Fresnel lens and optical device

A refractive Fresnel lens used for an optical system including an image plane, which includes a plurality of zone lens surfaces disposed concentrically and a plurality of side wall surfaces each formed between adjacent zone lens surfaces, is characterized in that the side wall surfaces are modulated so as to spatially spread in the image plane noise light due to reflection and/or refraction at the side wall surfaces.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a Fresnel lens and an optical device.

2. Description of Related Art

A Fresnel lens known in the related art includes a plurality of zone lenses disposed in a concentric pattern (see Japanese Patent Gazette No. 3310460).

SUMMARY OF THE INVENTION

There is an issue with regard to the Fresnel lens known in the related art in that light reflected and/or refracted at a side wall surface formed between adjacent zone lens surfaces becomes conspicuous noise.

According to the first aspect of the present invention, a refractive Fresnel lens used for an optical system including an image plane, that includes: a plurality of zone lens surfaces disposed concentrically; and a plurality of side wall surfaces each formed between adjacent zone lens surfaces, wherein: the side wall surfaces are modulated so as to spatially spread in the image plane noise light due to reflection and/or refraction at side wall surfaces.

According to the second aspect of the present invention, in the Fresnel lens of the first aspect, it is preferred that the side wall surfaces are modulated so that noise light attributed to diffraction does not spatially concentrate along a direction in the image plane.

According to the third aspect of the present invention, in the Fresnel lens of the second aspect, it is preferred that angles assumed by the side wall surfaces relative to an optical axis are modulated.

According to the fourth aspect of the present invention, in the Fresnel lens of the second aspect, it is preferred that positions of a side wall surface are modulated along a radial direction while the side wall surface sustains a constant angle relative to an optical axis regardless of the positions thereof assumed along a circumferential direction.

According to the fifth aspect of the present invention, in the Fresnel lens of the second aspect, it is preferred that an angle assumed by the side wall surface relative to an optical axis is periodically modulated in correspondence to positions thereof assumed along a circumferential direction.

According to the sixth aspect of the present invention, in the Fresnel lens of the second aspect, it is preferred that positions of a side wall surface are periodically modulated along the radial direction in correspondence to the positions thereof assumed along the circumferential direction.

According to the seventh aspect of the present invention, in the Fresnel lens of any one of the first through sixth aspects, it is preferred that the optical system is a human eye, and the image plane is a retina, and wherein the Fresnel lens is on at least one side of an eye glass lens to be set for the eye, and the Fresnel lens includes a plurality of zone lens surfaces disposed concentrically and a plurality of side wall surfaces each formed between adjacent zone lens surfaces and side wall surface modulation is optimized so that noise light due to reflection and/or refraction at the sidewalls is minimized in the image plane for various eye gaze angles.

According to the eighth aspect of the present invention, in the Fresnel lens of the seventh aspect, it is preferred that the side wall surfaces modulation is adjusted so as noise light attributed to diffraction does not spatially concentrate on the retina after passing through the iris of the eye.

According to the ninth aspect of the present invention, an optical device, comprising: an imaging lens for forming an image on an image plane; an aperture that restricts light passing through the imaging lens; and a Fresnel lens, wherein: the Fresnel lens includes a plurality of zone lens surfaces disposed concentrically and a plurality of side wall surfaces each formed between adjacent zone lens surfaces and that side walls modulation is optimized so that noise light due to reflection and/or refraction at the side walls is minimized in the image plane.

According to the tenth aspect of the present invention, in the optical device of the ninth aspect, it is preferred that the side wall surface modulation is optimized so that the noise light due to reflection and/or refraction at the sidewalls does not pass through the aperture.

According to the eleventh aspect of the present invention, in the optical device of the ninth aspect, it is preferred that the side wall surfaces modulation is adjusted so as noise light attributed to diffraction does not spatially concentrate on the imaging plane after passing through the aperture.

