JPH1138314A - Scanning image formation optical system and optical scanner - Google Patents

Abstract

PROBLEM TO BE SOLVED: To effectively reduce the pitch unevenness of a scanning line by taking the ununiformity of refractive index distribution at the scanning image formation optical system of an optical scanner into consideration. SOLUTION: This optical system is the scanning image formation optical system of the optical scanner performing optical scanning by forming an image of linear image long in a direction corresponding to main scanning from a luminous flux from the side of a light source 10 and deflecting it by a polygon mirror 18 having a deflecting reflection surface in the vicinity of the image formation position of the linear image and condensing a deflected luminous flux as a light spot on a surface to be scanned 22 by the scanning image formation optical system. In this case, the optical system is constituted of a lens 20 which possesses refractive index distribution in the direction corresponding to subscanning and whose refractive index is ununiform, and the power changing quantity of the optical system in the direction corresponding to subscanning originating from the refractive index distribution in set as ΔPc on an optical axis and as ΔPE on the most peripheral optical path of an effective scanning area, and the image formation position of the deflected luminous flux when the lens 20 has a uniform refractive index N0 in the direction corresponding to subscanning by the scanning image formation optical system is set negative on the side of the polygon mirror 18 by measuring from the position of the surface to be scanned, and is set as Qc on the optical axis and as QE on the most peripheral optical path of the effective scanning area, and conditions such as (1) |ΔPc |>|ΔPE| and (2) QE>0>Qc are satisfied.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a scanning image forming optical system and an optical scanning device.

[0002]

2. Description of the Related Art A scanning image forming optical system is an "optical system for condensing a deflected light beam as a light spot on a surface to be scanned in an optical scanning device", and corrects constant velocity characteristics such as fθ characteristics and field curvature. Since it is difficult to realize the above optical characteristics only with a spherical surface, a special lens surface represented by an aspheric surface has been used, and accordingly, plastics formed by plastic molding have been used. The use of lenses is increasing. Plastic molding is performed by molding the molten plastic with a piece mold that molds the lens surface.When the molten plastic cools in the piece mold, the temperature gradually decreases from the part in contact with the piece mold. Temperature difference between the lens and the center of the lens. Due to this temperature difference, the molten plastic moves to a portion where the temperature is lowered by cooling. For this reason, in the state where the cooling is completed, the plastic density in the completed plastic lens is high in the peripheral portion of the lens where the cooling has begun first, and low in the central portion of the lens. In accordance with such non-uniform density, the refractive index in the plastic lens does not become uniform, and a “refractive index distribution” occurs in the lens. In the refractive index distribution, since the refractive index increases at a high plastic density, the refractive index generally increases around the lens. The occurrence of the refractive index distribution becomes particularly remarkable when the cooling time of the plastic lens in the bridge is shortened to perform rapid cooling.

In general, a lens used for a scanning image forming lens forms only a portion required as a lens function for a deflected light beam, and therefore, a lens in a sub-scanning direction (in a sub-scanning direction on an optical path from a light source to a surface to be scanned). (Corresponding direction) is formed in a strip shape with the width direction.
Since the temperature drop at both ends in the sub-scanning corresponding direction, which is the strip width direction, becomes remarkable, the unevenness of the refractive index tends to appear remarkably especially in the sub-scanning corresponding direction. The scanning imaging optical system is designed to have a uniform refractive index inside the lens, whether it is made of a plastic lens or includes a plastic lens. If a non-uniform distribution of the ratio exists, the scanning imaging optical system does not exhibit the designed optical performance. Therefore, in order to realize the desired optical performance, it is necessary to design in consideration of the refractive index distribution generated in the plastic lens. Japanese Patent Application Laid-Open No. 9-49976 discloses a scanning image forming optical system in consideration of the refractive index distribution in a lens.
This scanning imaging optical system adjusts the light spot diameter in the sub-scanning direction by matching the image plane where the wavefront aberration in the sub-scanning corresponding direction is minimized to the surface to be scanned, in consideration of the distribution of the refractive index in the lens. The diameter has been reduced.

