Fresnel lens

A Fresnel lens comprises a first surface, and a second surface being the reverse side surface of the first surface and having a plurality of lens surfaces. Each lens surface is configured from a part of a side surface of an elliptical cone, which has an apex located on the second surface side and a bottom surface located on the first surface side. Here, in the Fresnel lens, any normal line intersecting with the lens surface configured from the part of the side surface of the elliptical cone among normal lines of respective points on the first surface is non-parallel to a central axis of the elliptical cone corresponding to the lens surface with which the any normal line intersects.

TECHNICAL FIELD

The invention relates to a Fresnel lens.

BACKGROUND ART

In a lens with a lens surface71shown inFIG. 10, in order to collect a light beam Lb parallel to an optical axis Opaof the lens at a focal point F with a constant light path length, it is necessary to meet a condition of “RF=HF”, where “R” denotes a refraction point in the lens surface71, “H” denotes a point at the intersection the optical axis Opawith a perpendicular extending downward from the refraction point R (that is, a foot of a perpendicular extending toward the optical axis Opafrom the refraction point R), “RF” denotes a light path length between the refraction point R and the focal point F, and “HF” denotes a light path length between the intersection point H and the focal point F. In order to meet the condition of “RF=HF”, it is known that a hyperboloid or an ellipsoid is necessarily adopted as the lens surface71. Here, in a case where the lens surface71is a hyperboloid, when a refraction index of a lens material is denoted by “n” and a back focus of the lens is denoted by “f”, the lens surface71is represented by the following Formula (1).

Here, Formula (1) is obtained when defining a rectangular coordinate system, in which the focal point F of the lens is employed as an origin, a z-axis is specified on the optical axis Opa, a x-axis and a y-axis orthogonal to each other on any place surface orthogonal to the optical axis Opaare specified, and defining a coordinate of an arbitrary point on the lens surface71as (x, y, z). Then, a, b and c in Formula (1) are provided by the following Formula (2), Formula (3) and Formula (4), respectively.

Further, as shown inFIG. 11, there has been known a condenser lens101, in which a rotation axis C of a hyperboloid120that is an emission surface (a second surface) is oblique to a normal line N of a plane surface110that is an incident surface (a first surface) so that an angle θ is formed by the rotation axis C and the normal line N (Japanese Examined Patent Publication No. 7-36041). In the condenser lens101having the configuration shown inFIG. 11, when a light beam is incident upon the condenser lens101with an angle δ formed by the light beam and the rotation axis C, the light beam becomes parallel to the rotation axis C of the hyperboloid120, inside the condenser lens101, and then is aplanatically collected on the focal point. F. When a refraction index of the condenser lens101is denoted by “n”, the angle δ meets Snell's law, that is, sin(θ+δ)=n*sin θ. In this case, the hyperboloid120is represented by the abovementioned Formula (1), when defining a rectangular coordinate system, in which the focal point F is employed as an origin, a z-axis is specified on the rotation axis C of hyperboloid120, a x-axis and a y-axis orthogonal to each other on any place surface orthogonal to the rotation axis C are specified.

Further, in the abovementioned Japanese Examined Patent Publication, as shown inFIGS. 12A and 12B, there has been proposed the condenser lens101, which is a Fresnel lens, and in which the rotation axis C shared by hyperboloids121,122and123of a second surface is oblique to the plane surface110of a first surface in order to suppress occurrence of an off-axis aberration. In this case, the respective hyperboloids121,122and123configure lens surfaces.

The above-mentioned Japanese Examined Patent Publication describes that in the Fresnel lens101inFIGS. 12A and 12Ban angle can be formed between a parallel light beam aplanatically collected on a focal point and a normal line N of the plane surface110according to an angle formed by the rotation axis C shared by the hyperboloids121,122and123and the plane surface110. Therefore, in the Fresnel lens101inFIGS. 12A and 12B, the occurrence of the off-axis aberration can be suppressed, and light beams from a direction oblique to the normal line N of the plane surface110can be effectively collected.

However, in the Fresnel lens101configured such that the rotation axis C of the hyperboloids121,122and123configuring the emission surface is oblique to the normal line N of the plane surface110that is the incident surface, the hyperboloids121,122and123are not rotationally symmetric with respect to the normal line N of the plane surface110. Therefore, the Fresnel lens101or a metal mold for the Fresnel lens101is difficult to be produced by rotary forming with a lathe or the like.

So, when the Fresnel lens101or the metal mold for the Fresnel lens101is produced, it is necessary to use a multiaxis control processing machine and form the hyperboloids121,122and123or respective curved surfaces by cutting at minute pitches while only a blade edge of a sharp cutting tool (tool)130with a nose radius (also referred to as a corner radius) of a few micro-meters is brought into point contact with a workpiece140, as shown inFIG. 13. The workpiece140is a base material for directly forming the Fresnel lens101, or a base material for forming the metal mold. Therefore, the processing time for producing the aforementioned Fresnel lens101or metal mold for the Fresnel lens101is increased, and then the cost of the Fresnel lens101is increased.

On the other hand, in a case where the cross-sectional shape of each lens surface in the cross-sectional shape including the normal line of the plane surface that is the incident surface of the Fresnel lens is linear, the lens surfaces or the curved surfaces corresponding to the lens surfaces can be formed by cutting while the cutting tool130is inclined with respect to the workpiece140so as to bring a side surface of a blade into line contact with the workpiece140, as shown inFIG. 14, thus enabling significant reduction of the processing time. Here, in a Fresnel lens in which the shape of each lens surface in an emission surface is rotationally symmetric by employing a normal line of the incident surface as a rotation axis, it is known that each lens surface is approximated by a side surface of a frustum of cone, thereby enabling the cross-sectional shape of each lens surface to become linear (U.S. Pat. No. 4,787,722).