DESCRIPTION OF EMBODIMENTS

The following is a description of an embodiment of the present invention given in reference to drawings. The refractive Fresnel lens achieved in the embodiment, which is a lens having a Fresnel lens surface formed on a concave surface of, for instance, a meniscus lens, located toward the eye, and achieving either positive or negative refractive power, is used as an eyeglass lens or an imaging lens. Before describing the Fresnel lens in the embodiment in specific detail, a problem arising when a Fresnel lens in the related art is used as an eyeglass lens will be explained.FIGS. 6A and 6Brespectively present a schematic top view and a schematic sectional view of an example of the related art, i.e., a Fresnel lens1. It is to be noted thatFIGS. 6A and 6Bshow part of the Fresnel lens1. The Fresnel lens1, adopting a structure achieved by disposing on a flat plane separate concentric parts that form the lens surface of a concave lens, includes a plano-concave central lens3with an optical axis Ax passing through the center O thereof and a plurality of zone lenses4(41,42,43, . . . ,4n) disposed further outside of the central lens3and concentrically relative to the optical axis Ax. A plurality of side walls5(51,52,53, . . . ,5n), are formed between the central lens3and a zone lens4and between adjacent zone lenses4so as to connect the central lens3and the zone lens4and connect one zone lens4with the next zone lens4. It is to be noted that the Fresnel lens1may be manufactured by injection-molding of a polymer material in a die. In order to ensure that the molded product can be easily disengaged from the die, the side walls5are made to incline with a predetermined angle relative to the optical axis Ax.

FIG. 7schematically illustrates the optical paths of light traveling through the Fresnel lens1used as an eyeglass lens. As shown inFIG. 7, incoming light11having entered the Fresnel lens1is refracted at the central lens3or the zone lenses4and is output as regular outgoing light12, which then enters an eye20of the eyeglass wearer. However, some of the incoming light11is reflected at the side walls5and outgoes the Fresnel lens1as noise light13. Depending upon the angle at which the noise light13outgoes the Fresnel lens1, the noise light13may enter the eye20of the eyeglass wearer through an iris30of the eye20. It is to be noted thatFIG. 7, showing the Fresnel lens surface located on the object side of the meniscus lens and the eye-side surface taking on a flat contour, provides a simple illustration of the conditions of various light beams including the initial light transmitted through the Fresnel lens surface and the noise light occurring at the side wall surfaces5in a typical example. As an alternative to this example, the Fresnel lens surface may be formed at the concave surface located toward the eye, as will be explained later in reference toFIG. 5.

FIG. 8schematically illustrates the distribution of the regular outgoing light12and the noise light13reaching the retina through the iris30of the eye20. In the example presented inFIG. 8, light output from a point light source enters the Fresnel lens1. In this situation, an image of the point light source is formed on the retina with the regular outgoing light12. The noise light13, having reached the retina, on the other hand, forms circular arcs corresponding to the contour of the side walls5. As a result, the eyeglass wearer is bound to see the noise light13as circular arc lines in addition to the image of the point light source formed with the regular outgoing light12.

As long as the angle of incidence at which the light11enters the Fresnel lens1is constant, the entry of the noise light13into the iris30of the eye20of the eyeglass wearer can be prevented by adjusting the angle formed by the side walls5relative to the optical axis Ax (hereafter may be referred to as an angle of inclination) and thus adjusting the outgoing angle at which the noise light13outgoes the Fresnel lens1. However, under normal circumstances, eye glasses are worn in an environment where the incoming light11enters the eyeglass lenses (the Fresnel lens1in this example) at varying angles. Also, eyeball can rotate at wide gaze angles. This means that the angle of inclination of the side walls5, adjusted to the optimal value at which noise light13is not allowed to enter the eye20at all in correspondence to a given angle of incidence, may actually result in more noise light13entering the eye20at either another angle of incidence or a different eye gaze angle. In other words, it is extremely difficult to adjust the angle of inclination of the side walls5so as to completely disallow entry of all the noise light13into the eye20of the eyeglass wearer.

Bearing this challenge in mind, the Fresnel lens in the embodiment adopts a specific structure that renders noise light reflected at the side walls less noticeable. The following is a description of the Fresnel lens achieved in the embodiment.FIG. 1AandFIG. 1Bschematically illustrate a Fresnel lens100achieved in the embodiment respectively in a top view and in a sectional view, with part ofFIG. 1Bshown in an enlargement inFIG. 1C. It is to be noted thatFIGS. 1A, 1B and 1Conly show part of the Fresnel lens100. As is the Fresnel lens1in the related art described earlier, a Fresnel lens100achieved in the embodiment is a concave lens, the lens surface of which is formed with separate lens elements disposed concentrically over a flat plane. As does the Fresnel lens1, it includes a plano-concave central lens103with an optical axis Ax passing through the center O thereof and a plurality of zone lenses (zone lens surfaces)104(1041,1042,1043, . . . ,104n) disposed further outside relative to the central lens103and concentrically to the optical axis Ax. A plurality of side walls (side wall surfaces)105(1051,1052,1053, . . . ,105n), are formed between the central lens103and a zone lens104and between adjacent zone lenses104so as to connect the central lens103and the zone lens104and connect one zone lens104with the next zone lens104.

