JP2002098807A - Rod lens array for line scanning - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a rod lens array for line scanning which is bright with high resolution and which can suppress periodical irregularity of the light quantity within <10%. SOLUTION: A rod lens array 2 which produces an unmagnified image is used for the rod lens array for line scanning. The array 2 is manufactured by arranging a plurality of cylindrical rod lenses 1 having the gradient refractive index in its radial direction with the optical axes 1a of the lenses parallel to one another and by arranging the rod lenses into two lines along the main scanning direction. The effective overlap degree m is controlled to satisfy 0.89 D/d<=m<=0.95 D/d and 1.10 D/d<=m<=1.28 D/d, wherein d is the lens diameter of the rod lens 1 and D is the arrangement pitch of the rod lenses 1.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a rod lens array for line scanning as a line scanning optical system used for a scanner, a printer and the like.

[0002]

2. Description of the Related Art Conventionally, as a line scanning optical system used for a scanner, a printer, or the like, a rod lens having a refractive index distribution in a radial direction is mainly arranged in a plurality of rows so that their optical axes are parallel to each other mainly from the viewpoint of cost. A rod lens array in which a plurality of rod lenses are arranged is widely used. In this case, the degree of overlap m defined by the following (Equation 7) is set in consideration of the balance between the periodic light amount unevenness and the resolution. [Equation 7] m = X ₀ / 2r ₀ where, in the above (Equation 7), r ₀ is the radius of the rod lens, and X ₀ is the image radius (field radius) of the single rod lens on the image plane. Here, X ₀ is X ₀ where Z _{0 is} the length of the rod lens and P is the period length of the rod lens.
₀ = −r ₀ / cos (Z ₀ π / P)

[0003] When the degree of overlap m increases, the resolution deteriorates, and when the degree of overlap m decreases, the periodic light quantity unevenness increases. However, it is important to suppress the occurrence of the periodic light quantity unevenness in the rod lens array design. So
Generally, in order to suppress periodic light amount unevenness which causes vertical stripes (streaks) in the sub-scanning direction of an output image, the degree of overlap m
Is set relatively large.

In a printer using an LED array optical system as a light source, the light amount of each point light source is corrected so as to cancel out the periodic light amount unevenness of the rod lens array. Further, in the scanner, input correction (shading correction) is performed so as to cancel out periodic light amount unevenness of the rod lens array. These corrections have been made possible as a result of advances in digital data processing technology, and it is possible to easily correct periodic light amount unevenness of about 10%.

On the other hand, the resolution of each device has been improved, and the optical printer has a resolution of 600 dpi to 12 dpi.
The transition to 00 dpi has begun.

[0006]

However, when a lens design in which the degree of overlap m is set relatively large is adopted, it is difficult to realize a bright and high-resolution rod lens array for line scanning.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems in the prior art, and is a line scanning rod lens array which is bright, has high resolution, and can suppress periodic unevenness in light quantity to less than 10%. The purpose is to provide.

[0008]

