A partially coherent beam with flat-topped profile is proposed. The cross-spectral density of this beam can be expressed as a finite series of the cross-spectral density of partially coherent Gaussian-Schell-model beams with different parameters. Analytical propagation formulas for partially coherent flattopped beams are derived through aligned and misaligned optical systems. The propagation property of partially coherent flat-topped beams in free space is illustrated numerically. The fractional Fourier transform of partially coherent flat-topped beams is also studied. Our method provides a convenient way to describe partially coherent flat-topped beams and treat their propagation and transformation.
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