However, the Fresnel lens100in the embodiment differs from the Fresnel lens1in the related art in that, viewed from above (viewed along the direction in which the optical axis Ax extends), a top portion105tof each side wall surface105has a wavy circular contour achieved by periodically modulating a circle centered on the optical axis Ax, as illustrated inFIG. 1A. At a bottom portion105bthereof, a perfectly circular contour centered on the optical axis Ax is achieved as in the related art. It is to be noted that the description is provided by assuming that the top portion105t, present in the area where a zone lens104merges with a side wall surface105, is located on the side further away from a surface106of the Fresnel lens100, at which the zone lenses104and the side wall surfaces105are not formed (hereafter referred to as a back surface106) and that the bottom portion105bis located on the side closer to the back surface106.

This wavy circular contour formed at the top portion105tis achieved by periodically altering the angle of inclination θ of the side wall surface105at specific positions taken along the circumferential direction, instead of allowing the side wall surface105to sustain a constant angle of inclination through the entire circumference. In more specific terms, the angle of inclination θ of the side wall surface105at a given position P may be expressed as in (1) below. It is to be noted that α, β, γ and f in expression (1) respectively represent a reference angle of inclination, an angular amplitude relative to the reference angle of inclination, the initial phase and the number of cycles (frequency) occurring within the full circumference. It is assumed that α, β, γ and f each take a constant value for a sidewall in the embodiment. In addition, φ in expression (1) represents the argument (the angle formed by a half line OP starting from an end point assumed at the origin point O and passing through the position P) relative to a polar axis OX measured for the position P indicated by coordinates in a polar coordinate system, the origin point of which is set at the center O.
θ(φ)=α+β×½(1−cos(f×φ+γ))  (1)

Namely, the angle of inclination θ of the side wall surface105, is modulated with a cosine function that takes the argument φ as a variable so that the change thereof is comprised between the reference angle of inclination α and α+β.FIG. 1Cprovides a schematic illustration showing how the side wall surface105may be modulated. The side wall surface105is adjusted, in correspondence to its position along the circumferential direction, within the range between the side wall surfaces105indicated with the solid line inFIG. 1Cand the side wall surface105indicated with the dotted line inFIG. 1C. In addition, the Fresnel lens100is configured by splitting the lens surface of a concave lens in a concentric pattern and disposing the split portions on a flat plate, as has been described earlier. While the angle of inclination of the side wall surfaces105is modulated in the Fresnel lens100, the zone lens surfaces104retain the contours forming that part of the lens surface of the concave lens (i.e., the initial concave lens).

It is to be noted that the Fresnel lens100achieving such a contour or a die to be used to manufacture the Fresnel lens100may be formed through, for instance, lathing.

FIG. 9schematically illustrates the optical paths that are formed when the Fresnel lens100in the embodiment is used as an eyeglass lens. As shown inFIG. 9, initial light fluxes (regular exiting light)12having been transmitted through the zone lens surfaces104of the Fresnel lens100then pass through the iris30and form an image on the retina of the eye20. The side wall surfaces105of the Fresnel lens100are modulated so that the noise light13due to reflection and/or refraction at the side wall surfaces105is directed to travel outside of the eye iris (pupil)30. In other words, the side wall surfaces105are modulated and optimized so that the noise light13occurring at the side wall surfaces105do not reach the eye or are blocked by the eye iris30. This means that the noise light13is rarely allowed to reach the retina of the eye20and thus, the adverse effect of noise light reaching the image formed on the retina of the eye20is greatly reduced.

