Scanning Optical System

Abstract

Provided is a scanning optical system that includes first and second light sources, a polygon mirror, and first through fourth scanning lenses, the scanning optical system being configured so that the mathematical expressions below are satisfied, where A1 and A2 are the respective apexes of incidence-side surfaces of the first and second scanning lenses, an x-axis is defined as the direction of a rotational axis of the polygon mirror, a y-axis is defined as the scanning direction of a luminous flux, a z-axis is defined so as to be orthogonal to the x-axis and the y-axis, P1 and P2 are respective reference points of deflection of luminous fluxes from the first and second light sources, L1 is the distance between point P1 and point A1 in the z-axis direction, L2 is the distance between point P2 and point A2 in the z-axis direction, Lp12 is the distance between point P1 and point P2 in the z-axis direction, h1 is the thickness of the first scanning lens in the x-axis direction, h2 is the thickness of the second scanning lens in the x-axis direction, and θ1 and θ2 are each acute angles formed with the y-axis by straight lines obtained by projecting the principal ray of luminous fluxes arriving at the polygon mirror from the first and second light sources onto the plane that includes the x-axis and the y-axis.

Description

[Technical Field]

[0001] The present invention relates to a scanning optical system that causes a plurality of light beams to be incident on a single polygon mirror to perform scanning on a plurality of scanning surfaces. [Background technology]

[0002] A scanning optical system is used in which multiple light beams are incident on a single polygon mirror to scan multiple scanning surfaces. In such a scanning optical system, scanning lenses for focusing the light beams are arranged on both sides of the polygon mirror. As a result, in such a scanning optical system, a portion of one light beam is reflected by the scanning lens and incident as stray light from the scanning surface of that light beam onto another scanning surface located on the opposite side of the polygon mirror, which can cause streaks and other printing defects.

[0003] To solve the above problems, a scanning optical system has been developed that includes a light-blocking member between the polygon mirror and the scanning lens to prevent stray light (see Patent Document 1). However, the light-blocking member makes the above scanning optical system complicated and increases costs. In addition, the surface of the scanning lens that reflects the light beam must be convex toward the polygon mirror, which increases the lateral magnification in the sub-scanning direction and therefore increases the sensitivity to errors in the lens shape and installation position.

[0004] To date, no scanning optical system has been developed that is not complicated in configuration and has few restrictions on the scanning lens surface, and that allows multiple light beams to be incident on a single polygon mirror to perform scanning on multiple scanning surfaces.

[0005] Therefore, there is a need for a scanning optical system that is not complicated in configuration and has few restrictions on the surface of the scanning lens, and that allows multiple light beams to be incident on one polygon mirror to perform scanning on multiple scanning surfaces. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-206673 Summary of the Invention [Problem to be solved by the invention]

[0007] An object of the present invention is to provide a scanning optical system that is not complicated in configuration and has few restrictions on the surface of the scanning lens, and that allows multiple light beams to be incident on a single polygon mirror to perform scanning on multiple scanning surfaces. [Means for solving the problem]

[0008] The scanning optical system of the present invention includes first and second light sources, a polygon mirror, and first to fourth scanning lenses, and is configured so that a light beam from the first light source is reflected by the polygon mirror and then passes through the first scanning lens and third scanning lens, and a light beam from the second light source is reflected by the polygon mirror and then passes through the second scanning lens and fourth scanning lens. In the scanning optical system of the present invention, the vertices of the incident sides of the first and second scanning lenses are defined as A1 and A2, respectively, the midpoint of the line segment connecting points A1 and A2 is defined as point O, the x-axis is defined as the direction of the rotation axis of the polygon mirror, the y-axis is defined as the scanning direction of the light beam, and the z-axis is defined as being perpendicular to the x-axis and y-axis, the deflection reference points of the light beams from the first and second light sources are defined as P1 and P2, respectively, the distance in the z-axis direction between points P1 and A1 is defined as L1, the distance in the z-axis direction between points P2 and A2 is defined as L2, the distance in the z-axis direction between points P1 and P2 is defined as Lp12, the thickness in the x-axis direction of the first scanning lens is defined as h1, the thickness in the x-axis direction of the second scanning lens is defined as h2, and the acute angles formed by the straight lines, when the chief rays of the light beams reaching the polygon mirror from the first and second light sources are projected onto a plane including the x-axis and y-axis, are defined as θ1 and θ2, respectively,

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[0009] In the scanning optical system of the present invention, the first and second scanning lenses are arranged to satisfy predetermined conditions, so that the influence of stray light illuminance on other scanning surfaces arranged on the opposite side of the polygon mirror with respect to the light beams emitted from the first and second light sources is within an acceptable range, and streaks and other printing defects do not occur.

