Patent Publication Number: US-9885883-B2

Title: Optical element for correcting color blindness

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the U.S. national phase of International Application No. PCT/US2014/013653, filed Jan. 29, 2014, which claims priority to U.S. Provisional Application No. 61/759,260, filed Jan. 31, 2013. The entire contents of each of these applications are incorporated herein by reference. 
    
    
     BACKGROUND 
     Field 
     Some embodiments are related to optical elements for enhancing color discrimination by persons having visual insensitivity between colors, e.g., the correction of colorblindness, which can assist a person or other mammal in distinguishing a first visible color wavelength from a second visible color wavelength. 
     Description of the Related Art 
     Color blindness is generally recognized as a decreased ability to perceive differences between some of the colors that others can distinguish. Several types of colorblindness exist. A protanomalous individual is less sensitive to red light than normal individuals and thus, suffers from a darkening effect of the red end of the spectrum. A deuteranomalous individual possesses a mutated form of the green pigment, which is shifted towards the red end of the spectrum resulting in a reduction in sensitivity to the green area of the spectrum. Similar to the protanomates, deuteranomates are poor at discriminating small differences in hues in the red, orange, yellow, green region of the spectrum. This red-green colorblindness, which is the most common form of the condition, causes many of these hues to appear shifted towards the red end of the color spectrum. Other colorblind individuals are tritanomalous and possess a mutated form of the blue pigment, which causes a shift towards the green area of the spectrum. 
     Several methods have been proposed for the correction of colorblindness in human beings. The contents of each of the references discussed below are hereby incorporated herein by reference in their entirety. Generally, options to correct for lack of visual color discrimination include using differential coloration, filtration, and spectral transmission between concurrently used lenses. Other patents disclose associating color with other visual indicators, e.g., cross hatching, as a manner for correcting visual color deficiencies. 
     SUMMARY 
     Devices described herein may be used to improve a person&#39;s ability to distinguish colors. These devices may be of benefit to both individuals having normal color vision and individuals having an impaired ability to distinguish colors. The present embodiments relate to an optical element useful for enhancing color discrimination by persons having visual insensitivity between colors, e.g., correcting colorblindness, that enhances transmission of one or more desired emissive bandwidths corresponding to a color that a person perceives as difficult to identify or distinguish. The bandwidth can be in the red, yellow, green, or blue region of visible wavelength light. In an embodiment, the optical element can both enhance the transmission of a desired first emissive bandwidth and decrease the transmission of a second emissive bandwidth. For example, a person having colorblindness may be able to perceive a first color, but confuse a second color with the first color. In an embodiment, the optical element can enhance the contrast or intensity between the two colors, increasing their distinction from one another. 
     An embodiment provides an optical element for improving color discernment, such as correcting visual insensitivity between a first visible color wavelength and a second visible color wavelength. In an embodiment, the optical element comprises a substantially transparent matrix material and a luminescent compound dispersed within the substantially transparent matrix material. 
     In some embodiments, the luminescent compound is represented by general formula (1): 
     
       
         
         
             
             
         
       
     
     wherein R 1  and R 2  are selected from optionally substituted diphenylamine, optionally substituted phenylnaphthylamine, optionally substituted carbazolyl, and optionally substituted phenylakylamine, 
     wherein R 3  is a C 1 -C 6  alkyl, 
     wherein R 4  is selected from a C 1 -C 6  alkyl, an ether or a polyether. 
     In an embodiment, the luminescent compound has an emissive wavelength that substantially overlaps with the first visible color wavelength. In an embodiment, the luminescent compound has an absorption wavelength that substantially overlaps with the second visible color wavelength. In an embodiment, the luminescent compound is present in an amount selected to provide a transmittance that is greater than 100% at the first visible wavelength in the optical element. 
     Some embodiments include a device for improving color discernment, such as correcting an impaired ability to distinguish colors comprising: an optical element including a luminescent compound dispersed in a matrix material; wherein the optical element is sufficiently transparent to allow a person to see through the optical element; wherein the luminescent compound absorbs light at an absorption wavelength and emits light at an emission wavelength, wherein a human cone photopigment is substantially more sensitive to the emission wavelength than to the absorption wavelength; and wherein the device is configured so that a person, such as a person with an impaired ability to distinguish colors, can better distinguish the colors by viewing an image or an object comprising the colors through the optical element. 
     Some embodiments include a device for improving ability to distinguish colors comprising: an optical element comprising a luminescent compound, such as a compound of formula 1, dispersed in a matrix material; wherein the optical element is sufficiently transparent to allow a person to see through the optical element; wherein the luminescent compound absorbs light at an absorption wavelength and emits light at an emission wavelength, wherein a human cone photopigment is substantially more sensitive to the emission wavelength than to the absorption wavelength; and wherein the device is configured so that a person, such as a person with normal color vision, can better distinguish the colors by viewing an image or an object comprising the colors through the optical element. 
     Some embodiments include a device for improving color discernment or correcting an impaired ability to distinguish colors, such as a red-green color deficiency, comprising: an optical element including a luminescent compound in a substantially transparent matrix; and wherein the optical element absorbs light in a wavelength range near peak sensitivity for an M human cone photopigment and emits light of a longer wavelength in a wavelength range near peak sensitivity for an L human cone photopigment. 
     Some embodiments include a device for improving color discernment or correcting an impaired ability to distinguish colors, such as a red-green color deficiency, comprising: an optical element comprising a luminescent compound dispersed in a matrix material; the optical element is configured to absorb and emit visible light so that when an object or an image is viewed through the optical element, a first color having a first set of color coordinates is converted to a second color having a second set of color coordinates to aid in distinguishing colors; and the distance between the first set of color coordinates and the second set of color coordinates in the direction normal to a color confusion line nearest to the first set of color coordinates is at least about 0.02 color coordinate units. 
     Some embodiments include a device for improving color discernment or correcting an impaired ability to distinguish colors comprising: an optical element comprising a luminescent compound dispersed in a matrix material; wherein the optical element is sufficiently transparent to allow a person to see through the optical element; wherein the optical element is configured to absorb light of a shorter wavelength and emit light of a longer wavelength, so that a color having a first set of color coordinates is converted to a color having a second set of color coordinates; wherein the distance between the first set of color coordinates and the second set of color coordinates in the direction normal to a color confusion line nearest to the first set of color coordinates is at least about 0.02 color coordinate units; and wherein the device is configured so that a person with an impaired ability to distinguish colors can better distinguish the colors by viewing an image or an object comprising the colors through the optical element. 
     Some embodiments include a device for improving ability to distinguish colors comprising: an optical element comprising a luminescent compound dispersed in a matrix material; the optical element is configured to absorb and emit visible light so that when an object or an image is viewed through the optical element, a first color having a first set of color coordinates is converted to a second color having a second set of color coordinates to aid in distinguishing colors; and the distance between the first set of color coordinates and the second set of color coordinates is at least about 0.02 color coordinate units. 
     Some embodiments include a method for preparing a device for improving ability to distinguish colors comprising: selecting a luminescent compound for use in an optical element configured to convert a color having a first set of color coordinates to a color having a second set of color coordinates by absorption and emission of visible light; wherein the luminescent compound is selected so that the distance between the first set of color coordinates and the second set of color coordinates is at least about 0.02 color coordinate units. 
     Some embodiments include a device for improving the ability to distinguish colors prepared by such a method. 
     Some embodiments include a device for correcting a vision deficiency related to color discernment including an optical element comprising a composition including a polymer, such as a polymer comprising a polyvinyl alcohol or a derivative thereof, and a rhodamine or a rhodamine derivative. 
     Some embodiments include methods for preparing a device for correcting an impaired ability to distinguish colors comprising: selecting a luminescent compound for use in an optical element configured to convert a color having a first set of color coordinates to a color having a second set of color coordinates by absorption and emission of visible light; wherein the luminescent compound is selected so that the distance between the first set of color coordinates and the second set of color coordinates in the direction normal to a color confusion line nearest to the first set of color coordinates is at least about 0.02 color coordinate units. 
     Some embodiments include a device for improving the ability to distinguish colors prepared by such a method. 
     Some embodiments include an ocular lens comprising: an optical element comprising a luminescent compound in a substantially transparent matrix; wherein the device is configured so that optical element modifies a color of an object or image viewed through the optical element by a user to thereby allow the user to better distinguish colors. 
     Some embodiments include an electronic device comprising: an electronic display; an optical element comprising a luminescent compound in a substantially transparent matrix; and a touch screen component coupled to the optical element and the electronic display; wherein the touch screen component comprises: a first conductive layer, a second conductive layer, and a spacer between the first conductive layer and the second conductive layer, wherein the first conductive layer and the second conductive layer are substantially transparent; wherein the device is configured so that contact by a user to the touch screen can cause the first conductive layer to contact the second conductive layer to thereby allow current to flow between the first conductive layer and the second conductive layer; wherein the device is configured so that at least a portion of the light emitted from the display passes through the touch screen component and passes through the optical element; wherein the optical element modifies a color of the light emitted from the display that passes through the optical element. 
     Some embodiments include a device comprising: an optical element comprising a coating, wherein the coating comprises a luminescent compound in a substantially transparent matrix; wherein the device is configured so that the optical element modifies a color of an object or image viewed through the optical element by a user to thereby allow the user to better distinguish colors. 
     Some embodiments include a device for improving color discernment comprising: an optical element comprising a luminescent compound in a substantially transparent matrix; and wherein the optical element has a peak wavelength of visible absorption of about 540 nm to about 550 nm. 
     Some embodiments include a composition comprising a polymer and a rhodamine or a rhodamine derivative, wherein the polymer comprises polyvinyl alcohol or a derivative thereof comprising C 1-6  ester or C 1-6  acetal pendant groups. 
     Some embodiments include a method of correcting an impaired ability to distinguish colors comprising positioning a device or an optical element described herein so that an image or an object may be viewed by an individual having the impaired ability to distinguish colors through the optical element. 
     Some embodiments include a method of improving ability to distinguish colors comprising positioning a device or an optical element describe herein so that an image or an object may be viewed by an individual having normal color vision through the optical element. 
     Generally, the methods and devices described herein may be used to improve ability to distinguish colors by an individual having an impaired ability to distinguish colors and/or by an individual with normal color vision. 
     These and other embodiments are described in greater detail below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic associated with a method for determining the distance between two color coordinates in a direct normal to a color confusion line. 
         FIGS. 2A and 2B  are schematics of some embodiments of a device comprising a touch screen component. 
         FIG. 3  is a schematic of some embodiments of a device comprising a touch screen component. 
         FIG. 4  is a schematic of some embodiments of a device comprising a touch screen component. 
         FIG. 5  is a schematic of some embodiments of a device comprising a touch screen component. 
         FIG. 6  shows the light transmittance spectra for an embodiment of an optical element described herein. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of an optical element can correct visual insensitivity between a first visible color wavelength and a second visible color wavelength. In an embodiment, the optical element corrects visual insensitivity by enhancing the transmission in an emissive bandwidth that corresponds to the first visible color wavelength. The first visible color wavelength can be in the red, orange, yellow, green, or blue region of visible wavelength light. In an embodiment, the first visible color wavelength comprises a wavelength that is in the red bandwidth. In an embodiment, the first visible color wavelength is in the range of about 530 nm to about 800 nm, about 560 nm to about 720 nm, about 580 nm to about 710 nm, about 600 nm to about 700 nm, about 530 nm to about 720 nm, about 540 nm to about 710 nm, or about 550 nm to about 700. In some embodiments, the luminescent compound may provide the enhanced emission in the first visible color wavelength. 
     The second visible color wavelength can be in the red, yellow, orange, green, or blue region of visible wavelength light. In an embodiment, the second visible color wavelength comprises a wavelength that is in the green bandwidth. For example, for individuals suffering from a red-green color deficiency, it would be beneficial to increase the perception to red wavelength light, while optionally decreasing the perception to green wavelength light. In an embodiment, the second visible color wavelength is in the range of about 450 nm to about 600 nm, about 500 nm to about 580 nm, or about 520 nm to about 550 nm. 
     The amount of luminescent compound present in the substantially transparent matrix material to form the optical element can vary. Any amount of luminescent compound that increases the emission of the first visible color wavelength, increases the emission of the second visible color wavelength, further separates the peak emissive wavelength of the first color wavelength from the second color wavelength or both increases and separates the peak emissive wavelengths in the optical element, such that the first visible color wavelength is more easily discerned to a colorblind individual, is suitable. In one embodiment, the luminescent compound is present in an amount selected to provide a transmittance that is greater than 90% at the first visible wavelength in the optical element. This is surprising, particularly if the optical element also comprises a light absorbing dye. 
     The absorbance band of a light absorbing dye may overlap with the emission band of the luminescent compound in this case, resulting in less than 100% transmittance in the green wavelength. In an embodiment, the luminescent compound is present in an amount that provides a transmittance that is greater than 95%, greater than 100%, greater than 101%, greater than 102%, greater than 103%, greater than 104%, or greater than 105%, at the first visible wavelength in the optical element. In an embodiment, the luminescent compound may have an emissive wavelength that substantially overlaps with the first visible color wavelength, and an absorption wavelength that substantially overlaps with the second visible color wavelength 
     The term benzimidazol-2-yl refers to the ring system: 
                         
wherein R A  is selected from the group H, C 1 -C 3  alkyl, optionally substituted aryl, including, but not limited to phenyl and naphthyl
 
     The term 1-(phenylmethyl)benzimidazol-2-yl refers to the ring system: 
     
       
         
         
             
             
         
       
         
         
           
             1-(phenylmethyl)benzimidazol-2-yl 
           
         
       
    
     The term 1-phenylbenzimidazol-2-yl refers to the ring system: 
     
       
         
         
             
             
         
       
     
     1-phenylbenzimidazol-2-yl 
     The term benzoxazol-2-yl refers to the ring system: 
     
       
         
         
             
             
         
       
     
     The term benzthiozol-2-yl refers to the ring system: 
     
       
         
         
             
             
         
       
     
     The term “carbazolyl” refers to the ring system: 
                         
which includes, but is not limited to
 
                         
wherein R B  can be independently selected from H, optionally substituted C 1 -C 6  alkyl, optionally substituted C 1 -C 6 alkylC 6 -C 10 aryl, optionally substituted C 6 -C 10 arylC 1 -C 6 alkyl, optionally substituted C 6 -C 10  aryl, and C 1-3  perfluoroalkyl.
 
     The term “isopropyl” refers to the structure: 
     
       
         
         
             
             
         
       
     
     The term “isobutyl” refers to the structure: 
     
       
         
         
             
             
         
       
     
     The term “phenylcarbazolyl” refers to the ring systems: 
                         
wherein R C  can be independently selected from H, optionally substituted optionally substituted C 1 -C 6  alkyl, optionally substituted C 1 -C 6 alkylC 6 -C 10 aryl, optionally substituted C 6 -C 10  aryl, and C 1-3  perfluoroalkyl.
 
     The term “diphenylamine” refers to the ring system: 
     
       
         
         
             
             
         
       
     
     The term “phenylnaphthylamine” refers to the ring system: 
     
       
         
         
             
             
         
       
     
     The term “phenylnaphthylamine” refers to the ring system: 
                         
wherein R D  can be independently selected from H, optionally substituted C 1 -C 6  alkyl, and C 1-6  perfluoroalkyl. In some embodiments, R D  can be isopropyl and isobutyl
 
     The term 1,3 interphenylene refers to the ring system: 
     
       
         
         
             
             
         
       
     
     The term 1,4 interphenylene refers to the ring system: 
     
       
         
         
             
             
         
       
     
     In one embodiment, the luminescent compound is present in an amount that shifts and further separates the first peak emissive wavelength at least about 1 nm, 2 nm, 5 nm, or 8 nm relative the second peak emissive wavelength. In one embodiment, the luminescent compound is present in an amount that both increases intensity and shifts and further separates the first peak emissive wavelength by at least 1 nm, 2 nm, 5 nm, or 8 nm relative the second peak emissive wavelength. 
     The luminescent compound can be present in the substantially transparent matrix material in an amount in the range of about 0.01% to about 30%, about 0.01% to about 20%, about 0.01% to about 15%, about 1% to about 20%, about 1% to about 15%, about 2% to about 12%, about 5% to about 10%, or about 10% by weight, based upon the weight of the composition, or in any amount in a range bounded by, or between, any of these values. 
     The luminescent dye used in the optical element can vary. Examples of luminescent compounds suitable include those described in U.S. Provisional application, 61/749,225 filed Jan. 5, 2013, which is incorporated by reference in its entirety. In an embodiment, the luminescent compound comprises an optical element for correcting visual insensitivity between a first visible color wavelength and a second visible color wavelength is provided, comprising: a substantially transparent matrix material; and a luminescent compound dispersed within the substantially transparent matrix material, wherein the luminescent compound has an absorbance wavelength that substantially overlaps with the first visible color wavelength, and an emissive wavelength that substantially overlaps with the second visible color wavelength, where the first visible color wavelength is green and the second visible color wavelength is red, wherein the luminescent compound is represented by general formula (1): 
     
       
         
         
             
             
         
       
     
     wherein R 1  and R 2  can be selected from optionally substituted diphenylamine, optionally substituted phenylnaphthylamine, optionally substituted carbazolyl, and optionally substituted phenylakylamine, 
     wherein R 3  can be a C 1 -C 6  alkyl, and 
     wherein R 4  can be selected from a C 1 -C 6  alkyl, an ether or a polyether. 
     In some embodiments, R 1  and R 2  are selected from: 
     
       
         
         
             
             
         
       
     
     In some embodiments, R B  can be selected from C 1 -C 6  alkyl, C 1 -C 6 alkylC 6 -C 10 aryl and optionally substituted C 6 -C 10  aryl. In some embodiments, R B  is an optionally substituted phenyl. In some embodiments, R D  can be independently selected from H, optionally substituted C 1 -C 10  alkyl, and C 1-3  perfluoroalkyl. In some embodiments, R D  is selected from C 1 -C 6  alkyl. In some embodiments, R D  is selected from optionally substituted isopropyl and isobutyl. 
     In some embodiments, R 3  can be an optionally substituted C 1 -C 6  alkyl. In some embodiments, R 3  can be selected from optionally substituted isopropyl and isobutyl. 
     In some embodiments, R 4  can be selected from an optionally substituted C 1 -C 6  alkyl, an ether and a polyether. In some embodiments, the ether can be R 5 —O—R 6 , wherein R 5  and R 6  can be independently selected from C 1 -C 6  alkyl. In some embodiments, R 4  can be selected from: 
     
