Editing Moiré pattern (section)

==== Geometrical approach ====
{{multiple image
| total_width = 320
| align = right
| image1 = Moire parallel.svg
| alt1 = 
| caption1 = The patterns are superimposed in the mid-width of the figure.
| image2 = Moire ecart angulaire.png
| alt2 = 
| caption2 = Moiré obtained by the superimposition of two similar patterns rotated by an angle {{mvar|α}}
| footer = 
}}

Consider two patterns made of parallel and equidistant lines, e.g., vertical lines. The step of the first pattern is {{mvar|p}}, the step of the second is {{math|''p'' + ''δp''}}, with {{math|0 < ''δp'' < ''p''}}.

If the lines of the patterns are superimposed at the left of the figure, the shift between the lines increases when going to the right. After a given number of lines, the patterns are opposed: the lines of the second pattern are between the lines of the first pattern. If we look from a far distance, we have the feeling of pale zones when the lines are superimposed (there is white between the lines), and of dark zones when the lines are "opposed".

The middle of the first dark zone is when the shift is equal to {{math|{{sfrac|''p''|2}}}}. The {{mvar|n}}th line of the second pattern is shifted by {{math|''n δp''}} compared to the {{mvar|n}}th line of the first network. The middle of the first dark zone thus corresponds to
<math display="block">n \cdot \delta p = \frac{p}{2}</math>
that is
<math display="block">n = \frac{p}{2 \delta p}.</math>
The distance {{mvar|d}} between the middle of a pale zone and a dark zone is
<math display="block">d = n \cdot (p+\delta p) = \frac{p^2}{2 \delta p}+\frac{p}{2}</math>
the distance between the middle of two dark zones, which is also the distance between two pale zones, is
<math display="block">2d = \frac{p^2}{\delta p}+p</math>
From this formula, we can see that:
* the bigger the step, the bigger the distance between the pale and dark zones;
* the bigger the discrepancy {{mvar|δp}}, the closer the dark and pale zones; a great spacing between dark and pale zones mean that the patterns have very close steps.

The principle of the moiré is similar to the [[Vernier scale]].