[0010] In the scanning optical system of the first embodiment of the present invention, the shape of the first scanning lens is the same as the shape of the second scanning lens, the shape of the third scanning lens is the same as the shape of the fourth scanning lens, and the pair of the first scanning lens and the second scanning lens and the pair of the third scanning lens and the fourth scanning lens are parallel to the x-axis and y-axis, respectively, and are arranged symmetrically with respect to a plane including point O.

[0011] In the scanning optical system of the second embodiment of the present invention, the third scanning lens and the fourth scanning lens are each a lens having two entrance surfaces and two exit surfaces stacked in the x-axis direction.

[0012] In the scanning optical system of the third embodiment of the present invention, the incident surfaces of the first scanning lens and the second scanning lens are not concave surfaces in which the average absolute value of the radius of curvature of the x-z cross section of the area where the light beam is reflected is 200 millimeters or less.

[0013] In the scanning optical system of this embodiment, the incident surfaces of the first scanning lens and the second scanning lens are not concave surfaces with an average absolute value of the radius of curvature of the x-z cross section of the area where the light beam is reflected being 200 millimeters or less, so that it is possible to prevent the illuminance of the light beam reflected by the incident surfaces of the first scanning lens and the second scanning lens from increasing and the influence of stray light from increasing on other scanning surfaces arranged on the opposite side of the polygon mirror.

[0014] A scanning optical system according to a fourth embodiment of the present invention further includes third and fourth light sources, and is configured such that a light beam from the third light source passes through the first scanning lens and the third scanning lens after being reflected by the polygon mirror, and a light beam from the fourth light source passes through the second scanning lens and the fourth scanning lens after being reflected by the polygon mirror, a deflection reference point of the light beam from the third light source coincides with point P1, and a deflection reference point of the light beam from the fourth light source coincides with point P2, and the acute angles formed by straight lines, obtained by projecting chief rays of the light beams from the third and fourth light sources onto a plane including the x-axis and y-axis, with the y-axis are respectively θ3 and θ4,

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[0015] In the scanning optical system of this embodiment, the first and second scanning lenses are arranged to satisfy predetermined conditions, so that the influence of stray light illuminance on other scanning surfaces arranged on the opposite side of the polygon mirror with respect to the light beams emitted from the third and fourth light sources is within an acceptable range, and streaks and other printing defects do not occur.

[0016] In the scanning optical system according to the fifth embodiment of the present invention, the effective scanning width on the scanning surface of each of the light beams from the first to fourth light sources is 230 millimeters or less.

[0017] The scanning optical system of the sixth embodiment of the present invention further includes an incident optical system element between each light source and the polygon mirror, and is configured so that the light beams that pass through each incident optical system element become convergent light beams in the y-axis direction when they reach the scanning surface. [Brief explanation of the drawings]

