SPATIALLY RESOLVED COUNTER-COLORING

Abstract

The present invention relates to improved coloring of an optical glass, in particular of a spectacle lens, comprising a predetermined glass material, in order to obtain a target coloration of the optical glass. In this case, a method according to the invention comprises: determining a material-specific intrinsic coloration of the predetermined glass material; determining a glass thickness at a plurality of evaluation locations on the optical glass; identifying an intrinsic coloration of the optical glass from the material-specific intrinsic coloration of the predetermined glass material and the glass thickness at the plurality of evaluation locations on the optical glass; determining a reference color pigment amount for at least one color pigment in such a way that the reference color pigment amount applied on a reference substrate brings about for the reference substrate the target coloration to be obtained on the optical glass; specifying a color correction model which describes a relationship between a deviation of a color pigment amount for at least one color pigment from the reference color pigment amount of the at least one color pigment and a resultant deviation of a coloration of the reference substrate from the target coloration; and determining a target color pigment amount which deviates from the reference color pigment amount by a color pigment amount correction which compensates for the ascertained intrinsic coloration of the optical glass in accordance with the defined color correction model.

Claims

1-14. (canceled)

15. A method of coloring a spectacle lens, which includes a predetermined glass material, for obtaining a target coloration of the optical glass, the method comprising: determining a material-specific intrinsic coloration of the predetermined glass material; determining a glass thickness at a plurality of evaluation points on the optical glass; identifying an intrinsic coloration of the optical glass from the material-specific intrinsic coloration of the predetermined glass material and the glass thickness at the plurality of evaluation points on the optical glass; determining a reference color pigment amount for at least one color pigment such that the reference color pigment amount, applied to a reference substrate, causes the target coloration to be obtained on the optical glass for the reference substrate; specifying a color correction model describing a relationship between a deviation of a color pigment amount for at least one color pigment from the reference color pigment amount of the at least one color pigment and a resulting deviation of a coloration of the reference substrate from the target coloration; and determining a target color pigment amount that deviates from the reference color pigment amount by a color pigment amount correction, which compensates for the identified intrinsic coloration of the optical glass according to the specified color correction model.

16. The method according to claim 15, wherein the material of the reference substrate corresponds to the predetermined glass material.

17. The method according to claim 15, wherein the determining a glass thickness at a plurality of evaluation points on the optical glass comprises identifying a deviation d of the glass thickness of the optical glass at a plurality of evaluation points on the optical glass from a thickness of the reference substrate, and wherein identifying the intrinsic coloration of the optical glass comprises identifying a deviation {right arrow over (F)} of an intrinsic coloration of the optical glass from an intrinsic coloration of the reference substrate on the basis of the identified deviation d of the thickness of the optical glass from a thickness of the reference substrate according to
{right arrow over (F)}=d.Math.{right arrow over (D)} with a volume color vector {right arrow over (D)}.

18. The method according claim 17, wherein the specifying a color correction model comprises determining a pigment amount correction matrix such that the relationship between a deviation {right arrow over (P)}={right arrow over (P)}{right arrow over (P.sub.r)} of a color pigment amount {right arrow over (P)} for at least one color pigment from the reference color pigment amount {right arrow over (P.sub.r)} of the at least one color pigment and a resulting deviation {right arrow over (Z)}={right arrow over (Z)}{right arrow over (Z.sub.z)}{right arrow over ()} of a coloration {right arrow over (Z)} of the reference substrate from the target coloration {right arrow over (Z.sub.z)} is described by
{right arrow over (P)}=.Math.{right arrow over (Z)}

19. The method according to claim 18, wherein the pigment amount correction matrix is determined experimentally on the reference substrate.

20. The method according to claim 18, wherein the determining a target color pigment amount {right arrow over (P.sub.z)} can be performed according to
{right arrow over (P.sub.z)}={right arrow over (P.sub.r)}.Math.{right arrow over (F)}

21. The method according to claim 15, wherein the determining a glass thickness at a plurality of evaluation points on the optical glass takes place based on data sets of an optical calculation and optimization method at least one glass surface of the optical glass.

22. The method according to claim 15, wherein the target coloration {right arrow over (Z.sub.z)} to be obtained for the optical glass according to
{right arrow over (Z.sub.z)}({right arrow over (x)})=I({right arrow over (x)}).Math.{right arrow over (Z.sub.O,z)}+(1I({right arrow over (x)})).Math.{right arrow over (Z.sub.U,z)} depends on a position {right arrow over (x)} on the optical glass with a first target coloration {right arrow over (Z.sub.O,z)} to be obtained at a first evaluation point {right arrow over (x.sub.O)} on the optical glass, a second target coloration {right arrow over (Z.sub.U,z)} to be obtained at a second evaluation point {right arrow over (x.sub.U)} on the optical glass, and an interpolation function I({right arrow over (x)}) satisfying I({right arrow over (x.sub.O)})=1 and I({right arrow over (x.sub.U)})=0, and wherein the determining a reference color pigment amount comprises: determining a first reference color pigment amount {right arrow over (P.sub.O,r)} such that the first reference color pigment amount {right arrow over (P.sub.O,r)}, applied to the reference substrate, causes the first target coloration {right arrow over (Z.sub.O,z)} to be obtained on the optical glass for the reference substrate; and determining a second reference color pigment amount {right arrow over (P.sub.U,r)} such that the second reference color pigment amount {right arrow over (P.sub.U,r)}, applied to the reference substrate, causes the second target coloration {right arrow over (Z.sub.U,z)} to be obtained on the optical glass for the reference substrate.

