F-Theta lens and image forming apparatus using the same

Abstract: This specification disloses an fϑ lens acting to effect uniform speed scanning while causing a light beam deflected at a uniform angular velocity by the deflecting surface of a deflector to be imaged on a plane to be scanned, wherein the shape of the curved surface of at least the lens surface of the lens which is adjacent to the deflection point side of the deflecting surface in the main scanning plane is an aspherical shape and particularly, near the optical axis, in at least the main scanning plane, this aspherical shape is convex toward the deflection point, and when the radius of curvature of this convex shape near the optical axis in the main scanning plane is r₁ and the focal length of the fϑ lens near the optical axis in the main scanning plane is fm, 0 ≦ r₁<|fm| and yet, when with the point of intersection between the lens surface adjacent to the deflection point side and the optical axis as the origin and with the coordinates system of the x-axis plotted in the direction of the optical axis and the coordinates system of the y-axis plotted in the main scanning plane perpendicularly thereto, the surface shape in the main scanning plane is expressed as a function S₁(y) in which y is a variable, and when the maximum effective diameter of this surface in the main scanning plane is Ymax, S₁(y) is defined between 0 and Ymax, and when r₁ < Ymax, -1 < S₁(r₁)/r₁ < 0.5 and when r₁ ≧ Ymax, -1 x Ymax/r₁ < S₁(Ymax)/Ymax < 0.5 x Ymax/r₁. The specification also discloses an image forming apparatus using such fϑ lens.

Description: BACKGROUND OF THE INVENTION Field of the Invention This invention relates to an fϑ lens used in a laser scanning optical system or the like, and particularly to an fϑ lens comprised of a lens and an image forming apparatus using the same. Related Background Art An fϑ lens is known for example from JP-A-63-238417. The preamble of Claim 1 corresponds to this document. Heretofore, in a scanning optical system, chiefly a laser source such as a semiconductor laser has been used as a light source and light from the light source has been imaged on a plane to be scanned through an optical system to thereby form a laser spot, and the laser source has been subjected to modulation conforming to image information while the laser spot is scanned on the plane to be scanned by a deflector such as a polygon mirror disposed in the optical path, whereby a desired image has been formed on the plane to be scanned. Where such a laser scanning optical system is particularly an optical system which scans a laser by the rotation of a deflector such as a polygon mirror, it is desirable that a laser spot be uniformly formed on the whole plane to be scanned (that is, the curvature of image field of a lens system be corrected) and the angle of rotation of the deflector and the position of the spot formed on the plane to be scanned have a proportional relation (that is, the speed of the spot scanned on the plane to be scanned become constant on the whole plane to be scanned, i.e., have constant speed property.). For this purpose, a correcting optical system is used between the polygon mirror and the plane to be scanned. Usually, this lens for correction used in the laser scanning system is a lens called an fϑ lens having such a distortion characteristic that the angle of incident light and the image height are in a proportional relation, so as to have constant speed property. Further, even where a mirror surface which is the deflecting surface of the deflector has an inclination, it is regarded as desirable from the viewpoints of the manufacture of the deflector and the quality of image to have optical correcting means so that the position of the scanning line may not deviate (inclination correcting function). There have been made numerous inventions relating to an fϑ lens having such inclination correcting function. Particularly, regarding a type in which the number of constituent lenses is two or more, many inventions have been made and put into practical use. In contrast, several fϑ lenses in which the lens system is constructed of a lens have also been devised as simpler optical systems. As seen, for example, in Japanese Laid-Open Patent Application Nos. 55-7727 and 58-5706, there is an example in which an fϑ lens is comprised of a spherical lens. Also, like Japanese Laid-Open Patent Application Nos. 63-50812 and 1-224721, there is an example in which a toric surface is used as a lens surface and yet an fϑ lens is constructed. Further, in Japanese Laid-Open Patent Application Nos. 54-87540 and 54-98627, there is disclosed an example in which an aspherical surface term is introduced into a single lens, and in Japanese Laid-Open Patent Application Nos. 62-138823, 