[0018] [Figure 1] 1 is a perspective view of a scanning optical system according to an embodiment of the present invention; [Figure 2] FIG. 1 is a plan view of a scanning optical system according to an embodiment of the present invention. [Figure 3] FIG. 10 is a plan view of the path of a light beam emitted from a third light source in a scanning optical system of a comparative example, which will be described later. [Figure 4] FIG. 10 is a side view of the path of a light beam emitted from a third light source in a scanning optical system of a comparative example, which will be described later. [Figure 5] 4 is an enlarged view of an area in FIG. 3 including a polygon mirror, a first scanning lens, and a second scanning lens. [Figure 6] 1 is a diagram showing the path of the chief ray of the light beam emitted from the first light source projected onto a plane including the x-axis and y-axis. [Figure 7] 10 is a diagram showing the positions through which the light beam emitted from the first light source and the light beam emitted from the third light source pass in a cross section perpendicular to the z-axis that includes point A1. FIG. [Figure 8] FIG. 10 is a plan view of the path of a light beam emitted from a third light source in a scanning optical system of an embodiment described later. [Figure 9] FIG. 10 is a side view of the path of a light beam emitted from a third light source 103 in a scanning optical system of an embodiment described later. [Figure 10] 3A and 3B are diagrams showing beam waist positions in the main scanning direction (y-axis direction) and the sub-scanning direction (x-axis direction) of the scanning optical system of the embodiment. [Figure 11] 10 is a diagram showing beam waist positions in the main scanning direction (y-axis direction) and the sub-scanning direction (x-axis direction) of a scanning optical system of a comparative example. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0019] FIG. 1 is a perspective view of a scanning optical system according to one embodiment of the present invention.

[0020] FIG. 2 is a plan view of a scanning optical system according to an embodiment of the present invention.

[0021] The scanning optical system of the present invention scans multiple scanning planes by irradiating multiple light beams onto a single polygon mirror. In the embodiment shown in FIGS. 1 and 2, four light beams are incident on a single polygon mirror from four light sources. The first scanning optical system includes a first light source 101, a first aperture, a first incident optical system element 1011, a polygon mirror 200, a first scanning lens 301, and a third scanning lens 303. The second scanning optical system includes a second light source 102, a second aperture, a second incident optical system element 1021, a polygon mirror 200, a second scanning lens 302, and a fourth scanning lens 304. The third scanning optical system includes a third light source 103, a third aperture, a third incident optical system element 1031, a polygon mirror 200, a first scanning lens 301, and a third scanning lens 303. The fourth scanning optical system includes a fourth light source 104, a fourth aperture, a fourth incident optical element 1041, a polygon mirror 200, a second scanning lens 302, and a fourth scanning lens 304. That is, the polygon mirror 200 is shared by the first to fourth scanning optical systems, the first scanning lens 301 and the third scanning lens 303 are shared by the first and third scanning optical systems, and the second scanning lens 302 and the fourth scanning lens 304 are shared by the second and fourth scanning optical systems.

[0022] The x-axis is defined as the direction of the rotation axis of the polygon mirror 200, the y-axis is defined as the scanning direction of the light beam, and the z-axis is defined as being perpendicular to the x-axis and y-axis. The directions of the x-axis, y-axis, and z-axis are shown in Figures 1 and 2. The direction of the y-axis is also called the main scanning direction, and the direction of the x-axis is also called the sub-scanning direction.

[0023] In the first scanning optical system, a light beam emitted from a first light source 101 passes through a first incident optical element 1011 and a first aperture, is reflected by a surface of a polygon mirror 200, passes through a first scanning lens 301 and a third scanning lens 303, and is then focused on a scanning surface 401. In the second scanning optical system, a light beam emitted from a second light source 102 passes through a second incident optical element 1021 and a second aperture, is reflected by a surface of a polygon mirror 200, passes through a second scanning lens 302 and a fourth scanning lens 304, and is then focused on a scanning surface 402. In the third scanning optical system, a light beam emitted from a third light source 103 passes through a third incident optical element 1031 and a third aperture, is reflected by a surface of a polygon mirror 200, passes through a first scanning lens 301 and a third scanning lens 303, and is then focused on a scanning surface 403. In the fourth scanning optical system, the light beam emitted from the fourth light source 104 passes through the fourth incident optical system element 1041 and the fourth aperture, is reflected by the surface of the polygon mirror 200, and is focused on the scanning surface 404 after passing through the second scanning lens 302 and the fourth scanning lens 304. Each scanning optical system is configured so that the light beam emitted from the light source is approximately focused at the reflection point on the surface of the polygon mirror 200 in the x-axis direction when it reaches the scanning surface, and becomes a focused light beam after passing through the incident optical system element in the y-axis direction when it reaches the scanning surface. The incident optical system element is an anamorphic element (anamorphic lens) whose focal length in the main scanning direction is different from that in the sub-scanning direction. In each optical system, the section from the light source to the polygon mirror is called the incident optical system, and the section from the polygon mirror to the scanning surface is called the imaging optical system.

