Scanning Optical System

Abstract

This scanning optical system is equipped with a deflector and an imaging optical system equipped with a first scanning lens which is nearer said deflector and a second scanning lens which is farther from said deflector. The scanning optical system is configured in a manner such that: the scanning direction is perpendicular to the axis of rotation of the deflector and to the optical axis of the imaging optical system; 0.88≤f / L and d / L≤0.3 are satisfied, if a value obtained by dividing half the scan width by the maximum value of a deflection angle θ is a system focal distance f, the distance from the deflection surface of said deflector to the scanning surface along the optical axis is L, and the distance from the deflection surface to the surface of the second scanning lens which is farther from the deflector is d; when the scanning direction is the y-axis direction, the y-coordinate of the optical axis is 0, and the y-coordinates at the location on the scanning surface of the principal ray of the luminous flux is expressed as a deflection angle θ function, the absolute value of a differential function dy / dθ of said function increases according to the absolute value of the deflection angle θ; and the differential function dy / dθ has a plurality of inflection points which are each in the ranges of -1≤r≤-0.4 or 0.4≤r≤1 if the ratio of the deflection angle to the maximum value of the absolute value of the deflection angle θ is r.

Description

[Technical field]

[0001] The present invention relates to a scanning optical system. [Background technology]

[0002] The imaging optical system used in printers and multifunction machines is required to have a function of scanning a scanning spot on the scanning surface at a constant speed (constant speed scanning function) in addition to a function of converging a light beam on the scanning surface (convergence function). However, it is difficult to miniaturize a scanning optical system that realizes the convergence function and the constant speed scanning function. Therefore, a scanning optical system that achieves miniaturization by sacrificing the convergence function and the constant speed scanning function to some extent has been proposed (for example, Patent Document 1).

[0003] In such a scanning optical system, the function of scanning the scanning spot at a constant speed can be realized by electrically controlling the light emission timing of the light source, even if it cannot be realized by the scanning optical system itself. On the other hand, the focusing function of such an optical system has a problem in that the diameter of the scanning spot of the light beam increases, especially at the periphery of the scanning area.

[0004] Therefore, there is a need for a scanning optical system that achieves miniaturization by sacrificing the convergence function and the constant speed scanning function to some extent, and that suppresses an increase in the scanning spot diameter of the light beam at the periphery of the scanning area. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2015-31824 A Summary of the Invention [Problem to be solved by the invention]

[0006] An object of the present invention is to provide a scanning optical system which is compact in size at the expense of convergence and constant speed scanning functions to some extent, and which suppresses an increase in the scanning spot diameter of the light beam at the periphery of the scanning area. [Means for solving the problem]

[0007] The scanning optical system of the present invention includes a deflector that deflects a light beam from a light source, and an imaging optical system that includes a first scanning lens closer to the deflector and a second scanning lens farther from the deflector, and that guides the polarized light beam to a scanning surface. The scanning direction is perpendicular to the rotation axis of the deflector and the optical axis of the imaging optical system, and the angle formed by the line that is the projection of the principal ray of the deflected light beam onto a plane perpendicular to the rotation axis of the deflector and the line that is the projection of the optical axis onto the plane is defined as a deflection angle θ, and the value obtained by dividing half the scanning width W / 2 by the maximum value of the deflection angle θ is defined as a system focal length f, the distance on the optical axis from the deflection surface of the deflector to the scanning surface is defined as L, and the distance from the deflection surface to the surface of the second scanning lens farther from the deflector is defined as d, 0.88≦f / L d / L≦0.3 satisfies the above condition, the scanning direction is the y-axis direction, the y-coordinate of the optical axis is 0, and the y-coordinate of the position of the principal ray of the light beam on the scanning surface is expressed as a function of the deflection angle θ. When this function's differential function dy / dθ increases in absolute value according to the absolute value of the deflection angle θ, and the ratio of the deflection angle to the maximum absolute value of the deflection angle θ is r, the differential function dy / dθ is -1 ≦ r ≦ -0.4 and 0.4 ≦ r ≦ 1 Each of these has multiple inflection points in the range.

[0008] The scanning optical system of the present invention comprises: 0.88≦f / L Since the above relation is satisfied, f is relatively large and the length of the second scanning lens in the y-axis direction is relatively small. d / L≦0.3 Since the second scanning lens is disposed relatively close to the deflector, the scanning optical system becomes compact.