23. The method according to claim 17, wherein specifying a color correction model comprises: determining a first pigment amount correction matrix such that the relationship between a first deviation {right arrow over (P.sub.O)}={right arrow over (P.sub.O)}{right arrow over (P.sub.O,z)} of a first color pigment amount {right arrow over (P.sub.O)} for at least one color pigment from the first reference color pigment amount {right arrow over (P.sub.O,r)} of the at least one color pigment and a resulting first deviation {right arrow over (Z.sub.O)}={right arrow over (Z.sub.O)}{right arrow over (Z.sub.O,z)} of a first coloration {right arrow over (Z.sub.O)} of the reference substrate from the first target coloration {right arrow over (Z.sub.O,z)} is described by
{right arrow over (P.sub.O)}=.Math.{right arrow over (Z.sub.O)} and determining a second pigment amount correction matrix such that the relationship between a deviation {right arrow over (P.sub.U)}={right arrow over (P.sub.U)}{right arrow over (P.sub.U,z)} of a second color pigment amount {right arrow over (P.sub.U)} for at least one color pigment from the second reference color pigment amount {right arrow over (P.sub.U,r)} of the at least one color pigment and a resulting second deviation {right arrow over (Z.sub.U)}={right arrow over (Z.sub.U)}{right arrow over (Z.sub.U,z)} of a second coloration {right arrow over (Z.sub.U)} of the reference substrate from the second target coloration {right arrow over (Z.sub.U,z)} is described by
{right arrow over (P.sub.U)}=.Math.{right arrow over (Z.sub.U)}

24. The method according to claim 23, wherein the determining a target color pigment amount comprises: determining a first target color pigment subset {right arrow over (P.sub.O,k)} according to
{right arrow over (P.sub.O,z)}={right arrow over (P.sub.O)}.Math.{right arrow over (F)}; determining a second target color pigment subset {right arrow over (P.sub.U,k)} according to
{right arrow over (P.sub.U,z)}={right arrow over (P.sub.U)}.Math.{right arrow over (F)}; and determining the target color pigment amount {right arrow over (P.sub.z)} according to
{right arrow over (P.sub.z)}=I({right arrow over (x)}).Math.{right arrow over (P.sub.O,z)}+(1I({right arrow over (x)})).Math.{right arrow over (P.sub.U,z)}.

25. The method according to claim 15, further comprising applying the target color pigment amount to at least one surface of the optical glass.

26. A coloring system for coloring a spectacle lens, which includes a predetermined glass material, for obtaining a target coloration of the optical glass, the system comprising: a glass material data determiner configured to determine a material-specific intrinsic coloration of the predetermined glass material; a glass thickness determiner configured to determine a glass thickness at a plurality of evaluation points on the optical glass; an intrinsic coloration identifier configured to identify an intrinsic coloration of the optical glass from the material-specific intrinsic coloration of the predetermined glass material and the glass thickness at the plurality of evaluation points on the optical glass; a reference determiner configured to determine a reference color pigment amount for at least one color pigment such that the reference color pigment amount, applied to a reference substrate, causes the target coloration to be obtained on the optical glass for the reference substrate; a color correction model configured to specify a color correction model that describes a relationship between a deviation of a color pigment amount for at least one color pigment from the reference color pigment amount of the at least one color pigment and a resulting deviation of a coloration of the reference substrate from the target coloration; and a target color pigment amount determiner configured to determine a target color pigment amount that deviates from the reference color pigment amount by a color pigment amount correction, which compensates for the identified intrinsic coloration of the optical glass according to the specified color correction model.

27. The coloring system according to claim 26, further comprising a color pigment application configured to apply the target color pigment amount to at least one surface of the optical glass.

28. A non-transitory computer program product comprising program code that, when loaded and executed in a computer system, causes it to perform a method according to claim 15.

Description

[0038] Further preferred details in the implementation of the invention will be described below with reference to the accompanying figures with reference to preferred embodiments. The figures show:

[0039] FIG. 1: a schematic representation of the profile of exemplary interpolation functions for a possible determination of a target color function, as may be used in connection with the present invention;

[0040] FIG. 2A: an exemplary distribution of the material thickness as a function of the location of a prismatic glass;

[0041] FIG. 2B: a sectional view taken along the horizontal axis (x axis) through the center (y=0) of the glass of FIG. 2A;

[0042] FIG. 2C: a profile of the material thickness for a section according to FIG. 2B along the x axis with y=0;

[0043] FIG. 3A: an exemplary distribution of material thickness as a function of the location of a cylindrical glass;

[0044] FIG. 3B: a sectional view taken along the vertical axis (y axis) through the center (x=0) of the glass of FIG. 3A; and

[0045] FIG. 3C: a profile of the material thickness for a section according to FIG. 3B along the y axis with x=0.

[0046] In the case of materials that possess a thickness-dependent intrinsic coloration, it is possible to set a target coloration or a spatially resolved target coloration function by targeted spatially resolved counter-coloring. With this method, it is possible to obtain colorations independent of the material thickness.