[0024] In this embodiment, the cross section of the polygon mirror 200 perpendicular to the x-axis is square, but in other embodiments, the cross section of the polygon mirror perpendicular to the x-axis may be hexagonal, octagonal, or the like.

[0025] Generally, the present invention is applied to a compact scanning optical system in which the lateral magnification in the sub-scanning direction from the reflection point of the polygon mirror to the scanning surface is in the range of 2 to 3 and the effective scanning width on the scanning surface is 230 millimeters or less.

[0026] Next, stray light caused by reflection of a light beam on the incident surface of the scanning lens will be described.

[0027] Fig. 3 is a plan view of the path of a light beam emitted from a third light source 103 of a scanning optical system of a comparative example, which will be described later. Fig. 3 shows a plane parallel to the y-axis and z-axis. Note that the reference numerals for elements such as the light source of the comparative example are the same as those of the embodiment shown in Figs. 1 and 2.

[0028] 4 is a side view of the path of a light beam emitted from a third light source 103 of a scanning optical system of a comparative example, which will be described later. FIG. 4 shows a plane parallel to the x-axis and z-axis.

[0029] As described above, the light beam emitted from the third light source 103 passes through the third incident optical element 1031, is reflected by the surface of the polygon mirror 200, passes through the first scanning lens 301 and the third scanning lens 303, and is then focused on the scanning surface 401. However, part of the light beam is reflected by the incident surface of the first scanning lens 301, passes through the second scanning lens 302 and the fourth scanning lens 304, and then reaches the scanning surface 402 as stray light. According to FIG. 4, the entire light beam reflected by the incident surface of the first scanning lens 301 passes through the second scanning lens 302 and the fourth scanning lens 304 and then reaches the scanning surface 402 as stray light.

[0030] Figure 5 shows the 31 is an enlarged view of an area including the polygon mirror 200, the first scanning lens 301, and the second scanning lens 302. The vertex of the incident side of the first scanning lens 301 is designated A1, the vertex of the incident side of the second scanning lens 302 is designated A2, and the midpoint of the line segment connecting points A1 and A2 is designated point O. The first scanning lens 301 and the second scanning lens 302 are arranged so that the line connecting points A1 and A2 is in the z-axis direction. The deflection reference point of the light beam from the first light source 101 is designated P1, and the deflection reference point of the light beam from the second light source 102 is designated P2. Generally, the deflection reference point refers to the reflection point when the line obtained by projecting the principal ray of the light beam arriving at the deflector (polygon mirror) from the light source onto a plane including the y-axis and z-axis after the principal ray is reflected by the deflector is perpendicular to the y-axis. The deflection reference points P1 and P2 are configured to be located on the line connecting points A1 and A2.

[0031] FIG. 6 is a diagram showing the path of the chief ray of the light beam emitted from the first light source 101 projected onto a plane including the x-axis and y-axis. In FIG. 6, the chief ray is depicted so that its traveling direction does not change due to reflection on the incident surface of the first scanning lens 301. The distance in the z-axis direction between points P1 and A1 is defined as L1, the distance in the z-axis direction between points P2 and A2 is defined as L2, and the distance in the z-axis direction between points P1 and P2 is defined as Lp12. The acute angle formed by the line obtained by projecting the chief ray of the light beam from the first light source 101 reaching the polygon mirror 200 onto a plane including the x-axis and y-axis is defined as θ1, and the thickness of the second scanning lens 302 in the x-axis direction is defined as h2.

[0032] In reality, the coordinates of the positions of the incident surfaces of the first scanning lens 301 and the second scanning lens 302 differ in y-coordinate from the coordinates of the positions of the incident surfaces on a line that passes through point O and is parallel to the z-axis. This difference is ignored in Fig. 6.

[0033] The condition under which the chief ray of the light beam emitted from the first light source 101 is not incident on the incident surface of the second scanning lens 302 after being reflected on the incident surface of the first scanning lens 301 can be expressed by the following equation.

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[0034] Here, the thickness h1 of the first scanning lens 301 in the x-axis direction will be described.

