Optical: systems and elements – Deflection using a moving element – Using a periodically moving element
Reexamination Certificate
2000-01-06
2001-07-10
Phan, James (Department: 2872)
Optical: systems and elements
Deflection using a moving element
Using a periodically moving element
C359S207110, C359S216100
Reexamination Certificate
active
06259546
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a scanning and imaging lens and an optical scanning device.
2. Description of the Related Art
A scanning and imaging lens for use in an optical scanning device is required to have a proper f&thgr; characteristic in order to ensure a constant velocity in optical scanning. Further, the curvature of field of such a scanning and imaging lens must be corrected in order to reduce a variation in the diameter of a beam spot. In order to meet these requirements, the surface of the scanning and imaging lens needs to have a unique configuration (see Japanese Laid-Open Patent Application no. 7-359989).
Hereinafter, the term “direction corresponding to the main-scanning direction” is used to denote a direction, in an optical path between a light source and a scan surface, that corresponds to the main-scanning direction. The term “direction corresponding to the sub-scanning direction” is used to denote a direction, in an optical path between a light source and a scan surface, that corresponds to the sub-scanning direction.
A polygon mirror is normally used as a beam deflector for deflecting a light beam incident on a scanning and imaging lens. The center of rotation of a deflecting and reflecting surface of a polygon mirror is not located in the deflecting and reflecting surface. A beam may be focused so that a line image extended in a direction corresponding to the main-scanning direction is formed in the vicinity of the deflecting and reflecting surface, in order to correct a so-called facet inclination the surface. In such a construction, a sag may occur. A sag is a variation of a relative position at which the line image is formed with respect to the deflecting and reflecting surface, the variation being asymmetrical with respect to an optical axis of the scanning and imaging lens and occurring in response to the rotation of the polygon mirror.
The surface of the conventional scanning and imaging lens is symmetrical with respect to the optical axis in the direction corresponding to the main scanning direction. Therefore, when a sag occurs, the curvature of field of and the constant-velocity characteristic of the lens is significantly degraded. Such a degradation in the performance is conventionally corrected by a shift of the scanning and imaging lens or a tilt thereof. However, such means of correction is far from satisfactory.
SUMMARY OF THE INVENTION
Accordingly, a general object of the present invention is to provide a scanning and imaging lens and an optical scanning device in which the aforementioned problems are eliminated.
Another and more specific object of the present invention is to correct an unfavorable effect of a sag and provide a satisfactory optical scanning in an optical scanning device in which a polygon mirror is used as a beam deflector, a scanning and imaging lens formed of one or more lenses is used, and a facet inclination is corrected.
The scanning and imaging lens according to the present invention is used in an optical scanning device in which a light beam forming a line image extended in a direction corresponding to the main-scanning direction is deflected at a constant angular velocity by a polygon mirror having a deflecting and reflecting surface in the vicinity of the image forming position of the line image, and in which the deflected beam is focused by a scanning and imaging lens to form a beam spot on a scan surface so that a constant velocity optical scanning of the scan surface is effected.
The scanning and imaging lens according to the invention has the following features.
The scanning and imaging lens according to the invention has a single-lens construction. At least one of the lens surfaces has an asymmetrical configuration with respect to the optical axis within a plane of deflection (defined below). Such an asymmetrical configuration with respect to the optical axis is designed so that the field curvature is properly corrected and a proper constant-velocity characteristic is obtained over the entire effective optical scanning area.
The plane of deflection is defined as a plane including the plane through which a deflected beam passes. In the absence of a shift or a tilt in the scanning and imaging lens, the plane swept by a primary ray of the beam deflected ideally by a beam deflector coincides with the plane of deflection.
According to the invention at least one of the two lens surfaces may be asymmetrical with respect to the optical axis within the plane of deflection. Alternatively, both surfaces of the scanning and imaging lens may have a nonarcuate configuration asymmetrical with respect to the optical axis within the plane of deflection.
A nonarcuate configuration is a curve which is not an arc and is generally given by the following polynomial
X
=(
Y
2
/Rm
)/[1+(1−(1+
K
)(
Y/RM
)
2
)]+
A·Y
4
+B·Y
6
+C·Y
8
+D·Y
10
+ . . . (1)
where Rm denotes a radius of curvature on the optical axis within the plane of deflection, Y denotes a distance from the optical axis in the direction corresponding to the main-scanning direction, K is a conical constant, A, B, C, D . . . are high-order coefficients, and X coordinates are lined up in the direction of the optical axis. That the configuration of the lens surfaces is asymmetrical with respect to the direction corresponding to the main scanning direction means that the equation (1) is differently constructed for one side of the optical axis from that of the other side.
The scanning and imaging lens as described in the invention may be modified such that the radius of curvature of at least one of the lens surfaces within a plane perpendicular to the plane of deflection is denoted by a polynomial of high order &Sgr;a
n
·Y**n (n=0, 1, 2, 3 . . . ), where Y denotes a distance from the optical axis in the direction corresponding to the main-scanning direction, and a configuration provided by this polynomial is asymmetrical with respect to the optical axis.
By definition, a plane perpendicular to the plane of deflection is parallel to the optical axis of the scanning and imaging lens. In the polynomial of high order above, Y**n denotes an nth power of Y.
One of the lens surfaces may have a nonarcuate configuration asymmetrical with respect to the optical axis within the plane of deflection, and the other lens surface may be symmetrical with respect to the optical axis. The surface whose radius of curvature within the plane perpendicular to the plane of deflection is given by a polynomial asymmetrical with respect to Y may be combined with a nonarcuate configuration asymmetrical with respect to the optical axis within the plane of deflection. Alternatively, such a surface may be combined with a configuration symmetrical with respect to the optical axis.
Irrespective of whether only one of the lens surfaces is asymmetrical with respect to the optical axis within the plane of deflection or both the lens surfaces are asymmetrical with respect to the optical axis, the both surfaces may have a radius of curvature within the plane of deflection given by a polynomial asymmetrical with respect to Y.
The scanning and imaging lens as described in the invention may be formed by molding a plastic.
For correction of a facet inclination of a polygon mirror, a general approach is to cause the image forming position of the line image and the deflecting and reflecting surface to approach each other so that the scanning and imaging lens provides a conjugated relationship between the position in the vicinity of the deflecting and reflecting surface and the scan surface in the direction corresponding to the sub-scanning direction. The deflecting and reflecting surface of the polygon mirror and the scan surface may be in a conjugated formation over the entire effective optical scanning area in the direction corresponding to the sub-scanning direction. The image forming position of the line image and the scan surface may be in a conjugated formation over the entire optica
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
Phan James
Ricoh & Company, Ltd.
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