# Calculating Optical Interferometry Telescope Resolution

• jumpjack
In summary, calculating the equivalent resolution of an optical interferometric telescope involves using the standard formula of R=1.22*lambda/D, where R is the resolution in radians and D is the separation of the telescopes. The size of the individual elements of the interferometer does not directly affect the resolution, only the separation does. However, the main practical limit for an optical interferometer is the delay line, which must be moved with precision in order to maintain the same accuracy as the telescope separation increases. This can be challenging for distances longer than a few hundred meters.
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 physics constraint must exist!
Which ones?
How distance and diameters of single telescopes relates to equivalent-telescope angular resolution?

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.

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 traveled 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 across 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.

## 1. What is optical interferometry telescope resolution?

Optical interferometry telescope resolution is a measure of the smallest detail that can be observed by an optical interferometer. It is typically expressed in units of arcseconds, with smaller values indicating higher resolution.

## 2. How is optical interferometry telescope resolution calculated?

Optical interferometry telescope resolution is calculated using the formula λ/D, where λ is the wavelength of light being observed and D is the diameter of the telescope's aperture. This formula takes into account the properties of the telescope's optics and the diffraction limit of light.

## 3. What factors affect optical interferometry telescope resolution?

The two main factors that affect optical interferometry telescope resolution are the wavelength of light being observed and the diameter of the telescope's aperture. Other factors that can have an impact include the quality of the telescope's optics, atmospheric conditions, and the stability of the interferometer.

## 4. How does optical interferometry improve resolution compared to single telescopes?

Optical interferometry combines the light from multiple telescopes, effectively creating a larger virtual telescope with a larger aperture. This larger aperture allows for higher resolution imaging, as it reduces the diffraction limit of light and increases the amount of light collected.

## 5. What are the limitations of optical interferometry telescope resolution?

The resolution of an optical interferometer is ultimately limited by the atmosphere and the stability of the interferometer. Atmospheric turbulence can cause distortions in the incoming light, reducing the resolution. Additionally, any imperfections or instabilities in the interferometer can also affect the resolution. Finally, the limited number of telescopes available for interferometry can also limit the resolution that can be achieved.

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