I liked to know quantitatively where the spot is on a mirror.
With an interferometer and A2L scripts, one can make the balance of the coil actuators
so that the angle actuation does not couple to the longitudinal motion.
i.e. node of the rotation is on the spot
Suppose you have actuator balancing (1+α) f and (1-α) f.
=> d = 0.016 x α [m]
Full Imbalance α = 1 -> d = 15 [mm]
10% Imbalance α = 0.1 -> d = 1.5 [mm]
1% Imbalance α = 0.01 -> d = 0.15 [mm]
Eq of Motion:
I ω^{2} θ = 2 R f
(correction) - I ω^{2} θ = D f cos(arctan(L/2/D))
(re-correction on Sep 26, 2017) - I ω^{2} θ = D f
m ω^{2} x = 2 α f ,
(correction) - m ω^{2} x = 2 α f ,
where R is the radius of the mirror, and D is the distance of the magnets. (kinda D=sqrt(2) R)
d, position of the node distant from the center, is given by
d = x/θ = α I / (m R) = 2 α β / D,
where β is the ratio of I and m. Putting R=37.5 [mm], L=25 [mm], β = 4.04 10^{-4} [m^{2}], D~R Sqrt(2)
i.e. d = 0.015 α [m] |