[0047] In principle, the present invention can be used with all coloring techniques that enable spatially resolved coloring. For example, with the following known coloring techniques, it is possible to obtain a targeted spatially resolved counter-coloring for the use of the present invention:

[0048] As a suitable coloring technique, mention is to be made of the Nidek method (e.g., EP0982432B1, EP1905890A2, EP1992734B1, EP2261419B1, EP2532781B1): [0049] printing sublimation ink on special sublimation paper, [0050] transferring the color from the sublimation paper to the spectacle lens surface in a vacuum oven by thermal heating, [0051] tempering the glass to diffuse the color into the glass surface.

[0052] In addition, a coloring technique known from EP1683645B1 is suitable (Essilor method): [0053] coating a glass with a primer film; [0054] drying the primer film; [0055] applying a porous color-sensitive film; [0056] applying ink (inkjet process); [0057] tempering the glass to diffuse the color into the glass surface; [0058] removing the porous color-sensitive film.

[0059] Similar coloring techniques (e.g., Itoh method) are suitable as well.

[0060] Further coloring techniques are known from EP2319981B1 and EP2460666B1 (in some cases special high-index polymers that allow coloring): [0061] applying a CAB (cellulose acetate butyrate) layer; [0062] drying the CAB layer; [0063] printing of sublimation ink; [0064] tempering the glass to diffuse the color into the glass surface; [0065] removing the CAB layer.

[0066] Classical coloring by means of dip dyeing baths is basically possible, but the flexibility in spatially resolved color correction is very limited.

[0067] Preferably, the glass material used is first of all characterized with regard to its optical properties. This is preferably done via a material-specific intrinsic coloration vector

{right arrow over (F)}(d):={right arrow over (F.sub.0)}+d.Math.{right arrow over (D)}equation (1),

which is made up of a surface percentage

[00001]$\begin{array}{cc}\stackrel{.fwdarw.}{F_0}.Math.\text{:}=\left(\begin{array}{c}{T}_0\\ a_0^{*}\\ b_0^{*}\end{array}\right)& \mathrm{equation}.Math..Math.\left(2\right)\end{array}$

and a volume percentage

[00002]$\begin{array}{cc}\stackrel{.fwdarw.}{D}.Math.\text{:}=\left(\begin{array}{c}.Math.T\\ .Math.a^{*}\\ .Math.b^{*}\end{array}\right)& \mathrm{equation}.Math..Math.\left(3\right)\end{array}$

the intrinsic coloration as a function of the material thickness d. The representation of the intrinsic coloration as a vector takes place in the selected, and essentially freely selectable, color space. In the following, the L*a*b* color space (CIELAB) is chosen as an example. However, the invention could also be used with other color space models, e.g. RGB color space, CMYK color space, etc.

[0068] Three examples of possible glass materials are mentioned below:

[0069] Material #1:

[00003]$\begin{array}{cc}\mathrm{Surface}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{F_0^{\mathrm{\#1}}}.Math.:=\left(\begin{array}{c}92.06\\ 0.02\\ 0.31\end{array}\right)& \mathrm{equation}.Math..Math.\left(4\right)\\ \mathrm{Volume}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{D^{\mathrm{\#1}}}.Math.:=\left(\begin{array}{c}-0.974\\ -0.060\\ -0.114\end{array}\right)& \mathrm{equation}.Math..Math.\left(5\right)\end{array}$

[0070] Material #2:

[00004]$\begin{array}{cc}\mathrm{Surface}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{F_0^{\mathrm{\#2}}}.Math.\text{:}=\left(\begin{array}{c}94.83\\ -0.35\\ 1.13\end{array}\right)& \mathrm{equation}.Math..Math.\left(6\right)\\ \mathrm{Volume}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{D^{\mathrm{\#2}}}.Math.\text{:}=\left(\begin{array}{c}-0.252\\ -0.141\\ 0.228\end{array}\right)& \mathrm{equation}.Math..Math.\left(7\right)\end{array}$

[0071] Material #3:

[00005]$\begin{array}{cc}\mathrm{Surface}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{F_0^{\mathrm{\#3}}}.Math.\text{:}=\left(\begin{array}{c}94.84\\ -0.46\\ 1.34\end{array}\right)& \mathrm{equation}.Math..Math.\left(8\right)\\ \mathrm{Volume}.Math..Math.\mathrm{percentage}.Math.\text{:}.Math..Math.\stackrel{.fwdarw.}{D^{\mathrm{\#3}}}.Math.\text{:}=\left(\begin{array}{c}-0.193\\ -0.384\\ -0.600\end{array}\right)& \mathrm{equation}.Math..Math.\left(9\right)\end{array}$

[0072] With a reference value for the thickness: d.sub.Ref=8 mm (thickness of a reference substrate of the corresponding material), the intrinsic coloration of the reference substrate results:

[0073] Material #1:

[00006]$\begin{array}{cc}\stackrel{.fwdarw.}{F_8^{\mathrm{\#1}}}.Math.\text{:}=\left(\begin{array}{c}84.26\\ -0.47\\ -0.60\end{array}\right)& \mathrm{equation}.Math..Math.\left(10\right)\end{array}$

[0074] Material #2:

[00007]$\begin{array}{cc}\stackrel{.fwdarw.}{F_8^{\mathrm{\#2}}}.Math.\text{:}=\left(\begin{array}{c}92.82\\ -1.48\\ 2.95\end{array}\right)& \mathrm{equation}.Math..Math.\left(11\right)\end{array}$

[0075] Material #3:

[00008]$\begin{array}{cc}\stackrel{.fwdarw.}{F_8^{\mathrm{\#3}}}.Math.\text{:}=\left(\begin{array}{c}92.30\\ -3.53\\ 6.14\end{array}\right)& \mathrm{equation}.Math..Math.\left(12\right)\end{array}$

[0076] Preferably, at least one target coloration of the glass is determined in the same color space. Distributed across the glass, i.e. in each visual point, this may be the same target coloration. However, the target coloration may also be determined as a color gradient (e.g., stronger or darker coloration at the top than at the bottom). The target coloration constitutes the color tone in which the entire, colored glass should appear at the end. The representation takes place in a selected color space.