63-157122 and 2-87109, there is disclosed an example in which a high-order aspherical surface is introduced into a lens surface to thereby construct an fϑ lens. However, in the plano-convex fϑ lens disclosed in Japanese Laid-Open Patent Application No. 55-7727 among the above-mentioned examples of the prior art, constant speed property is corrected, but curvature of image field remains and it is difficult to keep the uniformity of spot. In this case, if design is made such that the size of the effective scanning width by this lens is sufficiently large relative to the plane to be scanned, curvature of image field can be made small, but the entire apparatus will become bulky, and this cannot be said to be practical. In Japanese Laid-Open Patent Application No. 58-5706, the fϑ lens comprising a spherical lens is made into a meniscus lens having its concave surface facing the deflecting surface side to thereby accomplish aberration correction, but as in Japanese Laid-Open Patent Application No. 55-7727, an attempt to sufficiently correct curvature of image field and constant speed property at a time would give rise to the necessity of making the distance between this lens and the plane to be scanned great. In Japanese Laid-Open Patent Application No. 63-50812, a toric lens is used to make a lens in which curvature of image field and constant speed property are corrected. Particularly, the aberrations in the main scanning plane (curvature of image field and constant speed property) and the aberrations in the sub-scanning plane perpendicular to the main scanning plane can be corrected independently and therefore, better correction than in the aforedescribed two examples is accomplished. Further, the deflecting surface and the plane to be scanned are made into a conjugate relation on the sub-scanning cross-section, thereby accomplishing the correction of the inclination of the mirror surface of the deflector as well. The distance from the deflecting surface to the plane to be scanned is also kept relatively small. However, a toric lens, if viewed only in the main scanning plane, is equivalent to a spherical single lens, and it is difficult to correct curvature of image field and constant speed property at a time. Therefore, to provide a lens shape in which aberrations are good, it is necessary to make the thickness t of the lens considerably great relative to the focal length f, i.e., 0.3 < t/f < 0.5, as described in this patent application. For this reason, as an actual lens, the manufacture thereof is difficult and the use of a single lens will lead to no merit. In Japanese Laid-Open Patent Application No. 1-224721, a toric lens is also used and further, design is made such that convergent light is caused to enter the toric lens, thereby accomplishing aberration correction, but as in Japanese Laid-Open Patent Application No. 63-50812, even in the main scanning plane alone, it is difficult to make curvature of image field and constant speed property compatible. In this example, as described in the specification thereof, constant speed property is restricted to such a degree of correction that it can be electrically corrected (expressed as substantially constant speed in the specification), whereby the correction of curvature of image field is effected preponderantly. Thus, during image writing, the timing of image information is varied to thereby correct the distortion of the written image. In this case, however, constant speed property is under-corrected and thus, the speed of the spot on the plane to be scanned varies at all times, and the quantity of light received per unit time by the plane to be scanned is varied. It is possible to correct this by varying the quantity of laser light produced from the light source, but this will lead to too many correcting circuits, which does not mean the obtainment of the merit of using a single lens. In the case of a single lens whose lens shape is a spherical shape in the main scanning plane as in these examples, it has been difficult to realize an fϑ lens having a sufficient characteristic. In contrast, as described in Japanese Laid-Open Patent Application Nos. 54-87540 and 54-98627, there is known an example in which an aspherical term is introduced to construct an fϑ lens. The aspherical lenses described in Japanese Laid-Open Patent Application Nos. 62-138823, 63-157122 and 1-99013 are such that the shape of the lens near the optical axis thereof is that of a meniscus lens in which the deflecting surface side is a concave surface or a biconvex lens, and in any of these lenses, the thickness t of the lens is great relative to the width of the plane to be scanned. The example shown in Japanese Laid-Open Patent Application No. 62-138823 is a meniscus lens in which the deflecting surface