Optical scanning lens, optical scanning and imaging system and optical scanning apparatus incorporating same

An optical scanning apparatus in which a light beam emanating from a light source is converged to form a line image elongated in a direction of main scanning via a first image formation optical apparatus, deflected by a light deflector having a deflecting reflective surface located near an image forming position for the line image, and then converged as a light spot on a surface to be scanned via a second image formation optical system for scanning the surface to be scanned, said second image formation optical system including a scanning and image forming lens that is a single anamorphic lens having a distribution of different refractive indices in a direction of sub-scanning;

• wherein
• assuming that a refractive index on the optical axis of said scanning and image forming lens is n.sub.0 (0), the distribution of refractive indices is reproduced by an approximate expression of n(z)=n.sub.0 (0)+.DELTA.n(0).times.z.sup.2 in relation to a distance z from the optical axis in a direction of sub-scanning;
• and
• assuming that the radii of curvature on the surfaces of said scanning and image forming lens facing said light deflector and scanned surface within said section of sub-scanning are r.sub.S1 (0) and r.sub.S2 (0), respectively, the thickness of said lens is d, a focal length in the direction of sub-scanning calculated using the radii of curvature r.sub.S1 (0) and r.sub.S2 (0), the thickness d, and the refractive index n.sub.0 (0) is f(0), a distance from the position of image formation for the line image to a front principal point in the direction of sub-scanning of said scanning and image forming lens is S.sub.0 (0), a distance from a rear principal point to said scanned surface is S.sub.L (0), .DELTA.n(0) is a constant, and the tolerance for change of the diameter of a light spot in the direction of sub-scanning is .omega..sub.0, the following condition is satisfied:
• ##EQU6##

A method of forming a lens for use in an optical scanning apparatus, the method comprising the steps of:

• determining a distribution of refractive index of the lens before forming the lens;
• determining a minimum beam spot diameter;
• providing a mold having a shape configured to form at least one lens having a distribution of different refractive indices such that a beam spot diameter produced by the lens on a scanned surface is within a range of tolerance of about 10% to about 25% of the minimum beam spot diameter;
• filling the mold with heated liquid plastics material;
• and
• allowing the plastics material in the mold to cool.

An optical scanning apparatus in which a light beam emanating from a light source is converged to form a line image elongated in a direction of main scanning via a first image formation optical system, deflected by a light deflector having a deflecting reflective surface located near an image forming point for the line image, and then converged as a light spot on a surface to be scanned via a second image formation optical system for scanning the surface to be scanned;

• wherein
• said second image formation optical system includes a system of lenses for scanning and image formation having at least two lenses, and at least one lens includes a non-uniform distribution of refractive indices in a direction of sub-scanning;
• and
• a lens located closest to said scanned surface has a positive power in the direction of sub-scanning;
• and
• assuming that the power in the direction of sub-scanning of one lens facing said light deflector is P.sub.1 and the power therein of another lens facing said scanned surface is P.sub.2, the following condition is satisfied:
• P.sub.2 >P.sub.1.

An optical scanning apparatus in which a light beam emanating from a light source is converged to form a line image elongated in a direction of main scanning via a first image formation optical system, deflected by a light deflector having a deflecting reflective surface located near an image forming position for the line image, and then converged as a light spot on a surface to be scanned via a second image formation optical system for scanning the surface to be scanned, wherein said scanning and image forming lens system of said second image formation optical system is composed of two lenses, and only one lens opposed to said light deflector includes a non-uniform distribution of refractive indices in the direction of sub-scanning;

• and assuming that a refractive index at the optical axis of said lens opposed to said light deflector is n.sub.0 (0), the distribution of refractive indices inside said lens is reproduced by an approximate expression of n(z)=n.sub.0 (0)+.DELTA.n(0).times.z.sup.2 in relation to a distance z in the direction of sub-scanning from the optical axis within the section of sub-scanning;
• and assuming that the radii of curvature on the surfaces of said lens opposed to said light deflector, which face said deflector and scanned surface respectively, within the section of sub-scanning are r.sub.S1 (0) and r.sub.S2 (0), respectively, the thickness of said lens is d.sub.1, a focal length in the direction of sub-scanning calculated using the radii of curvature r.sub.S1 (0) and r.sub.S2 (0), the thickness d.sub.1, and the refractive index n.sub.0 (0) is f.sub.1 (0), a distance from the position of image formation for the line image to a front principal point in the direction of sub-scanning of said lens opposed to said light deflector is S.sub.0 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said light deflector to a front principal point of said lens opposed to said scanned surface is S.sub.1 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said scanned surface to said scanned surface is S.sub.L (0), a focal length in the direction of sub-scanning of said lens opposed to said scanned surface is f.sub.2 (0), and the tolerance for change of the diameter of a light spot in the direction of sub-scanning is .omega..sub.0, when the equality of equality of ##EQU7## established, the following condition is satisfied:
• .vertline.S.sub.L (0)-1/[{1/f.sub.2 (0)}+{.LAMBDA./(1-S.sub.1 (0).times..LAMBDA.)}].vertline.<.omega..sub.0 /2.
• 12.