FIG. 2AandFIG. 2Bschematically illustrate the distribution of noise light13that is reflected at a side wall surface105and then reaches the retina through the iris of an eye of an eyeglass wearer observed when the Fresnel lens100in the embodiment is used as an eyeglass lens. It is to be noted thatFIG. 2AandFIG. 2Bonly show noise light reflected and/or refracted at a single side wall surface105so as to simplify the illustration. InFIG. 2A, the solid lines indicate noise light13having entered the eyes and the dotted lines indicate noise light that has not entered the eye. In addition, the angular amplitude β and the frequency f of the periodical modulation applied to achieve the wavy circular contour at the top portion105tof the side wall surface105in the example presented inFIG. 2Aare different from the angular amplitude β and the frequency f of the periodical modulation applied to achieve the wavy circular contour at the top portion105tof the side wall surface105in the example presented inFIG. 2B. Namely, a greater angular amplitude β of periodical modulation is assumed at the side wall surface105inFIG. 2Acompared to that inFIG. 2B. In addition, a higher frequency f of periodical modulation is assumed at the side wall surface105inFIG. 2Bcompared to that inFIG. 2A. According to the ray tracing simulation software developed by us, we confirmed the simulated noise light distribution on the retina shown inFIG. 2AorFIG. 2Bis well consistent with the simulation result.

In the example presented inFIG. 2A, with a greater angular amplitude β of periodical modulation assumed at the side wall surface105, the angle of inclination θ changes greatly and thus the outgoing angle at which the noise light13outgoes the Fresnel lens also changes greatly through the full circumference of the side wall surface105. As a result, noise light13reflected at some positions does not enter the eye of the eyeglass wearer. Thus, while the noise light13reflected at side walls5of the Fresnel lens1in the related art forms continuous circular arc lines simulating the contour of the side walls5as shown inFIG. 8, the noise light13forms a disjoined contour, i.e., the wavy circular contour of the side wall surface105is reproduced with missing portions, in the example presented inFIG. 2A. Namely, while the part of the noise light13indicated by the solid lines inFIG. 2A, which is allowed to enter the eye, is visible to the eyeglass wearer, the part of the noise light13indicated by the dotted lines inFIG. 2Adoes not enter the eye due to the modulation effect and thus remains invisible to the eyeglass wearer. This means that the noise light13can be rendered less noticeable to the eyeglass wearer in the example presented inFIG. 2Acompared to the related art.

In addition, in the example presented inFIG. 2B, with a higher frequency f of periodical modulation assumed at the side wall surface105, a change occurs over a greater number of cycles through the full circumference of the side wall surface105, causing scattering of the noise light13. Thus, while the noise light13concentrates in a circular arc pattern resembling the contour of the side walls5at the Fresnel lens1in the related art, as indicated inFIG. 8, the noise light13spreads in a band in the example presented inFIG. 2B. This means that the brightness per unit area of the noise light13having reached the retina is lower compared to that in the related art, thereby rendering the noise light13less noticeable to the eyeglass wearer.

The noise light13occurring as light is reflected at the side wall surfaces105of the Fresnel lens100achieved in the embodiment is thus rendered less noticeable compared to noise light occurring at the Fresnel lens1in the related art.

In addition, the contour of the side wall surfaces105(the outline of the zone lens surfaces104) are less noticeable to a third party looking at the wearer of the eyeglasses with the Fresnel lenses100in the embodiment compared to the contour of the side walls in the Fresnel lens1in the related art. Thus, the appearance of the eyeglass wearer viewed by a third party is likely to improve.

It is to be noted that a plurality of side wall surfaces105, formed at positions closer to the center O through positions closer to the outer circumference of the Fresnel lens100in the embodiment, may all assume the wavy circular contour or only some of the side wall surfaces105may assume the wavy circular contour. In addition, the reference angle of inclination α, the angular amplitude β, the phase γ and the frequency f of periodical modulation applied to achieve the wavy circular contour may vary from one side wall surface105to another or matching reference angle of inclination α, angular amplitude β and frequency f of periodical modulation may be assumed for all the side wall surfaces105.

The following advantage is achieved through the embodiment described above. In the Fresnel lens100that includes a plurality of zone lens surfaces104set in a concentric pattern and a plurality of side wall surfaces105each formed between one zone lens surface104and the next zone lens surface104, the side wall surfaces105modulation is optimized so that noise light occurring at the side wall surfaces105is directed to travel outside an optical system or be blocked by apertures. Through these measures, noise light, attributable to light reflected and/or refracted at the side wall surfaces105, entering the retina through the iris of the eye can be rendered less noticeable.