EXAMPLE (1)

[0077] [00009]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{z,1}}.Math.\text{:}=\left(\begin{array}{c}{L}_1^{*}\\ a_1^{*}\\ b_1^{*}\end{array}\right)=\left(\begin{array}{c}49.57\\ -0.51\\ 0.59\end{array}\right)& \mathrm{equation}.Math..Math.\left(13\right)\end{array}$

[0078] This coloring vector {right arrow over (Z.sub.z,1)} of the target coloration is to be valid for all evaluation points on the glass (homogeneous target coloration) in example (1). Thus, no location-dependent definition of the target coloration {right arrow over (Z.sub.z,1)} is necessary.

[0079] In the case of a two-color glass (bicolor glass), preferably two visual points (evaluation points) are initially defined especially in a 2-dimensional Cartesian coordinate system, the zero point of which is e.g. in the circle center of the (uncut) glass. The glass is preferably oriented such that the cx side is perpendicular to the x-y plane and the zero angle points to the right. This corresponds to the definition according to the so-called TABO degree scheme.

[0080] A first local target coloration for the visual point at the top (first or top reference point) is defined at the location:

[00010]$\begin{array}{cc}\stackrel{.fwdarw.}{V_O}:=\left(\begin{array}{c}{V}_{x.Math.O}\\ V_{y.Math.O}\end{array}\right)& \mathrm{equation}.Math..Math.\left(14\right)\end{array}$

and the associated first local target coloration vector by:

[00011]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{O,z}}:=\left(\begin{array}{c}{L}_O^{*}\\ a_O^{*}\\ b_O^{*}\end{array}\right)=\left(\begin{array}{c}72,73\\ 2,5.Math.4\\ 10,89\end{array}\right)& \mathrm{equation}.Math..Math.\left(15\right)\end{array}$

[0081] A second local target coloration for the visual point at the bottom (second or bottom reference point) is defined at the location:

[00012]$\begin{array}{cc}\stackrel{.fwdarw.}{V_U}:=\left(\begin{array}{c}{V}_{x.Math.U}\\ V_{y.Math.U}\end{array}\right)& \mathrm{equation}.Math..Math.\left(16\right)\end{array}$

and the associated second local target color vector by:

[00013]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{U,z}}:=\left(\begin{array}{c}{L}_U^{*}\\ a_U^{*}\\ b_U^{*}\end{array}\right)=\left(\begin{array}{c}82,72\\ -2,13\\ 2,3.Math.3\end{array}\right)& \mathrm{equation}.Math..Math.\left(17\right)\end{array}$

[0082] By specifying a target color function

[00014]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_z}\left(x,y\right):=\left(\begin{array}{c}{L}^{*}\left(x,y\right)\\ a^{*}\left(x,y\right)\\ b^{*}\left(x,y\right)\end{array}\right)& \mathrm{equation}.Math..Math.\left(18\right)\end{array}$

a local target coloration can be defined for each position on the glass.

EXAMPLE (2)

[0083] [00015]$\begin{array}{cc}\stackrel{.fwdarw.}{V_O}:=\left(\begin{array}{c}0\\ V_{y.Math.O}\end{array}\right)& \mathrm{equation}.Math..Math.\left(19\right)\\ \mathrm{with}.Math..Math.V_{y.Math.O}=+2.Math.0,0.Math..Math.\mathrm{mm}.Math..Math.\mathrm{and}& \mathrm{equation}.Math..Math.\left(20\right)\\ \stackrel{.fwdarw.}{V_U}:=\left(\begin{array}{c}0\\ V_{y.Math.U}\end{array}\right).Math..Math.\mathrm{and}& \mathrm{equation}.Math..Math.\left(21\right)\\ V_{y.Math.U}=-2.Math.0,0.Math..Math.\mathrm{mm}& \mathrm{equation}.Math..Math.\left(22\right)\end{array}$

[0084] In principle, arbitrary functions that best describe the desired color density distribution can be defined as the interpolation function. As a linear interpolation, for example, the function

[00016]$\begin{array}{cc}{I}_1\left(y\right):=\{\begin{array}{ccc}0& & y<V_{\mathrm{yU}}\\ \frac{y-V_{y.Math.U}}{V_{\mathrm{yO}}-V_{y.Math.U}}& f.Math.\stackrel{\mathrm{.Math.}}{u}.Math.r& V_{\mathrm{yU}}y{V}_{\mathrm{yO}}\\ 1& & y>V_{\mathrm{yO}}\end{array}& \mathrm{equation}.Math..Math.\left(23\right)\end{array}$

can be chosen. Less hard transitions are obtained, for example, by the following interpolation.

