Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C7/00—Optical parts
  • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
  • G02C7/04—Contact lenses for the eyes

Definitions

• a new and improved aspheric contact lens made of transparent homogeneous hard plastic lens material and made of transparent homogeneous soft lens material, and of a diameter ranging from 7 to 14 mm, wherein one or both of its surfaces, generally the posterior concave surface, is a novel aspheric surface of revolution with an apical umbilical point at which the derivative of curvature vanishes, said novel surface decreasing continuously and regularly in curvature along a meridian from its apex to its peripheral edge, there being three parameters the combination of which define said novel surface: the first parameter being the apical radius of curvature; the second parameter being apical eccentricity; and the third parameter being collectively one or a combination of several preselected derivatives of eccentricity.
• the apical radius of curvature and apical eccentricity of said novel surface are those of the coaxial osculating conicoid of revolution which osculates the novel surface at its apex, said apex being an umbilical point at which the derivative of curvature vanishes, the instantaneous eccentricity at any given point on said novel surface being quantitatively the same as that of the coaxial conicoid of revolution which osculates said novel surface at the given point and wherein the novel surface and the coaxial osculating conicoid of revolution have, at the given point, a common tangent plane, a common normal to said tangent plane, and identical principal curvatures and principal directions about said common normal.
• said novel surface When said novel surface is used as the posterior concave surface of a contact lens, its apical radius of curvature may lie within the range of from 6.0 to 9.2 mm, and its apical eccentricity may lie within the range of from 0.0 to 2.5, and along a meridian section of said novel surface, from its apex to its peripheral edge the change in instantaneous eccentricity resulting from the derivatives of eccentricity may lie within the range of from 0.00 to 2.00 eccentricity units.
• the apical radius of curvature of the front convex surface of the contact lens of this invention may lie within the range of from 4.5 mm to 15.0 mm and its apical eccentricity may lie within the range of from 0.0 to 2.5 and along a meridian section of said novel surface from its apex to its peripheral edge, the change in instantaneous eccentricity resulting from preselected derivatives of eccentricity may lie within the range of from 0.00 to 2.0 eccentricity units.
• the novel aspheric lens of this invention is designed to provide a concave posterior aspheric surface of revolution which is substantially of the shape of the front surface of a cornea to which the lens is applied, said back surface of the lens combined with the front surface of the lens provides correction for the refractive error of the eye and correction of presbyopia when it exists.
• the novel surface of the contact lens of this invention is the posterior surface of the lens of this invention
• the front convex surface may be spherical, toric, conicoid of revolution, general ellipsoid, or the novel surface.
• the general ellipsoid has a major, a mean, and a minor axis, each of which may be used as the axis of the front surface, which axis is generally coaxial with the axis of the novel surface, but may be tilted for the purpose of introducing prism into the lens.
• the novel surface of the contact lens of this invention is the anterior convex surface
• the posterior concave surface may be spherical, toric, conicoid of revolution, or general ellipsoid about its major axis, or the novel surface.
• the two surfaces may be coaxial or tilted with respect to each other to induce prism into the lens.
• This invention describes a corneal lens in which the concave posterior surface is toroidal, in which the concavity has a given radius in the horizontal meridian and a different radius, generally smaller, in the vertical meridian.
• the posterior concavity is provided with one or more discrete areas which extend out from the generally concave contour.
• the facets or protuberances constitute the only portion of the lens which actually contacts the cornea.
• eccentricity may be expressed in the form of a Taylor series. Using MacLaurin's formula, the eccentricity of modified ellipsoid can be written: where e x given by (3) is defined as the generalized or effective eccentricity.”
• Patent No. 3,227,507 Corneal Contact Lens Having
• the inner concave surface of the contact lenses of the Feinbloom patent has an optic zone area an inscribed sphere of radius r o .
• the spherical optic zone usually varies from 6 to 7.50 mm in diameter.
• the zone of inner surface beyond the central spherical optic zone may be an elliptical torus, or toric ellipsoid, or general ellipsoid, or some variation thereof, depending upon grinding and polishing procedures used.