side is a concave surface or a biconvex lens, but the thickness of the lens is 20 mm at smallest relative to the effective scanning width of 200 mm. The example shown in Japanese Laid-Open Patent Application No. 63-157122 is a meniscus lens in which near the optical axis, the deflecting surface side is a concave surface, but the thickness of the lens is 30 mm at smallest relative to the maximum scanning width (the scanning width corresponding to the angle of view mentioned as the maximum scanning angle ϑmax in the specification; 254 mm or so in any embodiment). The example shown in Japanese Laid-Open Patent Application No. 2-87109 is a lens which is biconvex near the optical axis and therefore, the thickness of the lens is also great. It is difficult to make such aspherical lenses by carrying out the processing as is done in the manufacture of ordinary spherical lenses. Therefore, processing and molding are carried out by the use of materials such as plastics rich in workability to make such aspherical lenses, thereby solving the problem in manufacture. However, plastics are generally apt to be affected by environmental fluctuations, and are particularly apt to be varied in refractive index by humidity and temperature. Especially, where the thickness of the lens is great, a light beam passing therethrough is greatly subjected to a variation in refractive index and thus, the imaging position is varied by environmental fluctuations. Further, a great thickness of the lens is a factor which increases internal homogeneity, distortion, molding termination time, etc. in carrying out processing and molding. Thus, the aspherical lenses known as the above-described three examples of the prior art could not be said to be practical because of their great lens thicknesses. Particularly in these examples, the shape of the deflection point side lens surface in the main scanning plane is not appropriate and therefore, to satisfy the performance necessary as an fϑ lens, it is necessary to make the lens thicker than the practical range, and this has been low in realizability. SUMMARY OF THE INVENTION The present invention has been made in view of the above-noted circumstances and the object thereof is to provide an fϑ lens as defined in Claim 1 which satisfies the performance required of an fϑ lens and yet whose lens thickness is kept small and which is suitable for plasticization and comprises a single lens, and an image forming apparatus as defined in Claim 12 which uses such fϑ lens, whereby the apparatus can be made compact and thin. The above object of the present invention is achieved by the fϑ lens of the present invention which will hereinafter be described and an image forming apparatus using the same. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a cross-sectional view of a first embodiment of the present invention in the main scanning plane. Figures 2A and 2B illustrate the shape of the main scanning cross-section of the surface shape of the fϑ lens of the present invention which is adjacent to the deflection point side, Figure 2A referring to a case where r₁ < Ymax, and Figure 2B referring to a case where r₁ ≧ Ymax. Figure 3 illustrates the arrangement of the entire scanning system of the fϑ lens of the present invention. Figure 4 illustrates the state of a light beam incident on the fϑ lens of the present invention in the main scanning plane. Figure 5 illustrates the radius of curvature of the fϑ lens of the present invention in the subscanning plane. Figure 6 is a cross-sectional view of a second embodiment of the present invention in the main scanning plane. Figure 7 is a cross-sectional view of a third embodiment of the present invention in the main scanning plane. Figure 8 is a cross-sectional view of a fourth embodiment of the present invention in the main scanning plane. Figure 9 is a cross-sectional view of a fifth embodiment of the present invention in the main scanning plane. Figure 10 is a cross-sectional view of a sixth embodiment of the present invention in the main scanning plane. Figure 11 is a cross-sectional view of a seventh embodiment of the present invention in the main scanning plane. Figure 12 is a cross-sectional view of an eighth embodiment of the present invention in the main scanning plane. Figures 13 to 20 show aberrations in the embodiments of the fϑ lens of the present invention. Figure 21 is a cross-sectional view of an image forming apparatus using the fϑ lens of the present invention. DESCRIPTION OF THE PREFERRED EMBODIMENTS In the fϑ lens of the present invention which is an fϑ lens comprised of a lens, the shape of the curved surface of at least the lens surface of said lens which is adjacent to the deflection point side of a deflector in the main scanning plane is an aspherical shape and