Measuring the squared amplitudes of the Laguerre-Gaussian beams via a single intensity frame

We propose the use of an intensity technique to decompose superpositions consisting of two, three, or four basis Laguerre-Gaussian (LG) modes, and measure the orbital angular momentum (OAM) of such superpositions. The mode generation and decomposition are both accomplished only on a 2f optical imaging system. We demonstrate numerically and experimentally that the squared amplitudes of superpositions can be determined by recording a single frame of the intensity distribution. This is accomplished by measuring the intensity along certain circles and solving a linear set of equations relating the sampled intensities to squared amplitudes. The accuracy of better than 98% for composite beams consisting of two, and about 90% for composite beams consisting of more than two basis modes are achieved. Finally, we report the value of the measured OAM of the superpositions with excellent accuracy regarding theoretical values, for small and large integer and non-integer OAM.