[00017]$\begin{array}{cc}{I}_2\left(y\right):=\{\begin{array}{ccc}0& & y<V_{y.Math.U}\\ \frac{1}{2}.Math.\left(1+\sin \left(\left(2.Math.\frac{y-V_{y.Math.U}}{V_{\mathrm{yO}}-V_{y.Math.U}}-1\right).Math.\frac{}{2}\right)\right)& f.Math.\stackrel{\mathrm{.Math.}}{u}.Math.r& V_{y.Math.U}y{V}_{\mathrm{yO}}\\ 1& & y>V_{\mathrm{yO}}\end{array}& \mathrm{equation}.Math..Math.\left(24\right)\end{array}$

[0085] For example (2), the target color function is thus defined by:

{right arrow over (Z.sub.z)}({right arrow over (x)}):={right arrow over (Z.sub.z)}(y).Math.{right arrow over (Z)}.sub.O,z+(1I.sub.1(y)).Math.{right arrow over (Z.sub.U,z)}equation (25)

or for softer transitions by:

{right arrow over (Z.sub.z)}({right arrow over (x)}):={right arrow over (Z.sub.z)}(y)=I.sub.2(y).Math.{right arrow over (Z.sub.O,z)}+(1I.sub.2(y)).Math.{right arrow over (Z.sub.U,z)}equation (26)

[0086] The following describes, by way of example, how the location-dependent coloring is preferably carried out. In a preferred embodiment, three color pigments are used to set the target coloration. This may be three different color pigments of the types red, yellow, blue, but also e.g. color pigments of the types orange, yellow, and blue. In another preferred embodiment, four different color pigments are used, e.g. red, orange, yellow, blue. In specific embodiments, it may also be sufficient to use only two different color pigments or even just one type of color pigment. For the sake of simplicity, it is assumed here by way of example that a three-color pigment system with the pigment colors red, yellow and blue is present.

[0087] If a pigment system has been specified, the amount of pigment used can be defined by a pigment amount vector

[00018]$\begin{array}{cc}\stackrel{.fwdarw.}{P}:=\left(\begin{array}{c}{P}_{\mathrm{Red}}\\ P_{Y.Math.e.Math.l.Math.l.Math.o.Math.w}\\ P_{B.Math.l.Math.u.Math.e}\end{array}\right)& \mathrm{equation}.Math..Math.\left(27\right)\end{array}$

[0088] Preferably, the units of P.sub.Red, P.sub.Yellow and P.sub.Blue are indicated in %, where 100% represents a color pigment reference amount specified once for the respective color pigment.

[0089] In order to obtain a target coloration {right arrow over (Z.sub.z)}, a reference color pigment amount {right arrow over (P.sub.r)} can be specified for a material and a thickness d of a reference substrate. The values of {right arrow over (P.sub.r)} are preferably determined experimentally.

EXAMPLE (1)

[0090] Material #3, thickness d=1.5 mm, homogeneous coloration:

[00019]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{z.Math.1}}:=\left(\begin{array}{c}49,57\\ -0,51\\ 0,5.Math.9\end{array}\right)& \mathrm{equation}.Math..Math.\left(28\right)\\ \stackrel{.fwdarw.}{P_{r,1}}=\left(\begin{array}{c}38,21.Math.\%\\ 48,29.Math.\%\\ 5.Math.8,9.Math.7.Math.\%\end{array}\right)& \mathrm{equation}.Math..Math.\left(29\right)\end{array}$

EXAMPLE (2)

[0091] Material #3, thickness d=1.5 mm, location-dependent coloration at the top:

[00020]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{O,z}}:=\left(\begin{array}{c}72,73\\ 2,54\\ 1.Math.0,8.Math.9\end{array}\right)& \mathrm{equation}.Math..Math.\left(30\right)\\ \stackrel{.fwdarw.}{P_{O,r}}=\left(\begin{array}{c}18,16.Math.\%\\ 34,08.Math.\%\\ 6,30.Math.\%\end{array}\right)& \mathrm{equation}.Math..Math.\left(31\right)\end{array}$

[0092] Material #3, thickness d=1.5 mm, location-dependent coloration at the bottom:

[00021]$\begin{array}{cc}\stackrel{.fwdarw.}{Z_{U,z,}}:=\left(\begin{array}{c}82,72\\ -2,13\\ 2,3.Math.3\end{array}\right)& \mathrm{equation}.Math..Math.\left(32\right)\\ \stackrel{.fwdarw.}{P_{U,r}}=\left(\begin{array}{c}1,74.Math.\%\\ 6,77.Math.\%\\ 6,2.Math.6.Math.\%\end{array}\right)& \mathrm{equation}.Math..Math.\left(33\right)\end{array}$

[0093] In the vicinity of the target coloration {right arrow over (Z.sub.z)}, the change of the color pigments ({right arrow over (P)}{right arrow over (P.sub.r)}) can be described based on the deviation of the color change {right arrow over (Z)}{right arrow over (Z.sub.z)}. Preferably, the coloration in this environment is described by the linear relationship:

{right arrow over (P)}={right arrow over (P.sub.r)}+.Math.({right arrow over (Z)}{right arrow over (Z.sub.z)})(equation (34)

[0094] In this equation, is preferably a 33 matrix whose entries are preferably determined experimentally. In particular, matrix entries have the unit of color % per L*a*b* unit. This pigment amount correction matrix can be specified once for each desired target coloration, in particular independently of the glass material selected in the individual case and the specific glass thickness (i.e. independently of an intrinsic coloration of the glass body).

