JPS6236210B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a scanning optical system that eliminates pitch irregularities in scanning lines. Conventionally, in light beam scanning devices that use a deflecting reflective surface such as a rotating polygon mirror, even if the traveling direction of the deflected and scanned light beam changes within a plane perpendicular to the deflecting surface due to the tilting of the deflecting reflective surface. Various scanning optical systems have been proposed that do not cause unevenness in the pitch of scanning lines on a surface to be scanned (a medium to be scanned). Incidentally, in this specification, the term "deflection surface" refers to a ray bundle surface formed over time by a light beam deflected by a deflection reflection surface of a deflector. For example, in Japanese Patent Publication No. 52-28666, the configuration of the optical system between the deflector and the scanned medium consists of a beam shaping means and a second converging means. The beam reflected by the deflection mirror is collimated. In this way, providing a collimating function imposes constraints on the shape of the beam shaping means, which improves the imaging performance on the scanned surface and the distortion characteristics to keep the scanning speed constant. This reduces the degree of freedom in which the lens can be used, and it becomes impossible to obtain good performance unless the number of lenses in the second focusing means is increased. Next, in JP-A-48-98844, certain restrictions are imposed on the ratio of the focal lengths of two types of lenses constituting the optical system between the deflector and the scanned medium.
Satisfying this constraint is equivalent to collimating the light beam within a cross section perpendicular to the deflection plane between the two types of lenses. Therefore, as described above, this example is also undesirable because the degree of freedom for correcting the imaging performance and distortion characteristics is reduced. Next, in JP-A No. 50-93720, a cylindrical lens is arranged between a lens having distortion characteristics and a medium to be scanned to realize constant speed scanning. With such a configuration, a good image cannot be obtained unless the cylindrical lens is positioned close to the scanned medium. When the cylindrical lens approaches the scanned medium, the cylindrical lens becomes longer in the generatrix direction as the scanning width becomes longer, making it impossible to realize a compact configuration. SUMMARY OF THE INVENTION An object of the present invention is to improve the drawbacks of the conventional scanning device described above and to provide a scanning optical system that has a simple and compact configuration and can correct the tilting of a deflector. A further object of the present invention is to provide a scanning optical system in which the beam scanning speed is constant on the surface to be scanned. In the scanning optical system according to the present invention, the scanning imaging optical system disposed between the deflector and the medium to be scanned is composed of, in order from the deflector side, a spherical single lens and a single lens having a toric surface. By doing so, the above purpose is achieved. That is, the scanning optical system according to the present invention includes a light source device, a first imaging optical system that forms a linear image of the light beam from the light source device, a deflector having a deflection reflecting surface near the linear image, and the linear image. A second imaging optical system is provided for forming an image as a spot on the scanned medium, and the second imaging optical system is comprised of a spherical single lens and a toric single lens in order from the deflector side.
The term "Tory lens" as used herein means a lens that has power in a direction perpendicular to the optical axis of the lens, and has different powers in the perpendicular direction. In the scanning optical system according to the present invention, the toric lens includes the optical axis of the spherical single lens and is perpendicular to the deflection plane formed by the beam whose deflection is changed by the deflector. It is a positive meniscus lens consisting of a surface with negative refractive power on the side and a surface with positive refractive power on the side of the scanned medium. In the scanning optical system according to the present invention, the scanning imaging optical system disposed between the deflector and the scanned medium is
Unlike the conventional art, there is no beam shaping means for collimating the light beam deflected by the deflector. That is, since a means having a collimating function is not used, there are no restrictions on the degree of freedom in favorably correcting the imaging performance and distortion characteristics of this imaging optical system. As a result, a simple and compact configuration can be realized. Furthermore, in the present invention, a torrefaction lens is provided on the scanned medium side of the spherical single lens, which makes it possible to correct distortion characteristics and make the device more compact than in the case of a cylindrical lens. . That is, when a cylindrical lens is used, its refractive power within the deflection plane is zero, and there is no degree of freedom for correcting field curvature. On the other hand, since a Tory lens has refractive power within the deflection plane, it is possible to correct field curvature. Furthermore, if a cylindrical lens is used to make a scanning imaging optical system compact, a large