# Optical interferometry

1. Feb 1, 2008

### jumpjack

I can't find any useful page which explains in detail how to calculate the equivalent resolution of an optical interferometric telescope.

I found out, after LONG search, the formula to calculate standard-telescope resolution:
Resolution (Km) = 5,5680 * 10^-4 * Distance (Km) / diameter (mm)

Does it exist such a formula for interferometric telescopes?
I don't think I can just use two 110mm telescope 1 Km far away to obtain a 1.000.000 m equivalent telescope! Some physic constraint must exist!
Which ones?
How distance and diameters of single telescopes relates to equivalent-telescope angular resolution?

2. Feb 1, 2008

The standard formula used is R=1.22*lambda/D

R is the resolution in radians and lambda/D is the ratio of light wavelength to telescope aperture size. In the case of an interferometer, D is the separation of the telescopes.

3. Feb 1, 2008

### mgb_phys

The size of the individual elements of an interferometer don't directly effect the resolution only the separation - so in you original equation use the separation (in mm!) for the diameter.

The main practical limit for an optical interferometer is the delay line.
Since the light has to be in phase when it reaches the detector the distance travelled by the light from the object through the different telescopes must be the same. In optical inteferometry this is acheived by a delay line = a mirror on a slide. This mirror must be moved to an accuracy of 1/20 a wavelength at a constantly varying rate as the star tracks accross the sky. As the telescope separation increases the delay line must be longer and move faster - while keeping the same accuracy. Delay lines of more than a few 100m are tricky to engineer.