In order to achieve the above object, a first configuration of a linear scanning rod lens array according to the present invention comprises a rod lens having a refractive index distribution in a radial direction, and optical axes of the rod lenses having a refractive index distribution in the radial direction. 1 in the main scanning direction to be parallel
A rod lens array for linear scanning constituted by arranging a plurality of rod lenses in a row, wherein the lens diameter of the rod lens is d, the arrangement pitch of the rod lenses is D, and the image radius of a single rod lens on the image plane. Is defined as X ₀ and the degree of overlap is defined as m = X ₀ / d, and the degree of overlap m is within the range defined by the following (Equation 8) and (Equation 9). [Equation 8] 1.57 D / d ≦ m ≦ 1.70 D / d [Equation 9] 2.04 D / d ≦ m ≦ 2.42 D / d The second of the rod lens array for line scanning according to the present invention.
Has a configuration in which a rod lens having a refractive index distribution in the radial direction is moved in the main scanning direction so that its optical axes are parallel to each other.
A line lens array for linear scanning constituted by arranging a plurality of lines in an even-numbered or more rows, wherein the lens diameter of the rod lenses is d, the arrangement pitch of the rod lenses is D, and a single rod lens is an image surface. X ₀ , the overlap radius is m
= X ₀ / d, the degree of overlap m is:
It is within the range defined by (Equation 11). [Equation 10] 0.89 D / d ≦ m ≦ 0.95 D / d [Equation 11] 1.10 D / d ≦ m ≦ 1.28 D / d Also, the third of the rod lens array for line scanning according to the present invention.
Is that a rod lens having a refractive index distribution in the radial direction is moved in the main scanning direction so that its optical axes are parallel to each other.
A linear scanning rod lens array configured by arranging a plurality of odd-numbered rows or more, wherein the lens diameter of the rod lenses is d, the arrangement pitch of the rod lenses is D, and a single rod lens is an image surface. X ₀ , the overlap radius is m
= X ₀ / d, the degree of overlap m is as follows (Equation 12):
It is characterized by being within the range defined by (Equation 13). [Equation 12] 1.44 D / d ≦ m ≦ 1.56 D / d [Equation 13] According to the configuration of the linear scanning rod lens array of 1.80 D / d ≦ m ≦ 2.13 D / d, it is bright. High resolution and 10% periodic light intensity unevenness
It is possible to realize a rod lens array for line scanning that can be suppressed to less than.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described more specifically with reference to embodiments.

FIG. 1 shows a first embodiment of the present invention.
FIG. 2 is a perspective view showing a rod lens array for line scanning in the embodiment, and FIG. 2 is a perspective view showing a rod lens used in the rod lens array.

As shown in FIGS. 1 and 2, in the present embodiment, as a linear scanning rod lens array, a columnar rod lens 1 having a refractive index distribution in the radial direction is formed. A rod lens array 2 of a same-magnification image is used in which a plurality of lenses are arranged in two rows in the main scanning direction so as to be parallel. Here, the “main scanning direction” refers to the longitudinal direction of the rod lens array 2. Rod lens array 2
The document surface 3 and the image surface 4 are respectively located on both sides of the document. In the line scanning method, an image on the brightest center line of the rod lens array 2 is used. That is, the image is received as a line.

As shown in FIG. 3, the refractive index n of the rod lens 1 is distributed in the radial direction.
It is represented by the following (Equation 14). [Expression ^{14] n (r) 2 =} n 0 2 · {1- (g · r) 2 + h 4 · (g ·
r) ⁴ + h ₆ · (g · r) ⁶ + h ₈ · (g · r) ⁸ ｝ where, in the above (Equation 14), r is a radial distance measured from the optical axis 1 a of the rod lens 1, and n ( r) is the refractive index at the position of distance r in the radial direction measured from the optical axis 1a of the rod lens 1, n ₀ is the refractive index at the optical axis 1a of the rod lenses 1 (central refractive index), g, h _4, h _6, h ₈ is a refractive index distribution coefficients.

The radius r ₀ of the rod lens 1 is 0.05 m
It is desirable that the range is m ≦ r ₀ ≦ 0.60 mm.

The amount of blurring of an image due to various aberrations of the rod lens 1 increases in proportion to the size of the entire lens.
_A lens with a smaller ₀ is easier to achieve high resolution. But,
The rod lens 1 whose r ₀ is less than 0.05 mm is difficult to manufacture and assemble, and the rod lens array 2 in which the radius r ₀ of the effective lens portion of each rod lens 1 exceeds 0.60 mm. Causes the aberration amount to be too large.

The achievable value of the refractive index (center refractive index) n ₀ on the optical axis 1a of the rod lens 1 is determined by the material (glass or synthetic resin) of the rod lens.
It is in the range of 1.4 ≦ n ₀ ≦ 1.8.

The brightness of the rod lens 1 is a dimensionless number g ·
It is defined by r ₀ or an opening angle (maximum incident angle) indicating a range in which the lens can take in light. Here, the opening angle θ (°) is represented by the following (Equation 15). [Equation 15] θ = (n ₀ · g · r ₀ ) / (π / 180) The dimensionless number g · r ₀ is desirably in the range of 0.04 ≦ g · r ₀ ≦ 0.27. When g · r ₀ is less than 0.04, the image becomes dark and scanning takes time, and when g · r ₀ exceeds 0.27, the influence of field curvature and astigmatism is obtained. Is increased, and the resolution is reduced.