particularly, near the optical axis, in at least the main scanning plane, this aspherical shape is convex toward the deflection point, and when the radius of curvature of this convex shape near the optical axis in the main scanning plane is r₁ and the focal length of the fϑ lens near the optical axis in the main scanning plane is fm, there is the relation that 0 ≦ r₁ < |fm| between r₁ and the absolute value of fm and yet, when with the point of intersection between the lens surface adjacent to the deflection point side and the optical axis as the origin and with the coordinates system of the x-axis plotted in the direction of the optical axis and the coordinates system of the y-axis plotted in the main scanning plane perpendicularly thereto, the surface shape in the main scanning plane is expressed as a function S₁(y) in which y is a variable, and when the maximum effective diameter of this surface in the main scanning plane is Ymax and S₁(y) is defined between 0 and Ymax, and when as shown, the relation between the aspherical shape and the radius of curvature near the optical axis is r₁ < Ymax, that is, when a spherical lens having the radius of curvature r₁ cannot have the effective diameter Ymax (e.g. Figure 2-a), the lens shape S₁(r₁) at a position y = r₁ satisfies -1 < S₁(r₁)/r₁ < 0.5 and when r₁ ≧ Ymax, that is, when a spherical lens having the radius of curvature r₁ can have the effective diameter Ymax (e.g. Figure 2-b), the lens shape S₁ (Ymax) at a position y = Ymax satisfies. -1 x Ymax/r₁ < S₁ (Ymax)/Ymax < 0.5 x Ymax/r₁ whereby a more practical fϑ lens is realized. In this case, if the shape of the lens surface adjacent to the deflection point side in the main scanning plane is convex toward the deflection point and does not satisfy expression (1), the constant speed property near the optical axis will be under-corrected, and if said shape does not satisfy expression (2a) or expression (2b), the correction of the curvature of image field in the main scanning surface will become insufficient. That is, it is the condition necessary for the fϑ lens of the present invention to satisfy the performance required of an fϑ lens that expression (1) and expression (2a) or (2b) be satisfied at a time. Further, in the fϑ lens of the present invention, even when a material whose refractive index is varied by an environmental fluctuation such as the fluctuation of humidity or temperature is chosen as the material of the lens, so that the influence thereof may be small, the thickness t of the lens, relative to the effective scanning width L (see Figure 3), can be kept in a range expressed as 0 < t/L < 0.08 or when the distance from the deflecting surface of the lens to the plane to be scanned is g, the thickness t can be kept in a range expressed as 0 < t/g < 0.15 and the fluctuation of the imaging position by an environmental fluctuation can be kept small. Further, the choosing the lens shape so that the shape of the lens near the optical axis may be a convex meniscus lens in at least the main scanning plane, the thickness of the lens can be kept small and yet, the thickness of the lens near the optical axis and the thickness of the lens in the effective end portion thereby can be made not to differ greatly from each other to thereby improve the homogeneity during processing and molding, and processing conditions such as distortion and processing time. Also, by choosing the focal length fm of the lens near the optic axis in the main scanning plane relative to the distance g from the deflecting surface to the plane to be scanned so as to satisfy |fm|/g > 0.8 and by using an aspherical lens, assemblage property such as the mounting accuracy of the lens can be prevented from being remarkably aggravated. In this case, the sign of fm may be + or -. Also, if the light beam incident on this lens is made into convergent light in at least the main scanning plane, the distance from the lens to the plane to be scanned can be shortened to thereby make the size of the entire scanning system small. In this case, when the distance from the deflection point to a point at which this convergent light is imaged in the main scanning plane is p and the distance from the deflection point to the plane to be scanned is g (see Figure 4), design is made such that convergent light which will satisfy the condition that 0.7 < p/g is caused to be incident on the lens, the aggravation of the constant speed property in the end portion of the plane to be scanned which is caused by the lens being made compact can be suppressed within a practical range. On the other hand, if this incident light beam is made into substantially parallel light in at least the main scanning plane, there will be a limit in making the lens compact, but it will become possible to alleviate