[0009] In the scanning optical system of the present invention, when the y-coordinate of the position of the principal ray of the light beam on the scanning surface is expressed as a function of the deflection angle θ, the shape of the curve of the differential function dy / dθ of the function can be appropriately determined, thereby making it possible to suppress an increase in the scanning spot diameter of the light beam at the periphery of the scanning area.

[0010] In the scanning optical system of the first embodiment of the present invention, the direction of the optical axis is the z-axis direction, and the refractive power of the first scanning lens in the yz cross section is positive for light rays passing near the optical axis, decreases in accordance with the absolute value of the y coordinate of the position through which the light rays pass, and is negative for light rays passing through the peripheral portion in the y-axis direction, while the refractive power of the second scanning lens in the yz cross section is negative for light rays passing near the optical axis, increases in accordance with the absolute value of the y coordinate of the position through which the light rays pass, and is positive for light rays passing through the peripheral portion in the y-axis direction.

[0011] In the scanning optical system of this embodiment, the relationship between the absolute value of the y coordinate of the position through which the light ray passes and the refractive powers of the first and second scanning lenses with respect to that light ray is adjusted, and the shape of the curve of the differential function dy / dθ is appropriately specified, thereby making it possible to suppress an increase in the scanning spot diameter of the light beam at the periphery of the scanning area.

[0012] In the scanning optical system of the second embodiment of the present invention, the value of (|dy / dθ| - f) / f is -3% or less when the deflection angle θ is 0, and is 5% or more when the absolute value of the deflection angle θ is at its maximum value.

[0013] The present invention is particularly effective when the value of (|dy / dθ|−f) / f satisfies the above condition. [Brief description of the drawings]

[0014] [Figure 1] 1 is a perspective view showing an example of an optical system including a scanning optical system of the present invention. [Diagram 2] FIG. 1 is a plan view showing an example of an optical system including a scanning optical system of the present invention. [Diagram 3] 1 is a diagram showing an embodiment of a scanning optical system of the present invention, which will be described later. [Figure 4]4 is a diagram for explaining a deflection angle of a scanning optical system. FIG. [Figure 5A] 1 is a diagram showing the relationship between the deflection angle and the image height of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B. FIG. [Figure 5B] 10 is a diagram showing the difference between the image height of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B and the image height of a scanning optical system in which B is 0. FIG. [Figure 6] 1 is a diagram showing the relationship between the deflection angle of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B and the partial magnification of a light beam at that deflection angle. [Figure 7] 1 is a diagram showing the deflection angle of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B, and the diameter in the main scanning direction of a light beam spot on a scanning surface of a light beam at that deflection angle. [Figure 8] FIG. 2 is a diagram showing a scanning optical system according to a comparative example of the present invention. [Figure 9] FIG. 4 is a diagram showing the partial magnification of a scanning optical system of a comparative example. [Figure 10] 11 is a diagram showing a diameter in the main scanning direction of a light beam spot on a scanning surface of a scanning optical system of a comparative example. [Figure 11] 4 is a diagram for explaining the refractive power of a scanning lens in a yz cross section. FIG. [Figure 12] 10 is a diagram showing the refractive power of the first scanning lens of the comparative example in the yz cross section. FIG. [Figure 13] 13 is a diagram showing the refractive power of the second scanning lens of the comparative example in the yz cross section. FIG. [Figure 14] FIG. 4 is a diagram showing the refractive power of the first scanning lens in the yz cross section of the embodiment. [Figure 15] FIG. 11 is a diagram showing the refractive power of the second scanning lens in the yz cross section of the embodiment. [Figure 16] 3A and 3B are diagrams for explaining the functions of a first scanning lens 301 and a second scanning lens 302 in the embodiment. [Figure 17] FIG. 4 is a diagram showing the partial magnification of the scanning optical system of the embodiment. [Figure 18] FIG. 13 is a diagram showing differential values ​​of partial magnification with respect to the deflection angle of the scanning optical system of the embodiment. [Figure 19]4 is a diagram showing a diameter in the main scanning direction of a light beam spot on a scanning surface of a scanning optical system of an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] FIG. 1 is a perspective view showing an example of an optical system including a scanning optical system of the present invention.

[0016] FIG. 2 is a plan view showing an example of an optical system including a scanning optical system of the present invention.