       
         
         
             
             
         
       
     
     In some embodiments, the luminescent compound can be selected from: 
     
       
         
         
             
             
         
       
       
         
         
             
             
         
       
     
     Unless otherwise indicated, any reference to a compound herein by structure, name, or any other means, includes salts, including zwitterionic forms; alternate solid forms, such as polymorphs, solvates, hydrates, etc.; tautomers; or any other chemical species that may rapidly convert to a compound described herein under conditions in which the compounds are used as described herein. 
     Any structure or name for a compound used herein may refer to any stereoisomer or any mixture of stereoisomers. 
     Unless otherwise indicated, when a compound or chemical structural feature such as alkyl, cycloalkyl, alkoxy, alkoxyalkyl, aryl, arylalkyl, perylene, etc., is referred to as being “optionally substituted,” it includes a feature that has no substituents (i.e. “unsubstituted”), or a feature that is “substituted,” meaning that the feature has one or more substituents. The term “substituent” has the ordinary meaning known to one of ordinary skill in the art, and includes a moiety that replaces one or more hydrogen atoms attached to a parent compound or structural feature. In some embodiments, the substituent may be an ordinary organic moiety known in the art, which may have a molecular weight (e.g. the sum of the atomic masses of the atoms of the substituent) of 15 g/mol to 50 g/mol, 15 g/mol to 100 g/mol, 15 g/mol to 150 g/mol, 15 g/mol to 200 g/mol, 15 g/mol to 300 g/mol, or 15 g/mol to 500 g/mol. In some embodiments, the substituent comprises: 0-30, 0-20, 0-10, or 0-5 carbon atoms; and 0-30, 0-20, 0-10, or 0-5 heteroatoms independently selected from: N, O, S, Si, F, Cl, Br, or I; provided that the substituent comprises at least one atom selected from: C, N, O, S, Si, F, Cl, Br, or I. In some embodiments, a substituent may consist of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 non-hydrogen atoms and any necessary hydrogen atoms. Some non-hydrogen atoms may include C, N, O, S, Si, F, Cl, Br, I, P, etc. 
     Examples of substituents include, but are not limited to, alkyl (including linear, branched, and cycloalkyl), alkenyl (including linear, branched, and cycloalkenyl), alkynyl (including linear, branched, and cyclo alkynyl), heteroalkyl, heteroalkenyl, heteroalkynyl, aryl, heterocyclic substituents (including heteroaryl and heteroalicyclic substituents), hydroxy, protected hydroxy, alkoxy, aryloxy, acyl, acyloxy, alkylcarboxylate, carboxylate, thiol, alkylthio, arylthio, cyano, halo, carbonyl, thiocarbonyl, O-carbamyl, N-carbamyl, O-thiocarbamyl, N-thiocarbamyl, C-amido, N-amido, S-sulfonamido, N-sulfonamido, isocyanato, thiocyanato, isothiocyanato, nitro, silyl, sulfenyl, sulfinyl, sulfonyl, haloalkyl, haloalkoxyl, trihalomethanesulfonyl, trihalomethanesulfonamido, and amino, including mono- and di-substituted amino groups, and the protected derivatives thereof, etc., or a combination thereof. The term “combination thereof” in the previous list indicates that substituents may also include a combination of any of the above substituents, wherein a hydrogen atom of one substituent is replaced by another substituent. For example, substituents may be a combination of alkyl and aryl (e.g. arylalkyl such as CH 2 -phenyl, or heteroarylalkyl such as C 2 H 4 -heteraryl, etc.), alkyl and a heterocyclic substituent (e.g. heterocyclylalkyl), alkyl and alkoxy (e.g. CH 2 OCH 3 ), alkyl and halo (e.g. C 2 H 4 Cl, C 3 H 6 F, etc.), acyl and hydroxyl (e.g. —COCH 2 OH), etc. 
     For convenience, the term “molecular weight” is used with respect to a moiety or part of a molecule to indicate the sum of the atomic masses of the atoms in the moiety or part of a molecule, even though it may not be a complete molecule. “Molecular weight” may also refer to complete molecules. 
     Structures associated with some of the chemical names referred to herein are depicted below. These structures may be unsubstituted, as shown below, or a substituent may independently be in any position normally occupied by a hydrogen atom when the structure is unsubstituted. 
     
       
         
         
             
             
         
       
     
     Unless a point of attachment is indicated by 
                         
attachment may occur at any position normally occupied by a hydrogen atom.
 
     As used herein the term “alkyl” has the broadest meaning generally understood in the art, and may include a moiety composed of carbon and hydrogen containing no double or triple bonds. Alkyl may be linear alkyl, branched alkyl, cycloalkyl, or a combination thereof, and in some embodiments, may contain from one to thirty-five carbon atoms. In some embodiments, alkyl may include C 1-10  linear alkyl, such as methyl (—CH 3 ), ethyl (—CH 2 CH 3 ), n-propyl (—CH 2 CH 2 CH 3 ), n-butyl (—CH 2 CH 2 CH 2 CH 3 ), n-pentyl (—CH 2 CH 2 CH 2 CH 2 CH 3 ), n-hexyl (—CH 2 CH 2 CH 2 CH 2 CH 2 CH 3 ), etc.; C 3-10  branched alkyl, such as C 3 H 7  (e.g. iso-propyl), C 4 H 9  (e.g. branched butyl isomers), C 5 H 11  (e.g. branched pentyl isomers), C 6 H 13  (e.g. branched hexyl isomers), C 7 H 15  (e.g. heptyl isomers), etc.; C 3-10  cycloalkyl, such as C 3 H 5  (e.g. cyclopropyl), C 4 H 7  (e.g. cyclobutyl isomers such as cyclobutyl, methylcyclopropyl, etc.), C 5 H 9  (e.g. cyclopentyl isomers such as cyclopentyl, methylcyclobutyl, dimethylcyclopropyl, etc.) C 6 H 11  (e.g. cyclohexyl isomers), C 7 H 13  (e.g. cycloheptyl isomers), etc.; and the like. In some embodiments, and alkyl group may include methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, isohexyl, isooctyl, 2-ethyl-hexyl, etc. 
     An alkoxy group may also be linear, branched, or cyclic. Some examples of useful alkoxy groups include methoxy, ethoxy, propoxy, and butoxy. An alkoxyalkyl group may also be linear or branched. Some examples of useful alkoxyalkyl groups include methoxymethyl, methoxyethyl, methoxypropyl, ethoxymethyl, ethoxyethyl, ethoxypropyl, propoxymethyl, propoxyethyl, and propoxypropyl. 
     Some examples of useful cycloalkyl groups include cyclopentyl, cyclohexyl, or cyloheptyl. Some examples of useful aryl groups include phenyl, diphenyl, tolyl, naphthyl, phenanthryl, and anthracenyl. Some examples of useful arylalkyl groups include benzyl, phenethyl, diphenylmethyl, trityl, naphthylmethyl, phenanthylmethyl, and anthranylmethyl. 
     Some optionally substituted bistriazolylbenzenes may be represented by Formula 1: 
     In an embodiment, the luminescent compound comprises (Compound 8): 
     
       
         
         
             
             
         
       
     
     An optical element may comprise more than one luminescent compound so that the absorption and emission spectrum of the optical element may be different from that of one of the luminescent compounds. For example, a spectrum of an optical element may be a combination, such as a concentration related sum, of the spectrum of the individual dyes. 
     In some embodiments, the luminescent compound or the optical element may absorb light at an absorption wavelength and emit light at an emission wavelength, wherein a human cone photopigment is substantially more sensitive to the emission wavelength than to the absorption wavelength. For example, the human cone photopigment may be at least about 1.5, about 2, about 3, or about 4 times; and/or up to about 10 times, about 20 times, about 50 times, or about 100 times as sensitive to the emission wavelength as it is to the absorption wavelength. In some embodiments, a human cone photopigment is less sensitive to at least about 50%, at least about 70%, at least about 80%, or at least about 90%; and/or up to about 100%; of the visible light absorbed by the luminescent compound as compared to the visible light emitted by the luminescent compound. 
     Enhanced sensitivity may be with respect to any photopigment, such as a normal human cone middle-wavelength sensitive (M) photopigment, a variant human cone middle-wavelength sensitive (MV) photopigment, a normal human cone long-wavelength sensitive (L) photopigment, variant human cone long-wavelength sensitive (LV) photopigment, or a normal human cone short-wavelength sensitive (S) photopigment, provided that the absorption and emission sensitivities are compared with respect to the same photopigment. 
     In some embodiments, a luminescent feature such as an optical element, a luminescent compound, or a combination of luminescent compounds has a median wavelength of visible absorption, an average wavelength of visible absorption, a peak wavelength of visible absorption, a maximum wavelength of visible absorption, or at least about 20%, about 50%, about 70%, or about 90% of its visible absorption, in a range of about 380 nm to about 450 nm, about 420 nm to about 480 nm, about 510 nm to about 550 nm, about 520 nm to about 540 nm, or about 530 nm to about 550 nm. In some embodiments, a luminescent feature has a median wavelength of visible emission, an average wavelength of visible emission, a peak wavelength of visible emission, a maximum wavelength of visible emission, or at least about 20%, at least about 50%, at least about 70%, or at least about 90% of its visible absorption in a range of about 500 nm to about 600 nm, about 540 nm to about 580 nm, about 550 nm to about 570 nm, or about 560 nm to about 580 nm. 
     A median wavelength of visible absorption is the wavelength at which the number of visible photons absorbed having a longer wavelength than the median wavelength is substantially the same as the number of visible photons absorbed having a shorter wavelength than the median wavelength. A median wavelength of visible emission of is the wavelength at which the number of visible photons emitted having a longer wavelength than the median wavelength is substantially the same as the number of visible photons emitted having a shorter wavelength than the median wavelength. A median wavelength may be visually estimated on a spectrum by choosing a wavelength that divides the area of the visible spectrum into two substantially equal halves. An average wavelength of visible absorption (or visible emission) is the average wavelength of all photons in the visible range. A peak wavelength of visible absorption or visible emission is a peak in the spectrum in the visible range. A maximum wavelength of visible absorption or visible emission is the highest peak wavelength in the visible spectrum. As used herein, the terms “absorption,” “absorb,” or a form of these terms, are used as shorthand for “a median wavelength of visible absorption, an average wavelength of visible absorption, a peak wavelength of visible absorption, a maximum wavelength of visible absorption, or a wavelength range in which at least about 50%, about 80%, or about 90% of visible light absorption occurs.” As used herein, the terms “emission,” “emit,” or a form of these terms are used as shorthand for “a median wavelength of visible emission, an average wavelength of visible emission, a peak wavelength of visible emission, a maximum wavelength of visible emission, or a wavelength range in which at least about 50%, about 80%, or about 90% of visible light emission occurs.” 
     In some embodiments, an optical element may absorb light in a wavelength range near peak sensitivity for an M human cone photopigment, such as a wavelength range where relative sensitivity (Table 4) is at least about 0.9 (e.g. about 510 nm to about 550 nm), about 0.93, about 0.95, about 0.96, about 0.97, about 0.98, about 0.99, or about 1.0; and emit light of a longer wavelength in a wavelength range near peak sensitivity for an L human cone photopigment, such as a wavelength range where relative sensitivity (Table 4) is at least about 0.9 (e.g. about 540 nm to about 580 nm for M human cone photopigments), about 0.93, about 0.95, about 0.96, about 0.97, about 0.98, about 0.99, or about 1.0. An optical element may generally emit at a higher wavelength than it absorbs, such as at a wavelength that is at least about 5 nm, about 10 nm, about 20 nm, or about 30 nm higher. In some embodiments, an optical element may have an absorption that is slightly red-shifted with respect to peak sensitivity for an M human cone photopigment and may have an emission that is slightly blue-shifted with respect to peak sensitivity for an L human cone photopigment. 
     Relative sensitivities of an M, an L, an S, an MV, and an LV human photopigment are listed in Table 4. The relative sensitivities are scaled to a maximum sensitivity of 1.00 for each photopigment. Suitable absorption and emission ranges for an optical element, a luminescent compound, or a combination of luminescent compounds may be derived from any set of values in Table 4. For example, a luminescent compound may absorb in a low sensitivity range for the M photopigment, such as about 384 nm to about 440 nm, about 380 nm to about 410 nm, or any other range defined by any values in Table 4 in these ranges; and may emit in a high sensitivity range for the M photopigment such as about 465 nm to about 585 nm, about 510 nm to about 550 nm, or any other range defined by any values in Table 4 in these ranges. In some embodiments, a luminescent compound may absorb in a low sensitivity range for the L photopigment, such as about 384 nm to about 460 nm, about 380 nm to about 430 nm, or any other range defined by any values in Table 4 in these ranges; and may emit in a high sensitivity range for the L photopigment such as about 495 nm to about 620 nm, about 540 nm to about 580 nm, or any other range defined by any values in Table 4 in these ranges. 
     Suitable ranges for absorption and emission of an optical element, a luminescent compound, or a combination of luminescent compounds may also be derived from the sensitivity values from Table 4. For example, for a given photopigment, an absorption range may correspond to wavelengths with sensitivity values below about 0.15, about 0.2, about 0.25, or about 0.3, and an emission range may correspond to wavelengths with sensitivity values about above about 0.4, about 0.5, about 0.6, about 0.7, about 0.8, about 0.9, or about 1 from Table 4. Ranges derived from Table 4 may include median visible wavelength ranges, average visible wavelength ranges, peak visible wavelength ranges, maximum visible wavelength ranges, etc., or may include ranges within which at least about 50%, about 70%, about 80%, or about 90% of the photons in the visible spectrum are emitted or absorbed. In some embodiments, absorption may correspond to a sensitivity value of at least about 0.5, about 0.6, about 0.7, about 0.8, about 0.9, up to about 1 for an M photopigment. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Relative Sensitivity of Various Photopigments in the Visible Range 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Wavelength (nm) 
                 M 
                 L 
                 S 
                 MV 
                 LV 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 384 
                 0.125 
                 0.123 
                 0.709 
                 0.125 
                 0.123 
               
               
                   
                 385 
                 0.125 
                 0.123 
                 0.724 
                 0.125 
                 0.123 
               
               
                   
                 386 
                 0.125 
                 0.123 
                 0.739 
                 0.125 
                 0.123 
               
               
                   
                 387 
                 0.125 
                 0.123 
                 0.768 
                 0.125 
                 0.123 
               
               
                   
                 388 
                 0.125 
                 0.123 
                 0.788 
                 0.125 
                 0.123 
               
               
                   
                 389 
                 0.125 
                 0.123 
                 0.798 
                 0.125 
                 0.123 
               
               
                   
                 390 
                 0.125 
                 0.123 
                 0.808 
                 0.125 
                 0.123 
               
               
                   
                 391 
                 0.125 
                 0.123 
                 0.818 
                 0.125 
                 0.123 
               
               
                   
                 392 
                 0.125 
                 0.123 
                 0.828 
                 0.125 
                 0.123 
               
               
                   
                 393 
                 0.126 
                 0.123 
                 0.847 
                 0.125 
                 0.123 
               
               
                   
                 394 
                 0.126 
                 0.123 
                 0.867 
                 0.125 
                 0.123 
               
               
                   
                 395 
                 0.126 
                 0.123 
                 0.887 
                 0.125 
                 0.123 
               
               
                   
                 396 
                 0.126 
                 0.123 
                 0.897 
                 0.125 
                 0.123 
               
               
                   
                 397 
                 0.126 
                 0.123 
                 0.906 
                 0.125 
                 0.123 
               
               
                   
                 398 
                 0.126 
                 0.123 
                 0.926 
                 0.125 
                 0.123 
               
               
                   
                 399 
                 0.127 
                 0.123 
                 0.936 
                 0.125 
                 0.123 
               
               
                   
                 400 
                 0.127 
                 0.123 
                 0.946 
                 0.125 
                 0.123 
               
               
                   
                 401 
                 0.127 
                 0.123 
                 0.956 
                 0.126 
                 0.123 
               
               
                   
                 402 
                 0.127 
                 0.123 
                 0.966 
                 0.126 
                 0.123 
               
               
                   
                 403 
                 0.127 
                 0.123 
                 0.978 
                 0.126 
                 0.123 
               
               
                   
                 404 
                 0.127 
                 0.123 
                 0.983 
                 0.126 
                 0.123 
               
               
                   
                 405 
                 0.127 
                 0.123 
                 0.987 
                 0.126 
                 0.123 
               
               
                   
                 406 
                 0.127 
                 0.123 
                 0.990 
                 0.126 
                 0.123 
               
               
                   
                 407 
                 0.127 
                 0.123 
                 0.993 
                 0.127 
                 0.123 
               
               
                   
                 408 
                 0.127 
                 0.123 
                 0.995 
                 0.127 
                 0.123 
               
               
                   
                 409 
                 0.127 
                 0.123 
                 0.997 
                 0.127 
                 0.123 
               
               
                   
                 410 
                 0.127 
                 0.123 
                 0.999 
                 0.127 
                 0.123 
               
               
                   
                 411 
                 0.127 
                 0.123 
                 1.000 
                 0.127 
                 0.123 
               
               
                   
                 412 
                 0.127 
                 0.123 
                 1.000 
                 0.127 
                 0.123 
               
               
                   
                 413 
                 0.128 
                 0.123 
                 1.000 
                 0.127 
                 0.123 
               
               
                   
                 414 
                 0.127 
                 0.123 
                 0.999 
                 0.127 
                 0.123 
               
               
                   
                 415 
                 0.129 
                 0.123 
                 0.998 
                 0.127 
                 0.123 
               
               
                   
                 416 
                 0.131 
                 0.123 
                 0.997 
                 0.127 
                 0.123 
               
               
                   
                 417 
                 0.133 
                 0.123 
                 0.990 
                 0.127 
                 0.123 
               
               
                   
                 418 
                 0.135 
                 0.123 
                 0.988 
                 0.127 
                 0.123 
               
               
                   
                 419 
                 0.137 
                 0.123 
                 0.985 
                 0.127 
                 0.123 
               
               
                   
                 420 
                 0.139 
                 0.123 
                 0.977 
                 0.127 
                 0.123 
               
               
                   
                 421 
                 0.141 
                 0.123 
                 0.966 
                 0.128 
                 0.123 
               
               
                   