[0004] An important characteristic of an optical scanning device is "scanning line pitch". The “scanning line” is a trajectory of scanning by the light spot, and the scanning line pitch is “interval between adjacent scanning lines”. However, if the scanning line pitch is not constant and “pitch unevenness” is present, writing is performed by optical scanning. Since an image is distorted, it is necessary to “pitch unevenness as small as possible” to write a good image. The main cause of the pitch unevenness is “surface tilt” of the polygon mirror used as the optical deflector. That is, if the deflecting reflection surface of the polygon mirror is not completely parallel to the rotation axis of the polygon mirror, the deflecting light beam fluctuates in the sub-scanning corresponding direction according to each deflecting reflection surface, and Is fluctuated in the sub-scanning direction on the surface to be scanned, causing pitch unevenness. As a method of preventing the occurrence of pitch unevenness, a light beam from the light source side is lengthened in the main scanning direction (direction corresponding to the main scanning direction on the optical path from the light source to the surface to be scanned) near the deflecting reflection surface of the polygon mirror. A “plane tilt correction” method is known in which an image is formed as a line image, and the vicinity of the deflecting reflection surface and the position of the surface to be scanned are conjugated with respect to the sub-scanning corresponding direction by a scanning image forming optical system.

However, if the lens used in the scanning imaging optical system has a non-uniform refractive index, the desired surface tilt correction cannot be realized even if the above-described surface tilt correction is performed without taking this into account.
Pitch unevenness occurs due to surface tilt in the polygon mirror. In the invention described in JP-A-9-49976, no consideration is given to pitch unevenness caused by such a refractive index distribution. Further, since the rotation axis of the deflecting and reflecting surface of the polygon mirror is displaced from the deflecting and reflecting surface, there is a problem of so-called "sag" in which the image forming position of the line image and the deflecting and reflecting surface are shifted according to the rotation of the deflecting and reflecting surface. In order to reduce the pitch unevenness, it is necessary to consider the effect of sag on the scanning line pitch.

[0006]

SUMMARY OF THE INVENTION The present invention has been made in consideration of the above circumstances, and has been made to reduce unevenness in the pitch of scanning lines in consideration of non-uniformity of a refractive index distribution in a scanning image forming optical system in an optical scanning device. It is an issue.

[0007]

SUMMARY OF THE INVENTION A scanning image forming apparatus according to the present invention is arranged such that "a light beam from a light source side is formed into a long line image in a direction corresponding to the main scanning, and a deflecting reflection surface is provided in the vicinity of the line image forming position. Scanning imaging optical system in an optical scanning device that performs optical scanning by deflecting by a polygon mirror, condensing the deflected light beam as a light spot on the surface to be scanned by the scanning imaging optical system,
The features are as follows. That is, the scanning image forming optical system has a “non-uniform refractive index lens having a refractive index distribution in the sub-scanning corresponding direction”. Deflection light beam scanning when the amount of power change in the sub-scanning corresponding direction of the scanning imaging optical system due to the refractive index distribution is “ΔP” and the non-uniform refractive index lens has a uniform refractive index: N _0. The image forming position in the sub-scanning corresponding direction by the image forming optical system is defined as Q (measured from the position of the surface to be scanned, and the polygon mirror side is “negative”). These quantities: Δ
Although P and Q differ depending on the deflection angle of the deflected light beam, the value on the optical axis of the scanning image forming optical system is represented by "suffix: C", and the effective scanning area (the area where image writing by optical scanning is performed). The value on the outermost optical path is “Suffix: E”
Will be represented by Hereinafter, the same applies to amounts other than ΔP and Q.

[0008] The first aspect of the present invention provides a method for detecting Δ on an optical path.
P, [Delta] P is Q _C, Q _C and, [Delta] P in the most peripheral light path, [Delta] P is Q _E, is Q _E, the _{condition: (1) | ΔP C |} > | ΔP E | (2) Q E>0> to satisfy the Q _C. The scanning imaging optical system “having a non-uniform refractive index lens” means that the non-uniform refractive index lens is included as a part of the scanning imaging optical system, and that the scanning imaging optical system has the non-uniform refractive index lens. And the case where it comprises.

According to a second aspect of the present invention, there is provided a scanning image forming optical system according to the first aspect of the invention, wherein the direction of the deflection beam in the sub-scanning direction by the scanning image forming optical system is considered in consideration of the refractive index distribution in the non-uniform refractive index lens. Position on the optical axis of Q ′ (measured from the position of the surface to be scanned, and the polygon mirror side is “negative”): Q _C ′, value on the most peripheral optical path of the effective scanning area: Q _E ′ Satisfies the condition: (3) Q _E ′> Q _C ′ (claim 2). Claim 3
The scanning imaging optical system according to claim 1, wherein the distance from the rear principal point of the scanning imaging optical system in the sub-scanning corresponding direction to the imaging point in the sub-scanning corresponding direction is S ′. The value on the optical axis: S _C ′, the value on the outermost optical path of the effective scanning area: S _E ′ is the condition: (4) Q _E −S _E ′ ² · ΔP _E > Q _C −S _C ' ² · satisfies the [Delta] P _C "be characterized (claim 3).