• Aspheric Corneal Contact Lens Series defines the posterior corneal surfaces of the contact lenses of the lens series disclosed as conicoids of revolution including prolate ellipsoids, paraboloids and hyperboloids of two sheets, and shows the domain of the two parameters which define each lens in the series, apical radius of curvature and eccentricity.
• the aspheric surface of the contact lens of the invention is a conicoid of revolutionas determined by two parameters within a two dimensional domain; apical radii of curvature ranging from 6.50 to 8.50 mm and eccentricity ranging from 0.4 to 1.6, see Figure 1.
• the novel surface of the contact lens of this invention distinguishes from the prior art and in particular from the aforedescribed Volk invention of United States Patent No. 3,482,906 by defining the aspheric surface of the lens of the present invention by at least three predetermined parameters: apical radius of curvature; apical eccentricity; and derivatives of eccentricity, i.e. one or more of the first, second, third, etc.
• FIG. 1 is a schematic representation of the three- dimensional domain or boundary whose coordinates represent the magnitudes of the parameters which define a novel aspheric surface of revolution of a lens of this invention.
• FIGURE 1 is a graph illustrating the two- dimensional domain of the two parameters of the prior art aspheric surface of revolution of the lens of the Volk U.S. Patent No. 3,482,906;
• FIGURE 2 is a graph of the schematic representation of the three-dimensional domain of the three parameters of the novel aspheric surface of revolution of the lens of this invention
• FIGURE 3 is a drawing of a typical conic and its axis XX', showing the focus F and the directrix LL'
• FIGURE 4 is a schematic representation of the novel aspheric surface of revoluation of the lens of the present invention showing a point on a circle of latitude, a common tangent plane at said point, and a common normal to the tangent plane at said point intersecting axis of revolution XX' at an angle ⁇ ;
• FIGURE 5 is an exaggerated schematic representation of a meridian section of the novel aspheric surface of revolution of increasing eccentricity of the lens of this invention including the meridian sections of three coaxial osculating conicoids of revolution osculating the novel surface at three circles of latitude;
• FIGURE 6 is a sketch of meridian sections of two lens surfaces, drawn to scale, showing the relationship between the novel aspheric surface of revolution of the lens of this invention and the aspheric surface of revolution of the lens of the Volk U.S. Patent No.
• arc AAA is the meridian section of the novel aspheric surface of revolution of increasing eccentricity of the lens of this invention and arc EAE is the meridian section of the aspheric surface of revolution of Volk U.S. Patent No. 3,428,906, said two surfaces osculating at point A on common axis of revolution XX';
• FIGURE 7 is an exaggerated schematic representation of a meridian section of the novel aspheric surface of revolution of decreasing eccentricity of the lens of this invention including the meridian section of three coaxial osculating conicoids of revolution osculating the novel surface at three circles of latitude;
• FIGURE 8 is a sketch of meridian sections of two lens surfaces, drawn to scale, showing the relationship between the novel aspheric surface of revolution of the lens of this invention and the aspheric surface of revolution of the lens of the Volk U.S. Patent No. 3,482,906 wherein arc AAA is the meridian section of the novel aspheric surface of revolution of decreasing eccentricity of the lens of this invention and arc EAE is the meridian section of the aspheric surface of revolution of Volk U.S. Patent No. 3,482,906, said two surfaces osculating at point A on common axis of revolution XX';
• FIGURE 9 is a graphic representation similar to FIGURE 2 showing the three parameters of another example of the novel surface of the lens of this invention.
• Eccentricity is a specific mathematical term applied to conies or conicoids of revolution. It defines a specific shape of a conic which is a plane curve, or of a conicoid of revolution which is a solid geometrical figure whose meridian sections are all identical conies.
• eccentricity is defined as the ratio of the distance between a given point on the axis of the conic and a point on the conic, to the distance from the point on the conic and a given line perpendicular to the axis of the conic, the ratio being a constant for all pairs of such distances in a given conic.
• FIGURE 3 is a drawing of a typical conic and its axis XX', showing the focus F of the conic and the directrix LL'.