The desirable range of the above-mentioned g · r ₀ is, for example, when the central refractive index is set to n ₀ = 1.60, 4 ° ≦ θ ≦ 2
Corresponds to 4 °.

In order to form an erect image as shown in FIG.
Assuming that the length of the rod lens 1 is Z ₀ and the periodic length of the rod lens 1 is P (= 2π / g), Z ₀ / P is 0.5 <
It is necessary to be in the range of Z ₀ /P<1.0.

End surface (lens surface) of rod lens array 2
The distance between the image surface 4 and the document surface 3 and the distance L ₀ between the end surface (lens surface) of the rod lens array 2 and the image surface 4 (see FIG. 1) are represented by the following (Equation 16). [Equation 16] L ₀ = − (1 / (n ₀ · g)) · tan (Z ₀ π / P) Here, the distance between the document surface 3 and the image surface 4 (Z ₀ + 2L ₀ )
Is called “conjugate length (TC)”.

In the rod lens array 2 as described above, as shown in FIG. 5, since a composite image is formed by the plurality of rod lenses 1 on the image plane 4, there is no overlapping condition, that is, no "overlapping degree". It is convenient to use dimensional quantities. The degree of overlap m is represented by the following (Equation 17). [Equation 17] m = X ₀ / d However, in the above (Equation 17), d is the lens diameter of the rod lens 1 (= 2r ₀ ). X ₀ is the image radius (field radius) of the single rod lens 1 extending to the image plane 4 and is defined by X ₀ = −r ₀ / cos (Z ₀ π / P).

Incidentally, as the degree of overlap m increases, the brightness of the lens decreases and the resolution deteriorates.

The present inventor has proposed that the opening angle θ is 12 °,
Using the linear scanning rod lens array 2 having the above-described configuration including the 17 ° and 20 ° rod lenses 1,
The periodic light amount unevenness ΔE with respect to the degree of overlap m was calculated by real ray tracing and evaluated. FIG. 6 shows the calculation results.

Further, as shown in FIG. 7, the periodic light amount unevenness ΔE is obtained by making uniform light incident on the rod lens array 2 by using a diffusion surface light source 5 such as a halogen lamp. The emitted light is detected by the CCD image sensor 6, and the maximum value I _max of the light intensity change in the array direction is obtained.
By obtaining the minimum value I _min , the average value of the light intensity change in the array direction can be experimentally measured from the following ( _Equation 18) as I _ave . [Equation 18] ΔE = 100 (I _max −I _min ) / I _ave (%) It was found that the experimental measurement result substantially coincided with the simulation result by the above-described real ray tracing.

From the calculation results shown in FIG. 6, the effective overlapping degree m that can suppress the periodic light amount unevenness to less than 10%.
Is as shown in (Table 1) below. As shown in FIG. 6, the periodic light amount unevenness repeatedly increases and decreases periodically with respect to the degree of overlap m, and tends to decrease as the degree of overlap m increases. However, as described above, as the degree of overlap m increases, the brightness of the lens decreases and the resolution deteriorates. Therefore, in the following (Table 1), the range of the effective overlap degree m is defined so that the periodic light amount unevenness is less than 10% in the range where the overlap degree m is small. [Table 1] Aperture angle (maximum incidence angle) Range of effective overlapping degree m 12 ° 0.89 to 0.93, 1.10 to 1.25 17 ° 0.89 to 0.94, 1.10 to 1 .27 20 ゜ 0.89 to 0.95, 1.10 to 1.28 Note that the results in Table 1 above are for the case where the adjacent rod lenses 1 are arranged so as to be in contact with each other. When there is a gap between the rod lenses 1, that is, when the lens diameter d (= 2r ₀ ) of the rod lenses 1 is smaller than the arrangement pitch D of the rod lenses 1 (d ≦ D) as shown in FIG. Is D / d to the value of each overlap degree m.
Multiplied by. That is, when the rod lens 1 having an aperture angle of 12 ° is used, the effective range of the degree of overlap m is 0.1 mm.
89D / d ≦ m ≦ 0.93D / d, 1.10D / d ≦ m
<1.25 D / d.

