JPH06305195A - Image forming device - Google Patents

Abstract

PURPOSE:To prevent a change in image-forming performance caused by temperature fluctuation in an image forming device having a monocular lens to prevent occurrence of white stripes or black stripes at a boundary between image arrays. CONSTITUTION:An array 6 of monocular rod lenses 8 of a distributed refractive index type is disposed opposedly to an LED array 2. The lens 8 is shaped into a rod form and has no curved surface, thus having a small fluctuation of an image forming performance caused by temperature fluctuation. The rod lens 8 has a refractive index (n) distributed to be n = n0(1-ar<2>+br<3>) (n0 is a refractive index at a center axis, and (a), (b) are a positive constant). A refractive index in the vicinity of the peripheral part of the rod lens is set to be larger than a refractive index distribution of n = n0(1-ar<2>) for a self-focusing lens. As a result, incident angles of a light from each end of the array 2 to an image forming surface 12 and the lens 8 are reduced, whereby a formed image is hardly affected by the positional shift of the array 2 or the image forming surface 12.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image device such as an LED head, a liquid crystal shutter array head, a plasma head and an image sensor.

[0002]

2. Description of the Related Art An image device in which a light emitting / receiving array and a monocular lens for image formation are combined has been known for a long time (for example, U.S. Pat. Nos. 4,532,526 and 4,532,527).
issue). However, an image device using a monocular lens has not yet been put to practical use. The inventor studied the problems of the image device using the monocular lens and found the following. 1) The monocular lens that has been studied so far is a curved lens, and its tolerance range for the temperature fluctuation of the imaging device is narrow. That is, when the temperature fluctuates, the curvature of the lens surface changes, and in a curved lens, the image formation position is determined by the curved surface shape of the lens surface.
The change of the image forming position due to the temperature change is remarkable. In an image device, there is heat generation in the device and heat generation from a peripheral photosensitive drum and the like, and the range of temperature change is wide. For this reason, even a monocular lens that is sufficiently used in ordinary applications can only be used in a narrow temperature range in an image device, which is impractical. 2) The performance of curved lenses depends on the shape of the lens surface and is generally expensive. 3) The image quality is likely to deteriorate due to the turn of the light emitting and receiving array. For example, an image forming apparatus tends to cause white streaks or black streaks in a printed image, and an image reading apparatus tends to cause white streaks or black streaks in a read image.

[0003]

SUMMARY OF THE INVENTION An object of the present invention is to 1) widen the permissible range of a monocular lens with respect to temperature fluctuations, and 2) to obtain a homogeneous lens at low cost.

In addition to the above, an object of the present invention is to 3) prevent deterioration of image quality at the turn of the light emitting and receiving array.

[0005]

According to the present invention, the light emitting and receiving array is opposed to
In an image device in which a monocular lens array is arranged, each monocular lens of the lens array is a distributed index type rod lens, the refractive index of the lens is n, the refractive index at the central axis of the lens is n0, and the central axis of the lens is The radial distance from r, a
As positive constants, is approximately ^{n = n0 (1-ar 2} ) the refractive index distribution of the lens, characterized in that the the.

[0006] The preferred refractive index distribution of the lens, n = n0 (1-ar 2 + f (r)), where the f (r) has a positive value in the vicinity of the outer periphery of the lens, substantially elsewhere It is assumed that | f (r) | <ar ² at an arbitrary position in the lens with a correction function of 0.

[0007]

The imaging apparatus of the present invention uses an array of monocular lenses using distributed index type rod lenses. The refractive index distribution of a lens is the refractive index n at the central axis of the lens.
0, r is the radial distance from the center axis of the lens,
Approximately ^{n = n0 (1-ar 2} ) and (1). Expression (1) is an expression of the refractive index distribution for the self-focusing lens. In the present invention, an array of monocular lenses is used instead of an array of compound-eye lenses such as a self-focusing lens array. By selecting the length of the rod-shaped lens, the image can be changed to an inverted reduced image, an inverted enlarged image, an erect reduced image, or an erect enlarged image.