[0017] In the example shown in Fig. 1 and Fig. 2, multiple light beams are incident on a deflector that is a polygon mirror to perform scanning on multiple scanning surfaces. In the example shown in Fig. 1 and Fig. 2, four light beams are incident on one polygon mirror by four light sources. The first scanning optical system includes a first light source 1, a first lens 1 of the incident optical system, a polygon mirror, a first scanning lens 1, and a third scanning lens 3. The second scanning optical system includes a second light source 2, a second lens 2 of the incident optical system, a polygon mirror, a second scanning lens 2, and a fourth scanning lens 4. The third scanning optical system includes a third light source 3, a third lens 3 of the incident optical system, a polygon mirror, a first scanning lens 1, and a third scanning lens 3. The fourth scanning optical system includes a fourth light source 4, a fourth lens 4 of the incident optical system, a polygon mirror, a second scanning lens 2, and a fourth scanning lens 4. That is, the polygon mirror is shared by the first to fourth scanning optical systems, the first scanning lens 1 and the third scanning lens 3 are shared by the first and third scanning optical systems, and the second scanning lens 2 and the fourth scanning lens 4 are shared by the second and fourth scanning optical systems.

[0018] 3 is a diagram showing an embodiment of the scanning optical system of the present invention, which will be described later. A light beam emitted from a light source 101 passes through an aperture and a lens 103, is deflected by a deflector 200, which is a polygon mirror, and is then focused on a scanning surface 400 by an imaging optical system including a first scanning lens 301 and a second scanning lens 303. The x-axis is the direction of the rotation axis of the deflector, the z-axis is the direction of the optical axis of the imaging optical system, and the y-axis is perpendicular to the x-axis and z-axis. The scanning direction is the direction of the y-axis. The y-axis direction is also called the main scanning direction, and the x-axis direction is also called the sub-scanning direction.

[0019] FIG. 4 is a diagram for explaining the deflection angle of the scanning optical system. The deflection angle θ is an angle between a straight line which is a projection of the principal ray of the light beam deflected by the deflector 200 onto the yz plane and a straight line which is a projection of the optical axis of the imaging optical system onto the yz plane. In FIG. 4, P represents a reflection point of the principal ray on the deflection surface of the deflector 200. In FIG. 4, the path of the principal ray of the first scanning optical system having a relatively small maximum value of the deflection angle θ is shown by a solid line, and the path of the principal ray of the second scanning optical system having a relatively large maximum value of the deflection angle θ is shown by a solid line. If the effective scanning width of both scanning optical systems is W, the passing range of the light beam of the first scanning lens 301 and the second scanning lens 303 of the first scanning optical system is smaller than the passing range of the light beam of the first scanning lens 301 and the second scanning lens 303 of the second scanning optical system.

[0020] On the other hand, in the scanning optical system, a constant speed scanning function of the scanning spot on the scanning surface 400 is realized.

number

[0021] In order to realize the converging function and the uniform speed scanning function of the scanning optical system, the scanning lens needs to be disposed sufficiently far away from the deflector, and as a result, the scanning lens and the scanning optical system cannot be made sufficiently compact.

[0022] In order to realize a compact scanning optical system, Patent Document 1 proposes a scanning optical system in which the y coordinate of the scanning spot and the deflection angle θ have the following relationship:

number

number

number

[0023] Next, we consider the properties of the scanning optical system that satisfy the relationship of formula (1) for various values ​​of B. As an example, if the scanning width W is 220 millimeters and the maximum absolute value of the deflection angle is 45 degrees, the various values ​​of B and the corresponding values ​​of K are as shown in Table 1 below. The unit of K is millimeters. [Table 1]

[0024] Figure 5A is a diagram showing the relationship between deflection angle and image height of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B. The horizontal axis of Figure 5A indicates the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of Figure 5A indicates the y coordinate on the scanning plane of the light ray of the deflection angle on the horizontal axis, that is, the image height. The unit of the vertical axis is millimeters.

[0025] FIG. 5B is a diagram showing the difference between the image height of a scanning optical system that satisfies the relationship of formula (1) for various values ​​of B and the image height of a scanning optical system in which B is 0. The horizontal axis of FIG. 5B indicates the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of FIG. 5B indicates the difference between the y coordinate on the scanning plane of the light beam at the deflection angle on the horizontal axis of the scanning optical system and the y coordinate on the scanning plane of the light beam at the same deflection angle of a scanning optical system in which B is 0. The unit of the vertical axis is millimeters.

