in theory and in experiment [12][13][14][15][16][17][18]. Borghi and Santarsiero [12] analyzed the model decomposition of the partially coherent FT beam produced by stable resonators. Zhang et al. [16] investigated the spectrum properties of a partially coherent FT beam in dispersive and gain media and found that the spectral shift was affected by the refractive index of dispersive media. Baykal and Eyyuboğlu [17] studied the scintillations index for a FT Gaussian beam in a free-space optics (FSO) link. Wang and Cai [18] reported the experimental generation and measurement of a partially coherent FT beam. Recently, partially coherent FT beams propagating through turbulent atmosphere have attracted much attention [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. It has been found that a partially coherent FT beam has an advantage over a Gaussian Schellmodel (GSM) beam, a coherent FT beam and a Gaussian beam for overcoming the turbulence-induced degradation.It is reported by Wolf that the spectrum of partially coherent polychromatic light changes on propagation due to the spatial coherence properties of the source [35][36][37]. Since then, numerous efforts have been paid to the spectral changes of partially coherent beam both theoretically and experimentally [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. It is demonstrated that spectral shift has important applications in determining the angular diameter of the stars, determining the angular separation of a double star, spectroradiometry, determining the intensity distribution across a distant source, optical signal processing and solving the inverse problems of scattering, information encoding and exchange. Recently, spectral changes of light beams propagating through optical system, human tissue and turbulent atmosphere have been extensively investigated [54][55][56][57][58][59][60][61][62]. To our knowledge, the generation and investigation of the spectral changes of polychromatic partially coherent FT beams have not been reported. In this paper, we theoretically present the spectral changes of a polychromatic partially coherent FT beam and carry out experiment Abstract An analytical propagation formula for a focused polychromatic partially coherent flat-topped beam with circular symmetry is derived in a tensor form that is based on the alternative flat-top beams model proposed by Li (Opt Lett 27:1007, 2002. The dependence of the relative spectral shift on the flat-top order N is investigated numerically in detail. It is shown that the on-axis maximum relative spectral shift occurs at the back focal plane, while the no spectral shift observes at the image plane. Furthermore, we report the experimental generation of a polychromatic partially coherent FT beam. The on-axis and off-axis spectral measurement verifies the theoretical study.