A scanning image forming optical system according to a fourth aspect of the present invention comprises:
4. The scanning image forming optical system according to claim 2, wherein ΔP
_{It is characterized in that E} , Q _E , Q _E ′, and S _E ′ are “values on the outermost optical path on the side where sag is large”. According to a fifth aspect of the present invention, in the scanning image forming optical system according to the second or third aspect, ΔP _E , Q _E , Q _E ′, and S _E ′ deflect the non-uniform refractive index lens. The value is the value on the longest optical path on the long side through which the light beam passes.

The scanning image forming optical system according to the first, second, third, fourth or fifth aspect of the present invention can be "configured with one non-uniform refractive index lens, and has a biconvex sectional shape in the main scanning direction." (Claim 6). `` Main scanning section shape ''
Is a cross-sectional shape of a plane cross-section that includes the optical axis of the non-uniform refractive index lens and is parallel to the main scanning corresponding direction.

The values for the image heights of the light spots of ΔP, Q, Q ′ and S ′ described above: h (arbitrary image height between the optical axis and the outermost optical path) are represented by ΔP _h , Q _h and Q _h. ', S _h' when the above condition (2), (3), _{(4), (2 ') Q E>} Q h> Q C, 0> Q C (3') Q E '> _{Q h '> Q C' (} 4 ') Q E -S E' 2 · ΔP E> Q h -S h '2 · ΔP h>
Q _C -S _C 'it is more preferable to satisfy the ² · ^ΔP _C.

According to the optical scanning device of the present invention, "a light beam from the light source side is formed into a long linear image in the main scanning direction, and the light beam is deflected by a polygon mirror having a deflecting / reflecting surface near the image forming position of the linear image. An optical scanning device that performs light scanning by condensing a light beam as a light spot on a surface to be scanned by a scanning imaging optical system. "
Wherein the scanning imaging optical system according to any one of claims 1 to 6 is used as the scanning imaging optical system (claim 7).

The non-uniform refractive index lens included in the scanning imaging optical system of the present invention or constituting the scanning imaging optical system is manufactured by plastic molding, but is molded by the same material and under the same conditions. Therefore, the refractive index distribution in the manufactured non-uniform refractive index lens also has no substantial difference between the lenses, and the refractive index distribution can be known in advance through experiments and the like. The design in consideration of the refractive index distribution of the non-uniform refractive index lens is possible.

[0015]

FIG. 1 is a diagram showing an embodiment of an optical scanning device according to the present invention. A light beam from a semiconductor laser 10 as a light source is coupled to a subsequent optical system by a coupling lens 12. The coupled light beam becomes a “parallel light beam” or a “weakly divergent light beam” or a “weakly convergent light beam”. Coupling lens 12
The light beam coupled by the light source is then passed through an aperture 14 to block the light beam at its peripheral portion and is "beam-shaped". The light beam is converged by a cylinder lens 16 in a sub-scanning corresponding direction (a direction orthogonal to the drawing). An image is formed as a long line image in the main scanning direction in the vicinity of the deflecting and reflecting surface of the polygon mirror 18, which is a device. The cylinder lens 1
4 can be replaced with a "cylinder concave mirror".

The light beam reflected by the deflecting / reflecting surface of the polygon mirror 18 is turned into a deflecting light beam deflected at a constant angular velocity as the polygon mirror 18 rotates at a constant speed.
Is incident on the lens 20. The lens 20 has different positive powers in the main scanning corresponding direction and the sub-scanning corresponding direction, condenses the deflected light beam as a light spot on the scanned surface 22, and uses the same light spot to scan the scanned surface 22 (substantially). Is
The effective scanning area W of the photosensitive surface of the photosensitive member provided at this portion is optically scanned at a constant speed.

That is, the optical scanning device shown in FIG.
The light beam from the side is formed into a long line image in the main scanning corresponding direction,
Deflected by a polygon mirror 18 having a deflecting / reflecting surface in the vicinity of the image forming position of the line image, and the deflected light beam is
The light scanning device performs light scanning by condensing the light as a light spot on the surface 22 to be scanned (claim 7).

The scanning image forming optical system includes a single lens 20. The lens 20 is a “non-uniform refractive index lens”, and the main scanning cross-sectional shape (the shape shown in FIG. 1) is a “biconvex shape” (at least at a portion near the optical axis) (claim 6).

