1. Field of the Invention
The present invention relates to erecting equal-magnification lens array plates used in image reading devices and image forming devices and to image sensor units and image reading devices using the erecting equal-magnification lens array plate.
2. Description of the Related Art
Some image reading devices such as scanners according to the related art are known to use erecting equal-magnification optics. Erecting equal-magnification optics are capable of reducing the size of devices better than reduction optics. In the case of image reading devices, an erecting equal-magnification optical system comprises a line light source, an erecting equal-magnification lens array, and a line image sensor.
A rod lens array capable of forming an erect equal-magnification image is used as an erecting equal-magnification lens array in an erecting equal-magnification optical system. Normally, a rod lens array comprises an array of rod lenses in the longitudinal direction (main scanning direction of the image reading device) of the lens array. By increasing the number of columns of rod lenses, the proportion of light transmitted is improved and unevenness in the amount of light transmitted is reduced. Due to price concerns, it is common to use one or two columns of rod lenses in a rod lens array.
Meanwhile, an erecting equal-magnification lens array plate could be formed as a stack of a plurality of transparent lens array plates built such that the optical axes of individual convex lenses are aligned, where each transparent lens array plate includes a systematic arrangement of micro-convex lenses on one or both surfaces of the plate. Since an erecting equal-magnification lens array plate such as this can be formed by, for example, injection molding, erecting equal-magnification lens arrays in a plurality of columns can be manufactured at a relatively low cost.
An erecting equal-magnification lens array plate lacks a wall for beam separation between adjacent lenses. Therefore, there is a problem of stray light wherein a light beam diagonally incident on an erecting equal-magnification lens array plate travels diagonally inside the plate and enters an adjacent convex lens, creating a ghost image as it leaves the plate.
Patent document No. 1 discloses a technology to address stray light whereby a light shielding wall is provided on the surface of an erecting equal-magnification lens array plate and a partition having a slit opening is provided around the erecting equal-magnification lens array plate. Patent document No. 2 discloses an imaging optical system provided with a light shielding means on an intermediate imaging surface of an erecting equal-magnification lens array plate.
In the case of the imaging optical system disclosed in patent document No. 1, however, it is difficult to reduce the size and weight of the optical system due to the partition having a slit opening and provided around the erecting equal-magnification lens array plate.
In the case of an imaging optical system disclosed in patent document No. 2, stray light in the sub-scanning direction (lateral direction of the erecting equal-magnification lens array plate) can be eliminated by the light shielding means. Our study revealed, however, that it is difficult to eliminate stray light in the main scanning direction.
Due to an error occurring when a convex lens of a lens array plate is formed, the optical axes of the convex lenses on the respective sides of the plate may not be aligned. In this case, unless a shielding means for eliminating stray light is properly located, it will be difficult to locate a line image sensor properly to achieve desired optical performance, with the result that the manufacturing cost is increased.
In this background, a purpose of the present invention is to provide an erecting equal-magnification lens array plate capable of eliminating stray light suitably, allowing reduction of the size and weight of an optical system, and reducing the cost of manufacturing an image sensor unit, and an image sensor unit and an image reading device using the inventive erecting equal-magnification lens array plate.
An erecting equal-magnification lens array plate addressing the purpose includes a stack of a plurality lens array plates built such that pairs of corresponding lenses form a coaxial lens system, where each lens array plate is formed with a plurality of lenses on both surfaces of the plate, the plate receiving light from a substantially straight light source facing one side of the plate, and the plate forming an erect equal-magnification image of the substantially straight light source on an image plane facing the other side of the plate, wherein the plurality of lenses in each lens array plate are arranged such that the main lens array direction differs from the main scanning direction, a light shielding member operative to shield light not contributing to imaging is formed in the neighborhood of a position in the intermediate plane in the erecting equal-magnification lens array plate where an inverted image of the substantially straight light source is formed, and the light shielding member restricts a light transmitting region of each lens such that lens regions outside a slit opening, which is substantially parallel with the main scanning direction, are totally prevented from transmitting light, and the position of the slit opening is determined with reference to the lens coordinates of the lens surface closest to the image plane, of a plurality of lens surfaces in the plurality of lens array plates.
By providing a light shielder in the neighborhood of a position in the intermediate plane in the erecting equal-magnification lens array plate where an inverted image of the substantially straight light source is formed, and by ensuring that the main lens array direction differs from the main scanning direction, stray light is suitably eliminated and a ghost-free erect equal-magnification image is formed on the imaging plane. Since a light shielder is provided in the intermediate plane in the erecting equal-magnification lens array plate, the size and weight of the imaging optical system is reduced more successfully than when a partition is provided around the erecting equal-magnification lens array plate.
Since the position of the slit opening is determined with reference to the lens coordinates of the lens surface closest to the image plane, the assembly of the image sensor unit is facilitated and the manufacturing cost is reduced, even when the corresponding convex lenses of the respective surfaces of the lens array plate are formed such that the surfaces of each lens are not in alignment with each other.
Given that the lens array plate has a plate thickness t, the lens's working distance is denoted by WD, and the lens array plate has a refractive index n, and a distance between a reference plane perpendicular to the erecting equal-magnification lens array plate and parallel with the main scanning direction and the center of the lens in the lens surface closest to the image plane is denoted by y1, the slit opening may be formed such that a distance Y between the reference plane and the center of the slit opening in the sub-scanning direction is given by Y=y1×{1+t/(WD×n)}.