                 422 
                 0.143 
                 0.123 
                 0.961 
                 0.127 
                 0.123 
               
               
                   
                 423 
                 0.145 
                 0.123 
                 0.956 
                 0.129 
                 0.126 
               
               
                   
                 424 
                 0.147 
                 0.123 
                 0.946 
                 0.131 
                 0.126 
               
               
                   
                 425 
                 0.149 
                 0.123 
                 0.936 
                 0.133 
                 0.132 
               
               
                   
                 426 
                 0.151 
                 0.123 
                 0.926 
                 0.135 
                 0.133 
               
               
                   
                 427 
                 0.153 
                 0.123 
                 0.916 
                 0.137 
                 0.134 
               
               
                   
                 428 
                 0.155 
                 0.123 
                 0.906 
                 0.139 
                 0.135 
               
               
                   
                 429 
                 0.157 
                 0.123 
                 0.897 
                 0.141 
                 0.136 
               
               
                   
                 430 
                 0.164 
                 0.126 
                 0.887 
                 0.143 
                 0.137 
               
               
                   
                 431 
                 0.166 
                 0.126 
                 0.868 
                 0.145 
                 0.138 
               
               
                   
                 432 
                 0.166 
                 0.132 
                 0.857 
                 0.147 
                 0.139 
               
               
                   
                 433 
                 0.171 
                 0.133 
                 0.845 
                 0.149 
                 0.140 
               
               
                   
                 434 
                 0.176 
                 0.134 
                 0.833 
                 0.151 
                 0.141 
               
               
                   
                 435 
                 0.181 
                 0.135 
                 0.821 
                 0.153 
                 0.142 
               
               
                   
                 436 
                 0.186 
                 0.136 
                 0.808 
                 0.155 
                 0.144 
               
               
                   
                 437 
                 0.191 
                 0.137 
                 0.795 
                 0.157 
                 0.146 
               
               
                   
                 438 
                 0.196 
                 0.138 
                 0.778 
                 0.164 
                 0.148 
               
               
                   
                 439 
                 0.201 
                 0.139 
                 0.768 
                 0.166 
                 0.150 
               
               
                   
                 440 
                 0.206 
                 0.140 
                 0.759 
                 0.166 
                 0.152 
               
               
                   
                 441 
                 0.212 
                 0.141 
                 0.749 
                 0.171 
                 0.154 
               
               
                   
                 442 
                 0.218 
                 0.142 
                 0.729 
                 0.176 
                 0.156 
               
               
                   
                 443 
                 0.224 
                 0.144 
                 0.709 
                 0.181 
                 0.158 
               
               
                   
                 444 
                 0.230 
                 0.146 
                 0.690 
                 0.186 
                 0.160 
               
               
                   
                 445 
                 0.236 
                 0.148 
                 0.675 
                 0.191 
                 0.162 
               
               
                   
                 446 
                 0.242 
                 0.150 
                 0.660 
                 0.196 
                 0.164 
               
               
                   
                 447 
                 0.250 
                 0.152 
                 0.645 
                 0.201 
                 0.166 
               
               
                   
                 448 
                 0.258 
                 0.154 
                 0.631 
                 0.206 
                 0.167 
               
               
                   
                 449 
                 0.266 
                 0.156 
                 0.616 
                 0.212 
                 0.169 
               
               
                   
                 450 
                 0.274 
                 0.158 
                 0.606 
                 0.218 
                 0.171 
               
               
                   
                 451 
                 0.282 
                 0.160 
                 0.591 
                 0.224 
                 0.174 
               
               
                   
                 452 
                 0.290 
                 0.162 
                 0.576 
                 0.230 
                 0.178 
               
               
                   
                 453 
                 0.298 
                 0.164 
                 0.562 
                 0.236 
                 0.182 
               
               
                   
                 454 
                 0.306 
                 0.166 
                 0.547 
                 0.242 
                 0.186 
               
               
                   
                 455 
                 0.314 
                 0.167 
                 0.532 
                 0.250 
                 0.190 
               
               
                   
                 456 
                 0.322 
                 0.169 
                 0.517 
                 0.258 
                 0.194 
               
               
                   
                 457 
                 0.332 
                 0.171 
                 0.502 
                 0.266 
                 0.198 
               
               
                   
                 458 
                 0.340 
                 0.174 
                 0.488 
                 0.274 
                 0.202 
               
               
                   
                 459 
                 0.350 
                 0.178 
                 0.473 
                 0.282 
                 0.206 
               
               
                   
                 460 
                 0.358 
                 0.182 
                 0.458 
                 0.290 
                 0.210 
               
               
                   
                 461 
                 0.368 
                 0.186 
                 0.433 
                 0.298 
                 0.214 
               
               
                   
                 462 
                 0.376 
                 0.190 
                 0.404 
                 0.306 
                 0.218 
               
               
                   
                 463 
                 0.384 
                 0.194 
                 0.384 
                 0.314 
                 0.222 
               
               
                   
                 464 
                 0.392 
                 0.198 
                 0.369 
                 0.322 
                 0.228 
               
               
                   
                 465 
                 0.400 
                 0.202 
                 0.358 
                 0.332 
                 0.233 
               
               
                   
                 466 
                 0.408 
                 0.206 
                 0.346 
                 0.340 
                 0.239 
               
               
                   
                 467 
                 0.416 
                 0.210 
                 0.334 
                 0.350 
                 0.245 
               
               
                   
                 468 
                 0.424 
                 0.214 
                 0.322 
                 0.358 
                 0.251 
               
               
                   
                 469 
                 0.432 
                 0.218 
                 0.305 
                 0.368 
                 0.257 
               
               
                   
                 470 
                 0.440 
                 0.222 
                 0.276 
                 0.376 
                 0.266 
               
               
                   
                 471 
                 0.448 
                 0.228 
                 0.251 
                 0.384 
                 0.275 
               
               
                   
                 472 
                 0.456 
                 0.233 
                 0.239 
                 0.392 
                 0.284 
               
               
                   
                 473 
                 0.464 
                 0.239 
                 0.228 
                 0.400 
                 0.293 
               
               
                   
                 474 
                 0.472 
                 0.245 
                 0.216 
                 0.408 
                 0.300 
               
               
                   
                 475 
                 0.481 
                 0.251 
                 0.204 
                 0.416 
                 0.307 
               
               
                   
                 476 
                 0.490 
                 0.257 
                 0.192 
                 0.424 
                 0.315 
               
               
                   
                 477 
                 0.500 
                 0.266 
                 0.184 
                 0.432 
                 0.320 
               
               
                   
                 478 
                 0.513 
                 0.275 
                 0.176 
                 0.440 
                 0.327 
               
               
                   
                 479 
                 0.525 
                 0.284 
                 0.168 
                 0.448 
                 0.335 
               
               
                   
                 480 
                 0.535 
                 0.293 
                 0.161 
                 0.456 
                 0.342 
               
               
                   
                 481 
                 0.538 
                 0.300 
                 0.153 
                 0.464 
                 0.348 
               
               
                   
                 482 
                 0.551 
                 0.307 
                 0.145 
                 0.472 
                 0.354 
               
               
                   
                 483 
                 0.564 
                 0.315 
                 0.137 
                 0.481 
                 0.363 
               
               
                   
                 484 
                 0.577 
                 0.320 
                 0.129 
                 0.490 
                 0.369 
               
               
                   
                 485 
                 0.590 
                 0.327 
                 0.121 
                 0.500 
                 0.377 
               
               
                   
                 486 
                 0.603 
                 0.335 
                 0.113 
                 0.513 
                 0.385 
               
               
                   
                 487 
                 0.616 
                 0.342 
                 0.105 
                 0.525 
                 0.393 
               
               
                   
                 488 
                 0.629 
                 0.348 
                 0.098 
                 0.535 
                 0.401 
               
               
                   
                 489 
                 0.642 
                 0.354 
                 0.090 
                 0.538 
                 0.409 
               
               
                   
                 490 
                 0.655 
                 0.363 
                 0.082 
                 0.551 
                 0.417 
               
               
                   
                 491 
                 0.668 
                 0.369 
                 0.080 
                 0.564 
                 0.425 
               
               
                   
                 492 
                 0.681 
                 0.377 
                 0.074 
                 0.577 
                 0.433 
               
               
                   
                 493 
                 0.694 
                 0.385 
                 0.070 
                 0.590 
                 0.440 
               
               
                   
                 494 
                 0.707 
                 0.393 
                 0.066 
                 0.603 
                 0.448 
               
               
                   
                 495 
                 0.720 
                 0.401 
                 0.062 
                 0.616 
                 0.456 
               
               
                   
                 496 
                 0.733 
                 0.409 
                 0.058 
                 0.629 
                 0.464 
               
               
                   
                 497 
                 0.746 
                 0.417 
                 0.054 
                 0.642 
                 0.472 
               
               
                   
                 498 
                 0.759 
                 0.425 
                 0.050 
                 0.655 
                 0.480 
               
               
                   
                 499 
                 0.772 
                 0.433 
                 0.046 
                 0.668 
                 0.488 
               
               
                   
                 500 
                 0.785 
                 0.440 
                 0.042 
                 0.681 
                 0.500 
               
               
                   
                 501 
                 0.798 
                 0.448 
                 0.038 
                 0.694 
                 0.515 
               
               
                   
                 502 
                 0.820 
                 0.456 
                 0.034 
                 0.707 
                 0.527 
               
               
                   
                 503 
                 0.840 
                 0.464 
                 0.033 
                 0.720 
                 0.537 
               
               
                   
                 504 
                 0.850 
                 0.472 
                 0.031 
                 0.733 
                 0.550 
               
               
                   
                 505 
                 0.856 
                 0.480 
                 0.029 
                 0.746 
                 0.565 
               
               
                   
                 506 
                 0.867 
                 0.488 
                 0.027 
                 0.759 
                 0.577 
               
               
                   
                 507 
                 0.878 
                 0.500 
                 0.025 
                 0.772 
                 0.590 
               
               
                   
                 508 
                 0.889 
                 0.515 
                 0.023 
                 0.785 
                 0.603 
               
               
                   
                 509 
                 0.899 
                 0.527 
                 0.021 
                 0.798 
                 0.616 
               
               
                   
                 510 
                 0.908 
                 0.537 
                 0.021 
                 0.820 
                 0.629 
               
               
                   
                 511 
                 0.917 
                 0.550 
                 0.021 
                 0.840 
                 0.641 
               
               
                   
                 512 
                 0.926 
                 0.565 
                 0.020 
                 0.850 
                 0.654 
               
               
                   
                 513 
                 0.934 
                 0.577 
                 0.020 
                 0.856 
                 0.667 
               
               
                   
                 514 
                 0.942 
                 0.590 
                 0.020 
                 0.867 
                 0.680 
               
               
                   
                 515 
                 0.949 
                 0.603 
                   
                 0.878 
                 0.693 
               
               
                   
                 516 
                 0.956 
                 0.616 
                   
                 0.889 
                 0.705 
               
               
                   
                 517 
                 0.962 
                 0.629 
                   
                 0.899 
                 0.718 
               
               
                   
                 518 
                 0.968 
                 0.641 
                   
                 0.908 
                 0.731 
               
               
                   
                 519 
                 0.973 
                 0.654 
                   
                 0.917 
                 0.744 
               
               
                   
                 520 
                 0.978 
                 0.667 
                   
                 0.926 
                 0.757 
               
               
                   
                 521 
                 0.983 
                 0.680 
                   
                 0.934 
                 0.769 
               
               
                   
                 522 
                 0.986 
                 0.693 
                   
                 0.942 
                 0.782 
               
               
                   
                 523 
                 0.990 
                 0.705 
                   
                 0.949 
                 0.795 
               
               
                   
                 524 
                 0.993 
                 0.718 
                   
                 0.956 
                 0.801 
               
               
                   
                 525 
                 0.995 
                 0.731 
                   
                 0.962 
                 0.814 
               
               
                   
                 526 
                 0.997 
                 0.744 
                   
                 0.968 
                 0.825 
               
               
                   
                 527 
                 0.999 
                 0.757 
                   
                 0.973 
                 0.835 
               
               
                   
                 528 
                 0.999 
                 0.769 
                   
                 0.978 
                 0.847 
               
               
                   
                 529 
                 1.000 
                 0.782 
                   
                 0.983 
                 0.858 
               
               
                   
                 530 
                 1.000 
                 0.795 
                   
                 0.986 
                 0.869 
               
               
                   
                 531 
                 0.999 
                 0.801 
                   
                 0.990 
                 0.880 
               
               
                   
                 532 
                 0.998 
                 0.814 
                   
                 0.993 
                 0.890 
               
               
                   
                 533 
                 0.997 
                 0.825 
                   
                 0.995 
                 0.900 
               
               
                   
                 534 
                 0.995 
                 0.835 
                   
                 0.997 
                 0.910 
               
               
                   
                 535 
                 0.992 
                 0.847 
                   
                 0.999 
                 0.919 
               
               
                   
                 536 
                 0.989 
                 0.858 
                   
                 0.999 
                 0.927 
               
               
                   
                 537 
                 0.986 
                 0.869 
                   
                 1.000 
                 0.935 
               
               
                   
                 538 
                 0.982 
                 0.880 
                   
                 1.000 
                 0.943 
               
               
                   
                 539 
                 0.977 
                 0.890 
                   
                 0.999 
                 0.950 
               
               
                   
                 540 
                 0.973 
                 0.900 
                   
                 0.998 
                 0.956 
               
               
                   
                 541 
                 0.967 
                 0.910 
                   
                 0.997 
                 0.963 
               
               
                   
                 542 
                 0.961 
                 0.919 
                   
                 0.995 
                 0.968 
               
               
                   
                 543 
                 0.955 
                 0.927 
                   
                 0.992 
                 0.974 
               
               
                   
                 544 
                 0.948 
                 0.935 
                   
                 0.989 
                 0.978 
               
               
                   
                 545 
                 0.941 
                 0.943 
                   
                 0.986 
                 0.983 
               
               
                   
                 546 
                 0.933 
                 0.950 
                   
                 0.982 
                 0.987 
               
               
                   
                 547 
                 0.923 
                 0.956 
                   
                 0.977 
                 0.990 
               
               
                   
                 548 
                 0.912 
                 0.963 
                   
                 0.973 
                 0.993 
               
               
                   
                 549 
                 0.897 
                 0.968 
                   
                 0.967 
                 0.995 
               
               
                   
                 550 
                 0.887 
                 0.974 
                   
                 0.961 
                 0.997 
               
               
                   
                 551 
                 0.877 
                 0.978 
                   
                 0.955 
                 0.999 
               
               
                   
                 552 
                 0.866 
                 0.983 
                   
                 0.948 
                 1.000 
               
               
                   
                 553 
                 0.855 
                 0.987 
                   
                 0.941 
                 1.000 
               
               
                   
                 554 
                 0.843 
                 0.990 
                   
                 0.933 
                 1.000 
               
               
                   
                 555 
                 0.831 
                 0.993 
                   
                 0.923 
                 0.999 
               
               
                   
                 556 
                 0.818 
                 0.995 
                   
                 0.912 
                 0.998 
               
               
                   
                 557 
                 0.805 
                 0.997 
                   
                 0.897 
                 0.997 
               
               
                   
                 558 
                 0.792 
                 0.999 
                   
                 0.887 
                 0.995 
               
               
                   
                 559 
                 0.778 
                 1.000 
                   
                 0.877 
                 0.990 
               
               
                   
                 560 
                 0.771 
                 1.000 
                   
                 0.866 
                 0.986 
               
               
                   
                 561 
                 0.764 
                 1.000 
                   
                 0.855 
                 0.982 
               
               
                   
                 562 
                 0.749 
                 0.999 
                   
                 0.843 
                 0.978 
               
               
                   
                 563 
                 0.734 
                 0.998 
                   
                 0.831 
                 0.973 
               
               
                   
                 564 
                 0.719 
                 0.997 
                   
                 0.818 
                 0.968 
               
               
                   
                 565 
                 0.704 
                 0.995 
                   
                 0.805 
                 0.962 
               
               
                   
                 566 
                 0.688 
                 0.992 
                   
                 0.792 
                 0.956 
               
               
                   
                 567 
                 0.671 
                 0.990 
                   
                 0.778 
                 0.949 
               
               
                   
                 568 
                 0.655 
                 0.986 
                   
                 0.771 
                 0.942 
               
               
                   
                 569 
                 0.640 
                 0.982 
                   
                 0.764 
                 0.934 
               
               
                   
                 570 
                 0.625 
                 0.978 
                   
                 0.749 
                 0.926 
               
               
                   
                 571 
                 0.610 
                 0.973 
                   
                 0.734 
                 0.917 
               
               
                   
                 572 
                 0.595 
                 0.968 
                   
                 0.719 
                 0.908 
               
               
                   
                 573 
                 0.580 
                 0.962 
                   
                 0.704 
                 0.899 
               
               
                   
                 574 
                 0.565 
                 0.956 
                   
                 0.688 
                 0.889 
               
               
                   
                 575 
                 0.550 
                 0.949 
                   
                 0.671 
                 0.879 
               
               
                   
                 576 
                 0.535 
                 0.942 
                   
                 0.655 
                 0.868 
               
               
                   
                 577 
                 0.520 
                 0.934 
                   
                 0.640 
                 0.857 
               
               
                   
                 578 
                 0.505 
                 0.926 
                   
                 0.625 
                 0.845 
               
               
                   
                 579 
                 0.490 
                 0.917 
                   
                 0.610 
                 0.833 
               
               
                   
                 580 
                 0.475 
                 0.908 
                   
                 0.595 
                 0.821 
               
               
                   
                 581 
                 0.460 
                 0.899 
                   
                 0.580 
                 0.808 
               
               
                   
                 582 
                 0.445 
                 0.889 
                   
                 0.565 
                 0.795 
               
               
                   
                 583 
                 0.430 
                 0.879 
                   
                 0.550 
                 0.778 
               
               
                   
                 584 
                 0.415 
                 0.868 
                   
                 0.535 
                 0.768 
               
               
                   
                 585 
                 0.400 
                 0.857 
                   
                 0.520 
                 0.759 
               
               
                   
                 586 
                 0.385 
                 0.845 
                   
                 0.505 
                 0.749 
               
               
                   
                 587 
                 0.370 
                 0.833 
                   
                 0.490 
                 0.729 
               
               
                   
                 588 
                 0.355 
                 0.821 
                   
                 0.475 
                 0.709 
               
               
                   
