Imagine a screen for viewing fringes placed at the light source (alternatively, use a beamsplitter to send light from the source point to the screen). Given a steady light source, interference fringes will form on the screen with a fringe displacement given by Δ Δ ϕ ϕ ≈ ≈ 2 π π c λ λ Δ Δ T where the first factor is the frequency of light. This gives the generalized Sagnac formula Δ Δ ϕ ϕ ≈ ≈ 4 π π λ λ c ∮ ∮ v ⋅ ⋅ d x In the special case that the fiber moves like a rigid body with angular frequency ω ω , the velocity is v = ω ω × × x and the line integral can be computed in terms of the area of the loop: ∮ ∮ v ⋅ ⋅ d x = ∮ ∮ ω ω × × x ⋅ ⋅ d x = ∮ ∮ ω ω ⋅ ⋅ x × × d x = 2 ∮ ∮ ω ω ⋅ ⋅ d A = 2 ω ω ⋅ ⋅ A This gives Sagnac formula for ring interferometers of arbitrary shape and geometry Δ Δ ϕ ϕ ≈ ≈ 8 π π λ λ c ω ω ⋅ ⋅ A If one also allows for stretching one recovers the Fizeau interference formula.