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Hyperspectral imaging has proven effective for appearance inspection because it can identify material compositions and reveal hidden features. Similarly, direct/indirect separation provides essential information about surface appearance and internal conditions, including layer structures and scattering behaviors. This paper presents a novel illumination system incorporating dispersive optics to unify both advantages for scene analysis. In general, achieving distinct direct/indirect separation requires multiple images with varying patterns. In a hyperspectral scenario, using a hyperspectral camera or tunable filters extends exposure and measurement times, hindering practical application. Our proposed system enables the illumination of a wavelength-dependent, spatially shifted pattern. With proper consideration of reflectance differences, we demonstrate that robust separation of direct and indirect components for each wavelength can be achieved using a single hyperspectral image acquired under our single spatio-spectral pattern illumination.