As one of the next generation imaging spectrometers,the interferential spectrometer (IS) possesses the advantages of high throughput,multi-channel and great resolution.The data of IS are produced in the spatial domain,but optical applications are in the Fourier domain.Traditional compression methods can only protect the visual quality of interferometer data in the spatial domain but ignore the distortion in the Fourier domain.The relation between the distortion in the Fourier domain and the compression in the spatial domain is analyzed.By mathematical proof and validation with experiments,the relation between spatial and Fourier domains is discovered,and the significance in the Fourier domain is more important as optical path difference (OPD) increasing in the spatial domain.Based on this relation,a novel coding scheme is proposed,which can compress data in the spatial domain while reducing the distortion in the Fourier domain.In this scheme,the bit stream of the set partitioning in hierarchical trees (SPIHT) is truncated by adaptively lifting rate-distortion slopes according to the priorities of OPD based on rate-distortion optimization theory.Experimental results show that the proposed method can provide better protection of spectrum curves in the Fourier domain while maintaining a comparable visual quality in the spatial domain. As one of the next generation imaging spectrometers, the interferential spectrometer (IS) possesses the advantages of high throughput, multi-channel and great resolution. Data is IS are produced in the spatial domain, but optical applications are in the Fourier domain. TRADITIONAL compression methods can only protect the visual quality of interferometer data in the spatial domain but ignore the distortion in the Fourier domain.The relation between the distortion in the Fourier domain and the compression in the spatial domain is analyzed.By mathematical proof and validation with experiments , the relation between spatial and Fourier domains is discovered, and the significance in the Fourier domain is more important as optical path difference (OPD) increasing in the spatial domain.Based on this relation, a novel coding scheme is proposed, which can compress data in the spatial domain while reducing the distortion in the Fourier domain. this scheme, the bit stream of the set partitioning in hi erarchical trees (SPIHT) is truncated by adaptively lifting rate-distortion slopes according to the priorities of OPD based on rate-distortion optimization theory. Experimental results show that the proposed method can provide better protection of spectrum curves in the Fourier domain while maintaining a comparable visual quality in the spatial domain.