It is known in the prior art to manufacture non-corrective eyeglasses such as sunglasses or protective eyeglasses having wrap-around segments designed to shield the eye from incident light, wind, and foreign objects in the temporal vision field of the wearer. Such plano eyewear may curve horizontally around the eye sockets to “wrap” around and enclose the eyes as far as 100° from the line of sight. Vertical contouring of inferior regions of the lens inward toward the cheeks is variously called “pantoscopic tilt” or “rake”, depending how the effect is achieved. The lenses may be designed to fit into dual lens frames or they may be of the unitary shield type. Wrap and/or rake create aesthetically pleasing eyewear that provides wearer comfort, but introduce also optical distortions that present difficulties to wearers involved in precise visual tasks. Various surface forms and arrangements have been employed in order to improve the closeness of wrap and rake provided. Whilst some of these arrangements have allowed faithful imaging at a wearer's direct line of sight for distant vision, inherent oblique refractive errors are introduced by lack of spatial correspondence between the lens optical axis and the direct line of sight as worn. Some prior art of the early 20th century employed spherical and elliptical dual lens designs of approximately constant thickness, thus not having an optical axis, but these have negative power and exhibit substantial refractive and prismatic distortion whenever the curvature center does not fall on the direct line of sight. To achieve functionality for dual lens eyewear, this type of lens needs to have exceptionally high base curve (˜16 to 21D) so that it may be positioned approximately concentric with movement of the wearer's eyes. Alternatively, a unitary lens should be of such low base curve that the offset distance between the direct line of sight of one eye and the optical axis located within the wearer's medial plane is very much less than the vertex radius of curvature, being say in the range 1 to 2D. The vast majority of eyewear utilizes base curves intermediate between these conditions.
Prior art cited by Rayton 75 years ago (U.S. Pat. No. 1,741,536) attempted to achieve the effect of wrap and/or rake by tilting nominally zero power lenses outward and/or downward and aligning the optical center of the lens with the wearer's direct line of sight. The method was rejected owing to the existence of prismatic distortion in the as worn position. More recent art teaches a method of overcoming such prismatic error for pairs of low minus lenses. Reichow and Citek disclose in their U.S. Pat. No. 6,129,435 the achievement of the appearance of wrap and/or rake by inward and/or upward displacement of the geometric center of the lens, the induced-prismatic-error as worn being corrected without change in the physical appearance of the lens by rotating it about the center of curvature of its front surface to dispose the optical axis inward and/or upward. There remains, however, a negative mean power at the direct line of sight. It can be demonstrated that an opposed set of rotations would correct the prismatic error as worn for pairs of low plus lenses. However, the vast majority of non-corrective eyewear setup is based on Prentice's Rule (1888), an approximate analysis that predicts a linear relationship between the optical prism at a line of sight decentered with respect to a lens and the back vertex power of that lens. Most commonly, lenses are designed to provide zero back vertex power. Their optical axes and the wearer's direct lines of sight, as worn, are displaced laterally from each other as desired, while maintaining parallelism between them. This arrangement is shown in FIG. 1A; the line 2–2′ is the direct line of sight and 1–1′ is the displaced optical axis.
