- #1
lechris
- 4
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Hi there,
optical aberrations can be expressed by Zernike polynomials Vmn(ρ,θ).
Now, for my simulations i am using software that takes 4 inputs for creating aberrations onto an optical flat: m,n,R,A
m,n are the Zernike orders which is perfectly clear.
For R,A the manual says:
R: the radius
A: the amplitude of aberration in radians reached at R
I am still unclear how to interpret these parameters. I was looking through the source code and could make up the following:
ρ = sqrt( x*x + y*y )/ R*R) which i suppose does some kind of spatial scaling of the aberration
A is the Amplitude of the Zernike polynomial A*Vmn(ρ,θ), which i suppose does some kind of height scaling
Finally the optical field is composed as such:
RE{Field} = RE{Field_old}*cos(A*Vmn(ρ,θ)) - IM{Field_old}*sin(A*Vmn(ρ,θ))
IM{Field} = RE{Field_old}*sin(A*Vmn(ρ,θ)) + IM{Field_old}*cos(A*Vmn(ρ,θ))
Can someone explain to me how the parameters are supposed to work? Since when is amplitude expressed in radians?
I couldn't find the aforementioned formulas in any standard textbook yet (i see that the last 2 are just complex numbers multiplied, which represent the optical fields). Where are these formulas taken from?
optical aberrations can be expressed by Zernike polynomials Vmn(ρ,θ).
Now, for my simulations i am using software that takes 4 inputs for creating aberrations onto an optical flat: m,n,R,A
m,n are the Zernike orders which is perfectly clear.
For R,A the manual says:
R: the radius
A: the amplitude of aberration in radians reached at R
I am still unclear how to interpret these parameters. I was looking through the source code and could make up the following:
ρ = sqrt( x*x + y*y )/ R*R) which i suppose does some kind of spatial scaling of the aberration
A is the Amplitude of the Zernike polynomial A*Vmn(ρ,θ), which i suppose does some kind of height scaling
Finally the optical field is composed as such:
RE{Field} = RE{Field_old}*cos(A*Vmn(ρ,θ)) - IM{Field_old}*sin(A*Vmn(ρ,θ))
IM{Field} = RE{Field_old}*sin(A*Vmn(ρ,θ)) + IM{Field_old}*cos(A*Vmn(ρ,θ))
Can someone explain to me how the parameters are supposed to work? Since when is amplitude expressed in radians?
I couldn't find the aforementioned formulas in any standard textbook yet (i see that the last 2 are just complex numbers multiplied, which represent the optical fields). Where are these formulas taken from?
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