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  1. There are two established methods for measuring rotational Doppler shift: (1) heterodyne and (2) fringe. We identify a key distinction, that only the heterodyne method is sensitive to the rotating object’s phase, which results in significant differences in the signal-to-noise ratio (SNR) when measuring multiple rotating particles. When used to measure randomly distributed rotating particles, the fringe method produces its strongest SNR when a single particle is present and its SNR tends to zero as the number of particles increases, whereas the heterodyne method’s SNR increases proportionally to the number of particles in the beam. 
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  2. We propose the braiding of optical vortices in a laser beam with more than 2 π<#comment/> rotation by superposing Bessel modes with a plane wave. We experimentally demonstrate this by using a Bessel–Gaussian beam and a coaxial Gaussian, and we present measurements of three complete braids. The amount of braiding is fundamentally limited only by the numerical aperture of the system, and we discuss how braiding can be controlled experimentally for any number of vortices. 
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