Tomographic phase microscopy measures the 3-D refractive index distribution of cells and tissues by combining the information from a series of angle-dependent interferometric phase images. In the original device, the frame rate was limited to 0.1 frames per second (fps) by the technique used to acquire phase images, preventing measurements of moving or rapidly changing samples. We describe an improved tomographic phase microscope in which phase images are acquired via a spatial fringe pattern demodulation method, enabling a full tomogram acquisition rate of 30 fps. In addition, in this system the refractive index is calculated by a diffraction tomography algorithm that accounts for the effects of diffraction in the 3-D reconstruction. We use the instrument to quantitatively monitor rapid changes in refractive index within defined subregions of cells due to exposure to acetic acid or changes in medium osmolarity.