Given that the lens array plate has a plate thickness t, the lens's working distance is denoted by WD, the lens array plate has a refractive index n, the lens pitch is denoted by P, and a lens array angle is denoted by θ, a width w of the slit opening in the sub-scanning direction may be in the range given by w<2×{1+t/(WD×n)}×P×sin θ.
Given that a width of the erect equal-magnification image required on the image plane in the sub-scanning direction is denoted by w0, a width w of the slit opening in the sub-scanning direction may be in the range given by w≦2×{1+t/(WD×n)}×P×sin θ−w0×t/(WD×n).
Given that a width of the erect equal-magnification image required on the image plane in the sub-scanning direction is denoted by w0, a width w of the slit opening in the sub-scanning direction may be in the range given by w0×t/(WD×n)≦w≦2×{1+t/(WD×n)}×P×sin θ−w0×t/(WD×n).
Given that the lens array plate has a plate thickness t, the lens's working distance is denoted by WD, and the lens array plate has a refractive index n, a width of the slit opening in the sub-scanning direction is denoted by w, and the lens pitch is denoted by P, a lens array angle θ may be set to be larger than θ1 that fulfills a condition w=2×{1+t/(WD×n)}×P×sin θ1 and smaller than an angle θ2 obtained by subtracting θ1 from a first lens abutting angle determined by the array pattern of the lenses.
The lens array angle θ may be no smaller than the angle θ1 plus 1° and no larger than the angle θ2 minus 1°.
A light shielding wall for further reducing stray light not contributing to imaging may be formed at least on one surface of the erecting equal-magnification lens array plate.
Another aspect of the present invention relates to an image sensor unit. An image sensor unit comprises: a line light source operative to illuminate an image to be read; the erecting equal-magnification lens array plate according to claim 1 operative to condense light reflected by the image to be read; and a line image sensor for receiving light transmitted by the erecting equal-magnification lens array plate.
Since the aforementioned erecting equal-magnification lens array plate is used to form the image sensor unit, a quality image signal in which stray light is suitably eliminated is obtained, and the size, weight, and manufacturing cost of the image sensor unit is reduced.
Still another aspect of the present invention relates to an image reading device. An image reading device comprises: the aforementioned image sensor unit; and an image processing unit operative to process an image signal detected by the image sensor unit.
Since the aforementioned image sensor unit is used to form the image reading device, a quality image signal in which stray light is suitably eliminated is obtained, and the size and weight of the image sensor unit is reduced.
Since the image sensor unit with reduced manufacturing cost is used, an inexpensive image reading device can be produced.
Optional combinations of the aforementioned constituting elements, and implementations of the invention in the form of methods, apparatuses, and systems may also be practiced as additional modes of the present invention.
Embodiments will now be described, by way of example only, with reference to the accompanying drawings which are meant to be exemplary, not limiting, and wherein like elements are numbered alike in several Figures, in which:
The invention will now be described by reference to the preferred embodiments. This does not intend to limit the scope of the present invention, but to exemplify the invention.
The line light source 106 is a light source emitting a substantially straight light. The term “substantially straight” encompasses straight lines having a width of about 200 μm, or curves or staggered lines not exceeding a width of about 200 μm. The light exiting the line light source 106 is projected onto a document 120 (image to be read) placed on a document table 102. The document 120 reflects the substantially straight light from the line light source 106 toward the erecting equal-magnification lens array plate 10. The light-reflecting region of the document 120 will be referred to as a light source B as the case demands. The light source B emits substantially straight light toward the erecting equal-magnification lens array plate 10.
The erecting equal-magnification lens array plate 10 comprises a stack of a plurality of lens array plates built such that pairs of corresponding lenses form a coaxial lens system, where each lens array plate is formed with a plurality of lenses on both surfaces of the plate. The erecting equal-magnification lens array plate 10 receives substantially straight light from the light source B facing one side of the plate and forms an erect equal-magnification image on an image plane facing the other side of the plate. The line image sensor 104 as a light-receiving device is provided on an image plane on which the erect equal-magnification image is formed, so as to receive the erect equal-magnification image. By running the erecting equal-magnification imaging optical system 110 in the sub-scanning direction, the document 120 is scanned.
The erecting equal-magnification lens array plate 10 is installed in the image reading device 100 such that the longitudinal direction thereof is aligned with the main scanning direction and the lateral direction thereof is aligned with the sub-scanning direction. The erecting equal-magnification lens array plate 10 is installed the image reading device 100 such that the central line of the light source B and that of the line image sensor 104 are located on a reference plane 50, wherein the reference plane 50 is defined as a plane perpendicular to the erecting equal-magnification lens array plate 10 and passing through the central line of the erecting equal-magnification lens array plate 10 in the sub-scanning direction.
As shown in
Preferably, each of the first lens array plate 12 and the second lens array plate 14 is formed of a material amenable to injection molding, having high light transmittance in a desired wavelength range, and having low water absorptioin. Desired materials include cycloolefin resins, olefin resins, and norbornene resins.