amount of field curvature will occur, and for the reasons mentioned above, it is impossible to correct it with the cylindrical lens itself. On the other hand, the Torytsu lens has a degree of freedom in correction and can therefore be made more compact. The present invention will be described in detail below with reference to the drawings. FIG. 1 is a diagram showing the basic configuration of the present invention. A light source device 1 consisting of a light source or a light source and a condensing device, a line image forming system 2 that forms a linear image with the light beam emitted from the light source device 1, and a line image forming system 2 that forms a linear image of the light beam A deflector 3 having a deflection reflecting surface 3a near a position where it is converged, a spherical single lens 4 between the deflector 3 and the scanned medium 6, and a main axis and a sub-axis having different refractive powers in two orthogonal directions. A single lens 5 having a toric surface having an axis is disposed, and an imaging spot is formed on the scanned medium 6 by a composite system of these lenses. The image spot scans over the scanned medium 6. FIG. 2 is a diagram for explaining the function of the deflection surface of the above configuration, in other words, the function within a cross section parallel to a plane containing the principal axis of the toric lens 5 and the optical axis of the spherical single lens 4. After the light beam emitted from the light source device 1 passes through the cylindrical lens 2, it is reflected by the reflective surface 3a of the deflector 3, and as the deflector 3 rotates, the reflected light beam is deflected. Further, the deflected light beam is imaged onto the scanned medium 6 by a composite system of the spherical single lens 4 and the lens 5 having a toric surface, and the scanning speed of the imaged spot is kept constant. FIG. 3 is a developed view of a cross section along the light beam in a direction perpendicular to the deflection plane, that is, a cross section for correcting the influence of the tilting of the deflector. The light beam emitted from the light source device 1 is linearly imaged near the reflective surface 3a of the deflector 3 by the line image forming system 2. The refractive power of the single lens 5 in this cross section is different from the refractive power of the lens 5 in the deflection plane, and in a composite system with the spherical single lens 4, the reflective surface 3a of the deflector 3 and the scanned medium 6 make the positional relationship optically conjugate. Because of this relationship, even if the reflective surface 3a tilts in a direction perpendicular to the deflection surface and changes to the position 3a' during rotation of the deflector 3, it will still pass through the lens systems 4 and 5. Although the light flux changes as shown by the broken line, the imaging position on the scanned medium 6 does not change. Next, it will be explained how the scanning optical system of the present invention can scan a scanned medium at a constant speed with good imaging performance despite having a simple and compact configuration. When the aperture ratio is small, such as from 1:30 to 1:100, two single lenses are sufficient for obtaining good scanning performance. Generally, in a lens system with a small aperture ratio, the aberration coefficient that should be corrected is the astigmatism coefficient ()
and the distortion coefficient (). The aberration coefficients of the entire lens system are the characteristic coefficients a _i , b _i , c _i , a
The following relationship exists between _vi , b _vi , c _vi and the characteristic coefficients A _pi and B _pi . Here, the characteristic coefficient is a constant determined by the paraxial relationship or the medium, and the characteristic coefficients A _pi and B _pi are coefficients that determine the shape of the i-th constituent group. Equation (1) represents a general relationship when the number of constituent groups is N. (Lens Design Method by Matsui; Kyoritsu Shuppan) Furthermore, when each constituent group is a single lens, the following dependency exists between the characteristic coefficients A _pi and B _pi of each single lens. A _pi = α _i B ² _pi + β _i B _pi + γ _i (2) However, α _i , β _i , and γ _i are constants determined by the refractive index of the medium of the i-th single lens. Substituting equation (2) into equation (1) gives us becomes. However, ξ _i , η _i , ζ _i , ξ _vi , η _vi ,
ζ _vi is a constant determined by the characteristic coefficient and the constants α _i , β _i , and γ _i . In equation (3), set the desired aberration coefficient values for each to obtain distortion characteristics for obtaining good imaging performance and constant speed scanning, and further increase the number of constituent lenses to 2 groups (N
=2), it is possible to solve simultaneous equations with B _p1 and B _p2 as unknowns, and B _p1 and B _p2 can be obtained. B _pi is expressed by the radius of curvature R _i of the front surface of the i-th lens and the refractive index N _i of the medium of the lens as follows (Lens Design Method by Matsui). B _pi =-N _i /N _i -1+N _i +1/N _i (1/R _i
)(4) Therefore, R _i =(N _i +1/N _i )/(B _pi +N _i /N _i −1
