USOO7918555B2
`
`(12) United States Patent
`Sverdrup et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 7,918,555 B2
`Apr. 5, 2011
`
`(54) METHODS AND LENSES FOR CORRECTION
`OF CHROMATIC ABERRATION
`
`(75) Inventors: Lawrence H. Sverdrup, Poway, CA
`(US); Sean Sigarlaki, Chula Vista, CA
`(US); Jagdish M. Jethmalani, San
`Diego, CA (US); Andreas W. Dreher,
`Escondido, CA (US); Jeffrey S.
`Ch.
`San Di
`CA (US
`omyn, San Diego, CA (US)
`(73) Assignee: Ophthonix, Inc., Vista, CA (US)
`c
`(*) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 527 days.
`
`(21) Appl. No.: 11/861,196
`
`(22) Filed:
`
`Sep. 25, 2007
`
`(65)
`
`Prior Publication Data
`US 2008/OO88793 A1
`Apr. 17, 2008
`
`Related U.S. Application Data
`(60) Provisional application No. 60/847,175, filed on Sep.
`25, 2006, provisional application No. 60/847,019,
`filed on Sep. 25, 2006.
`
`(51) Int. Cl.
`(2006.01)
`GO2C 702
`(52) U.S. Cl. ....................................................... 351/159
`(58) Field of Classification Search .................. 351/159;
`359/645 646
`See application file for complete search history.
`References Cited
`
`(56)
`
`U.S. PATENT DOCUMENTS
`5,223,862 A * 6/1993 Dasher et al. ................. 351,163
`5,512.371 A
`4/1996 Gupta et al.
`5,684,636 A * 1 1/1997 Chow et al. ................... 359/665
`
`
`
`1/1999 Gupta et al. .................. 351,159
`5,859,685 A *
`3/2004 Dreher
`6,712.466 B2
`9, 2004 Altmann
`6,786,603 B2
`1/2006 Bruns
`6,989,938 B2
`2004/0080710 A1* 4/2004 Wooley et al. ................ 351,159
`2006/0052547 A1
`3/2006 Jethmalani et al.
`FOREIGN PATENT DOCUMENTS
`WO WO 2006/029.264 A2
`3, 2006
`OTHER PUBLICATIONS
`Flaim T. et al., “High-Refractive-Index Polymer Coatings for
`Optoelectronics Applications' SPIE, 2003, Advances in Optical Thin
`Films, paper #20, vol. 5250. (abstract only).
`Hampton L., et al. “Visual Acuity Degradation Resulting from Dis
`persion in Polycarbonate” Journal of the American Optometric Asso
`ciation, 1991, pp. 760-765, vol. 62.
`Keirl A., “Chromatism: The Optical Principles Underpinning Chro
`matic Aberration and its Significance in the Study of Ophthalmic
`Lens Materials' Dispensing Optics, Dec. 2000/Jan. 2001, pp. 1-5.
`Tang C. et al. “Effects of Monochromatic and Chromatic Oblique
`Aberrations on Visual Performance During Spectacle Lens Wear”
`Ophthalmic and Physiological Optics, Jul. 1992, pp. 340-349, vol.
`12.
`Varady G. et al., “Mesopic Spectral Sensitivity Functions Based on
`Visibility and Recognition Contrast Thresholds' Ophthalmic and
`Physiological Optics, 2006, pp. 246-253, vol. 26.
`ysiological Optics
`pp
`WO
`* cited by examiner
`
`Primary Examiner — Joseph Martinez
`Assistant Examiner — James R. Greece
`(74) Att
`Agent, or Fi
`Morrison & Foerster LLP
`Orney, Agent, or Firm — Morrison & Foerster
`
`ABSTRACT
`(57)
`The subject invention provides lenses, and methods for
`designing and manufacturing these lenses, with reduced
`chromatic aberration. Advantageously, these lenses are spe
`cifically designed to correct chromatic aberration that results
`as multichromatic light passes through the lenses.
