 Moiré fringe spacing formula

ID: moire-fringe-spacing-formula

Subtract the phases

2 π g_{1} \cdot r

and

2 π g_{2} \cdot r

of two projected periodic structures. Their relative phase repeats along the difference vector after distance

D = 1/∣ g_{1} - g_{2} ∣

. For magnitudes

1/ d_{1}

and

1/ d_{2}

separated by angle

θ

, this gives

D = d_{1} d_{2} / d_{1}^{2} + d_{2}^{2} - 2 d_{1} d_{2} cos θ

. At zero rotation it reduces to

d_{1} d_{2} /∣ d_{1} - d_{2} ∣

; equal spacings give

d / [2∣ sin (θ /2) ∣]

. Finite specimen extent limits how many periods can be observed.

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