JP2982041B2 - Aspherical reflecting mirror and light beam scanning optical system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a light beam scanning optical system used for a laser beam printer, a digital copying machine, and the like, and an aspherical reflecting mirror used therein.

[0002]

2. Description of the Related Art As a deflector of a light beam scanning optical system used in a laser beam printer, a digital copying machine, or the like, a polygon mirror capable of high-speed scanning is mainly used. Since the deflection by the polygon mirror is performed at a constant angular velocity, scanning is performed at a constant speed on an arc locus centered on the deflection point, but on a scanned surface that is linear in the main scanning direction such as a drum-shaped photoconductor. In, the scanning speed differs between the scanning center and both ends in the main scanning direction, and image distortion occurs. In order to solve this problem, conventionally, an fθ lens that corrects the scanning on the scanning surface so as to have a constant speed has been used.

However, an fθ lens generally composed of a plurality of lenses becomes expensive when a glass lens manufactured by polishing is used. Therefore, an fθ lens manufactured by plastic molding for the purpose of reducing the processing cost. Has been put to practical use.

However, plastic changes in shape and refractive index due to environmental changes such as temperature and humidity are larger than those of glass. For example, when a temperature change of about 40 °, which is assumed in actual use, occurs, a plastic lens is used. Fθ using
With the lens, the amount of change in the total scanning length causes expansion and contraction of the image that cannot be ignored. Most of the deterioration of the optical characteristics is caused by a change in the refractive index. In other words, if the fθ lens is made of plastic, an aspherical lens can be produced at low cost, but the environmental dependency due to the material properties cannot be ignored, and fluctuations in optical characteristics cannot be avoided. .

[0005] Plastic lenses are also disadvantageous in terms of surface accuracy which affects the imaging characteristics. In general, since the thickness of the lens in the light beam transmission direction varies in thickness depending on the transmission position, the cooling rate tends to vary during molding, and it is extremely difficult to ensure high precision surface accuracy.

[0006] These problems can be solved by using a concave reflecting mirror which does not allow the light beam to penetrate inside and allows a uniform and thin-walled part design. Instead of fθ lens,
Conventionally, the use of a concave reflecting mirror having a function of equalizing the scanning speed on the surface to be scanned includes a method using a spherical mirror (Japanese Patent Laid-Open No. 1-220020) and a method using a coaxial aspherical reflecting mirror. (JP-A-5-341218) using a concave barrel-shaped reflecting mirror formed by rotating a non-arc shape defined in the main scanning plane around an axis orthogonal to the optical axis in the main scanning plane. (JP-A-5-164981) has been proposed.

[0007]

However, in Japanese Patent Application Laid-Open No. 1-220020 using a spherical mirror, since the reflecting surface is symmetrical with respect to the optical axis, the power in the main scanning direction and the power in the sub-scanning direction are reduced. When using a polygon mirror as a deflector, in order to correct the phenomenon that the angle between the normal line of the polygon mirror reflection surface and the rotation axis differs for each surface due to processing errors and mounting errors, so-called surface tilt In order to make the polygon mirror reflection surface and the scanned surface geometrically conjugate with each other, it is necessary to dispose an anamorphic optical element separately from the spherical mirror, which increases the number of parts and the complexity of the apparatus, and reduces the cost. There is a limit to conversion.
Further, since the shape of the reflecting surface is spherical, the degree of freedom in optical design is poor, and it is difficult to sufficiently correct the field curvature and the fθ characteristic.

