目标光束重构面有效像素数对平顶光束整形的 影响与应用

Beam shaping involves the modulation of the amplitude，phase，or both of an incident optical beam by means of optical elements to alter its wavefront distribution，thereby enabling the generation of a targeted beam profile in the far field. This methodology serves to mitigate the constraints inherent in conventional Gaussian beams-specifically their non-uniform energy distribution characterized by central intensity maxima and peripheral attenuation-which limits their efficacy as processing sources or transmission media. Concurrently，Computer-Generated Holography （CGH） has gained prominence in beam shaping applications owing to its distinctive capacity for simultaneous recording and reconstruction of both amplitude and phase components of the output wavefront. This study endeavors to establish an optimal operational range for parameter M-defined as the pixel count spanned by the diameter of a circular target flat-top beam in the reconstruction plane-thus furnishing a reference framework for preliminary parameter selection and feasibility analysis in subsequent beam shaping implementations.This study employs the Weighted Gerchberg-Saxton（WGS）algorithm for phase retrieval. Key physical parameters were initially calibrated to replicate a typical femtosecond laser system configuration，and a circular flat-top beam with M = 100 was subjected to numerical validation. Following 500 iterations，the beam achieved a uniformity level of 94.72% with well-defined boundaries and absence of notable speckle noise or artifacts，thereby validating the algorithmic efficacy of the WGS approach. In consideration of both the impact of initial quadratic phase distribution and the need for intuitive performance representation，M was designated as the primary control parameter. A series of numerical simulations were subsequently performed to systematically examine the correlation between shaping performance and M values across varied combinations of pixel size，incident beam size （w），and focal lengths of Fourier lenses，thus establishing optimal M ranges for each parametric configuration. Furthermore，parameters were stochastically altered to verify the generalizability of the determined M range to non-circular beam geometries. Simulation results reveal that while variations in w exert negligible influence on flat-top beam uniformity，speckle noise displays a discernible dependence on w parameterization. Optimal selection of w effectively suppresses reconstruction artifacts and speckle phenomena. Under optimized w conditions，the correlation between M and shaping performance maintains remarkable consistency across disparate Fourier lens configurations and pixel size. At relatively small M values，the flat-top region exhibits uniform irradiance distribution devoid of speckle interference，with uniformity sustaining elevated levels across all tested configurations-manifested as closely superimposed uniformity curves. Progressive augmentation of M instigates peripheral speckle emergence，performance divergence across variable optical parameters. Further M value promotes speckle infiltration into the central flat-top region，concomitant with substantial uniformity degradation. The stochastic nature of speckle generation exacerbates performance variance under different conditions. The variation of speckle characteristics with the M value follows a non-monotonic dependence， characterized by an initial decay followed by a subsequent enhancement. The primary reduction phase stems from inadequate pixel sampling inducing abrupt irradiance transitions at beam peripheries，thereby generating pronounced diffraction phenomena. The subsequent resurgence of speckle noise is attributable to the Spatial Bandwidth Product （SBP） at the reconstruction plane surpassing the information encoding capacity of the incident beam，resulting in compromised reconstruction of high-gradient beam edges and ultimate speckle permeation into the central region. To further verify the applicability of the M Criterion，a comparative analysis of beam shaping performance between square flat-top beams and rectangular flat-top beams was incorporated into this study. The results demonstrate that the criterion is applicable to flat-top beams of diverse geometries. Furthermore，the impact of the M-value is more salient in rectangular flat-top beams. When the M-value corresponding to the long side of the rectangle exceeds the optimal range while that associated with the short side remains within this range，it is evident that speckle noise is predominantly concentrated along the long-side direction，whereas the noise perturbation on the short-side direction is negligible. These observations validate the feasibility of utilizing the M-value to predict the shaping performance of flat-top beams. This study proposes a unified M-based criterion for the evaluation and design of flat⁃-top beam shaping systems. Through integrated numerical simulations incorporating critical parameters from both the phase retrieval algorithm and the optical configuration， we systematically investigated how the shaping performance of circular flat-top beams varies with M under different parametric conditions，which enabled the identification of its optimal operational range. Furthermore，we extended the validation of the M criterion to square and rectangular flat⁃-top beam profiles，confirming its broad applicability. The consistent findings obtained across diverse simulation conditions and beam geometries establish a solid foundation for employing M as a universal metric for assessing flat⁃-top beam quality. This work offers principled guidance for parameter optimization in practical optical system design.