FIG. 2 is a schematic diagram for explaining the “refractive index distribution inside the lens” of the lens 20. (A)
Is a "contour display" of the distribution of the refractive index in the main scanning section of the lens 20. When the change in the refractive index along the chain line in the figure is seen, as shown in FIG. The refractive index gradually increases toward both ends (in the main scanning corresponding direction). (C) shows the refractive index distribution in the sub-scanning cross section of the lens 2 (the plane section including the optical axis of the lens 20 and being unfortunately parallel to the sub-scanning), and (d) shows the sub-scanning cross section. (E) shows the refractive index distribution in the sub-scanning direction in the sub-scanning cross section. As shown in (e), the refractive index distribution in the sub-scanning corresponding direction is a distribution that “increases as the optical axis is separated in the sub-scanning corresponding direction”. The tendency that the refractive index distribution in the sub-scanning corresponding direction increases with increasing distance from the optical axis in the sub-scanning corresponding direction is common not only in the sub-scanning section of the lens 20 but also in any plane section parallel to the sub-scanning section. . However, as the optical axis of the lens 20 is moved away from the main scanning direction, the change in the refractive index in the distribution of the refractive index in the sub scanning direction (the refractive index on the main scanning section and the refraction at the edge in the sub scanning direction). Rate difference) becomes smaller. This can be easily understood from the fact that in FIG. 2A, the “distance between contours of the refractive index” increases and the change in the refractive index decreases as the optical axis is separated in the main scanning corresponding direction. Would.

The influence of the "pitch unevenness of the scanning line pitch", which is a problem in the present invention, mainly depends on the refractive index distribution in the sub-scanning corresponding direction (see FIG. 2E). is there. The effect of the refractive index distribution in the sub-scanning corresponding direction on the optical performance of the lens 20 appears as “change in focal length in the imaging operation in the sub-scanning corresponding direction”. As described above, the refractive index distribution in the sub-scanning corresponding direction in the lens 20 is “a distribution in which the refractive index increases as the optical axis is separated in the sub-scanning corresponding direction”. Equivalent to a concave lens ".

FIG. 3 is a diagram showing the imaging performance of the lens 20 in the direction corresponding to the sub-scanning. In the sub-scanning corresponding direction, the front principal point of the lens 20 is H, the rear principal point is H ′, the distance from the front principal point H to the object point A is S, and the rear principal point is H ′.
If the distance from the lens 20 to the image point: B is S ′, the power in the sub-scanning corresponding direction when the refractive index of the lens 20 is a constant value: N ₀ is P (the reciprocal of the focal length), The equation is: (1 / S ′) = (1 / S) + P (5) Assuming that a change in the power: P caused by the refractive index distribution such that “increases as the distance from the optical axis in the sub-scanning corresponding direction increases” in the lens 20 is ΔP, a power change:
The amount of displacement of the image point B due to ΔP: ΔS ′ is obtained as follows. That is, when the equation (5) is solved for S ′, S ′ = S / (S · P + 1) (6) As a result, when the amount of change is P and the differential of both sides is obtained, ΔS ′ = S ² / (S · P + 1) ² · (−1) ΔP (7) Since the “refractive index distribution that increases with increasing distance from the optical axis in the sub-scanning corresponding direction” is equivalent to a concave lens, the power change: ΔP is “negative”, and the right side of equation (7) is “positive”.
It is. Therefore, the change in power: ΔP displaces the image point: B away from the rear principal point: H ′. This is nothing but an action to increase the focal length of the lens 20 (a value calculated as a uniform refractive index). Solving the above (7) for ΔP gives ΔP = ΔS ′ · (S · P + 1) ² / S ² (8) Here, the value of the power change amount ΔP in the sub-scanning corresponding direction of the scanning imaging optical system, which is derived from the refractive index distribution, is ΔP _C on the optical axis of the lens 20, and on the most peripheral optical path of the effective scanning area W. Assuming that ΔP _E , as described above, the change in the refractive index in the sub-scanning corresponding direction becomes smaller as the distance from the optical axis in the main scanning corresponding direction becomes smaller. .

That is, the condition in the first aspect of the present invention is as follows: (1) | ΔP _C |> | ΔP _E | is the refractive index non-uniformity of the non-uniform refractive index lens included in the scanning image forming optical system in the sub-scanning corresponding direction. This indicates that the degree of uniformity is greater at the optical axis than at the end in the main scanning direction.

FIG. 4 (a) shows the deflection light reflecting surface 18A of the polygon mirror 18 and the light flux (principal ray of light) from the light source side.
The positional relationship with L is shown. The deflecting / reflecting surface 18A of the polygon mirror changes as indicated by 18A (1), 18A (2), and 18A (3) with the rotation of the polygon mirror in the counterclockwise direction. The reflection positions (of the chief rays) are M: (-), M (0), M
It changes like (+).