The above-mentioned Japanese Patent Application Laid-Open No. Hei 5 (1993) using a coaxial aspherical reflecting mirror.
In the case of -341218, the reflecting mirror is made aspherical, and the field curvature correction and the fθ characteristic correction are performed. However, the image planes in the main scanning direction and the sub-scanning direction are formed by a coaxial aspherical surface symmetrical with respect to the optical axis. To perform the curvature correction at the same time, it is necessary to arrange the aspherical reflecting mirror closer to the scanned surface than the midpoint of the distance from the deflection point to the scanned surface. Since the curvature of field in the sub-scanning direction is corrected better as the aspherical reflecting mirror is brought closer to the surface to be scanned, in order to correct the curvature of field and the fθ characteristic satisfactorily, the aspherical reflecting mirror must be moved toward the surface to be scanned. Must be placed immediately before However, in an optical system using a reflecting mirror, in order to separate a light beam incident on the reflecting mirror and a light beam reflected by the reflecting mirror, a folding mirror, a half mirror, or the like is provided between the aspherical reflecting mirror and the surface to be scanned. Therefore, it is difficult to realize an arrangement for satisfactorily correcting the curvature of field in the sub-scanning direction. Further, since a coaxial aspherical surface is used, the deflection point and the surface to be scanned cannot be geometrically conjugated to each other. Therefore, when a deflector having a plurality of reflecting surfaces such as a polygon mirror is used, the scanning line pitch unevenness is increased. There is a problem that cannot be corrected.

In the above-mentioned Japanese Patent Application Laid-Open No. Hei 5-164981 using a concave barrel-shaped reflecting mirror having a non-circular shape rotated, correction of optical characteristics and correction of surface tilt can be performed only by the reflecting mirror. Because of the rotationally symmetric shape, the arrangement of the aspherical reflecting mirror that can obtain good optical characteristics is limited. That is, in order to rotate the non-circular shape defined in the main scanning plane at the radius of curvature necessary to make the deflection point and the scanned surface geometrically conjugate, the imaging relation in the main scanning direction and the auxiliary The imaging relationship in the scanning direction cannot be determined independently, and the arrangement of the aspherical reflecting mirror that can satisfactorily correct the field curvature in the main scanning direction and the sub-scanning direction and the fθ characteristic can be determined from the deflection point to the surface to be scanned. It is limited to almost the center of the distance to. When the aspherical reflecting mirror is closer to the deflector side than the center, the field curvature in the sub-scanning direction is under. When the aspherical reflecting mirror is closer to the surface to be scanned than the center, the field curvature in the sub-scanning direction is lower. Will be over. Further, since the shape in the main scanning plane is an aspherical shape represented by a conical constant, the aspherical coefficient of the higher order expansion term cannot be determined independently, and the field curvature in the main scanning direction and the fθ characteristic There is a limit to correction.

The present invention has been made in view of the above-mentioned problems of the prior art, and has as its object to arrange only an aspherical reflecting mirror as an optical element having a light condensing property between a deflector and a surface to be scanned. Despite being a light beam scanning optical system, the optical characteristics in the main scanning direction and sub-scanning direction can be corrected well regardless of the arrangement of the aspherical reflecting mirror, and high-density with a polygon mirror surface tilt correction function An object of the present invention is to provide an aspherical reflecting mirror and a light beam scanning optical system capable of performing an optical scanning.

[0011]

According to a first aspherical reflecting mirror of the present invention, which achieves the above object, a light beam emitted from a light source is provided on a main scanning plane by an optical system provided between the light source and a deflector. Aspherical reflection that reflects a deflected light beam that is condensed as a linear image parallel to and deflected by a deflector and is reflected and deflected at a uniform angular velocity to form a spot image on the surface to be scanned and also to perform constant-speed optical scanning It is a mirror. Here, the main scanning plane refers to a plane formed by sweeping the principal ray of the light beam, and the sub-scanning plane refers to a plane parallel to the optical axis and orthogonal to the main scanning plane.

That is, the first aspherical reflecting mirror condenses a linear image parallel to the main scanning plane in the vicinity of the deflecting surface, reflects the light beam deflected at a uniform angular velocity by the deflector, and scans the light beam. An aspherical reflecting mirror for spot imaging on a surface and performing uniform speed optical scanning, wherein the shape in the main scanning plane including the optical axis is such that the coordinates in the optical axis direction are Z, Assuming that the coordinates orthogonal to each other and included in the main scanning plane are Y, Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ¹⁰ (A, B, C, D: coefficient) And C satisfy the conditions of A <0 and C <0, and the shape in the sub-scanning plane which is parallel to the optical axis and orthogonal to the main scanning plane has any shape in the main scanning direction. Characterized in that the arc satisfies the geometric optic conjugate relationship of the surface It is.