[0035] 7 is a diagram showing the passing positions of the light beams emitted from the first light source 101 and the third light source 103 in a cross section perpendicular to the z-axis including point A1. The horizontal axis of FIG. 7 indicates the coordinate in the y-axis direction, and the vertical axis of FIG. 7 indicates the coordinate in the z-axis direction. x The x-axis coordinates are shown. The unit of length is millimeters. The three dashed lines indicate the passage positions of the light beam emitted from the first light source 101. The three alternate long and short dashed lines indicate the passage positions of the light beam emitted from the third light source 103. In each case, the three lines indicate the passage positions of the chief ray passing through the center of the aperture (aperture stop) and two rays passing through the two vertices on the diagonal of the aperture stop. The length in the x-axis direction of the smallest rectangle that includes all passage positions is the effective diameter, represented by AX1. The margin on one side of the effective diameter is represented by B. The thickness h1 in the x-axis direction of the first scanning lens 301 can be expressed by the following equation.

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[0036] Since the thickness h2 of the second scanning lens 302 in the x-axis direction is determined to the above value, it is necessary to increase the distance L1 in the z-axis direction between points P1 and A1 and the distance L2 in the z-axis direction between points P2 and A2 to appropriate values ​​so that equation (1) is satisfied.

[0037] 8 is a plan view of the path of the light beam emitted from the third light source 103 in the scanning optical system of an embodiment described later. FIG. 8 shows a plane parallel to the y-axis and z-axis.

[0038] 9 is a side view of the path of the light beam emitted from the third light source 103 in the scanning optical system of an embodiment described later. FIG. 9 shows a plane parallel to the x-axis and z-axis.

[0039] 9, a part of the light beam reflected at the incident surface of the first scanning lens 301 does not enter the incident surface of the second scanning lens 302, but the other part enters the incident surface of the second scanning lens 302 and finally enters the scanning surface. 402 According to a simulation, 56.4% of the light beam reflected by the incident surface of the first scanning lens 301 is incident on the incident surface of the second scanning lens 302.

[0040] The incident surface of the first scanning lens 301 is concave, and as the absolute value of the curvature increases (the absolute value of the radius of curvature decreases), the divergence of the light beam reflected at the incident surface of the first scanning lens 301 decreases. 402The illuminance of the light beam increases at the x-z cross section, and the influence of stray light becomes greater. Therefore, when the entrance surfaces of the first scanning lens 301 and the second scanning lens 302 are concave, it is preferable that the absolute value of the radius of curvature is equal to or greater than a certain value. Experiments have shown that it is preferable that the entrance surfaces of the first scanning lens 301 and the second scanning lens 302 are not concave surfaces in which the average absolute value of the radius of curvature of the x-z cross section of the region where the light beam is reflected is 200 millimeters or less.

[0041] Generally, if the following formula is satisfied, the influence of stray light illuminance on other scanning surfaces located on the opposite side of the polygon mirror will be within an acceptable range. If the following formula is not satisfied, the influence of stray light illuminance on the scanning surface will be so great that streaks and other printing defects may occur.

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[0042] Examples of the present invention and comparative examples are described below. The scanning lens is made of polycycloolefin resin with a refractive index of 1.503. The incident optical system element is also made of polycycloolefin resin with a refractive index of 1.528.

[0043] In the example and comparative example, the first scanning lens 301 and the second scanning lens 302 have the same shape, and the first scanning lens 301 and the second scanning lens 302 are arranged symmetrically with respect to a plane that is parallel to the x-axis and y-axis of the optical system and includes point O. The third scanning lens 303 and the fourth scanning lens 304 have the same shape, and the third scanning lens 303 and the fourth scanning lens 304 are arranged symmetrically with respect to a plane that is parallel to the x-axis and y-axis of the optical system and includes point O. The first light source 101 and the second light source are arranged symmetrically with respect to a plane that is parallel to the x-axis and y-axis of the optical system and includes point O, and the third light source 103 and the fourth light source 104 are arranged symmetrically with respect to a plane that is parallel to the x-axis and y-axis of the optical system and includes point O. The light sources are laser diodes.