In the Fresnel lens101disclosed in the above-mentioned Japanese Examined Patent Publication and the Fresnel lens disclosed in the above-mentioned US patent, an intended light beam is infrared light, and these two documents disclose that polyethylene is used as a lens material.

Incidentally, in the Fresnel lens in which the shape of each lens surface in an emission surface is rotationally symmetric by employing the normal line of the incident surface as the rotation axis, in the lens surface being approximated by the side surface of the frustum of cone, an off-axis aberration occurs.

DISCLOSURE OF THE INVENTION

An object of the present invention is to provide a Fresnel lens, which is capable of suppressing occurrence of an off-axis aberration in a case of utilizing incident light obliquely incident upon a first surface from the outside world, and is capable of reducing the cost.

A Fresnel lens of the present invention comprises a first surface, and a second surface being the reverse side surface of the first surface and having a plurality of lens surfaces, wherein at least one of the plurality of lens surfaces is configured from a part of a side surface of an elliptical cone, and wherein any normal line intersecting with the lens surface configured from the part of the side surface of the elliptical cone among normal lines of respective points on the first surface is non-parallel to a central axis of the elliptical cone corresponding to the lens surface with which the any normal line intersects. In this configuration, the Fresnel lens can suppress occurrence of an off-axis aberration in a case of utilizing incident light obliquely incident upon the first surface from the outside world, and can reduce the cost.

In this Fresnel lens, preferably, at least two of the plurality of lens surfaces are configured from parts of side surfaces of elliptical cones having the different central axes respectively, and wherein as a lens surface among the at least two of the plurality of lens surfaces is located further outside, an angle formed by the normal line and the central axis of the elliptical cone corresponding to the lens surface becomes larger.

In this Fresnel lens, preferably, a lens surface located on a center among the plurality of lens surfaces is configured from a part of an aspheric surface with continuously changing curvature, and wherein any normal line intersecting with the lens surface that is located on the center and is configured from the part of the aspheric surface among the normal lines of the respective points on the first surface is non-parallel to an axis of symmetry of the aspheric surface corresponding to the lens surface located on the center with which the any normal line intersects.

In this Fresnel lens, preferably, the aspheric surface is a hyperboloid.

In this Fresnel lens, preferably, a lens material is polyethylene, and the first surface is a curved surface that is convex toward a side opposite to the second surface.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, a Fresnel lens according to the present embodiment will be described with reference toFIGS. 1A,1B and2.

A Fresnel lens1according to the present embodiment includes a first surface10, that is a plane surface, and a second surface20, that is the reverse side surface of the first surface10and has a plurality of lens surfaces21(three in an example shown in these figures). The Fresnel lens1has a central lens portion1a, and a plurality of orbicular zone-shaped lens portions1b(two in an example shown in these figures) surrounding the central lens portion1a. The number of the orbicular zone-shaped lens portions1bis not particularly limited, and three or more orbicular zone-shaped lens portions may be employed. The Fresnel lens1is a condenser lens in which the second surface20, being the reverse side surface of the first surface10, has the plurality of lens surfaces21, and a lens surface21of the central lens portion1ais a convex surface. In short, the Fresnel lens1is a condenser lens capable of reducing a thickness as compared with a thickness of a convex lens.

Each orbicular zone-shaped lens portion1bhas a mountain portion11bon the second surface20side. Each mountain portion11bhas a rising surface (non-lens surface)22configured from a side surface on the central lens portion1a, and the lens surface21configured from a side surface on a side opposite to the central lens portion1aside. Therefore, the second surface20of the Fresnel lens1has the lens surfaces21of the respective orbicular zone-shaped lens portions1b. Further, the second surface20of the Fresnel lens1also has the lens surface21of the central lens portion1a. InFIG. 2B, when the first surface10is an incident surface and the second surface20is an emission surface, a traveling path of a light beam is represented by a thin solid line with an arrow. In the Fresnel lens1of the present embodiment, it is understood fromFIG. 1Bthat a light beam incident, upon the first surface10, from a direction oblique to a normal line of the first surface10of the Fresnel lens1is collected on the focal point F in the second surface20side of the Fresnel lens1.

Incidentally, in the Fresnel lens1, each lens surface21is configured from a part of a side surface of an elliptical cone30. Then, any normal line intersecting with each lens surface21configured from a part of a side surface of an elliptical cone30, among normal lines of respective points on the first surface10, is non-parallel (that is, inclined) to a central axis of the elliptical cone30corresponding to the lens surface21with which the any normal line intersects. Here, each elliptical cone30has an apex P located on the second surface20side and a bottom surface (not shown) located on the first surface10side. In the Fresnel lens1of the present embodiment, the first surface10is the plane surface, and hence the central axes of the elliptical cones30are oblique to the normal lines of the respective points on the first surface10. In a case where such a direction as to connect each point on the first surface10and an intersection at which the normal line of the point interests with the lens surface21is specified as a lens thickness direction, when the first surface10is the plane surface, a direction along the normal line of each point on the first surface10is the lens thickness direction. As a result, in each ofFIGS. 1A and 1B, a vertical direction is the lens thickness direction. Accordingly, each lens surface21of the Fresnel lens1is configured from a part of a side surface of an elliptical cone30that has an apex P located on the second surface20side, a bottom surface located on the first surface10side, and a central axis oblique to the lens thickness direction. In a cross-sectional shape including one virtual straight line along the lens thickness direction (in this case, a cross-sectional shape including the normal lines of the first surface10), an angle formed by a surface parallel to the first surface10and each lens surface21is an obtuse angle, and an angle formed by the surface parallel to the first surface10and each rising surface22is a substantially right angle.