`
`23 Claims, 7 Drawing Sheets
`
`APPL-1017 / Page 1 of 22
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`
`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 1 of 7
`
`US 7,918,555 B2
`
`--Red
`
`All Wavelengths
`
`White Licht
`
`-Red & Blue
`
`White Light
`
`
`
`Image Plane
`
`Image Plane
`
`Piano-Convex Lens
`
`Achromatic Lens
`
`FIG. 1
`
`Photopic & Scotopic Response
`
`
`
`Wavelength (nm)
`
`FIG. 2
`
`APPL-1017 / Page 2 of 22
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`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 2 of 7
`
`US 7,918,555 B2
`
`
`
`
`
`FIG. 3D
`
`APPL-1017 / Page 3 of 22
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`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 3 of 7
`
`US 7,918,555 B2
`
`
`
`
`
`FIG. 4A
`
`APPL-1017 / Page 4 of 22
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`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 4 of 7
`
`US 7,918,555 B2
`
`Photopic Peak
`(FWHM)
`|
`| -- 16 index- 100% cured zonik
`
`N
`
`YN
`
`O
`
`mu
`
`
`
`
`
`
`
`|
`A
`16800
`16600 V
`1.6400
`16200
`1.6000
`15800
`15600
`15400
`200
`
`
`
`400
`
`600
`
`1000 1200 1400 1600
`800
`Wavelength (nm)
`
`F.G. 5
`
`APPL-1017 / Page 5 of 22
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`

`

`APPL-1017 / Page 6 of 22
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`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 6 of 7
`
`US 7,918,555 B2
`
`
`
`60
`0. -
`INCIDENT ANGLE DEGREES)
`
`90
`
`FG. 7A
`
`FG. 7B
`
`
`
`Optical
`Center
`
`FIG. 8
`
`APPL-1017 / Page 7 of 22
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`

`

`U.S. Patent
`
`Apr. 5, 2011
`
`Sheet 7 of 7
`
`US 7,918,555 B2
`
`Beart
`Steering
`
`Spatial
`Filter
`Aperture
`
`Beam
`Forming
`Aperture
`
`Camera
`
`
`
`
`
`Variable
`Attenuator
`
`FG. 9
`
`Scaling of Laser Measured Dispersion
`With Abbe Number
`
`80
`
`
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`10
`
`vs
`
`a
`
`- -
`
`O
`
`0.005
`
`0.01
`
`0.015
`
`0.02
`
`0.025
`
`0.03
`
`0.035
`
`inverse Abbe Number
`
`F.G. 10
`
`APPL-1017 / Page 8 of 22
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`1.
`METHODS AND LENSES FOR CORRECTION
`OF CHROMATIC ABERRATION
`
`US 7,918,555 B2
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`
`The present application claims the benefit of U.S. Appli
`cation Ser. No. 60/847,175, filed Sep. 25, 2006, and U.S.
`Application Ser. No. 60/847,019, filed Sep. 25, 2006, which
`are hereby incorporated by reference herein in their entirety,
`including any figures, tables, or drawings.
`
`10
`
`BACKGROUND OF INVENTION
`
`15
`
`25
`
`A lens is a device usually formed from a piece of shaped
`glass or plastic that causes light to either converge and con
`centrate, or to diverge. One important use of lenses is as a
`prosthetic for the correction of visual impairments such as
`myopia, hyperopia, presbyopia, and astigmatism. Other uses
`are in imaging systems such as a monocular, binoculars,
`telescope, spotting scope, telescopic gun sight, theodolite,
`microscope, and camera (photographic lens).
`Lenses do not form perfect images; there is always some
`degree of distortion or aberration introduced by the lens that
`causes the image to be an imperfect replica of the object.
`Thus, aberrations result when the optical system misdirects
`some of the objects rays. There are several types of aberra
`tions that can affect image quality. Some aberrations occur
`when electromagnetic radiation of one wavelength is being
`imaged (monochromatic aberrations), and others occur when
`electromagnetic radiation of two or more wavelengths is
`30
`imaged (chromatic aberrations).
`Chromatic aberration is caused by a lens having a different
`refractive index for different wavelengths of light (the disper
`sion of the lens).
`Since the focal length f of a lens is dependent on the
`refractive index n, different wavelengths of light will be
`focused at different locations. Chromatic aberration can be
`both longitudinal, in that different wavelengths are focused at
`a different distance from the lens; and transverse or lateral, in
`that different wavelengths are focused at different positions in
`the focal plane (because the magnification of the lens also
`varies with wavelength). Longitudinal and lateral chromatic
`aberration of a lens is seen as “fringes” of color around the
`image, because each color in the optical spectrum cannot be
`focused at a single common point. For example, eyeglass
`wearers, with strong myopic correction, can experience color
`spreading in the periphery of the eyeglass lenses. Although
`the brain will mask perception of these colored fringes after a
`period of adaptation, their deleterious effect on visual acuity
`remain.