The convex lenses 18 are in the same array pattern in the first lens array plate 12 and in the second lens array plate 14 such that the lenses face each other when the first lens array plate 12 and the second lens array plate 14 are placed opposite to each other. The first lens array plate 12 and the second lens array plate 14 are placed such that the optical axes of corresponding convex lenses 18 are aligned. In this embodiment, it is assumed that the convex lenses 18 are spherical in shape. Alternatively, the convex lenses 18 may have aspherical shapes.
As shown in
In the case of forming an image of a point light source on an image plane using an erecting equal-magnification lens array plate in which lens array plates are placed opposite to each other, stray light occur in the proximal lens array direction. Therefore, if the main lens array direction matches the main scanning direction, as disclosed in JP 2005-122041, stray light will directly enter the line image sensor provided parallel with the main scanning direction, generating a ghost image. The phenomenon occurs irrespective of whether a lens is located on the reference plane or away from the reference plane. A ghost image is generated so long as the lenses (light transmitting portions thereof) are arranged parallel to the main scanning direction. The erecting equal-magnification lens array plate 10 according to this embodiment can reduce stray light directly entering the line image sensor because the direction in which stray light occurs is shifted in the sub-scanning direction as a result of ensuring that the main lens array direction is different from the main scanning direction.
The light shielding member 16 is a film member provided between the first lens array plate 12 and the second lens array plate 14. As shown in
The light shielding member 16 has the function of shielding light not contributing to imaging. As described, the erecting equal-magnification lens array plate 10 is configured such that the main lens array direction differs from the main scanning direction. This can only ensure that the direction in which stray light occurs is shifted in the sub-scanning direction and does not eliminate stray light itself. In this regard, the erecting equal-magnification lens array plate 10 according to this embodiment is provided with the light shielding member 16 so as to prevent stray light shifted in the sub-scanning direction from being transmitted by the erecting equal-magnification lens array plate 10. Even if stray light does not directly enter the line image sensor, illumination of the neighborhood of the line image sensor by stray light results in lower contrast and drop in image quality. By providing the light shielding member 16, stray light is suitably eliminated and image quality is improved.
As shown in
The light shielding member 16 may be implemented by printing a light absorbing layer on the surface of a film having high light transmittance and forming the slit openings 20 accordingly, or by providing holes in a film having low light transmittance and forming the slit openings 20 accordingly.
The slit opening 20 is formed in the neighborhood of a position in the intermediate plane occurring in the direction of stack in the erecting equal-magnification lens array plate 10 where an inverted image of the light source B is formed. Since the position where an inverted image of the light source B is formed differs from lens to lens, the position of the slit opening 20 differs from lens to lens. For example, in the case of the convex lens 18 the center of which is located on the reference plane 50, the center of the slit opening 20 is aligned with the lens center. The farther the lens center from the reference plane 50, the farther the center of the slit opening 20 from the lens center. The shape and position of the slit opening 20 will be described in detail later. By providing the light shielding member 16 formed with the slit openings 20 as shown in
Referring to
Referring back to
Given that the angle of incidence of light entering the convex lens 18a from the light source B is denoted by θ, and the refractive angle of light entering the convex lens 18a is denoted by θ′, Snell's law requires that the relation of expression (1) holds between θ and θ′.
sin θ=n×sin θ′ (1)
Referring to
tan θ=y1/WD (2)
tan θ′=y1′/t (3)
Approximating such that sin θ≅tan θ and sin θ≈tan θ′, expression (4) below is derived from expressions (1)-(3).
y1′/y1=t/(WD×n) (4)
Since t/(WD×n) on the right side of expression (4) is a constant, the position at which the inverted image A is formed is displaced from the lens center by an amount proportional to distance y1 between the reference plane 50 and the lens center.
Since a distance Y between the reference plane 50 and the inverted image A is denoted by Y=y1+y1′, the relation of expression (5) below holds.
Y/y1=1+t/(WD×n) (5)
(5) Since 1+t/(WD×n) on the right side of expression (5) is a constant (hereinafter, the constant will be referred to as F as appropriate), the distance Y between the reference plane 50 and the inverted image A is the distance y1 between the reference plane 50 and the lens center multiplied by a predetermined factor F. The position at which the inverted image A is formed is calculated for each convex lens 18 according to expression (5). The slit opening 20 is formed such that the center of the width thereof in the sub-scanning direction lies at the calculated position. In this way, imaging light is properly transmitted, while stray light is eliminated.
In this embodiment, the slit opening 20 is formed such that the center thereof lies at the position where the inverted image A is formed. However, the opening may be formed in the neighborhood of a position where the inverted image A is formed instead of exactly where the inverted image A is formed. That is, it would be required to form the slit opening 20 so that the light contributing to the formation of the inverted image A is transmitted. For example, the slit opening 20 may be directly formed at the position on the surface of the lower convex lens 18 of the first lens array plate 12 where the light contributing to the formation of the inverted image A passes, or at the position of the surface of the upper convex lens 18 of the second lens array plate 14 where the light contributing to the formation of the inverted image A passes, using a printing method or a photoresist process.
A description will now be given of the width of the slit opening 20 in the sub-scanning direction. As mentioned earlier, the slit opening 20 is formed in the neighborhood of a position on the inverted image formation plane 52 where the inverted image is formed. It would be sufficient, for the purpose of transmitting imaging light, for the width of the opening to be equal to the width of the imaging light. It is preferable, however, to ensure that the width of the slit opening 20 in the sub-scanning direction be as large as possible to facilitate the step of aligning the first lens array plate 12, the second lens array plate 14, and the light shielding member 16. By facilitating the alignment step, the manufacturing cost is reduced.