[0026] FIG. 6 is a diagram showing the relationship between the deflection angle of the scanning optical system that satisfies the relationship of formula (1) for various values ​​of B and the partial magnification of the light beam at that deflection angle. The horizontal axis of FIG. 6 indicates the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of FIG. 6 indicates the partial magnification. The vertical axis is expressed in percent. The partial magnification is defined by the following formula.

number

[0027] The partial magnification shown in Figure 6 indicates the deviation of the scanning spot of the scanning optical system from the uniform velocity characteristic. The scanning spot has a uniform velocity when the partial magnification is 0. As the absolute value of the partial magnification increases, the deviation of the scanning spot from the uniform velocity characteristic increases.

[0028] FIG. 7 is a diagram showing the deflection angle of the scanning optical system that satisfies the relationship of formula (1) for various values ​​of B, and the diameter in the main scanning direction of the light beam spot on the scanning surface of the light beam at that deflection angle. The horizontal axis of FIG. 7 shows the ratio of the deflection angle to the maximum absolute value of the deflection angle. The unit of the horizontal axis is millimeters. The vertical axis of FIG. 7 shows the diameter in the main scanning direction of the light beam spot. In FIG. 7, the diameter in the main scanning direction of the light beam spot is represented as the main spot diameter. The unit of the vertical axis is micrometers. The main spot diameter when the deflection angle is 0 is 60 micrometers.

[0029] The diameter of the light beam spot shown in FIG. 7 indicates the convergence function of the scanning optical system.

[0030] Ultimately, if B approaches 1, the imaging optical system can be made compact, but the partial magnification and the diameter of the light beam spot on the scanning surface in the main scanning direction increase according to the absolute value of the deflection angle θ, and reach a maximum at the maximum absolute value of the deflection angle θ. Here, even if the uniform speed scanning function of the scanning spot cannot be realized by the scanning optical system, it can be realized by electrically controlling the light emission timing of the light source. Therefore, a scanning optical system in which B is not 0, and in particular a scanning optical system in which the diameter of the light beam spot in the main scanning direction is relatively small near the maximum absolute value of the deflection angle θ, is required.

[0031] Next, comparative examples and examples of the present invention will be described.

[0032] The shapes of the entrance surface and exit surface of the first scanning lens in the comparative example and the example can be expressed by the following formula A. In the following description, the main scanning direction cross section means the yz cross section perpendicular to the x axis, and the sub-scanning direction cross section means the xz cross section perpendicular to the y axis.

number

number

[0033] The shapes of the entrance surface and the exit surface of the second scanning lens in the comparative example and the embodiment can be expressed by the following formula B.

number

number

number

number

number

number

[0034] Comparative Example 8 is a diagram showing a scanning optical system of a comparative example of the present invention. A light beam emitted from a light source 101 passes through an aperture and a lens 103', is deflected by a deflector 200 which is a polygon mirror, and is then focused on a scanning surface 400 by an imaging optical system including a first scanning lens 301' and a second scanning lens 303'.

[0035] The scanning optical system of the comparative example was designed so that the relationship of formula (1) was satisfied for the light beam at each deflection angle, the aberration was appropriately corrected, and the spot diameter of the light beam was usable.

[0036] In the scanning optical system of the comparative example, the formula (1)

number

[0037] Table 2 shows numerical data of the scanning optical system of the comparative example. In Table 2 and the following tables, the first scanning lens is referred to as Lens A, and the second scanning lens is referred to as Lens B. The "deflection reference point" is the reflection point of the principal ray of the deflected light beam on the surface of the deflector when the straight line obtained by projecting the principal ray of the deflected light beam onto the yz plane is in the z-axis direction. The "principal angle of incidence" and the "secondary angle of incidence" are the angles of incidence on the yz plane and the xz plane, respectively.

[0038] On the optical axis of the imaging optical system, the distance from the deflection surface of the deflector to the scanning surface is L, and the distance from the deflection surface to the surface of the second scanning lens that is farther away from the deflector is d. The following relationship holds: f / L = 139.4 / 158.32 = 0.88 d / L= (38.4+4.5) / 158.32=0.270 [Table 2]

[0039] Tables 3A and 3B are tables showing coefficients of the equations expressing the surface shapes of the first and second scanning lenses of the comparative example. [Table 3A]

[0040] [Table 3B]

[0041] Fig. 9 is a diagram showing the partial magnification of a scanning optical system of a comparative example. The horizontal axis of Fig. 9 shows the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of Fig. 9 shows the partial magnification of the scanning optical system for a light beam having a deflection angle shown on the horizontal axis. The curve showing the partial magnification in Fig. 9 is approximate to the curve showing the partial magnification when B in Fig. 6 is 0.6.

