JP2621838B2 - Optical scanning device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to an optical scanning device used for 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 the size and price are reduced. Therefore, as an optical writing head, which is an important component thereof, there is a great demand for an optical scanning device to be reduced in size and cost. An 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 miniaturization and cost reduction.

The scanning lens system is distorted such that the light spot moves at a constant speed on the scanning surface in accordance with the rotation 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. A high-performance, high-resolution scanning lens having these functions has conventionally been inevitably large, complicated, and expensive.

Accordingly, Japanese Patent Application Laid-Open Nos. Sho 54-98627 and Sho 5
As disclosed in JP-A-5-5727 and JP-A-58-5706, the use of a single scanning lens has been attempted. However, in Japanese Patent Application Laid-Open No. 54-98627, for a deflector having a sinusoidal vibration characteristic, it is possible to widely and satisfactorily correct aberrations for various values of a parameter such as a shape by using the rotation characteristic. From the point of view, the rotational angular characteristic of the rotary polygon mirror deflector, which is still widely used today, is aspherical to cope with it, but it can be used only in very limited conditions as a special case. Therefore, it is not possible to flexibly respond to 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 as compared with 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]

According to the present invention, there is provided an optical scanning apparatus which emits a thin light beam, a deflector which deflects and scans the light beam in a predetermined direction, and which is deflected by the deflector. A scanning lens that forms an image on the plane to be scanned with the light beam, wherein the scanning lens is formed of a single lens, and the sign of the radius of curvature of the surface on the side on which the light beam enters in the meridional plane is It is characterized in that the light is reversed from the middle according to the incident position of the light beam in the meridional plane.

In this case, if the radius of curvature is positive when the center of curvature is on the light beam exit side with respect to the lens surface, and the radius of curvature is negative when the center of curvature is on the light beam incident side, the above sign reversal starts from the middle as the ray height increases. It is desirable that the value be inverted from positive to negative.

In order to correct the curvature of field in the spherical missing direction, the curvature in the spherical missing direction at a position along the non-circular arc curve in at least one of the meridional planes on both surfaces of the single lens is corrected. Desirably, it is determined so as to change without correlation with the curvature in the meridian direction.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The principle of the present invention will be described below with reference to FIGS. 1, 2, 3, and 4. FIG. 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 converts the light beam into a point T on the plane to be scanned where the coordinate value Y is proportional to the deflection angle θ.
It is set to focus on _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.

According to a first principle of the lens surface shape according to the present invention, assuming that a light beam to be scanned is extremely thin, the light beam is represented only by the parameters of the position and direction of the principal ray and the imaging distance. One point on the surface is that the inclination and the curvature are determined so as to change the direction or the imaging distance only for the principal 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, the principal ray of a light beam deflected at an arbitrary deflection angle is always on the same plane (this is called a meridian plane). It can be seen that the point at which the inclination and the curvature are designated by is only on the curve where the meridional plane and the lens plane intersect. Therefore, the second construction principle of the present invention creates a curve on the meridian plane,
At any point on the curve, the inclination and curvature in the meridional plane attain the purpose of the above-described scanning lens, and at any point on the curve, the section perpendicular to the meridian plane containing the principal ray (spherical section) If a curvature of “cross section” is given, it means that a surface has been formed.

However, the inclination and curvature in the meridian direction are not determined independently of each other because they are continuously connected to form a lens surface position in the meridian plane. 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.

Hereinafter, the configuration principle of the lens according to the present invention will be specifically described 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} light flux {L _i } is g _{mi for} the meridional light flux and g _si for the spherical missing light 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. Well, surface S
direction of the principal ray L _ci after passing through _i may be controlled by the normal direction e _i in T _i surface S _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 first configuration principle described above.

As described above, since the principal ray L _{ci and the} like do not leave the meridional plane, the normal direction vector e _i of the plane S _i is also in the meridian plane and is shown in FIG. 2 as the degree of freedom representing the inclination of the plane. One degree of freedom of the angle α _i between the indicated optical axis 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 designating the slope and curvature has the same meaning as solving a differential equation and creating a two-dimensional curve on the meridian plane. Further, since the curvature of the sphere lacking 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.