For the purpose of preventing stray light transmitted by the convex lens 18e and passing through the position in the sub-scanning direction where the inverted image A1 is formed by the convex lens 18e from being transmitted by the slit opening 20, it will be ensured that half a distance w/2 of the width w of the slit opening 20 associated with the convex lens 18f in the sub-scanning direction is smaller than the distance F×P×sin θ between the inverted image A1 and the inverted image A2, assuming that the width of the inverted image A1 in the sub-scanning direction is negligibly small. In other words, it would be required for the width of the slit opening 20 in the sub-scanning direction to be in the range of expression (6) below.
w<2×F×P×sin θ (6)
Thus, the width w of the slit opening 20 in the sub-scanning direction should be smaller than 2×F×P×sin θ on the right side of expression (6) in order to shield stray light. In this regard, the right side of expression (6) will be referred to as a marginal opening width wmax.
wmax=2×F×P×sin θ (7)
It will be assumed that the width of the erect equal-magnification image required on the image plane (hereinafter, referred to as required image plane width) will be denoted by w0. The required image plane width w0 is equal to the width occupied by three CCDs in case a CCD line image sensor comprising three CCDs is provided on the image plane. Since the erecting lens array according to this embodiment is an erecting equal-magnification lens array, the width of the light source B in the sub-scanning direction is also denoted by w0. When the light from the light source B having the width w0 in the sub-scanning direction enters the convex lens 18e, a width w1 of the inverted image A1 formed on the inverted image formation plane will be given by w0×(F−1). For example, given that w0=20 μm and F=1.25, w1=5 μm.
Accordingly, as shown in
w2×F×P×sin θ−w0×(F−1) (8)
Since the slit opening 20 should completely transmit the light forming the inverted image A2 formed by the convex lens 18f, the width w in the sub-scanning direction need be no smaller than a width w2 of the inverted image A2, i.e., no smaller than w0×(F−1). Therefore, it is still desirable that the width w of the slit opening 20 in the sub-scanning direction be within the range given by expression (9) below.
w0×(F−1)≦w≦2×F×P×sin θ−-w0×(F−1) (9)
w≦F×P×sin θ (10)
However, the smaller the width w of the slit opening 20 in the sub-scanning direction, the smaller the amount of transmitted light for forming an erect equal-magnification image. It is therefore desirable that the opening width is as large as possible. Accordingly, it is more desirable that the width w of the slit opening 20 in the sub-scanning direction be the value given by expression (11) below.
W=F×P×sin θ (11)
It would be necessary for the width of the slit opening 20 in the main scanning direction to be equal to the diameter of the convex lens 18.
Described above is the position where the slit opening 20 is formed and the width thereof in the sub-scanning direction.
Expressions (6), (8), and (9) define the width w of the slit opening 20 in the sub-scanning direction considering the relative position of the reference lens 70 and the first adjacent lenses, stray light arrives via lenses other than the first adjacent lenses. Stray light from lenses remote from the reference lens 70 exercises little influence. Therefore, the relation between the reference lens 70 and the second adjacent lenses and the relation between the reference lens 70 and the third adjacent lenses will be considered in this embodiment.
As the lens array angle θ is increased beyond 0°, a third adjacent lens 72 will be located at the same sub-scanning direction position as the reference lens 70 in advance of those in the other groups. In the case of hexagonal array, the position of the reference lens 70 in the sub-scanning direction will be identical to that of the third adjacent lens 72, when the lens array angleθ=19.1°.
A distance d3 between the reference plane 50 and the lens center of the third adjacent lens 72 will be given by expression (12) below when the lens array θ is in a range 0°<θ<19.1°.
d3=P×{sin(60°−θ)−2×sin θ} (12)
Since a distance d3′ between the inverted image formed by the reference lens 70 and the inverted image formed by the third adjacent lens 72 in the sub-scanning direction is F times the distance d3, d3′ will be given by
d3′=F×P×{sin(60°−θ)−2×sin θ} (13)
Accordingly, the width w of the slit opening in the sub-scanning direction is set within the range defined by expression (14) below, if the third adjacent lens 72 in the neighborhood of the reference lens 70 is considered.
w<2×F×{P×{sin(60°−θ)−2×P×sin θ} (14)
Accordingly, if the lens array angle is within the range 0°<θ<19.1°, it is desirable that the width w of the slit opening in the sub-scanning direction be set so that expressions (6) and (14) are both fulfilled in consideration of the first adjacent lenses and the third adjacent lenses.
By setting the width w of the slit opening in the sub-scanning direction within such a range, stray light can be suitably eliminated.
As the lens array angle θ is increased beyond 19.1°, a second adjacent lens 74 will be located at the same sub-scanning direction position as the reference lens 70 in advance of those in the other groups. In the case of hexagonal array, the position of the reference lens 70 in the sub-scanning direction will be identical to that of the second adjacent lens 74, when the lens array angleθ=30°.
