Optical scanning system and image forming apparatus using the same Number:7,385,746 from the United States Patent and Trademark Office (PTO) owispatent An optical scanning system includes a deflecting device to scanningly deflect a light beam from a light source in a main scan direction, and an imaging optical system for imaging, upon a surface to be scanned, the light beam deflected by a deflecting surface of the deflecting device. First and second differences in wavefront aberration are respectively produced as a result of reflection by the deflecting surface and as a result of transmission through the imaging optical system. At least one optical surface inside the imaging optical system is non-arcuate in a main scan section, so as to assure that the first and second phase differences are made opposite to each other.<H apparatus, scanning, Optical, scannin, 7385746.html, Patent, pto, 7385746

Title: Optical scanning system and image forming apparatus using the same

Abstract: An optical scanning system includes a deflecting device to scanningly deflect a light beam from a light source in a main scan direction, and an imaging optical system for imaging, upon a surface to be scanned, the light beam deflected by a deflecting surface of the deflecting device. First and second differences in wavefront aberration are respectively produced as a result of reflection by the deflecting surface and as a result of transmission through the imaging optical system. At least one optical surface inside the imaging optical system is non-arcuate in a main scan section, so as to assure that the first and second phase differences are made opposite to each other.

Patent Number: 7,385,746 Issued on 06/10/2008 to Ishibe, et al.

Inventors: Ishibe; Yoshihiro (Utsunomiya, JP), Kato; Takahisa (Atsugi, JP), Yasuda; Susumu (Tsukuba, JP)
Assignee: Canon Kabushiki Kaisha (Tokyo, JP)

Appl. No.: 11/503,069

Filed: August 14, 2006

Foreign Application Priority Data


Aug 22, 2005 [JP]			2005-239770
May 25, 2006 [JP]			2006-145154
Jul 20, 2006 [JP]			2006-198159

Current U.S. Class: 359/215 ; 347/244; 359/205; 359/213

Field of Search: 359/205,213-215

References Cited [Referenced By]

U.S. Patent Documents


6069727	May 2000	Cho et al.
6104522	August 2000	Hayashi et al.
6133935	October 2000	Fujibayashi et al.
6275318	August 2001	Kamikubo et al.
6803843	October 2004	Kato et al.
6924915	August 2005	Hirose et al.
7068410	June 2006	Nomura et al.
7085031	August 2006	Tomioka
2002/0044326	April 2002	Kato
2002/0163704	November 2002	Hayashi et al.
2004/0119811	June 2004	Bush et al.

Foreign Patent Documents


1553752	Jul., 2005	EP
2004-191416	Jul., 2004	JP
2005-173082	Jun., 2005	JP
2005-189580	Jul., 2005	JP
2004/049034	Jun., 2004	WO

Other References

US. Appl. No. 11/603,058, filed Nov. 22, 2006 by Takahisa Kato and Yukio Furukawa. cited by other .
U.S. Appl. No. 11/603,060, filed Nov. 22, 2006 by Takahisa Kato and Yukio Furukawa. cited by other.

Primary Examiner: Allen; Stephone B.
Assistant Examiner: Callaway; Jade
Attorney, Agent or Firm: Fitzpatrick, Cella, Harper & Scinto

Claims

What is claimed is:

1. An optical scanning system, comprising: light source means; deflecting means configured to scanningly deflect a light beam from said light source means in a main scan direction; and an imaging optical system configured to image, upon a surface to be scanned, the light beam deflected by a deflecting surface of said deflecting means; wherein said deflecting surface is configured to perform reciprocating motion by which the surface to be scanned is reciprocatingly scanned in the main scan direction with the light beam deflected by said deflecting surface of said deflecting means; wherein as a result of reflection of the light beam by the deflecting surface, a first phase difference of wavefront aberration is produced in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface at an effective deflection angle of the same corresponding to a largest scan position in an effective scan region on the surface to be scanned; wherein as a result of transmission of the light beam through said imaging optical system, a second phase difference of wavefront aberration is produced in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface at an effective deflection angle thereof; and wherein at least one optical surface constituting said imaging optical system is non-arcuate shape in a main scan section, so that the first and second phase differences are made opposite to each other.

2. An optical scanning system according to claim 1, wherein .delta.L1.sub.+ is used to refer to an optical path difference, in the main scan section, between a marginal ray at a scan end portion side of the light beam and a principal ray of the same reflected by said deflecting surface at an effective deflection angle thereof, the difference being produced as a result of reflection of the light beam by said deflecting surface, wherein .delta.L1.sub.- is used to refer to an optical path difference between a marginal ray at a scan central portion side of the light beam and the principal ray of the same reflected by said deflecting surface at an effective deflection angle thereof, the difference being produced as a result of reflection of the light beam by said deflecting surface, wherein .delta.L2.sub.+ is used to refer to an optical path difference between the marginal ray at the scan end portion side of the light beam and the principal ray of the same reflected by said deflecting surface at an effective deflection angle of the same, the difference being produced as a result of transmission of the light beam through said imaging optical system, wherein .delta.L2.sub.- is used to refer to an optical path difference between the marginal ray at the scan central portion side of the light beam and the principal ray of the same reflected by said deflecting surface at an effective deflection angle of the same, the difference being produced as a result of transmission of the light beam through said imaging optical system, and wherein said imaging optical system satisfies the following relation: .ltoreq..delta..times..times..delta..times..times..delta..times..times..d- elta..times..times..ltoreq. ##EQU00025##

