Abstract
The turbulent atmosphere of the earth limits the resolution of conventional astrophotography to about 1 arc second. Much higher resolution can be obtained by Labeyrie's speckle interferometry. Speckle interferometry yields the diffraction-limited autocorrelation of astronomical objects, for example a resolution of 0.03 arc seconds in the case of a 3.6m telescope. After reviewing very briefly the method of speckle interferometry we will report the following projects (1) the reconstruction of direct images from speckle interferograms by using the speckle holography technique, i.e. the application of speckle interferometry for objects near to a point source. (2) Application of speckle interferometry for very faint astronomical objects by measuring the single photon events in speckle interferograms. We want to observe faint objects since many of the most interesting objects are rather faint as, for example, galactic nuclei and Quasars. In the following article we will describe various applications of speckle inter-ferometry and of speckle holography. The speckle holography measurements yielded direct images with diffraction-limited resolution. Speckle interferometry was successfully applied up to 14th magnitude.

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