Method and device for accelerated calculation of wavefronts through a complex optical system
Simulating an optical system by calculating wavefronts. The method includes: setting up at least one wavefront transfer function for the optical system, wherein the wavefront transfer function is designed to assign a respective associated emergent wavefront to wavefronts entering into the optical system, taking into account imaging errors with an order greater than the order of defocus; and evaluating the at least one wavefront transfer function for at least one wavefront entering into the optical system.
1 . A method for simulating a complex optical system using a wavefront calculation, wherein an effect of the complex optical system exceeds a single refraction, a single propagation, or a single reflection, the method comprising:
setting up at least one wavefront transfer function for the optical system, wherein the wavefront transfer function is designed to assign a respective associated emergent wavefront to wavefronts entering into the optical system, taking into account imaging errors with an order greater than the order of defocus; and
evaluating the at least one wavefront transfer function for at least one wavefront entering into the optical system.
2 . The method according to claim 1 , wherein the method is a method for optimizing a total optical system, wherein the optical system represents a second partial system of the total optical system, and the total optical system additionally comprises a first partial system, wherein in particular the first partial system and/or the second partial system can be varied during the optimization.
3 . The method according to claim 2 , wherein the first partial system is a spectacle lens and the second partial system is a model eye.
4 . The method according to claim 2 , wherein:
the at least one wavefront entering into the optical system is determined based on a predetermined test wavefront which passes through the first partial system.
5 . The method according to claim 2 , further comprising:
assessing the total optical system based on a result of the evaluation of the at least one wavefront transfer function for the at least one wavefront entering into the optical system, wherein the total optical system is assessed under variation of the first partial system until the assessment satisfies a predetermined condition, wherein
the variation of the first partial system in particular comprises a changing of at least one refracting surface and/or of at least one distance between refracting surfaces of the first partial system, and/or a tilting and/or displacement of the first partial system relative to the second partial system.
6 . The method according to claim 5 , wherein:
the assessment of the total optical system is performed based on the result of the evaluation of the at least one wave transfer function for a first wavefront entering into the optical system, and also based on the result of the evaluation of the at least one wave transfer function for a second incident wavefront, wherein the first partial system is located at a first position and a first orientation relative to the second partial system upon incidence of the first wavefront, wherein the first partial system is located at a second position and orientation relative to the second partial system upon incidence of the second wavefront, and wherein the first position differs from the second position and/or the first orientation differs from the second orientation.
7 . The method according to claim 5 , wherein
the assessment of the total optical system is performed based on the result of the evaluation of a first wave transfer function for a first wavefront entering into the optical system, and also based on the result of the evaluation of a second wave transfer function for an additional incident wavefront, wherein the first partial system is located at a first position and orientation relative to the second partial system upon incidence of the first wavefront, wherein the first partial system is located at a second position and orientation relative to the second partial system upon incidence of the additional wavefront, wherein the first position differs from the second position and/or the first orientation differs from the second orientation, and wherein the second wave transfer function differs from the first wave transfer function.
8 . The method according to claim 2 , wherein
the first partial system is a spectacle lens and the second partial system is a model eye, and wherein gaze movements of the model eye that produce a variation in a position of a piercing point of a principal ray through the spectacle lens surfaces, and/or a variation of an angle of incidence on a spectacle lens surface, are described as a variation of the position and/or of orientation of the spectacle lens in a coordinate system of the eye.
9 . The method according to claim 1 , wherein the optical system is a GRIN system or comprises at least one GRIN element.
10 . The method according to claim 1 , wherein the at least one wave transfer function has formula
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wherein the indices of the tuple k=(k 1 , k 2 , . . . , k p-1 ) run over the range P(k*)≤p−2 and 0≤k 1 ≤2(p−P(k*)−2)+δ P(k*),0 , wherein P(k*)=Σ j=1 p-1 jk j+1 , and wherein − r 1 0 (p−1)=p−δ (p-1),1 and −Δ r 1 (p−1, k*)=(p−3)+δ (p-1),1 −P(k**) apply, and wherein β=(−BE 2 +A) −1 is provided as a function of the at least one incident wavefront and of the optical system, and wherein A, B and the wavefront transfer function b pk are provided as a function of the components of the optical system.