3. An optical scanning system according to claim 2, wherein, where the number of the optical surfaces constituting said imaging optical system is m and where the surface shape of each optical surface in the main scan section is expressed by X=f(Y) while a point of intersection between each optical surface and an optical axis of said imaging optical system is taken as an origin, a direction of the optical axis is taken as an X axis and an axis being orthogonal to the optical axis in the main scan section is taken as a Y axis, at the effective deflection angle of said deflecting surface the following condition is satisfied: .times..times.< ##EQU00026## .times..times..function..times.dd.times.dd.times..times.dd.times..times.&- lt; ##EQU00026.2## .times..times..times.> ##EQU00026.3## .times..times..function..times.dd.times.dd.times..times.dd.times.> ##EQU00026.4## wherein U.sub.j is a coefficient which takes U.sub.j=-1 when the optical surface is a transmission surface and it is a light entrance surface, U.sub.j=+1 when the optical surface is a transmission surface and it is a light exit surface, and U.sub.j=+1 when the optical surface is a reflection surface; wherein N.sub.j is a coefficient which is equal to the refractive index of the glass material when the optical surface is a transmission surface, and which takes N.sub.j=2 when the optical surface is a reflection surface; wherein dX/dY.sub.(out)j is the tilt, in the main scan section, of the scan end portion with respect to the optical axis of the optical surface at the position where a marginal ray at the scan end portion side of the light beam, impinging on the largest scan position in the effective scan region on the surface to be scanned, passes through the j-th surface; wherein dX/dY.sub.(in)j is the tilt, in the main scan section, of the scan central portion with respect to the optical axis of the optical surface at the position where a marginal ray at a scan central portion side of the light beam, impinging on the largest scan position in the effective scan region on the surface to be scanned, passes through the j-th surface; and wherein dX/dY.sub.(p)j is the tilt, in the main scan section, with respect to the optical axis of the optical surface at the position where the principal ray of the light beam, impinging on the largest scan position in the effective scan region on the surface to be scanned, passes through the j-th surface.

4. An optical scanning system according to claim 1, wherein the reciprocating motion of said deflecting surface is based on resonance drive.

5. An optical scanning system according to claim 1, wherein the reciprocating motion of said deflecting surface is based on sine oscillation.

6. An optical scanning system according to claim 4, wherein the reciprocating motion of said deflecting surface based on resonance drive has a plurality of discrete natural oscillation modes, and wherein said plurality of discrete natural oscillation modes include a reference oscillation mode which is a natural oscillation mode based on a reference frequency and a multiple-number-oscillation mode which is a natural oscillation mode based on a frequency corresponding to a multiple, by an integer not less than 2, of the reference frequency.

7. An optical scanning system according to claim 6, wherein said deflecting means includes a plurality of movable plates, a plurality of torsion springs disposed along an axis, for connecting said plurality of movable plates in series, a support for locally supporting said plurality of torsion springs, driving means for applying a torque to at least one of said plurality of movable plates, and drive control means for controlling said driving means.

8. An optical scanning system according to claim 7, wherein said defecting surface is formed on one of said plurality of movable plates, and wherein said plurality of movable plates and said plurality of torsion springs are provided in an integral structure.

9. An optical scanning system according to claim 8, wherein said drive control means controls said driving means so as to excite said reference oscillation mode and said multiple-number-oscillation mode simultaneously.

10. An optical scanning system according to claim 6, wherein the light beam being scanningly deflected by said deflecting surface, reciprocating in the main scan direction, is scanningly deflected in the effective scan region at an angular speed different from a uniform angular speed, and wherein the following condition is satisfied: (d.theta..sub.1/dt).sub.max/(d.theta..sub.1/dt).sub.min<1.1 where (d.theta..sub.1/dt).sub.max is a largest value of the angular speed of said deflecting surface at an arbitrary scan position in the effective scan region, and (d.theta..sub.1/dt).sub.min is a smallest value of the angular speed of said deflecting surface at an arbitrary scan position in the effective scan region.

11. An optical scanning system according to claim 10, wherein said imaging optical system is configured to convert the light beam, scanningly deflected by said deflecting means at a speed different from a uniform angular speed, into a uniform-speed beam on the surface to be scanned.

12. An optical scanning system according to claim 1, wherein, where a largest value of spot diameter in the main scan direction of focused spots along one and the same scan line in the effective scan region on the surface to be scanned is denoted by .phi.m.sub.1, and a smallest value of spot diameter in the main scan direction of focused spots along one and the same scan line in the effective scan region on the surface to be scanned is denoted by .phi.m.sub.2, the following relation is satisfied: .phi.m.sub.1/.phi.m.sub.2<1.1

13. An optical scanning system according to claim 1, wherein said light source means has at least two light emission points.

14. An optical scanning system according to claim 1, wherein said deflecting surface of said deflecting means is deformed in the main scan direction due to an angular acceleration resulting from reciprocating motion, and wherein the amount of deformation thereof is changeable in dependence upon the position of said deflecting surface in the sub-scan direction.

15. An optical scanning system according to claim 14, wherein said imaging optical system does not function to bring said deflecting surface and the surface to be scanned into a conjugate relationship with each other in the sub-scan section.

16. An optical scanning system according to claim 14, wherein, at an effective deflection angle of said deflection surface, the shape of the sub-scan section at a position of said deflection surface in the main-scan direction which position corresponds to the scan end portion side, with respect to an axis of reciprocating motion of said deflecting surface, is deformed into a concave shape with respect to the surface to be scanned, and wherein the shape of the sub-scan section at a position of said deflection surface in the main-scan direction which position corresponds to the scan central portion side, with respect to the axis of reciprocating motion of said deflecting surface, is deformed into a convex shape with respect to the surface to be scanned.

17. An optical scanning system according to claim 16, wherein, when a parallel light beam is incident on said imaging optical system at a position where the light beam reflected by said deflecting surface at an effective deflection angle thereof passes through said imaging optical system, a curvature radius in the sub-scan direction of a wavefront of the light beam at a position through which a scan-end-portion-side marginal ray passes, with respect to a principal ray of the light beam passed through said imaging optical system, is made larger than a curvature radius of a wavefront in the sub-scan direction of the light beam at a position through which a scan-central-portion side marginal ray passes, with respect to the principal ray of the light beam.