the mutual mounting accuracy of the deflection point and the fϑ lens. In the fϑ lens of the present invention, the lens shape is not made into an axis-symmetrical lens shape and with regard to at least one of the curved surface on the deflection point side and the curved surface on the side of the plane to be scanned, the radius of curvature near the optical axis differ between the main scanning cross-section and the sub-scanning cross-section (a cross-section perpendicular to the main scanning cross-section and containing the optical axis), whereby the curvature of image field in the sub-scanning direction (a direction perpendicular to the direction in which the light beam is scanned by an optical deflector and the direction of the optical axis) can be kept small than when the lens is constructed of only an axis-symmetrical shape. Figure, with regard to at least one of the curved surface on the deflection point side and the curved surface on the side of the plane to be scanned, design is made such that the radius of curvature r′ (see Figure 5) of the curved surface of the lens determined in a plane containing a normal in the main scanning plane and perpendicular to the main scanning plane continuously varies in the effective portion of the lens, whereby the curvature of image field in the sub-scanning direction can be better corrected. In this case, if in the sub-scanning cross-section about the optical axis, the deflection point and the plane to be scanned are designed so as to be in an optically conjugate relation, the inclination of the deflecting surface of the deflector can be corrected in advance. Figure 1 shows a first embodiment of the fϑ lens according to the present invention. Figure 1 is a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 1, and the performance of this lens is shown in Table 2. The main scanning plane refers to a light beam surface the light beam deflected by the deflecting surface of the deflector forms with the lapse of time. The cross-sectional shape of this lens in the main scanning plane, when with the point of intersection between the lens surface and the optical axis as the origin, the coordinates system of the x-axis is plotted in the direction of the optic axis and the coordinates system of the y-axis is plotted in the main scanning plane perpendicularly to the dirction of the optical axis, is developed into the form of a polynominal including the high-order term that S(y) = y²/r₁ 1 + 1 - (1+K) ( y r₁ )² + By⁴ + Cy⁶ + Dy⁸ + Ey¹⁰, where r is the radius of curvature of the lens surface in the main scanning plane near the optical axis. In this case, with regard to respective surfaces, as shown in Table 1, the cross-sectional shape of the lens surface adjacent to the deflection point of the deflecting surface is expressed as a function S₁(y) in which y is a variable, the radius of curvature in the main scanning plane near the optical axis is expressed as r₁, the coefficients of the high-order term are expressed as k₁, B₁, C₁ , D₁ and E₁, the cross-sectional shape of the lens surface adjacent to the plane to be scanned is expressed as a function S₂(y) in which y is a variable, the radius of curvature in the main scanning plane near the optical axis is expressed as r₂, and the coefficients of the high-order term are expressed as k₂, B₂, C₂, D₂ and E₂. With regard to the lens surface adjacent to the deflection point, the functions S₁(y) and r₁ are shown in Figure 2 with the maximum effective diameter in the main scanning plane as Ymax. With regard to the arrangement of the entire scanning system, as shown in Figure 3, the distance from the deflection point of the optical deflector to the entrance surface of the lens is a, the thickness of the lens on the optical axis is t, the distance from the exist surface of the lens to the plane to be scanned is b, the distance from the deflection point to the plane to be scanned is g, the maximum scanning angle of the lens is ϑmax, and the effective scanning width on the plane to be scanned is L. Figure 3 shows a cross-sectional view of the scanning system as it is seen in the main scanning plane. Also, the incident light onto the optical deflector, as shown in Figure 4, is convergent light which is imaged at a distance p from the deflection point, in the main scanning plane. In the sub-scanning plane, the light beam emitted from a light source, not shown, passes through a cylindrical lens, not shown, and enters so as to be imaged on the deflection point of the optical deflector. In the sub-scanning plane, the lens assumes the construction of a so-called inclination correcting optical system. The shape of this lens in the sub-scanning direction, when the radius of curvature of the lens surface near the optical axis in the sub-scanning cross-section