A distance d3 between the reference plane 50 and the lens center of the third adjacent lens 72 will be given by expression (15) below when the lens array θ is such that 19.1°<θ<30°.
d3=P×{2×sin θ−cos(30°+θ)} (15)
Since a distance d3′ between the inverted image formed by the reference lens 70 and the inverted image formed by the third adjacent lens 72 in the sub-scanning direction is F times the distance d3 of expression (15), d3′ will be given by
d3′=F×P×{2×sin θ−cos(30°+θ)} (16)
Accordingly, the width w of the slit opening in the sub-scanning direction is set within the range defined by expression (17) below, if the lens array angle θ is such that 19.1°<θ<30° and if the third adjacent lens 72 in the neighborhood of the reference lens 70 is considered.
w<2×F×P×{2×sin θ−cos(30°+θ)} (17)
A distance d2 between the reference plane 50 and the lens center of the second adjacent lens 74 will be given by expression (18) below when the lens array θ is such that 19.1°<θ<30°.
d2=P×{sin(60°−θ)−sin θ} (18)
Since a distance d2′ between the inverted image formed by the reference lens 70 and the inverted image formed by the second adjacent lens 74 in the sub-scanning direction is F times the distance d2 of expression (18), d2′ will be given by
d2′=F×P×{sin(60°−θ)−sin θ} (19)
Accordingly, the width w of the slit opening in the sub-scanning direction is set within the range defined by expression (20) below, if the lens array angle θ is such that 19.1°<θ<30° and if the second adjacent lens 74 in the neighborhood of the reference lens 70 is considered.
w<2×F×P×{sin(60°−θ)−sin θ} (20)
Accordingly, if the lens array angle θ is such that 19.1°<θ<30°, it is desirable that the width w of the slit opening in the sub-scanning direction be set so that expressions (6), (17), and (20) are all fulfilled in consideration of the first adjacent lenses, the second adjacent lenses, and the third adjacent lenses. By setting the width w of the slit opening in the sub-scanning direction within such a range, stray light can be suitably eliminated.
The conditions of simulation are such that the lens array is a hexagonal array, the lens's working distance WD=6.7 mm, the plate thickness t of the lens array plate is such that t=2.4 mm, the lens pitch P=0.42 mm, the lens diameter D=0.336 mm, the refractive index n=1.53, the curvature radius=0.679 mm, and the TC conjugation length=18.2 mm. Two simulations were conducted assuming that the width w of the slit opening in the sub-scanning direction is 0.01 mm and that w is 0.0415 mm. As shown in
As shown in
A study will be made to determine the range the lens array angle θ should reside in order to reduce stray light suitably, assuming that the w of the slit opening in the sub-scanning direction is 0.01 mm. As mentioned above, the width w of the slit opening in the sub-scanning direction need be set to a value smaller than the marginal opening width wmax in order to reduce stray light suitably.
Assuming the marginal opening width wmax of 0.01 mm, the lens array angle θ1 will be determined as θ1=0.55° from expression (7).
w=2×F×P×sin θ1 (21)
in order to reduce stray light suitably.
As mentioned, the stray light ratio is plotted on a graph symmetrical around θ=30°. Therefore, it is desirable that the lens array angle θ be smaller than an angle θ2 obtained by subtracting θ1 from 60°, the first lens abutting angle. θ2=59.45° when the width w of the slit opening in the sub-scanning direction is such that w=0.01 mm, and θ2=57.7° when w=0.0415 mm.
To summarize the above, it is desirable that the lens array angle θ be set to be larger than the angle θ1 that fulfills expression (21) and smaller than the angle θ2 obtained by subtracting the angle θ1 from the first lens abutting angle.
It is desirable that the lens array angle θ be no smaller than the angle θ1 plus 1° and no larger than the angle θ2 minus 1°. For example, when the width w of the slit opening in the sub-scanning direction is such that w=0.01 mm, the lens array angle θ is set within the range 1.55°≦θ≦58.45°. When w=0.0415 mm, θ is set within the range 3.3°≦θ≦56.7°. The stray light ratio is 21.06% when w=0.01 mm, and 11.22% when w=0.0415 mm, demonstrating that the ratio is smaller than that occurring at the array angle θ4 mentioned later. By setting the lens array angle θ within such a range, stray light is more suitably reduced.
As shown in
Accordingly, it is desirable that the lens array angle θ be not set at a lens array angle θ3 where the reference lens and the third adjacent lens are located at the same position in the sub-scanning direction, and at a lens array angle θ4 where the reference lens and the second adjacent lens are located at the same position in the sub-scanning direction. To keep on the safe side, it is desirable that the lens array angle θ not be set within a range ±1° of the lens array angle θ3 and a range ±1° of the lens array angle θ4.
As shown in
t/n:h/2=y2′:D/2 (22)
Modifying (22), we obtain
h/D=t/(y2′×n) (23)
The height h of the light shielding wall 30 required to eliminate stray light from the fourth adjacent lens can be determined according to expression (23).