18. An image forming apparatus, comprising: an optical scanning system as recited in claim 1; a photosensitive material disposed at a scan surface to be scanned; a developing device for developing an electrostatic latent image formed on said photosensitive material through a light beam scanned by said optical scanning system, to produce a toner image; a transferring device for transferring the developed toner image onto a transfer material; and a fixing device for fixing the transferred toner image, on the transfer material.

19. An image forming apparatus, comprising: an optical scanning system as recited in claim 1; and a printer controller for converting code data supplied from an outside machine into an imagewise signal and for inputting the imagewise signal into said optical scanning system.

20. A color image forming apparatus, comprising: a plurality of optical scanning systems each being as recited in claim 1; and a plurality of image bearing members each being disposed at a scan surface, to be scanned, of corresponding one of said optical scanning systems, for forming images of different colors.

21. A color image forming apparatus according to claim 20, further comprising a printer controller for converting a color signal supplied from an outside machine into imagewise data of different colors and for inputting the imagewise data into corresponding optical scanning systems.

Description

FIELD OF THE INVENTION AND RELATED ART

This invention relates to an optical scanning system and an image forming apparatus using the same. More particularly, the present invention concerns an optical scanning system which can be suitably used in a laser beam printer (LBP) having an electrophotographic process, a digital copying machine or a multi-function printer, for example.

With regard to optical scanning systems having a reciprocating optical deflector as an optical deflector (deflecting means) for reflectively deflecting a light beam, many proposals have already been made such as, for example, Patent Documents Nos. 1 and 2 below.

In Patent Document No. 1, a light beam (rays of light) is multi-reflected between a sine-motion oscillation mirror (deflecting surface) and two fixed mirrors disposed opposed to the oscillation mirror, by which the scan angle of the light beam is enlarged.

Patent Document No. 1: Japanese Laid-Open Patent Application, Publication No. 2004-191416

Patent Document No. 2: Japanese Laid-Open Patent Application, Publication No. 2005-173082

If in Patent Document No. 1 the scan angle of the light beam is enlarged, since the light beam is multi-reflected by using a combination of a small oscillation mirror and two fixed mirrors which could inherently be constituted only by a single oscillation mirror, the structure becomes very complicated. Hence, it is undesirable from the standpoint of smallness in size.

Furthermore, in Patent Document No. 1, because the light beam is multi-reflected, the size of the oscillation mirror (deflecting surface) has to be made large in the main scan direction. This is unfavorable for high-speed scan. Additionally, it inevitably causes deformation of the oscillation mirror surface due to angular acceleration or air resistance during the sine oscillation.

In order to meet this, in Patent Document No. 1, as the oscillation angle of the oscillation mirror is made larger, a focus error resulting from deformation of the oscillation mirror is corrected by finely oscillating a coupling lens in synchronism with the oscillation period.

In the structure in which the scan angle of the light beam is enlarged by means of multiple reflections, as the oscillation angle of the oscillation mirror becomes larger, the light beam goes through the end portion of the oscillation mirror. This means that, as the deflection angle (oscillation angle) increases, the influence of the deformation amount of the oscillation mirror becomes large.

Therefore, as the deflection angle (oscillation angle) increases, the amount of focus error becomes large. This is the very reason for that the structure of Patent Document No. 1 requires quite complicated control of finely oscillating the coupling lens in synchronism with the oscillation period.

Moreover, in reciprocating type optical deflectors, reciprocating motion is inevitably followed by dynamic deformation of the deflecting surface in the main scan direction.

If the deflecting surface of an optical deflector is deformed in the main scan direction, the light beam reflected by that deflecting surface is affected by wavefront aberration of an amount twice the amount of deformation of the deflecting surface. This seriously deteriorates the imaging performance.

In Patent Document No. 2, on the other hand, in an attempt to reducing deformation of a deflection mirror surface in the main scan direction, slots are formed at the back of the deflection mirror, and the area of these slots as well as the disposition density of them are made different with the position in the main scan direction.

Furthermore, Y-shaped support beams for pivotally supporting the deflection mirror are used at two locations on the deflection mirror which locations are different with respect to the main scan direction, so as to reduce deformation of the deflection mirror surface in the main scan direction.

On the other hand, some of the optical scanning systems having a reciprocating optical deflector do not use a plane tilt correction optical system in their imaging optical system, taking an advantage that the deflecting surface is only one.

Such systems however involve a problem that, if deformation of the deflection mirror in the main scan direction changes with the position of the deflection mirror in the sub-scan direction, the imaging performance is deteriorated thereby.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an optical scanning system which is small in size and is capable of outputting high-quality images, and also to provide an image forming apparatus having such optical scanning system.

In accordance with an aspect of the present invention, to achieve the above object, there is provided an optical scanning system, comprising: light source means; deflecting means configured to scanningly deflect a light beam from said light source means in a main scan direction; an imaging optical system configured to image, upon a surface to be scanned, the light beam deflected by a deflecting surface of said deflecting means; wherein said deflecting surface is configured to perform reciprocating motion by which the surface to be scanned is reciprocatingly scanned in the main scan direction with the light beam deflected by said deflecting surface of said deflecting means; wherein a first direction refers to a direction of a phase difference of wavefront aberration in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface at an effective deflection angle of the same corresponding to a largest scan position in an effective scan region on the surface to be scanned, the phase difference being produced as a result of reflection of the light beam by the deflecting surface; wherein a second direction refers to a direction of the phase difference of wavefront aberration in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface at an effective deflection angle thereof, the phase difference being produced as a result of transmission of the light beam through said imaging optical system; and wherein at least one optical system inside said imaging optical system is provided with at least one optical surface of non-arculate shape in a main scan section, so as to assure that the first and second directions are made opposite to each other.

Briefly, in accordance with the present invention, an optical scanning system by which deterioration of a focused spot on the surface to be scanned can be reduced significantly even where a reciprocation type optical deflector is used, as well as an image forming apparatus having such optical scanning system, are accomplished.

