Method and system for reconstructing aberrated image profiles through simulation
AssigneeNikon Precision Inc.
InventorSteven Douglas Slonaker
Life of this patent
Estimating the term…
Abstract
A system and method of calculating estimated image profiles. The system and method includes providing lens characteristic data and performing simulation calculations for various levels of aberration components using the lens characteristic data. A response surface functional relation is built between selected variables of the lens characteristics, in particular the lens aberration components, and the Image Profile using the simulation calculations. Evaluation is then performed on the arbitrary specified aberration values of a lens in relation to the response surface functional relations to provide a calculated estimate of the Image Profile for the specified aberration values. A machine readable medium and exposure apparatus are also provided.
Claims17
A method of calculating estimated image profiles implemented on a tangibly-embodied storage medium resident on one or more computing devices, comprising the steps of:
- providing imaging configuration characteristic data;
- performing simulation calculations for various levels for each aberration component using the imaging configuration characteristic data using a processor of the one or more computing devices;
- building response surface functional relations using the processor of the one or more computing devices between variables of lens characteristics and an image profile of interest using the simulation calculations;
- and
- evaluating specified aberration values of a lens in relation to the response surface functional relations using the processor of the one or more computing devices to provide an estimate of the image profile in a presence of specified aberration(s),
- wherein the building steps includes:
- providing an order fitting function expressed as:
- Ispx(x)=b0+b1x+b2x2+b3x3+. . . .+bnxn
- where Ispx is aerial image intensity or amplitude at a simulation pixel (spx) and x indicates defocus;
- and
- expressing a change of the coefficients b0 . . . bn described by an order fitting function expressed as:
- b
- i
-
- (
- with
-
- _
-
- aberration
- )
- =
-
- b
- i
-
- (
- w
- /
- o
-
- _
-
- aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- Δ
-
-
- b
- i
-
- (
- cj
- )
- =
-
- b
- i
-
- (
- w
- /
- o
-
- _
-
- aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- φ
- 0
-
- (
- i
- ,
- j
- )
- +
- φ
- 1
-
- (
- i
- ,
- j
- )
-
- c
- j
- +
- φ
- 2
- (
- i
- ,
- j
- )
-
- c
- j
- 2
- +
-
- φ
- 3
-
- (
- i
- ,
- j
- )
-
- c
- j
- 3
- +
- …
- +
- φ
- n
-
- (
- i
- ,
- j
- )
-
- c
- j
- n
- wherein
- =0, 1, 2, 3, . . . . , n;
- bi(with aberration) and bi(w/o aberration) represents one of the coefficients b0. . . bn influenced by lens aberrations and the coefficients b0 . . . bn without aberrations, respectively, and
- Δbi indicates the change in coefficients and is expressed by an nth order fitting function of jth Zernike coefficient cj,
- φ0(ij) . . . φn(ij) are the coefficients of the fitting function, determined following the performing step of setup simulations of image profile as a function of regularly iterated values of lens aberration.
A method of calculating estimated image profiles implemented on a tangibly-embodied storage medium resident on one or more computing devices, comprising the steps of:
- performing simulation calculations using a processor of the one or more computing devices for various levels for each aberration component using image configuration characteristic data;
- building response surface functional relations using the processor of the one or more computing devices between variables of the image configuration characteristics and the image profile of interest using the simulation calculations as data input to be fit using:
- Ispx(x)=b0+b1x+b2x2+b3x3+. . . . +bnxn
- where Ispx indicates aerial image intensity or amplitude at a simulation pixel (spx) and x indicates defocus;
- and
- expressing a change of the coefficients b0 . . . bn using the processor of the one or more computing devices described by an order fitting function as:
- b
- i
-
- (
- with
-
- _
-
- aberration
- )
- =
-
- b
- i
-
- (
- w
- /
- o
-
- _
-
- aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- Δ
-
-
- b
- i
-
- (
- cj
- )
- =
-
- b
- i
-
- (
- w
- /
- o
-
- _
-
- aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- φ
- 0
-
- (
- i
- ,
- j
- )
- +
- φ
- 1
-
- (
- i
- ,
- j
- )
-
- c
- j
- +
- φ
- 2
- (
- i
- ,
- j
- )
-
- c
- j
- 2
- +
-
- φ
- 3
-
- (
- i
- ,
- j
- )
-
- c
- j
- 3
- +
- …
- +
- φ
- n
-
- (
- i
- ,
- j
- )
-
- c
- j
- n
- wherein
- bi(with aberration) and bi(w/o aberration) represents the coefficients b0 . . . bn influenced by lens aberrations and the coefficients b0 . . . bn, without aberrations, respectively,
- Δbi indicates the change in coefficients and it is expressed by an nth order fitting function of jth Zernike coefficient cj;
- and
- φ0(ij) . . . φn(ij) are the coefficients of the fitting function;
- and
- summing an impact from at least one of all new specified aberration coefficients and combinations of aberration coefficients from the built response surface functional relations using the processor of the one or more computing devices to provide lens adjustment data.
Dependencies are inferred from the claim text.