The light beam L from the light source is reflected at a reflection position: M (0).
Is formed as a “line image”. Therefore, when the light flux from the light source side enters the reflection positions: M (+) and M (-),
A “shift” occurs between the deflecting / reflecting surface 18A and the image forming position of the line image, and the light beam has not yet formed an image when the light enters the reflecting positions: M (+) and M (−). The “deviation” between the deflecting reflection surface and the reflection position is a so-called “sag”, and generally occurs asymmetrically on both sides of the reflection position: M (0) as shown in FIG. The sag at (−) is larger than the sag at M (+)), but by adjusting the positional relationship between the polygon mirror and the incident side optical system, the reflection position: M
It is also possible to cause sag to occur symmetrically on both sides of (0).

The scanning image forming optical system is generally arranged so that "the reflection position at which the sag becomes 0: the principal ray of the light beam reflected at M (0) coincides with the optical axis of the scanning image forming optical system". FIG.
(B) shows a state in which the position of the deflecting / reflecting surface 18A and the position of the surface to be scanned 22 have a substantially conjugate relationship in the sub-scanning corresponding direction. However, in FIG. 4B, the refractive index of the lens 20 is “uniform refractive index: N ₀ ”.
It is said to have. Reflection position: The light beam reflected at M (0) (the line image long in the main scanning corresponding direction coincides with M (0)) has an image forming position: q _C and the scanning surface 22 due to the above conjugate relationship. Matches. In FIG. 4B, assuming that the luminous flux indicated by the broken line is “a luminous flux reflected at the reflection position: M (+)”, a line image is formed at the position: p in FIG. image "is the image position of the line image: will be imaged to q _E.

Here, considering “the influence of the distribution of the refractive index (equivalent to the effect of increasing the focal length)” in the lens 20, the actual image forming positions: q _C and q _E are calculated as follows. Due to the action, it shifts rightward in FIG. 4B.

Then, the “deflection / reflection surface 1”
The position having a conjugate relationship with 8A moves to the right in FIG. 4B with respect to the surface 22 to be scanned, and does not coincide with the surface 22 to be scanned. Accordingly, the scanning line of the light spot on the surface to be scanned fluctuates a minute distance in the sub-scanning direction if the deflecting / reflecting surface is tilted, causing pitch unevenness. Therefore, in order to effectively reduce this, when designing the lens 22, it is necessary to consider in advance the distribution of the refractive index (which can be experimentally known as described above). First, considering the “refractive index distribution in the sub-scanning corresponding direction in the sub-scanning section” of the lens 20, the refractive index distribution shifts the “imaging position of the deflected light beam toward the back side of the surface to be scanned” as described above. considering that act "like, when designing the refractive index of the lens 20 as a uniform, an imaging position on the optical axis in the sub-scanning direction of the sag-free light beam: a Q _C (surface to be scanned position It can be seen that the position of q _C measured with the polygon mirror side being negative) should be located closer to the polygon mirror than the surface 22 to be scanned. That is, the Q _C should be "negative".

Looking at the imaging position on the outermost optical path of the effective scanning area: Q _E (the position of q _E measured from the position of the surface to be scanned), the light is incident on the reflection position: M (+). The formed light flux forms a line image at the position p in FIG.
_E is the distance in the figure: d _p is the longitudinal magnification of the lens 20: α (= β
² : β is enlarged by lateral magnification). Deflective reflection surface 1
If there is a surface tilt in 8A, the imaging position: p fluctuates in the sub-scanning corresponding direction according to the surface tilt, and the fluctuation is magnified by the lateral magnification β of the lens 20.

The imaging position: "displacement amount due to the action of the refractive index distribution" of q _E, given the less than the amount of displacement of the optical axis, it is better to keep the previously "positive" the Q _E You can see that. That is, if Q _{E is set} to “positive” in advance, the action of the refractive index distribution acts to increase Q _E to the positive side, so that the fluctuation of the light spot formed on the surface to be scanned is the outermost. It is effectively reduced in the optical path.

[0030] Therefore, considering that Q _C is negative, the _{condition: (2) Q E> 0} > can be seen to be satisfied Q _C. Therefore, conditions (1) and (2)
(Preferably, by satisfying (1) and (2 ′)), the tilt of the deflecting and reflecting surface can be corrected well regardless of the presence of the refractive index distribution, and the scanning line pitch unevenness can be improved. Can be effectively reduced.

When a refractive index distribution exists, the above Q
_C, and Q _E is Q _C, respectively ', Q _E' shall change to, the magnitude relation of Q _C ', Q _E', a condition: (3) Q _E satisfying the '> Q _C', That is, it is preferable that the actual image forming position in consideration of the refractive index distribution is close to the surface to be scanned in the optical axis portion. In this manner, in the portion near the optical axis, the pitch unevenness is effectively corrected by the conjugate relationship between the position of the deflection reflecting surface and the position of the surface to be scanned, and in the periphery of the scanning region, the fluctuation of the deflection light flux image point due to the effect of sag is reduced. It is effectively reduced on the surface to be scanned, thereby reducing pitch unevenness.

