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US 9,176,330 B2Granted
Method for optimizing a spectacle lens with a diffraction grating
AssigneeRodenstock GmbH
InventorsWolfgang Becken, Gregor Esser, Helmut Altheimer, Werner Mueller, Dietmar Uttenweiler
Life of this patent
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Abstract
A computer-implemented method and a device for optimizing an optical element comprising at least one diffraction grating, wherein at least one refractive surface contributing to the refractive light deflection and/or the at least one diffraction grating of the optical element are/is optimized in such a way as to minimize the color fringe and at least a second-order aberration of the optical element. Also, a corresponding production method and a corresponding device for producing an optical element comprising at least one diffraction grating.
Claims22
A method for designing and manufacturing an optical element having at least one diffraction grating, the method comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F1:
- F
- 1
- =
- ∑
- λ
-
- F
- monochrom
-
- (
- λ
- )
- ,
- wherein Fmonochrom(λ) is a monochromatic target function for the wavelength λ;
- and wherein the target function F1 is evaluated for at least two different wavelengths, and
- wherein the target function F1 is a target function:
- F
- 1
- =
- ∑
- i
- ,
- λ
-
- g
- Z
-
- (
- i
- ,
- λ
- )
-
- (
- Z
- Δ
-
- (
- i
- ,
- λ
- )
- -
- Z
- Δ
- ,
- target
-
- (
- i
- ,
- λ
- )
- )
- 2
- +
- g
- S
-
- (
- i
- ,
- λ
- )
-
- (
- S
- Δ
-
- (
- i
- ,
- λ
- )
- -
- S
- Δ
- ,
- target
-
- (
- i
- ,
- λ
- )
- )
- 2
- where
- ZΔ(i,λ) is the actual value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- ZΔ,target(i,λ) is the target value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ(i,λ) is the actual value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ,target(i,λ) is the target value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- gZ(i,λ) is the weighting of the amount of the astigmatic deviation at the ith evaluation point of the optical element for the wavelength λ;
- and
- gS(i,λ) is the weighting of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- and
- manufacturing the optical element on the basis of the designed at least one refractive surface and/or the at least one diffraction grating.
96 more elements
A method for designing and manufacturing an optical element having at least one diffraction grating, the method comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F2:
- F
- 2
- =
- F
- monochrom
-
- (
- λ
- 0
- )
- +
- ∑
- i
-
- g
- FL
-
- (
- i
- )
- ×
- f
-
- (
- S
- S
-
- (
- i
- ,
- λ
- 2
- )
- -
- S
- S
-
- (
- i
- ,
- λ
- 1
- )
- )
- 2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFLF(i) is the weighting of the longitudinal chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ1) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- and
- ƒ(SSK(i,λ2)−SSK(i,λ1)) is a function of the difference of the vergence matrices of the wavefront at the vertex sphere for two different wavelengths λ1 and λ2;
- and
- manufacturing the optical element on the basis of the designed at least one refractive surface and/or the at least one diffraction grating.
53 more elements
A method for designing and manufacturing an optical element having at least one diffraction grating, the method comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F3:
- F
- 3
- =
- F
- monochrom
-
- (
- λ
- 0
- )
- +
- ∑
- i
-
- g
- FQF
-
- (
- i
- )
- ×
- g
-
- (
- Δ
-
-
- φ
- SK
-
- (
- i
- ,
- λ
- 2
- ,
- λ
- 1
- )
- )
- 2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFQF(i) is the weighting of the lateral chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ1) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- ΔφSK(i, λ2, λ1) is the angle between the object-side main rays for different wavelengths λ1 and λ2;
- and
- g(ΔφSK(i, λ2, λ1)) is a function of the angle between the object-side main rays for different wavelengths λ1 and λ2;
- and
- manufacturing the optical element on the basis of the designed at least one refractive surface and/or the at least one diffraction grating.
50 more elements
A method for producing an optical element with at least one diffraction grating, comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F1;
- F
- 1
- =
- ∑
- λ
-
-
- F
- monochrom
-
- (
- λ
- )
- ,
- where Fmonochrom(λ) is a monochromatic target function for the wavelength λ;
- and wherein the target function F1 is evaluated for at least two different wavelengths, and
- wherein the target function F1 is a target function:
- F
- 1
- =
- ∑
- i
- ,
- λ
-
-
- g
- z
-
- (
- i
- ,
- λ
- )
-
- (
- Z
- Δ
-
- (
- i
- ,
- λ
- )
- -
- Z
- Δ
- ,
- target
-
- (
- i
- ,
- λ
- )
- )
- 2
- +
- g
- S
-
- (
- i
- ,
- λ
- )
-
- (
- S
- Δ
-
- (
- i
- ,
- λ
- )
- -
- S
- Δ
- ,
- target
-
- (
- i
- ,
- λ
- )
- )
- 2
- where
- ZΔ(i,λ) is the actual value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- ZΔ,target(i,λ) is the target value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ(i,λ) is the actual value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ,target(i,λ) is the target value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- gZ(i,λ) is the weighting of the amount of the astigmatic deviation at the ith evaluation point of the optical element for the wavelength λ;
- and
- gS(i,λ) is the weighting of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- providing, by the computer, processing data of the designed optical element;
- and
- manufacturing the optical element on the basis of the provided processing data.
