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Retrieval of Sun-Induced Chlorophyll Fluorescence (<i>F</i>) spectrum is one of the challenging perspectives for further advancing <i>F</i> studies towards a better characterization of vegetation structure and functioning. In this study, a simplified Spectral Fitting retrieval algorithm suitable for retrieving the <i>F</i> spectrum with a limited number of parameters is proposed (two parameters for <i>F</i>). The novel algorithm is developed and tested on a set of radiative transfer simulations obtained by coupling SCOPE and MODTRAN5 codes, considering different chlorophyll content, leaf area index and noise levels to produce a large variability in fluorescence and reflectance spectra. The retrieval accuracy is quantified based on several metrics derived from the <i>F</i> spectrum (i.e., red and far-red peaks, O₂ bands and spectrally-integrated values). Further, the algorithm is employed to process experimental field spectroscopy measurements collected over different crops during a long-lasting field campaign. The reliability of the retrieval algorithm on experimental measurements is evaluated by cross-comparison with <i>F</i> values computed by an independent retrieval method (i.e., SFM at O₂ bands). For the first time, the evolution of the <i>F</i> spectrum along the entire growing season for a forage crop is analyzed and three diverse <i>F</i> spectra are identified at different growing stages. The results show that red <i>F</i> is larger for young canopy; while red and far-red <i>F</i> have similar intensity in an intermediate stage; finally, far-red <i>F</i> is significantly larger for the rest of the season.