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Solar-induced chlorophyll fluorescence (SIF) is highly correlated with photosynthesis and can be used for estimating gross primary productivity (GPP) and monitoring vegetation stress. The far-red band of the solar Fraunhofer lines (FLs) is close to the strongest SIF emission peak and is unaffected by chlorophyll absorption, making it suitable for SIF intensity retrieval. In this study, we propose a retrieval window for far-red SIF, significantly enhancing the sensitivity of data-driven methods to SIF signals near 757 nm. This window introduces a weak O2 absorption band based on the FLs window, allowing for better separation of SIF signals from satellite spectra by altering the shape of specific singular vectors. Additionally, a frequency shift correction algorithm based on standard non-shifted reference spectra is proposed to discuss and eliminate the influence of the Doppler effect. SIF intensity retrieval was achieved using data from the GOSAT satellite, and the retrieved SIF was validated using GPP, enhanced vegetation index (EVI) from the MODIS platform, and published GOSAT SIF products. The validation results indicate that the SIF products provided in this study exhibit higher fitting goodness with GPP and EVI at high spatiotemporal resolutions, with improvements ranging from 55% to 129%. At low spatiotemporal resolutions, the SIF product provided in this study shows higher consistency with EVI and GPP spatially. [ABSTRACT FROM AUTHOR]