The second aspherical reflecting mirror of the present invention is characterized in that the first
In the aspherical reflecting mirror, the coordinate included in the sub-scanning plane orthogonal to the optical axis is X, and the radius of curvature R in the sub-scanning plane is
When (Y) is represented by the following formula: R (Y) = a ₀ + a ₂ Y ² + a ₄ Y ⁴ + a ₆ Y ⁶ (a ₀ , a ₂ , a ₄ , a ₆ : coefficient), The aspheric surface shape is expressed as follows: Z (X, Y) = Z (Y) + R (Y) − ｛R (Y) ² −X
It is characterized by being expressed by an equation of ² ｝ ^1/2 .

A light beam scanning optical system according to the present invention comprises: a light source for generating a modulated light beam; an optical system for forming the light beam from the light source as a line image parallel to the main scanning plane; A deflector having a reflecting surface and deflecting the light beam at a constant angular velocity; and an aspherical reflecting mirror for reflecting the deflected light beam and scanning the surface to be scanned at a constant speed, wherein the aspherical reflecting mirror is provided. Is the above-mentioned first or second aspherical reflecting mirror.

Here, a semiconductor laser can be used as the light source. The optical system disposed between the light source and the deflector is an optical system having an imaging characteristic of forming a divergent light beam emitted from the light source at different positions in the main scanning direction and the sub scanning direction, and in the sub scanning direction. Has a function of forming an image near the reflection surface of the deflector. As the deflector, a polygon mirror or the like having a reflection surface near a linear image formed by an optical system disposed between the light source and the deflector and capable of high-speed scanning can be used.

In the above light beam scanning optical system, when the distance from the deflection point to the aspherical reflecting mirror is L _m and the distance from the deflection point to the surface to be scanned is L ₀ , 0.3 <L _m / It is desirable to satisfy the condition L ₀ <0.7.

When the distance from the scanning center to the scanning end on the surface to be scanned is Y ₀ , 1.25 <1 / (2 | A | Y ₀ ) −2.43 (L _m / L
₀ ) <1.53.

[0018]

The operation of the above configuration will be described below. The first aspherical reflecting mirror of the present invention has a shape in the main scanning plane including the optical axis, wherein the coordinate in the optical axis direction is Z, and the coordinate orthogonal to the optical axis and included in the main scanning plane is Y. , Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ¹⁰ (A, B, C, D: Coefficients) Since the shape is a non-circular arc, the vicinity of the optical axis and the end of the aspherical reflecting mirror are The shape in the main scanning plane can be set independently, and the uniformity of the converging position of the deflected light beam in the main scanning plane and the scanning speed can be favorably corrected.

Now, the relationship between the aspheric coefficient in the above equation, the curvature of field in the main scanning direction, and the scanning position accuracy will be examined in detail. Here, the scanning position accuracy indicates a difference between an ideal scanning position and an actual scanning position for an arbitrary deflection angle. The ideal scanning position is obtained from the proportional relationship between the arbitrary deflection angle and the maximum deflection angle with reference to the image height (the distance from the scanning center on the surface to be scanned to the light beam arrival position) on the maximum deflection angle.

FIG. 14 is an example of a graph showing the effect of correcting the aspheric coefficient. The horizontal axis indicates the curvature of field, and the vertical axis indicates the scanning position accuracy. The change in the optical characteristics when the second-order, fourth-order, and sixth-order aspherical coefficients are changed from 0 is shown. The origin of the graph indicates an ideal correction state.

From this graph, it can be seen that changing the second-order, fourth-order, and sixth-order aspherical coefficients changes both the field curvature in the main scanning direction and the scanning position accuracy. The effects of the second-order aspherical coefficient A and the fourth-order aspherical coefficient B appear in directions orthogonal to each other. By appropriately selecting A and B, the field curvature in the main scanning direction and the scanning position accuracy can be simultaneously achieved. It can be seen that the correction can be made.

Further, as a result of examining the effect of the sixth-order aspherical coefficient C, after appropriately selecting the second-order aspherical coefficient A and the fourth-order aspherical coefficient B, the insufficiently corrected optical characteristics are corrected. I found that there was work.

