Polar image plot

Question

I would like to perform the polar plot of an electron microscope contrast transfer function, into a black and white image.

I have used the equation

t = -Sin[π/2 #^4 + π #^2 ] &;

Plot[t[x], {x, 0, 5}]

to generate the sample function.

enter image description here

However, I was unable to convert this image into the contrast transfer function plot.

In short, what function would convert the plot

enter image description here

into the image

enter image description here

$\begingroup$ Take a look at DensityPlot. $\endgroup$
– Kuba ♦
Jan 3 '15 at 11:37 — Kuba, Jan 3 '15 at 11:37

Dr. belisarius · Accepted Answer · 2015-01-03 12:47:33Z

2

a = 1.5;
DensityPlot[t[Norm[{x, y}]], {x, -a, a}, {y, -a, a}, PlotPoints -> 50, MaxRecursion -> 3]

Mathematica graphics

But beware of the tuning parameters:

a = 5;
DensityPlot[t[Norm[{x, y}]], {x, -a, a}, {y, -a, a}]

Mathematica graphics

answered Jan 3 '15 at 12:47

Dr. belisarius

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$\begingroup$ Thanks! I tried density plot first, but gave up after it gave me the ridiculous pattern. $\endgroup$
– March Ho
Jan 3 '15 at 14:24
$\begingroup$ @MarchHo Somehow I guessed that. That's why I included the last plot :) $\endgroup$
– Dr. belisarius
Jan 3 '15 at 15:03

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