), and the radii of curvature R ₁ and R ₂ of the front surface of each lens can be determined using equation (4) using the characteristic coefficients B _p1 and B _p2 of the two groups obtained from the above results, and each lens The radii of curvature R ₁ ′ and R ₂ ′ of the rear surface are also obtained from the following equations. R _i '=(1-N _i )/(1-N _i -1/R _i ) (5) In the above, each component lens is treated as a thin lens whose focal length is normalized to 1. In the actual system shown in Figure 2, if the refractive powers of lenses 4 and 5 are φ ₁ and φ ₂ , respectively, the radii of curvature r ₁ , r ₂ , r ₃ , r ₄ of the front and rear surfaces of each lens are as follows. become. r ₁ = R ₁ /φ ₁ r ₂ = R ₁ ′/φ ₁ r ₃ = R ₂ /φ ₂ r ₄ = R ₂ ′/φ ₂ As described above, the two single lens configuration provides a good It is possible to determine the shape of each lens such that the astigmatism coefficient for obtaining imaging performance and the distortion aberration coefficient corresponding to distortion characteristics for achieving uniform speed scanning have desired values. Next, since a toric surface is introduced in the direction perpendicular to the deflection plane, it is possible to provide a focal length different from that of the composite system of lenses 4 and 5 in the deflection plane. Therefore, it is possible to have a different imaging relationship with respect to the imaging relationship within the deflection plane, and the positions of the reflecting surface 3a of the deflector and the scanned medium 6 are in a conjugate relationship. Furthermore, what is important in the present invention is that at least one surface of the single lens 5 having a toric surface has negative refractive power in a cross section perpendicular to the deflection surface. This is convenient for correcting field curvature in the sagittal direction in order to form a good imaging spot on the scanned medium 6 with the light beam deflected in a cross section perpendicular to the deflection plane. In a cross section parallel to the deflection surface, the radius of curvature _r3 of the deflector side surface of the single lens 5 having a toric surface is equal to When f _p /r ₃ >−2.1 is satisfied for the composite focal length f _p , the effect of correcting the curvature of field is large. This condition means that the larger the deflection angle, the stronger the divergence force for the incident light beam in a cross section perpendicular to the deflection plane, producing the effect of correcting the image plane in the positive direction. In addition to the above condition f _p /r ₃ > -2.1, a single lens 5 having a toric surface in the cross section parallel to the deflection surface
For the ratio _{f t /} f _{t '} of the focal length f _t of It is also possible to satisfactorily correct the distortion characteristics within. Furthermore, another important point is that in the cross section perpendicular to the deflection surface, the shape of the single lens 5 having the toric surface has a surface having a positive refractive power on the scanned medium 6 side, and the entire lens has a positive refractive power. A single meniscus lens having a refractive power of . This has the effect of bringing the principal point position of the composite system of the spherical single lens 4 and the toric surface single lens 5 closer to the scanned medium side in the cross section perpendicular to the deflection plane, and as a result, the lens system It becomes possible to bring the whole device closer to the deflector, making it more compact. Assuming that the focal lengths of the above-mentioned composite system in the cross-section parallel to the deflection plane and in the cross-section perpendicular to the deflection plane are respectively f _p and f _v , the above effect is great if 3.0<f _p /f _v <4.0 is satisfied. In the above equation (3), the desired value to be corrected for the astigmatism coefficient depends on whether the light beam incident on the reflecting surface 3a of the deflector 3 is a divergent light beam, a parallel light beam, or a convergent light beam within the deflection surface. It depends. On the other hand, the desired value of the distortion aberration coefficient to be corrected depends on the rotational characteristics of the deflector 3. When the deflector 3 rotates at a constant angular velocity, the value of the distortion aberration coefficient that causes the light beam deflected by the deflector to move at a constant velocity on the scanned medium 6 is 2/3. The deflector 3 is φ=φ ₀ sinωt (φ is the rotation angle, φ ₀
is the amplitude, ω is a constant related to the period, and t is time). In the case of sinusoidal vibration, there is a distortion that causes the light beam deflected by the deflector 3 to move at a constant speed on the scanned medium surface 6. The value of the coefficient is =2/3 (1-1/8φ ₀ ² ). Since the present invention does not have the condition of collimating the light beam between the spherical single lens 4 and the single lens 5 having a toric surface, the degree of freedom of the refractive power of each lens is not limited, and the above two Good imaging performance and distortion characteristics can be obtained with just one lens. Examples of the spherical single lens 4 and the single lens 5 having a toric surface of the scanning optical system according to the present invention will be shown below. Tables 1 to 12 show examples of imaging optical systems 4 and 5 according to the present invention, respectively. In each table, the table with subscript (a) shows lens data. r ₁ to _{r 4} are the radii of curvature of the lens in a plane parallel to the deflection plane, and r′ ₁ to r′ ₄ are the radii of curvature of the lens in a cross section perpendicular to the deflection plane (therefore, the spherical single lens 4, r ₁ = r' ₁ , r ₂ = r' ₂ ),
_d1 is the axial thickness of the spherical single lens 4, and _d2 is the single lens 5 having the _r2 surface and the toric surface of the spherical single lens 4.