EXAMPLE (1)

[0095] Material #3, homogeneous target coloration {right arrow over (Z.sub.z,1)}:

[00022]$\begin{array}{cc}\stackrel{.fwdarw.}{M}:=\left(\begin{array}{ccc}-0,389& -0,524& -0,589\\ 0,2.Math.8.Math.9& -0,145& -0,488\\ 0,118& 0,6.Math.7.Math.7& -0,2.Math.4.Math.3\end{array}\right)& \mathrm{equation}.Math..Math.\left(35\right)\end{array}$

EXAMPLE (2)

[0096] Material #3, target coloration at the top {right arrow over (Z.sub.O,z)}:

[00023]$\begin{array}{cc}\stackrel{.fwdarw.}{M_O}:=\left(\begin{array}{ccc}-0,279& -0,375& -0,388\\ 0,2.Math.7.Math.6& -0,137& -0,462\\ 0,074& 0,6.Math.0.Math.8& -0,2.Math.2.Math.6\end{array}\right)& \mathrm{equation}.Math..Math.\left(36\right)\end{array}$

[0097] Material #3, target coloration at the bottom {right arrow over (Z.sub.U,z)}:

[00024]$\begin{array}{cc}\stackrel{.fwdarw.}{M_U}:=\left(\begin{array}{ccc}-0,256& -0,323& -0,389\\ 0,2.Math.8.Math.2& -0,111& -0,441\\ 0,104& 0,5.Math.4.Math.4& -0,2.Math.3.Math.5\end{array}\right)& \mathrm{equation}.Math..Math.\left(37\right)\end{array}$

[0098] In order to determine a suitable color correction for a glass to be colored, first the specific intrinsic coloration of the glass material is determined. FIG. 2A illustrates a thickness profile of a first exemplary prismatic glass. The lines represent the course of constant thicknesses. FIG. 2B illustrates a cross-section through the glass along the x axis with y=0 (i.e., through the center of the uncut glass). In general, the material thickness d is a function of the location d({right arrow over (x)}). In FIG. 2C, for the first exemplary glass, the thickness is given as a function of location along the section of FIG. 2B. The following table shows the material thicknesses for this section at position x in 5 mm increments:

TABLE-US-00001 TABLE 1 Material thicknesses for a section along the x axis with y = 0 in 5 mm increments. x [mm] d [mm] 35 1.9 30 1.76 25 1.68 20 1.65 15 1.66 10 1.73 5 1.84 0 2 5 2.21 10 2.47 15 2.77 20 3.13 25 3.54 30 3.99 35 4.5

[0099] Further, in this example, it is assumed that the material #3 is used.

[0100] Thus, for the thickness-dependent intrinsic coloration {right arrow over (D)}={right arrow over (D.sup.#3)}, equation (9) is applicable. The location-dependent color shift experienced by the glass is thus:

{right arrow over (F)}({right arrow over (x)})=d({right arrow over (x)}).Math.{right arrow over (D)}equation (38)

[0101] Thus, the color shift along the x axis is given by the following table values:

TABLE-US-00002 TABLE 2 Material thicknesses and the color shift L*, a*, b* when using the material # 3 for a section along the x axis with y = 0 in 5 mm increments. The reference thickness of the color shift is in this case 1.5 mm, for example. x [mm] d [mm] L* a* b* 35 1.9 0.077 0.154 0.240 30 1.76 0.050 0.100 0.156 25 1.68 0.035 0.069 0.108 20 1.65 0.029 0.058 0.090 15 1.66 0.031 0.061 0.096 10 1.73 0.044 0.088 0.138 5 1.84 0.066 0.131 0.204 0 2 0.097 0.192 0.300 5 2.21 0.137 0.273 0.426 10 2.47 0.187 0.372 0.582 15 2.77 0.245 0.488 0.762 20 3.13 0.315 0.626 0.978 25 3.54 0.394 0.783 1.224 30 3.99 0.481 0.956 1.494 35 4.5 0.580 1.152 1.800

[0102] In order to at least partially compensate for this color shift, the surface color is now corrected on the glass front and/or on the glass back in particular by a linear combination of front and back such that the target coloration is obtained at least approximately. As target coloration, the target coloration specified in Example (1) is to be obtained here. The overall coloration in transmission is thus independent of the glass thickness and, in the case of a homogeneous coloration, independent of the position {right arrow over (x)} on the glass. For each position on the glass, the color pigment amount can be specified in order to obtain the target coloration at this location, regardless of the pre-coloration.

[0103] Equations (29), (35) and (38) yield for Example (1):

{right arrow over (P.sub.z)}({right arrow over (x)}):={right arrow over (P.sub.r)}.Math.{right arrow over (F)}({right arrow over (x)})equation (39).