containing the optical axis is r s and as shown in Figure 5, the z-axis is plotted in a direction containing a normal to the curved surface of the lens in the main scanning plane and perpendicular to the main scanning plane and the radius of curvature determined in a plane containing the normal and the z-axis is r′ and when the position of the foot of this normal is at a position of y from the optical axis, is expressed by the use of a variable which gives a variation in radius of curvature in the form of S′(y) = Z²/r′ 1 + 1 - (1 + K′) ( Z r′ )² , where r′ = r s (1 + Ay² + By⁴ + Cy⁶ + Dy⁸ + Ey¹⁰). Thus, the shape of the lens in the sub-scanning direction perpendicular to the main scanning plane varies continuously in accordance with the value of y. In this case, with regard to each surface, as shown in Table 1, the lens shape of the lens surface adjacent to the deflection point in the sub-scanning plane is expressed as S′₁(y), the radius of curvature in the sub-scanning plane near the optical axis is expressed as r₁, coefficients which give a variation in curvature are expressed A′₁, B′₁, C′₁ and E′₁, the lens shape of the lens surface adjacent to the plane to be scanned in the sub-scanning plane is expressed as S′₂(y), the radius of curvature in the sub-scanning plane near the optical axis is expressed as r₂, and coefficients which give a variation in curvature are expressed as A′₂, B′₂, C′₂, D′₂ and E′₂. In this lens, with regard to the sub-scanning cross-section of the lens, the deflection point and the sub-scanning cross-section are in a conjugate relation, thereby correcting inclination. In the case of the first embodiment, S′₁(y) is constant over the whole lens surface and r′ = ∞. Figure 6 shows a second embodiment of the fϑ lens according to the present invention. Figure 6 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 3, and the performance of this lens is shown in Table 4. In the second embodiment, the shape of the lens in the main scanning cross-section is the same as that in the first embodiment, but the shape of the lens in the sub-scanning direction differs from that in the first embodiment. Particularly, the surface adjacent to the deflector is an aspherical surface symmetrical about the optical axis. In the other points, the shape of this lens is similar to that of the first embodiment. Thus, the fϑ lens of the present invention is wide in the degree of freedom of design with regard to the shape in the sub-scanning direction. Figure 7 shows a third embodiment of the fϑ lens according to the present invention. Figure 7 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 5, and the performance of this lens is shown in Table 6. This embodiment is one in which the thickness t of the lens is made thick as compared with the first embodiment. In the extent of this embodiment, the influence of environmental fluctuations or the like poses no problem in practical use. Figure 8 shows a fourth embodiment of the fϑ lens according to the present invention. Figure 8 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 7, and the performance of this lens is shown in Table 8. This embodiment is one in which the lens is made further thick as compared with the third embodiment. In this case, t/L is at the utmost possible limit of the range of expression (2), while t/g is sufficiently within the range of expression (3) and therefore, the influence of environmental fluctuations becomes great, but is within a practical range. Figure 9 shows a fifth embodiment of the fϑ lens according to the present invention. Figure 9 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 9, and the performance of this lens is shown in Table 10. This lens is such that the incident light is parallel light in the main scanning plane, and in the sub-scanning plane, it enters so as to be imaged on the deflecting surface of the optical deflector. Therefore, the value of p is greater than in the other embodiments having the same maximum scanning angle and the same effective scanning width, but this embodiment has the advantage that aberrations will not extremely change even if the incident light beam deviates in the main scanning plane. Figure 10 shows a sixth embodiment of the fϑ lens according to the present invention. Figure 10 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 11, and the performance of this lens is shown in Table 12. This embodiment is one in which the maximum scanning angle Qmax is designed at 32°. In the case of this lens, r₁ ≧ Ymax and therefore, not S₁(r₁)/r₁ < 0.5 of expression (2a) but S₁(Ymax)/Ymax < 0.5 x Ymax/r₁ of expression (2b) has a meaning. Accordingly, the values of S₁(Ymax) and 0.5 x Ymax/r₁ are shown in Table 11. Figure 11 shows a seventh embodiment of the fϑ lens according to the present invention. Figure 