In the embodiment described above, the side wall surfaces105, viewed from above, each assume a perfectly circular contour centered on the optical axis Ax at the bottom portion105bthereof and assume a wavy circular contour, which is achieved by periodically modulating a circle centered on the optical axis Ax at the top portion105tthereof. As an alternative, a side wall surface105, viewed from above, may assume a perfectly circular contour centered on the optical axis Ax at its top portion105tand assume a wavy circular contour, which is achieved by periodically modulating a circle centered on the optical axis Ax, at the bottom portion105b.

As a further alternative, a side wall surface105, viewed from above, may assume a wavy circular contour achieved by periodically modulating a circle centered on the optical axis Ax, both at the top portion105tand the bottom portion105bthereof. An example of a structure that may be adopted for such a Fresnel lens200is schematically illustrated in a top view and a sectional view provided respectively inFIG. 3AandFIG. 3B. In addition, a partial enlargement ofFIG. 3Bis provided inFIG. 3C.

The distance (radius) rt between a given position Pt taken at the top portion105tof a side wall surface105and the center O of the Fresnel lens200may be expressed as in (2) below. In addition, the distance (radius) rb between a given position Pb taken at the bottom portion105bof a side wall surface105and the center O may be expressed as in (3) below. It is to be noted that in expressions (2) and (3), Ct and Cb respectively represent the reference radii measured at the top portion105tand at the bottom portion105b, At and Ab respectively represent the radius amplitudes relative to the reference radii at the top portion105tand the bottom portion105b, γ and f represents respectively the initial phase and the number of cycles (frequency) occurring through the full circumference. In addition, φ in expressions (2) and (3) represents the argument (the angle formed by a half line OP starting from an end point assumed at the origin point O and passing through the position Pt or the position Pb) relative to the polar axis OX measured for the position Pt or Pb indicated by coordinates in a polar coordinate system, the origin point of which is set at the center O.
rt(φ)=Ct+At×½[1−cos(f×φ+γ)]  (2)
rb(φ)=Cb+Ab×½[1−cos(f×φ+γ)]  (3)

Namely, the radii rt and rb at the top portion105tand the bottom portion105bof the side wall surface105are modulated with a cosine function that includes the argument φ as a variable so that the changes in the radii are limited by the reference radii Ct and Cb respectively.

In addition, while the amplitude, the cycle and the phase of the periodical modulation applied so as to achieve the wavy contour at the top portion105tof the side wall surface105match those of the periodical modulation applied to achieve the wavy contour at the bottom portion105band thus, the side wall surface105sustains a constant angle of inclination θ through the entire circumference in the Fresnel lens200shown inFIGS. 3A and 3B. In addition, the position of the side wall surface105is periodically modulated along the radial direction in correspondence to its position along the circumferential direction.FIG. 3Cschematically illustrates how such modulation may be achieved. In correspondence to its position along the circumferential direction, the side wall surface105undergoes a parallel translation along the zone lens surface104within the range between the side wall surface105indicated with the solid line inFIG. 3Cand the side wall surface105indicated with the dotted line inFIG. 3C. In the Fresnel lens200described above, the positions of the side wall surfaces105are modulated along the radial direction while the side wall surfaces105sustain a constant angle of inclination θ, regardless of their positions along the circumferential direction. In addition, as is the Fresnel lens100described earlier, the Fresnel lens200is configured by splitting the lens surface of a concave lens in a concentric pattern and disposing the split portions on a flat plate. While the side wall surfaces105are modulated in the Fresnel lens200, the zone lens surfaces104retain the contours that form part of the lens surface of the concave lens (i.e., the initial concave lens).

However, the present invention is not limited to this example and the amplitude, the cycle and the phase of the periodical modulation applied to achieve the wavy contour at the top portion105tmay be different from those of the periodical modulation applied to achieve the wavy contour at the bottom portion105b, i.e., the side wall surface105does not have to sustain a constant angle of inclination through its entire circumference.

It is to be noted that the Fresnel lens200achieving such a contour or a die to be used to manufacture the Fresnel lens200may be formed through, for instance, lathing. It has been shown, based upon optical calculation results, that a noise light dispersing effect is achieved in a Fresnel lens200with the height of the side wall surfaces105thereof set to an optimal value, even when the amplitude of the periodical modulation at the side wall surfaces105is as little as 10 μm.