[0104] This results in the following color pigment amounts for the material #3 in the coloration according to Example (1) for a section along the x axis with y=0 in 5 mm increments:

TABLE-US-00003 TABLE 3 Material thicknesses and color pigment amounts Red [%], Yellow [%] and Blue [%] for material # 3 and coloration according to Example (1) for a section along the x axis with y = 0 in 5 mm increments. x [mm] d [mm] Red [%] Yellow [%] Blue [%] 35 1.9 38.24 48.41 59.15 30 1.76 38.23 48.37 59.09 25 1.68 38.23 48.34 59.05 20 1.65 38.23 48.33 59.04 15 1.66 38.23 48.34 59.04 10 1.73 38.23 48.36 59.07 5 1.84 38.24 48.39 59.12 0 2 38.25 48.44 59.19 5 2.21 38.27 48.50 59.28 10 2.47 38.29 48.58 59.39 15 2.77 38.31 48.66 59.52 20 3.13 38.34 48.77 59.67 25 3.54 38.37 48.89 59.85 30 3.99 38.41 49.02 60.04 35 4.5 38.44 49.18 60.26

[0105] FIG. 3A illustrates a thickness profile of a second exemplary cylindrical glass with high +power. The lines represent the course of constant thicknesses. FIG. 3B illustrates a cross-section through the second exemplary glass along the y axis with x=0 (i.e., through the center of the uncut glass). In general, the material thickness d is a function of the location d({right arrow over (x)}). In FIG. 3C, for the second exemplary glass, the thickness is given as a function of location along the section of FIG. 3B. The following table shows the material thicknesses for this section in 5 mm increments:

TABLE-US-00004 TABLE 4 Material thicknesses for a section along the y axis with x = 0 in 5 mm increments. y [mm] d [mm] 35 0.25 30 2.69 25 4.71 20 6.34 15 7.61 10 8.53 5 9.13 0 9.4 5 9.35 10 8.97 15 8.26 20 7.21 25 5.8 30 4 35 1.78

[0106] As in the previous example, in this example, it is assumed below that the material #3 is used. Thus, for the thickness-dependent intrinsic coloration {right arrow over (D)}={right arrow over (D.sup.#3)}, equation (9) is applicable. The location-dependent color shift experienced by the glass is thus defined by equation (38):

{right arrow over (F)}({right arrow over (x)})=d({right arrow over (x)}).Math.{right arrow over (D)}

[0107] Thus, the color shift along the y axis is given by the following table values:

TABLE-US-00005 TABLE 5 Material thicknesses and the color shift L*, a*, b* when using the material # 3 for a section along the y axis with x = 0 in 5 mm increments. The reference thickness of the color shift is in this case 1.5 mm, for example. Y [mm] d [mm] L* a* * 35 0.25 0.242 0.480 0.750 30 2.69 0.230 0.457 0.714 25 4.71 0.620 1.232 1.926 20 6.34 0.935 1.858 2.904 15 7.61 1.181 2.346 3.666 10 8.53 1.358 2.699 4.218 5 9.13 1.474 2.929 4.578 0 9.4 1.526 3.033 4.740 5 9.35 1.517 3.014 4.710 10 8.97 1.443 2.868 4.482 15 8.26 1.306 2.595 4.056 20 7.21 1.103 2.192 3.426 25 5.8 0.831 1.651 2.580 30 4 0.483 0.960 1.500 35 1.78 0.054 0.108 0.168

[0108] Now, the surface coloration is corrected either on the glass front or on the glass back or a linear combination of front and back, in order to approximate the overall coloration as well as possible to the desired target coloration. Since in the example described here, a bicolor coloration according to the target coloration given above as Example (2) is to be obtained, it is first assumed that this target coloration can be described starting from two homogeneous plain colorations. For each position on the glass, the color pigment amount of the coloration at the top (0) and at the bottom (U) can now be specified.

[0109] The equations (31), (36) and (38) yield for Example (2) for the upper target color pigment amount:

{right arrow over (P.sub.O,z)}({right arrow over (x)}):={right arrow over (P.sub.O,r)}.Math.{right arrow over (F)}({right arrow over (x)})equation (40).

[0110] The equations (33), (37) and (38) yield for Example (2) for the lower target color pigment amount:

{right arrow over (P.sub.U,z)}({right arrow over (x)}):={right arrow over (P.sub.U,r)}.Math.{right arrow over (F)}({right arrow over (x)})equation (41).

[0111] For the color pigment amounts of the two partial colorations, the following values result along the y axis (at x=0):

TABLE-US-00006 TABLE 6 Material Thicknesses and color pigment amounts Red[%], Yellow[%] and Blue[%] for Material # 3 and coloration at the top and coloration at the bottom for a section along the y axis with x = 0 in 5 mm increments. Top Bottom Y[mm] d[mm] Red[%] Yellow[%] Blue[%] Red[%] Yellow[%] Blue[%] 35 0.25 18.11 34.20 6.45 1.67 6.88 6.41 30 2.69 18.20 34.16 6.40 1.82 6.84 6.35 25 4.71 18.27 34.13 6.37 1.94 6.82 6.32 20 6.34 18.33 34.13 6.35 2.03 6.81 6.31 15 7.61 18.37 34.13 6.36 2.11 6.82 6.32 10 8.53 18.40 34.15 6.38 2.16 6.83 6.34 5 9.13 18.43 34.18 6.43 2.20 6.86 6.38 0 9.4 18.44 34.22 6.49 2.22 6.91 6.44 5 9.35 18.43 34.28 6.57 2.21 6.97 6.52 10 8.97 18.42 34.35 6.67 2.19 7.04 6.62 15 8.26 18.39 34.44 6.78 2.15 7.12 6.73 20 7.21 18.36 34.54 6.92 2.09 7.22 6.86 25 5.8 18.31 34.65 7.08 2.00 7.33 7.01 30 4 18.24 34.77 7.25 1.89 7.46 7.18 35 1.78 18.17 34.92 7.45 1.76 7.60 7.37

[0112] Analogous to the interpolation formula for the interpolated target colorations of equations (25) and (26), the color pigment amounts can be interpolated as well.