These and other objects, features and advantages of the present invention will become more apparent upon a consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view along a main-scan section, for explaining a first embodiment of the present invention.

FIG. 2 is a schematic view for explaining the state of a light beam as reflected by a deflecting surface, according to the first embodiment of the present invention.

FIG. 3 is a schematic view, showing the shape of a light spot in the scan end portion, according to the first embodiment of the present invention.

FIG. 4 is a schematic view, showing disposition of lenses of an imaging optical system in the sub-scan direction, according to the first embodiment of the present invention.

FIG. 5 is a schematic view, showing details of an optical deflector according to the first embodiment of the present invention.

FIG. 6A is a sectional view of a movable plate of an optical deflector according to the first embodiment of the present invention.

FIG. 6B is a schematic view for explaining deformation of the movable plate of the optical deflector according to the first embodiment of the present invention.

FIG. 7 is a schematic view, showing an approximation model prepared to consider deformation of the movable plate, in the first embodiment of the present invention.

FIG. 8 is a graph, showing the result of calculation made to deformation of the movable plate of the first embodiment of the present invention, in accordance with the finite element method.

FIG. 9 is a graph for explaining deformation of the movable plate where the tilt at the origin in FIG. 8 is taken as zero.

FIG. 10 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the first embodiment of the present invention.

FIG. 11 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in a comparative example.

FIG. 12 is a schematic view for explaining the shape of the wavefront (equi-phase plane) of a light beam in the main scan direction, after being reflected by a flexed distorted deflecting surface.

FIG. 13 is a schematic view for explaining the shape of the wavefront (equi-phase plane) defined after a parallel light beam (plane wave) passed through an f-.theta. lens system.

FIG. 14 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the first embodiment of the present invention.

FIG. 15 is a graph for explaining wavefront aberration as produced by deformation of the deflecting surface, in the first embodiment of the present invention.

FIG. 16 is a graph for explaining wavefront aberration as produced by an f-.theta. lens according to the first embodiment of the present invention.

FIG. 17 is a graph for explaining wavefront aberration that can be provided by correcting the wavefront aberration produced by deformation of the deflecting surface, in the first embodiment of the present invention.

FIG. 18 is a sectional view along a main scan section, for explaining a second embodiment of the present invention.

FIG. 19 is a schematic view, showing details of an optical deflector according to the second embodiment of the present invention.

FIG. 20 is a schematic view for explaining the principle of an optical deflector according to the second embodiment of the present invention.

FIG. 21 is a schematic view, showing a model for explaining a resonance type optical deflector having two movable plates.

FIG. 22 is a graph for explaining the oscillation angle (deflection angle) of a movable plate of an optical deflector according to the second embodiment of the present invention.

FIG. 23 is a graph for explaining the angular speed of a movable plate of an optical deflector according to the second embodiment of the present invention.

FIG. 24 is a graph for explaining the angular speed of a movable plate, in a comparative example wherein there is Mode 1 only.

FIG. 25 is a graph, showing an idealistic image height where the scan is made by using an idealistic f-.theta. lens in the second embodiment as well as an actual image height where the scan is made by using the same f-.theta. lens.

FIG. 26 is a graph, showing the difference (f-.theta. error) between two curves in FIG. 23.

FIG. 27 is a graph, showing an f-.theta. error of an f-.theta. lens according to the second embodiment of the present invention.

FIG. 28 is a graph for explaining the angular acceleration of a movable plate of an optical deflector according to the second embodiment of the present invention.

FIG. 29 is a graph for explaining the angular acceleration of a movable plate, in a comparative example wherein there is Mode 1 only.

FIG. 30 is a graph, showing the result of calculation made to deformation of the movable plate of the second embodiment of the present invention, in accordance with the finite element method.

FIG. 31 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the second embodiment of the present invention.

FIG. 32 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the second embodiment of the present invention.

FIG. 33 is a graph, showing the spot diameter in the main scan direction upon a photosensitive drum surface, in the second embodiment of the present invention.

FIG. 34 is a schematic view for explaining the state of scan lines on the photosensitive drum surface, in the second embodiment of the present invention.

FIG. 35 is a sectional view along a main-scan section, for explaining a third embodiment of the present invention.

FIG. 36 is a graph, showing the result of calculation made to deformation of a movable plate of the third embodiment of the present invention, in accordance with the finite element method.

FIG. 37 is a graph, showing the result of calculation made to deformation of a movable plate of the third embodiment of the present invention, in accordance with the finite element method.

FIG. 38 is a schematic and perspective view for three-dimensionally illustrating the amount of deformation of a movable plate in the third embodiment of the present invention.

FIG. 39 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the third embodiment of the present invention.

FIG. 40 is a schematic view, showing profiles of spots at respective scan positions on the surface to be scanned, in the third embodiment of the present invention.

FIG. 41 is a schematic view for explaining the magnitude relation in wavefront with respect to the sub-scan direction, which is defined after a parallel light passed through an f-.theta. lens system.

FIG. 42 is a schematic and sectional view, along the sub-scan section, of an image forming apparatus according to an embodiment of the present invention.

FIG. 43 is a schematic and sectional view, along the sub-scan section, of a color image forming apparatus according to an embodiment of the present invention.

FIG. 44 is a schematic view for explaining wavefront aberration being produced by an f-.theta. lens system according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will now be described with reference to the attached drawings.

Embodiment 1

FIG. 1 illustrates a section (main scan section) of a main portion of a first embodiment of the present invention, in the main scan direction.

In this specification, the term "main scan direction" refers to a direction perpendicular to the deflecting axis of an optical deflector and to the optical axis of an imaging optical system; that is, the direction along which a light beam is scanningly deflected by the optical deflector. The term "sub-scan direction" refers to a direction parallel to the deflecting axis of the optical deflector.

Furthermore, the term "main scan section" refers to a plane which contains the main scan direction and the optical axis of the imaging optical system. The term "sub-scan section" refers to a section which is parallel to the optical axis of the imaging optical system and is perpendicular to the main scan section.

