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There are many ways to measure tilt and separation changes using interferometry. As @Gilbert pointed out, for large displacements you need a way to keep track of the direction in which fringes are moving. Actually, that's not too difficult if a video record is kept of the fringes. An automated way to do it is to make a subsystem that locates the peak of a ...

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Iceland (the country) is about 250 km across. It would subtend an angle of about $2.5 \times 10^{-13}$ radians from 100 light years. Taking a simple angular resolution criterion of $\lambda/D$, where $\lambda$ is the wavelength of observation and $D$ is the diameter of your array, then if working at optical wavelengths ($\lambda = 500$nm) then $D>2000$ km....

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Some partial answers to some of your questions (a bit late, but for some reason this popped up in my feed now): In the limit of large z (distance from beam waist), the beam radius w(z) increases linearly with z and the half-angle of the cone becomes $\theta = \frac{\lambda}{\pi n w_0}$. The total angular spread of that cone is then $\Theta = 2\theta$, and ...

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