[0032] Q _C and Q _C relationship ', Q _E and Q _E' is' the use of, Q _C 'aforementioned _{ΔS = Q C + ΔS C'} , Q E ' because a = Q _E + ΔS _E' the (6), (7), the use of _{(8), Q C '= Q C -S} C' 2 · ΔP C, because the _{Q E '= Q E -S E} ' 2 · ΔP E The condition (3) is equivalent to the following condition: (4) Q _E -S _E ' ² · ΔP _E > Q _C -S _C ' ² · ΔP _C (claim 3).

Therefore, by satisfying the conditions (3) and (4), more preferably (3 ') and (4'), pitch unevenness can be effectively reduced.

In the description of the conditions (1) to (4), ΔP _E , Q _E , Q _E ′, S _E ′ are assumed to be “values related to the most peripheral light path in the effective scanning area”. The most peripheral light paths in the effective scanning area are on the start side and the end side of optical scanning. As described above, "sag" can be generated symmetrically on both sides of the reflection position: M (0) depending on the arrangement of the optical system. In such a case, the above-mentioned peripheral light path is located on the scanning start side. The same is true for both the scan end side and the scan end side.

However, in general, the occurrence of the sag is asymmetrically derived on both sides of the reflection position: M (0). In such a case, “ΔP _E , Q _E , Q _E ′, S _E ′” is used. It is preferable to use a value on the outermost optical path on the side where the sag is large in order to favorably reduce pitch unevenness (claim 4).

Alternatively, if the deflection of the deflected light beam is not symmetrical with respect to the optical axis of the non-uniform refractive index lens, and the distance that passes through the lens differs between the two outermost optical paths, the non-uniform refractive index lens is used. Since the power variation due to the refractive index distribution increases as the transmission distance increases, the above-mentioned “ΔP _E , Q _E ,
For Q _E ′ and S _E ′ ”, it is preferable to use values on the longest optical path on the long side where the deflecting light beam passes through the non-uniform refractive index lens (Claim 5).

[0037]

EXAMPLES Specific examples will be described. This example is an example of the optical scanning device whose embodiment is shown in FIG. The semiconductor laser 10 serving as a light source emits a laser beam having a wavelength of 780 nm. The coupling lens 12 couples the light beam from the semiconductor laser 10 into a “light beam having a weak focusing property”. The polygon mirror 18 has six deflection reflection surfaces.
In this case, the radius of the inscribed circle with respect to the deflection reflecting surface is 18 mm. The principal ray of the “light flux from the light source side” formed as a long line image in the main scanning corresponding direction by the cylinder lens 16 is from a “direction forming 60 degrees” with respect to the optical axis of the lens 20 as the scanning image forming optical system. When the light enters the polygon mirror 18 and the principal ray of the deflected light beam coincides with the optical axis of the lens 20 (when the sag is 0), the line image is formed at the position of the deflective reflection surface. The “weakly converging light flux” coupled by the coupling lens 12 is located on the side of the scanning surface 22 along the optical axis of the lens 20 from the position of the deflecting reflection surface, if there is no refraction effect of other optical systems. The light is focused at a position of 308.6 mm toward. The effective scanning area: W is 210 mm. The paraxial radius of curvature of the lens 20 in the main scanning section: Rm, the surface interval on the optical path from the deflecting / reflecting surface (the position where sag is 0) to the surface to be scanned: D, and the refractive index of the material of the lens 20: N ₀ The data is as follows.

Rm DN ₀ deflection reflection surface-48.06-entrance side surface 199.5 20.00 1.51933 exit side surface-216.0 106.64-.

The shape of the lens 20 in the main scanning section is a "non-arc shape" on both sides, and a well-known formula relating to the aspheric surface is as follows: X = Y ² / [Rm + Rm√ {1- (1 + K) (Y / Rm) ² }]
+ AY ⁴ + BY ⁶ + CY ⁸ + DY ¹⁰ +. . , The coordinates in the main scanning direction: Y (the position of the optical axis is the origin), the coordinates in the optical axis direction: X, and the shape is specified by giving Rm (paraxial radius of curvature), K, and A to D. . Shape of the incident side surface of the lens 20 in the main scanning section: Rm = 199.5, K = −35.1384, A = −1.
985E-7, B = 2.169E-11, C = 1.
902E-15, D = -1.880E-19 Shape of the exit side surface of the lens 20 in the main scanning section: Rm = -216.0, K = 2.106, A = -3.7
09E-7, B = 1.713E-11, C = -5.9
30E-15, D = 1.480E-18
.