[0042] Fig. 10 is a diagram showing the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the comparative example. The horizontal axis of Fig. 10 indicates the coordinates of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of Fig. 10 indicates the diameter in the main scanning direction of the light beam spot on the scanning surface of the light beam at the coordinates of the actual imaging position shown on the horizontal axis. The curve showing the diameter in the main scanning direction of the light beam spot in Fig. 10 is approximate to the curve showing the diameter in the main scanning direction of the light beam spot when B in Fig. 7 is 0.6.

[0043] FIG. 11 is a diagram for explaining the refractive power of the scanning lens in the yz section. FIG. 11 shows the yz section including the points where the principal ray of each deflection angle intersects with the optical surface. The radius of curvature at the incident position Ym1 of the light incident surface is Rm1, and the radius of curvature at the light incident surface position Ym2 of the exit surface is Rm2. The angle between the principal ray of the light beam incident on the incident surface and the normal to the incident surface is θo1, and the angle between the principal ray of the light beam passing through the incident surface and the normal to the incident surface is θi1. The angle between the principal ray of the light beam arriving at the exit position of the exit surface and the normal to the exit surface is θo2, the angle between the principal ray of the light beam passing through the exit surface and the normal to the exit surface is θi2, and the optical path length from the entrance surface to the exit surface is dm. The refractive index of the scanning lens material is N. The refractive power φm of the scanning lens in the yz section at this time is defined by the following formula.

number

[0044] Fig. 12 is a diagram showing the refractive power of the first scanning lens 301' of the comparative example in the yz cross section. The horizontal axis of Fig. 12 indicates the coordinates of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of Fig. 12 indicates the refractive power of the first scanning lens 301' of the comparative example in the yz cross section for a light ray that reaches the coordinates of the actual imaging position shown on the horizontal axis.

[0045] Fig. 13 is a diagram showing the refractive power of the second scanning lens 302' of the comparative example in the yz cross section. The horizontal axis of Fig. 13 indicates the coordinates of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of Fig. 13 indicates the refractive power of the second scanning lens 302' of the comparative example in the yz cross section for the light beam that reaches the coordinates of the actual imaging position shown on the horizontal axis.

[0046] Working Example The scanning optical system of the example was designed by adjusting the surface shapes of the first and second scanning lenses according to a procedure to be described later, using the scanning optical system of the comparative example as a reference.

[0047] In the scanning optical system of the embodiment, the effective scanning width is 216 millimeters, and the maximum absolute value of the deflection angle θ is 42 degrees.

[0048] Table 4 shows the numerical data of the scanning optical system of the embodiment.

[0049] On the optical axis of the imaging optical system, the distance from the deflection surface of the deflector to the scanning surface is L, and the distance from the deflection surface to the surface of the second scanning lens that is farther away from the deflector is d. The following relationship holds: 0.88≦f / L=147.3 / 158.07=0.93 d / L=(37.93+4.5) / 158.07=0.268≦0.3 Since f / L in the scanning optical system of the embodiment is larger than f / L in the scanning optical system of the comparative example, the length in the y-axis direction of the second scanning lens of the embodiment can be made shorter than that of the comparative example. Also, since d / L in the scanning optical system of the embodiment is smaller than d / L in the scanning optical system of the comparative example, the scanning optical system of the embodiment is more compact than the scanning optical system of the comparative example. [Table 4]

[0050] Tables 5A and 5B show coefficients of the equations expressing the surface shapes of the first and second scanning lenses of the embodiment. [Table 5A]

[0051] [Table 5B]

[0052] Fig. 14 is a diagram showing the refractive power of the first scanning lens 301 of the embodiment in the yz cross section. The horizontal axis of Fig. 14 indicates the coordinates of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of Fig. 14 indicates the refractive power of the first scanning lens 301 of the embodiment in the yz cross section for a light ray that reaches the coordinates of the actual imaging position shown on the horizontal axis. In Fig. 14, the solid line indicates the refractive power of the first scanning lens 301 of the embodiment in the yz cross section, and the dashed line indicates the refractive power of the first scanning lens 301' of the comparative example shown in Fig. 12 in the yz cross section. According to Figure 14, the refractive power in the y-z cross section of the first scanning lens 301' in the comparative example is a substantially constant positive value regardless of the coordinate of the actual imaging position, whereas the refractive power in the y-z cross section of the first scanning lens 301 in the embodiment is positive in areas where the absolute value of the coordinate of the actual imaging position is relatively small, decreases as the absolute value of the coordinate of the actual imaging position increases, and is negative in areas where the absolute value of the coordinate of the actual imaging position is relatively large.