As described above, the shape in the main scanning plane including the optical axis is defined as Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ^10. A,
By appropriately selecting B and C, it is possible to satisfactorily correct the field curvature in the main scanning direction and the scanning position accuracy. Where 8
It goes without saying that higher order aspherical terms D and E and higher order aspherical terms may be added.

Further, as a result of examining the conditions of the aspherical coefficients A, B, and C necessary for favorably correcting the field curvature in the main scanning direction and the scanning position accuracy, the sixth order aspherical surface coefficient C was changed to the second order. It has been found that the aspherical coefficient A needs to satisfy the conditions of A <0 and C <0. A and C
Are different, the balance between the field curvature correction in the main scanning direction and the correction of the scanning position accuracy is lost, and it is difficult to achieve the object.

Since the shape in the sub-scanning surface is an arc shape in which the reflecting surface of the deflector and the surface to be scanned are in a geometrically conjugate relationship, it is generated on the scanning surface due to the inclination of the reflecting surface of the deflector. Scan line unevenness can be corrected.

Next, the second aspherical reflecting mirror according to the present invention, in addition to the first aspherical reflecting mirror which satisfactorily corrects the optical characteristics in the main scanning plane, also has a good focusing position in the sub-scanning direction. This defines an aspherical shape for correction.

The radius of curvature in the plane in the sub-scanning direction is expressed by the following formula: R (Y) = a ₀ + a ₂ Y ² + a ₄ Y ⁴ + a ₆ Y ⁶ (a ₀ , a ₂ , a ₄ , a ₆ : coefficient) By expressing, the radius of curvature R (Y) in the sub-scanning plane at an arbitrary main scanning position can be arbitrarily determined. This indicates that the deflecting point and the surface to be scanned can have a geometrical conjugate relationship for any deflection angle.

Then, by combining the reflecting surface with the shape Z (Y) in the main scanning plane of the first aspherical reflecting mirror, Z (X, Y) = Z (Y) + R (Y)-｛R ( Y) ² -X
^{By using} an aspherical shape represented by a mathematical formula of ² ｝ ^1/2, it is possible to determine the shape in the main scanning plane and the shape in the sub-scanning direction independently of each other. It is possible to satisfactorily correct the field curvature and the scanning position accuracy.

In the light beam scanning optical system of the present invention, an optical system having a linear image forming function is arranged between a light source and a deflector, and the light beam scanning optical system using the first or second aspherical reflecting mirror is used. It is an optical system, and it is possible to satisfactorily correct optical characteristics required for a light beam scanning optical system.

In this light beam scanning optical system, a space for arranging a light beam separating means for inputting the light beam to the deflector and guiding the reflected light beam from the aspherical reflecting mirror to the surface to be scanned is provided. 0.3 <L _m / L ₀ <0.7, where L _{m is} the distance from the deflection point to the aspherical reflecting mirror and L ₀ is the distance from the deflection point to the surface to be scanned. If the lower limit of 0.3 of the conditional expression is exceeded, the distance between the deflector and the aspherical reflecting mirror becomes too small, and it becomes difficult for the light beam to enter the deflector. If the upper limit of 0.7 of the above conditional expression is exceeded, the distance between the aspherical reflecting mirror and the surface to be scanned is too small, and it is difficult to guide the light beam reflected from the aspherical reflecting mirror to the surface to be scanned. .

Further, as a condition for satisfactorily correcting the scanning position accuracy, a quadratic coefficient of an equation representing a non-circular shape in the main scanning plane is represented by A, and a distance from the scanning center to the scanning end on the surface to be scanned. If Y ₀ , the distance from the deflection point to the aspherical reflecting mirror is L _m , and the distance from the deflection point to the surface to be scanned is L ₀ , 1.25 <1 / (2 | A | Y ₀ ) -2. 43 (L _m / L
₀ ) <1.53. When the value exceeds the upper limit of 1.53 of the conditional expression, a negative scanning position error becomes excessive, and
If the lower limit of 1.25 is exceeded, the positive scanning position error becomes excessively large, and in any case, the scanning position accuracy deteriorates.