In order to solve the problem, that is, to provide a Fresnel lens which can suppress occurrence of off-axis aberration in a case of utilizing incident light obliquely incident upon the first surface10from the outside world and reduce the cost, the present inventors have conceived as follows: That is, as to a standard structure in which the second surface20is configured from the respective parts of a plurality of the hyperboloids (one sheet of hyperboloid of two sheets)25having principal axes oblique to the normal lines of the first surface10, the present inventors have conceived that, in a cross-sectional shape including one virtual straight line along the lens thickness direction, the aforementioned respective parts of the plurality of hyperboloids25are approximated by straight lines.

In each hyperboloid25, collection of tangents of respective points on a cross-section orthogonal to the rotation axis of the hyperboloid25becomes a circular cone. Therefore, in a Fresnel lens configured such that each lens surface of the emission surface is rotationally symmetric employing the normal line of the incident surface as a rotation axis, each lens surface can be approximated by the part of the side surface of the circular cone.

In a rectangular coordinate system, in which a center of any plane surface is employed as an origin, an x-axis and a y-axis orthogonal to each other on the any plane surface are specified, and a z-axis orthogonal to the any plane surface is specified, assuming that (x, y, z) denote coordinates of any points of the circular cone, and b and c denote coefficients, the equation of the circular cone is represented by the following standard form, where the coefficient c is a constant irrelevant to z.

In a frustum of cone configured by cutting this circular cone by two surfaces parallel to an xy plane surface, the aforementioned parts of the respective hyperboloids25in the above-mentioned standard structure cannot be approximated.

On the other hand, in each hyperboloid25, collection of tangents40of respective points on a cross-section not perpendicular to the rotation axis of the hyperboloid25becomes an elliptical cone. Here, the present inventors have focused on the fact that in the hyperboloids25having the above-mentioned structure can be approximated by the elliptical cones30coming in contact with the hyperboloids25on the respective points on the lines of intersection of the plane surfaces oblique to the principal axes of the hyperboloids25and the hyperboloids25. Then, the present inventors have conceived that the lens surfaces21are configured from the parts of the side surfaces of the elliptical cones30that have apexes P located on the second surface20side, bottom surfaces (not shown) located on the first surface10side, and central axes (not shown) oblique to the lens thickness direction.

In the Fresnel lens1shown inFIGS. 1A and 1B, when focusing on the lens surfaces21configured from the parts of the respective elliptical cones30, since the elliptical cones30have the hyperboloids25inscribed in the elliptical cones30, and inclinations of both of the tangents of the respective points on the lines of intersection of the elliptical cones30and the hyperboloids25coincide with each other, light beams passing through the respective points on the lines of intersection of the elliptical cones30and the hyperboloids25are collected on a single point on the rotation axis of the hyperboloids25. In the Fresnel lens1of the present embodiment, at least one of the plurality of lens surfaces21is configured so as to have a shape in which a part of the elliptical cone30is cut off so as to include the line of intersection of the elliptical cone30and the hyperboloid25, thereby being capable of suppressing occurrence of off-axis aberrations in a case of utilizing incident light obliquely incident upon the first surface10from the outside world and reducing the cost. Here, in the Fresnel lens1, the lower a height of the mountain portion11bis, the more easily light beams passing through this mountain portion11bare collected on a single point, and hence the line of intersection of the elliptical cone30and the hyperboloid25inscribed in the elliptical cone30is preferably intersect with the mountain portion11b.

The height of each mountain portion11band a space between the apexes of the adjacent mountain portions11bneed to be set at a value which is more than or equal to a wavelength of an electromagnetic wave that is an object to be collected in the Fresnel lens1. For example, in a case where infrared light with a wavelength of 10 μm is an object to be collected, the height of each mountain portion11band the space between the apexes of the adjacent mountain portions11bneed to be 10 μm or more. On the other hand, in the Fresnel lens1, it is conceivable to cause a problem that the larger the height of each mountain portion11band the space between the apexes of the adjacent mountain portions11bare, the larger the off-axis aberrations are, and a problem that lens patterns can be visually recognized from the first surface10side. Therefore, in a case where an allowable value (target value) of an off-axis aberration is, for example, less than or equal to 0.6*0.6 mm which is the size of the infrared photoelectric conversion element arranged on the focal point F, the Fresnel lens1is preferably configured such that a maximum height of the mountain portion11bis 150 μm or less. In addition, in a case where it is required that the lens patterns on the second surface20side is unable to be visually recognized when unintentionally viewed from a place separated from the first surface10by 30 cm, the Fresnel lens1is preferably configured such that the space between the adjacent mountain portions11bis 0.3 mm or less. On the other hand, the smaller the space between the adjacent mountain portions11bis, the larger the number of the mountain portions11bis, and hence the space between the adjacent mountain portions11bis preferably set in a range of, for example, 0.1 to 0.3 mm.