Although the scanning lens can be realized by the above-described configuration principle, the fact that it can be realized by a single aspherical lens will be described with reference to the principle diagram of FIG. In FIG. 3, the page represents the meridian plane.

First, the meridian plane is considered. Want to restrain now is two degrees of freedom that the principal ray L _ci coordinate value Y _I and T _I of intersection T _I of the scan plane S _I is image forming point. For example the inclination alpha ₁ surface to restrain the scanning position Y _I of the light beam is deflected by any angle θ specified in 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.

[0020] Next consider the sagittal light beam, while a single degree of freedom of sagittal direction image forming position g _si is like to restraint, which was stored the shape of state or curve restrained in meridional plane, Since the curve on the meridian plane can be controlled by giving a curvature in a direction perpendicular to the curve, it is not necessary to add a new plane to the above-mentioned two planes.

Accordingly, it is understood that the number of necessary lens surfaces is 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, consider the symmetry of the surface of the single lens aspherical lens having the above-described configuration. 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, since the scanning lens of the present invention has no symmetry except for two symmetry surfaces, it is possible to completely correct spherical aberration of curvature of field, meridional curvature of field, and distortion characteristic aberration. .

Hereinafter, a specific method for realizing the shape of a single-lens bi-aspherical lens for scanning according to the present invention will be described 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 distances s ₁ and s ₂ along the curve from the intersections P ₁ and P ₂ with the optical axis, respectively, and the inclination at that point from the direction perpendicular to the optical axis. It is defined 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

[0024] Now, as shown in FIG. 4, the deflection angle from the emission point P _M on the optical axis theta, the light beam L emitted by the meridional image formation distance g _m0
i (i = 0, ₁ , 2) are the surfaces S ₁ , S ₂ and T ₁ , respectively.
Assuming that the image plane S _I intersects with T _I at T ₂ , the light emitting position and the light emitting direction are represented as follows. That vector _{P M T 1 = (a 0} cosθ, a 0 sinθ) vector _{T 1 T 2 = (a 1} cosθ 1, a 1 sinθ 1) (2) vector _{T 2 T I = (a 2} cosθ 2, a 2 sin θ ₂ ). And R _m1, R _{m @ 2} further surface S _1, S ₂ of T _1, a meridional cross section radius of curvature at T _2, respectively, also the light beams L _1,
Let the meridional imaging distances of L _{2 be} g _m1 and g _m2 .

According to the above description method, the principle of the lens shape described above 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 beams on the surfaces are equal. Each point on the surface is 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 refraction surface and the direction of the light beam is
The well-known law of refraction is S₁, S _TwoPlane and L₁, L_Twoof
By applying for the intersection, sin (α₁−θ) = nsin (α)₁−θ₁): S₁Plane (3) nsin (α_Two−θ₁) = Sin (α)_Two−θ_Two): S_TwoPlane (4). Here, n is the refractive index of the lens medium.

The relationship between the curvature of the surface and the imaging distance of the light beam is
Thin S ₁ side of the meridional image formation distance relationship when the obliquely incident on the surface having a curvature which the light beam is, by applying the S ₂ side ^{_{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 side 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.

Regarding the above, it is assumed that the rectangular coordinate values of the surface position calculated by the above equation (1) are equal to the rectangular coordinate values of the refraction point of the light ray calculated based on the above equation (2). , There is a relationship. Here, 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.

Regarding the condition that the surface is continuous,
That is, the integration in the equations (7) to (10) is possible. The condition that the surface is smooth is determined by the surface inclination 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 point is scanned at a constant speed on the scanning plane is that the intersection (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) Where F ^-1 is an inverse function of F, τ is a time parameter, and K is an appropriate proportional constant. For example, if the rotation characteristic is a constant angular velocity deflection, then F (τ) = ωτω: angular velocity (17) Y _I = K · θ / ω = f · θ f = K / ω: constant ( 18) You can write X _I in addition (13) represents the optical axis length is x-coordinate of the scanning surface.