Denoted in FIG. 1 at 1 is light source means which may comprise a semiconductor laser, for example. Denoted at 2 is an aperture stop that serves to restrict the width of a light beam passing therethrough to determine the beam diameter of the same.

Denoted at 3 is a condensing optical system (collimator lens) having a function for converting a divergent light beam from the light source means 1 into a parallel light beam. Denoted at 4 is a lens system (cylindrical lens) that has a predetermined power (refractive power) only in the sub-scan section (sub-scan direction).

The lens system 4 functions to image the light beam, having been converted by the collimator lens 3 into a parallel light with respect to the sub-scan section, upon a deflecting surface 6a of an optical deflector (deflecting means) 6, to be described later, as an approximately linear image.

Denoted at 5 is a mirror which serves to deflect the light beam, passed through the cylindrical lens 4, with respect to the main scan direction and to direct the same to the optical deflector 6.

Here, the collimator lens 3 and the cylindrical lens 4 are structural components of an input (light incidence) optical system LA. The collimator lens 3 and the cylindrical lens 4 may be replaced by an integral structure of a single optical element (anamorphic lens).

The optical deflector (deflecting means) 6 comprises a resonance type optical deflector, having its deflecting surface 6a configured to perform reciprocating sine motion based on resonance. In this embodiment, the deflecting surface 6a of the optical deflector 6 reciprocates and, through this reciprocation, the surface 8 which is going to be scanned is reciprocatedly scanned in the main scan direction with the light beam provided by the input optical system LA.

The reciprocating motion of the deflecting surface 6a of the optical deflector 6 is based on resonance drive, and it is done in accordance with sine oscillation.

Denoted at 7 is an imaging optical system (f-.theta. lens system) including first and second imaging lenses (f-.theta. lenses) 71 and 72. It functions to image the light beam, produced on the basis of imagewise information and having been reflectively deflected by the optical deflector 6, upon the surface (surface to be scanned) 8 of a photosensitive drum.

The first and second f-.theta. lenses 71 and 72 that constitute the imaging optical system 7 of this embodiment are configured to reduce wavefront aberration of the light beam in the main scan section, which is produced in accordance with the amount of deformation of the deflecting surface 6a of the optical deflector 6 as the same is deformed in the main scan section during the reciprocating motion.

Denoted at 8 is the photosensitive drum surface, which is the surface to be scanned.

In this embodiment, a divergent light beam from the semiconductor laser 1 having been optically modulated in accordance with the imagewise information is rectified by the aperture stop 2 in terms of the light beam width and the sectional shape, and then it is converted into a parallel light beam by means of the collimator lens 3.

Subsequently, through the cylindrical lens 4 and the mirror 5, the light beam is projected on the deflecting surface 6a (in frontal incidence) from the center of the oscillation angle (deflection angle) of the optical deflector 6 with respect to the main scan section.

With regard to the sub-scan section, on the other hand, the light beam is incident on the deflecting surface 6a (in oblique incidence) with a finite angle with respect to the sub-scan direction.

By means of the reciprocating motion of the deflecting surface 6a of the optical deflector 6, the light beam is deflectively reflected in the main scan direction and is directed to the photosensitive drum surface 8 through the f-.theta. lens system 7. Hence, through the reciprocating motion of the deflecting surface 6a of the optical deflector 6, the photosensitive drum surface 8 is scanned with the light beam in the main scan direction. Through this process, image recording on the photosensitive drum (recording medium) is carried out.

The optical deflector 6 in this embodiment comprises a resonance type optical deflector, having its deflecting surface 6a configured to perform reciprocating sine oscillation based on resonance.

Generally, in optical deflectors configured to perform sine oscillation, if the area of the deflecting surface thereof is enlarged, high-speed oscillation becomes difficult to accomplish. For this reason, when such a deflector is to be incorporated into a laser beam printer or a digital copying machine, for example, the size of the deflecting surface should be made as small as possible.

In this embodiment, in this respect, the light beam is projected on the deflecting surface 6a of the optical deflector as frontal incidence: that is, in FIG. 1 the light beam is projected from the upper right side (f-.theta. lens system 7 side) toward the front of the deflecting surface. In other words, in the main scan section, the light beam is projected to the front of the deflecting surface 6a of the optical deflector 7 in the optical axis direction of the imaging optical system 7.

With the frontal incidence described above, the size of the deflecting surface 6a of the optical deflector 6 (i.e. the width in the main scan direction) can be made smallest, and hence high-speed oscillation can be accomplished easily.

On the other hand, if the light incidence method described above is used, the light beam incident on the deflecting surface 6a of the optical deflector may interfere with the light beam deflectively reflected by the deflecting surface 6a. To avoid this, the light beam is projected onto the deflecting surface 6a such that it is incident thereupon with a finite incidence angle in the sub-scan direction, with respect to a plane normal line to the deflecting surface 6a (i.e., an oblique-incidence optical system is provided).

Specifically, in this embodiment, the light beam is incident on the deflecting surface 6a with an incidence angle of 2 degrees in the sub-scan direction, to the plane-normal-line of the deflecting surface 6a, from below as viewed in the sub-scan direction (from below in the sheet of FIG. 1).

As a result of this, the light beam to be deflectively reflected by the deflecting surface 6a is similarly deflectively reflected with an angle of 2 degrees in the sub-scan direction to the plane-normal-line of the deflecting surface 6a, upwardly in the sub-scan direction (upwardly in the sheet of FIG. 1).

The f-.theta. lens system 7 which is an imaging optical system is disposed upwardly in the sub-scan direction and at a predetermined distance to make it sure that the deflected light beam having been upwardly deflectively reflected is incident thereupon. The deflected light beam thus incident on the f-.theta. lens system (imaging optical system)-7 is imaged on the photosensitive drum surface 8 as a light spot.