[0044] The shape of each surface of each scanning lens is described below. The coordinate system representing each surface, when the first through fourth scanning lenses are positioned, is defined as follows: the z-axis is the line connecting points A1 and A2; the origin is the point of intersection of the z-axis and each surface; the x-axis is the line passing through the origin and parallel to the x-axis of the optical system; and the y-axis is the line passing through the origin and parallel to the y-axis of the optical system. The z-axis is the direction of light propagation. Therefore, the z-coordinate of the concave entrance surface and the convex exit surface is zero or negative, and the z-coordinate of the convex entrance surface and the concave exit surface is zero or positive.

[0045] The shapes of the entrance surface and exit surface of the pair of lenses closer to point O in the example and comparative example, that is, the first scanning lens and the second scanning lens, can be expressed by the following equations.

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[0046] The pair of lenses farther from point O in the example and comparative example, i.e., the third and fourth scanning lenses, are lenses having two entrance surfaces and two exit surfaces stacked in the x-axis direction.

[0047] The shapes of the entrance surface and exit surface of the third scanning lens and the fourth scanning lens can be expressed by the following formulas.

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[0048] Example Table 1 shows the numerical data of the scanning optical system of the embodiment. In Tables 1 and 4, the effective scanning width W means the length of the scanning range on the scanning surface in the y-axis direction, and the system focal length f means the focal length of the optical system formed by the incident optical system element and two types of scanning lenses. In Tables 1 and 4, for the laser diode light source, θ⊥ and θ / / mean the divergence angles in the directions perpendicular and parallel to the semiconductor layered surface, respectively. In the embodiment and comparative example, θ⊥ is arranged in the x-axis direction. In Tables 1 and 4, the first and second scanning lenses are Lens A and the third and fourth scanning lenses are referred to as Lens B.

[0049] In Tables 1 and 4, the deflector refers to a polygon mirror. In Tables 1 and 4, the "center coordinates of the deflector" refer to the deflection reference point (point in Figure 5). P1 ) is used as a reference. In Tables 1 and 4, "principal angle of incidence to deflector" refers to the acute angle formed by the line between the z-axis and the principal ray of the light beam reaching the deflector from the light source, projected onto a plane including the y-axis and z-axis. In Tables 1 and 4, "minor angle of incidence to deflector" refers to the acute angle formed by the line between the y-axis and the principal ray of the light beam reaching the deflector from the light source, projected onto a plane including the x-axis and y-axis. In other words, "minor angle of incidence to deflector θin" corresponds to θ1-θ4 described above. [Table 1]

[0050] Table 2 shows the coefficients of equation (3) that represent the shapes of the surfaces of first scanning lens 301 and second scanning lens 302. The unit of length in Table 2 is millimeters. [Table 2]

[0051] Table 3 shows the coefficients of equation (4) that represent the shapes of the surfaces of the third scanning lens 303 and the fourth scanning lens 304. The unit of length in Table 3 is millimeters. [Table 3]

[0052] According to Table 1, L1 = L2 = 21.5 mm, Lp12 = 12.12 mm, θ1 = θ2 = θ3 = θ4 = 3.15 deg, and the right-hand side of equation (2)-(2)''' is 4.22 mm. On the other hand, h1 = h2 = 8.9 mm, and therefore equation (2)-(2)''' is satisfied. In addition, the entrance surfaces of the first scanning lens 301 and the second scanning lens 302 are flat.

[0053] As described above, 56.4% of the light beam reflected by the incident surface of first scanning lens 301 is incident on the incident surface of second scanning lens 302. However, this light beam acts as stray light and does not have a significant effect on the scanning surface.

[0054] The lateral magnification in the sub-scanning direction from the deflection reference point of the scanning optical system to the scanning surface is 2.90.

[0055] According to Table 1, the focal length of the incident optical element in the main scanning direction is 20.0 millimeters. On the other hand, the distance between the light source and the incident optical element is 100.14 - 78.63 = 21.51 millimeters, so the light beam after passing through the incident optical element becomes a convergent light beam in the main scanning direction. Note that the main scanning direction of the light beam refers to the main scanning direction (y-axis direction) of the light beam when it reaches the scanning surface.