To verify the effect of the light shielding wall, ray tracing simulations were conducted to calculate and compare the stray light ratio occurring when the light shielding wall is provided and when it is not. The calculation was conducted under the conditions mentioned above. A difference from the conditions observed in the aforementioned calculation is that the width w of the slit opening in the sub-scanning direction is such that w=0.13 mm and the lens array angle θ is 13.9°. Calculation showed that the stray light ratio is 15.64% in the absence of the light shielding wall. When the light shielding wall of a thickness 0.3 mm is provided to face the light source as in
Described above is the erecting equal magnification lens array plate according to the embodiment. In the erecting equal-magnification lens array plate, the light shielding member formed with the slit opening is provided on the intermediate plane between the first lens array plate and the second lens array plate. Moreover, it is ensured that the main direction of array of convex lenses is different from the main scanning direction of the erecting equal-magnification lens plate. In this way, imaging light is properly transmitted, while stray light is suitably eliminated. By forming the light shielding wall at least on one surface of the erecting equal-magnification lens array plate, stray light is more suitably eliminated.
The erecting equal-magnification lens array plate according to this embodiment is capable of eliminating stray light sufficiently without using a partition having a slit opening as disclosed in patent document No. 1. Accordingly, the size and weight of the optical system can be reduced. Since the number of parts is reduced, the cost is reduced accordingly. Further, since a partition is not provided, the likelihood of light reflected by a partition turning into stray light is eliminated. Since a ghost image is prevented from being created when the plate is built in an image forming device, image quality is improved.
Since the light shielding member is provided between the lens array plates, the adjustment of position of the partition and the lens array plate is not necessary. Since the light shielding member is integral with the lens array plate, the position of the member does not vary and so can prevent stray light in a stable manner once it is secured.
Since the erecting equal-magnification lens array plate eliminates stray light but does not eliminate imaging light, the plate can form an optical system highly transmissive of imaging light and allows a bright image, and particularly an image that is bright in the sub-scanning direction, to be obtained.
The erecting equal-magnification lens array plate according to this embodiment has the capability of eliminating stray light commensurate with that of the related-art erecting equal-magnification lens array plate using a partition with a slit opening. Accordingly, the erecting equal-magnification lens array plate according to this embodiment can be used in high-quality image reading devices and image writing devices.
As shown in
The erecting equal-magnification lens array plate 504 of the image sensor 500 may be the erecting equal-magnification lens array plate 10 shown in
The housing 510 is substantially cubic in shape and is integrally molded using a resin material. The housing 510 is formed with a line light source installation part 516 adapted to accommodate the line light source 502 and an erecting equal-magnification lens array plate installation part 512 adapted to accommodate the erecting equal-magnification lens array plate 504.
The erecting equal-magnification lens array plate installation part 512 is an elongated gutter formed on top of the housing 510 and extending in the main scanning direction. One of the inner wall surfaces of the erecting equal-magnification lens array plate installation part 512 represents an installation reference plane 514 provided to fit the erecting equal-magnification lens array plate 504 at a predetermined position in the housing 510. The erecting equal-magnification lens array plate 504 is built in the housing 510 such that the erecting equal-magnification lens array plate 504 is fitted to the erecting equal-magnification lens array plate installation part 512 and secured in its place while it is pressed against the installation reference plane 514. With this, the erecting equal-magnification lens array plate 504 is installed at a predetermined position in the housing 510.
A board installation part 518 adapted to accommodate the board 508 provided with the CCD line image sensor 506 is formed in the lower part of the housing 510. The board 508 is installed in the housing 510 such that an installation reference pin 520 provided in the housing 510 is engaged with a positioning hole 522 provided in the board 508. The shape of the installation reference pin 520 provided in the housing 510 may be as desired so long as it is convex. The hole 522 provided in the board 508 may be a through hole or a recess. Alternatively, a hole or a recess may be provided in the housing 510 and an installation reference pin may be provided in the board 508. In any case, at least one installation reference pin 520 is provided to secure the board 508 in the housing 510.
A plane perpendicular to the erecting equal-magnification lens array plate 504 and passing through the central line of the erecting equal-magnification lens array plate 504 in the sub-scanning direction will be defined as a reference plane 550. The installation reference plane 514 and the installation reference pin 520 are provided in the housing 510 such that the central line of the CCD line image sensor 506 resides on the reference plane 550 when the erecting equal-magnification lens array plate 504 and the board 508 are installed in the housing 510.
Thus, the erecting equal-magnification lens array plate 504 and the CCD line image sensor 506 of the image sensor unit 500 are installed in the housing 510 using passive alignment, without being subjected to fine adjustment of relative position. More specifically, the plate 504 and the sensor 506 are positioned using the installation reference plane 514 and the installation reference pin 520. Installation tolerance should be allowed when installing the erecting equal-magnification lens array plate 504 and the CCD line image sensor 506 in the housing 510 using passive alignment and so the erecting equal-magnification lens array plate 504 need be configured to address the tolerance. Since the image sensor unit 500 uses an erecting equal-magnification lens array plate provided with the light shielding member 16 as shown in
Therefore, the width w0 of the slit opening 20 in the sub-scanning direction is defined in consideration of a width wt0 of the erecting equal-magnification image required on the image plane, allowing for the installation tolerance allowed when the erecting equal-magnification lens array plate 504 and the CCD line image sensor 506 of the image sensor unit 500 are installed in the housing 510 (hereinafter, wt0 will be referred to as allowed installation tolerance required image plane width).