As described hereinbefore, the deflecting surface 6a of the optical deflector 6 is reciprocatingly oscillated in the main scan direction, within the range of largest amplitude (largest deflection angle) .+-..phi.max. More specifically, the deflecting surface 6a performs the sine oscillation in which the deflection angle (oscillation angle) .phi. can be expressed in terms of angular frequency .omega. and time t as follows: .phi.=.phi.maxsin .omega.t

In the optical deflector 6 of this embodiment, the largest amplitude .phi.max of the deflecting surface 6a is .+-.36 degrees. The range of .+-.22.5 degrees out of this amplitude is chosen as an effective deflection angle, and it is used for the image writing.

Generally, in many cases, an arcsine lens is used an imaging lens for converting a light beam deflectively reflected by a sine-oscillation optical deflector into a uniform-motion light beam on the surface to be scanned. Arcsine lenses have an optical characteristic that, as compared with the scan central portion of the surface to be scanned, the F-No. (F number) of the scan end portion of the surface to be scanned with respect to the main scan direction is liable to become larger. This leads to a problem that, as compared with the spot diameter, in the main scan direction, in the scan centreal portion of the surface to be scanned, the spot diameter in the scan end portion of the surface to be scanned, with respect to the main scan direction, becomes larger.

This is a phenomenon that results from scanning the light beam, having a sinusoidally changing angular speed, at uniform speed on the surface to be scanned. If there is irregularity in the spot diameter in the scan direction, on the surface to be scanned as described above, it causes various inconveniences such as deterioration of gradation reproducibility of a half-tone image, local deterioration of linewidth reproducibility of fine lines, and so on.

In this embodiment, in order to meet these, the imaging lens is provided by f-.theta. lenses 71 and 72 having a characteristic that, inside the effective scan region, the spot diameter in the main scan direction on the surface to be scanned can be kept constant.

On the other hand, if an f-.theta. lens is used simply as an imaging lens in combination with a sine-oscillation optical deflector 6, it raises a problem that, as compared with the scan central portion (optical axis of the f-.theta. lens system 7) on the photosensitive drum surface 8, the scan speed at the scan end portion becomes slower to cause contraction of an image in the main scan direction.

In this embodiment, in order to meet this, the modulation clock of the semiconductor laser 1 is changed continuously in synchronism with the scan position, in the main scan direction, on the photosensitive drum surface 8. The inconvenience described above is removed by this.

With the structure described above, undesirable irregularity of the spot diameter in the main scan direction on the photosensitive drum surface 8 as described above can be avoided completely. As a result, inconveniences such as deterioration of gradation reproducibility of a half-tone image, local deterioration of linewidth reproducibility of fine lines, and so on, are removed assuredly.

Furthermore, the slowdown of the scan speed in the scan end portion (largest image height portion) on the photosensitive drum surface 8 as compared with the scan central portion on the photosensitive drum surface 8 means that the exposure energy on the photosensitive drum surface 8 at the scan end portion becomes larger. From this, it is seen that the gradation reproducibility of a half-tone image can be improved by the control that the quantity of light emission of the semiconductor laser 1 is continuously decreased at the scan end portion (largest image height region).

In this embodiment, as described above, the light beam deflectively reflected by the deflecting surface 6a is directed upwardly in the sub-scan direction (upward in the sheet of FIG. 1), while an angle 2 deg. (2.degree.) is defined in the sub-scan direction and with respect to the plane-normal-line of the deflecting surface 6a. FIG. 2 schematically illustrates this.

It is seen from FIG. 2 that the light beam deflectively reflected by the deflecting surface 6a defines a conical plane having its vertex placed at the deflective reflection point 6b on the deflecting surface 6a. Hence, on the plane where the light beam enters the lens, the deflectively reflected light beam forms a locus which is curved in the sub-scan direction.

If such light beam enters the f-.theta. lens system 7, the scan line on the photosensitive drum surface 8 would be curved in the sub-scan direction. Furthermore, there is an inconvenience that, if a light beam scanning along a conical plane enters the f-.theta. lens system 7, in the scan center portion the light beam can be normally focused into a spot-like shape; whereas, as the light beam comes close to the scan end portion, the shape of the focused spot would be deteriorated as shown in FIG. 3.

FIG. 3 illustrates contour lines in terms of intensity distribution of a focused spot, being deteriorated, in the scan end portion on the surface to be scanned.

The contour lines in FIG. 3 depict intensities having been sliced with respect to the levels of (from the outside) 0.02, 0.05, 0.1, 0.1353, 0.3679, 0.5, 0.75 and 0.9, respectively, with the peak intensity of the focused spot being standardized to 1. In FIG. 3, the lateral direction corresponds to the main scan direction along which the focused spot scans, and the longitudinal direction corresponds to the sub-scan direction which is orthogonal to the main scan direction.

In this embodiment, as shown in FIG. 4, of the first and second f-.theta. lenses 71 and 72, the optical axis 71a of the first f-.theta. lens 71 is disposed with an upward angle of 2 degrees so that it coincides with the principal ray of the light beam deflectively reflected by the deflecting surface 6a toward the scan center on the surface to be scanned. Namely, about the axis of the main scan direction, it is upwardly and rotationally shifted by 2 deg. (2.degree.) in the sub-scan section and with respect to the normal of the deflecting surface 6a.

On the other hand, the optical axis 72a of the second f-.theta. lens 72 is disposed with a downward tilt of an angle 1.83383, in the opposite direction to the first f-.theta. lens 71, in the sub-scan section and with respect to a plane which is orthogonal to the rotational axis of the deflecting surface 6a. Namely, about the axis of the main scan direction, it is downwardly and rotationally shifted by 1.83383 deg. in the sub-scan section and with respect to the normal to the deflecting surface 6a.

Furthermore, the second f-.theta. lens 72 is disposed with a shift of a predetermined amount in the sub-scan direction, so as to make it sure that the light beam is incident at a position above the plane vertex 72b, in the sub-scan section, of the first surface (light entrance surface) of the second f-.theta. lens 72.