[0053] In other words, the refractive power in the yz cross section of the first scanning lens 301 is positive for light rays passing near the optical axis, decreases according to the absolute value of the y coordinate of the position through which the light rays pass, and is negative for light rays passing through the peripheral portion in the y-axis direction.

[0054] FIG. 15 is a diagram showing the refractive power in the yz section of the second scanning lens 302 of the embodiment. The horizontal axis of FIG. 15 indicates the coordinates of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of FIG. 15 indicates the refractive power in the yz section of the second scanning lens 302 of the embodiment for the light beam that reaches the coordinates of the actual imaging position shown on the horizontal axis. In FIG. 15, the solid line indicates the refractive power in the yz section of the second scanning lens 302 of the embodiment, and the dashed line indicates the refractive power in the yz section of the second scanning lens 302' of the comparative example shown in FIG. 13. According to FIG. 15, the refractive power in the yz section of both the second scanning lens of the comparative example and the embodiment increases with an increase in the absolute value of the coordinates of the actual imaging position. The refractive power in the yz section of the second scanning lens 302' of the comparative example is positive in the entire range of the coordinates of the actual imaging position. The refractive power in the yz cross section of the second scanning lens 302 of the embodiment is negative in areas where the absolute value of the coordinate of the actual imaging position is relatively small, increases as the absolute value of the coordinate of the actual imaging position increases, is positive in areas where the absolute value of the coordinate of the actual imaging position is relatively large, and is greater than the refractive power in the yz cross section of the second scanning lens 302' of the comparative example at the periphery of the scanning area.

[0055] In other words, the refractive power in the yz cross section of the second scanning lens 302 is negative for light rays passing near the optical axis, increases according to the absolute value of the y coordinate of the position where the light rays pass, and is positive for light rays passing through the peripheral portion in the y-axis direction.

[0056] 16 is a diagram for explaining the functions of the first scanning lens 301 and the second scanning lens 302 of the embodiment. In an area where the absolute value of the y coordinate of the first scanning lens 301 is relatively small, the refractive power in the yz cross section is positive, so the light beam is condensed. In an area where the absolute value of the y coordinate of the first scanning lens 301 is relatively large, the refractive power in the yz cross section is negative, so the light beam is diverged. In an area where the absolute value of the y coordinate of the second scanning lens 302 is relatively small, the refractive power in the yz cross section is negative, so the light beam is diverged. In an area where the absolute value of the y coordinate of the second scanning lens 302 is relatively large, the refractive power in the yz cross section is positive, so the light beam is condensed.

[0057] FIG. 17 is a diagram showing the partial magnification of the scanning optical system of the embodiment. The horizontal axis of FIG. 17 shows the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of FIG. 17 shows the partial magnification of the scanning optical system for the light beam of the deflection angle shown on the horizontal axis. The vertical axis is in percent. In FIG. 17, the solid line shows the partial magnification of the embodiment, and the dashed line shows the partial magnification of the comparative example shown in FIG. 9. The partial magnification of the embodiment and the comparative example is negative and minimum when the deflection angle is 0, increases according to the absolute value of the deflection angle, and is maximum at the maximum absolute value of the deflection angle. The partial magnification of the scanning optical system of the embodiment is smaller than the partial magnification of the comparative example, particularly near the maximum absolute value of the deflection angle, i.e., near the ratio of the deflection angle to the maximum absolute value of the deflection angle is 1 and -1.

[0058] In this embodiment, the partial magnification is approximately -8% when the deflection angle is 0, and the partial magnification is approximately 10% when the absolute value of the deflection angle is the maximum value.

