Real-time measurement of laser beam quality factor by the Fresnel phase-retrieval method

Conventionally, it is a tedious work to measure the beam quality factor for a laser beam because one needs to move a camera-based beam profiler from one location to another for many times to record intensity profiles at different positions around the beam waist. We present a simple method for determining the laser beam quality factor from only two laser intensity profiles at different cross sections around the waist. We first used an iterative phase-retrieval algorithm, based on the Huygens-Fresnel principle, to reconstruct the phase profiles at the two cross sections where the intensity profiles had been measured. Once the optical field amplitude (the square root of intensity) and phase distribution functions at certain cross section of a laser beam had been determined, we can propagate the light wave at this cross section by using the Fresnel diffraction formula to obtain the intensity profiles at different positions, from which the beam quality factor can be determined. Using a HeNe laser for test, we had experimentally demonstrated the feasibility of our idea by showing that the result from our proposed method is in good agreement with that obtained from the conventional method. Our setup is capable of executing a real-time measurement of the beam quality factor because the two intensity profiles can be simultaneously recorded by using a beam splitter and two beam-profilers controlled by the same computer.