In the above (Table 1), two ranges are listed as the effective overlap degree m (for example, a rod lens array 2 for line scanning provided with a rod lens 1 having an opening angle θ of 12 °). , The first range: 0.89-0.
93, second range: 1.10-1.25).

At the overlapping degree m smaller than the first range, the periodic light amount unevenness does not become 10% or less. Therefore, in the first range, the periodic light amount unevenness is 10%.
And the highest brightness and resolution of the lens. However, especially when the rod lens 1 having a small opening angle θ is used, the first range is considerably narrowed, and it is somewhat difficult to set an effective overlap degree m. For this reason, the second range is defined as a range of the effective overlap degree m. This second range is 3 times larger than the first range.
Since it is about twice as wide, the effective overlap degree m can be easily set.

As described above, the periodic light quantity unevenness repeatedly increases and decreases periodically as the overlap degree m increases, and the periodic light quantity unevenness increases when the overlap degree m is larger than the second range. There is a small range of. For example, FIG.
As shown in the figure, m = 1.31 to 1.54 corresponds to this. However, in this range, the brightness of the lens is reduced to about 70% of the first range, and the effective overlap m
Cannot be used as a range.

As described above, in the present embodiment,
Since the range of the effective overlapping degree m is specified so that the periodic light amount unevenness is less than 10% in the range where the overlapping degree m is small, the incident angle in the sub-scanning direction (the direction orthogonal to the main scanning direction) is large. As a result, vignetting of the effective light beam is reduced. As a result, a bright rod lens array 2 can be realized. When the degree of overlap m is small, the conjugate length: T
C = Z ₀ + 2L ₀ is also shorter, and the ray aberration is smaller, so that the resolution is improved. Also, the conjugate length (T
Since C) becomes small, the amount of position shift of the image point with respect to the inclination of the rod lens array 2 becomes small. As a result, the tolerance of the inclination (array accuracy) of the rod lens 1 increases.

As described above, the rod lens 1 having the refractive index distribution in the radial direction is arranged in two rows in the main scanning direction so that the optical axes 1a thereof are parallel to each other. In the rod lens array 2, the lens diameter of the rod lens 1 is d, the arrangement pitch of the rod lenses 1 is D, and the image radius of the single rod lens 1 on the image plane is X.
₀ , when the degree of overlap is m = X ₀ / d, if the degree of overlap m is within the range defined by the following (Equation 19) and (Equation 20), the light amount is bright, high in resolution, and periodic. It becomes a rod lens array for linear scanning that can suppress unevenness to less than 10%. [Equation 19] 0.89 D / d ≦ m ≦ 0.95 D / d [Equation 20] 1.10 D / d ≦ m ≦ 1.28 D / d In this embodiment, the rod lens array for line scanning is used. A rod lens array 2 having a same-magnification image in which a plurality of cylindrical rod lenses 1 having a refractive index distribution in a radial direction are arranged in two rows in a main scanning direction so that their optical axes 1a are parallel to each other is used. However, even when a rod lens array having the same magnification as that of a plurality of lenses arranged in even rows of two or more rows is used, the degree of overlap m is defined by the above (Equation 19) and (Equation 20). It has been found that a linear scanning rod lens array that is bright and has high resolution and that can suppress periodic light amount unevenness to less than 10% can be realized within the range. This is considered to be because light does not substantially go to the outer rod lens when the degree of overlap m is in a small range.

[Second Embodiment] FIG. 9 shows a second embodiment of the present invention.
It is a perspective view which shows the rod lens array for a line scanning in embodiment.

As shown in FIGS. 2 and 9, in the present embodiment, a cylindrical rod lens 1 having a refractive index distribution in the radial direction is used as a linear scanning rod lens array. A rod lens array 2 of a same-magnification image, which is arranged in a row in the main scanning direction so as to be parallel, is used. The other configuration is the same as that of the first embodiment, and the description is omitted.

Also in the present embodiment, the present inventor has proposed a line-scanning rod lens array 2 having the above-described configuration, which includes rod lenses 1 having opening angles θ of 12 °, 17 °, and 20 °, respectively. The periodic light amount unevenness ΔE with respect to the degree of overlap m was calculated by real ray tracing and evaluated.
FIG. 10 shows the calculation results.