In the Fresnel lens1according to the present embodiment, the lines of intersection of the elliptical cones30and the hyperboloids25inscribed in the elliptical cones30exist on a plane surface15which is orthogonal to the lens thickness direction (that is, parallel to the first surface10configured from the plane surface), and which has a height from a valley of the mountain portion11bof each orbicular zone-shaped lens portion1bthat is a half of the maximum height of the mountain portion11b. Therefore, in the Fresnel lens1according to the present embodiment, light beams passing on the intersections of the lens surfaces21and the plane surface15are collected on the focal point F, as shown inFIG. 1B.

In a rectangular coordinate system, in which a center of any plane surface is employed as an origin, an x-axis and a y-axis orthogonal to each other on the any plane surface are specified, and a z-axis orthogonal to the any plane surface is specified, assuming that (x, y, z) denote coordinates of any points of the elliptical cone, and a, b and c denote coefficients, the general equation of the elliptical cone is represented by the standard form of following Formula (6), where the coefficient c is a constant irrelevant to z.

Hereinafter, for convenience of description, the Fresnel lens1inFIGS. 1A and 1Bwill be described by denoting the three elliptical cones30with different reference numerals respectively. The elliptical cone corresponding to the central lens surface21is represented as an elliptical cone300, the elliptical cone corresponding to the lens surface21that is a first orbicular zone closest to the central lens surface21is represented as an elliptical cone301, and the elliptical cone corresponding to the lens surface21that is a second orbicular zone second closest to the central lens surface21is represented as an elliptical cone302. In short, among the elliptical cones30except the elliptical cone30corresponding to the central lens surface21, the elliptical cone corresponding to the lens surface21that is an n-th (n>=1) orbicular zone counting from a side closer to the central lens surface21is represented as an elliptical cone30n. Here, the respective apexes P of the elliptical cones300,301and302are represented as apexes P0, P1and P2, and the respective central axes of the elliptical cones300,301and302are denoted by CA0, CA1, and CA2. In short, the apex of the elliptical cone30ncorresponding to the lens surface21that is the n-th orbicular zone is denoted by Pn, and the central axis of the elliptical cone30nis denoted by CAn. As to the elliptical cones300,301and302, rectangular coordinate systems, in which the apexes P0, P1and P2are employed as origins, the central axes CA0, CA1, and CA2are employed as z-axes, x-axes are specified along major axis directions of ellipses in cross-section perpendicular to the z-axis, and y-axes are specified along minor axis directions, are defined. Then, a Formula of each of the elliptical cones300,301and302can be represented by the above-mentioned Formula (6) in each rectangular coordinate system. Further, inFIGS. 1A and 1B, the hyperboloids25inscribed in the elliptical cones300,301and302are represented by hyperboloid250,251and252, respectively.

As an example of the Fresnel lens1, a lens including six lens surfaces21each configured from a part of a side surface of an elliptical cone30is exemplified. In this Fresnel lens1, among the six elliptical cones30, the elliptical cone corresponding to the central lens surface21is represented as an elliptical cone300, and the elliptical cones corresponding to the lens surfaces21that are a first orbicular zone to a fifth orbicular zone are represented as elliptical cones301to305, respectively. In the Fresnel lens1of this example, in a case where a thickness t of a base portion configured from a portion other than each mountain portion11bis 0.5 mm, a height (lens step) Δt of the mountain portion11bon a point closest to a focal point F in each orbicular zone-shaped lens portion1bis 0.05 mm, and polyethylene with a refractive index of 1.53 is employed as a lens material, values of coefficients a, b and c in Formula (6) are shown in the following Table 1. However, the coefficients a, b and c shown in Table 1 are values obtained under a precondition that a distance from an image surface I parallel to the first surface10of the Fresnel lens1to the first surface10is 5.5 mm, and light beams incident at an incident angle of 45 degrees are collected on the focal point F.

The central axes of the lens surfaces21of the second surface20with which the normal lines intersect are inclined with respect to the normal lines of the respective points on the first surface10. Hereinafter, for convenience of description, in the Fresnel lens1inFIGS. 1A and 1B, the intersections of the respective normal lines of points A1, A2, B1, B2, C1and C2on the first surface10and the second surface20are referred to as A11, A22, B11, B22, C11and C22, and the respective normal line of the points A1, A2, B1, B2, C1and C2on the first surface10are referred to as A1-A11, A2-A22, B1-B11, B2-B22, C1-C11and C2-C22. Here, θ0denotes an angle formed by each of the normal lines A1-A11and A2-A22intersecting with the central lens surface21, and the central axis CA0of the elliptical cone300, θ1denotes an angle formed by each of the normal lines B1-B11and B2-B22intersecting with the lens surface21which is the first orbicular zone closest to the central lens surface21, and the central axis CA1of the elliptical cone301, and θ2denotes an angle formed by each of the normal lines C1-C11and C2-C22intersecting with the lens surface21which is the second orbicular zone second closest to the central lens surface21, and the central axis CA2of the elliptical cone302. Similarly, assuming that θ3denotes an angle formed by the normal line intersecting with the lens surface21which is the third orbicular zone, and the central axis CA3of the elliptical cone303, θ4denotes an angle formed by the normal line intersecting with the lens surface21which is the fourth orbicular zone, and the central axis CA4of the elliptical cone304, and θ5denotes an angle formed by the normal line intersecting with the lens surface21, which is the fourth orbicular zone, and the central axis CA5of the elliptical cone305, values of θ0to θ5are shown in the following Table 2.