The shape of the lens 20 in a plane perpendicular to the main scanning corresponding direction is such that the radius of curvature in the plane on both surfaces is determined by a polynomial: Rs (Y) = Rs +
Σb _n · Y ** n (n = 1, 2, 3,...)
The shape is specified by giving the radius of curvature on the optical axis: Rs and the coefficient: b _n . Radius of curvature in a plane orthogonal to the main scanning direction of the incident side surface of the lens 20: Rs = −40.03, b ₂ = −1.1900E−2, b _{4
= 1.6780E-5, b 6 =} -1.7646E-
8, b ₈ = 9.9902E-12, b ₁₀ = -2.83
_{55E-15, b 12 = 3.1540E} -19 lens in the plane perpendicular to the main scanning correspondence direction of the exit side of 20 curvature _{radius: Rs = -15.76, b 1 =} -4.0244E-4, b 2
_{= -1.0448E-3, b 3 =} 1.6834E-
_{6, b 4 = 7.8853E-7} , b 5 = -4.0206
_{E-10, b 6 = -1.0976E} -10
.

FIG. 5 shows the lens 2 specified by the above data.
0, the curvature of field in the main scanning direction when there is no refractive index distribution (FIG. 5A), the constant velocity characteristic calculated by the equation of fθ characteristic (FIG. 5B), and the sub-scanning direction. (Solid line in (c)). Each of the data in the embodiment is designed in consideration of “non-uniformity of the refractive index” in the lens 20, and the solid line in FIG.
Is represented. The values of the parameters in the conditions (1) to (4) are as follows. _{| ΔP C | = 3.22E-4} , | ΔP E | = 0 Q E = 4.72mm, Q C = -3.27mm Q E '= 4.72mm, Q C' = -0.05mm Q E - ^{_{S E '2 · ΔP E =}} 4.72mm, Q C -S C' 2 · Δ
P _C = −0.06 mm Accordingly, the embodiment satisfies all of the conditions (1) to (4). In the above, “E and the numerical value following it” are “1”
Power of zero. " Therefore, for example, if "E-9" is given, this means "10 to ⁹ ", and this numerical value is multiplied by the numerical value immediately before it.

The field curvature in the sub-scanning direction when the lens 20 has a refractive index distribution, that is, the “actual field curvature in the sub-scanning direction” is shown in FIG. The beam waist position in the corresponding direction, which is a wave optical imaging position, but does not substantially differ from geometric optical field curvature). As is clear from the field curvature (solid line and dot) in FIG. 5C, the conditions (2 ′), (3 ′),
(4 ′) is satisfied. Note that FIGS. 5A and 5B
The refractive index distribution does not substantially affect the curvature of field in the main scanning direction and the constant velocity characteristic shown in FIG.

FIG. 6 shows the "pitch unevenness characteristic" for the above embodiment and comparative example. The horizontal axis is the image height of the light spot,
The pitch unevenness on the vertical axis represents the shift amount of the light spot in the sub-scanning direction when the deflecting reflection surface has “60 ″ surface tilt”.

In FIG. 6, “は” is an example, and “×” is a comparative example. Numerical values in parentheses next to “○” and “×” indicate results of the deflection light beam in the sub-scanning direction. This is the distance measured from the image position to the surface to be scanned.

For example, looking at a portion where the image height is -105 mm, in the comparative example, the deflection light beam forms an image at the position of the surface to be scanned (Q '= 0.0 mm) in the sub-scanning corresponding direction at this time. Therefore, due to the influence of the above-mentioned “60 ″ plane tilt”, the image forming position of the light spot in the sub-scanning direction is shifted from the image forming position when there is no surface tilt by about 1 μm in the sub-scanning direction. On the other hand, in the embodiment, the image forming position of the deflected light beam in the sub-scanning corresponding direction is "4.7 m behind the surface to be scanned".
m, but the fluctuation amount of the light spot due to the surface tilt is reduced to about 0.2 μm. For example, image height: 0
mm, the image forming position of the light spot in the sub-scanning corresponding direction is-
5 mm (solid line in FIG. 5C) to 0 mm (FIG. 5C).
(C), the pitch unevenness is improved.

Looking at the entire effective scanning area, the above “6.
The deviation of the scanning line due to “0 ″ plane tilt” is larger than 0.5 μm in the comparative example, but smaller than 0.5 μm in the embodiment. That is, in the embodiment, the pitch unevenness of the scanning lines is corrected well.

