Optical devices, image sensors, and manufacturing methods of optical devices

Abstract

The optical device 1a of the present invention includes a lens array 10 and a transparent dielectric array 20. The lens array 10 includes a plurality of lenses 11. In the lens array 10, the plurality of lenses 11 are arranged such that their optical axes are substantially parallel to each other. The transparent dielectric array 20 includes a plurality of transparent dielectrics 21. In the transparent dielectric array 20, the plurality of transparent dielectrics 21 are arranged such that their central axes are substantially parallel to each other. The lens array 10 and the transparent dielectric array 20 are configured such that the optical axes of the lenses 11 and the central axes of the transparent dielectrics 21 are substantially parallel, and the end faces of the lens array 10 and the end faces of the transparent dielectric array 20 face each other.

Description

Technical Field

[0001] This invention relates to an optical device, an image sensor, and a method for manufacturing the optical device. Prior Technology

[0002] Previously, lens arrays were known to be formed by arranging multiple lenses in a predetermined direction with their optical axes or central axes parallel to each other and integrating them into a single unit. In such lens arrays, an image is formed by superimposing the images obtained by each individual lens. Although the image information of the object surface obtained is small, two-dimensional image information can be obtained. This characteristic and function are effectively utilized, and lens arrays are used together with light-receiving element arrays such as illumination devices and photodiode (PD) arrays in image sensors. For example, contact image sensors (CIS) are used as image sensors employing lens arrays.

[0003] Compared to scanners that use reduced optical imaging methods with two-dimensional sensors such as charge-coupled devices (CCDs) and complementary metal-oxide semiconductors (CMOS), multiple lenses, and mirrors, image sensors with lens arrays have advantages such as: shorter distances between the object and the light-receiving element (camera element), between the object point and the image point, or between the object surface and the image surface, making it easier to save space; fewer parts, better maintainability; and easier assembly.

[0004] Lens arrays used in devices such as contact image sensors offer advantages such as miniaturization, low cost, and the ability to easily obtain high-resolution and high-contrast images. On the other hand, the depth of field of lens arrays tends to be shallow. Therefore, image quality may degrade when capturing images of subjects with large protrusions, such as the portion of a book spanning both pages, photographs protected by transparent casings, or subjects that have moved away from the document tray.

[0005] For example, in Patent Document 1, as a method for improving the depth of field, an overlap-limiting member is described, which has a plurality of openings corresponding to a plurality of lens elements in a lens array. The optical axis of each lens element in the lens array is aligned with the center of its opening. According to this method, if the optical axis of the lens element is not aligned with the center of the opening of the overlap-limiting member, the overlap-limiting member cannot narrow the imaging field of view of the lens, thereby failing to reduce the overlap between images. On the other hand, it is considered difficult to arrange the plurality of lens elements in an ideal arrangement with perfect precision during the manufacturing of the lens array.

[0006] Patent Document 2 describes a method for placing a light shield with a diffraction effect on a surface orthogonal to the optical axis of a lens array between the original document surface and the light-receiving element array in a contact image sensor. Regarding this method, it can be argued that, from the viewpoint of fine resolution, it may result in difficulty in reflecting important high-frequency components in the image. Previous technical documents Patent Literature

[0007] Patent Document 1: Japanese Patent Application Publication No. 6-342131 Patent Document 2: Japanese Patent Application Publication No. 10-173862 Summary of the Invention

[0008] [The problem that the invention aims to solve]

[0009] In view of the above-mentioned problems, the present invention provides an optical device that is advantageous in obtaining high-resolution images even for subjects with uneven surfaces and height differences. [Technical means to solve the problem]

[0010] This invention provides an optical device comprising: A lens array comprising a plurality of lenses, wherein the plurality of lenses are arranged such that their optical axes are substantially parallel to each other; and A transparent dielectric array comprising a plurality of transparent dielectrics arranged such that the central axes of the plurality of transparent dielectrics are substantially parallel to each other; and The aforementioned lens array and the aforementioned transparent dielectric array are arranged such that the aforementioned optical axis and the aforementioned central axis are substantially parallel, and the end face of the aforementioned lens array faces the end face of the aforementioned transparent dielectric array.

[0011] Furthermore, the present invention provides an image sensor having the above-described optical device. [Effects of the Invention]

[0012] The aforementioned optical device is advantageous from the viewpoint that it can obtain high-resolution images even for subjects with concavity, convexity, and height differences. Furthermore, compared to using only a lens array, the aforementioned optical device is also advantageous in terms of having a relatively large depth of field. Simple Explanation of the Diagram

[0013] [Figure 1] is a perspective view showing an example of the optical device of the present invention. [Figure 2] is a schematic perspective view showing one example of a lens array related to the present invention. [Figure 3] is a diagram showing the relationship between the lens array and the object plane and the image plane. [Figure 4] is a diagram illustrating the imaging of a rod-shaped lens with a refractive index distribution. [Figure 5A] is a diagram illustrating the imaging state of two adjacent rod lenses when the object is in a conjugate position. [Figure 5B] is a diagram illustrating the imaging state of two adjacent rod lenses when the position of an object deviates from its conjugate position. [Figure 6] is a schematic diagram showing the spread of light rays that can be received at a position on the light incident surface of a rod lens at a distance r from the central axis. [Figure 7] is a graph that roughly shows the relationship between the angle θ determined by the definition of the opening of the rod lens and the distance r from the central axis. [Figure 8A] is a schematic diagram showing the propagation of light when there is no transparent dielectric array. [Figure 8B] is a schematic diagram showing the field of view limitation when a transparent dielectric is arranged along the optical axis of a rod lens. [Figure 8C] is a schematic diagram showing the field of view limitation when a transparent dielectric is arranged along the optical axis of a rod lens. [Figure 8D] is a schematic diagram showing the field of view limitation when a transparent dielectric is arranged along the optical axis of a rod lens. [Figure 9] is a perspective view showing an example of the transparent dielectric array of the present invention. [Figure 10A] is a diagram showing an optical system consisting of an array of rod lenses. [Figure 10B] is a diagram showing an optical system consisting of an array of rod lenses. [Figure 10C] is a diagram showing an optical system consisting of a rod lens array and a transparent dielectric array. [Figure 10D] is a diagram showing an optical system consisting of a rod lens array and a transparent dielectric array. [Figure 11] is a graph showing the relationship between the root mean square ratio of ray aberrations rms r and P 1 / P 0 in an optical system composed of a rod lens array and a transparent dielectric array. [Figure 12A] is a graph showing the relationship between the ratio of rms of light aberrations to H / (n 1·L 01) in an optical system consisting of a rod lens array α and a transparent dielectric array. [Figure 12B] is a graph showing the relationship between the ratio of rms of light aberrations to H / (n 1·L 01) in an optical system consisting of a rod lens array β and a transparent dielectric array. [Figure 12C] is a graph showing the relationship between the ratio of rms of light aberrations to H / (n 1·L 01) in an optical system consisting of a rod lens array γ and a transparent dielectric array. [Figure 13] is a graph showing the relationship between H / (n 1·L 01) th and P 1 / P 0 in an optical system composed of lenses α, β, or γ and an array of transparent dielectrics. [Figure 14] is a graph showing the relationship between illuminance non-uniformity ΔI and H / (n 1·L 01) in an optical system composed of lenses α, β, or γ and an array of transparent dielectrics. [Figure 15A] is a diagram showing an example of the image sensor of the present invention. [Figure 15B] is a diagram showing another example of the image sensor of the present invention. [Figure 15C] is a diagram showing another example of the image sensor of the present invention. Implementation Method

[0014] The following describes embodiments of the present invention. However, the following description is illustrative of the present invention and is not limited to these embodiments.

[0015] Figure 1 is a perspective view showing an example of the optical device of the present invention. As shown in Figure 1, the optical device 1a includes a lens array 10 and a transparent dielectric array 20. The directions represented by x, y, and z refer to the directions of the x, y, and z axes of an orthogonal coordinate system. The lens array 10 includes a plurality of lenses 11. In the lens array 10, the plurality of lenses 11 are arranged only in the x-direction (single row arrangement) with their optical axes substantially parallel to each other. For example, when the plurality of lenses 11 are viewed along a direction perpendicular to the optical axis of a particular lens 11, the optical axis of the particular lens 11 is substantially parallel to the optical axes of the other lenses 11. The transparent dielectric array 20 includes a plurality of transparent dielectrics 21. In the transparent dielectric array 20, the plurality of transparent dielectrics 21 are arranged in the x-direction and y-direction with their central axes substantially parallel to each other. In the transparent dielectric array 20, the transparent dielectrics 21 are arranged in two rows in the y-direction, and are arranged in a relatively larger and longer manner in the x-direction (two-row arrangement). Alternatively, the transparent dielectric array 20 can be described as a lens array formed by arranging the transparent dielectrics 21 in one row in the x-direction and then overlapping two layers in the y-direction. For example, when observing a plurality of transparent dielectrics 21 along a direction perpendicular to the central axis of a particular transparent dielectric 21, the central axis of the particular transparent dielectric 21 is approximately parallel to the central axes of the other transparent dielectrics 21. The lens array 10 and the transparent dielectric array 20 are arranged such that the optical axis of the lens 11 is approximately parallel to the central axis of the transparent dielectric 21, and the end faces of the lens array 10 and the transparent dielectric array 20 face each other. By combining the lens array 10 and the transparent dielectric array 20 in this configuration, an optical device 1a can be obtained. For example, when viewing the lens array 10 and the transparent dielectric array 20 along a direction perpendicular to the central axis of the transparent dielectric 21, the optical axis of the lens 11 extends along a direction parallel to the central axis of the transparent dielectric 21. Here, the term "complex axes" or "objects" being approximately parallel to each other means that the angle between them is less than 1°.

[0016] In a lens array, multiple lenses with focusing function are arranged in one or two dimensions with their central axes or optical axes approximately parallel. Lens arrays are widely used in optical systems for acquiring images in devices such as fax machines, photocopiers, and printers. End-face refractive lenses are known as lenses used in lens arrays. In an end-face refractive lens, at least one of the light-incident and light-exit end faces is curved, and focusing is achieved through the refraction of these end faces.

[0017] Furthermore, refractive index distribution rod lenses are also known as lenses used in lens arrays. Refractive index distribution rod lenses (hereinafter sometimes simply referred to as "rod lenses") are, for example, light-transmitting dielectric materials made of cylindrical resin or glass, with a refractive index distribution that decreases from the center towards the periphery. Even without forming part or all of the light-incident and light-outcrystal surfaces as curved surfaces, rod lenses can still function as light-focusing or light-diverging lenses. Because rod lenses do not require curved surface processing of the end faces, which directly increases manufacturing costs, and are easy to miniaturize, they can be used as focusing lenses for optical communication. Moreover, in a lens array where the central axes of multiple rod lenses are arranged approximately parallel to each other, linear or planar objects can be imaged onto the focusing surface. Therefore, such lens arrays exhibit high optical performance such as high resolution or high contrast, and also possess exceptionally good characteristics such as miniaturization, low cost, and high processability. In particular, lens arrays with glass rod-shaped lenses tend to have significantly higher weather resistance and long-term reliability. The technical fields in which such lens arrays can be applied are numerous.