It is to be noted that the plurality of side wall surfaces105, formed at positions closer to the center O through positions closer to the outer circumference of the Fresnel lens200in variation 1, may all assume the wavy circular contour or only some of the side wall surfaces105may assume the wavy circular contour. In addition, the amplitudes At and Ab and the frequency f of the periodical modulations applied to achieve the wavy circular contour may vary from one side wall surface105to another or matching amplitude At and Ab and frequency f of periodical modulation may be assumed for all the side wall surfaces105.

A side wall surface105with at least either the top portion105tor the bottom portion105bthereof assuming a wavy circular contour achieved by periodically modulating a circle centered on the optical axis Ax may incline with the angle of inclination θ that is continuously altered from the top portion105tthrough the bottom portion105bof the side wall surface105, as illustrated inFIG. 4A or 4B. It is to be noted thatFIG. 4Apresents an example of a side wall surface105with the angle of inclination θ thereof, set at a smallest value at the top portion105t, gradually increasing toward the bottom portion105b, whereasFIG. 4Bpresents an example of the side wall surface105with the angle of inclination θ thereof periodically changing as it ranges from the top portion105tthereof toward the bottom portion105b.

By continuously altering the angle of inclination θ of the side wall surface105as it ranges from the top portion105tthereof toward the bottom portion105bthereof, as in these examples, noise light can be spread in wider bands, rendering the noise light even less noticeable to the eyeglass wearer.

It is to be noted that the Fresnel lens achieved in variation 2 having such a contour or a die to be used to manufacture the Fresnel lens in variation 2 may be formed through, for instance, lathing.

While the angular amplitude β and the frequency f of the periodical modulation applied at the side wall surface105in the embodiment described earlier are constant, the present invention is not limited to this example and instead, the modulation applied at the side wall surface105may be an amplitude modulation through which the angular amplitude β is continuously altered, a frequency modulation through which the frequency f is continuously altered or a modulation through which the angular amplitude β or the frequency f is randomly altered. However, a better throughput is assured when a Fresnel lens or a die used to manufacture a Fresnel lens is formed through lathing by selecting a uniform angular amplitude β in a uniform frequency f for the periodical modulation applied at the side wall surface105. It is possible that noise attributable to light reflected and/or refracted at a side wall can be rendered less noticeable in case that the fluctuation of amplitude modulation is less than ±10% of local width of the zone lens surfaces or the frequency index modulation is less than 200%.

The Fresnel lens according to the present invention described above may be utilized as an eyeglass lens.FIG. 5is a schematic illustration of an eyeglass lens50that includes the Fresnel lens according to the present invention. The eyeglass lens50is a meniscus lens with the Fresnel lens according to the present invention formed at the surface toward the eyeball. In this case, the surface carrying the Fresnel lens is not limited to a flat surface. It is available to adapt the Fresnel lens to a concave surface or a convex surface. The Fresnel lens can be in the front and/or back surface. Also, the zones lenses can have a concave or convex shape. It is to be noted that the Fresnel lens according to the present invention may be used in other optical devices (e.g., optical systems such as a magnifying glass or an eyepiece lens), instead of an eyeglass lens. For instance, the Fresnel lens100according to the present invention may be used in an optical device that includes a photographic lens and an aperture that restricts light passing through the photographic lens. In an optical device achieved in such an application, the eye20and the iris30shown inFIG. 5will respectively correspond to the photographic lens and the aperture. The optical device achieved in an embodiment of the present invention will fulfill functions that will be described in reference to the light beams shown inFIG. 9. Namely, the initial light beams12, having been transmitted through the zone lens surfaces104of the Fresnel lens100, pass through the aperture (iris)30and form an image on the imaging surface (retina). The side wall surfaces105in the Fresnel lens100according to the present invention are modulated and optimized so that noise light13occurring at the side wall surfaces105does not pass through the aperture (iris)30. This means that the noise light13occurring at the side wall surfaces of the Fresnel lens100is not allowed to pass through the aperture (iris)30and thus, the noise light13never reaches the imaging surface (retina) through the photographic lens (eye)20. As a result, the adverse effect of noise light reaching the image formed on the imaging surface (retina) can be greatly reduced.