• Circular arcs AG and P H are drawn with their common center at F.
• Line segment FA is the axial focal radius while line segments FP 1 and FP 2 are focal radii and the line segments AD, P 1 D 1 and P 2 D 2 are the directrix distances corresponding to said focal radii.
• the novel aspheric surface of revolution of the contact lens of this invention is such a surface of revolution, having an apical umbilical point at which the derivative of curvature vanishes. Since the term eccentricity has always been used mathematically with respect to conies or conicoids of revolution, the application of the term eccentricity to the novel aspheric surface of revolution of the contact lens of this invention requires a redefining of the term eccentricity.
• the eccentricity at a given point on the novel surface i.e., the instantaneous eccentricity
• the term osculate is intended to mean that the two surfaces at a given point are in contact and have a common tangent plane,a common normal to the tangent plane at said point, and identical normal principal curvatures about said common normal, said common normal intersecting the common axis of revolution at an angle ⁇ .
• the eccentricity of the novel surface of the contact lens of this invention varies continuously and regularly along a meridian section of the surface.
• eccentricity in any descriptive phrase or term with respect to the novel aspheric surface of revolution of the contact lens of this invention is justified when it is understood that the term eccentricity when applied to a given point on said novel surface of varying eccentricity is still fundamentally applied to the coaxial osculating conicoid of revolution which osculates the novel surface at the given point.
• all meridian sections are identical, and a given point along one meridian section has corresponding points along all meridian sections, so that the locus of all such points is a circle of latitude of the surface, the plane containing said circle of latitude being perpendicular to the axis of revolution XX' of the surface as seen in FIGURE 4 and at a distance x from the apex of the novel surface along axis XX'.
• the coaxial osculating conicoid of revolution which osculates the novel surface at a given point will have a common tangent plane with said novel surface not only at said given point but will also have common tangent planes at all other points along the entire circle of latitude containing said point.
• the common normal to the tangent plane at a given point of osculation will be simply stated as the normal to the osculating surfaces at the given point, and the two osculating surfaces will be simply stated as tangent to each other at the given circle of latitude at which they osculate.
• df/dx is a preselected constant, and is the apical eccentricity, e o , to which the rate of change of eccentricity per unit x, d 2 f/dx 2 , multiplied by the value of x, is added.
• (d 2 f/dx 2 ) is a predetermined value and when multiplied by x, the result is a non-dimensional number.
• the. posterior concave surface of the contact lens is the novel aspheric surface or revolution in which the eccentricity increases along a meridian section from the apex to the periphery.
• the parameters of said novel surface are: 7.5 mm for the apical radius of curvature, hereinafter specified as r apex ; 0.2 for the apical eccentricity, hereinafter specified as e apex ; and +0.4 e units per mm of vertex depth, the first derivative of eccentricity, (d 2 f/dx 2 ), hereinafter defined as rate 1 . Additional derivatives of eccentricity in the polynomial series will be designated as rate 2 , rate 3 , etc.
• the novel aspheric surface of revolution of the contact lens of this invention of continuously and regularly varying eccentricity may be conceived of as formed by a continuum of coaxial osculating conicoids of revolution whose parameters r apex and e apex vary continuously and regularly together, osculating said novel surface in a corresponding continuum of circles of latitude.
• dx is an increment of constant infinitesimal dimension.
• dx 0.000001 mm for example
• vertex depth of the novel surface measured from the apex 0.000001 mm
• vertex depth of the novel surface measured from the apex 1.5 mm
• dx 1.5 mm.
• the apex of the novel surface may be considered a circle of latitude reduced to a point and can be numbered 0.
• the coaxial conicoid of revolution which osculates the novel surface at its apex can then be considered as part of the continuum of coaxial osculating conicoids of revolution whose osculations at the successive circles of latitude delineate the novel surface.
• n 1
• the parameters and associated dimensions of the coaxial osculating conicoid of revolution which osculates the novel surface at its apex are utilized as though they are of the preceding circle of latitude.