Rayton in U.S. Pat. No. 1,741,536 and Jannard in U.S. Pat. Nos. 4,674,851 and 4,859,048 disclose cylindrical lenses. Jannard (U.S. Pat. No. 4,867,550) and Burns (U.S. Pat. No. 4,741,611) describe toroidal lenses. Montesi and King (U.S. Pat. No. 4,271,538) and Conway (U.S. Pat. No. 5,555,038) describe unitary eyewear with left and right spherical lens portions whose optical axes are displaced nasally from the direct lines of sight as worn. Houston et al. (U.S. Pat. Nos. 5,648,832 5,689,323 and 6,010,218) describe spherical lenses that are decentered with respect to the direct line of sight in both a horizontal and a vertical plane. Fecteau et al. (U.S. Pat. Nos. 5,825,455, 6,019,469 and 6,254,236) describe unitary lenses having surfaces formed by rotation of an ellipse, parabola or hyperbola around a horizontal axis located rearward of the wearer's eyes. Davis and Waido (U.S. Pat. No. 5,604,547) describe unitary lenses whose surfaces are paraboloids that are bent in the lateral regions to form a side wrap beyond the wearer's visual fixation. They describe also unitary style sunglasses or eye protectors having a lens with inner and outer surfaces that are oblate ellipsoids. The surfaces they discuss also have a region of maximum surface astigmatism on the lens surface. Tackles (U.S. Pat. No. 5,774,201) describes both unitary and dual lens styles wherein the horizontal arc of a lens cross-section has a medial portion and lateral ends, the lateral ends having gradually tightening curvature relative to the curvature of the medial portion in substantial conformation to a portion of an ellipse with eccentricity in the range 0.1 to 0.85. The vertical curvature may take any desired form.
In order that a spherical lens can have zero back vertex power, its front and back radii R1 and R2 are related by R1−R2=t(n−1)/n where t is the lens center thickness and n is the material refractive index. This stipulates that the caliper thickness of the lens (measured normal to either surface) will have a maximum value at the lens center and taper everywhere away from the optical axis of the lens, a matter long known in ophthalmic optics. For example, Rayton describes lenses with wall thickness tapering away from the optical axis. Conway notes that a lens which tapers continuously outwardly from its point of maximum thickness (optical center) has constantly zero power and low prismatic imbalance at an eye sweep angle of 20° whereas a similar lens of constant wall thickness has negative power and relatively higher prism imbalance. Others, including Montesi, Jannard, Tackles and Houston et al., make claims directed specifically to non-corrective lenses characterized by tapering thickness.
In an apparently contrary viewpoint, Davis and Waido claim non-corrective unitary lenses having “substantially uniform thickness throughout”. Their stated development objective was to “provide improved sunglasses and safety eyewear with relatively uniform thickness throughout without sacrificing optical performance”. Specifically, the design task was to correct unwanted thinning of the lens in the region of the lateral bend and avoid any requirement to manufacture unnecessarily heavy lenses. Each of those designs disclosed in U.S. Pat. No. 5,604,547 have been analyzed and have found the corresponding lenses to have thickness that tapers from the optical center across the field of view to the lateral bend, in which region there is localized thickening of the lens wall. In the same region, there are consequent negative refractive errors. Accordingly, this disclosure does not contradict prior wisdom.
The design of non-corrective lenses has been simplified greatly by concentration of the industry on the quality of distant vision in forward gaze. Optical testing is typically undertaken using a telescope aligned with the geometric axes to evaluate the optics at the direct lines of sight as worn. Oblique refractive errors, very important to ophthalmic lens design, are frequently ignored in the analysis of non-corrective lenses. Industry standards typically quote tolerances for refractive and prismatic errors at the “as worn” position only. See Table 1 below.
TABLE 1Some specifications for refractive and prismatic errors of non-correctivelenses at the direct lines of sight, as worn.At Line of SightLeft/Right Imbalances at Lines of SightStandardPowerAstig.PowerAstig.Prism Prism ANSI Z80.3-1979+0.12/−0.250.180.180.180.4750.475 outANSI Z87.1-1979±0.060.120.060.120.1250.125 out, 0.52 inISO TC94/SC6 Gr. 1±0.060.120.060.120.12 1.00 out, 0.25 inISO TC94/SC6 Gr. 2±0.120.250.120.250.25 1.00 out, 0.25 inCEN 1836±0.090.090.180.180.24 0.24
Depending on the base curve, material and lens center thickness, these tolerances allow significantly different lens characteristics in the oblique visual field. The arrangements and devices of the prior art described above all result in the optical axis of a lens being placed somewhere in space other than coincident with the direct line of sight. The two vectors may intersect in some plane, they may be strictly parallel, or they may be skew. All such arrangements result in image aberrations for a simple object field that are asymmetric with respect to monocular rotation, which effect increases the magnitude of oblique errors experienced. It also causes a wearer's left and right eyes to experience mirrored image aberration fields, introducing binocular disparity for version movements. These being the primary optical demand in distance vision, the disparity is a distinct disadvantage of current designs. Ophthalmic lenses, on the other hand, are presented by convention in front of the eyes so that the optical axes and direct lines of sight are closely identical. The oblique fields are designed to be substantially symmetric with respect to monocular rotation and substantially free of binocular disparity in version and vergence movement, unless required by prescription.