[0059] FIG. 18 is a diagram showing the differential value with respect to the deflection angle of the partial magnification of the scanning optical system of the embodiment. The horizontal axis of FIG. 18 indicates the ratio of the deflection angle to the maximum absolute value of the deflection angle. The vertical axis of FIG. 18 indicates the differential value with respect to the deflection angle of the partial magnification of the scanning optical system for the light beam of the deflection angle shown on the horizontal axis. The unit of the vertical axis is percentage. In FIG. 18, the solid line indicates the differential value with respect to the deflection angle of the partial magnification of the embodiment, and the dashed line indicates the differential value with respect to the deflection angle of the partial magnification of the comparative example shown in FIG. 9. According to FIG. 18, the differential value with respect to the deflection angle of the partial magnification of the scanning optical system of the embodiment is expressed as r, where r is the ratio of the deflection angle to the maximum absolute value of the deflection angle. -1 ≦ r ≦ -0.4 and 0.4 ≦ r ≦ 1 Therefore, the partial magnification of the scanning optical system of the embodiment as a function of the deflection angle is -1 ≦ r ≦ -0.4 and 0.4 ≦ r ≦ 1 In the range, there are three inflection points.

[0060] From equation (2), when the y coordinate of the position of the principal ray of the light beam on the scanning surface is expressed as a function of the deflection angle θ, the absolute value of the derivative of the function with respect to the deflection angle θ is

number

number

[0061] By adjusting the relationship between the coordinates of the actual imaging position of the light beam and the refractive powers of the first and second scanning lenses with respect to the light rays that reach those coordinates using the scanning optical system of the comparative example as a reference, the shape of the partial magnification curve shown in Figure 17 for the scanning optical system of the embodiment can be adjusted.

[0062] Fig. 19 is a diagram showing the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the embodiment. The horizontal axis of Fig. 19 indicates the y coordinate of the actual imaging position of the light beam. The unit of the horizontal axis is millimeters. The vertical axis of Fig. 19 indicates the diameter in the main scanning direction of the light beam spot on the scanning surface of the light beam having a chief ray passing through the coordinate of the actual imaging position shown on the horizontal axis. In Fig. 19, the solid line indicates the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the embodiment, and the dashed line indicates the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the comparative example shown in Fig. 10. In Fig. 19, the maximum value of the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the embodiment is smaller than the maximum value of the diameter in the main scanning direction of the light beam spot on the scanning surface of the scanning optical system of the comparative example, and the difference is greater than 3 micrometers.

Claims

1. A deflector that deflects a light beam from a light source; a scanning optical system including a first scanning lens closer to the deflector and a second scanning lens farther from the deflector, and an imaging optical system that guides a polarized light beam to a scanning surface, wherein the scanning direction is perpendicular to the rotation axis of the deflector and the optical axis of the imaging optical system, the angle formed by a straight line which is a projection of a principal ray of the deflected light beam onto a plane perpendicular to the rotation axis of the deflector and a straight line which is a projection of the optical axis onto the plane is defined as a deflection angle θ, a value obtained by dividing half-value W / 2 of a scanning width W by the maximum value of the deflection angle θ is defined as a system focal length f, a distance on the optical axis from a deflection surface of the deflector to the scanning surface is defined as L, and a distance from the deflection surface to a surface of the second scanning lens farther from the deflector is defined as d, 0.88≦f / L d / L≦0.3 satisfies the above condition, the scanning direction is the y-axis direction, the y-coordinate of the optical axis is 0, and the y-coordinate of the position of the principal ray of the light beam on the scanning surface is expressed as a function of the deflection angle θ. When this function's differential function dy / dθ increases in absolute value according to the absolute value of the deflection angle θ, and the ratio of the deflection angle to the maximum absolute value of the deflection angle θ is r, the differential function dy / dθ is -1 ≦ r ≦ -0.4 and 0.4 ≦ r ≦ 1 A scanning optical system having a plurality of inflection points in each range.

2. 2. The scanning optical system according to claim 1, wherein the direction of the optical axis is the z-axis direction, and the refractive power of the first scanning lens in a y-z cross section is positive for light rays passing near the optical axis, decreases in accordance with the absolute value of the y coordinate of the position where the light rays pass through, and is negative for light rays passing through the peripheral portion in the y-axis direction, and the refractive power of the second scanning lens in the y-z cross section is negative for light rays passing near the optical axis, increases in accordance with the absolute value of the y coordinate of the position where the light rays pass through, and is positive for light rays passing through the peripheral portion in the y-axis direction.

3. 2. The scanning optical system according to claim 1, wherein the value of (|dy / dθ| - f) / f is -3% or less when the deflection angle θ is 0, and is 5% or more when the absolute value of the deflection angle θ is a maximum value.

Images