[0018] In the lens array 10, lens 11 is, for example, a rod-shaped lens with a refractive index distribution in the radial direction. In this case, lens 11 can be made of resin or glass. Ideally, lens 11 can also be made of glass. Lens 11 can also be an end-face refractive lens.

[0019] The arrangement of the complex lenses 11 in the lens array 10 is not limited to a specific shape. In the lens array 10, the lens 11 is, for example, a single lens with a focusing function, and the complex lenses 11 are arranged along at least one direction. The arrangement of the complex lenses 11 in the lens array 10 can be a one-dimensional arrangement of 1×n (n is an integer greater than 2) or a two-dimensional arrangement of m×l (m and l are integers greater than 2). Sometimes, the 1×n arrangement is called a single-row arrangement, the 2×l arrangement is called a two-row arrangement, the 3×l arrangement is called a three-row arrangement, etc., in which case m (m=1, 2, 3...) is called the row number. The arrangement of the complex lenses 11 in the lens array 10 can be such that when the complex lenses 11 are observed along a direction parallel to the optical axis, the points corresponding to the optical axis of the complex lenses 11 form the vertices of a square or rectangle, or it can be the densest arrangement. When the multiple lenses 11 are arranged in a single row, the direction corresponding to n can be defined as the first direction or the main scanning direction. When the multiple lenses 11 are arranged in two dimensions, the direction corresponding to the larger of m and l can be defined as the first direction or the main scanning direction. Alternatively, the direction perpendicular to the optical axis or central axis of the lens 11 and perpendicular to the first direction (main scanning direction) can be defined as the sub-scanning direction.

[0020] Figure 2 is a schematic perspective view showing one example of a lens array 10. As shown in Figure 2, in the lens array 10, the lenses 11 are, for example, rod lenses, and the multiple lenses 11 are arranged in a single row. In Figure 2, x, y, and z represent the directions of the x, y, and z axes of an orthogonal coordinate system. The x-direction is set as the main scanning direction, the y-direction as the sub-scanning direction, and the central axis of the lens 11 is parallel or approximately parallel to the z-direction. Furthermore, the following description of the lens array with multiple rod lenses is also applicable to other lens arrays, provided that it is not technically contradictory.

[0021] A composite image is obtained by superimposing the images formed by the individual lenses in a lens array, corresponding to the area where the lenses are arranged. For example, when the lens array is configured such that the relationship between the object plane and the imaging plane is an upright, equal-magnification system, an upright, equal-magnification image of the object plane or object point can be obtained by the lens array.

[0022] Figure 3 is a perspective view showing another example of the lens array 10, and is a diagram showing the relationship between the object plane OP and the image plane IP of the lens array 10. In Figure 3, the directions represented by x, y, and z refer to the directions of the x, y, and z axes of the orthogonal coordinate system. The complex lenses 11 in the lens array 10 shown in Figure 3 are arranged in two rows with m=2. In Figure 3, Z is the length of the central axis direction (z direction) of the lens 11, L0 is the distance between the object plane OP and the lens array 10 (the distance in the optical axis direction of the lens 11 between the object plane OP and the end face (light incident surface) of the lens array 10 closest to the object plane OP), L1 is the distance between the lens array 10 and the image plane IP (the distance in the optical axis direction of the lens 11 between the image plane IP and the end face (light exit surface) of the lens array 10 closest to the image plane IP), and TC is the conjugate length determined by the relationship TC=L0+Z+L1. When the rod lens is cylindrical, the optical axis of lens 11 can also be set as the central axis of lens 11 or the rotational symmetry axis of the rod lens. When the medium on the object surface and the imaging surface are the same (air, etc.) within the range of light transmission, and the relationship between the object surface and the imaging surface constitutes an upright equal magnification system, the positional relationship between the object surface OP, the rod lens array, and the image plane IP can satisfy the condition L0=L1. The distance between the object surface OP or the image plane IP and the lens array 10 can also be adjusted to maintain the condition L0=L1 and maximize the resolution of the image formed on the image plane IP. Furthermore, the values ​​or sets of values ​​such as L0, L1, and TC calculated based on them can also correspond to the standard conjugate configuration.

[0023] If the distance between the object surface or the image surface and the lens array deviates from the standard conjugate configuration (the standard configuration or the configuration of an erect and same-magnification system), the images formed by each lens deviate, and it is difficult to converge the images formed by adjacent lenses with good matching, resulting in a decrease in resolution. This is one of the factors that reduce the depth of field in the lens array. Regarding the composite image formed by the lens array, the overlap degree m value is considered as an index indicating the degree of overlap of the images obtained by a single lens. In FIG. 3, when the field radius at the standard conjugate position of a single lens is set to X0 [mm] and the distance (arrangement pitch) between the optical axes or central axes of adjacent lenses in the lens array is set to P0 [mm], the overlap degree m is expressed as m = X0 / P0. As shown in FIG. 3, the field radius X0 represents the radius of the area on the object surface OP that can be covered by a single lens. A larger overlap degree m means that the number of lenses in the lens array contributing to the formation of the composite image per unit area on the image surface IP is larger. Therefore, regarding the influence of the deviation of the image generated when the distance between the object surface OP or the image surface IP and the lens array 10 deviates from the standard conjugate configuration in the erect and same-magnification case, the larger the overlap degree m, the easier it is to increase, the composite image obtained by the lens array is likely to be blurred, and the resolution is likely to decrease. Furthermore, in FIG. 3, the case where the lenses 11 are arranged in two rows (m = 2) is shown, but the same applies when the lenses 11 are arranged in one row and when the lenses 11 are arranged in more than two rows.

[0024] FIG. 4 is a diagram for explaining the imaging of a rod lens having a refractive index distribution. On the image surface IP of the rod lens 11, a light-receiving element of an image sensor, for example, can be provided, and on the object position or the object surface, an object having a surface such as an original or a workpiece, for example, can be provided. As described above, when the lens array forms an erect and same-magnification optical system, the object surface and the image surface are in the conjugate relationship of an erect and same-magnification system (standard) that satisfies the condition L0 = L1. In this case, as shown in FIG. 4, an same-magnification image IU can be obtained. If the object or the object surface is displaced from the conjugate position PC that satisfies the condition L0 = L1 and becomes the relationship L1 < L0, a reduced image IR (erect and reduced system) is formed on the imaging surface IP (imaging position). The reason is that the field of view of a single lens with a specified aperture angle expands as L0 increases, and the ratio of the object to the field radius changes.

[0025] When the object position changes from the conjugate position that satisfies the condition L0 = L1 in the lens array, the following adverse conditions may further occur. FIG. 5A is a diagram for explaining the imaging state of adjacent rod lenses when the object is at the conjugate position, and FIG. 5B is a diagram for explaining the imaging state of adjacent rod lenses when the object deviates from the conjugate position. In FIGS. 5A and 5B, the character "A" is imaged on the image surface by two adjacent single lenses.

[0026] As shown in Figure 5A, if the relationship L0 = L1 holds, each individual lens captures a portion of character A within its field of view and forms an image of the same size as the object on the image plane. The composite image formed by the two individual lenses overlaps without any shift. On the other hand, as shown in Figure 5B, when the object deviates from the position where the conjugate relationship L0 = L1 holds, the image formed by the two individual lenses becomes a reduced image. Since L1 is fixed, the position and size of the circular images formed by the individual lenses on the image plane do not change. Therefore, the positional relationship between the object "A" and the images formed by the two adjacent individual lenses deviates, and the composite image formed by the two individual lenses may become mismatched. Consequently, a decrease in resolution may occur.

[0027] Thus, the more the object's position shifts from the conjugate position constituting the upright equal-magnification system towards the direction where L0 increases, the lower the magnification of the image formed by the single lens becomes. This accompanying decrease in resolution can be considered the main factor leading to the smaller depth of field of the lens array. Figures 4, 5A, and 5B illustrate this with examples of single-lens arrays where the single lens is a rod-shaped lens. The same problem may also occur when the single lens in the lens array is an end-face refractive lens whose incident and exit surfaces are composed of curved surfaces. Furthermore, there are also lens arrays formed by cascading two or more lenses arranged along the optical axis in a manner consistent with their optical axes, creating an upright equal-magnification system between the object plane and the image plane. Even when using such a lens array, the lens system arranged along the optical axis can be replaced with the single lens described in this specification, and the same explanation can be applied.

[0028] As mentioned above, in a lens array, the larger the value of the overlap degree m, the more lenses are involved in forming the composite image per unit area. Therefore, the decrease in resolution caused by changes in object position, offset, and displacement also becomes more significant with a larger value of overlap degree m. Consequently, in a lens array, the depth of field tends to decrease proportionally to the magnitude of the overlap degree m parameter.

[0029] A rod lens can be formed, for example, from a cylindrical transparent dielectric. A rod lens, for example, has a refractive index that decreases from the central axis towards the periphery in the radial direction. Therefore, because light bends inside the rod lens, even if the light-incident or light-exit surface is formed as a flat plane at the end of the rod lens, it can still perform functions such as light focusing.

[0030] When lens 11 is a rod lens, the refractive index distribution of the rod lens is approximated by, for example, the following equation (1). Furthermore, the numerical aperture (NA) of the rod lens is represented by equation (2). In equation (1), r is the radial distance from the optical axis of the rod lens. n(r) is the refractive index of the rod lens at a distance r. n0 is the refractive index of the optical axis or center of the rod lens. g is the refractive index distribution constant of the rod lens. r0 is the effective radius of the rod lens. The effective radius of the rod lens refers to half of the effective diameter, which is the range through which light can pass, and is expressed as the diameter of the circle around the central axis of the rod lens. n(r) 2=n 0 2{1-(g·r) 2} Equation (1) NA = n 0·g·r 0 equation (2)

[0031] Figure 6 schematically illustrates the angle θ of light that can be received at a position a distance r apart from the center of the light-incident surface of a rod lens. Here, the angle of light that can be received is the angle of light that can be transmitted through the rod lens to aid in imaging; incident light above this angle is absorbed by the sidewalls of the rod lens and does not exit the lens. In Figure 6, a cone with angle θ as its apex is used to represent the range of light that can be received at a position a distance r apart. The angle between the generatrix of this cone and the central axis of the cone is represented as the light-receiving angle θ.