Accordingly, it would be highly desirable to devise methods and means by which to place non-corrective lenses of aesthetically pleasing and useful shape before a wearer in a face-fitting configuration so that: the optical axes of the lenses and the wearer's direct lines of sight are substantially aligned, or; the visual fields are symmetric with respect to monocular rotation, preferably; both. Given the extent of prior art in this field, it should be expected that lenses meeting our objective could exhibit unusual physical characteristics, particularly in the conformation of their surfaces. Perspective views of a pair of lenses of an embodiment of the present invention are shown in FIGS. 2A–2D.
Reshef et al. have described very highly curved non-corrective goggle lenses with a spherical surface (radii below 35 mm) and having tapering thickness (U.S. Pat. No. 5,094,520). Applicant has developed also novel prescription lenses, sunlenses and eyewear characterized by steeply curved surfaces (˜16 to 18D) that are approximately spherical and are placed concentric with the centroid of rotation of the eye. These objects are described in detail in Sola International's U.S. Pat. No. 6,142,624, the entire disclosure of which is hereby incorporated by reference. Lenses of this type deviate substantially from conventional, relatively flat lens shapes. However, the overall shape of such lenses is based on generally spherical reference surfaces employed and their optical properties in the oblique field can be sensitive to lens placement errors.
Sola International has developed improved aspheric prescription lenses for use in wrap-around frames, as described in their U.S. Pat. No. 6,361,166 the entire disclosure of which is hereby incorporated by reference. Sola International has developed other novel optical lenses suitable for use in wrap-around or protective eyewear. These lenses are described in U.S. Pat. Nos. 6,334,681 and 6,454,408 to Sola International, the entire disclosures of which are hereby incorporated by reference. These applications describe close fitting prescription shields, visors or dual lens prescription sunglasses whose physical form is achieved by forcing local change in curvature of the Rx lenses, particularly in the forward visual field of the wearer, in order to depart significantly from conventional (quadratic) conicoidal forms and by employing significant shape asymmetry between horizontal and vertical meridians of the lenses. However, these surface forms lack overall global definition, introducing difficulty in optimizing lens appearance and wide-field visual function from the wearer's viewpoint. The lens surface construction is mathematically complex, even for lenses having a simple axial symmetry. Also, the oblique optical errors formed at the limits of a wearer's visual fixation field may be less desirable than those of more classical construction based on standard optical surfaces of quadratic form with or without surface aspheric corrections.
Terminology
There are several technical terms and descriptors used within the following discussion of the present invention that either have specific meaning herein, or that are unfamiliar terms within the field of non-corrective lens design. In the interests of clarity and understanding, we list those terms and their meanings as used herein below. Mathematical terms and meanings follow those found in CRC Concise Encyclopedia of Mathematics, by E. W. Weisstein, Chapman & Hall, New York 1999. Optical terms and principles follow those to found in Optical Society of America Handbook of Optics, Volume I, Part 1, M. Bass (Ed), Second Edition, McGraw Hill, New York 1995 or in The Principles of Ophthalmic Lenses, M. Jalie, Fourth Edition, London 1994.
