Does the structure of light influence the speckle size

It is well known that when a laser is reflected from a rough surface or transmitted through a diffusive medium, a speckle pattern will be formed at a given observation plane. An important parameter of speckle is its size, which for the case of homogeneous illumination, well-known relations for its computation have been derived. This is not the case for structured light beams of non-homogeneous intensity and phase distribution. Here, we propose and demonstrate, using Hermite- and Laguerre-Gaussian light modes, that the mean size of the speckle generated by these structured light beams can be measured assuming a homogeneous illumination. We further provide with mathematical expressions that relate the speckle size to the generalised definition of "spot size". To reinforce our assessment, we compare the mean speckle size generated by structured light modes with that generated by wave fronts of constant phase and amplitude and show that in both cases the mean speckle size is almost identical. Our findings reveal a fundamental property of speckle, which will be of great relevance in many speckle-based applications and will pave the way towards the development of novel applications.