An optical scanning apparatus in which a light beam emanating from a light source is converged to form a line image elongated in a direction of main scanning via a first image formation optical system, deflected by a light deflector having a deflecting reflective surface located near an image forming position for the line image, and then converged as a light spot on a surface to be scanned via a second image formation optical system for scanning the surface to be scanned, wherein said scanning and image forming lens system of said second image formation optical system is composed of two lenses, and only one lens opposed to said light deflector includes a non-uniform distribution of refractive indices in the direction of sub-scanning;

• assuming that a focal length of said lens opposed to the light deflector is f.sub.1 (0), a distance from the position of image formation for the line image to a front principal point in the direction of sub-scanning of said lens opposed to said light deflector is S.sub.0 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said light deflector to a front principal point of said lens opposed to said scanned surface is S.sub.1 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said scanned surface to said scanned surface is S.sub.L (0), a refractive index on the optical axis of said lens opposed to said scanned surface n.sub.0 '(0), the distribution of refractive indices inside said lens is reproduced by an approximate expression of n'(z)=n.sub.0 '(0)+.DELTA.n'(0).times.z.sup.2 in relation to a distance z in the direction of sub-scanning from the optical axis within the section of sub-scanning, and assuming that the radii of curvature on the surfaces of said lens opposed to said scanned surface, which face said deflector and scanned surface respectively, within the section of sub-scanning are r.sub.S3 (0) and r.sub.S4 (0) respectively, the thickness of said lens is d.sub.3, a focal length in the direction of sub-scanning calculated using the radii of curvature r.sub.S3 (0) and r.sub.S4 (0), the thickness d.sub.3, and the refractive index n.sub.0 '(0) is f.sub.2 (0), and the tolerance for change of the diameter of a light spot in the direction of sub-scanning is .omega..sub.0, when the equality of .LAMBDA.'={1/f.sub.1 (0)}-{1/S.sub.0 (0)} is established, the following condition is satisfied:
• .vertline.S.sub.L (0)-1/[{1/f.sub.2 (0)}+{.LAMBDA.'/(1-S.sub.1 (0).times..LAMBDA.')}-2.DELTA.n'(0).times.d.sub.3 ].vertline.<.omega..sub.0 /2.

An optical scanning apparatus in which a light beam emanating from a light source is converged to form a line image elongated in a direction of main scanning via a first image formation optical system, deflected by a light deflector having a deflecting reflective surface located near an image forming position for the line image, and then converged as a light spot on a surface to be scanned via a second image formation optical system for scanning the surface to be scanned, wherein said scanning and image forming lens system of said second image formation optical system is composed of two lenses, and each of said two lenses includes a non-uniform distribution of refractive indices in the direction of sub-scanning;

• assuming that a refractive index on the optical axis of said lens opposed to said light deflector is n.sub.0 (0), the distribution of refractive indices inside said lens is defined by an approximate expression of n(z)=n.sub.0 (0)+.DELTA.n(0).times.z.sup.2 in relation to a distance z in the direction of sub-scanning from the optical axis within the section of sub-scanning, and assuming that the radii of curvature on the surfaces of said lens opposed to said scanned surface, which face said deflector and scanned surface respectively, within the section of sub-scanning are r.sub.S1 (0) and r.sub.S2 (0) respectively, the thickness of said lens is d.sub.1, a focal length in the direction of sub-scanning calculated using the radii of curvature r.sub.S1 (0) and r.sub.S2 (0), the thickness d.sub.1, and the refractive index n.sub.0 (0) is f.sub.1 (0), a refractive index on the optical axis of said lens opposed to said scanned surface n.sub.0 '(0), the distribution of refractive indices inside said lens is reproduced by an approximate expression of n'(z)=n.sub.0 '(0)+.DELTA.n'(0).times.z.sup.2 in relation to a distance z in the direction of sub-scanning from the optical axis within the section of sub-scanning, and assuming that the radii of curvature on the surfaces of said lens opposed to said light deflector, which face said deflector and scanned surface respectively, within the section of sub-scanning are r.sub.S3 (0) and r.sub.S4 (0) respectively, the thickness of said lens is d.sub.3, a focal length in the direction of sub-scanning calculated using the radii of curvature r.sub.S3 (0) and r.sub.S4 (0), the thickness d.sub.3, and the refractive index n.sub.0 '(0) is f.sub.2 (0), a distance from the position of image formation for the line image to a front principal point in the direction of sub-scanning of said lens opposed to said light deflector is S.sub.0 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said light deflector to a front principal point of said lens opposed to said scanned surface is S.sub.1 (0), a distance from a rear principal point in the direction of sub-scanning of said lens opposed to said scanned surface to said scanned surface is S.sub.L (0), and the tolerance for change of the diameter of a light spot in the direction of sub-scanning is .omega..sub.0, when the equality of equality of ##EQU8## is established, the following condition is satisfied:
• .vertline.S.sub.L (0)-1/[{1/f.sub.2 (0)}+{.LAMBDA./(1-S.sub.1 (0).times..LAMBDA.)}-2.DELTA.n'(0).times.d.sub.3 ].vertline.<.omega..sub.0.2.

An optical scanning imaging apparatus, the optical scanning apparatus causing a beam from a light source to form a linear image elongated in a main scanning direction, deflecting the beam via a polygon mirror having a deflecting reflective surface located near a position where a linear image is formed, and converging the deflected beam on a scanning surface as a light spot to perform optical scanning, the apparatus comprising:

• at least one gradient index lens having a non-uniform refractive index distribution in a sub-scanning direction;
• wherein
• when the refractive index distribution in the gradient-index lens is taken into consideration, when the image forming position of the deflected beam in the sub-scanning direction is indicated as Q.sub.E ' at a most remote optical path of an effective scanning region, the polygon mirror side being negative when measured from a position on the scanning surface, the following condition is satisfied:
• Q.sub.E '>0.