The term “optical lens element” means, in this application where appropriate in the context of particular embodiments, a finished optical or spectacle lens, a lens blank that requires cutting edging and fitting to a frame assembly, or a light transmitting article formed so as to provide a left and a right lens and being suited to finishing as an integral optical element or shield for non-corrective eyewear.
The term “monocular field of view” means, in this application where appropriate in the context of particular embodiments, a portion of solid angle before a wearer in which the human eye is able to receive and distinguish images. It is generally considered to extend approximately 90° temporally, and up to 60° nasally, 70° inferiorly and 50° superiorly, depending on an individual's facial structure, the illuminance and the stimulus size, duration and color.
The term “binocular field of view” means, in this application where appropriate in the context of particular embodiments, the overlapping region of left and right monocular fields of view, divided centrally by the wearer's medial plane.
The term “version movement” means, in this application where appropriate in the context of particular embodiments, binocular pursuits within an object plane wherein both eyes move equally in the same direction.
The term “vergence movement” means, in this application where appropriate in the context of particular embodiments, binocular pursuits at different distances from the observer wherein both eyes move equally in opposite directions.
The term “visual fixation field” means, in this application where appropriate in the context of particular embodiments, a region on the lens surface defined by a set of points that are the intersection of the lens surface and the wearer's line of sight as he or she fixates on objects in a median plane. This visual field is typically associated with ocular rotations in the order 40 to 50°.
The term “peripheral field of vision” means, in this application where appropriate in the context of particular embodiments, a region on the lens surface defined by a set of points which are the intersection of the lens surface and rays of light entering the wearer's pupil as he or she fixates on objects generally in the direct line of sight. The eyes are typically static, exhibiting only small ocular rotations.
The term “quadratic standard forms” means, in this application where appropriate in the context of particular embodiments, a surface belonging to any of the 17 general standard-form quadratic surfaces and special cases thereof as set forth in the CRC Concise Encyclopedia of Mathematics, by E. W. Weisstein, Chapman & Hall, New York 1999, p. 1485.
The term “standard optical surfaces of quadratic form” means, in this application where appropriate in the context of particular embodiments, any biconvex or plano-convex surface being a section of a cone, cylinder, sphere, spheroid or conicoid belonging to the generic families of ellipsoids or of toroids formed by the rotation of generally conic arcs around an axis that is a surface normal or is parallel to and spaced from a surface tangent. The surface form will be continuous at least to the third derivative and have discernable symmetry with respect to at least one reference normal vector.
The term “axis of symmetry” means, in this application where appropriate in the context of particular embodiments, the normal vector relative to which the surface sheet has at least reflection symmetry and on which the centers of sagittal curvature of individual surface elements are located.
The term “vertex” means, in this application where appropriate in the context of particular embodiments, the point of intersection of a surface and its axis of symmetry. By the term “apex”, we mean the forward-most point on a lens surface as worn.
The term “optical axis” means, in this application where appropriate in the context of particular embodiments, the axis on which the sagittal curvature centers of both surfaces is located. It is formed when the axes of symmetry are collinear. The surface sheet is usually defined in cylindrical polar coordinates (r, □, z) where the origin of coordinates is the surface vertex, the optical axis is the axis Oz and the radial distance r is measured within the surface tangential plane through the surface vertex, the “vertex plane”. The directed distance z(r) from the vertex plane to the surface is known as the surface “sag”. Preferably lenses according to the invention are located before a wearer so that the optical axis of the lens and the wearer's direct line of sight in distance vision are essentially coincident.
The term “optical center” means, in this application where appropriate in the context of particular embodiments, the point where the optical axis intersects the lens front surface. It may be determined in practice as a location where the lens has zero optical prism, while the orientation of the optical axis may be found by identifying the normal vector to a surface tangential plane at that location.