[0056] FIG. 10 shows the beam waist positions in the main scanning direction (y-axis direction) and sub-scanning direction (x-axis direction) of the scanning optical system of the embodiment. The beam waist position refers to the position where the diameter of the light beam is smallest. The horizontal axis of FIG. 10 represents the y-axis coordinate, measured in millimeters. The right side is the light source side. The vertical axis of FIG. 10 represents the beam waist position, measured in millimeters. A value of 0 on the vertical axis indicates that the beam waist position is on the scanning surface. For example, -1 millimeter on the vertical axis indicates that the beam waist position is shifted 1 millimeter from the scanning surface toward the polygon mirror, and 1 millimeter on the vertical axis indicates that the beam waist position is shifted 1 millimeter from the scanning surface toward the opposite side of the polygon mirror. The solid line in FIG. 10 indicates the beam waist position in the main scanning direction (y-axis direction), and the dashed line in FIG. 10 indicates the beam waist position in the sub-scanning direction (x-axis direction). According to FIG. 10, the beam waist position is within a range of ±1 millimeter, and the light beam is focused near the scanning surface.

[0057] Comparative Example Table 4 shows the numerical data of the scanning optical system of the comparative example. [Table 4]

[0058] Table 5 shows the coefficients of equation (3) that represent the shapes of the surfaces of first scanning lens 301 and second scanning lens 302. The unit of length in Table 5 is millimeters. [Table 5]

[0059] Table 6 shows the coefficients of equation (4) that represent the shapes of the surfaces of the third scanning lens 303 and the fourth scanning lens 304. The unit of length in Table 6 is millimeters. [Table 6]

[0060] According to Table 4, L1 = L2 = 17.5 mm, Lp12 = 12.12 mm, θ1 = θ2 = θ3 = θ4 = 3 deg., and the right-hand side of equation (2)-(2)''' is 3.39 mm. On the other hand, h1 = h2 = 8 mm, and therefore equation (2)-(2)''' is not satisfied. In addition, the average absolute value of the radii of curvature of the x-z cross section of the area where the light beam is reflected on the incident surfaces of the first scanning lens 301 and the second scanning lens 302 is approximately 48,000 millimeters.

[0061] As described above, all of the light beams reflected at the incident surface of the first scanning lens 301 reach the scanning surface 402 as stray light after passing through the second scanning lens 302 and the fourth scanning lens 304. In addition, because the incident surface of the first scanning lens 301 is concave, the collected light beams reach the scanning surface as stray light and have a significant effect on the scanning surface.

[0062] The lateral magnification in the sub-scanning direction from the deflection reference point of the scanning optical system to the scanning surface is 2.73.

[0063] According to Table 4, the focal length of the incident optical element in the main scanning direction is 20.0 millimeters. On the other hand, the distance between the light source and the incident optical element is 101.00 - 80.88 = 20.12 millimeters, so the light beam after passing through the incident optical element becomes a convergent light beam in the main scanning direction.

[0064] FIG. 11 shows the beam waist positions in the main scanning direction (y-axis direction) and sub-scanning direction (x-axis direction) of the scanning optical system of the comparative example. The horizontal axis of FIG. 11 represents the y-axis coordinate, measured in millimeters. The right side is the light source side. The vertical axis of FIG. 11 represents the beam waist position, measured in millimeters. A value of 0 on the vertical axis indicates that the beam waist position is on the scanning surface. For example, -1 millimeter on the vertical axis indicates that the beam waist position is shifted 1 millimeter from the scanning surface toward the polygon mirror, and 1 millimeter on the vertical axis indicates that the beam waist position is shifted 1 millimeter from the scanning surface toward the opposite side of the polygon mirror. The solid line in FIG. 11 indicates the beam waist position in the main scanning direction (y-axis direction), and the dashed line in FIG. 11 indicates the beam waist position in the sub-scanning direction (x-axis direction). According to FIG. 11, the beam waist position is within a range of ±1 millimeter, and the light beam is focused near the scanning surface.