                 589 
                 0.340 
                 0.808 
                   
                 0.460 
                 0.690 
               
               
                   
                 590 
                 0.328 
                 0.795 
                   
                 0.445 
                 0.675 
               
               
                   
                 591 
                 0.316 
                 0.778 
                   
                 0.430 
                 0.660 
               
               
                   
                 592 
                 0.304 
                 0.768 
                   
                 0.415 
                 0.645 
               
               
                   
                 593 
                 0.292 
                 0.759 
                   
                 0.400 
                 0.631 
               
               
                   
                 594 
                 0.280 
                 0.749 
                   
                 0.385 
                 0.616 
               
               
                   
                 595 
                 0.268 
                 0.739 
                   
                 0.370 
                 0.606 
               
               
                   
                 596 
                 0.256 
                 0.729 
                   
                 0.355 
                 0.591 
               
               
                   
                 597 
                 0.244 
                 0.709 
                   
                 0.340 
                 0.576 
               
               
                   
                 598 
                 0.232 
                 0.690 
                   
                 0.328 
                 0.562 
               
               
                   
                 599 
                 0.220 
                 0.675 
                   
                 0.316 
                 0.547 
               
               
                   
                 600 
                 0.208 
                 0.660 
                   
                 0.304 
                 0.532 
               
               
                   
                 601 
                 0.200 
                 0.645 
                   
                 0.292 
                 0.517 
               
               
                   
                 602 
                 0.192 
                 0.631 
                   
                 0.280 
                 0.502 
               
               
                   
                 603 
                 0.184 
                 0.616 
                   
                 0.268 
                 0.488 
               
               
                   
                 604 
                 0.176 
                 0.606 
                   
                 0.256 
                 0.473 
               
               
                   
                 605 
                 0.170 
                 0.591 
                   
                 0.244 
                 0.458 
               
               
                   
                 606 
                 0.164 
                 0.576 
                   
                 0.232 
                 0.443 
               
               
                   
                 607 
                 0.158 
                 0.562 
                   
                 0.220 
                 0.429 
               
               
                   
                 608 
                 0.152 
                 0.547 
                   
                 0.208 
                 0.414 
               
               
                   
                 609 
                 0.146 
                 0.532 
                   
                 0.200 
                 0.399 
               
               
                   
                 610 
                 0.140 
                 0.517 
                   
                 0.192 
                 0.384 
               
               
                   
                 611 
                 0.134 
                 0.502 
                   
                 0.184 
                 0.369 
               
               
                   
                 612 
                 0.128 
                 0.488 
                   
                 0.176 
                 0.358 
               
               
                   
                 613 
                 0.122 
                 0.473 
                   
                 0.170 
                 0.346 
               
               
                   
                 614 
                 0.116 
                 0.458 
                   
                 0.164 
                 0.334 
               
               
                   
                 615 
                 0.110 
                 0.443 
                   
                 0.158 
                 0.322 
               
               
                   
                 616 
                 0.104 
                 0.429 
                   
                 0.152 
                 0.310 
               
               
                   
                 617 
                 0.098 
                 0.414 
                   
                 0.146 
                 0.299 
               
               
                   
                 618 
                 0.092 
                 0.399 
                   
                 0.140 
                 0.287 
               
               
                   
                 619 
                 0.086 
                 0.384 
                   
                 0.134 
                 0.275 
               
               
                   
                 620 
                 0.080 
                 0.369 
                   
                 0.128 
                 0.263 
               
               
                   
                 621 
                 0.076 
                 0.358 
                   
                 0.122 
                 0.251 
               
               
                   
                 622 
                 0.072 
                 0.346 
                   
                 0.116 
                 0.239 
               
               
                   
                 623 
                 0.068 
                 0.334 
                   
                 0.110 
                 0.228 
               
               
                   
                 624 
                 0.064 
                 0.322 
                   
                 0.104 
                 0.216 
               
               
                   
                 625 
                 0.060 
                 0.310 
                   
                 0.098 
                 0.204 
               
               
                   
                 626 
                 0.056 
                 0.299 
                   
                 0.092 
                 0.192 
               
               
                   
                 627 
                 0.052 
                 0.287 
                   
                 0.086 
                 0.184 
               
               
                   
                 628 
                 0.048 
                 0.275 
                   
                 0.080 
                 0.176 
               
               
                   
                 629 
                 0.044 
                 0.263 
                   
                 0.076 
                 0.168 
               
               
                   
                 630 
                 0.040 
                 0.251 
                   
                 0.072 
                 0.161 
               
               
                   
                 631 
                 0.038 
                 0.239 
                   
                 0.068 
                 0.153 
               
               
                   
                 632 
                 0.036 
                 0.228 
                   
                 0.064 
                 0.145 
               
               
                   
                 633 
                 0.034 
                 0.216 
                   
                 0.060 
                 0.137 
               
               
                   
                 634 
                 0.032 
                 0.204 
                   
                 0.056 
                 0.133 
               
               
                   
                 635 
                 0.030 
                 0.192 
                   
                 0.052 
                 0.129 
               
               
                   
                 636 
                 0.028 
                 0.184 
                   
                 0.048 
                 0.125 
               
               
                   
                 637 
                 0.026 
                 0.176 
                   
                 0.044 
                 0.121 
               
               
                   
                 638 
                 0.024 
                 0.168 
                   
                 0.040 
                 0.117 
               
               
                   
                 639 
                 0.022 
                 0.161 
                   
                 0.038 
                 0.113 
               
               
                   
                 640 
                 0.020 
                 0.153 
                   
                 0.036 
                 0.109 
               
               
                   
                 641 
                 0.018 
                 0.145 
                   
                 0.034 
                 0.105 
               
               
                   
                 642 
                 0.016 
                 0.137 
                   
                 0.032 
                 0.101 
               
               
                   
                 643 
                 0.014 
                 0.129 
                   
                 0.030 
                 0.098 
               
               
                   
                 644 
                 0.014 
                 0.121 
                   
                 0.028 
                 0.093 
               
               
                   
                 645 
                 0.013 
                 0.113 
                   
                 0.026 
                 0.088 
               
               
                   
                 646 
                 0.012 
                 0.105 
                   
                 0.024 
                 0.083 
               
               
                   
                 647 
                 0.012 
                 0.098 
                   
                 0.022 
                 0.078 
               
               
                   
                 648 
                 0.011 
                 0.090 
                   
                 0.020 
                 0.073 
               
               
                   
                 649 
                 0.011 
                 0.082 
                   
                 0.018 
                 0.068 
               
               
                   
                 650 
                 0.010 
                 0.080 
                   
                 0.016 
                 0.063 
               
               
                   
                 651 
                 0.010 
                 0.074 
                   
                 0.014 
                 0.058 
               
               
                   
                 652 
                 0.009 
                 0.070 
                   
                 0.014 
                 0.053 
               
               
                   
                 653 
                 0.009 
                 0.066 
                   
                 0.013 
                 0.052 
               
               
                   
                 654 
                 0.008 
                 0.062 
                   
                 0.012 
                 0.050 
               
               
                   
                 655 
                 0.008 
                 0.058 
                   
                 0.012 
                 0.049 
               
               
                   
                 656 
                 0.007 
                 0.054 
                   
                 0.011 
                 0.047 
               
               
                   
                 657 
                 0.007 
                 0.050 
                   
                 0.011 
                 0.046 
               
               
                   
                 658 
                 0.006 
                 0.046 
                   
                 0.010 
                 0.044 
               
               
                   
                 659 
                 0.006 
                 0.042 
                   
                 0.010 
                 0.043 
               
               
                   
                 660 
                 0.005 
                 0.038 
                   
                 0.009 
                 0.041 
               
               
                   
                 661 
                 0.005 
                 0.034 
                   
                 0.009 
                 0.040 
               
               
                   
                 662 
                 0.004 
                 0.033 
                   
                 0.008 
                 0.038 
               
               
                   
                 663 
                 0.004 
                 0.031 
                   
                 0.008 
                 0.037 
               
               
                   
                 664 
                 0.003 
                 0.029 
                   
                 0.007 
                 0.035 
               
               
                   
                 665 
                 0.003 
                 0.027 
                   
                 0.007 
                 0.034 
               
               
                   
                 666 
                 0.003 
                 0.025 
                   
                 0.006 
                 0.033 
               
               
                   
                 667 
                 0.003 
                 0.023 
                   
                 0.006 
                 0.031 
               
               
                   
                 668 
                 0.003 
                 0.021 
                   
                 0.005 
                 0.030 
               
               
                   
                 669 
                 0.003 
                 0.019 
                   
                 0.005 
                 0.028 
               
               
                   
                 670 
                 0.003 
                 0.017 
                   
                 0.004 
                 0.027 
               
               
                   
                 671 
                 0.003 
                 0.015 
                   
                 0.004 
                 0.025 
               
               
                   
                 672 
                 0.003 
                 0.013 
                   
                 0.003 
                 0.024 
               
               
                   
                 673 
                 0.003 
                 0.011 
                   
                 0.003 
                 0.022 
               
               
                   
                 674 
                 0.003 
                 0.009 
                   
                 0.003 
                 0.021 
               
               
                   
                 675 
                 0.003 
                 0.008 
                   
                 0.003 
                 0.019 
               
               
                   
                   
               
            
           
         
       
     
     In some embodiments, and optical element may absorb at about 530 nm to about 540 nm, about 534 nm to about 537 nm, about 535 nm to about 536 nm, about 545 nm to about 565 nm, about 549 nm to about 562 nm, about 535 nm, about 536 nm, about 549 nm, about 557 nm, or about 562 nm; and may have a transmittance of less than about 90%, about 85%, or about 80% in one of those ranges. 
     In some embodiments, an optical element may absorb at about 540 nm to about 550 nm, about 545 nm to about 550 nm, or about 547 nm; and/or may emit at about 560 nm to about 580 nm, about 565 nm to about 575 nm, or about 569 nm. 
     In some embodiments, an optical element is configured to absorb and emit light, e.g. absorb light of a shorter wavelength and emit light of a longer wavelength, so that a first color having a first set of color coordinates is converted to a second color having a second set of color coordinates. In some embodiments, the distance between the first set of color coordinates and the second set of color coordinates may be at least about 0.005, about 0.01, about 0.02, about 0.03, about 0.04, or about 0.05 color coordinate units. A distance Δ between two sets of color coordinates, (x 1 ,y 1 ) and (x 2 ,y 2 ), may be obtained by the formula:
 
Δ=√{square root over ([ x   2   −x   1 ] 2   +[y   2   −y   1 ] 2 )}
 
     For individuals with an impaired ability to discern colors, the distance between the first set of color coordinates and the second set of color coordinates in the direction normal to a color confusion line nearest to the first set of color coordinates (referred to hereafter as “normal distance”) may be at least about 0.02, about 0.03, about 0.04, or about 0.05 color coordinate units. A “color coordination unit” refers to a distance on a CIE color triangle. CIE (1932).  Commission Internationale de l&#39;Eclairage proceedings,  1931 . Cambridge University Press,  Cambridge. This exemplary standard is known in the art as the 1931 CIE XYZ color space and was set by the International Commission on Illumination. For example, the CIE color (0.332, 345) is 0.332 color coordinate units in distance from the y-axis and 0.345 color coordination units in distance from the x axis. For the purposes of this disclosure, the two color coordinates in a CIE color triangle (x, y) will be referred to as “the x color coordinate” and “the y color coordinate.” 
     For example, Table 5 shows how colors may be converted by an optical element for use with individuals with an impaired ability to discern colors. Some optical elements may convert color A to color A′, and/or may convert color B to color B′. Normal distances may be obtained by subtracting the distance normal to a color confusion line of a first color coordinates from the distance normal to a color confusion line of a second color coordinate. A negative (−) distance value indicates that the point has a lower y value than the color confusion line, and a positive distance value indicates that the point has a higher y value than the color confusion line. The distance between the color coordinates of A and A′ in the direction normal to the color confusion line closest to the color coordinates of A is about 0.0095. The distance between the color coordinates of B and B′ in the direction normal to the color confusion line closest to the coordinates of B is about 0.0133. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                   
                   
                 deuteranopia 
                 distance normal to 
               
               
                 Color 
                 x 
                 y 
                 color confusion line 
                 color confusion line 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 A 
                 0.379 
                 0.486 
                 8 
                 −0.0020 
               
               
                 A′ 
                 0.384 
                 0.468 
                 8 
                 0.0075 
               
               
                 B 
                 0.478 
                 0.414 
                 9 
                 0.0180 
               
               
                 B′ 
                 0.523 
                 0.39 
                 9 
                 0.0313 
               
               
                   
               
            
           
         
       
     
     In some embodiments, the x color coordinate may be about 0.290 to about 0.295, about 0.325 to about 0.335, about 0.330 to about 0.335, about 0.370 to about 0.375, about 0.375 to about 0.385, about 0.380 to about 0.385, about 0.475 to about 0.485, about 0.475 to about 0.480, about 0.51 to about 0.52, about 0.520 to about 0.525, about 0.520 to about 0.523, about 0.56 to about 0.57, about 0.570 to about 0.575, about 0.293, about 0.332, about 0.37, about 0.371, about 0.379, about 0.476, about 0.478, about 0.482, about 0.514, about 0.566, or about 0.573; and/or the y color coordinate may be about 0.34 to about 0.35, about 0.385 to about 0.395, about 0.395 to about 0.400, about 0.41 to about 0.42, about 0.465 to about 0.470, about 0.465 to about 0.475, about 0.48 to about 0.49, about 0.495 to about 0.50, about 0.46 to about 0.47, about 0.344, about 0.345, about 0.39, about 0.398, about 0.463, about 0.468, about 0.47, about 0.486, or about 0.497. 
     In some embodiments, the first set of color coordinates may be about (0.375-0.380, 0.485-0.490), about (0.475-0.480, 0.410-0.415), about (0.330-0.335, 0.340-0.345), about (0.570-0.575, 0.340-0.345), about (0.510-0.515, 0.340-0.344), about (0.480-0.485, 0.388-0.392), about (0.475-0.480, 0.468-0.473), about (0.565-0.570, 0.395-0.400), about (0.290-0.295, 0.495-0.500), about (0.368-0.373, 0.485-0.490), or about (0.370-0.375, 0.460-0.465). 
     In some embodiments, the first set of color coordinates is A or B and/or the second set of color coordinates is A′ or B′. In some embodiments, the first set of color coordinates is one of colors 1-9 in Table 6. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                   
                   
                   
                 deuteranopia 
                 distance normal to 
               
               
                 Color 
                 x 
                 y 
                 color confusion line 
                 color confusion line 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 0.332 
                 0.345 
                 6 
                 −0.0194 
               
               
                 2 
                 0.573 
                 0.344 
                 9 
                 −0.0153 
               
               
                 3 
                 0.514 
                 0.344 
                 8 
                 −0.0069 
               
               
                 4 
                 0.482 
                 0.390 
                 8 
                 0.0041 
               
               
                 5 
                 0.476 
                 0.470 
                 9 
                 0.0021 
               
               
                 6 
                 0.566 
                 0.398 
                 9 
                 0.0171 
               
               
                 7 
                 0.293 
                 0.497 
                 7 
                 0.0120 
               
               
                 8 
                 0.37 
                 0.486 
                 8 
                 −0.0042 
               
               
                 9 
                 0.371 
                 0.463 
                 8 
                 −0.0201 
               
               
                   
               
            
           
         
       
     
     A color confusion line includes any line on a CIE color triangle along which a person with a color blindness condition has difficulty distinguishing colors. Some examples of color confusion lines for deuteranopia are provided in Table 7 and some examples of color confusion lines for protanopia are provided in Table 8. The color confusion lines have a formula y=mx+b, where m is the slope and b is the y-intercept. In some embodiments, the color confusion line nearest to the first set of color coordinates is deuteranopia color confusion line 1, deuteranopia color confusion line 2, deuteranopia color confusion line 3, deuteranopia color confusion line 4, deuteranopia color confusion line 5, deuteranopia color confusion line 6, deuteranopia color confusion line 7, deuteranopia color confusion line 8, or deuteranopia color confusion line 9, as shown in Table 7. In some embodiments, the color confusion line nearest to the first set of color coordinates is protanopia color confusion line 1, protanopia color confusion line 2, protanopia color confusion line 3, protanopia color confusion line 4, protanopia color confusion line 5, protanopia color confusion line 6, protanopia color confusion line 7, protanopia color confusion line 8, protanopia color confusion line 9, or protanopia color confusion line 10, as shown in Table 8. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Slopes (m) and y-intercepts (b) of deuteranopia color confusion lines 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 deutoronopia color confusion line 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 m 
                 −0.4 
                 −0.46 
                 −0.54 
                 −0.63 
                 −0.71 
                 −0.79 
                 −0.87 
                 −0.96 
                 −1.04 
               
               
                 b 
                 0.112 
                 0.207 
                 0.312 
                 0.418 
                 0.527 
                 0.632 
                 0.736 
                 0.847 
                 0.962 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 value of D 
                 0.02 
                 0.019 
                 0.018 
                 0.018 
                 0.017 
                 0.016 
                 0.016 
                 0.015 
                 0.014 
                 0.014 
               
               
                 when b 2  − b 1  is: 
                 0.03 
                 0.028 
                 0.027 
                 0.026 
                 0.025 
                 0.024 
                 0.024 
                 0.023 
                 0.022 
                 0.021 
               
               
                   
                 0.04 
                 0.037 
                 0.036 
                 0.035 
                 0.034 
                 0.033 
                 0.031 
                 0.030 
                 0.029 
                 0.028 
               
               
                   
                 0.05 
                 0.046 
                 0.045 
                 0.044 
                 0.042 
                 0.041 
                 0.039 
                 0.038 
                 0.036 
                 0.035 
               
               
                   
                 0.06 
                 0.056 
                 0.055 
                 0.053 
                 0.051 
                 0.049 
                 0.047 
                 0.045 
                 0.043 
                 0.042 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Slopes (m) and y-intercepts (b) of protanopia color confusion lines 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 protanopia color confusion line 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 M 
                 0.36 
                 0.23 
                 0.08 
                 −0.06 
                 −0.19 
                 −0.32 
                 −0.45 
                 −0.58 
                 −0.71 
                 −0.87 
               
               
                 B 
                 −0.04 
                 0.06 
                 0.18 
                 0.28 
                 0.38 
                 0.48 
                 0.58 
                 0.68 
                 0.78 
                 0.9 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 value of D 
                 0.02 
                 0.019 
                 0.019 
                 0.020 
                 0.020 
                 0.020 
                 0.019 
                 0.018 
                 0.017 
                 0.016 
                 0.015 
               
               
                 when b 2  − b 1  is: 
                 0.03 
                 0.028 
                 0.029 
                 0.030 
                 0.030 
                 0.029 
                 0.029 
                 0.027 
                 0.026 
                 0.024 
                 0.023 
               
               
                   
                 0.04 
                 0.038 
                 0.039 
                 0.040 
                 0.040 
                 0.039 
                 0.038 
                 0.036 
                 0.035 
                 0.033 
                 0.030 
               
               
                   
                 0.05 
                 0.047 
                 0.049 
                 0.050 
                 0.050 
                 0.049 
                 0.048 
                 0.046 
                 0.043 
                 0.041 
                 0.038 
               
               
                   
                 0.06 
                 0.056 
                 0.058 
                 0.060 
                 0.060 
                 0.059 
                 0.057 
                 0.055 
                 0.052 
                 0.049 
                 0.045 
               
               
                   
               
            
           
         
       
     
     While there may be many methods that can be used to determine the distance between two sets of color coordinates in a direction normal to a color confusion line, one method is shown in  FIG. 1 . First line  210  is calculated that incorporates or intersects first set of color coordinates  215  and is parallel to color confusion line  220 . Second line  230  is calculated that incorporates or intersects second set of color coordinates  235  and is parallel to color confusion line  220 . 
     First line  210  and second line  230  have the same slope as the color confusion line. Y-intercept b 1  can be determined from the first set of color coordinates  215 , and y-intercept b 2  can be determined from the second set of color coordinates  235 . For example, if the second set of color coordinates is (x 2 ,y 2 ), the y-intercept b 2  would be:
 
 b   2   =y   2   −mx   2 ,
 
where m is the slope of the color confusion line (and any lines parallel to the color confusion line).
 