`Because the distortion introduced by aberrations into an
`optical system significantly degrades the quality of the
`images on the image plane of Such system, there are advan
`tages to the reduction of those aberrations. Various techniques
`are often used to reduce the aberrations. One such technique
`involves the use of a wavefront aberrator.
`Wavefront aberrators are particularly useful in eyeglasses
`or contact lenses for use in correcting human eye sight. U.S.
`Pat. No. 6,989,938 describes one such wavefront aberrator
`and methods for manufacturing it. U.S. Pat. No. 6,712.466
`describes eyeglass lenses having a variable index of refrac
`tion.
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`BRIEF SUMMARY
`
`The subject invention provides lenses, and methods for
`designing and manufacturing these lenses, with reduced
`
`65
`
`2
`chromatic aberration. Advantageously, these lenses are spe
`cifically designed to correct chromatic aberration that results
`as multi-chromatic light passes through the lenses.
`Specific embodiments of the subject invention pertain to
`lenses that have a first Sub-lens, a second Sub-lens, and a
`material between the first sub-lens and the second sub-lens,
`where the shape, index of refraction, and Abbe number of the
`materials of the first Sub-lens, second Sub-lens, and material
`between the first sub-lens and the second sub-lens are
`selected to reduce chromatic aberrations of the lenses.
`A further embodiment of the present invention provides
`methods for educating customers about the advantages of the
`lenses of the Subject invention and/or promoting the sale or
`use of these lenses. In this embodiment, promotional materi
`als including, but not limited to, pamphlets, newsletters and
`other written materials describe the deleterious effects of
`chromatic aberration and explain that the lenses of the subject
`invention reduce chromatic aberration, especially compared
`to traditional eyeglass lenses.
`
`BRIEF DESCRIPTION OF DRAWINGS
`
`FIG. 1 shows the use of two lenses to reduce chromatic
`aberration of the resulting lens system.
`FIG. 2 shows the photopic and Scotopic response curves,
`which represent the sensitivity versus wavelength for the
`cones and rods, respectively, in the human retina.
`FIGS. 3A-3D show a schematic of an embodiment of the
`subject invention, where FIG.3A shows a base with negative
`sphere, FIG.3B shows an polymer layer with positive sphere,
`FIG. 3C shows a cover with no power, and FIG. 3D shows an
`embodiment of the invention incorporating the elements of
`FIGS 3A-3C.
`FIGS. 4A-4E show various embodiments of the subject
`invention incorporating a first Sub-lens, a second Sub-lens and
`a material between the first and second sub-lenses.
`FIG. 5 shows ellipsomatic data for a 1.6 index lens and
`polymer material.
`FIG. 6 shows the refractive index spectra of lower titanium
`dioxide content hybrid coatings.
`FIGS. 7A-7B show deviation due to a prism.
`FIG. 8 shows the geometry specifying the angle of inci
`dence.
`FIG. 9 shows a schematic of the experimental setup; the
`beam forming aperture, spatial filteraperture, the test lens and
`the camera are not moved during measurements with the
`various wavelengths.
`FIG.10 shows the laser measured data scales with the Abbe
`number.
`
`DETAILED DESCRIPTION
`
`The subject invention provides wavefront aberrators (in
`cluding lenses for correcting vision) with reduced chromatic
`aberration. Advantageously, these lenses are specifically
`designed to correct chromatic aberration of the lens that
`results as multichromatic light passes through the lenses. The
`Subject invention further provides methods for designing
`these lenses as well as methods for manufacturing them.
`Specific embodiments of the subject invention pertain to
`composite lenses that have a first Sub-lens, a second sub-lens,
`and a material between the first sub-lens and the second
`sub-lens, where the shape, index of refraction, and Abbe
`number of the materials of the first sub-lens, second sub-lens,
`and material between the first sub-lens and the second sub
`lens are selected to increase the overall effective Abbe value
`and reduce chromatic aberrations of the lenses.
`
`APPL-1017 / Page 9 of 22
`APPLE INC. v. COREPHOTONICS LTD.
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`

`

`3
`Chromatic aberration can be addressed in lenses by com
`bining two different materials with differing Abbe numbers.
`One of the materials is made into a positive lens, and the other
`into a negative lens. The powers are not equal, so that the
`overall power is non-zero. The lower power lens preferably
`has the smaller (worse) Abbe number. That way, dispersion in
`the more powerful of the two lenses can be made to counter
`balance the opposite but stronger dispersion in the less pow
`erful lens.