Bar-shaped distributed index lenses have hardly been studied. For example, a known distributed index lens is a curved lens such as a hemisphere. On the other hand, the advantage of using the distributed index type rod lens is that the deviation of the image forming position due to the temperature change is small. That is, even if the rod-shaped lens thermally expands due to temperature change, the internal refractive index distribution itself hardly changes. Therefore, the image forming position is hardly affected by the temperature change. On the other hand, in the case of a curved lens, when the shape of the lens surface changes due to temperature change, the image forming position changes significantly. As a material of the rod-shaped distributed index lens, for example, glass or plastic is used. In the case of a plastic lens, when the ambient humidity increases, the lens swells and the curved surface shape of the lens changes, so that the imaging position changes. On the other hand, the water vapor hardly enters the inside of the rod-shaped lens, so that even if a plastic lens is used, the influence of humidity is small.

The rod-shaped lens of the present invention can be produced by a usual method for manufacturing a self-focusing lens, and it is not necessary to cut out the lens like a glass curved lens. Therefore, homogeneous lenses can be mass-produced at low cost.

[0010] Preferably, the refractive index distribution of the rod lens is expressed by
It is slightly deformed from (1), and the refractive index is calculated near the lens outer periphery.
Make it slightly larger than (1). Then, even if the positions of the light emitting surface and the document surface are changed from the proper positions or the positions of the image forming planes are changed from the proper positions, the influence on the image forming performance is reduced. And this has the effect of preventing the occurrence of white streaks, black streaks, etc. at the transition between image arrays.

Light tends to travel in a region having a large refractive index. Here, slightly deformed from the formula (1) of the refractive index distribution for the self-focusing lens, if the refractive index near the outer peripheral portion of the lens is increased, the light incident near the outer peripheral portion of the lens is attracted to the outer peripheral portion, Trying to turn bigger. On the other hand, the light incident near the center of the lens has almost no effect even if the refractive index near the outer periphery is changed. The light passing near the outer peripheral portion of the lens is mainly light near the transition between the light emitting / receiving array and the light receiving / emitting array. Such light is bent more in the lens than light from other parts and thus has a smaller angle of incidence on the image plane. The smaller the angle of incidence on the image plane, the smaller the positional deviation when the position of the image plane changes. In this way, the position shift at the transition between the light emitting / receiving array and the light receiving / emitting array with respect to the variation of the image plane position is reduced, and the occurrence of white streaks or black streaks is prevented. This also applies to the displacement of the light emitting surface and the document surface, and if the refractive index in the vicinity of the outer peripheral portion of the lens is set to be slightly larger than the expression (1),
Even if the positions of the light emitting surface and the document surface are changed, the influence on the imaging performance is reduced. This effect is particularly strong for light related to the light emitting / receiving array and the transition between the light receiving / emitting array.

Even if the refractive index distribution of the rod-shaped distributed refractive index type lens is slightly modified from the equation (1), if the value of the correction function f (r) is small, it hardly affects the imaging performance. The correction function f (r) of the refractive index distribution for the equation (1) is preferably the radius r
To the third power or the fourth power, or to decrease exponentially from the outer edge to the inside of the lens, so that the correction function f (r) has a large value near the outer edge of the rod lens. To do. In order not to disturb the imaging performance, the absolute value of the correction function f (r) is calculated by the formula
It should be smaller than ar ^{2 in} (1).

[0013]

EXAMPLES FIGS. 1 to 4 show an example of an LED head. FIG. 1 shows an optical system. In the figure, 2 is an LED array, for example, array 2 having a resolution of 508 DPI is arranged at intervals. Reference numeral 4 denotes a substrate of the LED array 2, which is, for example, a glass substrate. Reference numeral 6 denotes an array of monocular lenses, in which a rod-shaped lens 8 of the distributed index type is fitted in a black resin 10. The distributed index type rod-shaped lens 8 is produced by, for example, a method for manufacturing a self-focusing lens, and is formed by cutting from a long lens. Unlike the self-focusing lens array, the rod-shaped lens 8 has a large lens diameter, so that the surface can be easily polished to be smooth. On the other hand, in the case of the self-focusing lens array, since a thin fiber lens is used, it is difficult to smooth the surface and there is a problem of surface roughness. Roughness of the lens surface causes scattering of light and deteriorates the imaging performance. Reference numeral 12 denotes an image forming surface, and in practice, the photosensitive drum serves as the image forming surface 12.

The distance L between the LED array 2 and the image plane 12 can be made large, for example, about 20 mm, and the LED array 2, the lens array and the photosensitive drum are very small as in the case of the self-focusing lens array. No need to assemble at small intervals. In the embodiment, the rod-shaped monocular lens 8 is a lens capable of obtaining a magnified inverted image with a magnification of 1.692, and the LED array 2 of 508 DPI gives an image of resolution 300 DPI on the image plane 12. Along with this, the diameter of the monocular lens 8 becomes, for example, about 3 mm.