[0032] Figure 7 is a schematic graph showing the relationship between the angle θ determined by the definition of the opening of the rod lens in equation (2) and the distance r from the central axis. As shown in Figure 7, the angle θ received at the center of the light incident surface of the rod lens with r=0 represents the maximum value, and at the outer periphery of the rod lens, the angle θ becomes zero. The maximum value of this angle θ is defined as the opening angle θ0. The opening angle θ0 and the opening NA are in the relationship NA=sinθ0.

[0033] The method of manufacturing a rod lens is not limited to a specific method. A rod lens may be manufactured, for example, by methods including (i), (ii), and (iii) below. (i) Obtaining rod-shaped glass with a specified composition and a generally circular cross-section by means of a pull-down method. (ii) A concentration gradient of elements such as Li is formed inside the rod-shaped glass obtained in (i) by means of ion exchange, and a refractive index distribution is formed in the radial direction of the rod-shaped glass. (iii) By cutting a rod-shaped glass with a refractive index distribution into a specified length in a direction approximately perpendicular to the central axis and grinding it, a planar end face is provided as the light incident surface and the light exit surface.

[0034] For example, step (iii) above includes steps (iiia) and (iiib) below. (iiia) Arrange a plurality of rod-shaped glass in such a way that the central axes of the plurality of rod-shaped glass are approximately parallel to each other, and hold the plurality of rod-shaped glass with a pair of side plates. (iiib) By cutting a plurality of rod-shaped glass pieces into suitable lengths that achieve the required optical performance, approximately perpendicular to the central axis of the rod-shaped glass, and then grinding them, a planar end face is provided to function as a light incident surface. The two end faces corresponding to the light incident surface may also be parallel.

[0035] In the optical device 1a, the transparent dielectric array 20 is arranged, for example, to overlap with the lens array 10 in a direction perpendicular to the optical axis of the lens 11 of the lens array 10.

[0036] Figure 8A schematically illustrates the spread of light rays passing through lens 11, which functions as a rod lens. Figures 8B, 8C, and 8D schematically illustrate the field-of-view limitations when a transparent dielectric is positioned along the optical axis of the rod lens 11. In the optical systems schematically represented in Figures 8A-8D, the medium from the object surface OP to the rod lens 11, and from the transparent dielectric 21 to the imaging surface IP, is air (refractive index = 1). The rod lens 11 and the transparent dielectric 21 can be in contact along the optical axis of the rod lens 11, or there can be a space composed of air between the rod lens 11 and the transparent dielectric 21 along the optical axis of the rod lens 11. In Figure 8A, the directions represented by x, y, and z refer to the directions of the x, y, and z axes of an orthogonal coordinate system, and the same applies in Figures 8B-8D. These figures represent cross-sectional views obtained using a plane comprising the central axis of a cylindrical rod lens 11 and the central axis of a transparent dielectric 21. Furthermore, these models illustrate a system for imaging an object surface OP onto an imaging surface IP. Object points on the object surface OP are imaged onto the imaging surface IP as upright, full-magnification images by an optical device composed of the rod lens 11, or of the rod lens 11 and the transparent dielectric array 20. The dashed lines in the figures represent the area of ​​the subject on the object surface included by the optical system and the area projected onto the imaging surface by the optical system.

[0037] In Figures 8B to 8D, the interior of the transparent dielectric 21 is transparent and does not absorb light. Alternatively, the amount of light absorbed inside the transparent dielectric 21 is very small. The transparent dielectric 21 has a refractive index of 1 or higher (or higher than the refractive index of air). Part or all of the light reaching the side of the transparent dielectric 21 is absorbed. This blocks light. Furthermore, the thickness of the portion absorbing light reaching the side of the transparent dielectric 21 can be minimized as much as possible, and this thickness can be considered zero. Also, when a black coating for absorbing light is present on the side of the transparent dielectric, its wall thickness can be 50 μm or less. Arranging such transparent dielectrics 21 can form a transparent dielectric array 20. In other words, the transparent dielectric array is obtained by arranging a plurality of transparent dielectrics in a manner in which their central axes are approximately parallel to each other, wherein the plurality of transparent dielectrics are configured to have a certain refractive index and absorb a portion of light on their side (peripheral) surfaces.

[0038] The shape of the transparent dielectric 21 is not limited to a specific shape. For example, the transparent dielectric 21 can be cylindrical, or it can be a polygonal prism such as a tetragonal prism or a hexagonal prism. The transparent dielectric 21 can also be an elliptical prism or a long cylindrical shape. In such cases, the field of view in a particular direction may be easily restricted.

[0039] As a transparent dielectric with a refractive index of 1, if air is considered as a dielectric, it can be a thin-walled cylindrical shape, or it can be an array of transparent dielectrics (more precisely, a cylindrical array) with the central axes of the cylinders parallel and arranged in at least one direction.

[0040] In Figure 8A, the distance between the object surface OP and the light incident surface of the rod lens 11, and the distance between the light emitting surface of the rod lens 11 and the imaging surface IP are equal. On the other hand, in Figures 8B-8D, since the transparent dielectric 21 has a certain refractive index, it should be noted that the distance between the object surface OP and the light incident surface of the rod lens 11, and the distance between the light emitting surface of the rod lens 11 and the imaging surface IP are different. Furthermore, the light emitting surface of the rod lens 11 (the side opposite to the object surface OP) and the light incident surface of the transparent dielectric array 20 (the side opposite to the imaging surface IP) can be in contact or separated.

[0041] In Figure 8A, the rod lens 11 is configured to form an upright, equal-magnification image of the object point. Therefore, the maximum value of the light-receiving angle, i.e., the aperture angle θ0, is the extension of the light rays that produce the maximum angle θ at the center of the light-emitting surface in the rod lens 11. Thus, regarding the field of view limitation caused by the transparent dielectric 21, we focus on the light rays emitted from the center of the rod lens 11.

[0042] In Figure 8A, as described above, the object plane OP, the rod lens 11, and the image plane IP are positioned at conjugate positions in an upright, equal-magnification system. In Figure 8A, the dashed lines schematically represent the propagation of light rays corresponding to the opening of the rod lens 11. In Figure 8A, since there is no transparent dielectric 21, the field-of-view diameter of the object plane OP and the imaging diameter of the image plane are conjugate, and since there are no obstructions, they are the same size.

[0043] In Figure 8B, firstly, three transparent dielectrics 21 with diameters approximately the same as the diameter of the rod lens are arranged parallel to each other's central axes, and the end faces perpendicular to the central axes of each transparent dielectric 21 are made to form a transparent dielectric array 20. The transparent dielectric 21 is positioned on the imaging surface IP side of the rod lens 11, with the central axis of one transparent dielectric 21 aligned with the extension of the central axis of the rod lens 11, and the light exit surface of the rod lens 11 (the end face of the rod lens 11 near the imaging surface IP) and the light incident surface of the transparent dielectric 21 (the end face of the transparent dielectric 21 near the rod lens 11) parallel to each other. The lens array 10 and the transparent dielectric array 20 satisfy, for example, the conditions shown in Equation (3) below. In Equation (3), H is the length [mm] of the transparent dielectric 21 along its central axis. n1 is the refractive index of the transparent dielectric 21, which is 1≦n1, or 1.2≦n1≦2.0, or 1.4≦n1≦1.8. When the refractive index n1 of the transparent dielectric is 1, the transparent dielectric can also be constructed from a thin-walled cylindrical shape. Furthermore, by forming it with an organic-inorganic mixture containing hollow silicon dioxide or magnesium fluoride particles (for example, a material containing hollow particles and composed of alkoxysilane or its hydrolysate, polymer, or other binders), a transparent dielectric with a refractive index n1 close to 1 can be obtained. P1 is the distance [mm] between the central axes of adjacent transparent dielectrics 21 in the transparent dielectric array 20 (the spacing between transparent dielectrics). The left side represents the distance between the light exit point on the opposite surface (light exit surface) of the transparent dielectric 21 and the center of the light exit surface when the light is incident on the center of the end face (light incident surface) of the transparent dielectric 21 at an incident angle of θ 0. (Using the approximation of sinθ 0 ≒ tanθ 0). The right side represents the radius of the end face of the transparent dielectric 21 when adjacent transparent dielectrics 21 are arranged without gaps. tanθ 0·H / n 1>P 1 / 2 Equation (3)

[0044] In Figure 8B, when equation (3) holds, a portion of the light emitted from the rod lens 11 is absorbed after reaching the side of the transparent dielectric 21, and the light that does not reach the side but passes through the transparent dielectric 21 forms an image. The diameter of the image formed on the image plane becomes smaller than the field of view diameter on the object surface OP. For example, if a plurality of transparent dielectrics 21 are arranged in the first direction (main scanning direction) such that the distance between the adjacent central axes of the plurality of transparent dielectrics 21 is equal to the diameter of the rod lens 11, the extension of the light corresponding to the field of view diameter of each rod lens 11 is narrowed by the side of the transparent dielectric 21, and a composite image can be obtained with a substantially small overlap m.

[0045] In Figure 8C, the rod lens 11 and the transparent dielectric array 20 are the same as those described using Figure 8B. The difference lies in the degree to which the central axis of the transparent dielectrics 21 in the transparent dielectric array 20 is offset relative to the optical axis of the rod lens 11 by half the spacing P1 between the transparent dielectrics. This offset in the position of the transparent dielectric array 20 prevents the outermost light rays from being blocked by the sides of the transparent dielectrics 21, making it easier for them to reach the image plane IP. Therefore, the field of view of the rod lens is less limited by the transparent dielectrics 21. If the rod lenses and transparent dielectrics 21 are arranged such that "when the central axis of the transparent dielectric 21 is offset from the optical axis of the rod lenses, the distance between the optical axes of the rod lenses and the distance between the central axes of the transparent dielectrics 21 are the same," then the extension of light corresponding to the field of view diameter of each rod lens will not be narrowed due to the light-blocking properties of the sides of each transparent dielectric 21 in the transparent dielectric array 20. Therefore, the overlap m in this state can be almost the same as the overlap m in the state where the transparent dielectric array 20 is not present. Therefore, when the diameter of the transparent dielectric 21 is equal to the diameter of the rod lenses, the side of the transparent dielectric 21 can, for example, be positioned in the direction of the arrangement of the rod lenses in the lens array at a position offset from the optical axis of the rod lenses.

[0046] In Figure 8D, the spacing P1 between the transparent dielectric elements is smaller than the diameter of the rod lens 11. For example, if the diameter of the transparent dielectric 21 is half the diameter of the rod lens 11, the spacing P1 between the transparent dielectric elements is also adjusted to half the diameter of the rod lens. Thus, if the spacing P1 between the transparent dielectric elements is small, even if there is a side of the transparent dielectric 21 near the straight line containing the optical axis of the rod lens 11 in the arrangement direction of the rod lens 11 in the lens array 10, the opening of the rod lens 11 can be restricted. In this way, a plurality of transparent dielectric elements 21 are arranged such that the spacing P1 between the transparent dielectric elements in the transparent dielectric array 20 is smaller than the distance P0 between the optical axes of adjacent rod lenses, and the transparent dielectric array 20 contains subdivided light-transmitting portions with a size smaller than the diameter of the rod lens. Therefore, even if the transparent dielectric 21 is configured such that "the side of the transparent dielectric 21 exists near the straight line containing the optical axis of the rod lens 11 in the arrangement direction of the rod lens 11 in the lens array 10", the overlap m is easily reduced.

