Instantaneous speckle reduction? Yes - but there is no free lunch

We are motivated by the question if scanning laser projection with low speckle noise is possible. Scanning laser projection requires "instantaneous" speckle reduction, within a few nanoseconds - meaning that no moving diffusors can be used. We will argue that instantaneous speckle reduction is possible by conversion of spatial coherence to spatial incoherence - but nature demands for a compensation. The cost can be estimated via the information theoretical concept "channel capacity", which incorporates the etendue as well as the signal-to-noise ratio. We will show that an optical system with low spatial coherence (=low speckle noise) must provide significantly more degrees of freedom than a coherent imaging system. The consequence for the technical optical system is serious: significant speckle reduction can only be achieved by an excessively large projection aperture. This is not just a sophistic consideration, it seriously restricts the design of scanning laser projectors.