99 more elements
A device for producing an optical element with at least one diffraction grating, comprising:
- a designer adapted to perform a design of the optical element by designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F1;
- F
- 1
- =
- ∑
- λ
-
-
- F
- monochrom
-
- (
- λ
- )
- ,
- where Fmonochrom(λ) is a monochromatic target function for the wavelength λ;
- and wherein the target function F1 is evaluated for at least two different wavelengths, and
- wherein the target function F1 is a target function:
- F1=Σi,λgZ(i,λ)(ZΔ(i,λ)−ZΔ,target(i,λ))2+gS(i,λ)(SΔ(i,λ)−SΔ,target(i,λ)2,
- where
- ZΔ(i,λ) is the actual value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- ZΔ,target(i,λ) is the target value of the amount of the astigmatic error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ(i,λ) is the actual value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- SΔ,target(i,λ) is the target value of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- gZ(i,λ) is the weighting of the amount of the astigmatic deviation at the ith evaluation point of the optical element for the wavelength λ;
- and
- gS(i,λ) is the weighting of the refractive error at the ith evaluation point of the optical element for the wavelength λ;
- and
- a processor adapted to manufacture the designed optical element.
27 more elements
A method for producing an optical element with at least one diffraction grating, comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F2:
- F
- 2
- =
- F
- monochrom
-
- (
- λ
- 0
- )
- +
- ∑
- i
-
-
- g
- FL
-
- (
- i
- )
- ×
- f
-
- (
- S
- S
-
- (
- i
- ,
- λ
- 2
- )
- -
- S
- S
-
- (
- i
- ,
- λ
- 1
- )
- )
- 2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFLF(i) is the weighting of the longitudinal chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- and
- ƒ(SSK(i,λ2)−SSK(i,λ1)) is a function of the difference of the vergence matrices of the wavefront at the vertex sphere for two different wavelengths λ1 and λ2;
- providing, by the computer, processing data of the designed optical element;
- and
- manufacturing the optical element on the basis of the provided processing data.
55 more elements
A device for producing an optical element with at least one diffraction grating, comprising:
- a designer adapted to perform a design of the optical element by designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F2:
- F
- 2
- =
- F
- monochrom
-
- (
- λ
- 0
- )
- +
- ∑
- i
-
-
- g
- FL
-
- (
- i
- )
- ×
- f
-
- (
- S
- S
-
- (
- i
- ,
- λ
- 2
- )
- -
- S
- S
-
- (
- i
- ,
- λ
- 1
- )
- )
- 2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFLF(i) is the weighting of the longitudinal chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ1) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- and
- ƒ(SSK(i,λ2)−SSK(i,λ1)) is a function of the difference of the vergence matrices of the wavefront at the vertex sphere for two different wavelengths λ1 and λ2;
- and
- a processor adapted to manufacture the designed optical element.
54 more elements
A method for producing an optical element with at least one diffraction grating, comprising:
- designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F3:
- F3=Fmonochrom(λ0)+ΣigFQF(i)×g(ΔφSK(i,λ2,λ1))2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFQF(i) is the weighting of the lateral chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ1) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- ΔφSK(i, λ2, λ1) is the angle between the object-side main rays for different wavelengths λ1 and λ2;
- and
- g(ΔφSK(i, λ2, λ1)) is a function of the angle between the object-side main rays for different wavelengths λ1 and λ2;
- providing, by the computer, processing data of the designed optical element;
- and
- manufacturing the optical element on the basis of the provided processing data.
11 more elements
A device for producing an optical element with at least one diffraction grating, comprising:
- a designer adapted to perform a design of the optical element by designing, by a computer, at least one refractive surface contributing to refractive light deflection and/or the at least one diffraction grating of the optical element in such a way as to minimize the color fringe and at least one second-order aberration of the optical element, by minimizing or maximizing a target function, which depends on the at least one second-order aberration and on the longitudinal and/or lateral chromatic aberration(s) of the optical element,
- wherein the target function is a target function F3:
- F
- 3
- =
- F
- monochrom
-
- (
- λ
- 0
- )
- +
- ∑
- i
-
-
- g
- FQF
-
- (
- i
- )
- ×
- g
-
- (
- Δφ
- SK
-
- (
- i
- ,
- λ
- 2
- ,
- λ
- 1
- )
- )
- 2
- where
- Fmonochrom(λ) is a monochromatic target function for a predetermined wavelength λ0;
- gFQF(i) is the weighting of the lateral chromatic aberration at the ith evaluation point of the optical element;
- SSK(i,λ1) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ1 and for the ith evaluation point;
- SSK(i,λ2) is the vergence matrix of the wavefront at the vertex sphere for the wavelength λ2 and for the ith evaluation point;
- ΔφSK(i, λ2, λ1) is the angle between the object-side main rays for different wavelengths λ1 and λ2;
- and
- g(ΔφSK(i, λ2, λ1)) is a function of the angle between the object-side main rays for different wavelengths λ1 and λ2;
- and
- a processor adapted to manufacture the designed optical element.
48 more elements
Dependencies are inferred from the claim text.