[0047] As shown in Figure 8D, if the spacing P1 between the transparent dielectric elements is smaller than the diameter of the rod lens 11, the necessity to precisely align the optical axis of the rod lens 11 with the central axis of the transparent dielectric 21 in order to reduce the overlap m is reduced. Therefore, even if there are errors in the spacing between the lenses 11 in the lens array 10, the depth of field is less likely to become unstable. Moreover, the problem of misalignment (coaxiality) between the optical axis of the rod lens 11 and the central axis of the transparent dielectric 21 due to the difference in thermal expansion caused by temperature changes in the components is less likely to occur.

[0048] The transparent dielectric array 20 may also include a plurality of transparent dielectrics 21 arranged in one or more rows. The transparent dielectrics 21 can function as opening limiting elements. In the transparent dielectric array 20, the plurality of transparent dielectrics 21 are arranged in a manner in which the central axes of the plurality of transparent dielectrics 21 are substantially parallel to each other.

[0049] Figure 9 is a perspective view showing an example of a transparent dielectric array 20. In Figure 9, the transparent dielectric array 20 is composed of two rows, but the following description also applies to transparent dielectric arrays with one or more rows. A plurality of transparent dielectrics 21 are integrally formed by filling the gaps between a pair of plates 22 with resin or adhesive 23. The plates 22 are, for example, made of fiber-reinforced plastic (FRP). The resin 23 is colored black. With this configuration, for example, it is easy to arrange a plurality of transparent dielectrics 21 in a plurality of rows within the transparent dielectric array 20.

[0050] The material of the transparent dielectric 21 is not limited to a specific material. The transparent dielectric 21 can also be formed from the same material as the rod lens. In this case, the difference in thermal expansion between the transparent dielectric 21 and the rod lens is less likely to occur, making it easier to mount the transparent dielectric array 20 relative to the lens array 10. Furthermore, regarding the glass before and after the formation of the refractive index distribution by ion exchange as described above (ii), although there is a certain increase or decrease in the metal content, it can be considered to be essentially the same material. Moreover, the refractive index n0 at the central axis of the single lens constituting the rod lens array and the refractive index n1 of the transparent dielectric can also be approximately the same value. The so-called approximately the same value of complex refractive indices means that the absolute value of the difference between these refractive indices does not reach 0.0005.

[0051] The transparent dielectric 21 can be formed, for example, from glass or plastic having a roughly uniform refractive index n1. For example, the refractive index n1 of the transparent dielectric 21 can satisfy the condition 1 ≤ n1, or the condition 1.2 ≤ n1 ≤ 2.0, or the condition 1.4 ≤ n1 ≤ 1.8. The surface roughness of the side surface of the transparent dielectric 21 is not limited to a specific value. This surface roughness can also be adjusted by the way in which some or all of the light reaching this side surface through the interior of the transparent dielectric 21 is scattered. For example, the arithmetic mean roughness Ra of the side surface of the transparent dielectric 21 is 0.1 to 5.0 μm. The arithmetic mean roughness Ra is determined according to Japanese Industrial Standard JIS B0601:1994. A coating can also be formed on the side surface of the transparent dielectric 21 to absorb some or all of the light. This coating can be formed from a resin colored to absorb light such as black. The coating can also achieve the same effect as that achieved by blackening the periphery or sides in a typical lens (e.g., an optical element composed of concave, convex, planar, or diffraction grating surfaces, used to refract or diffract light at these surfaces to diverge or focus it). Ideally, the coating material should include curable resins such as epoxy resin, acrylic resin, polyurethane resin, phenolic resin, melamine resin, unsaturated polyester resin, alkyd resin, and silicone resin; mixtures of one or more of these may also be used. Furthermore, the coating material should ideally have a matte appearance after curing. In addition to the aforementioned resins, the coating material may also include black particles such as carbon black, titanium black (titanium-based black pigment), magnetite-type iron oxide, oxides containing copper and chromium, and VALIFAST BLACK (azochromium compound). Alternatively, the raw yarn of the rod lens can be immersed in a chloroform solution containing VALIFAST BLACK (manufactured by ORIENT CHEMICAL), allowing the solution to adhere to the side of the raw yarn. The chloroform is then evaporated and dried to produce a black-dyed glass rod or raw yarn for the rod lens. Furthermore, when each lens constituting the lens array 10 is a refractive index distribution type lens, the same resin used to coat the side surfaces of each lens with black can be used to coat the side surfaces of the transparent dielectric 21.

[0052] The transparent dielectric array 20 can also be manufactured, for example, by a method including the following steps: arranging the plurality of rod-shaped glass pieces, obtained by a pull-down method, in a manner that is substantially parallel to the central axis of the glass; and forming a face roughly perpendicular to the central axis of the glass to obtain a transparent dielectric 21. The transparent dielectric array 20 can also be manufactured, for example, by a method including (I) and (II) below. (I) A plurality of rod-shaped glass manufactured by methods such as the pull-down method are arranged in a manner in which the refractive index distribution is not formed inside the rod-shaped glass, but the central axis or rotational symmetry axis of the plurality of rod-shaped glass is roughly parallel to each other, and they are clamped by a pair of plate-shaped side plates and integrated by adhesives or resins. (II) By cutting a plurality of rod-shaped glass into a specified length along a direction approximately perpendicular to their central axes and grinding them, a light incident surface is formed, and an end face perpendicular to the central axis is provided.

[0053] According to this method, the composition of the glass forming the transparent dielectric 21 of the manufactured transparent dielectric array 20 can also be made approximately the same as the composition of the rod-shaped glass obtained in (i) above. Therefore, the differences in physical properties such as the coefficient of thermal expansion and light transmittance between the transparent dielectric 21 and the rod-shaped lens are easily reduced. Because the difference in the coefficient of thermal expansion between the multiple parts is small, even in the case of temperature changes, the relative positional relationship between the parts is less likely to change with the expansion and contraction of the parts, and the variation in the positional accuracy between the multiple parts and the optical performance performed by the multiple parts in cooperation is easily reduced.

[0054] For example, a transparent dielectric 21 of the required size can be manufactured by heating one side of a glass or resin rod that has been pre-formed into a polygonal column or other specified shape, thereby extending it.

[0055] For example, resin can be filled into the gaps between the transparent dielectrics 21, and the resin can be hardened to integrate the plurality of transparent dielectrics 21. In this case, the resin can also be colored black to improve light absorption. The resin filling can also be carried out by, for example, supplying liquid resin to one end of the gap while vacuuming at the other end of the gap, so that the resin covers the entire gap between the plurality of transparent dielectrics 21. Alternatively, a black adhesive resin can be pre-coated on the surface of a pair of plates, and after arranging and clamping the plurality of transparent dielectrics 21 between the pair of plates, the pair of plates and the plurality of transparent dielectrics 21 are heated and pressed, and the gaps between the transparent dielectrics 21 are filled with resin.

[0056] The transparent dielectric 21 may also have a structure comprising a core and a cladding. In this case, the cladding may be a colored layer that absorbs a portion of the light that travels toward its periphery or reaches the vicinity of the side surface of the transparent dielectric 21. Ideally, fine irregularities that promote light scattering and absorption may also be formed on the side surface of the transparent dielectric 21.

[0057] The arrangement pattern of the plurality of transparent dielectrics 21 in the transparent dielectric array 20 is not limited to a specific pattern. The arrangement pattern of the plurality of transparent dielectrics 21 can be one-dimensional or two-dimensional. In a two-dimensional arrangement, the plurality of transparent dielectrics 21 form, for example, a plurality of rows. In this case, the central axes of the plurality of transparent dielectrics 21 in each row can be approximately parallel.

[0058] In the optical device 1a, the conditions for the distance P0 and the spacing P1 between the transparent dielectric elements are not limited to specific conditions. Ideally, the optical device 1a satisfies the condition P1 ≤ 0.8 × P0. This allows for a greater depth of field in the optical device 1a, enabling the acquisition of images with less degradation and higher resolution, even for subjects with uneven surfaces and varying heights, in a machine equipped with the optical device 1a. For example, the optical device 1a may further satisfy the condition 0.3 × P0 ≤ P1. Furthermore, P0 is the distance between the optical axes of adjacent rod lenses 11 in the lens array 10, and is sometimes defined as the spacing between the rod lenses or the inter-lens spacing. P1 is the distance between the central axes of adjacent transparent dielectric elements 21 in the transparent dielectric array 20, and is sometimes defined as the spacing between the transparent dielectric elements or the inter-dielectric spacing. By ensuring the spacing P1 of the transparent dielectric array is 0.3 × P0 or greater, it is less likely to cover the effective diameter of the lens, thus easily preventing light reduction and minimizing lens aperture division. Therefore, it is easier to prevent the NA in the sub-scanning direction (y-direction) from decreasing while the dot diameter increases, and it is also easier to prevent side peaks in the scanning direction (x-direction) due to the periodic structure of the transparent dielectric array. Furthermore, P0 and P1 can satisfy the conditions 0.4 × P0 ≤ P1 and 0.5 × P0 ≤ P1. Also, for a single-row lens array, the conditions 0.45 × P0 ≤ P1 ≤ 0.65 × P0 and 0.5 × P0 ≤ P1 ≤ 0.6 × P0 can be satisfied.

[0059] In optical device 1a, the conditions satisfied by the length H [mm] of the central axis of the transparent dielectric 21, the refractive index n1 of the transparent dielectric 21, the distance L01 [mm] between the rod lens and the object surface, the spacing P1 of the transparent dielectric, and the spacing P0 of the rod lens are not limited to specific conditions. The distance L01 between the rod lens and the object surface is the distance between the end face of the lens closest to the object surface and the object surface when an upright, equal-magnification image of an object point on the object surface is formed on the imaging surface at the highest resolution in the optical system using optical device 1a. Ideally, in optical device 1a, the condition H / (n1·L01)>0.27×(P1 / P0)+0.023 should be satisfied. In this way, optical device 1a can more easily have a larger depth of field. For example, even for subjects or workpieces with thickness, concavity, unevenness, and height differences, it is easier to obtain images with less degradation of optical performance and high resolution.

[0060] Ideally, the optical device 1a should satisfy the condition H / (n 1·L 01)≦0.6. In this case, uneven illumination is less likely to occur in the optical device 1a.

