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Student Support Forum: 'Spot diagram for spherical aberration' topicStudent Support Forum > General > Archives > "Spot diagram for spherical aberration"

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J.E
09/21/07 00:17am

Hi all,

Now I am trying to get a spot diagram for spherical aberration. Here is the code.

\[Theta] := RandomReal[]*2 \[Pi]
\[Rho] := RandomReal[]^(1/2)
x := \[Rho]*Cos[\[Theta]]
y := \[Rho]*Sin[\[Theta]]

y1 := (x^2 + y^2)*y
x1 := (x^2 + y^2)*x
t4 = ListPlot[
Table[(i = x1; j = y1; If[i^2 + j^2 < 1, {i, j}]), {4000}],
PlotRange -> {{-1, 1}, {-1, 1}}];
Show[t1, t4]

Mathematically, spherical aberration is given by the derivative of rho^4, so 4*rho^3 is what I want to plot. I simply ignore a coefficient 4.
I suppose to see circular spot having high density at the center but I could not see it. However, if I use

ListPolarPlot[Table[\[Rho]^3, {4000}],
PlotRange -> {{-1, 1}, {-1, 1}}];

I can see what I want. Only difference is whether I use polar coordinate. If someone know a problem, could you help me?

Thanks,

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Subject (listing for 'Spot diagram for spherical aberration')
Author Date Posted
Spot diagram for spherical aberration J.E 09/21/07 00:17am
Re: Spot diagram for spherical aberration yehuda ben-s... 09/23/07 11:35am
Re: Re: Spot diagram for spherical aberration J.E 09/23/07 5:02pm
Re: Re: Re: Spot diagram for spherical aberration yehuda ben-s... 09/24/07 00:27am
Re: Re: Re: Re: Spot diagram for spherical aber... J.E 09/24/07 11:58am
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