`FIG. 1 illustrates an example of combining two lenses of
`different materials in this manner.
`Mathematically, the power of a lens in diopters P is related
`to the focal length f in meters by the relation
`
`5
`
`10
`
`The Abbe number of an optical material is defined by the
`indices of refraction nat three different wavelengths accord
`ing to
`
`V - '587 on 1
`fi-186.1nn
`fie56.3nn
`
`The equations for an achromatic doublet lens are
`
`P + P = P
`P.
`P.
`- - - - = 0
`v, * v.
`
`15
`
`25
`
`30
`
`35
`
`40
`
`In the above equations the subscript “1” and '2' refer to the
`two types of materials. P is the net power of the overall lens.
`With most available materials, the Abbe number V is always
`positive. Thus, in order to satisfy the second equation above,
`P and P. must have opposite sign. Also, the lens with the
`smaller power must also have a smaller Abbe number. The
`only problem with the equations as given so far, is that the
`conventional Abbe number is not optimized as a description
`of the dispersion for ophthalmic use.
`45
`Referring to FIG. 2, a graph is shown of the photopic and
`Scotopic curves, which represent the sensitivity versus wave
`length for the cones and rods, respectively, in the human
`retina. The scotopic curve is significantly blue-shifted with
`respect to the photopic curve. The photopic peak is located at
`555 nm while the scotopic peak is at 505 nm. The mesopic
`curve, representing vision at dusk or nighttime driving when
`both cones and rods are involved, is a matter of debate and
`perhaps lies somewhere in between.
`For daytime vision, the photopic curve is relevant. The
`ideal analog of the Abbe number relevant to ophthalmic appli
`cations, which will be denoted as the photopic Abbe number
`(V), can be defined as follows:
`
`50
`
`55
`
`n55nm - 1
`V
`Photopic ns, -n
`
`610 - 510
`(56.3 - 486.
`
`60
`
`The index in the numerator is at the photopic peak, and the
`indices in the denominator are the 50% points of the photopic
`curve. The area under the photopic curve between the 50%
`points represents 80% of the total area. The trailing numerical
`
`65
`
`US 7,918,555 B2
`
`4
`factor is to scale the result so that the photopic and conven
`tional Abbevalues have identical value in the case of constant
`dispersion (refractive index varies linearly with wavelength).
`For night vision, the scotopic curve is relevant. The ideal
`analog of the Abbe number relevant to ophthalmic applica
`tions at night time, which will be denoted as the Scotopic
`Abbe number (V), could be defined as follows:
`
`550-455
`n505nm - 1
`Vscotopic -
`n 455 - n550, 656.3 - 486.1
`
`The index in the numerator is at the Scotopic peak, and the
`indices in the denominator are the 50% points of the scotopic
`curve. The area under the scotopic curve between the 50%
`points again represents 80% of the total area.
`For vision at dusk, and nighttime driving, the mesopic
`sensitivity curve is relevant. The appropriate mesopic curve is
`currently an area of active research (see G. Varady, P. Bodrogi.
`“Mesopic spectral sensitivity functions based on visibility
`and recognition thresholds.” Ophthal. Physiol. Opt., Vol 26
`(2006) pp. 246-253). For foveal vision on-axis the photopic
`curve always applies, regardless of lighting level. What has
`been done is to take a linear combination of the photopic and
`Scotopic curves and determine the best mix for various light
`ing levels and tasks. The appropriate formula for the mesopic
`Abbe number can be guessed at, but is not known for arbitrary
`tasks and lighting levels. However, obtaining the lowest net
`dispersion across both the photopic and mesopic range (455
`nim-610 nm) may be optimum. In this case the mesopic Abbe
`number could be defined as:
`
`610 - 455
`n555nm - 1
`Vmesopic =
`n 455 - no.10, 656.3 - 486.1
`
`The index in the numerator is at the photopic peak, and the
`indices in the denominator are the short-wavelength 50%-
`point of the scotopic curve, and the long-wavelength 50%-
`point of the photopic curve. Unless the lenses are specifically
`for very dark conditions, the numerator probably should be
`the photopic peak. But even when designed strictly for
`mesopic vision, foveal vision is always photopic, and it is not
`clear that the numerator should be the index at a bluer wave
`length such as 530 nm, which is the arithmetic mean of the
`Scotopic and photopic peaks.