It is understood from Table 2 that in the Fresnel lens1, the angle, which is formed by a normal line of each point on the first surface10and a central axis of a lens surface21of the second surface20with which the normal line intersects, becomes larger as a orbicular zone-shaped lens portion1bis located further outside.

FIG. 3shows a spot diagram on the focal point F of this Fresnel lens1.FIG. 3shows a spot diagram in the range of 2*2 mm employing the focal point F as a center. The size of a focal spot should be less than or equal to the size of the photoelectric conversion element arranged so as to correspond to the focal point F of the Fresnel lens1(here, 0.6*0.6 mm or less).

In the Fresnel lens1according to the present embodiment, in the cross-sectional shape including one virtual straight line along the lens thickness direction (in this case, a cross-sectional shape including the normal lines of the first surface10), the respective lens surfaces21are straight lines, and hence it is possible to form the lens surfaces21or curved surfaces according to the lens surfaces21by cutting while a cutting tool130is inclined with respect to a workpiece140(base material for forming directly the Fresnel lens1, or base material for forming a metal mold) so as to bring a side surface of a blade into line contact with the workpiece140, as shown inFIG. 14. Therefore, in the Fresnel lens1according to the present embodiment, when the Fresnel lens1or the metal mold for the Fresnel lens1is produced, the processing time for producing the workpiece140by the cutting tool130can be reduced. The lens material of the Fresnel lens1may be selected as someone thinks fit, according to wavelengths of light beams or the like. For example, the lens material may be selected from plastic (e.g., polyethylene, acrylic resin or the like), glass, silicon, germanium or the like as someone thinks fit. Further, for example, when the wavelengths of light beams are within the infrared wavelength region, the lens material should be selected from polyethylene, silicon, germanium or the like. When the wavelengths of light beams are within the visible-light wavelength region, the lens material should be selected from acrylic resin, glass, or the like. The material of the metal mold is not particularly limited, and phosphor bronze or the like can be employed, for example. When the Fresnel lens1is formed using the metal mold, the injection molding method, the compression molding method, or the like may be employed, for example.

As explained above, in the Fresnel lens1according to the present embodiment, the first surface10is a plane surface, and the second surface20has the plurality of lens surfaces21, and then each lens surface21is configured from a part of a side surface of an elliptical cone30, which has an apex P located on the second surface20side, a bottom surface located on the first surface10side and a central axis oblique to the lens thickness direction. Here, in the Fresnel lens1according to the present embodiment, any normal line intersecting with each lens surface21configured from a part of a side surface of an elliptical cone30, among normal lines of respective points on the first surface10, is non-parallel to a central axis of the elliptical cone30corresponding to the lens surface21with which the any normal line intersects. Thus, the Fresnel lens1according to the present embodiment can suppress occurrence of off-axis aberrations in a case of utilizing incident light obliquely incident upon the first surface10from the outside world and reduce the cost. In addition, at least one of a plurality of lens surfaces21is configured from a part of a side surface of an elliptical cone30, and thereby the Fresnel lens1can suppress occurrence of off-axis aberrations in a case of utilizing incident light obliquely incident upon the first surface10from the outside world and reduce the cost.

As applications for the above-mentioned Fresnel lens1, for example, a sensor device is shown inFIGS. 4A,4B and4C. In this sensor device, a package4is mounted on a circuit board8configured from a printed-wiring board. This package4is configured by a disk-shaped stem5, a closed-bottomed cylindrical cap6connected to the stem5, and a light beam transmitting member7arranged so as to close an opening6aformed on a bottom of this cap6and having a function of transmitting desired light beam. Here, the package4houses an element holding member (e.g., MID board or the like)3that holds a photoelectric conversion element2. Then, in the sensor device, a cover member9is provided with a multi-segment lens, which is configured by three Fresnel lenses1,1A and1, and is located on one surface side of the circuit board8so as to cover the package4. In this case, an infrared sensor element such as a pyroelectric element, or a light receiving element such as a photodiode can be adopted as the photoelectric conversion element2. When the infrared sensor element is adopted as the photoelectric conversion element2, a silicon substrate, a germanium substrate or the like is preferably adopted as the light beam transmitting member7.

In a Fresnel lens1A arranged on the center of the multi-segment lens, each lens surface21A in a second surface20A is configured from a part of a side surface of a circular cone, which has an apex (not shown) located on the second surface20A side, a bottom surface (not shown) located on a first surface10A side, and a central axis coinciding with a normal line of a center of the first surface10A. Therefore, the multi-segment lens can be provided at low cost. For example, when the infrared sensor element is adopted as the photoelectric conversion element2, the infrared sensor having a wide angle of view can be achieved as the sensor device.

The number of the Fresnel lenses1,1A in the multi-segment lens is not particularly limited.

Hereinafter, a Fresnel lens according to the present embodiment will be described with reference toFIGS. 5A and 5B.

A basic configuration of a Fresnel lens1according to the present embodiment is substantially similar to that of Embodiment 1, the difference therebetween being in that a lens surface21located on a center, among a plurality of lens surfaces21, is configured from a part of a hyperboloid25in which a rotation axis is inclined with the lens thickness direction and which is an aspheric surface with continuously changing curvature. In addition, the constituent elements similar to those of Embodiment 1 are assigned with same reference numerals and the explanation thereof is herein omitted.