• Glossary dx the infinitesimal increment of x by which the value of x is increased in each of the sequence of x values
• n an integral number used both as a subscript and as a prefix, ranging from 1 to 1,500,000 or more than 1,500,000 in the case of surfaces having greater sagital depth.
• a o the apex of the novel surface and that of the coaxial conicoid of revolution which osculates the novel surface at its apex.
• F n the focus of the coaxial conicoid of revolution which osculates the novel surface at the nth circle of latitude.
• f n(ave) the length of the focal radius from the focus F n-1 , to the nth circle of latitude.
• df n the incremental increase in the length of the focal radius f n(ave) from the focus F n-1 to the nth circle of latitude over the length of the focus radius f n-1 from the focus F n-1 , to the (n-1)th circle of latitude.
• y n the y coordinate of the novel surface at the nth circle of latitude.
• C o the center of curvature of the apex of the novel surface and of the coaxial osculating conicoid of revolution which osculates the novel surface at its apex.
• C n the center of curvature of the coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude, the increment of the axial focal radius
• ⁇ x n from the apex A n of the nth coaxial osculating conicoid of revolution to the plane of the nth circle of latitude of the novel surface.
• s n the distance from the plane of the nth circle of latitude to C n .
• d n the distance from A o to C n .
• b n the distance from A o to A n .
• b n is a negative value for the novel surfaces which increase in eccentricity from the apex to the periphery and a positive value for the novel surfaces which decrease in eccentricity from the apex to the periphery.
• h n the distance of the focus F n from the plane of the nth circle of latitude.
• r ap(n) the apical radius of curvature of the nth coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude.
• f ap(n) the axial focal radius of the nth coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude.
• f n the length of the focal radius from F n to a point in the nth circle of latitude.
• ⁇ n the angle which the normal to the novel surface at a point in the nth circle of latitude makes the axis of revolution
• r t(n) the transmeridian radius of curvature of the novel surface and that of its coaxial osculating conicoid of revolution which osculates the novel surface at a point in the nth circle of latitude.
• r m(n) the meridian radius of curvature of the novel surface and that of its coaxial osculating conicoid of revolution which osculates the novel surface at a point in the nth circle of latitude.
• g n the distance of the focus F n of the coaxial osculating conicoid of revolution which osculates the novel surface at.
• the mathematical description of the novel aspheric surface of revolution of the lens of this invention requires a series of calculations by means of a series of equations, to determine the parameters and coordinates of each of the coaxial osculating conicoids of revolution which osculate the novel surface in the sequence of circles of latitude, beginning with the coaxial osculating conicoid of revolution which osculates the novel surface at its apex and proceeding in order through the entire sequence.
• the value of dx is 0.000001 mm and remains constant for all calculations.
• f ap(O) is calculated to be 6.25 mm.
• a focus F serving as origin of a focal radius to a point in the nth circle of latitude can also be used as the origin of a second "focal radius" to a point in the next succeeding circle of latitude providing the angular separation of the two focal radii is infinitesimal. From the practical standpoint, this is achieved by utilizing a very small value for dx in the calculations.
• the first may be considered that of the coaxial osculating conicoid of revolution which osculates the novel surface at a given circle of latitude, while the second, of increased length, is a function of the average eccentricity of the novel surface between the given circle of latitude and the next successive circle of latitude in the sequence of circles of latitude.
• the first of the two focal radii will be designated by means of the subscript n-1, as f n-1
• the second will be designated by the subscript n(ave) as f n(ave) .
• the incremental increase, df n in the length of the focal radius f n(ave) extending from the focus F n-1 to the nth circle of latitude, over the length of the focal radius f n-1 , extending from the focus F n-1 to the
• (n-1)th circle of latitude is determined by means of a modification of Equation 5, which modification takes into account the fact that the eccentricity of the novel surface varies continuously and regularly from the apex to the periphery.
• Averaging the eccentricity between consecutive circles of latitude, including the average eccentricity between that of the apex and that of the first circle of latitude, and rewriting Equation 5 to incorporate the average eccentricity, df n is determined by means of the following equation:
• Equation 11 df 1 is calculated to be 0.00000020000 mm.