`The layer of material between the first sub-lens and the
`second sub-lens can be referred to as a polymer layer. The
`polymer material can include the monomer and polymer
`compositions as disclosed in published U.S. Patent Applica
`tion 2006/0052547 (Ser. No. 10/936,030), which is hereby
`incorporated by reference in its entirety. The standard form of
`color correction is to form an achromatic doublet as previ
`ously described and illustrated in FIG.1. However, the color
`correction need not be complete to provide visual benefit.
`Most patients are myopic and require a negative lens, so
`that is the version shown in FIG. 3D. FIG. 3D shows an
`embodiment of the invention incorporating the elements of
`FIGS. 3A-3C, where FIG. 3A shows a base with negative
`sphere, FIG. 3B shows a polymer layer with positive sphere,
`and FIG. 3C shows a cover with no power. For a hyperopic
`patient, an overall positive lens is required and color correc
`tion would require a thinner polymer layer in the center than
`at the edges, the opposite of what is depicted in FIG. 3B.
`In specific embodiments, the Subject composite lenses
`have a polymer layer that is thicker in the center and thinner
`
`APPL-1017 / Page 10 of 22
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`

`

`US 7,918,555 B2
`
`15
`
`5
`at the edges. FIGS. 4A, 4B, and 4C show schematics of
`specific embodiments of lenses in accordance with the inven
`tion. FIGS. 4A, 4B, and 4C show schematics of specific
`embodiments of lenses in accordance with the invention
`where the polymer compensating element is shown as the
`shaded area between a first Sub-lens and a second Sub-lens.
`FIG. 4D shows a lens configuration where the polymer com
`pensation element is positioned only in the middle area of the
`lens to provide chromatic aberration in that area of the com
`10
`posite lens. FIG. 4E shows a composite lens configuration
`where the polymer compensation element has a doughnut
`shape where it is thicker around the periphery of the compos
`ite lens and provides chromatic aberration reduction in that
`area where it is most desired, namely the periphery of the lens.
`In another embodiment of the present invention, polycar
`bonate is used as the sub-lens material for either or both of the
`first and second Sub-lenses to make a composite lens. A
`negative polycarbonate lens has a very low Abbe number
`(~30) and making a negative polycarbonate composite lens
`with a compensating polymer with an Abbe value of about 36
`and a positive power will produce a composite lens with an
`Abbe value greater than 36. Similarly, a positive polycarbon
`ate lens has a very low Abbe number (-30) and making a
`positive polycarbonate composite lens with a compensating
`polymer with an Abbevalue of about 36 and a negative power
`will produce a composite lens with an Abbe value greater than
`36. Similar results are obtained with similar sub-lens materi
`als where the goal is to increase the Abbe number of the
`composite lens.
`In a specific embodiment, lenses have a polymer layer that
`is shaped to combat chromatic aberration in negative lenses as
`typically dispensed to myopic patients. The polymer thick
`ness variation can then be controlled by modifying the cur
`Vatures of the cap and base lenses. Accordingly, by control
`ling the curvatures of the top of the base and the inside of the
`caps, the effect can be optimized for every patient, where
`optimum color correction depends upon the prescription.
`According to embodiments, composite lenses mode have a
`polymer layer that can be thicker in the center and thinner at
`the edges. The following Table 1 shows data for typical 75
`mm Samsung 1.6 lens blanks used for production, in a variety
`of base curves. As illustrated by Table 1, the center thickness
`almost always exceeds the edge thickness. The thickness
`disparity depends upon base curve and is largest for 3-base.
`The 2-base and 4-base have a significant disparity. The 5-base
`has a small disparity and 7-base has at best a small disparity.
`
`6
`The following Tables 2 and 3 present data where the center
`was compared against the edge.