Similarly to the Fresnel lens1of Embodiment 1, all lens surfaces21can be configured from parts of elliptical cones30, respectively. However, when all lens surfaces21are configured from parts of elliptical cones30, respectively, the lens surface21in the central lens portion1aincludes an apex P of an elliptical cone30and the curved surface becomes discontinuous in the apex P, and therefore, it is difficult for a light beam, passing through the apex P, to be collected on a focal point F.

On the other hand, in the Fresnel lens1of the present embodiment, the lens surface21located on the center among the plurality of lens surfaces21(that is, the lens surface21in the central lens portion1a) is configured from the part of the above-mentioned hyperboloid25.

Therefore, the Fresnel lens1of the present embodiment can further reduce aberration as compared with that of Embodiment 1, and the focusing performance can be improved. Accordingly, when the Fresnel lens1of the present embodiment is applied to the sensor device that has been explained in Embodiment 1, the sensitivity can be improved.

In the Fresnel lens1of the present embodiment, the lens surface21in the central lens portion1ais configured from the part of the hyperboloid25, thereby being capable of reducing aberration, as compared with that configured from a part of an aspheric surface other than the hyperboloid25. In a case where the lens surface21in the central lens portion1ais configured from the part of the hyperboloid25, when a metal mold for the Fresnel lens1is produced, processing can be performed by reciprocating a cutting tool130while inclining a cutting face131perpendicular to the curved surfaces according to the lens surfaces21as shown inFIGS. 6A and 6B. In this case, the processing can be performed as far as a nose radius of the cutting tool130is smaller than the curvature radius of the hyperboloid25, and hence the processing time can be reduced even when the lens surface21in the central lens portion1aare the part of the hyperboloid25.

Here, in the Fresnel lens1of the present embodiment, the lens surface21in the central lens portion1ais not limited to the hyperboloid25. As long as the lens surface21in the central lens portion1ais an aspheric surface having an axis of symmetry inclined with respect to a lens thickness direction and having continuously changing curvature, the focusing performance can be further improved as compared with Fresnel lens1of Embodiment 1. In short, in the Fresnel lens1, preferably, a lens surface21located on a center among the plurality of lens surfaces21is configured from a part of an aspheric surface with continuously changing curvature, and then any normal line intersecting with the lens surface21located on the center configured from a part of the aspheric surface among normal lines of respective points on the first surface10is non-parallel (that is, inclined) to an axis of symmetry of the aspheric surface corresponding to lens surface21located on the center with which the any normal line intersects (in a case where the aspheric surface is a hyperboloid25, the axis of symmetry is a rotation axis OP1of the hyperboloid25). Thereby, the focusing performance can be improved. In this case, in the Fresnel lens1, the axis of symmetry of the aspheric surface should be non-parallel to normal lines of respective points on a projection domain formed in the first surface10when the lens surface21located on the center is projected in a direction parallel to a central axis of the first surface10.

Similarly to the Fresnel lens1of Embodiment 1, in the Fresnel lens1of the present embodiment, the line of intersection of the elliptical cone30and the hyperboloid25inscribed in the elliptical cone30is preferably intersect with the mountain portion11b. In the Fresnel lens1shown inFIGS. 5A and 5B, the lines of intersection of the elliptical cones30and the hyperboloids25inscribed in the elliptical cones30exist on a plane surface15which is orthogonal to the lens thickness direction (that is, parallel to the first surface10configured from the plane surface), and which has a height from a valley of the mountain portion11bof each orbicular zone-shaped lens portion1bthat is a half of the maximum height of the mountain portion11b. Therefore, in the Fresnel lens1of the present embodiment, light beams passing on the intersections of the lens surfaces21and the plane surface15are collected on the focal point F, as shown inFIG. 5B.

In the Fresnel lens1inFIGS. 5A and 5B, assuming that a rectangular coordinate system, in which the focal point F is employed as an origin, the rotation axis OP1of the hyperboloid25is employed as a z-axis, and x-axis and a y-axis are orthogonal to the z-axis, is defined, the hyperboloid25that becomes the lens surface21of the central lens portion1ais represented by the above-mentioned Formula (1). Further, assuming that rectangular coordinate systems, in which the apexes P1and P2are employed as origins, the central axes CA1and CA2are employed as z-axes, x-axes are specified along major axis directions of ellipses in cross-sections orthogonal to the z-axes, and y-axes are specified along minor axis directions, and are defined, the elliptical cones301and302can be represented by the above-mentioned Formula (6).

As an example of the Fresnel lens1, a lens including a central lens surface21configured from a part of a hyperboloid25, and five lens surfaces21each configured from a part of a side surface of an elliptical cone30is exemplified. In the Fresnel lens1of this example, the five elliptical cones30corresponding to the lens surfaces21that are a first orbicular zone to a fifth orbicular zone are represented as elliptical cones301to305, respectively. In the Fresnel lens1of this example, in a case where a thickness t of a base portion configured from a portion other than each mountain portion11bis 0.5 mm, a height (lens step) Δt of the mountain portion11bon a point closest to a focal point F in each orbicular zone-shaped lens portion1bis 0.05 mm, and polyethylene with a refractive index of 1.53 is employed as a lens material, values of coefficients a, b and c in Formula (1) or (6) are shown in the following Table 3. Table 3 shows values of a, b and c in Formula (1) as to the hyperboloid25, and shows values of a, b and c in Formula (6) as to the elliptical cones301to305. However, the coefficients a, b and c shown in Table 3 are the values obtained under a precondition that a distance from an image surface I parallel to the first surface10of the Fresnel lens1to the first surface10is 5.5 mm, and light beams incident at an incident angle of 45 degrees are collected on the focal point F.