Given that the installation tolerance of the erecting equal-magnification lens array plate 504 and the CCD line image sensor 506 in the sub-scanning direction is denoted by ±tv (an absolute value of tolerance will be 2×tv) and that the width of one column CCDs in the sub-scanning direction is denoted by wc, the allowed installation tolerance required image plane width wt0 defined when the CCD line image sensor 506 with one column of CCDs will be given by
wt0=2×tv+wc (24)
For example, wt0=120 μm, when tv=±40 μm and wc=40 μm. The allowed installation tolerance required image plane width wt0 defined when the CCD line image sensor 506 with three columns of CCDs will be given by
wt0=2×tv+3×wc (25)
For example, wt0=200 μm, when tv=±40 μm and wc=40 μm.
The range required of the width w of the slit opening 20 in the sub-scanning direction defined for the allowed installation tolerance required image plane width wt0 can be derived in the same way as expression (9) above is derived. Thus, the range can be defined by expression (26) below, in which the required image plane width w0 in expression (9) is replaced by the allowed installation tolerance required image plane width wt0.
wt0×(F−1)≦w≦2×F×P×sin θ−wt0×(F−1) (26)
The larger the width w of the slit opening 20 in the sub-scanning direction, the larger the tolerance for shifts occurring at the time of installation. Therefore, the optimum value that meets the requirements for tolerance for shifts and for elimination of stray light will be given by
w=F×P×sin θ (27)
An exemplary range of the width w of the slit opening 20 in the sub-scanning direction will be discussed below. It will be assumed here that the plate thickness t of the lens array plate is such that t=2.4 mm, the refractive index n of the lens array plate is such that n=1.53, the lens's working distance WD=6.7 mm, the lens pitch P=0.42 mm, the lens array angle θ=13.9°, the width we of one column of CCDs in the sub-scanning direction is such that wc=0.04 mm, and the installation tolerance of the erecting equal-magnification lens array plate 504 and the CCD line image sensor 506 in the sub-scanning direction is ±0.04 mm.
The allowed installation tolerance required image plane width wt0 defined when the CCD line image sensor 506 with one column of CCDs will be such that wt0=0.120 mm based on expression (24).
Since F=1+{t/(WD×n)}, F=1.234.
Applying these values to expression (26), the range of the width w of the slit opening 20 in the sub-scanning direction defined when the CCD line image sensor 506 with one column of CCDs is used is given by
0.028 mm≦w≦0.2219 mm (28)
The allowed installation tolerance required image plane width wt0 defined when the CCD line image sensor 506 with three columns of CCDs is used will be such that wt0=0.200 mm based on expression (25). F=1.234. Applying these values to expression (26), the range of the width w of the slit opening 20 in the sub-scanning direction defined when the CCD line image sensor 506 with three columns of CCDs is used is given by
0.0468 mm≦w≦0.2032 mm (29)
Expression (27) gives the optimum value of w that meets the requirements for tolerance for shifts and for elimination of stray light such that
w=0.125 mm (29)
regardless of whether one column of CCDs or three columns of CCDs are used. Application of the optimum value of w to the inequality on the left side of expression (26) results in
wt0×(F−1)≦0.125 mm (30)
Substituting F=1.234 into expression (30) and modifying the result, we obtain
wt0≦0.534 mm (31)
Expression (31) shows that the maximum value of the allowed installation tolerance required image plane width wt0 is 0.534 mm.
Described above is the image sensor unit 500. Since the erecting equal-magnification lens array plate described with reference to
The housing 510 of the image sensor unit 500 is an integrally molded, one-piece component. By forming the housing 510 as an integrally molded, one-piece component, the precision of the position of the installation reference plane 514 and the installation reference pin 520 is increased. This allows larger tolerance in installing the erecting equal-magnification lens array plate and light-receiving devices, with the result that the assembly of the image sensor unit is facilitated.
The image sensor unit 500 shown in
The first lens array plate 12 and the second lens array plate 14 are placed such that the optical axes of corresponding convex lenses 18 are aligned, as described above. However, the optical axes of the convex lenses may not be aligned due to an error that occurs in manufacturing the convex lenses. Referring to
Describing the process of manufacturing the erecting equal-magnification lens plate 10 in brief, the erecting equal-magnification lens array plate 10 is manufactured by forming the light shielding member 16 on the second lens array plate 14 and then providing the second lens array plate on the light shielding member 16. In forming the light shielding member 16 on the second lens array plate 14, the position at which the inverted image A is formed is calculated for each convex lens 18 according to expression (5), as described above. The slit opening 20 is formed such that the center of the width thereof in the sub-scanning direction lies at the calculated position. The position of the inverted image A is calculated by tracing the optical path backward from the erect equal-magnification image C. Expression (5) can be equally applied as in
As indicated by expression (5), the position where the slit opening 20 is formed is proportional to the distance y1 between the reference plane 50 and the lens center. Thus, when the convex lens 18c is formed such that the optical axis thereof in the third lens surface 14a of the second lens array plate 14 is not aligned with that of the convex lens 18d in the fourth lens surface 14b in the sub-scanning direction, the question will be whether the slit opening 20 is formed with reference to the convex lens 18c in the third lens surface 14a or the convex lens 18d in the fourth lens surface 14b. In other words, the question is whether the distance ys between the reference plane 50 and the center of the convex lens 18d in the fourth lens surface 14b or the distance y1+Δy1 between the reference plane 50 and the third lens surface 14a should be used as y1 in expression (5).