[0032]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An aspherical reflecting mirror and a light beam scanning optical system according to the present invention will be described below based on specific embodiments with reference to the drawings. FIG. 1 is a diagram for explaining the surface shape of an embodiment of an aspherical reflecting mirror according to the present invention. As shown in FIG. 1, orthogonal coordinate axes X, Y, and Z are defined.
The Z plane corresponds to the main scanning plane.

Non-circular arc Z (Y) defined in the YZ plane
Is determined as a shape for correcting field curvature and scanning position accuracy in the main scanning direction. The shape of the aspherical reflecting mirror in the sub-scanning plane parallel to the optical axis, that is, in the plane parallel to the XZ plane, is such that the reflecting surface of the deflector and the surface to be scanned have a geometrical conjugate relationship regardless of the deflection angle. Is determined as a concave arc shape.

In order for the deflection point and the surface to be scanned to be in a geometrical conjugate relationship regardless of the deflection angle, a smooth curved surface which does not impair the light condensing characteristic and a circular arc at an arbitrary position along the Y axis are required. The radius of curvature may be determined as an optimal value.

The non-circular arc Z (Y) defined in the main scanning plane is defined by the radius of curvature in the sub-scanning plane parallel to the optical axis.
When the deflection point and the surface to be scanned on the optical axis are rotated around a rotational symmetry axis 11 parallel to the Y axis through the center of curvature O of an arc satisfying the geometrical conjugate relationship, Then r
₁ and r ₂ at the end. However, such a rotationally symmetric aspherical surface cannot determine the shape in the main scanning plane and the shape in the sub-scanning plane independently, and it is necessary to sacrifice one of the optical characteristics or to allocate corrections uniformly. There is.

Therefore, in order to be able to independently correct the optical characteristics in the main scanning plane and the sub-scanning plane, the shape in the main scanning plane is expressed as a mathematical expression not including X, and the shape in the sub-scanning plane is defined as Y. Only the function needs to be defined. Such a surface shape is obtained by substituting the non-arc shape Z (Y) in the main scanning plane by Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ¹⁰ (A, B, C, D: coefficients). the curvature radius R of the scanning plane (Y), R (Y) = a 0 + a 2 Y 2 + a 4 Y 4 + a 6 Y 6 (a 0, a 2, a 4, a 6: factor) to define, The aspherical shape of the reflecting surface is expressed as follows: Z (X, Y) = Z (Y) + R (Y) − ｛R (Y) ² −X
^It can be realized by an aspherical reflecting mirror expressed by the formula ^{2 21/2} .

For example, in the example shown in FIG. 1, the radius of curvature r ₂ ′ at the end is defined by the non-arc Z defined in the main scanning plane.
(Y) in which are shown a case where less than the radius of curvature r ₂ which is determined by rotating about an axis of rotation 11. The magnitude of the radius of curvature may be in a relationship of r ₂ ′> r ₂ , and the arrangement of the aspherical reflecting mirror, specifically, the distance from the deflection point to the aspherical reflecting mirror is L _m ,
Assuming that the distance from the deflection point to the surface to be scanned is L ₀ , r ₂ ′ = r _{2 in} a range satisfying the condition of 0.35 <L _m / L ₀ <0.4. There may be.

By determining the arc shape in the sub-scanning plane independently of the shape of the main scanning plane, it is possible to satisfactorily correct the field curvature in the sub-scanning direction regardless of the arrangement of the aspherical reflecting mirror. It is the intention of the invention. In FIG. 1, the trajectory connecting the centers of curvature of the arcs in the sub-scanning plane is indicated by dotted lines.

FIG. 2 shows the configuration of an embodiment of a light beam scanning optical system according to the present invention. A light beam emitted from a semiconductor laser 21 as a light source is converged or diverged by a condenser lens 22 and then converted into a cylindrical lens 23.
To form a line image parallel to the main scanning plane. The polygon mirror 24 is arranged so as to have a reflection surface near the line image, is rotated at a constant angular speed by a scanner motor (not shown), and reflects and deflects the light beam. The deflected light beam passes through a beam splitter 25 disposed between the deflector composed of the polygon mirror 24 and the aspherical reflecting mirror 1, and is then transmitted by the aspherical reflecting mirror 1 at a constant speed in the main scanning direction of the surface to be scanned. While being optically scanned, the light is reflected as a light beam focused as a light spot on the surface to be scanned. The light beam reflected in the direction opposite to the direction of incidence on the aspherical reflecting mirror 1 is split in the optical path by the beam splitter 25 and reaches the photosensitive drum 26 which is the surface to be scanned.