In a case where light beams incident at an incident angle of 45 degrees with respect to the first surface10are collected on the focal point F, an angle formed by the rotation axis OP1of the hyperboloid25of the central lens portion1aand the normal line of the first surface10should be 27.5 degrees according to Snell's law. That is, the rotation axis OP1should be inclined by 27.5 degrees with respect to the normal line of the first surface10. The central axes of the lens surfaces21of the second surface20intersecting with the normal lines are inclined with the normal lines of the respective points on the first surface10. θ1denotes an angle formed by each of the normal lines B1-B11and B2-B22intersecting with the lens surface21which is the first orbicular zone closest to the central lens surface21, and the central axis CA1of the elliptical cone301. θ2denotes an angle formed by each of the normal lines C1-C11and C2-C22intersecting with the lens surface21which is the second orbicular zone second closest to the central lens surface21, and the central axis CA2of the elliptical cone302. Similarly, assuming that θ3denotes an angle formed by the normal line intersecting with the lens surface21which is the third orbicular zone, and the central axis CA3of the elliptical cone303, θ4denotes an angle formed by the normal line intersecting with the lens surface21which is the fourth orbicular zone, and the central axis CA4of the elliptical cone304, and θ5denotes an angle formed by the normal line intersecting with the lens surface21which is the fifth orbicular zone, and the central axis CA5of the elliptical cone305, values of θ0to θ5are shown in the following Table 4.

It is understood from Table 4 that in the Fresnel lens1, the angle, which is formed by a normal line of each point on the first surface10and a central axis of each lens surface21of the second surface20with which the normal line intersects, becomes larger as a orbicular zone-shaped lens portion1bis located further outside.

FIG. 7shows a spot diagram of the focal point F of this Fresnel lens1.FIG. 7shows a spot diagram in the range of 2*2 mm employing the focal point F as a center. The size of a focal spot should be less than or equal to the size of the photoelectric conversion element arranged so as to correspond to the focal point F of the Fresnel lens1(here, 0.6*0.6 mm or less). When comparingFIG. 3withFIG. 7, it is understood that the aberration of the Fresnel lens1of the present embodiment can be reduced as compared with that of the Fresnel lens1of Embodiment 1.

In the Fresnel lens1, the lens surface21of at least one orbicular zone-shaped portion1bamong a plurality of the orbicular zone-shaped lens portions1bis configured from a part of a side surface of an elliptical cone30, thereby being capable of suppressing occurrence of off-axis aberration in a case of utilizing incident light obliquely incident upon the first surface10from the outside world, and reducing the cost.

Hereinafter, a Fresnel lens1according to the present embodiment will be described with reference toFIGS. 8A and 8B. A basic configuration of a Fresnel lens1according to the present embodiment is substantially similar to that of Embodiment 2, the difference therebetween being in that the first surface10is a curved surface that is convex toward a side opposite to the second surface20. In the Fresnel lens1of the present embodiment, the first surface10is configured from a part of a spherical surface having a large curvature radius, but is not limited to the part of the spherical surface.

In the Fresnel lens1of Embodiment 2, in a case where polyethylene is employed as a lens material, the first surface10is a plane surface. As a result, sink marks or waviness occur due to cooling of the injection molding, shrinkage unevenness caused during a solidification process, or the like, and appearance may be damaged. Further, for example, in a case where of equipping an apparatus such as a television or an air conditioner with the sensor device shown inFIGS. 4A to 4C, the Fresnel lens1configures a part of the appearance of the apparatus. Therefore, in order not to damage the design of the apparatus, preferably, the first surface10is formed so as to be substantially flush with a portion on the periphery of the first surface10on a surface of the apparatus.

So, in a case of employing polyethylene as the lens material and producing the lens by injection molding, the Fresnel lens1is preferably configured such that a curved surface has a large curvature radius (curved surface with small curvature), as shown inFIGS. 8A and 8B. In this case, the lens thickness direction is a normal line direction of each point on the first surface10. In the Fresnel lens1of the present embodiment, the first surface10is configured to be a curved surface that is convex toward a side opposite to the second surface20, thereby being capable of suppressing a direction of waviness in one direction, and preventing appearance from being damaged. In addition, the Fresnel lens1is preferably configured such that the first surface10has a curvature radius larger than the central lens surface21configured from a part of the hyperboloid25having an aspheric surface, and is a smoothly curved surface that is convex toward the side opposite to the hyperboloid25.

In the Fresnel lens1of the present embodiment, when the curvature of the first surface10is designed in a range where an off-axis aberration does not exceed an allowable value (less than or equal to the size of the photoelectric conversion element), polyethylene is employed as the lens material, and occurrence of sink marks or waviness can be suppressed while suppressing occurrence of off-axis aberrations. Further, when the first surface10that is a surface of appearance of the Fresnel lens1is configured so as to have the same curvature as a portion on the periphery of the first surface10on a surface of the apparatus, the design of the apparatus can be enhanced.