In such a case, it is desirable that the position where the slit opening 20 is formed be determined with reference to the coordinates of the convex lens 18d in the fourth lens surface 14b, which is closest to the image plane. In other words, the distance y1 between the reference plane 50 and the center of the convex lens 18d in the fourth lens surface 14b is selected to be used as y1 in expression (5). This is because the position of the inverted image A, where the slit opening 20 should be formed, is determined only by the convex lens 18d in the fourth lens surface 14b and is irrelevant to the other lenses.
If the amount of displacement Δy1 is uniform in the main scanning direction, the amount of displacement of the position of the slit opening 20 will be uniform in the main scanning direction. Accordingly, the problem can be avoided if the position of the center of the line image sensor 104 can be translated and readjusted. Even when Δy1 is not uniform in the main scanning direction and varies in the main scanning direction in a proportional manner, the positions of slit openings 20 will be linearly aligned. Therefore, the problem will be avoided by tilting and readjusting the sensor instead of translating the sensor. However, the amount of displacement Δy1 is not uniform in the main scanning direction and does not vary in a proportional manner, the positions of slit openings 20 will not be linearly aligned. The problem will no longer be avoided by adjusting the position of the line image sensor 104 and the consumption of the allowed installation tolerance required image plane width wt0 cannot be avoided. Even if the position of the line image sensor 104 can be adjusted, the allowed installation tolerance required image plane width wt0 will still be consumed due to displacement from the position as designed. Therefore, in whatever manner Δy1 varies, the amount of displacement in the erect equal-magnification image C Δy1×F/(F−1) consumes the allowed installation tolerance required image plane width wt0, with Δy1 being the maximum value.
Given below will be a specific amount decrease in the allowed installation tolerance required image plane width wt0 occurring when the distance y1+Δy1 between the reference plane 50 and the center of the convex lens 18c in the third lens surface 14a is selected to substitute y1 in expression (5). It will be assumed here that the plate thickness t of the lens array plate is such that t=2.4 mm, the refractive index n of the lens array plate is such that n=1.53, the lens's working distance WD=6.7 mm, the width w of the slit opening 20 is such that w=0.13 mm, the lens diameter D=0.336 mm, the lens pitch P=0.42 mm, the curvature radius=0.679 mm, the lens array angleθ=15°, and the height of the light shielding wall h=0.3 mm.
In this case, the constant F on the right side of expression (5) will be 1+{t/(WD×n)}=1.234. The maximum value of the allowed installation tolerance required image plane width wt0 is 0.13/0.234=0.555 mm since wt0=w/(F−1). Displacement of Δy1=0.02 mm between the corresponding lenses on the respective surfaces of the second lens array plate 14 in this optical system will result in the displacement Δy1×F/(F−1) of the erect equal-magnification image C is 0.02×5.274=0.105 mm. Since there is a consumption of 0.105 mm from the allowed installation tolerance required image plane width wt0=0.555 mm, the allowed installation tolerance required image plane width wt0 is reduced to 0.450 mm.
Meanwhile, when the slit opening 20 is formed with reference to the lens coordinates of the fourth lens surface 14b, the erect equal-magnification image C is formed where it is designed to be. This is because the position of the inverted image A, where the slit opening 20 should be formed, is determined only by the convex lens 18d in the fourth lens surface 14b. Accordingly, by forming the slit opening 20 with reference to the lens coordinates of the fourth lens surface 14b, the allowed installation tolerance required image plane width wt0 is not consumed so that the ease of assembly of the image sensor unit is improved and the manufacturing cost is improved.
A description will now be given of results of experiments on the erect equal-magnification lens array plate actually manufactured.
The erecting equal-magnification lens array plate manufactured according to the comparative example produces the images of
Meanwhile, the images at the left end, the center, and the right end in the main scanning direction are scarcely displaced from each other as shown in
Described above is an explanation based on an exemplary embodiment. The embodiment is intended to be illustrative only and it will be obvious to those skilled in the art that various modifications to constituting elements and processes could be developed and that such modifications are also within the scope of the present invention.
For example, in the embodiment, the light shielding member is formed by sandwiching a film member between the first lens array plate and the second lens array plate. Alternatively, a light shielding member may be formed by printing the bottom of the first lens array plate or the top of the second lens array plate with a slit opening pattern using a light-shielding material such as black ink. In this case, the slit opening is formed at a position on the surface of the convex lens on the bottom of the first lens array plate where light contributing to formation of an inverted image passes, and a position on the surface of the convex lens on the top of the second lens array plate where light contributing to formation of an inverted image passes. Since this eliminates the step of adjusting the position of a light shielder, the fabrication cost is reduced.
In the erecting equal-magnification optical system shown in
In the embodiment described, a stack of two lens array plates is built to form an erecting equal-magnification lens array plate. The number of plates stacked is not limited to two. For example, three lens array plates may be stacked and a light shielding member may be provided on the intermediate plane in the lens array plate in the middle.
In the embodiment described, lenses are arranged in a hexagonal array. However, the lens array pattern may not be limited to a hexagonal array. The present invention is equally applicable when the lenses are arranged in a square array.
Number | Date | Country | Kind |
---|---|---|---|
2008-305195 | Nov 2008 | JP | national |