The optical path in the case of the formula (1) of the refractive index distribution for the self-focusing lens is shown by the broken line in FIG. On the other hand the refractive index distribution, in the case of the ^{n = n0 (1-ar 2} + f (r)) (2), showing an optical path in a solid line in FIG. 1. f (r) is an expression
It is only necessary that the correction function for (1) is such that the refractive index in the vicinity of the outer peripheral portion of the rod-shaped lens 8 is slightly larger than that of the expression (1). Further, the correction function f (r) is set to be substantially 0 near the central axis of the rod lens 8, and the absolute value of the correction function value f (r) is smaller than ar ^{2 at} an arbitrary point of the lens 8. To do so. In the embodiment, br is used as the correction function f (r).
³ was used. Where b is a constant and br ³ is always smaller than ar ² . The refractive index distribution used is as shown in equation (3). ^{n = n0 (1-ar 2} + br 3) (3)

Light generally tends to select a portion having a high refractive index to travel. Therefore, if a distribution in which the refractive index is slightly larger near the outer peripheral portion of the monocular lens 8 is used as in the formula (2), light in the lens 8 tries to travel along the vicinity of the outer peripheral portion of the lens, resulting in the optical path. Changes from the broken line to the solid line. Therefore, the incident angle with respect to the image plane becomes smaller than that in the case of the broken line in the figure. Further, the emission angle of light with respect to the same image forming position is also smaller than in the case of the broken line in the figure.
This has the effect of preventing the occurrence of white streaks or black streaks at the transition between the LED array 2 and the LED array 2, as will be shown later.

FIG. 2 shows the refractive index distribution and the optical path of the rod-shaped monocular lens 8. The broken line in FIG. 2 shows the characteristic when the refractive index distribution formula (1) for the self-focusing lens is followed. The solid line in FIG. 2 shows the characteristics when the refractive index is slightly increased in the outer peripheral portion of the lens 8 according to the equation (3). Lens 8
In the case of the formula (1), the refractive index distribution of is the parabolic distribution shown on the left side of FIG. On the other hand, in the formula (3), since br ³ is used as the correction function f (r), the refractive index is slightly increased near the outer peripheral portion of the lens 8 as shown by the solid line in the figure.

In the case of the refractive index distribution of the formula (1), the optical path in the lens 8 is as shown by the broken line in the figure, and the light travels while meandering. Here, for example, when the lens 8 is cut along the cutting plane A in FIG. 2, an inverted image is obtained. Further, when cut at the cutting plane B, an upright image is obtained. Then, when the positions of the cutting plane A and the cutting plane B are shifted, an enlarged image or a reduced image is obtained, and the magnification is changed. Here, if the refractive index is corrected to be slightly larger near the outer peripheral portion of the lens 8 as in the equations (2) and (3), the light travels as shown by the solid line in the figure. This means that the light tries to travel by selecting a portion having a high refractive index. The greater the amount of bending of the light in the lens, the smaller the incident angle and the exit angle of the light in the part other than the lens 8, and as a result, as shown in FIG.
The incident angle and the output angle decrease as indicated by the solid line. The above discussion relates to the light from both ends of the LED array 2,
Light from the central portion of the LED array 2 is emitted from the monocular lens 8
The incident angle is small, the light travels in the vicinity of the central axis of the monocular lens 8, and is not affected by the correction function f (r) on the refractive index in the vicinity of the outer peripheral portion. Therefore, the correction to the refractive index distribution according to the equation (2) acts only on the light from both ends of the LED array 2. In Expression (2), if the correction function f (r) is small, that is, if | f (r) | is always sufficiently smaller than ar ² , the resolution of the lens 8 is hardly affected.

FIG. 3 shows the influence of the refractive index distribution of the rod-shaped lens 8 on the positional deviation of the image plane 12. One of the causes of easy occurrence of white streaks and black streaks when a monocular lens is used is the positional shift of the image plane 12. That is, the light from the light emitters near both ends of the LED array 2 is incident on the image plane 12 at a large incident angle. Here, if the position of the image plane 12 is displaced by δ,
Suppose you have shifted to position 12 '. Then, in the case of the refractive index distribution of Expression (1), the position of the dot on the image plane changes greatly as shown by the broken line in FIG. On the other hand, in the case of the refractive index distribution of the formula (2), the change of the dot position on the image plane 12 ′ is smaller than that of the formula (1) as indicated by the solid line in FIG. Image plane 12
When the angle of incidence on is θ, the change in dot position due to the displacement of the image plane 12 is proportional to tan θ. Therefore, the smaller the incident angle θ, the smaller the influence when the position of the image plane 12 is displaced.