[0065] Summary of Examples and Comparative Examples In the embodiment, the formula (2)-(2)''' is satisfied, and the illuminance on the scanning surface of the light beams reflected at the entrance surfaces of the first and second scanning lenses is small and does not affect printing. Comparative Example In this case, equation (2)-(2)'' is not satisfied, and the illuminance on the scanning surface of the light beams reflected at the incident surfaces of the first and second scanning lenses becomes large, which may result in streaks and other printing defects in the print.

Claims

1. A scanning optical system including first and second light sources, a polygon mirror, and first to fourth scanning lenses, wherein a light beam from the first light source is reflected by the polygon mirror and then passes through the first scanning lens and the third scanning lens, and a light beam from the second light source is reflected by the polygon mirror and then passes through the second scanning lens and the fourth scanning lens, wherein vertices of the incident sides of the first and second scanning lenses are designated as A1 and A2, respectively, an x-axis is defined in the direction of the rotation axis of the polygon mirror, a y-axis is defined in the scanning direction of the light beam, and a y-axis is defined in the direction perpendicular to the x-axis and y-axis. The z-axis is defined so as to intersect, deflection reference points of the light beams from the first and second light sources are defined as P1 and P2, respectively, the distance in the z-axis direction between point P1 and point A1 is defined as L1, the distance in the z-axis direction between point P2 and point A2 is defined as L2, the distance in the z-axis direction between point P1 and point P2 is defined as Lp12, the thickness in the x-axis direction of the first scanning lens is defined as h1, the thickness in the x-axis direction of the second scanning lens is defined as h2, and the acute angles formed by the straight lines, obtained by projecting the chief rays of the light beams reaching the polygon mirror from the first and second light sources onto a plane including the x-axis and y-axis, with the y-axis are defined as θ1 and θ2, respectively; [Equation 1] [Equation 2] is satisfied, and the light beams emitted from the respective light sources are configured to be substantially focused at the respective deflection reference points in the x-axis direction when they reach the scanning surface, and the lateral magnification in the x-axis direction from the respective deflection reference points to the scanning surface is configured to be in the range of 2 to 3.

2. 2. The scanning optical system according to claim 1, wherein the first scanning lens and the second scanning lens have the same shape, the third scanning lens and the fourth scanning lens have the same shape, and the pair of the first scanning lens and the second scanning lens and the pair of the third scanning lens and the fourth scanning lens are parallel to the x-axis and the y-axis, respectively, and are arranged symmetrically with respect to a plane including a midpoint O of a line segment connecting points A1 and A2.

3. 2. The scanning optical system according to claim 1, wherein each of the third scanning lens and the fourth scanning lens is a lens having two entrance surfaces and two exit surfaces stacked in the x-axis direction.

4. 2. The scanning optical system according to claim 1, wherein the incident surfaces of the first scanning lens and the second scanning lens are not concave surfaces, and the average absolute value of the radius of curvature of the xz cross section of the area where the light beam is reflected is 200 millimeters or less.

5. the optical system further includes third and fourth light sources, wherein a light beam from the third light source is reflected by the polygon mirror and then passes through the first scanning lens and the third scanning lens, and a light beam from the fourth light source is reflected by the polygon mirror and then passes through the second scanning lens and the fourth scanning lens, wherein a deflection reference point of the light beam from the third light source coincides with point P1 and a deflection reference point of the light beam from the fourth light source coincides with point P2, and wherein the acute angles formed by straight lines, obtained by projecting chief rays of the light beams reaching the polygon mirror from the third and fourth light sources onto a plane including the x-axis and y-axis, with the y-axis are respectively θ3 and θ4; [Equation 3] [Equation 4] 2. The scanning optical system according to claim 1, wherein the following condition is satisfied: the light beams emitted from the respective light sources are configured to be substantially focused at the respective deflection reference points in the x-axis direction when they reach the scanning surface; and the lateral magnification in the x-axis direction from the respective deflection reference points to the scanning surface is configured to be in the range of 2 to 3.

6. 6. The scanning optical system according to claim 5, wherein the effective scanning width of each of the light beams from the first to fourth light sources on the scanning plane is 230 millimeters or less.

7. 6. The scanning optical system according to claim 1, further comprising an incident optical system element between each light source and the polygon mirror, and configured so that the light beams passing through each incident optical system element become converged light beams in the y-axis direction when they reach the scanning surface.

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