From the calculation results shown in FIG. 10, the effective overlapping degree m that can suppress the periodic light amount unevenness to less than 10% is as shown in the following Table 2. [Table 2] Aperture angle (maximum incident angle) Range of effective overlapping degree m 12 ゜ 1.57 to 1.65, 2.04 to 2.34 17 ゜ 1.57 to 1.68, 2.04 to 2 .38 20 ゜ 1.57 to 1.70, 2.04 to 2.42 Also in the present embodiment, when there is a gap between adjacent rod lenses 1, the value of each degree of overlap m is multiplied by D / d. Value.

As described above, a linear scanning rod in which a plurality of rod lenses 1 having a refractive index distribution in the radial direction are arranged in a row in the main scanning direction so that their optical axes 1a are parallel to each other. In the lens array 2, the lens diameter of the rod lens 1 is d, the arrangement pitch of the rod lens 1 is D,
Assuming that the image radius that the single rod lens 1 stretches on the image plane is X ₀ and the degree of overlap is m = X ₀ / d, the degree of overlap m is within the range defined by the following (Equation 21) and (Equation 22). In this case, a linear scanning rod lens array can be obtained which is bright, has high resolution, and can suppress periodic light amount unevenness to less than 10%. [Equation 21] 1.57 D / d ≦ m ≦ 1.70 D / d [Equation 22] 2.04 D / d ≦ m ≦ 2.42 D / d [Third Embodiment] FIG. 11 shows a third embodiment of the present invention. It is a perspective view which shows the rod lens array for a line scanning in embodiment.

As shown in FIGS. 2 and 11, in the present embodiment, a columnar rod lens 1 having a refractive index distribution in the radial direction is used as a linear scanning rod lens array.
3 in the main scanning direction so that the optical axes 1a are parallel to each other.
A rod lens array 2 having a same size image formed by arranging a plurality of lines in a row is used. The other configuration is the same as that of the first embodiment, and the description is omitted.

In the present embodiment, the present inventor has also proposed a line-scanning rod lens array 2 having the above-described configuration, which includes rod lenses 1 having opening angles θ of 12 °, 17 °, and 20 °, respectively. The periodic light amount unevenness ΔE with respect to the degree of overlap m was calculated by real ray tracing and evaluated.
FIG. 12 shows the calculation results.

From the calculation results shown in FIG. 12, the effective overlapping degree m that can suppress the periodic light amount unevenness to less than 10% is as shown in Table 3 below. [Table 3] Aperture angle (maximum incidence angle) Range of effective overlapping degree m 12 ゜ 1.44 to 1.54, 1.82 to 2.10 17 ゜ 1.44 to 1.55, 1.81 to 2 .12 20 ゜ 1.44 to 1.56, 1.80 to 2.13 Also in the present embodiment, when there is a gap between adjacent rod lenses 1, the value of each degree of overlap m is multiplied by D / d. Value.

As described above, the rod lens 1 having the refractive index distribution in the radial direction is arranged in a plurality in three rows in the main scanning direction so that the optical axes 1a thereof are parallel to each other. In the lens array 2, the lens diameter of the rod lens 1 is d, the arrangement pitch of the rod lens 1 is D,
Assuming that the image radius that the single rod lens 1 stretches on the image plane is X ₀ and the degree of overlap is m = X ₀ / d, the degree of overlap m is within the range defined by the following (Equation 23) and (Equation 24). In this case, a linear scanning rod lens array can be obtained which is bright, has high resolution, and can suppress periodic light amount unevenness to less than 10%. [Equation 23] 1.44 D / d ≦ m ≦ 1.56 D / d [Equation 24] 1.80 D / d ≦ m ≦ 2.13 D / d In the present embodiment, the rod lens array for line scanning is used. A rod lens array 2 of the same-magnification image, in which a plurality of cylindrical rod lenses 1 having a refractive index distribution in a radial direction are arranged in three rows in the main scanning direction so that their optical axes 1a are parallel to each other, is used. However, even in the case where a rod lens array of the same magnification is used in which a plurality of odd-numbered rows are arranged in three or more rows, the degree of overlap m is defined by the above (Equation 23) and (Equation 24). It has been found that a linear scanning rod lens array that is bright and has high resolution and that can suppress periodic light amount unevenness to less than 10% can be realized within the range. This is considered to be because light does not substantially go to the outer rod lens in the range where the degree of overlap m is small, as described above.