`
`TABLE 2
`
`75 mm Lenses, Polymer layer
`too. Thick in Center
`
`Lens Area
`
`Polymer
`Cap (mm) (mm)
`
`Base (mm)
`
`Tot
`
`Tot Dig
`Caliper
`
`1
`
`2
`
`3
`
`4
`
`Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`
`0.57
`O.S6
`0.55
`O.65
`O48
`0.55
`O.61
`O.S9
`O.62
`O.65
`0.55
`O.S8
`O49
`O.66
`O48
`O.S4
`O.65
`O43
`O.S1
`O.63
`
`O.S8
`O.S2
`O.S3
`O.S4
`O.S1
`O.61
`O.S2
`O.S4
`O.S1
`O.S2
`O.61
`O.S1
`O.S
`O.S4
`O.S1
`O.S9
`O.S2
`O.S1
`O.S
`O.S2
`
`O.39
`O.35
`O.43
`O.26
`O.48
`O.43
`O41
`0.44
`0.44
`O40
`O.S6
`O.S4
`O.65
`0.44
`0.67
`O.S9
`O.47
`O.71
`O.64
`O46
`
`S6
`43
`S1
`45
`47
`59
`54
`57
`57
`57
`72
`63
`.64
`.64
`66
`72
`.64
`.64
`.65
`61
`
`54
`41
`S1
`42
`48
`61
`53
`57
`55
`55
`.71
`.6
`.6
`61
`63
`7
`62
`.64
`63
`63
`
`TABLE 3
`
`70 mm lenses, Polymer too. Thin in Center
`Polymer
`Cap (mm) (mm)
`
`Base (mm)
`
`Tot
`
`Lens Area
`
`5198 Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`5199 Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`52O1 Center
`Edge 1
`Edge 2
`Edge 3
`Edge 4
`
`O.64
`O.66
`O.62
`O.69
`O6
`O.63
`O.S6
`O.68
`0.7
`O.S4
`O.61
`0.57
`O.64
`O.71
`O.S1
`
`O43
`O46
`O49
`O.S2
`O49
`O46
`O.S1
`O48
`O.S
`O.S
`O.47
`O49
`O49
`O.S
`O49
`
`O.47
`O41
`O.38
`O.32
`0.37
`O.47
`O.43
`O.35
`O.31
`O.45
`O.47
`O.45
`O.36
`O.31
`O.48
`
`1.54
`1.53
`1.49
`1.53
`1.46
`1.56
`1.5
`1.51
`1.51
`1.49
`1.55
`1.51
`1.49
`1.52
`148
`
`Tot Dig
`Caliper
`
`1.52
`1.51
`1.47
`1.51
`1.46
`1.53
`1.49
`1.49
`1.5
`1.47
`1.52
`148
`1.47
`1.5
`1.47
`
`In the Table 3 above, the data for lens numbers 5198,5199
`and 5201 (4-base 70mm Samsung 1.6 lens blanks) shows that
`the polymer layers are actually thinner in the center than at the
`edge. This illustrates that various thickness behavior is pos
`sible if perhaps even subtle changes are made in the assembly
`protocol. Optimization of the effect can be accomplished by
`reproducibility in the manufacturing process.
`The data presented So far compares the center thickness to
`four isolated points in the periphery. To determine the varia
`tion of the thickness of the polymer layer LB #18760 (5-base
`curve) was sawed in half through the optical center and the
`sawn edge Smoothed with 320 grit sand paper. The optical
`center was marked on the edge, and every 1 cm along the edge
`from the optical center was also marked. Photographs were
`made of the edge at or near all of the marks. After staining, the
`polymer layer was discernable. A special build with colored
`(tinted) polymer may be used to improve the measurements.
`The polymer thickness was measured at all of the marked
`
`25
`
`30
`
`35
`
`40
`
`45
`
`TABLE 1.
`
`75 mm
`75 mm
`polymer
`polymer
`Thickness Thickness
`(Center)
`(Edge 1)
`
`75 mm
`polymer
`Thickness
`(Edge 2)
`
`75 mm
`75 mm
`polymer
`polymer
`Thickness Thickness
`(Edge 3)
`(Edge 4)
`
`Base
`Curve
`
`2
`2
`3
`3
`4
`4
`5
`5
`7
`7
`
`0.55
`0.57
`O.70
`O.71
`O.S8
`O.S6
`O.SO
`O.S2
`O.S2
`O.SO
`
`OSO
`O48
`OSO
`O.S1
`OSO
`O49
`O49
`O48
`O.47
`OSO
`
`O46
`O.S2
`0.55
`O.S1
`0.44
`O48
`O48
`O48
`O.S1
`O.S4
`
`O40
`O.S1
`O.S2
`O.S4
`O.49
`O.49
`O.49
`O.45
`O.SO
`O.49
`
`OSO
`O.S1
`O.47
`O.S3
`O.S1
`O.S2
`O48
`OSO
`O48
`O.S1
`
`50
`
`55
`
`60
`
`For center-edge comparisons, lens blanks are sawed into
`sections, the polymer is stained and the polymer thickness is
`measured at the edges versus the center under a microscope.