(Equivalent to the axial air distance between the _r'2 surface of the spherical single lens ₄ and the r'3 surface of the single lens ₅ having a toric surface.) _d3 is the toric surface n ₁ is the refractive power of the spherical single lens 4, and n ₂ is the refractive index of the single lens 5 having a toric surface. In each table, the table with subscript (b) will be explained. In a plane parallel to the deflection plane (hereinafter referred to as the “deflection plane”)
It is written as ), in a cross section perpendicular to the deflection plane (hereinafter referred to as "vertical cross section"), the column f indicates the focal length in the composite system of the spherical single lens 4 and the single lens 5 having a toric surface. . In particular, for convenience of explanation, the focal length is f _p in the above-mentioned "deflection plane" and the "vertical section" is
The focal length within is written as _fv . The column _f5 shows the focal length of the single lens 5 having a toric surface. For convenience of explanation, the focal length in the "deflection plane" is denoted by f _t and the focal length in the "vertical section" is denoted by f' _t . b.
In column f., write the back focus. The S ₁ column shows the first surface (i.e. the r ₁ surface of a spherical single lens, or
Indicates the object distance from r′ ₁ plane). In the S _k ′ column,
When the object distance is _S1 , the distance from the final surface ( _r4 surface or _r'4 surface) of the single lens 5 having a toric surface to the Gaussian image surface is described. In the effective F No. column, write the effective F number on the image field side when the object distance is _S1 . In each table, the table with subscript (c) shows the third-order aberration coefficient when normalized to f _p =1 in a plane parallel to the deflection surface. In each table, the table with subscript (d) will be explained. In the column of δ, when normalized to f _v = 1, in the cross section perpendicular to the deflection surface, the near field that is incident on the r′ ₁ surface of the spherical single lens 4 at a height of 1 on the principal plane is shown. After the axial ray exits the _r'2 surface of the spherical single lens 4, the angle (unit: rad.) it forms with the optical axis when it enters the r'3 surface of the single lens ₅ having a toric surface is described. δ
If ≠0, it means that the light beam is not collimated between the _r'2 surface of the spherical single lens 4 and the _r'3 surface of the lens 5 having a toric surface.

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[Table] As shown in Fig. 4, r ₃ at the intersection of the deflected chief ray and the r ₃ plane of the single lens 5 having a toric surface in a plane parallel to the deflection plane.