[0039]

As described above, according to the present invention,
Bright, high resolution and periodic light intensity unevenness of 10
% Can be realized.

[Brief description of the drawings]

FIG. 1 is a perspective view showing a rod lens array for linear scanning according to a first embodiment of the present invention.

FIG. 2 is a perspective view showing a rod lens used for a line scanning rod lens array according to the embodiment of the present invention.

FIG. 3 is a refractive index distribution curve of a rod lens used in a rod lens array for linear scanning according to an embodiment of the present invention.

FIG. 4 is a schematic diagram showing an image formation state by a rod lens used in a line scanning rod lens array according to an embodiment of the present invention.

FIG. 5 is a schematic view showing a state where images are synthesized by a plurality of rod lenses of a rod lens array for line scanning according to an embodiment of the present invention.

FIG. 6 is a diagram illustrating a calculation result of periodic light amount unevenness of the rod lens array for linear scanning according to the first embodiment of the present invention.

FIG. 7 is a perspective view showing a system for measuring periodic light quantity unevenness of the rod lens array for line scanning according to the embodiment of the present invention.

FIG. 8 shows a lens diameter d and an arrangement pitch D of the rod lenses of the linear scanning rod lens array according to the embodiment of the present invention.
Schematic diagram showing the relationship

FIG. 9 is a perspective view showing a rod lens array for linear scanning according to a second embodiment of the present invention.

FIG. 10 is a diagram illustrating a calculation result of periodic light amount unevenness of a rod lens array for linear scanning according to a second embodiment of the present invention.

FIG. 11 is a perspective view showing a rod lens array for linear scanning according to a third embodiment of the present invention.

FIG. 12 is a diagram showing a calculation result of periodic light amount unevenness of a rod lens array for linear scanning according to a third embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Rod lens 1a Optical axis 2 Rod lens array for line scanning

Claims (3)

[Claims] 1. A linear scanning rod lens array comprising a plurality of rod lenses having a refractive index distribution in a radial direction arranged in a row in a main scanning direction such that their optical axes are parallel to each other. And the lens diameter of the rod lens is d,
The arrangement pitch of the rod lenses is D, the image radius of a single rod lens on the image plane is X ₀ , and the degree of overlap is m = X ₀ /
When d is set, the overlapping degree m is in a range defined by the following (Equation 1) and (Equation 2). [Equation 1] 1.57 D / d ≦ m ≦ 1.70 D / d [Equation 2] 2.04 D / d ≦ m ≦ 2.42 D / d 2. A line scanning rod comprising a plurality of rod lenses having a refractive index distribution in a radial direction arranged in two or more even rows in the main scanning direction such that their optical axes are parallel to each other. A lens array, wherein the lens diameter of the rod lens is d, the arrangement pitch of the rod lenses is D, the image radius of a single rod lens on the image plane is X ₀ , and the degree of overlap is m = X ₀ / d. Wherein the degree of overlap m is in a range defined by the following (Equation 3) and (Equation 4). [Equation 3] 0.89 D / d ≦ m ≦ 0.95 D / d [Equation 4] 1.10 D / d ≦ m ≦ 1.28 D / d 3. A rod for linear scanning constituted by arranging a plurality of rod lenses having a refractive index distribution in the radial direction in three or more odd rows in the main scanning direction so that their optical axes are parallel to each other. A lens array, wherein the lens diameter of the rod lens is d, the arrangement pitch of the rod lenses is D, the image radius of a single rod lens on the image plane is X ₀ , and the degree of overlap is m = X ₀ / d. Wherein the degree of overlap m is in the range defined by the following (Equation 5) and (Equation 6). [Equation 5] 1.44 D / d ≦ m ≦ 1.56 D / d [Equation 6] 1.80 D / d ≦ m ≦ 2.13 D / d