[0061] When using an optical device with a lens array and a transparent dielectric array arranged such that the optical axes of the lenses in the lens array and the central axis of the transparent dielectric are approximately parallel, the required precision in the arrangement of the lenses and transparent dielectrics is an important research matter in ensuring the performance of the optical device. Therefore, this study investigates the impact of deviations from ideal positions in the x and y directions of the relative positions of the lenses in the lens array and the transparent dielectrics in the transparent dielectric array on the performance of the optical device.

[0062] To perform ray tracing or image evaluation, we used OSLO Premium rev 6, a geometric optics calculation software from Lambda Research Corporation in the United States, to study the effect on depth of field when the relative positions of the rod lens array and the transparent dielectric array are changed, considering a suitable optical system model.

[0063] Figure 10A schematically illustrates an optical system consisting of an object plane OP, a rod lens array 10p, and an imaging plane IP. The object plane OP is defined as a plane perpendicular to the paper. The point on the object plane OP at position A is designated as the origin. The axis passing through the origin, perpendicular to the object plane OP, and pointing towards the imaging plane IP is designated as the z-axis. The axis passing through the origin, perpendicular to the z-axis, and parallel to the paper is designated as the x-axis. The axis passing through the origin and perpendicular to the x-axis, z-axis, and paper is designated as the y-axis. The rod lenses 10p are arranged in a row along the x-direction, with the central axis of one rod lens in the rod lens array 10p coinciding with a portion of the z-axis. In the case of cylindrical rod lenses or rotationally symmetric lenses, their central axis or rotational symmetry axis can also be designated as the optical axis of the lens. Therefore, the z-axis can also be aligned with the optical axis of the rod lens. In Figure 10A, the upright, full-magnification image IQ of the object point on the object surface OP at the location indicated by A is formed on the imaging plane IP at the highest resolution by the rod lens array 10p. Assume that the object surface OP, the rod lens array 10p, and the imaging plane IP are in standard configuration.

[0064] Figure 10B is a schematic diagram of the optical system shown in Figure 10A viewed from the side of the object surface OP along the z-direction. Furthermore, it is assumed that the object surface OP, the rod lens array 10p, and the imaging plane IP are set in air (refractive index = 1).

[0065] Figure 10C schematically illustrates an optical system consisting of an object surface OP, a rod lens array 10p, a transparent dielectric array 20p, and an imaging surface IP. The object surface OP is defined as a plane perpendicular to the paper. In Figure 10C, the point on the object surface OP represented by A is designated as the origin. The axis passing through the origin, perpendicular to the object surface OP, and pointing towards the imaging surface IP is designated as the z-axis. The axis passing through the origin, perpendicular to the z-axis, and parallel to the paper is designated as the x-axis. The axis passing through the origin and perpendicular to the x-axis, z-axis, and the paper is designated as the y-axis. The rod lenses 10p are arranged in a row along the x-direction, with the central axis of one rod lens in the rod lens array 10p roughly coinciding with a portion of the z-axis. In the case of cylindrical rod lenses or rotationally symmetric lenses, their central axis or rotational symmetry axis can also be designated as the optical axis of the lens. Therefore, the z-axis can also be roughly aligned with the optical axis of the rod lens. In Figure 10C, the upright, full-magnification image IQ of the object point on the object surface OP at the location indicated by A is formed on the imaging surface IP with the highest resolution using an optical system consisting of a rod lens array 10p and a transparent dielectric array 20p. The object surface OP at the location indicated by A, the optical device consisting of the rod lens array 10p and the transparent dielectric array 20p, and the imaging surface IP are the standard configuration.

[0066] Figure 10D is a schematic diagram of the optical system shown in Figure 10C viewed from the object surface OP along the z-direction. Furthermore, assume that the object surface OP, the rod lens array 10p, the transparent dielectric array 20p, and the imaging surface IP are positioned in air (refractive index = 1). As shown in Figure 10D, the transparent dielectric array 20p is formed by overlapping transparent dielectric arrays arranged in a row along the x-direction in a manner that minimizes the gap in the y-direction (two-row arrangement). The transparent dielectric array 20p is configured such that the width of the transparent dielectric array 20p in the y-direction is bisected by the xz plane, and the yz plane includes the central axis of one transparent dielectric element of the transparent dielectric array 20p and the central axis of the rod lens.

[0067] As described above, the object point and image point IQ, located at the origin on the object plane OP represented by A, are in a conjugate positional relationship within an upright, equal-multiplication system. When the object plane OP is located at position A, the intersection of the extension of the optical axis of the specific rod lens and the object plane OP is also the origin of a coordinate system defined by the x-axis, y-axis, and z-axis. The point light source is placed at this origin, and the image formed by this light source on the image plane IP is evaluated. It is assumed that the light source is an ideal point light source.

[0068] In the optical systems shown in Figures 10A to 10D, the rod lens array 10p possesses the optical performance shown in Table 1. Furthermore, L0 in the table represents the distance between the rod lens array 10p and the object surface OP in the optical systems composed of the rod lens array 10p in Figures 10A and 10B, when the upright, equal-magnification image of the object surface OP at position A is formed on the imaging plane IP at the highest resolution, i.e., in the standard configuration.

[0069] [Table 1] project symbol unit Specifications Number of rows of rod lens array 1 Central refractive index n 0 1.600 Refractive index distribution constant g [ / mm] 0.4400 Lens period length PP=2π / g [mm] 14.28 Lens spacing P 0 [mm] 0.600 Rod lens diameter D 0 [mm] 0.600 Effective radius of rod lens r 0 [mm] 0.285 Number of openings NA≈n 0·g·r 0 0.20 Opening angle θ 0 [deg.] 11.5 Lens length Z [mm] 7.65 Lens conjugate length TC [mm] 33.01 Lens-object surface distance L 0 [mm] 12.68 The ratio of the distance between the lens and the object surface to the length of the lens period L 0 / PP 0.89

[0070] The transparent dielectric system comprising the transparent dielectric array 20p in the optical device shown in Figure 10C or Figure 10D is a non-absorbing cylindrical transparent dielectric composed of a medium with a uniform refractive index n 1. It is considered that light incident and emitted from the transparent dielectric does not scatter, but strictly follows Snell's law. Furthermore, it is considered that a light-absorbing layer with negligible thickness is formed on the side of the transparent dielectric to absorb the arriving light.

[0071] In the optical systems shown in Figures 10C and 10D, the rod lens array 10p is configured to be the same rod lens array used by the user in the optical systems shown in Figures 10A and 10B as described in Table 1. Regarding the transparent dielectric array 20p, it is prepared to possess the characteristics and physical quantities shown in Table 2. Furthermore, in the optical system shown in Figures 10C and 10D, which includes an optical device composed of the rod lens array 10p and the transparent dielectric array 20p, when an upright, equal-magnification image of the object surface OP is formed on the imaging plane IP at the highest resolution, i.e., in the standard configuration, the distance between the end face of the rod lens array 10p on the object surface OP side and the object surface OP is defined as L01. Regarding the relationship shown in Figures 10C and 10D, since it can be considered as the optical system containing the rod lens array 10p shown in Figures 10A and 10B, with a transparent dielectric array inserted directly behind the rod lens array 10p, the distance L01 in the standard configuration shown in Figures 10C and 10D is approximately the same as the distance L0 in the standard configuration shown in Figures 10A and 10B. Regarding the distance between the end face of the rod lens array and the object surface, the two values ​​being approximately the same means that the absolute value of the difference between the two values ​​is less than 2% relative to the reference value. In Table 2, the values ​​of P1 / P0 and H / (n1·L01) of the transparent dielectric array 20p represented by (i)~(v) also include the relationship of the rod lens array 10p shown in Table 1 included in each optical device combined with it in the standard position.

[0072] [Table 2] Specification symbol unit Transparent dielectric array (i) (ii) (iii) (iv) (v) Number of rows of transparent dielectric array 2 2 2 2 2 Refractive index of transparent dielectrics n 1 1.600 1.600 1.600 1.600 1.600 Spacing of transparent dielectrics P 1 mm 0.600 0.540 0.480 0.360 0.240 Diameter of transparent dielectric D 1 mm 0.600 0.540 0.480 0.360 0.240 Effective radius of transparent dielectric r 1 mm 0.285 0.257 0.228 0.171 0.114 The ratio of the spacing between transparent dielectric elements to the spacing between the lenses in a rod-shaped lens array P1 / P0 1.0 0.9 0.8 0.6 0.4 Length of transparent dielectric H mm 9.60 8.64 7.68 5.76 3.84 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.473 0.426 0.379 0.284 0.189

[0073] In the optical simulation, when performing optical calculations for the optical system consisting of a rod lens array 10p shown in Figures 10A and 10B, the point light source is positioned at the origin on the object surface at position A in the figure. The point light source is set at the origin O and emits light with a wavelength of 570 nm that has no intensity difference due to the angle, and 7380 ray tracing calculations are performed. This aspect is also the same in subsequent optical calculations using the point light source. During the process of adjusting the distances to the object surface OP and the imaging surface IP, L0 and L1 of the upright equal magnification system of the rod lens array are obtained as shown in Equation (4), and then the object surface OP, the rod lens array, and the imaging surface IP are positioned. L 0=L 1=-(1 / n 0)·tan(π·Z / PP) Formula (4)

[0074] In this way, while obtaining L0 and L1, the standard configuration is obtained, and the conjugate point of the origin on the object surface OP on the imaging surface IP is set as the image point IQ. The adjustment of the resolution of the image surface calculated in the simulation and the setting of the condition for setting the highest resolution are performed as follows. First, while providing L0 and L1 calculated using Equation (4), the object surface OP, the imaging surface IP, and the rod lens array 10p represented by the parameters in Table 1 are provided, and a spot diagram of the image on the imaging surface IP is obtained. Then, on the imaging surface IP, the distance to the self-image point IQ for each ray is calculated, that is, the lateral ray aberration. Then, as an evaluation index of the image, the root mean square (rms) value of the ray aberration is calculated as rms A, and the higher-order coefficients of the rod lens array 10p are optimized in a way that minimizes the value of rms A. This is synonymous with the correction of spherical aberration on the axis. The so-called higher-order coefficients of the 10p bar lens array refer to the coefficients h4 and h6 when the refractive index distribution n(r) of the bar lens is expressed by the following formula (5). n 2(r)=n 0 2·{1-(g·r) 2+h 4(g·r) 4+h 6(g·r) 6} Formula (5)

[0075] Secondly, the object surface OP at position B in the figure becomes the object surface OP at position A in the figure when the point light source is displaced by -1 [mm] along the z-direction. At this time, the distance between the rod lens and the object surface is L 0+1 [mm]. In this configuration of the optical system that shifts the object surface OP, a dot plot of the image on the imaging surface IP is similarly obtained. On the imaging surface IP, the distance to the self-image point IQ for each ray is calculated, i.e., the lateral ray aberration, which is used as an evaluation index of the image. The root mean square (rms) value of the ray aberration is calculated as rms B. Position B, for example, corresponds to the original or workpiece that should originally be located at position A being in a so-called "floating" state in the direction away from the rod lens array or the image sensor containing the rod lens array. Furthermore, in an optical system that includes an object surface OP represented by position B after a position displacement represented by A belonging to the standard configuration, in order to reduce the increased RMS value (improve imaging performance or light focusing), a so-called defocusing displacement of the imaging surface IP is not performed.