To describe this aspect of the Fresnel lens according to the present invention in further details, the side wall surfaces are modulated and optimized so that noise light due to reflection and/or refraction at the side wall surfaces105does not generally pass through the iris30(or the aperture in the optical device in variation 4). In addition, the side wall surfaces105are modulated so that noise light due to diffraction does not concentrate along a specific direction, i.e., onto the imaging surface (i.e., the retina or the imaging surface).

In the refractive Fresnel lens according to the present invention described above, diffracted light of a plurality of orders other than the 0th order light (±1st order light, ±2nd order light, . . . ,) emitted due to discontinuities between the zone lens surfaces104, may become noise visible to the eyeglass wearer. Accordingly, the refractive Fresnel lens described earlier may be configured by taking further measures so as to minimize noise attributable to diffracted light. In more specific terms, since the intensity of the diffractive light increases if the zone lens surfaces104are set over equal intervals, the zone lens surfaces104should be set with irregular pitches so as to reduce the intensity of the diffracted light, level out the diffracted light intensity levels and thus lower the peak.

FIG. 10illustrates a Fresnel lens300configured so as to attenuate noise due to diffracted light.FIG. 10shows the modulated side wall surfaces105as straight shape to facilitate an explanation in an enlargement of part of the top surface of the Fresnel lens300. It is to be noted that except for the feature that will be described below, the Fresnel lens300is structurally similar to the Fresnel lens200described earlier in reference to variation 1. Based upon the results obtained through rigorous optical calculation, periodical modulation is applied with regard to the positions of the side wall surfaces105in the Fresnel lens300in the embodiment so that different initial phases are assumed from one side wall surface to another in order to ensure that the distance between adjacent side wall surfaces105facing each other across an optical surface are set non-constant. To describe this concept in terms of the functions of an optical grating, when all the grooves, not just consecutive grooves, are formed over uniform intervals and are parallel to each others, very dense diffracted light peaks (i.e., noise light) are formed. In order to lessen the extent of such diffraction effect, grooves can be formed at non uniform intervals and tilted from one each other. In the embodiment, it can be done by offsetting the initial phases of individual side walls sharing a given frequency or by modulating adjacent side wall surfaces at frequencies that do not share a common divisor (hereafter referred to as frequency represented by values coprime to each other), so as to disallow generation of diffracted light along a specific direction. It will be obvious that the initial phases may also be offset in conjunction with frequencies represented by values coprime to one another.

By modulating the individual side wall surfaces105with varying modulation frequencies, amplitudes or varying initial phases as described above, the zone lens surfaces104can be set with locally irregular shapes and, as a result, noise peaks attributable to diffracted light can be reduced. It is to be noted that in addition to the modulation frequency, at least either the amplitude or the phase may be varied from one side wall surface105to the next side wall surface105.

FIG. 11is a plan view of a Fresnel lens400achieved in another variation of the present invention. The plan view inFIG. 11shows a Fresnel lens400having each pair of side wall surfaces105located on the two sides of a given zone lens surface104(i.e., located on the inner side and on the outer side) modulated with the same frequency f but having an initial phase difference of 180 deg. Otherwise, the Fresnel lens400assumes a basic structure corresponding to that of the Fresnel lens100shown inFIG. 1A.FIG. 12is a plan view of a Fresnel lens500achieved in yet another variation of the present invention. While the initial modulation values pertaining to the modulation applied at the side wall surfaces105located on the two sides of each zone lens surface104, (i.e., located on the inner side and on the outer side of the zone lens surface104) are also out of phase by 180 deg in the Fresnel lens500shown in the plan view inFIG. 12, the basic structure of the Fresnel lens500corresponds to that of the Fresnel lens200shown inFIG. 3A.

The phase difference between adjacent side wall surfaces105is set to 180 deg in the variations shown inFIG. 11andFIG. 12. This represents the maximum out of phase situation. In practical application, it is effective to have at least 30 deg initial phase difference between adjacent side wall surfaces105.

In short when the area on the Fresnel lens, through which light flux for forming an image of a point object on the retina passes, includes plural zone lens surfaces, the frequency, the amplitude and relative phase of modulation on each side wall would be selected so that the local width of the zone lens surfaces104change by approximately 10%. Through these measures, noise due to diffracted light can be reduced even more effectively.

The embodiments described above and variations thereof are simply provided as examples and the present invention is in no way limited to the particulars of these examples. In addition, other modes of embodiment conceivable within the technical scope of the present invention are all within the scope of the present tension.