The condition for forming an image on the scanning plane is (6)
It satisfies if the meridional light flux imaging distance g _{m2 in the} equation is equal to a ₂ represented by the equations (13) and (14). G _m2 = a ₂ (19) As described above, the configuration principle of the lens shape according to the present invention is (3), (4), (5), (6), (7), (8),
(9), (10), (11), (12), (13),
Formulas (14), (16) and (19) are formalized, but it will be described below that by calculating these, the lens surface shape can actually be directly expressed in some form. Among the variables appearing in the expression, 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 K for constant-speed scanning is a constant value independent of 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 I} is 14 and the above 14 equations are all independent, the simultaneous equations can be solved and the above 14 variables can be expressed as a function of the deflection angle θ, for example. Thus, for example when representing the surface S ₁ may be made to correspond to the deflection angle θ as a parameter the relationship between the distance s ₁ along the plane of inclination alpha ₁ and the optical axis.

Incidentally, since the above-mentioned 14-way simultaneous equations are nonlinear and include a differential term and an integral term, they cannot be directly solved and must use a numerical solution method. The present invention is not limited to a variety of numerical solutions, but the present invention is not limited thereto.Here, as an example, it is assumed that this equation can be actually solved by numerical calculation and the lens shape can be determined by a numerical integration method in a differential vector field. I will show you.

Solving with a differential vector field means expressing all equations in a differential form, assuming that all current variable values are known, and calculating the increment of each variable (differential variable) to obtain the value of the next variable. It 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.

Equations (7) to (10) are as follows: da ₀ cos θ−a ₀ sin θ dθ = −sin α ₁ ds ₁ (24) da ₀ sin θ + a ₀ cos θd θ = 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 θdθ = cos α ₂ ds ₂ (27) (13), (14) The equation is: 0 = da ₂ cos θ ₂ −a ₂ sin θ ₂ dθ ₂ + da ₁ cos θ ₁ −a ₁ sin θ ₁ dθ ₁ + da ₀ cos θ−a ₀ sin θd θ (28) dY _I = da ₂ sin θ ₂ + a ₂ cos θ ₂ dθ _{2 1} sin θ ₁ + a ₁ cos θ ₁ dθ ₁ + da ₀ sin θ + a ₀ cos θd θ (29) The expression (16) becomes dY _I = K ｛F ⁻¹ (θ)｝ d θ (30). Equation (19) may be simply 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 And the deflection angle θ can be expressed as a parameter.
However θ ⁰ ₁ is the initial value. The actual calculations ₁ the initial value _{θ, θ 2, α 1,} α 2, s 1, the s ₂ is 0, a
^{_{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.

Now, the curve on the meridian plane of the lens shape of the present invention is embodied as described above. The constants n, X ₁ , X ₂ , X _I , g _m0 , and g appear during the embodying process. K is the degree of freedom that the lens shape of the present invention can take. 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 initial meridional imaging position g _m0 ^* is set to infinity, that is, if the meridional light beam before entering the scanning lens is set as a parallel light beam, the beam diameter and the like can be easily controlled and the optical system can be easily handled. Become. The scanning lens of the present invention is naturally applicable to a parallel light beam as described above.

Next, a method for determining the radiuses of curvature R _s1 and R _s2 of the sphere lacking section for controlling the sphere missing image 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, if R _s1 is always set to infinity and the second term on the right side of the equation (34) is set to 0 for simplification of the surface shape, the first surface becomes a surface having no curvature in the ball missing direction.

Note that the initial sphere-missing image distance g _s0 may be arbitrarily given, but when the deflector is a rotating polygon mirror, if g _s0 = 0, the reflection point and scanning point of the mirror surface become conjugate image points. It can be provided with a face tilt correction function.

[0039]

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 according to the present invention is such that the refractive index n of the lens medium, the initial imaging distance g ₀ , the first
The six parameters of the position X ₁ , X _{2 at which} the surface and the second surface intersect the optical axis, the optical axis length X _I , and the scanning speed constant K can be independently changed. 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 as follows: Refractive index of lens medium n = 1.486 Optical axis length from deflection point to plane to be scanned X _I = 200 mm Deflector is rotating polygon mirror deflection・ Initial meridional imaging distance g _m0 is infinite. That is, the light beam before entering the scanning lens is a parallel light beam. -Spherical section curvature 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. It is.