In the Fresnel lens1of the present embodiment, while the lens surface21of the central lens portion1ais configured from a part of a hyperboloid25similarly to Embodiment 2, in a case where the rotation axis OP1of the hyperboloid25is inclined by 27.5 degrees similarly to an example of Embodiment 2, the off-axis aberration becomes larger with respect to light beams incident at an incident angle of 45 degrees. Therefore, as the Fresnel lens1of the present embodiment, in a case where the first surface10is configured from a part of a spherical surface, the rotation axis OP1of the hyperboloid25is further inclined while rotating about the apex Pxof the hyperboloid25in an xz plane of a rectangular coordinate system defined in Embodiment 1 as to this hyperboloid25, thereby being capable of reducing the off-axis aberration.

The Fresnel lens1of the present embodiment is preferably configured such that lines of intersection of the elliptical cones30and the hyperboloids25inscribed in the elliptical cones30intersect with the mountain portions11b, similarly to the Fresnel lenses1of Embodiments 1 and 2. In the Fresnel lens1inFIGS. 8A and 8B, the lines of intersection of the elliptical cones30and the hyperboloids25inscribed in the elliptical cones30exist on a plane surface15which has a height from a valley of the mountain portion lib of each orbicular zone-shaped lens portion1bthat is a half of the maximum height of the mountain portion11b. Therefore, in the Fresnel lens1of the present embodiment, light beams passing on the intersections of the lens surfaces21and the plane surface15are collected on the focal point F, as shown inFIG. 8B.

In the Fresnel lens1ofFIGS. 8A and 8B, assuming that a rectangular coordinate system, in which the focal point of the hyperboloid25is employed as an origin, the rotation axis OP1is employed as a z-axis, and an x-axis and a y-axis are orthogonal to the z-axis, is defined, the hyperboloid25of the central lens portion1ais represented by the above-mentioned Formula (1). Assuming that rectangular coordinate systems, in which the apexes P1and P2are employed as origins, the central axes CA1and CA2are employed as z-axes, and x-axes are specified along major axis directions of ellipses in cross-sections orthogonal to the z-axes and y-axes are specified along minor axis directions, are defined, the elliptical cones301and302can be represented by the above-mentioned Formula (6).

Here, as an example of the Fresnel lens1, a lens including a central lens surface21configured from a part of a hyperboloid25, and five lens surfaces21each configured from a part of a side surface of an elliptical cone30is exemplified. In the Fresnel lens1of this example, the five elliptical cones30corresponding to the lens surfaces21that are a first orbicular zone to a fifth orbicular zone are represented as elliptical cones301to305. In the Fresnel lens1of this example, in a case where the first surface10is configured from a part of a spherical surface having a curvature radius of 100 mm, a minimum height t of a base portion configured from a portion other than each mountain portion11bis 0.5 mm, a height (lens step) Δt of the mountain portion11bon a point closest to a focal point F in each orbicular zone-shaped lens portion1bis 0.05 mm, and polyethylene with a refractive index of 1.53 is employed as a lens material, values of coefficients a, b and c in Formula (1) or Formula (6) are shown in the following Table 5. Here, Table 5 shows values of a, b and c in Formula (1) as to the hyperboloid25, and shows values of a, b and c in Formula (6) as to the elliptical cone301to305. The coefficients a, b and c shown in Table 5 are values obtained under a precondition that a distance from an image surface I of the Fresnel lens1to the plane surface parallel to the image surface I and being in contact with the first surface10is 5.5 mm, and light beams incident at an incident angle of 45 degrees are collected on the focal point F.

Here, in the Fresnel lens1, as to the hyperboloid25corresponding to the lens surface21of the central lens portion1a, the rotation axis OP1of the hyperboloid25of the central lens portion1aof Embodiment 2 is inclined while rotating about the apex Pxof the hyperboloid25in the xz plane by 2.5 degrees, thereby being capable of reducing an off-axis aberration. Further, the normal lines of the respective points on the first surface10are directed to a curvature center of the first surface10, and are inclined with respect to the central axes CA1and CA2of the respective lens surfaces21of the second surface20with which the normal lines intersect.01denotes an angle formed by the normal line of the image surface I, and the central axis CA1of the elliptical cone301corresponding to the lens surface21which is the first orbicular zone. θ2denotes an angle formed by the image surface I, and the central axis CA2of the elliptical cone309corresponding to the lens surface21which is the second orbicular zone. Similarly, assuming that θ3denotes an angle formed by the normal line of the image surface I, and the central axis CA3of the elliptical cone303corresponding to the lens surface21which is the third orbicular zone, θ4denotes an angle formed by the normal line of the image surface I, and the central axis CA4of the elliptical cone304corresponding to the lens surface21which is the fourth orbicular zone, and θ5denotes an angle formed by the normal line of the image surface I, and the central axis CA5of the elliptical cone305corresponding to the lens surface21which is the fourth orbicular zone, values of θ0to θ5are shown in the following Table 6.

FIG. 9shows a spot diagram of the focal point F of this Fresnel lens1.FIG. 9shows a spot diagram in the range of 2*2 mm employing the focal point F as a center. The size of a focal spot should be less than or equal to the size of the photoelectric conversion element arranged so as to correspond to the focal point F of the Fresnel lens1(here, 0.6*0.6 mm or less). When comparingFIG. 7withFIG. 9, it is understood that the aberration of the Fresnel lens1of the present embodiment is equivalent to that of the Fresnel lens1of Embodiment 2.

Although the present invention has been described with reference to certain preferred embodiments, numerous modifications and variations can be made by those skilled in the art without departing from the true spirit and scope of this invention, namely claims.