The term “sagittal curvature center” means, in this application where appropriate in the context of particular embodiments, the center of rotational curvature defined by the surface slope in any meridian. It is located to the concave side of the surface at a distance from the vertex given by
  R  =            z      +                        r                      z            ′                          ⁢                                  ⁢        where        ⁢                                  ⁢                  z          ′                      ≡                  ∂        z                    ∂        r            
The term “standard optical reference surface” means, in this application where appropriate in the context of particular embodiments, a quadratic surface, including aspheric correction terms if any, such a surface being characterized by tangential and sagittal surface curvatures changing monotonically without local maxima or minima away from the axis of symmetry.
The term “significant deviation from standard optical reference surface” means, in this application where appropriate in the context of particular embodiments, a surface having quadratic and higher order components, including aspheric correction terms if any, the overall surface being characterized in that at least the tangential curvature or mean curvature exhibits a maximum value at an oblique position along at least one meridian.
The term “significant deviation in surface curvature from a standard optical surface of quadratic form” means, in this application where appropriate in the context of particular embodiments, that the tangential and/or sagittal curvatures of individual surface elements show at first increasing difference for elements away from the axis of symmetry, and thereafter a declining difference more distant from the axis of symmetry.
The term “significant deviation in surface astigmatism from a standard optical surface” means, in this application where appropriate in the context of particular embodiments, that the tangential and sagittal surface curvatures deviate sufficiently to introduce major optical astigmatic distortions to the lens surface.
The term “static prism” means, in this application where appropriate in the context of particular embodiments, the component of prism that is perceived when sampling rays that enter the wearer's pupil as he or she fixates on objects in the straight ahead viewing position and where the eye is static. This prism is typically associated with peripheral visual perception.
The term “rotational prism” means, in this application where appropriate in the context of particular embodiments, the component of prism that is perceived when sampling rays along the wearer's line of sight as he or she rotates the eye. This prism is typically related to ocular rotations in the order 40 to 50 degrees.
The term “sagittal depth” means, in this application where appropriate in the context of particular embodiments, the distance between the surface tangential plane at the front vertex of the lens and the temporal-most edge point of the front surface. By the term “difference in sagittal depth”, we mean the difference between the sagittal depths at the temporal-most edge point of the front surface and at the nasal-most edge point of the front surface.
“Mean Through Power” is the average of the through power in one principal meridian along a given line of sight and the through power in the other principal meridian along that line of sight. “Mean Power Error” (MPE) is the arithmetic mean value of the actual errors in lens through powers in the principal meridians along a given line of sight, compared with the desired refractive correction. “RMS Power Error” (RMSPE) is the root mean squared error of actual lens through powers in the principal meridians along a given line of sight, compared with the desired refractive corrections. The term “substantially zero mean through power” means, in this application where appropriate in the context of particular embodiments, that the mean through power is in the range −0.50D to +0.125D, preferably −0.30D to +0.05D, more preferably within ±0.09D, most preferably within ±0.05D in the visual fixation field of the wearer.
The term “surface Q-value” means, in this application where appropriate in the context of particular embodiments, a measure of the degree to which a curve or a surface may be described as quadratic. It is determined for a curve from the first and second derivatives along the curve length. For a surface, it is determined from the tangential and sagittal curvatures or radii of curvature.
The terms “eccentricity” and “shape factor” mean, in this application where appropriate in the context of particular embodiments, the standard measures of the degree of departure of a conic section from a perfect circular section.
The term “surface curve” in accordance with a preferred embodiment of the present invention means, in this application where appropriate in the context of particular embodiments, a planar curve that has; an axis of symmetry; relatively low curvature at the central portion and relatively higher curvature at the lateral ends; a local maximum of curvature at an intermediate position between the central portion and the lateral ends, and is further characterized in that the normal vectors to the curve at its opposed regions of greatest tangential curvature are inclined angularly with respect to each other.
The term “osculating surfaces” means, in this application where appropriate in the context of particular embodiments, a pair of surfaces that are co-tangential with each other at a closed curve of intersection between them. The surfaces have equal sagittal curvature at their intersection.