     The shortest distance D between first line  210  and second line  230  is equal to the distance between the two sets of color coordinates in a direction normal to the color confusion lines. This distance may be determined using the following formula: 
             D   =           [         b   2     -     b   1             -   1     m     -   m       ]     2     +       [         b   2     -     b   1           -   1     -     m     2   ⁢                   ]     2               
wherein D is the distance between the two parallel lines, or the distance in the direction normal to the color confusion line; b 2  is the y-intercept for the line incorporating second set of color coordinates; b 1  is the y-intercept for the line incorporating first set of color coordinates; and m is the slope of the color confusion line. Tables 2 and 3 show the values of D for some color confusion lines at various values of b 2 -b 1 . The distance may also be estimated by plotting the lines and measuring the distance between the lines. In some embodiments, b 2 -b 1  may be at least about 0.02, about 0.03, about 0.04, about 0.05, or about 0.06.
 
     The optical element can also comprise a light absorbing dye, which can also be dispersed in the substantially transparent matrix material. In an embodiment, a light absorbing dye has an absorption band that substantially overlaps with the second visible color wavelength. The combination of a luminescent compound that emits light at the first visible light wavelength and a light absorbing dye that absorbs light at the second visible light wavelength can help improve distinction between the two colors. For example, a luminescent compound that emits in the green wavelength of visible light used in combination with a light absorbing dye that absorbs red wavelength visible light may improve the ability of a user to distinguish between red and green color hues. 
     A light-absorbing dye may absorb one color, such as red, and is transparent to all other wavelengths of light. A light-absorbing dye may or may not be fluorescent. In an embodiment, a purpose of the light-absorbing dye is to make objects of the same color as the dye&#39;s absorption band appear darker when viewed through the filter. Known light absorbing dyes can be used. In an embodiment, a light absorbing dye comprises a phthalocyanine dye, such as, for example, Epolight 6661 and/or Epolight 6084, both of which are products of Epolin, Inc (Newark, N.J., USA). More than one light absorbing dye can be used. However, the substantial transparency of the optical element should be maintained. 
     An optical element can be manufactured in accordance with known film-forming or lens-forming techniques, as guided by the teachings provided herein. The luminescent compound and/or light absorbing dye can be combined with the substantially transparent matrix material in an appropriate weight ratio. The ingredients can be dissolved in an appropriate solvent, such as toluene, optionally with the use of sonication. The solution can then be spin-coated into a film or onto any substantially transparent substrate. Heating the resulting film to evaporate the solvent provides a corrective optical element, which can be placed between a colorblind person&#39;s eyes and an object that they are viewing to be effective. 
     To enhance the effectiveness of the filter, particularly in low-light settings, some luminescent compounds may have an absorption band(s) that is (are) as narrow as possible. Some luminescent compounds may have a narrow Stokes shift, for example, of less than about 150 nm, or less than about 120 nm. A Stokes shift is the difference (in wavelength or frequency units) between positions of the band maxima of the absorption and emission spectra of the same electronic transition. If, for example, a compound has an absorption peak wavelength of about 485 nm and an emission peak wavelength of about 550 nm, the compound has a Stokes Shift of about 65 nm. 
     In an embodiment, a luminescent compound absorbs from within the UV/blue absorption spectrum and emits within the green emission spectrum, enhancing the perceived emitted green light. In an embodiment, a luminescent compound absorbs from within the green absorption spectrum and emits within the red emission spectrum, enhancing the perceived emitted red light. In an embodiment, a luminescent compound absorbs from within the UV or blue absorption spectrum and emits within the red emission spectrum, enhancing the perceived emitted red light. In some embodiments, the luminescent compound can be a light-absorbing dye. In some embodiments, the light-absorbing dye may absorb color approaching UV or blue light wavelengths, in the range of about 200 to about 450 nm, to increase color contrast and improve color discernment while minimizing fatigue and visual stress associated with prolonged exposure to such short, high energy wavelengths. In an embodiment, this can have the additional effect of protecting the user from undesireable UV radiation. Some undesirable UV wavelengths are classified as mid-range UVB, ranging from about 290 to about 320 nm, and long range UVA, ranging from about 320 to about 400 nm. In some embodiments, UV absorbing materials for use with lenses may be benzophenones and benzotriazoles and their derivatives, described in U.S. Pat. Nos. 8,106,108 and 5,621,052 and incorporated by reference herein. In some embodiments, an optical element may be infiltrated or layered with UV absorbing material. 
     In some embodiments, the luminescent compound has a Stokes shift that is less than about 120 nm, less than about 110 nm, less than about 100 nm, less than about 90 nm, less than about 80 nm, less than 50 nm, less than 30 nm, less than 20 nm, less than 10 nm, about 50 nm to about 120 nm, about 50 nm to about 110 nm, about 50 nm to about 100 nm, about 50 nm to about 90 nm, about 60 nm to about 80 nm, or about 70 nm. 
     In some embodiments the luminescent compound has an anti-Stokes shift, or a blue shift. An anti-Stokes shift can occur through photon upconversion where multiple photons are absorbed or when a photon is absorbed along with thermal energy, and a photon can be emitted of shorter wavelength. This can allow conversion of IR light to a visible wavelength. Conversion of IR to visible light may provide night vision. Luminescent compounds having an anti-Stokes shift may include compounds that contain d and f block elements or fifth and sixth row elements, such as osmium, rhenium, tungsten, gold, yttrium, and gadolinium, and potentially others on the same two rows of the periodic table. In some embodiments a luminescent compound having a blue shift could include yttrium oxysulfide doped with gadolinium oxysulfide. 
     In an embodiment, the luminescent compound has a narrow absorption band. The full width at half maximum (FWHM) is the width of an absorption or emission band in nanometers at the absorption or emission intensity that is half of the maximum absorption or intensity value for the band. In an embodiment, the luminescent compound has an absorption band with a FWHM value that is less than or equal to about 100 nm, less than or equal to about 90 nm, or less than or equal to about 85 nm, less than or equal to about 75 nm when dispersed in said substantially transparent matrix. The absorption peak of the luminescent compound can vary. In an embodiment, the absorption band peak of the luminescent compound is in the range of about 445 nm to about 525 nm, about 445 nm to about 505 nm, about 475 nm to about 490 nm, or about 483 nm. 
     In some embodiments a luminescent compound may have a high quantum yield, along with a maximum emission wavelength at the first visible color wavelength. For example, where the first visible color wavelength is green, a luminescent compound with a maximum emission in the green wavelength may be used. In some embodiments, the luminescent compound has a peak emission at a wavelength in the range of about 450 nm to about 600 nm, about 500 nm to about 580 nm, or about 520 nm to about 560 nm. Upon excitation by visual light, the luminescent compound enhances the emissive intensity within the first color wavelength. In some embodiments, the luminescent compound has a quantum yield that is greater than about 75%, about 80%, about 85%, or about 90%. 
     In some embodiments, the optical element further comprises a light emitting element. The light emitting element can be in optical communication with the luminescent compound to provide an excitation source for the luminescent compound. In an embodiment, the light emitting element comprises a light emitting thin film having a maximum emission peak within the absorption band range of the luminescent compound. The absorption band range includes, but is not limited to about 10 nm to about 20 nm of the absorption peak wavelength and or along the shoulder of the emissive peak spectrum. In an embodiment, the light emitting element comprises an inorganic or organic light emitting diode (LED). Examples of light emitting diodes include inorganic blue emitting LEDs, e.g., made by Nichia (Japan), organic light emitting diodes described in U.S. Patent Application Publication Nos. 2010/0326526 and 2011/0140093, and organic light emitting diodes described in U.S. patent application Ser. No. 13/166,246, the contents of each are hereby incorporated by reference in their entirety. In general, any thin film flexible light emitting element, such as edge-type LED with flexible waveguided thin flexible polymer film, can be used. In some embodiments, the optical element further comprises an optical waveguide in optical communication with the luminescent element and the light emitting element. 
     The optical element described herein is not limited in its form. Preferably, the optical element can be designed such that it can be placed in a known manner between a user&#39;s eye and any object or image to be perceived. In an embodiment, the optical element comprises a film. The film can have varying thickness. In an embodiment, the film is attached to a piece of eyewear. For example, the optical element can comprise a lens. The luminescent compound can be dispersed within the lens material, or it can be dispersed in a film that is attached to the lens material. In an embodiment, the lens comprises a contact lens or an eyeglass lens. A substantially transparent matrix may be composed of any suitable material. 
     Some optical elements may comprise a transparent matrix of polymer and a rhodamine or a rhodamine derivative as a luminescent compound, such as rhodamine 6G, wherein the polymer comprises polyvinyl alcohol or a derivative thereof comprising C 1-6  ester or C 1-6  acetal pendant groups. In some embodiments, a polyvinyl alcohol derivative may comprise repeat unit a, repeat unit b, repeat unit c, or a combination thereof. 
     
       
         
         
             
             
         
       
     
