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We present spatial light interference tomography (SLIT), a label-free method for 3D imaging of transparent structures such as live cells. SLIT uses the principle of interferometric imaging with broadband fields and combines the optical gating due to the micron-scale coherence length with that of the high numerical aperture objective lens. Measuring the phase shift map associated with the object as it is translated through focus provides full information about the 3D distribution associated with the refractive index. Using a reconstruction algorithm based on the Born approximation, we show that the sample structure may be recovered via a 3D, complex field deconvolution. We illustrate the method with reconstructed tomographic refractive index distributions of microspheres, photonic crystals, and unstained living cells.