[0076] In the simulation conducted under the conditions described above, at position A, RMS A is 0.0041 mm, while at position B, RMS B is 0.1014 mm. When the object surface OP is displaced from its standard configuration (position A) to position B, the RMS value of the ray aberration increases, resulting in a decrease in imaging performance. Furthermore, no compensation or defocusing (position adjustment of the imaging surface IP) was performed to improve the RMS value of the image on the imaging surface IP during the displacement to position B. The ratio of RMS A at position A to RMS B at position B, RMS r, is 0.040. In an optical system containing a rod lens array, when the workpiece or original undergoes a "bulge" (displacement in the -z direction), the imaging performance can be considered to decrease to this extent.

[0077] In the image evaluation of the optical systems shown in Figures 10C and 10D, firstly, for the optical system composed of the rod lens array 10p shown in Table 1, the standard position is determined, and the rms B of the imaging surface IP relative to the object surface OP after being displaced by -1 [mm] in the z-direction from the standard position is calculated in the same way as the calculation method described in Figures 10A and 10B above. The actual calculated value is the same, rms B = 0.1014 [mm]. Secondly, the rod lens array 10p is combined with each of the transparent dielectric arrays 20p shown in Table 2 to form an optical device, and the standard configuration of the object surface OP at the position indicated by A, the optical device composed of the rod lens array 10p and the transparent dielectric array 20p, and the imaging surface IP in the system is determined. At this time, the distance L01 between the end face of the rod lens array 10p on the object surface OP side and the object surface OP is approximately the same as L0. The object surface OP at position B in the figure is the surface after the object surface OP at position A in the figure has been displaced along the z-direction by -1 [mm] together with the point light source. At this time, the distance between the rod lens and the object surface is L 01+1 [mm]. In subsequent calculations or evaluations, when the optical system is configured by displacing the object surface OP along the -z-direction, the point light source is further displaced by 0, 0.25, 0.50, and 0.75 times the diameter of each transparent dielectric in the x-direction (0 mm, 0.25×D 1mm, 0.5×D 1mm, and 0.75×D 1mm, where D 1 is the diameter of the transparent dielectric), and by 0 mm, 0.1 mm, and 0.2 mm in the y-direction (y-direction). Relative to the transparent dielectric array 20p of (i)~(v), 12 point light sources are displaced along the x-axis and y-axis to obtain point maps of each image on the imaging surface IP. A total of 5×12=60 point maps are obtained. For each point map obtained, the lateral ray aberration is calculated on the imaging surface IP for each ray, representing the distance to the image point IQ. This lateral ray aberration is used as an evaluation index for the image, and the root mean square (rms) value of the ray aberration is calculated as the rms(k)(m×p) at position B. Regarding rms(k)(m×p), k is 0.4, 0.6, 0.8, 0.9, and 1.0, and is the suffix corresponding to P1 / P0 of the transparent dielectric arrays (i)~(v) shown in Table 2; m is 0, 0.25, 0.50, and 0.75, and is the suffix of the displacement coefficient in the x-direction; p is 0, 0.1, and 0.2, and is the suffix of the displacement in the y-direction. Finally, the ratio of rms(k)(m×p) to the rms B is calculated, i.e., rmsr(k)(m×p) (the properties of the suffixes k, m, and p are the same as above).This calculation considers the so-called "bulge" in which the original artwork moves away from its original height in a direction (-z direction) away from the optical system or the image sensor containing the optical system. It also takes into account the displacement of the object point on the original artwork within a plane perpendicular to the z direction. Furthermore, in studies of optical systems that include positions B after the object surface has shifted from its standard position A, defocusing displacement of the imaging plane IP is also not considered.

[0078] Figure 11 is a graph showing the relationship between the ratio of ray aberrations (rmsr(k)(m×p)) to rmsr(k)(m×p) and P1 / P0 in an optical system consisting of a rod lens array 10p and a transparent dielectric array 20p. In Figure 11, the white circles (plots) corresponding to each P1 / P0 represent the average value of rmsr(k)(m×p) calculated using 12 displacement patterns for a given P1 / P0. Furthermore, the error bars associated with each P1 / P0 represent the maximum and minimum values ​​of the ratio of rmsr(k)(m×p) among the 12 displacement patterns corresponding to the same P1 / P0. The magnitude of the error bars indicates the range of rmsr(k)(m×p) associated with each P1 / P0. Regarding the optical systems shown in Figures 10C and 10D, the average value of rmsr(k) (m×p) at each P1 / P0 is in the range of 0.4 to 0.45. This value is approximately 10 times that of the rmsr value (0.040) in an optical system with a 10p rod lens array but without a 20p transparent dielectric array. Therefore, it can be considered that even with displacement in the x and y directions based on the displacement of the object surface OP represented by position A (which belongs to the standard configuration) in the -z direction, the degradation of optical performance in the optical system containing the 10p rod lens array and the 20p transparent dielectric array is relatively small.

[0079] More specifically, considering the maximum value of the error line, the maximum value of the ratio rmsr(k)(m×p)(k=0.9~1.0) when P1 / P0 is 0.9 and 1 is greater than the maximum value of the ratio rmsrr(k)(m×p)(k=0.4~0.8) when P1 / P0 is below 0.8. Therefore, while optical systems including transparent dielectric arrays can generally be considered to increase depth of field, in optical systems combining rod lens arrays and transparent dielectric arrays arranged with P1 / P0 above 0.9, the displacement in the x and y directions cannot adequately compensate for the decrease in resolving power, resulting in a potential decrease in depth of field. Therefore, even when displacement occurs in the x and y directions, to achieve a greater depth of field, it is ideal for the spacing P1 of the transparent dielectric elements in the transparent dielectric array to be less than 0.8 times the spacing P0 of the rod lens array (P1 / P0≦0.8). Furthermore, it is ideal for the spacing P1 of the transparent dielectric elements in the transparent dielectric array to be more than 0.3 times the spacing P0 of the rod lens array (0.3≦P1 / P0). When P1 is 0.3×P0 or more, it is easier to prevent a reduction in light intensity or the segmentation of the lens openings, and it can prevent the NA in the sub-scanning direction (y direction) from becoming smaller and the dot diameter from becoming larger, or the generation of side peaks in the scanning direction (x direction) due to the periodic structure of the transparent dielectric array.

[0080] The optical device composed of a rod lens array 10p and a transparent dielectric array 20p was then evaluated. Rod lens arrays α, β, or γ with the optical properties shown in Table 3 were used instead of the rod lens array 10p with the optical properties shown in Table 1. Transparent dielectric arrays composed of groups a, b, and c with the properties and specifications shown in Tables 4 to 12 were also used. Table 4 shows the specifications and conditions for the optical device composed of a combination of rod lens array α and transparent dielectric array group a; Table 5 shows the specifications and conditions for the optical device composed of a combination of rod lens array α and transparent dielectric array group b; Table 6 shows the specifications and conditions for the optical device composed of a combination of rod lens array α and transparent dielectric array group c; Table 7 shows the specifications and conditions for the optical device composed of a combination of rod lens array β and transparent dielectric array group a; Table 8 shows the specifications and conditions for the optical device composed of a combination of rod lens array β and transparent dielectric array group a. Table 9 shows the specifications and conditions of an optical device composed of a combination of a rod lens array β and a transparent dielectric array c. Table 10 shows the specifications and conditions of an optical device composed of a combination of a rod lens array γ and a transparent dielectric array a. Table 11 shows the specifications and conditions of an optical device composed of a combination of a rod lens array γ and a transparent dielectric array b. Table 12 shows the specifications and conditions of an optical device composed of a combination of a rod lens array γ and a transparent dielectric array c.

[0081] First, for the rod lens arrays of α, β, and γ shown in Table 3, using Figures 10A and 10B, and then using the same method as described using these figures, we obtain the standard configuration, the distance L0 between the rod lens array and the object surface OP in the standard configuration, the dot plot on the imaging surface IP when the object surface OP and the point light source are displaced by 1 [mm] in the -z direction, and the (h)rms B value calculated from the dot plot. In (h)rms B, h is α, β, or γ, and is a suffix specifying the rod lens array shown in Table 3. The standard configuration refers to the configuration obtained by adjusting the distance between the object surface OP and the rod lens array, and the distance between the rod lens array and the imaging surface IP, so that the upright, equal-magnification image of the object point on the object surface OP is formed on the imaging surface IP at the highest resolution.

[0082] Secondly, in Table 4, we consider an optical device constructed by combining a rod lens array α and a group of transparent dielectric arrays a. In the group of transparent dielectric arrays a, six types of transparent dielectric arrays with P1 / P0 = 0.4 and H ranging from 1.920 to 38.400 mm are prepared. The rod lens array α is combined with one transparent dielectric array (H = 0.192 mm, H / (n1·L01) = 0.032) from the group of transparent dielectric arrays a to construct an optical device composed of a rod lens array and a transparent dielectric array.

[0083] Using Figures 10C and 10D, and further using the same method as described using these figures, the following are determined: the standard configuration; the distance (h)L01(k)(s) between the rod lens array and the object surface OP in the standard configuration; the dot plot on the imaging surface IP when the object surface OP and the point light source are displaced by 1 [mm] in the -z direction; and the value of (h)rmsB(k)(s) calculated from the dot plot. Then, the ratio (h)rmsB(k)(s) to the previously obtained (h)rmsB is determined, which is (h)rmsr(k)(s). The meanings of the suffixes in (h)L01(k)(s), (h)rmsB(k)(s), and (h)rmsr(k)(s) are as follows. h is α, β, or γ, and is a suffix after the bar-shaped lens array shown in Table 3; in Table 4, it is α. k is 0.4, 0.6, or 0.8, and is a suffix after P1 / P0; in Table 4, it is 0.4. s is a value in the range of 0.032 to 0.637, and is a suffix after H / (n1·L01); here, it is 0.032.

[0084] Similarly, referring to Table 4, construct an optical device consisting of a rod-shaped lens array α and another transparent dielectric array belonging to the transparent dielectric array group a, and calculate (h)rmsr(k)(s) in each optical device. h is α, k is 0.4, and s is a value in the range of 0.064~0.637, and is specified by the index after H / (n 1·L 01).

[0085] Furthermore, referring to Table 5, an optical device consisting of a rod-shaped lens array α and a transparent dielectric array belonging to the transparent dielectric array group b is constructed, and the values ​​(h)rmsr (k) (s) in each optical device are calculated. h is α, k is 0.6, and s is a value in the range of 0.095~0.764, and is a suffix after H / (n 1·L 01) for six specific levels.