     With respect to repeat unit a, R o  may be H or C 1-5  alkyl, such as CH 3 , C 2 H 5 , C 3 H 7 , C 4 H 9 , C 5 H 11 , C 3 -cycloalkyl, C 4 -cycloalkyl, C 5 -cycloalkyl, etc. In some embodiments, R o  is n-propyl. 
     With respect to repeat unit c, R p  may be H or C 1-5  alkyl, such as CH 3 , C 2 H 5 , C 3 H 7 , C 4 H 9 , C 5 H 11 , C 3 -cycloalkyl, C 4 -cycloalkyl, C 5 -cycloalkyl, etc. In some embodiments, R p  is methyl. 
     In some embodiments, repeat unit a may be about 70% to about 90% or about 80% of the weight of the polymer. 
     In some embodiments, repeat unit b may be about 5% to about 30% or about 17% to about 20% of the weight of the polymer. 
     In some embodiments, repeat unit c may be about 0.01% to about 3% or about 5% of the weight of the polymer. 
     Some compositions may include a poly(vinyl butyral-co-vinyl alcohol-co-vinyl acetate) (PVBAA), CAS No. 27360-07-2, a polymer which includes repeat unit a, repeat unit b, and repeat unit c. In some embodiments the PVBAA has an average molecular weight in a range of about 50,000 g/mol to about 1,000,000 g/mol, about 100,000 g/mol to about 50,000 g/mol, or about 170,000 g/mol to about 250,000 g/mol. Once commercially available PVBAA is available from Sigma-Aldrich (Milwaukee, Wis. #418420), which has an average molecular weight of 170,000-250,000 g/mol, and includes 0-2.5 wt. % acetate, 17.5-20 wt % hydroxyl, and 80 wt % vinyl butyral. 
     Some compositions may be about 1% (w/w) to about 20%, about 2% (w/w) to about 10% (w/w), about 4% (w/w) to about 6% (w/w), or about 5% (w/w) rhodamine 6G, and about 80% (w/w) to about 99% (w/w), about 90% (w/w) to about 99% (w/), about 90% (w/w) to about 95% (w/w), about 94% (w/w) to about 96% (w/w), or about 95% (w/w) PVBAA. Some compositions may be about 5% (w/w) rhodamine 6G and about 95% (w/w) PVBAA. 
     In some embodiments, when the optical element comprises a film, such as a thin film, the thin film can be laminated onto other conventional optical equipment, including, but not limited to eyeglasses, contact lenses, goggles, mirrors, LED screens (cellular telephone screens, IPOD&#39;s, PDA&#39;s, etc.), computer screens and/or windshields. In an embodiment, the substantially transparent matrix material comprises a polycarbonate. 
     In an embodiment, the optical element comprises a substantially transparent matrix material, which can be any material useful in making a film or lens. A “substantially transparent” material is any material that a user can see through. For example, a “substantially transparent” material is capable of transmitting light such that objects or images on the other side of the material can be seen. A “substantially transparent” material can optionally have some degree of shading, and need not be completely transparent. The transparency can be calculated by first measuring the total transmittance with a multi-channel photodetector across the whole visible wavelength range, for example, from about 380 nm to about 780 nm. The transparency percentage can be reported from the arithmetic average of each transmittance percentage value recorded at 1 nm wavelength increments from about 380 nm to about 780 nm. In such an instance, there would be 400 data points used to calculate the average. In an embodiment, the optical element has a transparency that is at least about 70%, about 80%, or about 90%. 
     The substantially transparent matrix material can comprise a composition that includes glass or various types of polymers in various combinations in combination with a luminescent compound. It may be desirable for the material to be non-harmful and robust. In an embodiment, the substantially transparent matrix material comprises a material, including, but not limited to, glass; a thiourethane; PC; allyl diglycol carbonate (such as CR-39); a polyacrylate, such as polyacrylic acid, polyalkacrylic acid (including methacrylic acid), esters of a polyacrylic acid or a polyacrylic acid such as methyl, ethyl, propyl, isopropyl, n-butyl, sec-butyl, isobutyl, t-butyl, pentyl isomers, hexyl isomers, cyclobutyl, cyclopentyl, or cyclohexyl esters, etc., 2-hydroxyethylmethacrylate, and including polyacrylate hydrogels; polyvinylpyrrolidinone; one or more terpolymers of hexafluoroacetone-tetrafluoroethylene-ethylene (HFA/TFE/E terpolymers), PMMA, PVB, ethylene vinyl acetate, ethylene tetrafluoroethylene, a polyimide, a polystyrene, a polyurethane, organosiloxane, a poly(vinyl butyral-co-vinyl alcohol-co-vinyl acetate, and combinations thereof. 
     Some optical elements may comprise a substantially transparent component that is coated with a substrate layer. The substrate layer may be coated with a layer comprising a substantially transparent layer and a luminescent compound dispersed in the transparent layer. A Substrate layer may comprise any suitable polymeric material such as: poly(ethylene teraphthalate) (PET), cellulose triacetate TAC, a thiourethane; a polycarbonate (PC); allyl diglycol carbonate (such as CR-39); a polyacrylate, such as polyacrylic acid, polyalkacrylic acid (including methacrylic acid), esters of a polyacrylic acid or a polyacrylic acid such as methyl, ethyl, propyl, isopropyl, n-butyl, sec-butyl, isobutyl, t-butyl, pentyl isomers, hexyl isomers, cyclobutyl, cyclopentyl, or cyclohexyl esters, etc., 2-hydroxyethylmethacrylate, and including polyacrylate hydrogels; polyvinylpyrrolidinone; one or more terpolymers of hexafluoroacetone-tetrafluoroethylene-ethylene (HFA/TFE/E terpolymers), polymethyl methacrylate (PMMA), a polyvinyl butyral (PVB), ethylene vinyl acetate, ethylene tetrafluoroethylene, a polyimide, a polystyrene, a polyurethane, organosiloxane, a poly(vinyl butyral-co-vinyl alcohol-co-vinyl acetate, and combinations thereof. 
     For devices in the form of eyewear such as glasses or sunglasses, a lens or optical element may be composed of any optically suitable plastic, or they may be composed primarily of glass, or other vitreous material. Included among the suitable optical plastics are thermoplastic synthetic resins, including poly(diethylene glycol bis(allyl carbonate)); polyurethane comprising a diethylene glycol polyol; thiourethane resins from isocyanate and polythiol; acrylates such as polymers of C 1-6  alkyl esters of methacrylic acid (including methyl methacrylate, ethyl methacrylate, propyl methacrylate, butyl methacrylate, etc.), C 1-6  alkyl esters of acrylic acid (including methyl acrylate, ethyl acrylate, propyl acrylate, butyl acrylate, etc.), and related acrylic resins; polystyrenes, including polystyrene homopolymers, as well as copolymers of styrene and acrylonitrite, polybutadiene-modified polystyrene, etc.; polycarbonates; vinyl resins such as polyethylene, polyvinyl chloride, polyvinyl acetate, polyvinyl alcohol, polyvinyl butyral, etc.; ionomers and monochlorotrifluoroethylene resins; cellulose derivatives, including cellulose acetate, cellulose nitrate, ethyl cellulose, cellulose acetate butyrate, etc; epoxies; polyester resins; etc. 
     For devices in the form of an ocular lens, such as a soft contact lens, a hard contact lens, or an intraocular lens (referred to collectively herein as “ocular lens”), matrix materials of a lens or an optical element may include an ocular polymer. 
     For a softer ocular lens, such as a soft contact lens, a soft monomer may be incorporated into an ocular polymer. For harder lenses, such as hard contact lenses, a hard monomer may be incorporated into an ocular polymer. Many ocular lenses may incorporate, or may be a reaction product of a mixture comprising, a combination of soft and hard monomers. In some embodiments, an ocular lens may comprise an ocular polymer that is a product of a reaction of a mixture comprising a soft and/or a hard monomer, and may optionally further comprise a cross-linking agent, other polymerizable monomers, an initiator, and/or other materials. 
     Soft monomers may include hydrogel forming monomers, or monomers that form hydrogel polymers. Hydrogel polymers include polymeric systems that can absorb and retain water in an equilibrium state. Hydrogel polymers may incorporate hydrogel forming monomers including hydrophilic acrylates, such as hydroxyalkyl acrylates, hydroxyl alkyl methacrylates, acrylic acid, methacrylic acid, etc.; vinyl lactams, including optionally substituted N-vinylpyrrolidones, such as unsubstituted 1-vinyl-2-pyrrolidinone; acrylamides, such as methacrylamide and N,N-dimethylacrylamide; etc. Some hydrogel polymers may be a reaction product of polymerization reaction comprising an optional cross-linking agent and: 2-hydroxyethyl methacrylate (HEMA), HEMA and methacrylic acid; HEMA and 1-vinyl-2-pyrrolidinone; HEMA and 1-vinyl-2-pyrrolidinone and methacrylic acid; HEMA and 1-vinyl-2-pyrrolidinone and methyl methacrylate; HEMA and N-(1,1-dimethyl-3-oxobutyl) acrylamide; or 1-vinyl-2-pyrrolidinone and methyl methacrylate and allyl methacrylate. 
     Hard monomers include acrylate monomers that lack hydrophilic functional groups other than the CO 2  group of the ester, such as alkyl acrylate monomers or alkyl methacrylate monomers. Other hard monomers may include cellulose derivatives, such as cellulose acetate butyrate, and styrenes. 
     Hard alkyl acrylate monomers may include alkyl esters of acrylic acid, such as methyl acrylate, ethyl acrylate, propyl acrylate, butyl acrylate, pentyl acrylate, hexyl acrylate, heptyl acrylate, isobutyl acrylate, n-pentyl acrylate, tert-pentyl acrylate, hexyl acrylate, 2-methylbutyl acrylate, heptyl acrylate, octyl acrylate, 2-ethylhexyl acrylate, nonyl acrylate, decyl acrylate, dodecyl acrylate, stearyl acrylate, cyclopentyl acrylate, cyclohexyl acrylate, etc. Alkyl methacrylate monomers may include alkyl esters of methacrylic acid, such as methyl methacrylate, ethyl methacrylate, propyl methacrylate, butyl methacrylate, pentyl methacrylate, hexyl methacrylate, heptyl methacrylate, isobutyl methacrylate, n-pentyl methacrylate, tert-pentyl methacrylate, hexyl methacrylate, 2-methylbutyl methacrylate, heptyl methacrylate, octyl methacrylate, 2-ethylhexyl methacrylate, nonyl methacrylate, decyl methacrylate, dodecyl methacrylate, stearyl methacrylate, cyclopentyl methacrylate, cyclohexyl methacrylate, isopropyl methacrylate, s-butyl methacrylate, t-butyl methacrylate, 3,3,5-trimethylcyclohexyl methacrylate t-butyl acrylate, etc. In some alkyl acrylates or alkyl methacrylates, the alkyl group of the alkyl ester may contain 1, 2, 3, or 4 carbon atoms. Some ocular lens polymers are products of a polymerization reaction comprising methyl acrylate, ethyl acrylate, propyl acrylate, butyl acrylate, methyl methacrylate, ethyl methacrylate, propyl methacrylate, or butyl methacrylate. 
     For some ocular lenses, repeating units derived from an alkyl acrylate and/or an alkyl methacrylate are at least about 10%, about 20%, about 30%, and may be up to about 90%, about 95%, about 99%, or may approach about 100% of the weight of an ocular polymer. 
     Other hard acrylate monomers may include phenyl methacrylate, tetrahydrofurfuryl acrylate, tetrahydrofurfuryl methacrylate, allyl methacrylate, etc. 
     Examples of a cross-linking agent may include: ethyleneglycol diacrylate, butanediol diacrylate, hexanediol diacrylate, hexanediol dimethacrylate, diethyleneglycol diacrylate, triethyleneglycol diacrylate, propyleneglycol diacrylate, dipropyleneglycol diacrylate, divinylbenzene, allyl acrylate, vinyl acrylate, trimethylolpropane triacrylate, acryloyloxyethyl acrylate, diallyl fumarate, diallyl phthalate, diallyl adipate, divinyl adipate, α-methylene-N-vinyl pyrrolidone, 4-vinylbenzyl acrylate, 3-vinylbenzyl acrylate, 2,2-bis(acryloyloxyphenyl)hexafluoropropane, 2,2-bis(acryloyloxyphenyl)propane, 1,2-bis(2-(acryloyloxyhexafluoroisopropyl)benzene, 1,3-bis(2-(acryloyloxyhexafluoroisopropyl)benzene, 1,4-bis(2-(acryloyloxyhexafluoroisopropyl)benzene, 1,2-bis(2-(acryloyloxyisopropyl)benzene, 1,3-bis(2-(acryloyloxyisopropyl)benzene, 1,4-bis(2-(acryloyloxyisopropyl)benzene, ethyleneglycol dimethacrylate, butanediol dimethacrylate, diethyleneglycol dimethacrylate, triethyleneglycol dimethacrylate, propyleneglycol dimethacrylate, dipropyleneglycol dimethacrylate, divinylbenzene, allyl methacrylate, vinyl methacrylate, trimethylolpropane trimethacrylate, methacryloyloxyethyl methacrylate, 4-vinylbenzyl methacrylate, 3-vinylbenzyl methacrylate, 2,2-bis(methacryloyloxyphenyl)hexafluoropropane, 2,2-bis(methacryloyloxyphenyl)propane, 1,2-bis(2-(methacryloyloxyhexafluoroisopropyl)benzene, 1,3-bis(2-(methacryloyloxyhexafluoroisopropyl)benzene, 1,4-bis(2-(methacryloyloxyhexafluoroisopropyl)benzene, 1,2-bis(2-(methacryloyloxyisopropyl)benzene, 1,3-bis(2-(methacryloyloxyisopropyl)benzene, 1,4-bis(2-(methacryloyloxyisopropyl)benzene, N,N′-bis-acryloylcystamine, N,N′-bis-methacryloylcystamine, methylene bis-acrylamide, or methylene bis-methacryloylcystamine. Some acrylic polymers are a product of a polymerization reaction of a mixture that includes ethyleneglycol diacrylate, butanediol diacrylate, 4-vinylbenzyl methacrylate, ethyleneglycol dimethacrylate, butanediol dimethacrylate, and/or 4-vinylbenzyl methacrylate as a crosslinker. For some acrylic polymers, the cross-linking agent is about 0.001% to 15% by weight or about 0.1% to 10% of the weight of a polymerization reaction mixture. In some embodiments, excessive use of a cross-linking agent may cause an ocular lens to be fragile. 
     One or more additional polymerizable monomers may optionally be added to a polymerization reaction mixture. In some embodiments, polymerizable monomers that are not acrylate monomers may be less than about 90% by weight, about 80% by weight, about 50% by weight, about 30% by weight, about 20% by weight, about 10% by weight, or about 5% by weight of the polymerization reaction mixture. 
     A specific example of a hydrogel-forming monomer mixture is polymacon, composed primarily of 2-hydroxyethylmethacrylate with a small amount of diethyleneglycol dimethacrylate as a crosslinking monomer. 
     Examples of additional polymerizable monomers may include a silicon-containing methacrylate monomer, a derivative of a silicon-containing styrene, a derivative of a fluorine-containing styrene, a fluorine-containing acrylate monomer, a silicon-containing macromonomer, etc. These types of polymerizable monomers may improve oxygen transmission and/or contamination resistance in an ocular polymer. A styrene may be added to improve the mechanical strength and hardness of an ophthalmic lens such as an ocular lens. 
     Silicon-containing acrylate monomers may include, pentamethyldisiloxanylmethyl acrylate, pentamethyldisiloxanylpropyl acrylate, methylbis(trimethylsiloxy)silylpropyl acrylate, tris(trimethylsiloxy)silylpropyl acrylate, mono[methyl-bis(trimethylsiloxy)siloxy]bis(trimethylsiloxy)silylpropyl acrylate, tris[methyl-bis(trimethylsiloxy)siloxy]silylpropyl acrylate, methyl-bis(trimethylsiloxy)silylpropylglycerol acrylate, tris(trimethylsiloxy)silylpropylglycerol acrylate, mono[methyl-bis(trimethylsiloxy)siloxy]bis(trimethylsiloxy)silylpropylglycerol acrylate, trimethylsilylethyltetramethyldisiloxanylpropylglycerol acrylate, trimethylsilylmethyl acrylate, trimethylsilylpropyl acrylate, trimethylsilylpropylglycerol acrylate, pentamethyldisiloxanyl propylglycerol acrylate, methylbis(trimethylsiloxy)silylethyltetramethyldisiloxanylmethyl acrylate, tetramethyltriisopropylcyclotetrasiloxanylpropyl acrylate, tetramethyltriisopropylcyclotetrasiloxybis(trimethylsiloxy)silylpropyl acrylate pentamethyldisiloxanylmethyl methacrylate, pentamethyldisiloxanylpropyl methacrylate, methylbis(trimethylsiloxy)silylpropyl methacrylate, tris(trimethylsiloxy)silylpropyl methacrylate, mono[methyl-bis(trimethylsiloxy)siloxy]bis(trimethylsiloxy)silylpropyl methacrylate, tris[methyl-bis(trimethylsiloxy)siloxy]silylpropyl methacrylate, methyl-bis(trimethylsiloxy)silylpropylglycerol methacrylate, tris(trimethylsiloxy)silylpropylglycerol methacrylate, mono[methyl-bis(trimethylsiloxy)siloxy]bis(trimethylsiloxy)silylpropylglycerol methacrylate, trimethylsilylethyltetramethyldisiloxanylpropylglycerol methacrylate, trimethylsilylmethyl methacrylate, trimethylsilylpropyl methacrylate, trimethylsilylpropylglycerol methacrylate, pentamethyldisiloxanyl propylglycerol methacrylate, methylbis(trimethylsiloxy)silylethyltetramethyldisiloxanylmethyl methacrylate, tetramethyltriisopropylcyclotetrasiloxanylpropyl methacrylate, tetramethyltriisopropylcyclotetrasiloxybis(trimethylsiloxy)silylpropyl methacrylate, etc. 
     Examples of silicon-containing derivatives of a styrene may include trimethylsilylstyrene, tris(trimethylsiloxy)silylstyrene, etc. 
     A silicon-containing macromonomer includes a macromonomer containing silicon (Si), such as a polysiloxane macro, having polymerzible groups at both ends of a polysiloxane macromer, bonded to a vinyl-containing monomer by an urethane bond. 
     Some polymerization reaction mixtures may include a silicone-containing monomer which may react in the polymerization mixture to form a silicone hydrogel copolymer. Examples of silicone-containing monomers include: monomers including a single activated double bond, such as methacryloxypropyl tris(trimethylsiloxy), pentamethyldisiloxanyl methylmethacrylate, tris(trimethylsiloxy)methacryloxy propylsilane, methyldi(trimethylsiloxy)methacryloxymethyl silane, 3-[tris(trimethylsiloxy)silyl]propyl vinyl carbamate, and 3-[tris(trimethylsiloxy)silyl]propyl vinyl carbonate; and multifunctional ethylenically “end-capped” siloxane-containing monomers, especially difunctional monomers having two activated double bonds. 
     Examples of fluorine-containing derivatives of a styrene may include o-fluorostyrene, m-fluorostyrene, p-fluorostyrene, trifluorostyrene, perfluorostyrene, p-trifluoromethylstyrene, o-trifluoromethylstyrene, and m-trifluoromethylstyrene, etc. 
     Examples of fluorine-containing acrylate monomers include, 2,2,2-trifluoroethyl acrylate, 2,2,3,3-tetrafluoropropyl acrylate, 2,2,3,3,3-pentafluoropropyl acrylate, 2,2,2-trifluoro-1-trifluoromethylethyl acrylate, 2,2,3,3-tetrafluoro-tert-pentyl acrylate, 2,2,3,4,4,4-hexafluorobutyl acrylate, 2,2,3,3,4,4-hexafluorobutyl acrylate, 2,2,3,4,4,4-hexafluoro-tert-hexyl acrylate, 2,2,3,3,4,4,4-heptafluorobutyl acrylate, 2,2,3,3,4,4,5,5-octafluoropentyl acrylate, 3,3,4,4,5,5,6,6-octafluorohexyl acrylate, 2,3,4,5,5,5-hexafluoro-2,4-bis(trifluoromethyl) pentyl acrylate, 2,2,3,3,4,4,5,5,5-nonafluoropentyl acrylate, 2,2,3,3,4,4,5,5,6,6,7,7-dodecafluoroheptyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8-dodecafluorooctyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluorooctyl acrylate, 2,2,3,3,4,4,5,5,6,6,7,7,7-tridecafluoroheptyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10-hexadecafluorodecyl acrylate, 3,3,4,4,5,5,6,6, 7,7,8,8,9,9,10,10,10-heptadecafluorodecyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11-octadecafluoroundecyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,11-nonadecafluoroundecyl acrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12-eicosafluorododecyl acrylate, 2-hydroxy-4,4,5,5,6,7,7,7-octafluoro-6-trifluoromethylheptyl acrylate, 2-hydroxy-4,4,5,5,6,6,7,7,8,9,9,9-dodecafluoro-8-trifluoromethylnonyl acrylate, and 2-hydroxy-4,4,5,5,6,6,7,7,8,8,9,9,10,11,11,11-hexadecafluoro-10-trifluoro-methylundecyl acrylate, 2,2,2-trifluoroethyl methacrylate, 2,2,3,3-tetrafluoropropyl methacrylate, 2,2,3,3,3-pentafluoropropyl methacrylate, 2,2,2-trifluoro-1-trifluoromethylethyl methacrylate, 2,2,3,3-tetrafluoro-tert-pentyl methacrylate, 2,2,3,4,4,4-hexafluorobutyl methacrylate, 2,2,3,3,4,4-hexafluorobutyl methacrylate, 2,2,3,4,4,4-hexafluoro-tert-hexyl methacrylate, 2,2,3,3,4,4,4-heptafluorobutyl methacrylate, 2,2,3,3,4,4,5,5-octafluoropentyl methacrylate, 3,3,4,4,5,5,6,6-octafluorohexyl methacrylate, 2,3,4,5,5,5-hexafluoro-2,4-bis(trifluoromethyl) pentyl methacrylate, 2,2,3,3,4,4,5,5,5-nonafluoropentyl methacrylate, 2,2,3,3,4,4,5,5,6,6,7,7-dodecafluoroheptyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8-dodecafluorooctyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluorooctyl methacrylate, 2,2,3,3,4,4,5,5,6,6,7,7,7-tridecafluoroheptyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10-hexadecafluorodecyl methacrylate, 3,3,4,4,5,5,6,6, 7,7,8,8,9,9,10,10,10-heptadecafluorodecyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11-octadecafluoroundecyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,11-nonadecafluoroundecyl methacrylate, 3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12-eicosafluorododecyl methacrylate, 2-hydroxy-4,4,5,5,6,7,7,7-octafluoro-6-trifluoromethylheptyl methacrylate, 2-hydroxy-4,4,5,5,6,6,7,7,8,9,9,9-dodecafluoro-8-trifluoromethylnonyl methacrylate, and 2-hydroxy-4,4,5,5,6,6,7,7,8,8,9,9,10,11,11,11-hexadecafluoro-10-trifluoro-methylundecyl methacrylate, etc. 
     Examples of a styrene include unsubstituted styrene, o-methylstyrene, m-methylstyrene, p-methylstyrene, p-ethylstyrene, o-hydroxystyrene, m-hydroxystyrene, p-hydroxystyrene, trimethylstyrene, tert-butylstyrene, perbromostyrene, dimethylaminostyrene, a-methylstyrene, etc. 
     Polymerization of a reaction mixture may be accomplished by a heat polymerization. For example, a polymerization reaction mixture may be heated to an elevated temperature, such as about 50° C. to about 300° C., about 100° C. to about 200° C., or about 100° C. to about 150° C. when a polymerization initiator is present in a polymerization reaction mixture. Heat polymerization may reduce discoloration or fading after the polymerization as compared to other polymerization methods. Alternatively, a polymerization reaction may be photopolymerized, such as by exposure to an electromagnetic radiation such as microwave, an ultraviolet radiation, a radiant ray (γ-ray), etc. 
     A polymerization initiator may be selected based on the method of polymerization to be employed. For example, if the heat polymerization is employed, a radical polymerization initiator may be used. If a polymerization is achieved by the exposure to the electromagnetic radiation, a photopolymerization initiator or a photosensitizer may be used. Polymerization may also be initiated by a base or an acid catalyst, or by an electrophilic agent or a nucleophilic agent. 
     Any suitable radical polymerization initiator may be used. Examples of radical polymerization initiators may include azobisisobutyronitrile, azobis-2,4-dimethylvaleronitrile, benzoyl peroxide, dibenzoyl peroxide, benzoin methyl ether, tert-butyl hydroperoxide, cumene hydroperoxide, etc. 
     Any suitable photopolymerization initiator may be used in a photopolymerization reaction of a polymerization reaction mixture. Examples of photopolymerization initiators include: benzoin based photopolymerization initiators such as methylorthobenzoylbenzoate, methylbenzoylformate, benzoinmethylether, benzoinethylether, benzoinisopropylether, benzoinisobutylether, benzoin-n-butylether, etc.; phenone photopolymerization initiators such as 2-hydroxy-2-methyl-1-phenylpropane-1-one, p-isopropyl-α-hydroxyisobutylphenone, p-tert-butyltrichloroacetophenone, 2,2-dimethoxy-2-phenylacetophenone, α,α-dichloro-4-phenoxyacetophenone, N,N-tetraethyl-4,4-diaminobenzophenone, etc.; 1-hydroxycyclohexylphenylketone; 1-phenyl-1,2-propanedione-2-(o-ethoxycarbonyl)oxime; thioxanthone photopolymerization initiator such as 2-chlorothioxanthone, 2-methylthioxanthone etc.; dibenzosuberone; 2-ethylanthraquinone; benzophenoneacrylate; benzophenone; benzyl; etc. 
     Any suitable amount of polymerization initiator may be used, such as at least about 0.005 parts by weight or at least about 0.01 parts by weight per 100 parts by weight of a polymer reaction mixture. In some embodiments, the amount of polymerization initiator may be less than about 2 parts by weight, or 1 part by weight per 100 parts by weight of a polymerization reaction mixture. 
     Any of a number of methods may be used to form an ocular lens. For example, a cutting method may be used. In a cutting method, a polymer may be formed into a desired configuration by a mechanical processing method such as cutting, grinding, etc. An ocular lens may also be formed using a molding method. In a molding method, a polymerization reaction mixture may be placed into a mold cavity, and a desired shape may be obtained by reaction of the polymerization reaction mixture in the mold cavity. Other forming methods may also be used. Additionally, molding and cutting methods may be combined. 
     A luminescent compound may be incorporated into an ocular polymer when casting a lens, or a finished lens can treated with a luminescent compound, such as by soaking in or coating with solution containing a luminescent compound. 
     Optionally, a mixture of monomers to be polymerized into a hydrogel copolymer may include a silicone-containing monomer in order to form a silicone hydrogel copolymer. Examples of silicone-containing monomers include: monomers including a single activated double bond, such as methacryloxypropyl tris(trimethylsiloxy)silane, pentamethyldisiloxanyl methylmethacrylate, tris(trimethylsiloxy)methacryloxy propylsilane, methyidi(trimethylsiloxy)methacryloxymethyl silane, 3-[tris(trimethylsiloxy)silyl]propyl vinyl carbamate, and 3-[tris(trimethylsiloxy)silyl]propyl vinyl carbonate; and multifunctional ethylenically “end-capped” siloxane-containing monomers, especially difunctional monomers having two activated double bonds. 
     In some embodiments, an optical element of a device may comprise a coating, such as a scratch resistant coating, wherein a substantially transparent matrix comprises a scratch resistant material, and a luminescent material may be dispersed in the scratch resistant material. Examples of a scratch resistant material such as cellulose acetate butyrate, cellulose nitrate, cellulose triacetate, a hard acrylate (such as a hard acrylate described above), a polyalkylene such as polyethylene or polypropylene, poly(acrylonitrile), poly(vinyl acetate), poly(vinyl chloride), an optionally substituted polystyrene, polybutadiene, nylon, a vinyl chloride-vinyl acetate copolymer, a polycarbonate, a styrene-butadiene copolymer resin, a polyurethane, such as a lightly cross-linked thermoplastic polyurethane, a polyurea urethane, a polysiloxane, a polysilane, a fluoropolymer such as a polymer or copolymer of fluoroethylene, difluoroethylene, trifluoroethylene, tetrafluoroethylene (e.g. poly(tetrafluoroethylene)), an epoxy functional alkoxy silane, an silicon oxynitride PECVD film, a metal oxide, etc. 
     Any suitable polycarbonate may be used, such as a homo polycarbonate, a co-polycarbonate, a branched polycarbonate, or a mixture thereof. Some polycarbonates may be prepared by reaction of a carbonic acid derivative, such as phosgene, and a dihydroxy compound. Useful dihydroxy compounds include bisphenol compounds which may be represented by Formula S: 
     