Note that the lens shape according to the present invention is not represented by simple numerical values or mathematical expressions, but results are obtained as numerical examples. 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%.

[0043] Table 1, Table 2, the coefficient R _m1 indicating the curve shape of the first surface S ₁ of the meridional plane in Table 3, B _1, C _1, D _1, E ₁
Tables 4, 5, and 6 show coefficients R _m2 , B ₂ , C ₂ , D ₂ , and E ₂ showing the curved shapes on the meridional plane of the second surface S ₂ in Tables 7, 8, and 9 respectively. listed sagittal cross section direction of the curvature factor R _s ⁰ indicating the radius _{variation, a s, B s, C} s, D s, the E _s, the calculated value by changing the parameters θ _e, X _1, X ₂ in .
However, the effective deflection angle θ _e is a parameter used in place of the scanning speed coefficient K in the expression (18), and the effective scanning width is 20
When defined as 0 mm, is _{θ e = 200 / K (rad} ). As described above, X ₁ and X ₂ are the first surface S ₁ and the second surface S ₁
Surface S ₂ is the position of the point of intersection with the optical axis. Under the above-mentioned common calculation conditions, a set of parameters θ _e , X ₁ , X
Those having the same value of ₂ are the same lens.

Further, for some of the examples shown in the table, an outline of the curved shape on the meridian plane is shown in FIGS. 5 to 12 together with the optical path diagrams. 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, perfectness is an ideal state, and the actual lens shape may have a slight numerical field curvature error or distortion characteristic aberration due to a numerical calculation error in calculating the shape or a 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.

[0046]

[Table 1]

[0047]

[Table 2]

[0048]

[Table 3]

[0049]

[Table 4]

[0050]

[Table 5]

[0051]

[Table 6]

[0052]

[Table 7]

[0053]

[Table 8]

[0054]

[Table 9]

FIG. 13 is a perspective view showing an overall image of an optical system of a laser beam printer using one embodiment of a lens shape according to the present invention. The light beam emitted from the semiconductor laser 2 is converted into a parallel light beam by the collimator lens 3, converged only in the direction of the sphere 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 missing direction of the sphere, the mirror surface and the photosensitive drum surface are conjugate image forming points, forming 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 forms an image on a straight line without curvature of field. The latent image is formed on the photosensitive drum by rotating the photosensitive drum by one pitch for each scan and repeating the rotation.

[0056]

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. 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. Also, as shown in FIGS. 1 and 8, when the sign of the radius of curvature of the surface on the incident side of the scanning lens according to the present invention reverses from positive to negative from the middle as the ray height increases, the scanning lens is The size can be reduced. Therefore, there is an effect that a compact, low-cost, and high-performance optical scanning device can be provided.

[Brief description of the 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 configuring 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 view 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 view 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.

[Description of Signs] 1 ... Scanning lens 2 ... Semiconductor laser 5 ... Polygon mirror 6 ... Rotating polygon mirror deflector 7 ... Scanned surface (photosensitive drum)

Claims (3)

(57) [Claims] 1. A light source for emitting a thin light beam, a deflector for deflecting and scanning the light beam in a predetermined direction, and a scanning lens for forming an image of the light beam deflected by the deflector on a plane to be scanned. The scanning lens is a single lens, and the sign of the radius of curvature of the surface on the side on which the light beam enters in the meridional plane is reversed halfway according to the incident position of the light beam in the meridian plane. An optical scanning device characterized by the above-mentioned. 2. If the radius of curvature is positive when the center of curvature is on the light beam exit side with respect to the lens surface, and the radius of curvature is negative when the center of curvature is on the light beam incident side, the sign inversion becomes positive from the middle as the ray height increases. 2. The optical scanning device according to claim 1, wherein the optical scanning device is inverted from. 3. A curvature in a ball missing direction at a position along a non-circular arc curve in at least one of meridional planes of both surfaces of the single element lens so as to correct a field curvature aberration in a ball missing direction. 2. The optical scanning device according to claim 1, wherein the optical scanning device is determined so as to change without correlation with the curvature in the meridian direction.