11 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 13, and the performance of this lens is shown in Table 14. This embodiment is one in which the maximum scanning angle Qmax is designed at 56°. Figure 12 shows an eighth embodiment of the fϑ lens according to the present invention. Figure 12 shows a cross-sectional view of the lens as it is seen in the main scanning plane. The design values of this lens are shown in Table 15, and the performance of this lens is shown in Table 16. This embodiment is one in which design is made such that a becomes great as compared with the other embodiments having the same maximum scanning angle. The tables of the design values of the embodiments of the fϑ lens of the present invention will be shown below. Figures 13 to 20 show aberrations in the embodiments of the fϑ lens of the present invention. Description will now be made of an image forming apparatus using an optical scanning device to form an image on an image carrier. Figure 21 is a cross-sectional view of a laser beam printer which is an image forming apparatus for recording images by a laser beam to which the fϑ lens of the present invention is applied. Description will hereinafter be made of Figure 21. In Figure 21, the reference numeral 39 designates a photosensitive drum rotated in the direction of arrow. Around the photosensitive drum 39, there are provided in succession a charger 40 for uniformly charging the surface of the drum, a developing device 41 for developing a latent image on the photosensitive drum, a transfer charger 44 for transferring the image developed by the developing device 41 to paper, and a cleaner 46 for removing any unnecessary developer remaining on the surface of the photosensitive drum after the image transfer. The reference numeral 42 denotes a paper supply cassette containing recording paper therein, the reference numeral 43 designates register rollers, and the reference numeral 45 denotes a fixating device for making the transferred image semipermanent. The reference numeral 49 designates a fan for forming an air stream on the underside of a housing to thereby prevent the temperature rise of an optical system. A semiconductor laser output portion 6 contained in a containing portion formed integrally with a base plate 5 outputs a laser beam optically modulated by an extraneous signal in conformity with recording information, and this laser beam emerges from a housing comprised of the base plate 5 and a cover member 27 through a cylindrical lens 33 highly accurately held and positioned by a supporting portion formed integrally with the base plate 5 and the containing portion, a rotatable polygon mirror 2 for deflecting the light beam at a uniform angular velocity, and an fϑ lens 31, and scans on the photosenstive drum 39 via a mirror 48, whereby a charge pattern conforming to the recording information is formed on the photosensitive drum 39. The reference numeral 34 denotes a positioning member for the housing provided on the underside of the base plate 5 integrally with the base plate, and positioned highly accurately with the photosensitive drum 39 and the mirror 48. Positioning accuracy is enhanced by this positioning member, whereby the positional accuracy relative to the photosenstive drum is enhanced and therefore, it becomes possible to obtain more excellent images. The charge pattern on the drum is visualized by the developing device 41. This visualized image is transferred by the transfer charger 44 onto the recording paper fed from the paper supply cassette 42, whereafter the recording paper is fed to the fixating device 45 for fixation of the image. Any developer remaining on the photosensitive drum after the image transfer is removed by the cleaner 46 and prepared for another use. Such an image forming apparatus to which the fϑ lens of the present invention is applied can be made compact and thin. As described above, according to the present invention, there can be realized an fϑ lens comprising a single lens in which the shape of the curved surface of at least the lens surface on the deflection point side in the main scanning plane is an aspherical shape and particularly near the optical axis, this aspherical shape becomes convex toward the deflection point side and further, the shape of this surface in the main scanning plane is made to satisfy expressions (1) and (2-a) or (2-b), whereby the fϑ lens satisfies the performance required of an fϑ lens and yet the thickness of the lens is kept small so as to be suitable for plasticization. Also, the use of such fϑ lens can realize an image forming apparatus which can be made compact and thin. This specification disloses an fϑ lens as defined in Claim 1. The specification also discloses an image forming apparatus using such fϑ lens.