In the beam splitter 25 shown in FIG. 2, when the aspherical reflecting mirror 1 is disposed at an angle with respect to the optical axis, the beam reflected by the aspherical reflecting mirror 1 is prevented from bowing. However, if the amount of bowing can be tolerated, as shown in FIGS. 3A and 3B, the aspherical reflecting mirror 1 is disposed at an angle without using a beam splitter. Alternatively, the scanning light beam may be directed to the surface to be scanned by using a normal folding mirror 31.

Tables 1 to 4 show numerical data of Examples 1 to 10 of the light beam scanning optical system using the aspherical reflecting mirror of the present invention. The concave surface is shown as a negative curvature.

[0042] .

[0043] .

[0044] .

[0045] Note) R _m : Inscribed radius of polygon mirror (mm) S: Distance from the reflection point with deflection angle of 0 ° to the converging point in the main scanning direction of the incident beam (mm) L _m : From reflection point with deflection angle of 0 ° Distance to aspherical reflecting mirror (mm) L ₀ : Distance (m) from the reflection point at deflection angle of 0 ° to the surface to be scanned
m).

FIGS. 4 to 13 show the scanning position accuracy (constant scanning speed) (a) and the field curvature (b) of the first to tenth embodiments, respectively. It can be seen that in each of the embodiments, the field curvature and the scanning position accuracy are satisfactorily corrected. As for the scanning position accuracy, the traveling direction of the light beam on the surface to be scanned corresponds to the positive direction of the graph.

As described above, the aspherical reflecting mirror and the light beam scanning optical system of the present invention have been described based on the embodiments. However, the present invention is not limited to these embodiments, and various modifications are possible.

[0048]

As described above, according to the present invention, it is possible to provide an aspherical reflecting mirror and a light beam reflecting optical system capable of performing high-speed optical scanning at a constant speed.

In the first aspherical reflecting mirror of the present invention, since the shape in the main scanning plane is a non-circular arc having a higher order aspherical term, the field curvature in the main scanning direction and the scanning position accuracy are favorably corrected. It is possible.

Since the second aspherical reflecting mirror is defined by a polynomial in which the radius of curvature in the sub-scanning plane is a function of the distance from the optical axis, the optical characteristics in both the main scanning direction and the sub-scanning direction are well corrected. can do.

Since the light beam scanning optical system according to the present invention uses the aspherical reflecting mirror, the number of components is small.
Since a large deflection angle can be obtained, a small scanning optical system can be realized.

The light beam scanning device according to the present invention
Since good optical characteristics can be obtained regardless of the arrangement of the aspherical reflecting mirrors, the optical characteristics do not deteriorate due to the design of the light beam scanning device.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining a surface shape of an embodiment of an aspherical reflecting mirror according to the present invention.

FIG. 2 is a diagram showing a configuration of an embodiment of a light beam scanning optical system according to the present invention.

FIG. 3 is a diagram showing a schematic configuration of a modification in which an aspherical reflecting mirror is arranged to be inclined with respect to an optical axis.

FIGS. 4A and 4B are diagrams showing scanning position accuracy (constant scanning speed) (a) and field curvature (b) of the first embodiment.

FIG. 5 is a view similar to FIG. 4 of the second embodiment.

FIG. 6 is a view similar to FIG. 4 of a third embodiment.

FIG. 7 is a view similar to FIG. 4 of a fourth embodiment;

FIG. 8 is a view similar to FIG. 4 of a fifth embodiment.

FIG. 9 is a view similar to FIG. 4 of a sixth embodiment.

FIG. 10 is a view similar to FIG. 4 of a seventh embodiment.

FIG. 11 is a view similar to FIG. 4 of the eighth embodiment.