The angle formed by the normal to the surface (indicated by a broken line in the figure) and the chief ray is expressed in ε (unit: degrees, counterclockwise is taken as positive direction), and the maximum image height (=0.5・f _p ) is written as εmax. Figure 5 shows Table 1-(a)
The relationship between ε and image height in the embodiments shown in ~(d) is shown. FIG. 6 shows the relationship between ε and image height in the examples shown in Tables 12-(a) to (d). As shown in FIG. 5, in the embodiment shown in Table 1, as the image height increases, ε also increases. That is,
As the incident angle of view increases, the _r'3 surface of the lens 5, which has a toric surface, has a stronger power for the light beam in a cross section that includes the principal ray and is perpendicular to the deflection plane, compared to the case of axial rays. Due to the synergistic effect with r ₃ of the lens 5 having a toric surface, an image surface is formed in the cross section to form a good imaging spot of the deflected light beam on the scanned medium 6. This is convenient for correcting curvature, and the entire optical system after the deflection surface has distortion characteristics such that uniform speed scanning is performed on the surface to be scanned in a plane parallel to the deflection surface, and
It has the effect of correcting inclination in a cross section perpendicular to the deflection plane. In the embodiment shown in Table 12, the value of ξ is approximately 0° as shown in FIG. In this example, in a plane parallel to the deflection surface, when effective F No. = 60, spherical aberration = -0.00037・f _p , and when image height = 0.5・f _p , astigmatism =−0.11・
f _p , LIN=1.4. However, LIN is a quantity representing inearity, and inearity=y'-f _p・θ/f _p・θ×100 (however, y
′ is the image height). Also, in the cross section perpendicular to the deflection surface, when effective FNo. = 100, spherical aberration = -
When 0.0061・f _p , image height = 0.5・f _p , astigmatism =
−0.003・f _p . Further, as shown in Table 12-(b), the difference between S _k ' in a plane parallel to the deflection plane and S _k ' in a cross section perpendicular to the deflection plane is 0.0434·f _p . Therefore, in this embodiment, in a plane parallel to the deflection plane and in a cross section perpendicular to the deflection plane, the performance as a scanning optical system according to the present invention deteriorates considerably, but is close to the diffraction limit. In this example, as shown in Table 12-(d), f _p /r ₃ =-2.04. Figure 7-a shows the lens shape of the example shown in Table 1 in a plane parallel to the deflection plane, and Figure 7-b
2 shows the lens shape of this example in a cross section perpendicular to the deflection plane. FIG. 8-a shows an aberration diagram in a plane parallel to the deflection surface of this example.
Figure b shows an aberration diagram in a cross section perpendicular to the deflection surface. In the aberration diagrams shown in FIGS. 8-a and b, the single lens 5 having a toric surface is shown in the S _k ' column of the tables with internal subscript (b) in each of the above-mentioned tables.
The distance from the final plane (r ₄ plane or r' ₄ plane) to the Gaussian image plane differs within each plane. In view of the embodiments according to the present invention shown in Tables 1 to 12 above, in a plane parallel to the deflection surface, the radius of curvature on the deflector side of the single lens 5 having a toric surface is
The relationship between r ₃ and the radius of curvature r ₄ on the scanned medium side is 1/r ₃ > 1/r ₄ , and in the plane, the radius of curvature r ₃ on the deflector side of the single lens 5 is f _p /r ₃ >−2.1 with respect to the composite focal length f _p of the scanning lens system within the plane, and the composite system consisting of the spherical single lens 4 and the toric surface single lens 5 , the relationship between the focal length f _p in a plane parallel to the deflection plane and the focal length f _v in a cross section perpendicular to the deflection plane is 3.0<f _p /f _v <4.0, and the toric The relationship between the focal length f _t in a plane parallel to the deflection plane of the single lens 5 having a surface and the focal length f _t ′ in a cross section perpendicular to the deflection plane is f _t /f _t ′<13.0. For example, in the scanning optical system according to the present invention, in a plane parallel to the deflection surface, the scanning optical system has distortion characteristics such that uniform speed scanning is performed on the scanned medium 6,
In addition, in a cross section perpendicular to the deflection surface, it has the effect of correcting tilt. In the above description, the sign of the radius of curvature is positive when the surface is convex to the deflector side, and negative when it is opposite. FIG. 9 shows an embodiment in which the scanning optical system according to the present invention is applied to a laser beam printer. In FIG. 9, a laser beam oscillated by a laser oscillator 11 is guided to an entrance aperture of a modulator 13 via a reflecting mirror 12. After being modulated by the information signal to be recorded by the modulator 13, the laser beam is directed near the deflection reflection surface of the deflector 15 by a line image forming system 14 consisting of, for example, a cylindrical lens, perpendicular to the rotation axis 15a of the deflector. form a line image. The beam deflected by the deflector 15 is imaged onto the photosensitive drum 17 by an imaging lens system 16 consisting of the above-mentioned spherical single lens 16a and toric single lens 16b, and scans the photosensitive drum 17 at a constant speed. Note that 18 is a first corona charger and 19 is an AC corona discharger, both of which are part of the electrophotographic process. The laser oscillator 11 is a light source device consisting of a self-modulating semiconductor laser and a beam shaping optical system that corrects the cross-sectional shape of the laser beam from the semiconductor laser and converts the laser beam into an afocal light. It's okay. Furthermore, in the above application example, the light beam incident on the spherical single lens 16a in a plane parallel to the deflection surface does not necessarily have to be parallel light, but may be divergent light,
Either convergent light or convergent light is possible, and at the same time,
For the purpose of forming a beam near the reflective surface of the deflector 15 in a cross section perpendicular to the deflection surface, a light source device 11 consisting of a light source and a condensing device and a line image forming device 14 are used. easily achieved. Further, in the above application example, when a light source such as a semiconductor laser, which has different emission angles on two orthogonal planes, is used as the light source device 11, the light emission source point in the two orthogonal planes is By using different things (i.e., within the two orthogonal planes,
Since this is equivalent to the fact that the object point has an astigmatic difference),
Even if a rotationally symmetric optical system is used as the line image forming system 14, the deflector 15 cannot be used in the cross section perpendicular to the deflection plane.