With the arrangement described above, curvature of scan lines on the photosensitive drum in the sub-scan direction as well as deterioration of focused spots at the scan end portion on the surface to be scanned are both well corrected.

Next, the optical deflector 6 of this embodiment will be explained in greater detail. As described hereinbefore, the optical deflector 6 comprises a resonance type optical deflector, having its deflecting surface 6a configured to perform reciprocating sine motion based on resonance.

FIG. 5 shows details of the optical deflector 6 in this sembodiment. As shown in FIG. 5, the optical deflector 6 comprises a movable plate 67 and a torsion spring 26 for resiliently supporting the movable plate 67 and mechanical ground supports 25. All of these components are torsionally oscillated by driving means 16 around a torsional axis C (an axis parallel to the sub-scan direction). The driving means 16 may comprise a fixed electromagnet coil and a movable magnet mounted on the movable plate 67, for example.

The movable plate 67 is provided with a deflecting surface (not shown) for deflecting the light beam, and the light beam from the light source means 1 is deflectively scanned on the basis of the torsional oscillation of the movable plate 67.

Generally, in optical deflectors for which high-speed motion is required, the deflecting surface thereof receives large angular acceleration since it is torsionally oscillated within a particular angle. Hence, during the drive, an inertia force due to the dead weight thereof is applied to the deflecting surface such that the deflecting surface would be distorted largely.

FIG. 6A is a sectional view, taken along a line A-A in FIG. 5, of the movable plate 67 in a case where it comprises a flat plate (rectangular parallelepiped).

The optical deflector 6 of this embodiment is driven near the resonance frequency and is torsionally oscillated. Hence, the deflection angle of the movable plate 67 with respect to time changes sinusoidally. Thus, at the moment whereat a largest angular speed is applied (e.g., largest deflection angle in the case of sine oscillation), largest deformation occurs.

FIG. 6B shows deformation of the movable plate 67 at that moment. It is seen from FIG. 6B that, if the movable plate 67 deforms, the deflecting surface 6a formed on the movable plate 67 is deformed similarly.

Where the movable plate 67 comprises a rectangular parallelepiped, deformation of the movable plate 67 during torsional oscillation can be explained by using an approximation model shown in FIG. 7.

The illustration made in FIG. 7 corresponds specifically to the right-hand half of the sectional view of the movable plate 67 in FIG. 6A. The deformation of the movable plate 67 is point-symmetrical about the torsional axis C, and it can be approximated as a deformation of a structural beam having its central portion fixed-end supported as illustrated in the drawing.

When an angular acceleration .theta.x(2.pi.f).sup.2 (where .theta. is the deflection angle and f is a torsional oscillation frequency) is applied to the movable plate 67 due to torsional oscillation, a resultant deformation (distortion) y of the structual beam shown in FIG. 7 can be given by Equation (1) below.

.theta..times..pi..rho..times..times. ##EQU00001## wherein:

x is the distance from the torsional axis C shown in FIG. 7;

.rho. is the density of the movable plate 67;

E is the Young's modulus of the movable plate 67;

t is the thickness of the movable plate 67; and

W.sub.h is a half value of the width D of the deflecting surface in the main scan direction.

From Equation (1) it is seen that, since the deformation (distortion) y is proportional to the deflection angle .theta., the fifth power of W.sub.h and the square of the frequency f, the influence of deformation of the movable plate 67 due to the dead weight thereof would be notable in a case where the width of the deflection surface in the main scan direction is large (namely, the deflection surface opening is large), a case where the deflection angle is large and a case where high frequency drive is necessary.

The optical deflector 6 of this embodiment is arranged so that the natural oscillation frequency of the torsional oscillation is 2 KHz, the width (the value of aforementioned W) of the movable plate 67 in the main scan direction is 3 mm, the width thereof in the sub-scan direction is 1 mm, and the thickness t is 200 .mu.m. As described above, the movable plate 67 receives an inertia force due to the dead weight thereof during the oscillation, and it is deformed thereby.

FIG. 8 is a graph showing the result of calculation made to the deformation of the movable plate 67 in accordance with the finite element method. It shows deformation of the A-A section in FIG. 5 in a case where the mechanical effective deflection angle during 2 KHz driving is +22.5 degrees. Here, the tilt of connection between the torsion spring 26 and the movable plate 67 (that is, the portion B in FIG. 5) was taken as zero.

Here, definitions of the scan angle and the deflection angle are given as follows.

The scan angle can be specified as an angle defined in the main scan section and between the optical axis of the imaging optical system 7 and the principal ray of the light beam deflectively scanned by the deflecting surface of the optical deflector 6. Hence, the scan angle is twice the deflection angle (oscillation angle).

Here, it is assumed that, while taking the scan center (optical axis of the imaging optical system 7) of the scan line on the surface to be scanned as a center, the deflection angle at the scan-line-writing-start-position side on the surface to be scanned (upper in the sheet of FIG. 1 and on the opposite side of the input optical system LA) has a positive (+) sign.

On the other hand, it is assumed that, while taking the scan center (optical axis of the imaging optical system 7) of the scan line on the surface to be scanned as a center, the deflection angle at the scan-line-writing-end-position side on the surface to be scanned (lower in the sheet of FIG. 1 and at the input optical system LA side) has a negative (-) sign.

The direction of positive sign of y in FIG. 8 corresponds to the advancement direction (rightward direction in the drawing) of the light beam reflected by the deflecting surface 6a in FIG. 1, whereas the direction of positive sign of x corresponds to the scan-line-writing-start-position side of the deflecting surface 6a in FIG. 1 (upper in the sheet of FIG. 1 and on the opposite side of the input optical system LA).

FIG. 9 is a graph showing deformation of the A-A section in FIG. 5, wherein the tilt at the origin in the graph of FIG. 8 is taken as zero. It is seen in FIG. 9 that a deformation analogous to the deformation y given by Equation (1) above was obtained, and that the movable plate 67 was deformed by torsional oscillation.