       
         
         
             
             
         
       
     
     R A1  may be H, or C 1-12  alkyl, including: linear or branched alkyl having a formula C a H a+1  or C a H a , or cycloalkyl having a formula C a H a−1  or C a H a−2 , wherein a is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, such as linear or branched alkyl of a formula: CH 3 , C 2 H 5 , C 3 H 7 , C 4 H 9 , C 5 H 11 , C 6 H 13 , C 7 H 15 , C 8 H 17 , C 9 H 19 , C 10 H 21 , etc., or cycloalkyl of a formula: C 3 H 5 , C 4 H 7 , C 5 H 9 , C 6 H 11 , C 7 H 13 , C 8 H 15 , C 9 H 17 , C 10 H 19 , etc. 
     R A2  may be H, or C 1-12  alkyl, including: linear or branched alkyl having a formula C a H a+1  or C a H a , or cycloalkyl having a formula C a H a−1  or C a H a−2 , wherein a is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, such as linear or branched alkyl of a formula: CH 3 , C 2 H 5 , C 3 H 7 , C 4 H 9 , C 5 H 11 , C 6 H 13 , C 7 H 15 , C 8 H 17 , C 9 H 19 , C 10 H 21 , etc., or cycloalkyl of a formula: C 3 H 5 , C 4 H 7 , C 5 H 9 , C 6 H 11 , C 7 H 13 , C 8 H 15 , C 9 H 17 , C 10 H 19 , etc. 
     In some embodiments R A1  and R A2  are hydrogen, methyl, propyl, or phenyl, or 
                         
In some embodiments R A1  and R A2  are methyl. A polycarbonate may have any suitable molecular weight. In some embodiments a polycarbonate may have a molecular weight of about 10,000 g/mol to about 200,000 g/mol or about 20,000 g/mol to about 80,000 g/mol.
 
     Generally, a polyurethane includes a polymer that may be formed by reaction of a polyisocyanate and a polyol. A polyurea urethane includes a polymer that may be formed by reaction of a polyisocyanate, a polyol, and a polyamine. 
     Polyisocyanates include organic isocyanates having 2 or more isocyanate functional groups. Some polyisocyanates may have, on average, about 2 to about 3 isocyanate functional groups per molecule. A polyisocyanate may be an aliphatic polyisocyanate, a cycloaliphatic polyisocyanate wherein one or more of the isocyanato groups are attached directly to the cycloaliphatic ring, a cycloaliphatic polyisocyanate wherein one or more of the isocyanato groups are not attached directly to the cycloaliphatic ring, an aromatic polyisocyanate wherein one or more of the isocyanato groups are attached directly to the aromatic ring, and aromatic polyisocyanates wherein one or more of the isocyanato groups are not attached directly to the aromatic ring, or a mixture thereof. Non-limiting examples of suitable polyisocyanates include tetramethylene-1,4-diisocyanate, hexamethylene-1,6-diisocyanate, 2,2,4-trimethylhexane-1,6-diisocyanate, cyclobutane-1,3-diisocyanate, cyclohexane-1,3-diisocyanate, cyclohexane-1,4-diisocyanate, methyl cyclohexyl diisocyanate, e.g., 2,4- and 2,6-methyl cyclohexyl diisocyanate, isophorone diisocyanate, the isomers and mixtures of isomers of 4,4′-methylene-bis(cyclohexyl isocyanate), e.g., the trans-trans, cis-cis and cis-trans isomers, hexahydrotoluene-2,4-diisocyanate, hexahydrotoluene-2,6-diisocyanate, hexahydrophenylene-1,3-diisocyanate, hexahydrophenylene-1,4-diisocyanate, hexahydrophenylene-1,4-diisocyanate, phenyl cyclohexylmethane diisocyanate, etc. 
     A polyamine may be any compound comprising two or more primary (e.g. —NH 2 ) and/or secondary amino functional groups, such as 2 primary amino functional groups, 2 secondary amino functional groups, or 1 primary amino functional group and 1 secondary amino functional group. Some examples of suitable polyamines include aliphatic polyamines such as aliphatic diamines having from 2 to 10 carbon atoms, e.g. 1,2-ethane diamine, 1,3-propane diamine, 1,4-butane diamine, 1,5-pentane diamine, 1,6-hexane diamine, 1,8-octane diamine, and 1,10-decane diamine, etc.; cycloaliphatic polyamines; aromatic polyamines, such as 1,2-benzene diamine, 1,3-benzene diamine, 1,4-benzene diamine, 1,5-naphthalene diamine, 1,8-naphthalene diamine, 2,4-toluene diamine, 2,5-toluene diamine, 3,3′-dimethyl-4,4′-biphenyldiamine, 4,4′-methylene bis(aniline), 4,4′-methylene bis(2-chloroaniline); dialkyl toluene diamines in which the alkyl groups each contain from 1 to 3 carbon atoms, such as 3,5-dimethyl-2,4-toluene diamine, 3,5-dimethyl-2,6-toluene diamine, 3,5-diethyl-2,4-toluene diamine, 3,5-diethyl-2,6-toluene diamine, 3,5-diisopropyl-2,4-toluene diamine, 3,5-diisopropyl-2,6-toluene diamine, etc.; 4,4′-methylene-bis(dialkylaniline) in which the alkyl groups each contain from 1 to 3 carbon atoms, such as 4,4′-methylene bis(2,6-dimethylaniline), 4,4′-methylene bis(2,6-diethylaniline), 4,4′-methylene bis(2-ethyl-6-methylaniline), 4,4′-methylene bis(2,6-diisopropylaniline), 4,4′-methylene bis(2-isopropyl-6-methylanili-ne) and 4,4′-methylene bis(2,6-diethyl-3-chloroaniline), etc. Dialkyl toluene diamines may be sold as isomeric mixtures, e.g., an isomeric mixture of 3,5-diethyl-2,4-toluene diamine and 3,5-diethyl-2,6-toluene diamine. Polyamines may also contain more than two amino groups, such as diethylenetriamine, triethylenetetramine, and tetraethylenepentamine. 
     A polyurethane or a polyurea urethane may be a polyether-based polyurethane or polyurea urethane, a polycarbonate-based polyurethane or polyurea urethane, or a polyester-based polyurethane or polyurea urethane, referring to the type of polyol used to form the polyurethane or polyurea urethane. 
     Examples of polyether polyols include, but are not limited to, polyoxyalkylene polyols, and polyalkoxylated polyols. Polyoxyalkylene polyols include polyols that may be prepared by reacting an alkylene oxide, or a mixture of alkylene oxides, using with a polyhydric initiator or a mixture of polyhydric initiators, such as ethylene glycol, propylene glycol, glycerol, sorbitol and the like. Examples of alkylene oxides include ethylene oxide, propylene oxide, butylene oxide, amylene oxide, aralkylene oxides, e.g., styrene oxide, mixtures of ethylene oxide and propylene oxide, etc. Polyoxyalkylene polyols prepared with mixtures of alkylene oxide can be prepared using random or step-wise oxyalkylation. Examples of such polyoxyalkylene polyols include polyoxyethylene, e.g., polyethylene glycol, polyoxypropylene, e.g., polypropylene glycol. Polyalkoxylated polyols include polyols that may be prepared by reacting a diol such as a C 1-8  alkylene diol, a dihydroxybenzene, etc., with an alkylene oxide such as ethylene oxide, propylene oxide, butylene oxide, etc. 
     A polyether polyol may have any suitable molecular weight. For example, some polyether polyols may have a weight average molecular weight of about 500 g/mol to about 3000 g/mol, about 650 g/mol to about 2000 g/mol, about 650 g/mol to about 1400 g/mol, about 850 g/mol to about 1000 g/mol, or about 1200 g/mol. 
     Polycarbonate polyols include polyols that may be prepared by reaction of an organic glycol, e.g., a diol, such a glycol, and a dialkyl carbonate. Some polycarbonate polyols may be represented by a formula H—(O—C(O)—O—(CH 2 ) m ) n —OH, wherein m is 2, 3, 4, 5, 6, 7, 8, 9, or 10, and n is 4 to 24, 4 to 10, or 5 to 7. In some embodiments, a dialkyl carbonate is a polyhexamethylene carbonate, where m is 6. A polycarbonate polyol may have any suitable molecular weight, such as a number average molecular weight of about 500 g/mol to 3500 g/mol or about 650 g/mol to about 1000 g/mol. 
     A glycol includes low molecular weight polyols, e.g., polyols having a molecular weight of less than 500 g/mol, such as low molecular weight diols and triols. Some glycols contain 2 to 16, 2 to 6, or 10 carbon atoms. Non-limiting examples of glycols include: ethylene glycol, propylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, dipropylene glycol, tripropylene glycol, 1,2-, 1,3- and 1,4-butanediol, 2,2,4-trimethyl-1,3-pentanediol, 2-methyl-1,3-pentanediol, 1,3-, 2,4- and 1,5-pentanediol, 2,5- and 1,6-hexanediol, 2,4-heptanediol, 2-ethyl-1,3-hexanediol, 2,2-dimethyl-1,3-propanediol, 1,8-octanediol, 1,9-nonanediol, 1,10-decanediol, 1,4-cyclohexanediol, 1,4-cyclohexanedimethanol, 1,2-bis(hydroxyethyl)-cyclohexane, glycerin, tetramethylolmethane, e.g., pentaerythritol, trimethylolethane, and trimethylolpropane. Other isomers of these glycols may also be used. The amount of glycol used in relation to a polyether polyol and/or polycarbonate polyol component may vary from 3 to 20 weight percent. 
     Polyester polyols include polyols that may be prepared by esterification of saturated dicarboxylic acids or anhydrides thereof (or combinations of acids and anhydrides) with polyhydric alcohols; polylactones, e.g., polycaprolactone and polyvalerolactone, which may be prepared by polymerizing a lactone, such as epsilon caprolactone or delta-valerolactone, in the presence of minor amounts of difunctional active hydrogen compounds, such as water or a low molecular glycol, e.g., 1,4-butane diol. 
     Saturated dicarboxylic acids include those containing from 4 to 10 carbon atoms or 6 to 9 carbon atoms, such as succinic acid, glutaric acid, adipic acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, etc. 
     Polyhydric alcohols include aliphatic alcohols containing at least two hydroxy groups, e.g., straight chain glycols containing from 2 to 10 or 4 to 8 carbon atoms. Non-limiting examples include the glycols described above. In some embodiments, a polyhydric alcohol is 1,4-butane diol. 
     A polyester polyol may have any suitable molecular weight, such as a number average molecular weight of about 1000 g/mol to about 3000 g/mol or about 1000 g/mol to about 2000 g/mol. Non-limiting examples of polyester polyols include poly(butane diol-1,4-adipate), poly(butane diol-1,4-succinate), poly(butane diol-1,4-glutarate), poly(butane diol-1,4-pimelate), poly(butane diol-1,4-suberate), poly(butane diol-1,4-azelate), poly(butane diol-1,4-sebacate) and poly(epsilon caprolactone). 
     A scratch resistant coating may include from 0 to 20 weight percent or about 1 to about 90 weight percent based on the total weight of the composition, of a metal oxide such as silicon dioxide, aluminum oxide, antimony oxide, tin oxide, titanium oxide, zirconium oxide, etc., or a mixture thereof. 
     A scratch resistant coating have any suitable thickness, such as a thickness of about 1 mil to about 20 mils (about 0.025 mm to about 0.5 mm) or about 5 mil to about 10 mils (about 0.125 mm to about 0.25 mm). A scratch resistant coating may be directly applied to another material, or may be applied using an adhesive layer, such as a substantially transparent layer having a thickness less than 25 microns, about 0.1 micron to about 10 microns, about 0.1 microns to about 5 microns, or about 1 micron. 
     The resistance of a coating to scratching may be measured by the rotary steel wool test, which involves subjecting the coating to five revolutions of a pad of 0000 grade steel wool at a defined pressure, usually 12 or 24 psi. The scratching abrasion resistance is rated by measuring the increase in haze from the abrasion. Test methods such as ASTM D-1044 have been developed for optically measuring the resistance of transparent plastic materials to abrasion. Other standard tests for abrasion resistance are the Taber abrasion test described in ASTM D-1004-56. 
     In many applications, toughness and resistance to impact may be important for a scratch resistant coating. The toughness or impact abrasion resistance of a coating is commonly measured by the “falling sand” test (ASTM D968-51). A coating which has good scratch abrasion resistance may not necessarily have good impact abrasion resistance. With the falling sand test, sand is poured onto a coating from a predetermined height, while the thickness of the coating is observed. The results are expressed in terms of the number of liters of sand required to abrade away one tenth of a mil of the coating thickness. 
     An optical element may be integrated into an electronic device that comprises an electronic display, an optical element, and a touch screen component. An example of such a device  10  is depicted in  FIG. 2 . In this type of device, touch screen component  30  may be disposed over electronic display  20 . Optical element  15  is also included. Optical element  15  may be disposed over touch screen component  30 , as shown in  FIG. 2 , or optical element  15  may be disposed between electronic display  20  and touch screen component  30 , as shown in  FIG. 3 , or in another position that allows light from electronic display  20  to pass through optical element  15 . Touch screen element  30  comprises first conductive layer  40 , second conductive layer  50 , and spacer  60  disposed between first conductive layer  40  and second conductive layer  50 . As shown in  FIG. 2A , when there is no contact between a user and device  10 , there is no electrical contact between first conductive layer  40  and second conductive layer  50 . As shown in  FIG. 2B , contact  80  by a user can cause first conductive layer  40  to contact second conductive layer  50 , which may create electrical contact between first conductive layer  40  and second conductive layer  50 . This may allow current to flow between first conductive layer  40  and second conductive layer  50 . Thus, the touch screen component may act as an on/off switch that is sensitive to a user&#39;s touch. Light  70  emitted from display  20  passes through touch screen component  30  and passes through optical element  15 . Optical element  30  may modify a color of light  70  from display  20 . 
     As depicted in  FIG. 4 , a touch screen component, e.g. touch screen component  30 , may further comprise a first support layer, such as first support layer  90 . First support layer  90  may be positioned so that first conductive layer  40  is disposed between spacer  60  and first support layer  90 . Additionally a touch screen component may further comprise a second support layer, e.g. second support layer  100 . Second support layer  100  may be positioned so that second conductive layer  50  is disposed between spacer  60  and second support layer  100 . As depicted in  FIG. 5 , a touch screen component may also comprise a first dielectric layer, such as first dielectric layer  110 , which may be disposed between first conductive layer  40  and first support layer  90 . Touch screen component  30  may also comprise a second dielectric layer, such as second dielectric layer  120 , which may be disposed between second conductive layer  50  and second support layer  100 . 
     A touch screen element, such as touch screen element  30 , should be sufficiently transparent for a display, such as display  20 , to be viewed through the touch screen element. 
     A conductive layer, such as first conductive layer  40  or second conductive layer  50 , may be composed of any conductive material. A first conductive layer and a second conductive layer may be composed of the same material, or may be composed of different material. Examples of conductive materials that may be used include, but are not limited to, metals such as gold, silver, platinum, palladium, copper, aluminum, nickel, chromium, titanium, iron, cobalt, tin etc., and alloys of these; metal oxides, such as indium oxide, tin oxide, titanium oxide, cadmium oxide, and mixtures of these. Other metal compounds, such as copper iodine, may also be used. In some embodiments, a conductive layer comprises indium oxide containing tin oxide, or tin oxide containing antimony. A conductive layer may have any thickness that allows the film to be sufficiently conductive and sufficiently transparent, such as about 10 nm to about 300 nm. 
     A spacer, e.g. spacer  60 , may be a vacuum, or may be composed of any nonconductive material, such as air, nitrogen, argon, or another inert gas. A spacer may be of any suitable thickness, such as in about 10 μm to about 500 μm, about 100 μm to about 200 μm, or about 150 μm. 
     A support layer may be any layer that facilitates the desired function of a conductive layer. A first support layer, e.g. first support layer  90  and a second support later, e.g. second support layer  100 , may be the same or different, and make may be composed of the same or different materials. Examples of suitable support materials include but are not limited to polyester-based resins, acetate-based resins, polyethersulfone-based resins, polycarbonate-based resins, polyamide-based resins, polyimide-based resins, polyolefin-based resins, acrylate-based resins, polyvinyl chloride-based resins, polystyrene-based resins, polyvinyl alcohol-based resins, poly phenylene sulfide-based resins, polyvinylidene chloride-based resins, etc. In some embodiments a support layer comprises a polyester-based resin, a polycarbonate-based resin, or a polyolefin-based resin. A support later may have any suitable thickness, such as about 75 μm to about 400 μm, about 100 μm to about 200 μm, about 2 μm to about 300 μm, or about 10 μm to about 130 μm. 
     A dielectric layer may be composed of any dielectric material. A first dielectric layer, e.g. first dielectric layer  110 , and a second dielectric layer, e.g. second dielectric layer  120 , may be the same or different, and may be composed of the same or different materials. Non-limiting examples include NaF, Na 3 AlF 6 , LiF, MgF 2 , CaF 2 , BaF 2 , SiO 2 , LaF 3 , CeF 3 , Al 2 O 3 , etc. A dielectric layer may have any suitable thickness, such as about 10 nm to about 300 nm, about 10 nm to about 200 nm, about 10 nm to about 120 nm, or about 15 nm to about 60 nm. 
     The optical elements described herein are useful in methods for correcting visual insensitivity in a mammal. In an embodiment, the method comprises identifying an individual having a visual insensitivity between a first visible color wavelength and a second visible color wavelength. In an embodiment, the method comprises selecting an optical element as described herein that corrects the visual insensitivity. In an embodiment, the method comprises providing or arranging to provide the optical element to the individual. In an embodiment, the visual insensitivity comprises deuteranomaly. 
     In one embodiment, identifying an individual having a visual insensititivity between a first visible color wavelength and a second visible color wavelength includes genotype determination. For example, identifying an individual having a visual insensitivity can include using a sampling kit having at least a medical subject sampling swab used in conjunction with amino acid sequencing. Comparison to standardized sequence listings (Neitz, Jay, et al, The genetics of normal and defective color vision, Vision Res. 51(2011):633-651; Neitz, Maureen, et al, Molecular Genetics of Color Vision and Color Vision Defects, Arch Ophthalmol 118:691-700 (2000)) can provide the geneotypic information regarding the conformity or non-conformity of the subject&#39;s amino acid sequence with normal or dysfunctional sequences. Any suitable sequencing procedure and determination is appropriate to make such determination, see for example U.S. Pat. No. 5,837,461, which is incorporated by reference in its entirety. The diagnosis of cone-photoreceptor-based vision disorders by these methods can involve the use of standard molecular biology methods, including the polymerase chain reaction (PCR), to examine the identities of all or a subset of at least 18 dimorphic nucleotide positions among the red and green photopigment genes. The pattern of nucleotide differences predicts the presence or absence of vision disorder. Different patterns of nucleotide identities correspond to different disorders and different degrees of severity within one class of disorder. 
     In one exemplary method, the test determines the amino acids specified at positions 65, 111, and 116 in exon 2; 153, 171, 174, 178, and 180 in exon 3; 230, 233, and 236 in exon 4; and 274, 275, 277, 279, 285, 298, or 309 in exon 5 of the red and green cone photopigments and to look for “poison” combinations of amino acids at these positions in the diagnosis of vision disorders. One might not have to examine all 18 dimorphic positions to make a diagnosis. For example, because the dimorphic positions in exon 5 are tightly linked, one typically only has to examine one of the codon positions within exon 5 to make an initial identification of the gene as encoding either a red or green cone photopigment. The dimorphic positions encoded in exons 2, 3, and 4 are preferably all examined. However, some disorders do not require that all positions be reviewed. 
     There are currently a variety of molecular biological methods available that allow examination of the DNA sequences of the red and green photopigment genes. For example, gene fragments may be amplified using the polymerase chain reaction (PCR). The red and green pigment genes can be separately and selectively amplified as described previously (J. Neitz, M. Neitz and Grishok, Vision Research 35: 2395-2407, 1995). 
     Amplified gene fragments may be subjected to one or more of the following procedures that provide information about the DNA sequence: 1) Direct DNA sequence of the PCR products as described previously (J. Neitz, M. Neitz and Grishok, supra, 1995); and/or 2) Restriction digestion analysis (described previously in J. Neitz, M. Neitz and Grishok, supra, 1995). Some of the amino acid substitutions indicated above are accompanied by a restriction site polymorphism. For example, the amino acid at position 180 is either a serine or an alanine. If alanine is encoded, the DNA fragment contains a BsoFl restriction site that is absent if serine is the amino acid encoded. Thus, PCR-amplified DNA fragments can be digested with appropriate restriction enzyme and the digestion products will be electrophoretically separated. The sizes of the fragments may be determined. Based on the sizes of the fragments observed, information about the DNA sequence and therefore about the amino acid sequence will be deduced. 3) Single strand conformation polymorphism or other similar procedures. The amplified DNA fragment is fluorescently or radioactively end labeled, denatured into single strands, and the strands are separated electrophoretically. Based on the mobility of the strands in the electric field, information about the DNA sequence can be deduced. 
     Once one has determined the amino acid specified at the above-described codon positions, one can then compare this amino acid data to the previously determined amino acid combinations suggestive of various color vision deficiencies. See U.S. Pat. No. 5,837,461. The “eyedox” brand geneotypic test kit and sequencing services provided by Genevolve Vision Diagnostics, Inc. (Albuquerque, N. Mex., USA), is another suitable manner of securing such information. 
     In some embodiments, identifying an individual having a visual insensititivity between a first visible color wavelength and a second visible color wavelength includes phenotypically determining an individual. In some embodiments, these phenotypic determinations can be achieved by exhibiting color photographs or plates and asking the subject to indicate what he or she sees depicted in the plate. In an embodiment, the method for correcting a visual insensitivity in a mammal comprises providing a standardized examination. In an embodiment, the method for correcting a visual insensitivity in a mammal comprises correlating the score of the examination with vision disorders. Those skilled in the art will recognize that these include isochromic test plates and their use, e.g., Ishihara 14/24/38 plate editions (Kanehara Trading, Tokyo JP, 2009), Hardy Rand and Ritter Pseudoisocromic Plate test, 4 th  Ed.; Dvorine 2d Ed, American Optical Company, 1965; and/or Richmond HRR pseudo isochromic plates, (1991 ed). Another suitable example includes the pencil and paper test described in A New Mass Screening Test for Color-Vision Defiencies in Children, Neity, Maureen, et al, Color Research and Application, Supp. Vol. 26, S239-S249 (2000). Other instrumentation is available to make such vision deficieny determinations, e.g., Farnswarth 100 Hue Test, (Richmond Products, Inc., Albuquerque, N. Mex., USA), Heidelberg Multi-color (HMC) Anomaloscopes (Oculus, Inc., Lynwood, Wash., USA). The determination of the presence of vision deficiencies and/or the severity of such deficiencies can be attained by the above instrumentations or methods and or combinations thereof. 
     In some embodiments, the deficiencies are determined and described in differences in spectral separation between at least two photopigments. In some embodiments, the at least two photopigments are the L photopigment, the M photopigment, and or combinations, hybrids or variants of the L or M photopigments. In some embodiments, the spectral separation is described as the differences in the spectral excitation at least two photopigments are the L photopigment, the M photopigment, and or combinations, hybrids or variants of the L or M photopigments. 
     In an embodiment, the method comprises providing an optical element as described herein that corrects the visual insensitivity. In some embodiments, providing an optical element further comprises incorporating a sufficient amount of a fluorescent compound into the optical element to increase the visual sensitivity between a first visible color wavelength and a second visible color wavelength. 
     In some embodiments, providing an optical element further comprises incorporating a sufficient amount of a second fluorescent material into the optical element to increase the visual sensitivity between a first visible color wavelength and a second visible color wavelength. 
     EXAMPLES 
     It has been discovered that embodiments of optical elements described herein improve the ability of colorblind individuals to distinguish a first color from a second color having a different wavelength. These benefits are further shown by the following examples, which are intended to be illustrative of the embodiments of the disclosure, but are not intended to limit the scope or underlying principles in any way. 
     Example 1 
     Luminescent Dye 
     The luminescent dye, Red-1, was synthesized in the following process: 
                                           