11 . The method according to claim 1 , wherein both incident wavefronts and emergent wavefronts are respectively represented by coefficients with regard to basic elements of a basic system whose basic elements are classified according to at least one order parameter, and wherein the at least one wave transfer function is provided in that it assigns the respective associated emergent wavefront to the wavefronts entering into the optical system in that it determines, for a basic element appearing in the representation of an emergent wavefront, the coefficients with regard to this basic element appearing in the representation of the emergent wavefront, depending on coefficients of the associated incident wavefront with regard to a plurality of those basic elements whose value of the order parameter is less than or equal to the value of the order parameter of the respective basic element appearing in the representation of the emergent wavefront.
12 . The method according to claim 11 , wherein the basic system is a decomposition for aberrations, wherein the order parameter is an order p of the aberrations, wherein the coefficients associated with the basic elements of the basic system are provided in that a p-th order coefficient of the incident wavefront is an aberration E p of the incident wavefront, and in that a p-th order coefficient of the associated emergent wavefront is an aberration E′ p of the associated emergent wavefront, and wherein p≥2.
13 . The method according to claim 11 , wherein the order parameter is a first order parameter, and wherein the basic elements of the basic system are additionally classified according to at least one second order parameter whose value range depends on the value of the first order parameter.
14 . The method according to claim 13 , wherein the basic system is a decomposition for aberrations, wherein the first order parameter is the sum of orders p x and p y of the aberrations, wherein the second order parameter is one of the orders p x and p y , wherein the coefficients associated with the basic elements of the basic system are provided in that p-th order coefficients of the incident wavefront are aberrations E px,py of the incident wavefront, and in that p-th order coefficients of the associated emergent wavefront are aberrations E′ px,py of the associated emergent wavefront, and wherein p≥2 and p x ≥0 and p y ≥0.
15 . The method according to claim 13 , wherein the basic system is a decomposition for Taylor series of wavefront vertex depths, wherein the first order parameter is the sum p of orders p x and p y of the Taylor series of the wavefront vertex depths; wherein the second order parameter is one of the orders p x and p y , wherein the coefficients associated with the basic elements of the basic system are provided in that a p-th order coefficients of the incident wavefront are Taylor series w (px,py) of the vertex depth of the incident wavefront, and in that the p-th order coefficients of the associated emergent wavefront are Taylor series w′ (px,py) of the vertex depth of the associated emergent wavefront; and wherein p≥2 and p x ≥0 and p y ≥0.
16 . The method according to claim 13 , wherein the basic system is a decomposition for Taylor series of a wavefront OPD, wherein the order parameter is the sum p of orders p x and p y of the Taylor series of the wavefront OPD, wherein the second order parameter is one of the orders p x and p y , wherein the coefficients associated with the basic elements of the basic system are provided in that p-th order coefficients of the incident wavefront are Taylor series OPD (px,py) of the incident wavefront, and in that p-th order coefficients of the associated emergent wavefront are Taylor series OPD′ (px,py) of the associated emergent wavefront, and wherein p≥2 and p x ≥0 and p y ≥0.
17 . The method according to claim 13 , wherein the basic system is a decomposition for derivatives of direction functions, wherein the order parameter is the sum i of orders i x and i y of the derivatives of the direction functions, wherein the second order parameter is one of the orders i x and i y , wherein the coefficients associated with the basic elements of the basic system are provided in that i-th order coefficients of the incident wavefront are derivatives t x (ix,iy) , t y (ix,iy) of direction functions t x (x,y), t y (x,y) of the incident wavefront, and in that i-th order coefficients of the associated emergent wavefront are derivatives t′ x (ix,iy) , t′ y (ix,iy) of the direction functions t′ x (x′,y′), t′ y (x′,y′) of the associated emergent wavefront, and wherein i≥1 and i x ≥0 and i y ≥0.