Here, if the deflecting surface 6a of the optical deflector 6 is being deformed such as shown in FIG. 9, the light beam reflected by the deflecting surface 6a would have wavefront aberration of an amount twice the deformation y shown in FIG. 9. Hence, an adverse influence would be exerted to the focused spot on the photosensitive drum surface 8.

Actually, from FIG. 9, it is seen that coma of wavefront aberration was being produced.

In optical scanning systems having a rotational polygonal mirror as an optical deflector 6, since the rotational polygonal mirror is being rotated at a constant angular speed, the angular acceleration is continuously zero. Hence, a large angular acceleration is not put on it as compared with optical deflectors using sine oscillation. Normally, therefore, wavefront aberraton such as mentioned above would not be produced.

For these reasons, when an imaging lens to be used in optical scanning systems having a rotational polygonal mirror is designed, in many cases no particular attention is paid to the deformation of the deflecting surface.

However, if an optical deflector having sine oscillation is used in combination with an imaging lens having been designed as above (namely, without paying attention to deformation of the deflecting surface), due to wavefront aberration caused by deformation of the deflecting surface 6a the focused spot would be deteriorated.

FIG. 10 shows an example wherein an imaging lens having been designed to be used with a rotational polygonal mirror is used and, on the other hand, an optical deflector according to this embodiment (natural oscillation frequency of the torsion oscillation is 2 KHz, the width W of the movable plate in the main scan direction is 3 mm, the width thereof in the sub-scan direction is 1 mm, and the thickness t is 200 .mu.m) is used as an optical deflector.

FIG. 10 illustrates the shapes of spots on the photosensitive drum 8 surface where the mechanical deflection angle is +22.5 degrees, +21.028 degrees, +16.822 degrees, +12.617 degrees, +8.411 degrees, +4.206 degrees and 0.0 degree, respectively.

Furthermore, similarly to FIG. 3, contours of the intensity distribution of each spot are illustrated there. These contours correspond to the intensities being sliced with respect to the levels of (from the outside) 0.02, 0.05, 0.1, 0.1353, 0.3679, 0.5, 0.75 and 0.9, respectively, when the peak intensity of the focused spot is standardized to 1.

As a comparative example, FIG. 11 shows shapes of spots on the photosensitive drum surface 8 in a case where the same imaging lens is used and the deflecting surface 6a is not deformed at all. In these drawings, similarly to FIG. 3, the lateral direction corresponds to the main scan direction along which the spot scans the surface, while the longitudinal direction corresponds to the sub-scan direction which is orthogonal to the main-scan direction.

It is seen from FIGS. 10 and 11 that the spot shapes in FIG. 10 where the deflecting surface 6a is being deformed include a large sidelobe in the main scan direction, as compared with the shapes of the focused spots shown in FIG. 11 where the deflecting surface 6a is not deformed at all.

In addition to this, the outer configuration itself of the focused spot is distorted asymmetrically, and the shape of the focused spot is deteriorated seriously. Furthermore, in the case of effective deflection angle +22.5 degrees, the peak intensity of the sidelobe exceeds 0.05 (namely, 5% of the peak intensity of the main spot).

It is well known that the image quality degrades as the peak intensity of a sidelobe becomes large. Particularly, when the peak intensity of the sidelobe exceeds 5% with respect to the peak intensity of a main spot, deterioration of image quality becomes quite large. This is undesirable for optical scanning systems image forming apparatuses where high quality image output is required.

Also it is seen that the larger the deflection angle is, the larger the deterioration of the spot shape of the focused spot is. The reason is that, as described hereinbefore, the larger the largest deflection angle of the deflecting surface is, the larger the deformation of the deflection surface is.

In this embodiment, to meet this, the effective deflection angle of the deflecting surface corresponding to the end portion (largest image height) of the scan line inside the effective image region on the surface to be scanned is made equal to .+-.22.5 degrees.

In order to reduce deterioration of the spot shape of the focused spot, the effective deflection angle of the deflecting surface should preferably be made not greater than .+-.30 degrees.

As described above, if an optical deflector having sine oscillation is used in combination with an imaging lens having been designed without attention to deformation of the deflecting surface, the focused spot would be deteriorated due to the wavefront aberration resulting from deformation of the deflecting surface 6a. If this occurs, it becomes very difficult to accomplish optical scanning systems or image forming apparatuses which are required to produce high quality image outputs.

The first and second f-.theta. lenses 71 and 72 of this embodiment shown in FIG. 1 are configured to reduce the amount of wavefront aberration produced by the deflection surface 6a, being distorted as shown in FIG. 9 due to application of large angular acceleration thereto as a result of its sine oscillation.

Here, in this embodiment, the term "first direction" is now used to refer to the direction of the phase difference of wavefront aberration in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface 6a at an effective deflection angle of the same, the phase difference being produced as a result of reflection of the light beam by that deflecting surface. Furthermore, the term "second direction" is used to refer to the direction of the phase difference of wavefront aberration in the main scan direction between a marginal ray and a principal ray of the light beam reflected by the deflecting surface 6a at an effective deflection angle thereof, the phase difference being produced as a result of transmission of the light beam through the imaging optical system 7.

Then, in this embodiment, at least one optical system inside the imaging optical system 7 is provided with at least one optical surface having non-arculate shape in the main scan section, so as to assure that the first and second directions mentioned above are made opposite to each other.

Here, the words "light beam reflected by the deflecting surface at an effective deflection angle thereof" refer to a light beam that reaches the scan end portion (largest image height) of the scan line inside the effective image region on the surface to be scanned.

The optical principle for that will be explained below.

FIG. 12 is a schematic view, showing the shape W1 of the wavefront (equi-phase plane) in the main scan direction, of the light beam after an inputted parallel light beam (plane wave) is reflected by the distorted deflecting surface 6a as shown in FIG. 9.

The direction y in FIG. 12 corresponds to the