Claims: An fϑ lens acting (31) to effect uniform speed scanning while causing a light beam deflected at a uniform angular velocity by the deflecting surface of a deflector to be imaged on a plane to be scanned, wherein the shape of the curved surface of at least the lens surface of the lens which is adjacent to the deflection point side of the deflecting surface in the main scanning plane is of an aspherical shape and particularly, near the optical axis, in at least the main scanning plane, this aspherical shape is convex toward said deflection point, characterised in that the radius of curvature of this convex shape near the optical axis in the main scanning plane is r₁ and the focal length of the fϑ lens near the optical axis in the main scanning plane is fm, that 0 ≦ r₁ < |fm| and that when with the point of intersection between the lens surface adjacent to the deflection point side and the optical axis as the origin and with the coordinates system of the x-axis plotted in the direction of the optical axis and the coordinates system of the y-axis plotted in the main scanning plane perpendicularly thereto, the surface shape in the main scanning plane is expressed as a function S₁(y) in which y is a variable, the maximum effective diameter of this surface in the main scanning plane is Ymax, S₁(y) is defined between 0 and Ymax, that when r₁ < Ymax, then -1 < S₁(r₁)/r₁ < 0.5 or that when r₁ ≧ Ymax, then -1 x Ymax/r₁ < S₁(Ymax)/Ymax < 0.5 x Ymax/r₁. An fϑ lens according to Claim 1, wherein when the thickness of the fϑ lens on the optical axis thereof is t and the effective scanning width on the plane to be scanned is L, 0 < t/L < 0.08. An fϑ lens according to Claim 1, wherein when the thickness of the fϑ lens on the optical axis thereof is t and the distance from the deflection point of the deflecting surface to the plane to be scanned is g, 0 < t/g < 0.15. An fϑ lens according to Claim 1, wherein the focal length fm near the optical axis in the main scanning plane and the distance g from the deflection point of the deflecting surface to the plane to be scanned are |fm|/g > 0.8. An fϑ lens according to Claim 1, wherein the shape of the lens near the optical axis is a meniscus lens convex toward the deflection point side of the deflecting surface in at least the main scanning plane. An fϑ lens according to Claim 1, wherein the light beam incident on the lens is substantially convergent light in at least the main scanning plane. An fϑ lens according to Claim 6, wherein the light beam incident on the lens is substantially convergent light in at least the main scanning plane, and the distance p from the deflection point of the deflecting surface to a point at which the convergent light is imaged in the main scanning plane and the distance g from the deflection point of the deflecting surface to the plane to be scanned are 0.7 < p/g. An fϑ lens according to Claim 1, wherein the light beam incident on the lens is substantially parallel light in at least the main scanning plane. An fϑ lens according to Claim 1, wherein with regard to at least one of a curved surface adjacent to the deflection point and a curved surface adjacent to the plane to be scanned, the radius of curvature near the optical axis differs between the main scanning cross-section and the sub-scanning cross-section (a plane containing the optical axis of the lens and perpendicular to the main scanning plane). An fϑ lens according to Claim 9, wherein with regard to at least one of a curved surface adjacent to the deflection point and a curved surface adjacent to the plane to be scanned, the radius of curvature of the curved surface of the lens determined in a plane containing a normal in the main scanning plane and perpendicular to the main scanning plane varies continuously in the effective portion of the lens. An fϑ lens according to Claim 9 or 10, wherein in the sub-scanning cross-section near the optical axis, the deflection point and the plane to be scanned are in an optically substantially conjugate relation. A scanning optical system comprising a light source (6), a first optical system (33) for condensing light from the light source (6) and causing the light to emerge toward the deflection point of the deflecting surface of a deflector (2) for deflecting the light beam from the first optical system at a uniform angular velocity on the deflection point of the deflecting surface thereof, a second optical system comprising an fϑ lens (31) acting to effect uniform speed scanning while causing the light beam deflected at a uniform angular velocity from the deflection point of the deflector to be imaged on a plane to be scanned on which a recording material such as a photosensitive member is placed, characterized in that said fϑ lens (31) is an fϑ lens according to any one of Claims 1-11. A scanning optical system according to Claim 12, wherein a semiconductor laser is used as the light source. An image forming apparatus for effecting image formation comprising a scanning optical system according to Claim 12 or 13.

Inventors: MAKINO JUN CANON KABUSHIKI KAI, MAKINO, JUN, CANON KABUSHIKI KAISHA
Applicants: CANON KK, CANON KABUSHIKI KAISHA
Application year: 1991
Main classification: G02B13
IPC codes: G02B26, G02B13, G02B3, G03G15