It is also possible to form an image of the light beam near the reflecting surface, and to make the diverging light or convergent light incident on the spherical single lens 16a in a plane parallel to the deflection surface.

[Brief explanation of the drawing]

Figure 1 is a diagram showing the principle of the scanning optical system according to the present invention, Figure 2 is a sectional view to explain the function of the present invention in a plane parallel to the deflection plane, and Figure 3 is the deflection plane. Fig. 4 is a diagram for explaining the function of the present invention in a cross section perpendicular to Figures 5 and 6 are diagrams showing the relationship between the image height and the above-mentioned angle ξ in the scanning lens system used in the present invention, and Figures 7a and 7b are diagrams showing the relationship between the deflection angle ξ, respectively. FIG. 2 is a lens cross-sectional view showing the shape of an embodiment of a scanning lens applied to the present invention in a plane parallel to the plane and in a cross section perpendicular to the plane. FIGS. 8a and 8b respectively show the seventh
Aberration diagrams of the lenses shown in Figures a and b at each Gaussian image plane, and Figure 9 is a schematic diagram showing an embodiment of a laser beam printer to which the present invention is applied. 1... Light source device, 2... Line image imaging system, 3... Deflector,
4...Spherical single lens, 5...Toritz lens, 6...
Scanned medium.

Claims (1)

[Scope of Claims] 1. A light source section, a first imaging optical system that forms a linear image of the light beam generated from the light source section, and a deflection reflecting surface thereof in the vicinity of the linear image formed by the first imaging optical system. a second imaging optical system that focuses the light flux changed by the deflector onto the scanned medium, and the second imaging optical system includes, in order from the deflector side, a spherical single lens and a toric surface. In a cross section that includes the optical axis of the spherical single lens and is perpendicular to the deflection surface, the single lens having the toric surface has a surface having negative refractive power on the deflector side and a surface to be scanned. A scanning optical system having a tilt correction function characterized by having a meniscus shape having a positive refractive power and a surface having a positive refractive power on the medium side. 2 In the deflection plane of the single lens having a toric surface, when the radius of curvature of the surface on the deflector side is r ₃ and the radius of curvature of the surface on the side to be scanned is r ₄ , 1/r ₃
The scanning optical system according to claim 1, wherein >1/r ₄ . 3 In the single lens having the above-mentioned toric surface, the radius of curvature r ₃ of the surface on the deflector side in the deflection plane is f with respect to the focal length f _p of the second imaging optical system in the deflection plane. The scanning optical system according to claim 1, wherein _p /r ₃ >−2.1. 4 The focal length f _p of the second imaging optical system in the deflection plane is the focal length f of the second imaging optical system in a plane perpendicular to the deflection plane and including the optical axis of the spherical single lens. 2. The scanning optical system according to claim 1, wherein 3.0<f _p /f _v <4.0 for _v . 5 The focal length f _t of the single lens having a toric surface within the deflection plane is the focal length of the single lens having a toric surface in a plane perpendicular to the deflection plane and including the optical axis of the spherical single lens. f for f _t ′
The scanning optical system according to claim 1, which satisfies _t /f _t '<13.0.