Let’s say that the filament is straight and is composed of N equal segments of length Δs₀ . But due to experimental error, there is a deviation from the straight line; at the k^th point, the deviation is ε_k and at k+1^th point it is ε_k+1 . Then the k^th segment has the length:

(33.1)

and angle

(33.2)

Where, we have neglected the terms of order  and higher. If we substitute these expressions in equation 32.9, then these errors lead to amplitude of Fourier modes for the error,

(33.3)

Where,  is the mid point of the k^th segment. The variance is calculated by regrouping terms on the right hand side of equation 33.3, in terms of each distinct and by considering the fact that are independent, identical random variables and using,

	(33.4)