`
`65
`
`APPL-1017 / Page 11 of 22
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`US 7,918,555 B2
`
`7
`locations. The result is presented in Table 4 below. The thick
`ness appears to decrease monotonically and Smoothly from
`the optical center.
`
`TABLE 4
`
`3-cm
`Left
`
`2-cm
`Left
`
`1-cm
`Left
`
`Optical
`Center
`
`1-cm
`Right
`
`2-cm
`Right
`
`3-cm
`Right
`
`442
`
`462
`
`483
`
`488
`
`480
`
`465
`
`439
`
`10
`
`8
`For reference, the refractive index values used are repro
`duced in the following Table 6:
`
`TABLE 6
`
`Wavelength (nm)
`
`1.6 Plastic
`
`455
`505
`510
`550
`555
`610
`
`160928
`1.60206S
`1.6O146
`1.59719
`1.596.72
`1.59225
`
`Polymer
`
`16O231
`1.59273
`1.591.94
`158644
`1.58584
`1.58028
`
`In all cases the polymer Abbe number is worse (smaller)
`than the Abbe number for 1.6 plastic. This can facilitate
`chromatic correction. The power that is optimum in the poly
`mer layer for chromatic correction can be determined by
`routine experimentation using various shapes and thicknesses
`of the polymer layer.
`In specific embodiments, one or more high index materials,
`Such as those including TiO2 nano-particles, can be added to
`the polymer material to further decrease the Abbe number of
`the polymer formulation used as the compensating element.
`The advantage of adding high index materials that further
`reduce the effective Abbe number is that less power is
`required in the polymer layer for a given degree of color
`correction.
`A further embodiment of the present invention provides
`methods for educating customers about the advantages of the
`lenses of the Subject invention and/or promoting the sale or
`use of these lenses. In this embodiment, promotional materi
`als including, but not limited to, pamphlets, newsletters and
`other written materials describe the deleterious effects of
`chromatic aberration and explains that the lenses of the sub
`ject invention reduce chromatic aberration, especially com
`pared to traditional eyeglass lenses.
`General Equations for Chromatic Correction
`In order to completely eliminate chromatic aberration at
`two wavelengths in a lens of power P, the following equations
`need to be satisfied:
`
`Plens = Polymer = P
`Plens . Ppolymer
`--
`Vpolymer
`Viens
`
`are the appropriate versions of the Abbe
`V, and V
`numbers of the 1.6 plastic and the fully cured polymer mate
`rial respectively. The general Solution to these equations is
`
`-P
`Ppolymer = Viens
`( Vpolymer
`
`l
`r)
`Viens
`
`P
`
`Pl =
`
`as (
`
`For a 1-diopter lens using the photopic Abbe numbers
`calculated based upon the ellipsometric data from FIG. 5 (65
`for 1.6 material and 50 for the polymer material), the solution
`becomes
`
`15
`
`Table 4 shows a polymer thickness in LB 18760 along a
`"chord” passing through the optical center—average of three
`separate measurements.
`If color correction effects attributable to the geometry of
`the polymer layer are based on certain base curvatures then
`some lenses may be able to achieve better chromatic aberra
`tion correction than other lenses (2-diopter and a 4-diopter
`composite lens (both 4-base curves) may be different from a
`6-diopter lens (3-base curve)). 3-base curve lenses have the
`most unusual polymer shape according to Table 1.
`The thickness variations are not, however, very large. In the
`previous example the thickness variation was 0.05 mm. Ear
`lier data on Some lens blanks showed at most a 0.1 mm
`25
`thickness variation. New data indicates that 3-base lenses are
`anomalous and have a 0.2 mm thickness variation.
`Two things are necessary for conventional achromatic dou
`blet design. The power of the compensation element must
`have the opposite sign as the main element, and the dispersion
`30
`of the compensating element must be larger (the Abbe num
`ber smaller) than that of the main element. In a specific
`embodiment, the polymer layer, or a material between a first
`Sub-lens and a second Sub-lens, has positive power and can
`correct or partially correct the color in a negative composite
`lens dispensed to a myope, where a composite lens is a lens
`having a first Sub-lens, a second Sub-lens, and a polymer
`material layer between the first sub-lens and the second sub
`lens.
`Ellipsometer data was taken for 1.6 plastic and fully cured
`polymer material that can be used as a compensating element
`described herein and also disclosed in U.S. Pat. Nos. 6,989,
`938, 6,712.466, as well as International Published Applica
`tion No. WO 2006/029264, all of which are hereby incorpo
`rated by reference in their entirety. FIG. 5 shows a plot of the
`ellipsometer data. Clearly, the polymer compensating ele
`ment material has a larger slope and thus greater dispersion
`than 1.6 plastic in the Scotopic and photopic range.
