Spectral imaging acquires a three-dimensional (3D) spectral data cube, in which additional spectral information contains a significant amount of object information. It plays an important role in many applications, such as astronomical imaging, remote sensing, and biomedical imaging^[1,2]. In contrast to conventional spectral imaging, which requires time scanning along either the spatial or wavelength axis, snapshot spectral imaging acquires a 3D spectral data cube in a single exposure^[3,4]. Depending on whether reconstruction is required, snapshot spectral imaging can be divided into computational snapshot spectral imaging and non-computational snapshot spectral imaging. Integral field spectrometry with faceted mirrors (IFS-M)^[5], multi-aperture filtered camera (MAFC)^[6], and image-replicating imaging spectrometer (IRIS)^[7] are representative methods of non-computational snapshot spectral imaging. Meanwhile, computational snapshot spectral imaging^[8–13] usually modulates the spatial and spectral information of an object by light-field spatial intensity fluctuation and reconstructs the 3D spectral data cube information from the detected intensity light distribution. With the development of computational snapshot spectral imaging via light-field amplitude modulation^[8], the use of light-field phase modulation to achieve spatial intensity fluctuation has also made considerable progress in computational snapshot spectral imaging^[9–13]. For example, spectral ghost imaging modulates the image in the entire spectral band by utilizing a spatial random phase modulator, and the spectral images of the object are obtained by second-order spatial mutual light-field correlation^[11].