The cause of the occurrence of white streaks and black streaks due to the displacement of the image plane 12 will be described. When the position of the image forming surface 12 is shifted, the image forming positions of the light emitting bodies near both ends of the LED array 2 are changed as shown in FIG. Using an inverted image here,
Light from LED array 2 on the left side and LED array 2 on the right side
With respect to the light from, the image forming position shifts in the opposite direction at the transition between the arrays. Then, when these image forming positions approach each other, black streaks occur. Further, when these image forming positions are separated from each other, white streaks are generated. On the other hand, if the refractive index distribution of equation (2) is used, the angle of incidence on the image plane 12 is made small, the change in dot position due to the position shift of the image plane 12 is suppressed, and the white stripes and black stripes are suppressed. Occurrence can be prevented.

The second cause of the occurrence of white streaks and black streaks is LED.
The position of the array 2 varies with respect to the lens array 6. This mechanism is shown in FIG. Reference numeral 14 in the figure is an individual light emitter, and the position of the LED array 2 is displaced and it is assumed that it is shifted to the position 2 '. When the angle of incidence on the monocular lens 8 is large,
The incident position of light on the lens 8 largely changes as shown in the right side of FIG. On the other hand, when the incident angle on the monocular lens 8 is small, the incident position on the lens 8 changes as shown on the left side in FIG. Also here, the shift of the incident position of the light emitting body 14 on the lens 8 is proportional to tan θ. Therefore the formula
By using the refractive index distribution of (2) and reducing the incident angle θ to the lens 8, even if the position of the LED array 2 shifts, the influence on the image forming position can be reduced. The image forming position of the light from the light-emitting body in the same LED array 2 does not relatively change relatively even if the position of the LED array 2 shifts. On the other hand, since the inverted image is used, the image formation position of the light from the adjacent LED array 2 changes remarkably due to the position shift at the transition between the arrays 2 and 2. Therefore, by using the refractive index distribution of the equation (2), the angle of incidence on the lens 8 is made small and the influence of the positional displacement of the LED array 2 is made small. In this way L
The occurrence of white streaks and black streaks due to the positional shift of the ED array 2 and the positional shift of the image plane is suppressed.

[0022]

According to the invention of claim 1, the following effects can be obtained. 1) The allowable range for the temperature fluctuation of the monocular lens is widened, and the fluctuation of the image forming position can be prevented even in an image device having a wide temperature range. 2) A homogeneous lens can be obtained at low cost.

According to the invention of claim 2, in addition to the above, 3) it is possible to prevent deterioration of image quality at the transition between the light emitting and receiving arrays.

[Brief description of drawings]

FIG. 1 is a diagram showing an optical system in an image device according to an embodiment.

FIG. 2 is a characteristic diagram showing a refractive index distribution in a monocular lens and an optical path in the lens in the image device of the embodiment.

FIG. 3 is a characteristic diagram showing an influence of a shift of an image plane in the image device of the embodiment.

FIG. 4 is a characteristic diagram showing an influence of displacement of a light emitting surface in the image device of the embodiment.

[Explanation of symbols]

 2 LED array 4 Substrate 6 Monocular lens array 8 Rod-shaped monocular lens 10 Black resin 12 Image plane 14 Light emitter

Claims (2)

[Claims] 1. An image device in which a monocular lens array is arranged facing a light emitting / receiving array, each monocular lens of the lens array is a distributed index type rod lens, and the refractive index of the lens is n The refractive index at the central axis is n
0, characterized in that the radial distance from the central axis of the lens r, the a is a positive constant, the refractive index distribution of the lens was approximately ^{n = n0 (1-ar 2} ), the image device. The refractive index distribution of 2. A lens, n = n0 (1-ar 2 + f (r)), where the f (r) is approximately elsewhere have a positive value in the vicinity of the outer periphery of the lens 0 ^2. The image device according to claim 1, wherein the correction function is such that | f (r) | <ar ^{2 at} an arbitrary position in the lens.