`The polymer material used for the testing was peeled out of
`50
`microscope slides after a flood at 12J/cm. This value is less
`than the standard flood cure of 60J/cm. It should be noted
`that when material is peeled from a glass cell or lens bank,
`stress and strain due to boundary conditions is relieved. It is
`not currently known if this has an effect upon the measure
`mentS.
`The formulas were given earlier for the calculations using
`the photopic and Scotopic Abbe numbers. Using the ellipsom
`eter data from FIG. 5, the following Table 5 gives the results.
`
`35
`
`40
`
`45
`
`55
`
`60
`
`TABLE 5
`
`Material
`
`Photopic Abbe # Mesopic Abbe #
`
`Scotopic Abbe #
`
`Polymer
`1.6 Plastic
`
`50
`65
`
`27
`35
`
`37
`50
`
`65
`
`PZ-3.3D
`
`P-4.3D
`
`APPL-1017 / Page 12 of 22
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`US 7,918,555 B2
`
`9
`To obtain a good degree of color compensation without
`large powers for the individual elements, V
`should be
`Smaller compared to V. This can be accomplished with the
`use of other polymer materials, such as titanium dioxide
`nano-particles, which have relatively poor Abbe values.
`Titanium dioxide nano-particles can be used as a high
`index additive in the polymer formulation. In Tony Flaim,
`Yubao Wang, Ramil Mercado, “High Refractive Index Poly
`mer Coatings for Optoelectronic Applications. SPIE, Vol.
`5250, Advances in Optical Thin Films, paper #20, contained
`in SPIE Vol. CDS106 Optical Systems Design 2003, the data
`shown in FIG. 6 is presented.
`Estimating the refractive index versus wavelength from the
`graph for the lowest concentration of TiO, (35%), which has
`the index closest to 1.6, the following data was obtained.
`
`TABLE 7
`
`Wavelength (nm)
`
`Refractive Index
`
`455
`510
`555
`610
`
`1.6917
`1.67SO
`16688
`1.6596
`
`Using the data shown in Table 7, a photopic Abbe number
`of 43 and a mesopic Abbe number of 21 are obtained. These
`are smaller than the current polymer values (50 and 27 respec
`tively) and so a material based upon titanium dioxide nano
`particles can be useful for optimizing chromatic correction in
`composite lenses in accordance with the Subject invention.
`A table of the photopic and mesopic Abbe numbers for
`previously discussed components is presented below in Table
`8:
`
`TABLE 8
`
`Abbe Numbers
`
`Photopic
`
`Mesopic
`
`V16
`Vpolymer
`VTiO2
`
`65
`50
`43
`
`35
`27
`21
`
`The equations for optimum color correction are then pre
`sented in the following Table 9:
`
`TABLE 9
`
`Filler Material
`
`Photopic
`
`Mesopic
`
`Polymer
`Polymer
`TiO2
`TiO,
`
`Pete = -3.3P
`P = +4.3P
`P2 = -2.0P
`P = +3.OP
`
`Pete = -3.4P
`P = +4.4P
`P2 = -1.5P
`P = +2.5P
`
`The lowest powers are found for titanium dioxide filler and
`mesopic optimization, but even in that case, the component
`powers needed are quite substantial compared to the intended
`power P. All of the “excess' power, however, can be generated
`inside of the lens blank, either at the back of the cover or the
`top of the base. A cosmetic penalty of a thicker lens is,
`however, to be avoided. Otherwise one would be better off to
`use a non-composite lens of higher Abbe value.
`A-2 diopter composite lens is schematically described in
`FIG. 4A at about twice actual size. The lens blank is 50 mm in
`diameterand the center thickness of all three layers is 0.5 mm.
`The base-curve of the base is 5.00, which means that the top
`of the base is supposed to have a radius of curvature of 106
`mm, since base curves powers assume an index of 1.530. In
`
`10
`order for the polymer layer to have a constant thickness of 0.5
`mm, the radius of the convex polymer surface must be 106.5
`mm. In order for the cap to have a constant thickness of 0.5
`mm, the radius of the convex surface of the cap must be 107
`mm. The power of a thin lens in air is given by the formula
`
`10
`
`15
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`1
`
`1
`
`P- (n-1)(-)
`In the above formula, n is the index