Compound 1:
 
     A mixture of benzotriazole (11.91 g, 100 mmol), 1-iodo-2-methylpropane (13.8 mL, 120 mmol), potassium carbonate (41.46 g, 300 mmol), and dimethylformamide (200 mL) was stirred and heated under argon at about 40° C. for 2 days. The reaction mixture was poured into ice/water (1 L) and extracted with toluene/hexanes (2:1, 2×500 mL). The extract was washed with 1 N HCl (2×200 mL) followed by brine (100 mL), dried over anhydrous MgSO 4 , and the solvent was removed under reduced pressure. The residue was triturated with hexane (200 mL) and set aside at room temperature for about 2 hours. The precipitate was separated and discarded, and the solution was filtered through a layer of silica gel (200 g). The silica gel was washed with hexane/dichloromethane/ethyl acetate (37:50:3, 2 L). The filtrate and washings were combined, and the solvent was removed under reduced pressure to give 2-isobutyl-2H-benzo[d][1,2,3]triazole (Compound 1) (8.81 g, 50% yield) as an oily product 
     Compound 2: 
     A mixture of 2-isobutyl-2H-benzo[d][1,2,3]triazole (Compound 1) (8.80 g, 50 mmol), bromine (7.7 mL, 150 mmol) and 48% HBr (50 mL) was heated at about 130° C. for about 24 hours under a reflux condenser connected with an HBr trap. The reaction mixture was poured into ice/water (200 mL), treated with 5 N NaOH (100 mL) and extracted with dichloromethane (2×200 mL). The extract was dried over anhydrous magnesium sulfate, and the solvent was removed under reduced pressure. A solution of the residue in hexane/dichloromethane (1:1, 200 mL) was filtered through a layer of silica gel and concentrated to give 4,7-dibromo-2-isobutyl-2H-benzo[d][1,2,3]triazole compound 2, (11.14 g, 63% yield) as an oil that slowly solidified upon storage at room temperature. 
     Compound 3: 
     4,7-dibromo-2-isobutyl-2H-benzo[d][1,2,3]triazole (compound 2) (17.8 g, 53 mmol) was added at about 0-5° C. to a premixed fuming HNO 3  (7.0 mL) and TFMSA (110 g) portionwise and after approx. 10 minutes the reaction mixture was placed in an oil bath and heated at about 55° C. for about 8 hours and then cooled, then poured into 500 mL of ice/water. The solid obtained was thoroughly washed with water, followed by MeOH and dried in a vacuum oven to give 7-dibromo-2-isobutyl-5,6-dinitro-2H-benzo[d][1,2,3]triazole (compound 3) as yellowish solid (20.4 g, 91%). 
     Compound 4: 
     4-Bromotriphenylamine (65.0 g, 200 mmol) was placed in 500 ml dry three necked RB flask equipped in magnetic stirring bar, low temperature thermometer and argon inlet. Tetrahydrofurane was transferred to the reaction flask using a cannula (200 ml) and cooled in a dry-ice acetone bath to −78° C. and n-BuLi (1.6M in hexane, 130 mL) was added dropwise over a period of about 30 minutes. The reaction mixture was left stirring at the same temperature for about 30 minutes and then tributyltin chloride (65.0 mL) was added dropwise over about 30 minutes. The resulting mixture was left stirring overnight, allowing slow warm-up to room temperature. It was then poured into ice-cold water (approx. 500 mL) and extracted with diethyl ether (2×250 mL). The organic layer was dried with MgSO 4  and the solvent was removed by evaporation to give 106.5 g of compound 4 as yellowish oil, by  1 H NMR approx. 95% pure. 
     Compound 5: 
     Compound 5 was formed by combining compounds 3 and 4 in a 1:2 ratio in the presence of bis(triphenylphosphine)palladium(II)dichloride. 100 ml of anhydrous 1,4-dioxane was added to a flask containing compound 4 (6.80 g, 12.7 mmol), and argon was bubbled through the solution. Compound 3 was added (2.12 g, 5 mmol), followed by the bis(triphenylphosphine)palladium(II)dichloride (0.448 g, 0.640 mmol) and argon was continually bubbled through the solution for an additional 10 minutes. Then, the flask was heated to about 100° C. for 2 hours. The reaction mixture was then poured into a separatory funnel and partitioned between brine and ethyl acetate. The organic layer was separated and concentrated to dryness, then dissolved in minimal dichloromethane and poured into methanol, followed by filtration of the precipitate and drying to yield 3.51 g (93%) of compound 5 as a dark red solid.
 
Compound 6:
 
     The diamine of compound 6 was prepared by dissolving compound 5 (3.51 g, 4.6 mmol) in glacial acetic acid (75 ml), then adding iron powder (2.8 g, 10 equivalents). The reaction vessel was purged with argon and then heated to about 130° C. After 3 hours at 130° C., the reaction mixture was poured into ice and the yellow precipitate was collected by vacuum filtration. The filtrate was washed with water, then dried under vacuum. The dried product was further purified by dissolving it in dichloromethane and filtering through a plug of silica gel. After removing the solvent, 3.16 g (98%) of compound 6 was obtained as a yellow solid. 
     Compound 7: 
     The diamine of compound 6 was converted to the corresponding benzotriazole of compound 7 by treating it with sodium nitrite in the presence of acetic acid. Compound 6 (3.03 g, 4.38 mmol) was dissolved in THF (20 ml), and glacial acetic acid (10 ml) was added. The mixture was cooled to about 0° C. in an ice bath and a solution of sodium nitrite (0.363 g, 5.26 mmol) in water (6 ml) was added dropwise with magnetic stirring. After stirring for about 10 minutes, the reaction vessel was removed from the ice bath and allowed to stir at room temperature for an additional 20 minutes. The resulting bright red mixture was then poured into a solution of sodium bicarbonate in a separatory funnel and dichloromethane was added to extract the organic products. The combined organic layers were washed with brine and dried with magnesium sulfate, then filtered and concentrated to yield 3 g (97%) of compound 7 as a red solid. 
     Compound 8 (Red-1): 
     Compound 8 was formed by reacting compound 7 with 2-butoxyethyl 4-methylbenzenesulfonate under basic conditions in N,N-dimethylformamide. Compound 7 (3 g) was combined with N,N-dimethylformamide and potassium carbonate (2.4 g) in a round bottom flask. A solution of 2-butoxyethyl 4-methylbenzenesulfonate (1.5 g) in DMF was added slowly to the stirring solution. The mixture was stirred at 80° C. for 3 hours, then allowed to cool. It was poured into a separatory funnel containing water, and the organic product was extracted with dichloromethane. After drying the organic portion with magnesium sulfate, it was filtered and dried under vacuum. The final product was purified using a Teledyne Isco CombiFlash RF200 chromatography system, with hexanes and ethyl acetate as the mobile phase. After pooling and drying the product-containing fractions, 700 mg of a fine red powder was collected. The material was further purified by recrystallization from dichloromethane and methanol to yield 600 mg (18%) of Compound 8 (Red-1) as a red powder with a purity of 98% by LCMS. 
     Optical Element 
     The luminescent dye, Compound 8, made in accordance with Example 1, was used without additional extraction or purification, and was intermixed with a solution of 5 wt % PVB in 1:1 N-methylpyrrolidone: cyclopentanone then spin coated onto glass at 2000 RPM for about 10 seconds followed by drying on a hot plate at 100° C. for about 10 minutes. The transmittance spectrum, shown in  FIG. 6 , was found: 
     The total light transmittance of the resulting optical element was measured on a Photal MCPD-7000 (Otsuka Electronics, Osaka, JP) using the Photal MC-2530 UV/Vis Light Source I 2  lamp as the illumination source. 
     Results 
     Thus, in some embodiments, an optical element may have an absorption and/or emission profile similar to that depicted in  FIG. 6 . For example, an optical element may absorb light having a wavelength of about 425 nm to about 500 nm, about 440 nm to about 500 nm, about 450 nm, or about 530 nm. In some embodiments, an optical element may emit light having a wavelength of about 510 nm to about 585 nm, about 515 nm to about 575 mm, about 530 nm, or about 560 nm. Similarly, in some embodiments and optical element may have a transmittance spectrum to that of the  FIG. 7 . For example, an optical element may have a transmittance peak at a wavelength of about 500 nm to about 700 nm, about 510 nm to about 550 nm, about 550 nm to about 620 nm, or about 640 nm to about 720 nm. In some embodiments the transmittance at a peak may be greater than: about 90%, about 95%, or about 100%. 
     Unless otherwise indicated, all numbers expressing quantities of ingredients, properties such as molecular weight, reaction conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. 
     The terms “a,” “an,” “the” and similar referents used in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of any claim. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention. 
     Groupings of alternative elements or embodiments disclosed herein are not to be construed as limitations. Each group member may be referred to and claimed individually or in any combination with other members of the group or other elements found herein. It is anticipated that one or more members of a group may be included in, or deleted from, a group for reasons of convenience. When any such inclusion or deletion occurs, the specification is deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims. 
     Certain embodiments are described herein, including the best mode known to the inventors for carrying out the invention. Of course, variations on these described embodiments will become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventor expects skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than specifically described herein. Accordingly, the claims include all modifications and equivalents of the subject matter recited in the claims as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is contemplated unless otherwise indicated herein or otherwise clearly contradicted by context. 
     In closing, it is to be understood that the embodiments disclosed herein are illustrative of the principles of the claims. Other modifications that may be employed are within the scope of the claims. Thus, by way of example, but not of limitation, alternative embodiments may be utilized in accordance with the teachings herein. Accordingly, the claims are not limited to embodiments precisely as shown and described.