18 . The method according to claim 13 , wherein the basic system is a decomposition for Zernike polynomials, wherein the first order parameter is a radial order n of the Zernike polynomials; wherein the second order parameters is an azimuthal order m of the Zernike polynomials; wherein the coefficients associated with the basic elements of the basic system are provided in that n-th order coefficients of the incident wavefront are Zernike coefficients Z n m of the incident wavefront, and in that n-th order coefficients of the associated emergent wavefront are Zernike coefficient Z′ n m of the associated emergent wavefront; wherein n≥2 and −n≤m≤n; wherein m is even for even n and odd for odd n;′ and wherein the Zernike coefficients in particular relate to an established pupil.
19 . The method according to claim 11 , wherein the basic system is a decomposition for Taylor series of wavefront vertex depths, wherein the order parameter is an order p of the Taylor series of the wavefront vertex depths; wherein the coefficients associated with the basic elements of the basic system are provided in that a p-th order coefficient of the incident wavefront is a Taylor series w (p) of the vertex depth of the incident wavefront, and in that the p-th order coefficient of the associated emergent wavefront is a Taylor series w′ (p) of the vertex depth of the associated emergent wavefront; and wherein p≥2.
20 . The method according to claim 11 , wherein the basic system is a decomposition for Taylor series of a wavefront OPD, wherein the order parameter is an order p of the Taylor series of the wavefront OPD, wherein the coefficients associated with the basic elements of the basic system are provided in that a p-th order coefficient of the incident wavefront is a Taylor series OPD (p) of the incident wavefront, and in that the p-th order coefficient of the associated emergent wavefront is a Taylor series OPD′ (p) of the associated emergent wavefront, and wherein p≥2.
21 . The method according to claim 11 , wherein the basic system is a decomposition for derivatives of direction functions, wherein the order parameter is an order i of the derivatives of the direction functions, wherein the coefficients associated with the basic elements of the basic system are provided in that an i-th order coefficient of the incident wavefront is a derivative t (i) of a direction function t(x) of the incident wavefront, and in that an i-th order coefficient of the associated emergent wavefront is a derivative t′ (i) of a direction function t′(x′) of the associated emergent wavefront, and wherein i≥1.
22 . The method according to claim 11 , wherein the basic system is a decomposition for Zernike polynomials, wherein the order parameter is a radial order n of the Zernike polynomials; wherein the coefficients associated with the basic elements of the basic system are provided in that an n-th order coefficient of the incident wavefront is a Zernike coefficient Z n of the incident wavefront, and in that an n-th order coefficient of the emergent wavefront is a Zernike coefficient Z′ n of the associated emergent wavefront; wherein n≥2; and wherein the Zernike coefficients in particular relate to an established pupil.
23 . A non-transitory computer program product comprising computer-readable instructions which, when loaded into a memory of a computer and executed by the computer, have the effect that the computer implements a method according to claim 1 .
24 . A method for producing a spectacle lens, comprising:
calculating or optimizing a spectacle lens using a method according to claim 1 ; and
providing manufacturing data of the spectacle lens calculated or optimized in such a way, and/or producing the spectacle lens calculated or optimized in such a way.
25 . A device for producing a spectacle lens, comprising:
a calculator or optimizer designed to calculate or optimize the spectacle lens using a method according to claim 1 ; and
a finisher designed to finish the spectacle lens.
26 . A device for simulating an optical system by means of calculating a wavefront, wherein the optical system is a complex optical system whose effect exceeds a single refraction, a single propagation, or a single reflection, comprising:
a modeling module designed to provide at least one wavefront transfer function for the optical system, wherein the wavefront transfer function is designed to assign an associated emergent wavefront to every wavefront entering into the optical system, under consideration of imaging errors with an order greater than the order of defocus; and
an evaluation module designed to evaluate the at least one wavefront transfer function for at least one wavefront entering into the optical system.