• the generalized equation for the determination of the length f n(ave is the following:
• Equation 12 f l(ave) is calculated to be 6.2500002000 mm.
• the coordinate y n of each of the successive circles of latitude is determined by means of the following generalized equation:
• rt(1) is calculated to be 7.5000000400 mm.
• Equation 16 Applying the actual values to Equation 16, r m(1) is calculated to be 7.5000001200 mm.
• r ap(1) is calculated to be 7.5000000000 mm.
• the distance ⁇ x n of the apex A n of the coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude, from the plane of the nth circle of latitude, is determined by means of the quadratic formula:
• Equation 18 At the first circle of latitude, by means of Equation 18, and applying the actual values to said equation, ⁇ x 1 is calculated to be 0.0000010000 mm.
• Equation 20 b 1 is calculated to be - 0.0000000000 mm, the negative sign indicating that A 1 is external to the convex aspect of the novel surface.
• the length of the axial focal radius, f ap(n) , of the coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude is determined by means of Equation 10: . (21)
• f ap(1) is calculated to be 6.2499979166 mm.
• h n f ap(n) - ⁇ x n . (22)
• h 1 is calculated to be 6.2499969167 mm.
• the length of the focal radius, f n measured from the focus F n of the coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude, to the nth circle of latitude, is determined by means of the following equation: (23) Applying the actual values to Equation 23, f 1 is calculated to be 6.2499981167 mm.
• s 1 is calculated to be 7.4999989999 mm.
• d 1 is calculated to be 7.5000000000 mm.
• the distance g n Of the focus F n of the coaxial osculating conicoid of revolution which osculates the novel surface at the nth circle of latitude, from the apex A o of the novel surface, is determined by the following equation:
• Equation 26 g 1 is calculated to be 6.2499979167 mm.
• the determination of the parameters and the locations of the cardinal points of the coaxial osculating conicoid of revolution which osculates the novel surface at the second circle of latitude of cordinates 2dx and y 2 proceeds in the same manner and utilizes the same equations as demonstrated for the determination of the parameters and cardinal points of the coaxial osculating conicoid of revolution which osculates the novel surface at the first circle of latitude.
• the parameters and the location of the cardinal points of the coaxial osculating conicoid of revolution which osculates the novel surface at the first circle of latitude provides the data required for the calculations related to the second circle of latitude.
• Equations 11 through 26 are utilized, with the coefficients and subscripts n all increased by 1.
• n becomes 2 and n-1 becomes 1.
• f (n-1) , r ap(n-1) and ⁇ x (n-1) are those of the coaxial osculating conicoid of revolution which osculates the novel surface at the first cicle of latitude and whose values are 6.2499981167 mm, 7.5000000000 mm and 0.0000010000 mm respectively.
• Equation 11 through 26 At each successive circle of latitude in the sequence of calculations, the value of n is increased by 1 in each of the above equations, Equations 11 through 26.
• FIGURE 5 is an exaggerated schematic representation of a meridian section of the novel surface of increasing eccentricity of the lens of this invention, and includes the meridian sections of three of the coaxial osculating conicoids of revolution which osculate the novel surface at three circles of latitude.
• XX' is the axis of revolution of the novel surface AAA, and of the coaxial osculating conicoids of revolution BBB, CCC, and DDD, which conicoids of revolution osculate the novel surface at circles of latitude 1-1, 2-2, and 3-3 respectively.
• FIGURE 6 drawn to scale, demonstrates the difference in contour between a meridian section of the novel aspheric surface of revolution of the contact lens of this invention of increasing eccentricity whose parameters and coordinates are presented in Table 1, and a meridian section of the coaxial osculating conicoid of revolution which osculates the novel aspheric surface of revolution at its apex, and whose parameters are identical to the r apex and e apex of the novel surface.
• Table 1 a meridian section of the coaxial osculating conicoid of revolution which osculates the novel aspheric surface of revolution at its apex, and whose parameters are identical to the r apex and e apex of the novel surface.
• XX' is the common axis of revolution of the novel surface whose meridian section is AAA and of the coaxial osculating conicoid of revolution which osculates the novel surface at its apex and whose meridian section is EAE.
