Physicist (Dipl. Phys.) and System Engineer (M. Sys. Eng.)

# Stellar Interferometry

## Size Matters

Astronomy aims at the observation and detailed scientific characterization of distant objects. In order to achieve these goals two physical quantities, optical sensitivity and spatial resolution, are of paramount importance for astronomical telescopes. In the first place, both quantities are not only determined but also linked via one specific characteristic of the telescope system, namely its size. As a rule of thumb it can be stated that the bigger the telescope’s primary mirror is, the higher will be its optical sensitivity and spatial resolution.

As optical sensitivity refers by definition to the light gathering capacity of the telescope it is intuitively understandable that it scales with the primary mirror diameter. More precisely, it is proportional to the photon collecting area which in turn is proportional to the diameter squared, D2, of the telescope’s primary mirror.

On the other hand, the relation between the size of the primary mirror and the spatial resolution of the telescop, might be not that obvious for people who have no background knowledge in wave optics.
Therefore it is shortly sketched in the following.

The spatial resolution of a telescope is a measure for the minimal angular separation at which two points of the observed objects can still be distinguished as two points on the image. The term point can be almost understood in the mathematical sense as a one-dimensional structure with basically zero spatial extent. Hypothetically, if a telescope, as an optical system, was imaging a point exactly as a point, its spatial resolution would only be determined by the pixel size of the detector that registers the light. As long as the detector pixel size is significantly smaller than the distance between two points, these two points might be distinguished. However, due to diffraction, which is an inherent physical phenomenon of wave propagation, a point is not imaged as a point but as an extended disk with rings, the so-called Airy disk. The size of this disk is inversely proportional to the diameter of the telescopes aperture which basically corresponds to the size of the primary mirror. This implies that, for a given detector pixel size, the telescope resolving capability scales with its primary mirror size; the bigger the telescope, the better its spatial resolution.

From the above considerations, it is understandable that the most demanding astronomical science cases require telescopes which are as large as possible. On the other hand, it seems obvious that in practice there are technical limits on the size of telescopes that can actually be built. As will be seen in the subsequent section, interferometry offers a way to increase the spatial resolving power for astronomical observations beyond these limits.