Objective In laser applications, the propagation characteristics of the beam directly affect its application quality. Accordingly, various standards for measuring the laser beam quality have been proposed to better evaluate the laser beam quality. The laser beam quality factor M² is the product of the beam waist diameter and the far-field divergence angle, which does not change with the optical system. Therefore, using M² for the beam quality measurement is stricter and more comprehensive. The representative measurement methods of the M² factor are knife-edge and array detection, among others. However, the measurement process of these methods is slow and requires multiple captures, exhibiting high requirements on the beam stability. A pulsed beam (e.g., laser output from a high-power driver) shows a certain degree of instability; hence, a simple pulsed beam quality measurement method is required.

Methods The algorithm of coherent modulation imaging based on amplitude coding(CAMI), which uses a binary random amplitude plate to modulate the incident beam. A single-shot method based on coherent modulation imaging is presented for the measuring of the beam quality. The laser beam to be measured first illuminates a highly random phase plate with a known structure and subsequently the intensity of the resulting diffraction pattern is recorded by a charge-coupled device positioned behind the phase plate. Intensity distribution of the laser beam is accurately reconstructed with the coherent modulation imaging method, then the scalar diffraction theory is used to perform numerical inversion, the beam intensity distribution of any plane can be obtained by calculation. According to the standard beam quality analysis algorithm, the quality of the laser beam is calculated. In addition, since the CAMI method adopts an amplitude modulation structure and does not require calibration, in theory, this method is applicable to any wavelength. Therefore, compared with the existing method, the structure is simpler, suitable for single exposure measurement, and theoretically can be used as a brand-new beam quality analysis technology.

Results and Discussions First, the feasibility of using CAMI algorithm to realize beam quality parameters was simulated and verified. It is assumed that the incident beam is an ideal Gaussian beam with a wavelength of 351nm. Considering the diffraction pattern saturation error, uniform random background noise (0~1) and quantization noise, the reconstruction results are shown in Fig.3. The incident beam at the amplitude plate recovered by CAMI is transmitted through the angular spectrum, and the beam parameters are calculated using the calculation method described in section 2.2. The maximum error is 2.12%, and all errors are within acceptable limits. For further verification, the CAMI optical path diagram shown in Fig.1 and the Ophir-Spiricon beam quality analyzer (model: BSQ-SP920) were used to measure the beam. Ophir-Spiricon beam quality analyzer measured the He-Ne laser beam quality factor Mx2=1.044,My2=1.042, CAMI method calculated Mx2=1.090,My2=1.044, the relative error along x direction and y direction was 4% and 0.2%. Finally, using the CAMI 351nm pulsed beam algorithm actual measurement, the beam path diagram is shown in Fig.6(a). After 300 iterations, the saturated area of the diffraction spot is restored, and the reconstruction results are shown in Fig.6(b)--(e). Through wavefront inversion, the beam intensity distribution of other vertical sections along the optical axis can be calculated. The beam width expands outward along the transmission direction in accordance with the hyperbolic law, and the coefficients of the hyperbola are fitted by multiple sets of beam intensity data, thereby calculating the beam quality factor Mx2=1.4746,My2=1.2101.

Conclusions Compared with the far-field divergence angle and focal spot size, the laser beam quality factor M² is a technical evaluation that can strictly characterize the laser beam quality. A real-time complex amplitude reconstruction method based on the coherent amplitude modulation imaging algorithm is proposed to determine the laser beam quality factor M². CCD is used as an image sensor to directly detect the laser beam distribution, and the wavefront distributions at different positions are obtained by numerical calculation. Laser beam quality measurement is based on the theory of second-order moments, and the M² is measured by the method of propagation trajectory curve fitting. Compared with the traditional mobile CCD method to obtain the wavefront distribution at different positions, the automatic measurement is more convenient and faster, and the wavefront distribution information of laser beam can be accurately obtained, which is suitable for measuring the quality of pulsed laser beam. Simulations and experiments have proved the effectiveness of proposed method.