• the posterior concave surface of the contact lens is the novel surface and the eccentricity decreases along a meridian section from the apex to the periphery.
• the first derivative of eccentricity will be utilized.
• FIGURE 7 is an exaggerated schematic representation of a meridian section of the novel surface of decreasing eccentricity of the lens of this invention, and includes the meridian sections of three of the coaxial osculating conicoids of revolution which osculate the novel surface at three circles of latitude.
• XX' is the axis of revolution of the novel surface AAA, and of the coaxial osculating conicoids of revolution BBB, CCC, and DDD, which conicoids of revolution osculate the novel surface at circles of latitude 1-1, 2-2, and 3-3 respectively.
• FIGURE 8 drawn to scale, demonstrates the difference in contour between a meridian section of the novel aspheric surface of revolution of the contact lens of this invention of decreasing eccentricity whose parameters and coordinates are presented in Table 2, and a meridian section of the coaxial osculating conicoid of revolution which osculates the novel aspheric surface of revolution at its apex, and whose parameters are identical to the r apex and e apex of the novel surface.
• XX' is the common axis of revolution of the novel surface whose meridian section is AAA and of the coaxial osculating conicoid of revolution which osculates the novel surface at its apex and whose meridian section is EAE.
• the posterior concave surface of the contact lens is the novel surface .
• dx 0.000001 mm.
• this third example is depicted graphically in FIGURE 9.
• the novel surface it is desirable for the novel surface to have a small rate of change in eccentricity in the vicinity of the apex of the surface and to have an accelerating increase in the rate of change in eccentricity with increasing distance from the apex.
• e is a small value within the range from 0.000 to 2.500, a value of 0.300 for example, it is desirable for e to increase with increasing x, and where e apex is a large value within the range, a value of 1.350 for example, it is desirable for e to decrease with increasing x.
• the usefulness of the novel surface as the posterior surface of the lens of this invention depends upon the fact that substantially. constant eccentricities may be achieved in the apical area of the novel surface while the peripheral area changes relatively rapidly in eccentricity to enable the novel surface to conform to the complimentary part of the cornea.
• the apical eccentricity should be a small value, generally less than 0.300, and should increase slowly to the edge of the central part of the novel surface which is an area of about 3.5 mm in diameter.
• the eccentricity changes more rapidly and the rate of change increases with increasing distance from the apex of the novel surface, so that the contour of the novel back surface of the lens of this invention approximately matches the contour of the cornea to which the lens is applied.
• the apical eccentricity should be a relatively high value, 1.000 or greater, and the eccentricity should change very little from its apical value to the edge of the central area, which is about 3.5 mm in diameter, and should then decrease in an accelerated manner to the periphery of the novel surface so that the contour of the novel surface of the lens of this invention approximately matches the contour of the cornea to which it is applied.
• the novel aspheric surface of revolution of the lens of this invention can be accurately produced by a numerically controlled lathe with a cutting tool having a fine steel or diamond cutting point, the cutting point passing through a series of points having the x and y coordinates calculated for the surface, as the lens rotates about its axis of revolution.
• the cutting tool point may move linearly from point to point on the surface or may move in small arcs from point to point, using circular interpolation to locate the center of curvature for each small arcuate movement of the cutting point of the tool. Since the point to point movements of the cutting tool point may be very small, linear motion of the cutting tool point is quite satisfactory.
• the apparatus consists of a measuring microscope having a lens mount which provides means for tilting the axis of the novel surface about an axis perpendicular to both the microscope optical axis and the optical axis of said novel surface as well as means for translational movement of the lens, to cause said normal to the novel surface to coincide with said microscope optical axis for measurement of the principal normal radii of curvature, r meridian , r m , and r transmeridian , r t , when said optical axis and said novel surface axis are inclined an angle ⁇ with respect to each other.
• the instantaneous eccentricity is then determined by means of the following equation:

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• 1985
  • 1985-08-08 WO PCT/US1985/001494 patent/WO1987000936A1/en not_active Application Discontinuation
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