{right arrow over (P.sub.z)}({right arrow over (x)}):={right arrow over (P.sub.z)}(y)=I.sub.2(y).Math.{right arrow over (P.sub.O,z)}+(1I.sub.2(y)).Math.{right arrow over (P.sub.U,z)}equation (42)

[0113] The color pigment amount of the upper (first) partial coloration can thus be specified as follows:

TABLE-US-00007 TABLE 7 Percentage of color pigments from the Percentage Top Top Percentage Top Y[mm] Red[%] Yellow[%] Blue[%] I2 Red[%] Yellow[%] Blue[%] 35 18.11 34.20 6.45 0.000 0.00 0.00 0.00 30 18.20 34.16 6.40 0.000 0.00 0.00 0.00 25 18.27 34.13 6.37 0.000 0.00 0.00 0.00 20 18.33 34.13 6.35 0.000 0.00 0.00 0.00 15 18.37 34.13 6.36 0.038 0.70 1.30 0.24 10 18.40 34.15 6.38 0.146 2.70 5.00 0.94 5 18.43 34.18 6.43 0.309 5.69 10.55 1.98 0 18.44 34.22 6.49 0.500 9.22 17.11 3.24 5 18.43 34.28 6.57 0.691 12.74 23.70 4.54 10 18.42 34.35 6.67 0.854 15.72 29.32 5.69 15 18.39 34.44 6.78 0.962 17.69 33.13 6.52 20 18.36 34.54 6.92 1.000 18.36 34.54 6.92 25 18.31 34.65 7.08 1.000 18.31 34.65 7.08 30 18.24 34.77 7.25 1.000 18.24 34.77 7.25 35 18.17 34.92 7.45 1.000 18.17 34.92 7.45

[0114] The color pigment amount of the lower (second) partial coloration can thus be specified as follows:

TABLE-US-00008 TABLE 8 Percentage of color pigments from the Percentage Bottom Bottom Percentage Bottom Y[mm] Red[%] Yellow[%] Blue[%] 1.0 -I2 Red[%] Yellow[%] Blue[%] 35 1.67 6.88 6.41 1.000 1.67 6.88 6.41 30 1.82 6.84 6.35 1.000 1.82 6.84 6.35 25 1.94 6.82 6.32 1.000 1.94 6.82 6.32 20 2.03 6.81 6.31 1.000 2.03 6.81 6.31 15 2.11 6.82 6.32 0.962 2.03 6.56 6.08 10 2.16 6.83 6.34 0.854 1.85 5.83 5.41 5 2.20 6.86 6.38 0.691 1.52 4.75 4.41 0 2.22 6.91 6.44 0.500 1.11 3.45 3.22 5 2.21 6.97 6.52 0.309 0.68 2.15 2.01 10 2.19 7.04 6.62 0.146 0.32 1.03 0.97 15 2.15 7.12 6.73 0.038 0.08 0.27 0.26 20 2.09 7.22 6.86 0.000 0.00 0.00 0.00 25 2.00 7.33 7.01 0.000 0.00 0.00 0.00 30 1.89 7.46 7.18 0.000 0.00 0.00 0.00 35 1.76 7.60 7.37 0.000 0.00 0.00 0.00

TABLE-US-00009 TABLE 9 Overall color pigment amounts Red [%], Yellow [%] and Blue [%] for material # 3 and coloration 1 (Example (1)) for a section along the y axis with x = 0 in 5 mm increments. Overall Y [mm] Red [%] Yellow [%] Blue [%] 35 1.67 6.88 6.41 30 1.82 6.84 6.35 25 1.94 6.82 6.32 20 2.03 6.81 6.31 15 2.73 7.85 6.32 10 4.54 10.83 6.35 5 7.21 15.30 6.40 0 10.33 20.57 6.47 5 13.43 25.85 6.55 10 16.04 30.35 6.66 15 17.78 33.40 6.78 20 18.36 34.54 6.92 25 18.31 34.65 7.08 30 18.24 34.77 7.25 35 18.17 34.92 7.45

[0115] Although preferred embodiments have been described by way of example with reference to a color space vector in the L*a*b* color space and by coloring with color pigments of the types red, yellow and blue, the invention is not limited to this color space representation or the color pigment selection described by way of example. Instead, the invention can also be applied analogously in other color space models and with other basic colors. The invention is not limited to the use of 3 basic colors. In particular, the invention is also applicable to coloring processes in which the target coloration is obtained with 4 or more basic colors. In this case, only the dimension of the color pigment amount vector {right arrow over (P)} and the pigment amount correction matrix are adjusted accordingly. If the material and three colors are given, the result is always clear. If, for example, a color pigment or a mixture of color pigments representing an exact compensation of the counter-coloration is provided, then the problem simplifies to local counter-coloring by means of color or of the color mixture. The disadvantage of such a firmly defined color mixture is that possible adjustments are not possible afterward. However, this method does without an adjustment color.