[0047]

As described above, according to the present invention, a novel scanning image forming optical system and an optical scanning device using the same can be realized. Since the scanning imaging optical system of the present invention is designed to obtain predetermined optical characteristics by considering the refractive index of the non-uniform refractive index lens in advance, the refractive index of the non-uniform refractive index lens is adjusted. Irrespective of the distribution, it is possible to effectively reduce the scan line pitch unevenness.

Further, since the optical scanning device of the present invention uses the above-mentioned scanning image forming optical system, it is possible to effectively reduce the unevenness of the scanning line pitch and realize good optical scanning.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining one embodiment of an optical scanning device of the present invention.

FIG. 2 shows a non-uniform refractive index lens 2 according to the embodiment.
It is a schematic diagram explaining the refractive index distribution of 0.

FIG. 3 is a diagram for explaining an image forming function of a non-uniform refractive index lens 20 in a direction corresponding to sub-scanning.

FIG. 4 is a diagram for explaining sag by a polygon mirror and its influence.

FIG. 5 is a diagram illustrating field curvature and constant velocity characteristics according to the embodiment.

FIG. 6 is a diagram for explaining a pitch unevenness reducing effect according to the embodiment.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Semiconductor laser 12 Coupling lens 14 Aperture 16 Cylinder lens 18 Polygon mirror 20 Non-uniform refractive index lens 22 Scanning surface W Effective scanning area

 ────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Hiroyuki Suhara 1-3-6 Nakamagome, Ota-ku, Tokyo, Ricoh Co., Ltd.

Claims (7)

[Claims] A light beam from a light source side is formed into a long line image in a direction corresponding to the main scanning, and the light beam is deflected by a polygon mirror having a deflecting / reflecting surface in the vicinity of the image forming position of the line image. A scanning image forming optical system in an optical scanning device that performs light scanning by condensing a light spot on a surface to be scanned by an optical system, and has a non-uniform refractive index lens having a refractive index distribution in a sub-scanning corresponding direction. The amount of power change in the sub-scanning corresponding direction of the scanning imaging optical system derived from the refractive index distribution is ΔP _C on the optical axis, ΔP _E on the outermost optical path of the effective scanning area, and the refractive index non-uniformity When the lens has a uniform refractive index: N ₀ , the image forming position of the deflected light beam in the sub-scanning corresponding direction by the scanning image forming optical system is measured from the position of the surface to be scanned, and the polygon mirror side is defined as a negative value. Q _C, effective run in When the Q _E at the outermost peripheral light path of査領zone _{conditions: (1) | ΔP C |} > | ΔP E | (2) Q E>0> scanning imaging optics, characterized by satisfying the Q _C system. 2. A scanning imaging optical system according to claim 1, wherein an image forming position of the deflected light beam in the sub-scanning corresponding direction by the scanning imaging optical system is taken into consideration when a refractive index distribution of the non-uniform refractive index lens is considered. When the polygon mirror side is negative on the basis of the scanning plane position and Q _C ′ on the optical axis and Q _E ′ on the most peripheral optical path of the effective scanning area, condition: (3) Q _E ′> Q _C ′ A scanning imaging optical system characterized by satisfying. 3. The scanning imaging optical system according to claim 1, wherein a distance from a rear principal point in the sub-scanning corresponding direction of the scanning imaging optical system to an imaging point in the sub-scanning corresponding direction is set on the optical axis. When S _C ′ and S _E ′ are on the outermost optical path of the effective scanning area, the condition: (4) satisfies Q _E −S _E ′ ² · ΔP _E > Q _C −S _C ' ² · ΔP _C A scanning imaging optical system characterized by the above. 4. A scanning image forming optical system according to claim 2, wherein ΔP _E , Q _E , Q _E ′, S _E ′ are values on the most peripheral optical path on the side where the sag is large. Scanning imaging optical system. 5. The scanning imaging optical system according to claim 2, wherein ΔP _E , Q _E , Q _E ′, and S _E ′ are on the long side of the distance through which the deflecting light beam passes through the non-uniform refractive index lens. A scanning image forming optical system characterized by being a value on an outermost optical path. 6. The scanning image forming optical system according to claim 1, wherein the scanning image forming optical system is constituted by one non-uniform refractive index lens, and has a main scanning sectional shape of both. A scanning imaging optical system having a convex shape. 7. A light beam from a light source side is formed into a long line image in a direction corresponding to the main scanning, and the light beam is deflected by a polygon mirror having a deflecting reflection surface near an image forming position of the line image. An optical scanning device that performs optical scanning by condensing a light spot on a surface to be scanned by an optical system, wherein the scanning imaging optical system according to any one of claims 1 to 6 is used as a scanning imaging optical system. An optical scanning device characterized by being used.