In a quest to recreate this incredible effect, I’m trying to find $p^{-1}(x')$ where
$p(x') = \mathcal{F}^{-1}\{\mathcal{F}\{p_1\}(u)\mathcal{F}\{p_2\}(-u)\}$
and both p1 and p2 are the same basic periodic function:
p(x) = ½ + ½ cos x
Context:
I’m trying to use the moiré effect as a tool for optical encryption. Using target image $I$, I want to generate two random-looking key images that when superimposed reveal $I$. Turns out, quite a bit of math is involved.
I found this paper and have been following the steps. My math skills are limited, but I’ve been able to understand most of it. The gap in my knowledge concerns Fourier transform. I understand the concept thanks to videos like this, but I have no idea how to practically perform it. From what I understand, it actually seems senseless to take a Fourier transform of a simple cos function.
Other sources:
- a French blogpost about manipulating moiré artifacts, by the same people who made that elephant gif.