the initial image forming distance g ₀ , and the first lens of the lens.
The six parameters of the positions X ₁ and X ₂ where the surface and the second surface intersect with the optical axis, the optical axis length X _I , and the scanning speed constant K can be changed independently, respectively. In contrast, there is one lens shape. Therefore, there are so many examples that seemingly completely different shapes, and it is impossible to list all of them,
Here, only a typical embodiment is shown.

Calculation conditions common to the following embodiments are: refractive index of lens medium n = 1.486; optical axis length from deflection point to scanned plane X _I = 200 mm Deflection at a constant angular velocity with an instrument-The initial meridional imaging distance g _m0 is infinite. That is, the light beam before entering the scanning lens is a parallel light beam. -The curvature of the spherical section is given only to the second surface. The initial sphere-missing image distance g _s0 is 0. Therefore, the reflection point and the scanning point of the rotary polygon mirror are conjugate image points, and a plane tilt correction function is provided. Is.

It should be noted that the lens shape according to the present invention is not expressed by simple numerical values or mathematical expressions, and the result can be obtained, for example, as a numerical example. Therefore convenience, the formula ^{x = (y 2 / R)} / [1 + √ {1- (y / R) 2}] Using the well-known aspherical coefficients for the curve shape of the meridian plane +
By ⁴ + Cy ⁶ + Dy ⁸ + Ey ¹⁰ : where x is the x-axis value when the optical axis is the x-axis and the intersection of the plane and the optical axis is the origin. And the radius of curvature R _s2 of the spherical section of the second surface is R _s2 = R _s2 ⁰ + Ay ² + By ⁴ + Cy ⁶ + Dy ⁸ + Ey
Expressed as ¹⁰ . The error from the true shape at the time of such approximation is about 0.001% to 0.01%.

In Table 1, Table 2 and Table 3, the first surface S₁Meridian plane
Coefficient R indicating the upper curve shape_m1, B₁, C₁, D₁, E₁
The second surface S is shown in Tables 4, 5 and 6.₂On the meridian plane of
Coefficient R indicating the shape_m2, B₂, C₂, D₂, E₂The table
7, Table 8 and Table 9 show the changes in the radius of curvature in the spherical section direction.
Number R_s ⁰, A_s, B_s, C_s, D_s, E_sThe parameter
Θ_e, X₁, X₂The value calculated by changing is shown.
However, effective deflection angle θ_eIs the scanning speed factor of the above formula (18).
It is a parameter used instead of several K, and the effective scan width is 20
If set to 0 mm, θ_e= 200 / K (rad). X₁, X₂As mentioned above, the first side S₁, Second
Surface S₂Is the position of the point that intersects the optical axis. In addition,
Parameter set θ under common calculation conditions_e, X ₁, X
₂Lenses having the same value of are the same lens.

Further, an outline of the curved shape on the meridian plane of some of the examples shown in the table is shown in FIGS. 5 to 12 together with the optical path diagram. However, since the curve is symmetric about the optical axis, the opposite side of the optical axis is omitted.
In all the embodiments described here, the spherical aberration of curvature and the meridional curvature of field are completely eliminated in accordance with the constitutional principle of the present invention, and the distortion characteristics are completely adjusted so that the scanning point moves at a constant speed. Stipulated.

However, perfect is an ideal state, and field curvature aberrations and distortion characteristic aberrations may be slightly different from the actual lens shape due to numerical calculation error when calculating the shape or manufacturing error. Occurs. Of course, these aberrations have a certain allowable range, and if they are within that range, they are effective as a scanning lens. Therefore, the present invention does not exclude them.

[0044]

[Table 1]

[0045]

[Table 2]

[0046]

[Table 3]

[0047]

[Table 4]

[0048]

[Table 5]

[0049]

[Table 6]

[0050]

[Table 7]

[0051]

[Table 8]

[0052]

[Table 9]

FIG. 13 is a perspective view showing an overall image of an optical system of a laser beam printer using an embodiment of the lens shape according to the present invention. The light beam emitted from the semiconductor laser 2 becomes a parallel light beam by the collimator lens 3, is converged only in the spherical direction by the cylindrical lens 4, and forms a linear image near the mirror surface of the rotary polygon mirror deflector 6. The light beam is deflected at a constant angular velocity in the meridional plane by the rotation of the polygon mirror 5, passes through the scanning lens 1 according to the present invention, and forms an image on the photosensitive drum 7. In the direction of the eccentricity, the mirror surface and the photosensitive drum surface form a conjugate image forming point, which constitutes a surface tilt correction system. The image point is scanned at a constant speed in the axial direction of the photosensitive drum 7 by the scanning lens 1 of the present invention, and an image is formed on a straight line without a field curvature. The latent image is formed on the photosensitive drum by rotating the photosensitive drum by one pitch for each scan and repeating the rotation.

[0054]

As described above, in the optical scanning device of the present invention, the scanning lens has a distortion characteristic such that the light beam moves at a constant speed on the plane to be scanned, and the scanning lens has Since it is a single lens with both surfaces being aspherical so that the field curvature aberration of the light beam is zero or almost zero, even a single lens has very little aberration and very good imaging spot is obtained. A scanning lens having a short optical axis length can be configured. Further, for the same reason, even if the lens medium has a low refractive index, there is no problem in designing, and therefore the lens medium can be made plastic. Therefore, small size and low price,
Moreover, there is an effect that a high-performance optical scanning device can be provided.

[Brief description of drawings]

FIG. 1 is a principle diagram showing a schematic configuration of an optical scanning device of the present invention.

FIG. 2 is a principle diagram for explaining the principle of forming the lens shape of the present invention.

FIG. 3 is a principle diagram for explaining that the scanning lens of the present invention can be realized by a single-lens bi-aspherical lens.

FIG. 4 is a principle diagram for explaining a method of calculating the shape of a scanning lens according to the present invention.

FIG. 5 is a view showing one embodiment of a lens shape according to the present invention.

FIG. 6 is a view showing another embodiment of the lens shape of the present invention.

FIG. 7 is a diagram showing another embodiment of the lens shape of the present invention.

FIG. 8 is a view showing another embodiment of the lens shape of the present invention.

FIG. 9 is a view showing another embodiment of the lens shape of the present invention.

FIG. 10 is a view showing another embodiment of the lens shape of the present invention.

FIG. 11 is a view showing another embodiment of the lens shape of the present invention.

FIG. 12 is a diagram showing another embodiment of the lens shape of the present invention.

FIG. 13 is a perspective view showing an embodiment of the entire optical scanning device of the present invention.

[Explanation of symbols]

 1 ... Scanning lens 2 ... Semiconductor laser 5 ... Polyhedral mirror 6 ... Rotating polygon mirror deflector 7 ... Scanned surface (photosensitive drum)

Claims (1)

[Claims] 1. A light source which emits a thin light beam, a deflector which deflects and scans the light beam in a predetermined direction, and a scanning lens which forms an image of the light beam deflected by the deflector on a scanning plane. The scanning lens is composed of a single lens, and has a distortion characteristic that a light beam deflected by the unique rotation characteristic of the deflector moves at a constant speed on the scanned plane, and on the scanned plane. In order to correct the field curvature aberration in the meridional direction of the light flux at any position in the It is formed into a non-arc shape with an independently defined shape.
The curvature in the sagittal direction at a position along the non-arc curve in at least one of the meridional planes of the both surfaces changes without correlation with the curvature in the meridional direction so as to correct the field curvature aberration in the sagittal direction. An optical scanning device characterized by being defined as follows.