  Photons that are entangled or correlated in orbital angular momentum have
been extensively used for remote sensing, object identification and imaging. It
has recently been demonstrated that intensity fluctuations give rise to the
formation of correlations in the orbital angular momentum components and
angular positions of random light. Here, we demonstrate that the spatial
signatures and phase information of an object, with rotational symmetries, can
be identified using classical orbital angular momentum correlations in random
light. The Fourier components imprinted in the digital spiral spectrum of the
object, measured through intensity correlations, unveil its spatial and phase
information. Sharing similarities with conventional compressive sensing
protocols that exploit sparsity to reduce the number of measurements required
to reconstruct a signal, our technique allows sensing of an object with fewer
measurements than other schemes that use pixel-by-pixel imaging. One remarkable
advantage of our technique is the fact that it does not require the preparation
of fragile quantum states of light and works at both low- and high-light
levels. In addition, our technique is robust against environmental noise, a
fundamental feature of any realistic scheme for remote sensing.
