  We propose and demonstrate a simple and easy-to-implement
projective-measurement protocol to determine the radial index 'p' of a
Laguerre-Gaussian (LGlp) mode. Our method entails converting any specified
high-order LG0p mode into a near-Gaussian distribution that matches the
fundamental mode of a single-mode fiber (SMF) through the use of two
phase-screens (unitary transformations) obtained by applying a phase-retrieval
algorithm. The unitary transformations preserve the orthogonality of modes and
guarantee that our protocol can, in principle, be free of crosstalk. We measure
the coupling efficiency of the transformed radial modes to the SMF for
different pairs of phase-screens. Because of the universality of
phase-retrieval methods, we believe that our protocol provides an efficient way
of fully characterizing the radial spatial profile of an optical field.