FIG. 12 is a view similar to FIG. 4 of a ninth embodiment;

FIG. 13 is a view similar to FIG. 4 of the tenth embodiment.

FIG. 14 is a diagram showing the effect of correcting an aspheric coefficient.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Aspherical reflecting mirror, 11 ... Rotational symmetry axis, 21 ... Semiconductor laser, 22 ... Condensing lens, 23 ... Cylindrical lens, 24 ... Polygon mirror, 25 ... Beam splitter,
26: photoreceptor drum, 31: folding mirror

Claims (6)

(57) [Claims] 1. A light beam condensed near a deflecting surface as a line image parallel to a main scanning plane and reflected by a deflector at a uniform angular velocity is reflected to form a spot image on a surface to be scanned. An aspherical reflecting mirror for performing speedy optical scanning, wherein a shape in a main scanning plane including an optical axis has a coordinate in the optical axis direction as Z, and a coordinate perpendicular to the optical axis and included in the main scanning plane. Is Y
Where Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ¹⁰ (A, B, C, D: coefficients) where coefficients A and C are A <0 and C <0 An arc that satisfies the conditions and has a shape in the sub-scanning plane that is parallel to the optical axis and orthogonal to the main scanning plane, and that satisfies the geometric-optical conjugate relationship between the deflection surface and the scanned surface at any position in the main scanning direction. An aspherical reflecting mirror, characterized in that: 2. The method according to claim 1, wherein a coordinate included in a sub-scanning plane orthogonal to the optical axis is X,
The curvature in the sub-scanning plane radius R (Y) _{is, R (Y) = a 0} + a 2 Y 2 + a 4 Y 4 + a 6 Y 6 (a 0, a 2, a 4, a 6: coefficient) becomes a formula When expressed, it is assumed that the aspherical shape of the reflecting surface is expressed by the following equation: Z (X, Y) = Z (Y) + R (Y) − {R (Y) ² −X ² } ^1/2 Characterized aspherical reflector. 3. A light source for producing a modulated light beam;
An optical system that forms a light beam from a light source as a line image parallel to the main scanning plane, a deflector that has a reflecting surface near the line image and deflects the light beam at an equal angular velocity, and reflects the deflected light beam An aspherical reflecting mirror for optically scanning the surface to be scanned at a constant speed, wherein the shape in the main scanning plane including the optical axis of the aspherical reflecting mirror is such that the coordinates in the optical axis direction are Z, Assuming that the coordinates orthogonal to each other and included in the main scanning plane are Y, Z (Y) = AY ² + BY ⁴ + CY ⁶ + DY ⁸ + EY ¹⁰ (A, B, C, D: coefficient) And C satisfy the conditions of A <0 and C <0 , and the shape in the sub-scanning plane that is parallel to the optical axis and orthogonal to the main scanning plane has the same shape as the deflecting surface and the scanning target at any position in the main scanning direction. Light beam scanning characterized by an arc satisfying the geometric optical conjugation relation of the surface Manabu system. 4. The coordinate system according to claim 3, wherein a coordinate included in a sub-scanning plane orthogonal to the optical axis is X,
The curvature in the sub-scanning plane radius R (Y) _{is, R (Y) = a 0} + a 2 Y 2 + a 4 Y 4 + a 6 Y 6 (a 0, a 2, a 4, a 6: coefficient) becomes a formula When expressed, the aspherical shape of the aspherical reflecting mirror is represented by the following equation: Z (X, Y) = Z (Y) + R (Y) − {R (Y) ² −X ² } ^1/2 A light beam scanning optical system, comprising: 5. The method according to claim 3, wherein a distance from the deflection point to the aspherical reflecting mirror is L _m , and a distance from the deflection point to the surface to be scanned is L ₀ , wherein 0.3 <L _m / A light beam scanning optical system that satisfies a condition of L ₀ <0.7. 6. The scanning device according to claim 3, wherein the distance from the scanning center to the scanning end on the surface to be scanned is Y.
₀ the time, 1.25 <1 / (2 | A | Y 0) -2.43 (L m / L 0) < Light-beam scanning optical system that satisfies the 1.53 the relationship.