[0086] Furthermore, referring to Table 6, an optical device consisting of a rod-shaped lens array α and a transparent dielectric array belonging to group c of transparent dielectric arrays is constructed, and the values ​​(h)rmsr (k) (s) in each optical device are calculated. h is α, k is 0.8, and s is a value in the range of 0.127~0.764, and is a suffix after H / (n 1·L 01) for five specific levels.

[0087] Based on the above, the RMS index is calculated. The RMS index represents the imaging state of an optical device composed of a combination of a rod lens array α and a transparent dielectric array belonging to the group of transparent dielectric arrays a~c, when a displacement in the -z direction is applied to the surface of an object.

[0088] Similarly, referring to Tables 7-9, the RMS index (h)rmsr(k)(s) is calculated. This RMS index (h)rmsr(k)(s) represents the imaging state of an optical device composed of a rod lens array β and a transparent dielectric array belonging to the group of transparent dielectric arrays a-c, when a displacement in the -z direction is applied to the object surface. h is α, β, or γ, and is a suffix indicating the rod lens array shown in Table 3, which is β in this case. k is 0.4, 0.6, and 0.8, and is a suffix indicating P1 / P0, and s is a suffix indicating H / (n1·L01).

[0089] Similarly, referring to Tables 10-12, the RMS index (h)rmsr(k)(s) is calculated. This RMS index (h)rmsr(k)(s) represents the imaging state of an optical device composed of a rod lens array γ and a transparent dielectric array belonging to the group of transparent dielectric arrays a-c, when a displacement in the -z direction is applied to the object surface. h is α, β, or γ, and is a suffix specifying the rod lens array shown in Table 3, here it is γ. k is 0.4, 0.6, or 0.8, and is a suffix specifying P1 / P0, s is a suffix specifying H / (n1·L01).

[0090] [Table 3] project symbol unit Rod lens array α β γ Number of lines 1 1 1 Central refractive index n 0 1.600 1.600 1.600 Refractive index distribution constant g / mm 0.1667 0.4000 0.8333 Lens period length PP=2π / g mm 37.70 15.71 7.54 Lens spacing P 0 mm 0.600 0.600 0.600 Rod lens diameter D 0 mm 0.600 0.600 0.600 Effective radius of rod lens r 0 mm 0.285 0.285 0.285 Number of openings NA≈n 0·g·r 0 0.0760 0.1824 0.3800 Opening angle θ 0 4.4 10.5 21.8 Lens length Z mm 20.039 8.350 4.008 Lens conjugate length TC mm 95.4 39.8 19.1 Bar lens array - inter-plane distance L 0 mm 37.7 15.7 7.5

[0091] [Table 4] project symbol unit α-a-1 α-a-2 α-a-3 α-a-4 α-a-5 α-a-6 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 1.920 3.840 7.680 15.360 23.040 38.400 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.032 0.064 0.127 0.255 0.382 0.637

[0092] [Table 5] project symbol unit α-b-1 α-b-2 α-b-3 α-b-4 α-b-5 α-b-6 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 5.760 11.520 17.280 23.040 34.560 46.080 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01 ) 0.095 0.191 0.286 0.382 0.573 0.764

[0093] [Table 6] project symbol unit α-c-1 α-c-2 α-c-3 α-c-4 α-c-5 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 7.680 15.360 23.040 30.720 46.080 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.127 0.255 0.382 0.509 0.764

[0094] [Table 7] project symbol unit β-a-1 β-a-2 β-a-3 β-a-4 β-a-5 β-a-6 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 1.920 3.840 7.680 11.520 15.360 19.200 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.076 0.153 0.306 0.458 0.611 0.764

[0095] [Table 8] project symbol unit β-b-1 β-b-2 β-b-3 β-b-4 β-b-5 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 2.880 5.760 8.641 11.521 17.281 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.115 0.229 0.344 0.458 0.688

[0096] [Table 9] project symbol unit β-c-1 β-c-2 β-c-3 β-c-4 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 3.841 7.681 11.522 19.203 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.153 0.306 0.458 0.764

[0097] [Table 10] project symbol unit γ-a-1 γ-α-2 γ-α-3 γ-α-4 γ-a-5 γ-a-6 γ-a-7 γ-a-8 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 0.768 1.152 1.536 3.072 3.839 4.607 6.143 9.215 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.064 0.095 0.127 0.255 0.318 0.382 0.509 0.764

[0098] [Table 11] project symbol unit γ-b-1 γ-b-2 γ-b-3 γ-b-4 γ-b-5 γ-b-6 γ-b-7 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 1.152 2.304 3.457 4.609 5.761 7.489 9.218 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.096 0.191 0.287 0.382 0.478 0.621 0.764

[0099] [Table 12] project symbol unit γ-c-1 γ-c-2 γ-c-3 γ-c-4 γ-c-5 γ-c-6 γ-c-7 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 1.536 2.304 3.072 4.607 6.143 7.679 9.215 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.127 0.191 0.255 0.382 0.509 0.637 0.764

[0100] Figure 12A is a graph showing the relationship between the ratio of ray aberrations RMS (h)rmsr(k)(s) (the meanings of h, k, and s are the same as above; omitted hereafter) and H / (n1·L01) in an optical system composed of a rod lens array α and transparent dielectric arrays belonging to the group of transparent dielectric arrays a~c mentioned above. Figure 12B is a graph showing the relationship between the ratio of ray aberrations RMS (h)rmsr(k)(s) and H / (n1·L01) in an optical system composed of a rod lens array β and transparent dielectric arrays belonging to the group of transparent dielectric arrays a~c mentioned above. Figure 12C is a graph showing the relationship between the ratio (h)rmsr(k)(s) of ray aberrations and H / (n1·L01) in an optical system composed of a rod lens array γ and transparent dielectric arrays belonging to the group of transparent dielectric arrays a~c mentioned above. As shown in Figure 10C, L01 is the distance in the z-direction between the rod lens array and the object surface OP when the object surface OP and the imaging surface IP are in an upright, equal-magnification system at position A. Table 13 shows the values ​​of H / (n1·L01)th when the ratio (h)rmsr(k)(s) seen from Figures 12A to 12C is 0.5 or less. Furthermore, Figure 13 shows an approximate straight line depicting the relationship between the values ​​of P1 / P0 for each optical system and the value of H / (n1·L01)th when the ratio (h)rmsr(k)(s) is less than 0.5. This correlation indicates that regardless of the type of lens, it increases approximately proportionally to P1 / P0. That is, based on the relationship between the values ​​of P1 / P0 and the value of H / (n1·L01)th when the ratio (h)rmsr(k)(s) is less than 0.5 shown in Figure 11, it can be considered that in optical devices equipped with lens arrays and transparent dielectric arrays, in order to further improve the depth of field, it is advantageous for the following condition (6) to be met. H / (n 1·L 01)>0.27(P 1 / P 0)+0.023 Equation (6)

[0101] [Table 13] P1 / P0 H / (n 1·L 01) th Rod lens α 0.4 0.127 0.6 0.191 0.8 0.243 rod lens β 0.4 0.124 0.6 0.199 0.8 0.203 rod lens γ 0.4 0.124 0.6 0.195 0.8 0.250

[0102] As described above, a composite image is formed on the imaging plane by overlapping images of adjacent single lenses, including those in a lens array. Since the imaging using single lenses exhibits light distributions such as the Cosine Fourth Law, periodic illuminance unevenness may occur in the composite image. Illuminance unevenness can be corrected by adjusting the gain of the image signal from the image sensor. However, if this illuminance unevenness is large, for example, exceeding 0.5 times the average illuminance, a practical problem arises: there is a possibility of a significant decrease in the contrast of the readout image of the subject, leading to defects such as stripes.

[0103] Therefore, an optical simulation was performed in an optical device or system equipped with a rod lens array and a transparent dielectric array to determine the irradiance on the imaging plane. The irradiance calculation used Trace Pro Standard 7, an illumination resolution software from Lambda Research Corporation, USA. The optical systems shown in Figures 10C and 10D were used as conditions for the optical simulation. Rod lens arrays α, β, and γ as shown in Table 3 were used, and transparent dielectric arrays a', b', and c' as shown in Tables 14-22 were used. These were combined to form the optical system. Furthermore, in the optical simulation, the configuration of the object plane, rod lens array, transparent dielectric array, and imaging plane was defined to achieve the highest image resolution as an upright, equal-magnification system. The position of the object plane at this time is designated as A. Position A is the standard configuration.

[0104] [Table 14] project symbol unit α-a'-1 α-a'-2 α-a'-3 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P 1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 23.040 30.720 46.080 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.382 0.509 0.764

[0105] [Table 15] project symbol unit α-b'-1 α-b'-2 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 34.560 46.080 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.573 0.764

[0106] [Table 16] project symbol unit α-c'-1 α-c'-2 α-c'-3 Combined rod lens array Rod lens array α Spacing of transparent dielectrics P1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 23.040 38.400 46.080 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.382 0.637 0.764

[0107] [Table 17] project symbol unit β-a'-1 β-a'-2 β-a'-3 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 11.520 15.360 19.200 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.458 0.611 0.764

[0108] [Table 18] project symbol unit β-b'-1 β-b'-2 β-b'-3 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 11.520 17.280 20.160 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.458 0.688 0.802

[0109] [Table 19] project symbol unit β-c'-1 β-c'-2 β-c'-3 β-c'-4 Combined rod lens array Rod lens array β Spacing of transparent dielectrics P 1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 11.520 15.360 19.200 21.504 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.458 0.611 0.764 0.856

[0110] [Table 20] project symbol unit γ-a'-1 γ-a'-2 γ-a'-3 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P 1 mm 0.4×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.240 Effective radius of transparent dielectric r 1 mm 0.114 Length of transparent dielectric H mm 3.840 5.760 7.680 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.318 0.477 0.637

[0111] [Table 21] project symbol unit γ-b'-1 γ-b'-2 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P 1 mm 0.6×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.360 Effective radius of transparent dielectric r 1 mm 0.171 Length of transparent dielectric H mm 5.760 8.640 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.477 0.716

[0112] [Table 22] project symbol unit γ-c'-1 γ-c'-2 γ-c'-3 Combined rod lens array Rod lens array γ Spacing of transparent dielectrics P 1 mm 0.8×P 0 Number of rows of transparent dielectric array m 2 Refractive index of transparent dielectrics n 1 mm 1.600 Diameter of transparent dielectric D 1 mm 0.480 Effective radius of transparent dielectric r 1 mm 0.228 Length of transparent dielectric H mm 6.144 7.680 9.216 The value obtained by dividing the ratio of the length of the transparent dielectric array to L01 by the refractive index. H / (n 1·L 01) 0.509 0.637 0.764

[0113] In the optical simulation, a surface light source emitting uniform light from the object surface at position A is configured, and the illuminance non-uniformity on the imaging surface of each optical system is determined. The surface light source used for the optical simulation is set to emit light with a wavelength of 570 nm using a Lambert distribution, and 10 million ray tracings are performed. Due to the periodicity of the rod lens array and the transparent dielectric array, the irradiance also tends to have a periodicity in the main scanning direction (x-direction). In applications such as image sensors, the irradiance detected by the light-receiving element array is preferably fixed in the main scanning direction. When there is a deviation or periodic variation in irradiance in the main scanning direction, the image sensor acquires an image with deviations or variations in density or brightness, which is not suitable. Therefore, simulations are performed in each optical system to determine the irradiance distribution in the main scanning direction and evaluate the irradiance non-uniformity.

