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Terahertz digital holography (THz-DH) has the potential to be used for non-destructive inspection of visibly opaque soft materials due to its good immunity to optical scattering and absorption. Although previous research on full-field off-axis THz-DH has usually been performed using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally prevents a sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram. In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in full-filed off-axis THz-DH because ASM is more accurate at short reconstruction distances. We demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm. Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of 1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or in-process non-destructive inspection of soft materials.