[0114] Figure 14 shows the irradiance non-uniformity ΔI calculated within the range of x=0 [mm] to x=100 [mm] for each of the optical systems composed of three types of rod lens arrays (α, β, and γ) combined with the transparent dielectric arrays of group a' (P1=0.4×P0), group b' (P1=0.6×P0), and group c' (P1=0.8×P0) shown in Table 4, after determining the standard configuration. In Figure 14, the horizontal axis is H / (n1·L01D), and the vertical axis is the irradiance non-uniformity ΔI. The irradiance non-uniformity ΔI is calculated by determining the maximum irradiance Imax and the minimum irradiance Imin within the above range in the main scanning direction (x direction) and using the following formula (7). ΔI=2×(I max-I min) / (I max+I min) Formula (7)

[0115] Figure 14 illustrates the relationship between irradiance unevenness ΔI and the parameter H / (n1·L01). As shown in Figure 14, the ideal value of irradiance unevenness ΔI is small. However, regarding the correlation between irradiance unevenness ΔI and H / (n1·L01), ΔI exhibits a band-like width regardless of the lens type, and tends to increase as H / (n1·L01) increases. If H / (n1·L01) is large, the effect of limiting the opening of the rod lens is enhanced, and the angle of light rays radiating from the transparent dielectric array toward the imaging plane also decreases, suggesting insufficient overlap of the irradiance distributions of the transparent dielectric elements in the transparent dielectric array.

[0116] Furthermore, based on the correlation shown in Figure 14, if H / (n1·L01) is greater than 0.6, it can be inferred that the irradiance unevenness ΔI in an optical system combining a rod lens array and a transparent dielectric array will exceed 0.5. Based on the results of this study, it can be considered that to reduce irradiance unevenness in optical devices or systems equipped with rod lens arrays and transparent dielectric arrays, it is ideal to satisfy the condition H / (n1·L01) ≤ 0.6 or less. Furthermore, when the value of H / (n1·L01) is 0.46 or less, the irradiance unevenness ΔI becomes 0.3 or less, which is even more ideal.

[0117] In the optical device 1a, the irradiance non-uniformity ΔI is, for example, 0.5 or less. Ideally, the irradiance non-uniformity ΔI is 0.4 or less, and more ideally, 0.3 or less.

[0118] In the optical device 1a, an air or vacuum layer may also exist between the lens array 10 and the transparent dielectric array 20. A transparent adhesive, or a transparent adhesive layer or bonding layer such as optical clear adhesive (OCA) may also be present between the lens array 10 and the transparent dielectric array 20. When resin is present between the lens array 10 and the transparent dielectric array 20, it is ideal that the refractive index of the resin is close to the refractive index of the lens 11 of the lens array 10 and the refractive index of the transparent dielectric 21 of the transparent dielectric array 20. This is because it reduces light loss caused by interface reflection.

[0119] The use of optical device 1a is not limited to a specific purpose. For example, optical device 1a can be used in optical products or optical machines such as image sensors, scanners, printers, line sensor cameras, photocopiers, fax machines, multifunction printers (such as devices that include the functions of photocopiers and printers), appearance inspection devices, and endoscopes.

[0120] Figure 15A illustrates an example of an image sensor. As shown in Figure 15A, the image sensor 3a includes an optical device 1a. The image sensor 3a is, for example, a CIS (Computer Integrated System). In the image sensor 3a, the optical axes of the lenses 11 of the lens array 10 of the optical device 1a and the central axes of the transparent dielectrics 21 of the transparent dielectric array 20 extend in the z-axis direction. The plurality of lenses 11 in the lens array 10 are arranged along the x-axis direction (main scanning direction). Furthermore, the dimension of the image sensor 3a or the components included in the image sensor 3a in the x-axis direction may also be greater than its dimension in the y-axis direction, which is orthogonal to the x-axis and z-axis.

[0121] As shown in Figure 15A, the image sensor 3a includes a housing 30, a linear illumination device 31, a document stage 32, a light-receiving element array 33, and a circuit board 34. The optical device 1a, the linear illumination device 31, the light-receiving element array 33, and the circuit board 34 are disposed inside the housing 30. The document stage 32 is made of glass and is arranged to cover the opening of the housing 30. The linear illumination device 31 emits approximately uniform illumination light along the x-axis to illuminate the object S, such as the document. A portion of the illumination light reflected from the surface of the object S passes sequentially through the lens array 10 and the transparent dielectric array 20, and then reaches the light-receiving elements such as the PD or avalanche photodiode (APD) of the light-receiving element array 33, and the information of the surface of the object S is imaged on the light-receiving surface of the light-receiving element. In the image sensor 3a, an optical device 1a is manufactured such that the surface of the object corresponds to the object surface OP and the light-receiving surface of the light-receiving element corresponds to the image plane IP. The optical device 1a is arranged in an upright, equal-magnification system. The image sensor 3a acquires two-dimensional information of the object S by scanning along the y-axis.

[0122] In the image sensor 3a, the transparent dielectric array 20 is disposed on the light-emitting surface side of the lens array 10. The lens array 10 and the transparent dielectric array 20 can be separately assembled inside the housing 30, or they can be pre-integrated into each other by means of bonding before being assembled into the housing 30. Therefore, the optical device 1a can be configured to either assemble the lens array 10 and the transparent dielectric array 20 separately, or it can be configured to integrate the lens array 10 and the transparent dielectric array 20 into one unit.

[0123] Figure 15B shows another example of an image sensor, and Figure 15C shows yet another example of an image sensor. The image sensor 3b shown in Figure 15B and the image sensor 3c shown in Figure 15C are constructed in the same manner as image sensor 3a, except for the parts specifically described. The same symbols are used to label the constituent elements of image sensors 3b and 3c that are identical or corresponding to those of image sensor 3a, and detailed descriptions are omitted. Descriptions relating to image sensor 3a also apply to image sensors 3b and 3c, provided they are not technically contradictory.

[0124] As shown in Figure 15B, in the image sensor 3b, the transparent dielectric array 20 is disposed on the light incident surface side of the lens array 10.

[0125] As shown in Figure 15C, in the image sensor 3c, the transparent dielectric array 20 is disposed on the light emitting surface side of the lens array 10, and also on the light incident surface side.

[0126] 1a: Optical device 3a, 3b, 3c: Image sensors 10: Lens Array 11: Lens 20: Transparent Dielectric Array 21: Transparent dielectric

Claims

1. An optical device comprising: a lens array including a plurality of lenses arranged such that the optical axes of the plurality of lenses are substantially parallel to each other; and a transparent dielectric array including a plurality of transparent dielectrics arranged such that the central axes of the plurality of transparent dielectrics are substantially parallel to each other; wherein the lens array and the transparent dielectric array are arranged such that the optical axes and the central axes are substantially parallel, and the end faces of the lens array and the end faces of the transparent dielectric array face each other, wherein the arrangement spacing P0 of the lens array and the arrangement spacing P1 of the transparent dielectric array satisfy a first condition of 0.3×P0≦P1≦0.8×P0.

2. The optical apparatus as claimed in claim 1, wherein, The aforementioned lens is a rod-shaped lens with a refractive index distribution in the radial direction.

3. The optical apparatus as claimed in claim 1, wherein, The refractive index n1 of the above transparent dielectric array and the length H [mm] of the above transparent dielectric array satisfy the second condition H / (n1·L01)>0.27×(P1 / P0)+0.

023. In the above second condition, L01 is the distance [mm] between the above lens array and the above object surface when the upright isopleth image of the object surface is imaged at the highest resolution.

4. The optical apparatus of any one of claims 1 to 3, wherein, The irradiance unevenness ΔI is less than 0.

5. The aforementioned irradiance unevenness ΔI has the relationship ΔI = 2 × (Imax - Imin) / (Imax + Imin). In the above relationship, Imax is the maximum value of the irradiance in the main scanning direction of the aforementioned optical device, and Imin is the minimum value of the irradiance in the main scanning direction of the aforementioned optical device.

5. The optical apparatus of any one of claims 1 to 3, wherein, The refractive index n1 of the above transparent dielectric array and the length H [mm] of the above transparent dielectric array satisfy the third condition H / (n1·L01)≦0.

6. In the above third condition, L01 is the distance [mm] between the above lens array and the above object surface when the upright isopleth image of the object surface is imaged at the highest resolution.

6. The optical apparatus as claimed in claim 2, wherein, The optical axis of the lenses in the aforementioned lens array is approximately aligned with the central axis of the transparent dielectric in the aforementioned transparent dielectric array, satisfying the fourth condition tanθ0·H / n1>P1 / 2. n1 is the refractive index of the transparent dielectric, H is the length [mm] of the transparent dielectric in the direction parallel to the central axis, P1 is the distance [mm] between the central axes of adjacent transparent dielectrics in the aforementioned transparent dielectric array, and θ0 is the opening angle of the rod lens. When the refractive index distribution of the rod lens is expressed as n(r)2=n02·{1-(g·r)2}, θ0 has the relationship sinθ0=n0·g·r0, where r is the radial distance from the optical axis of the rod lens [mm], n(r) is the refractive index of the rod lens at a distance r, n0 is the refractive index at the optical axis of the rod lens, and g is the refractive index distribution constant of the rod lens. r0 represents the effective radius [mm] of the aforementioned rod-shaped lens.

7. An image sensor having the optical device of any one of claims 1 to 6.

8. A method for manufacturing an optical device, which is the method for manufacturing the optical device of claim 1, and includes the following steps: combining the transparent dielectric array and the lens array in such a manner that the central axis of the transparent dielectric is substantially parallel to the optical axis of the lens, and the end face of the transparent dielectric array is substantially parallel to the end face of the lens array.

9. A method for manufacturing an optical device as claimed in claim 8, comprising the steps of: arranging the plurality of rod-shaped glass pieces in a manner in which their central axes are substantially parallel to each other, obtained by a pull-down method; and forming a face roughly perpendicular to the central axis of the glass pieces to obtain the transparent dielectric.

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