High-speed volumetric imaging of dynamic neuronal activity over long periods is a challenging but essential goal in neuroscience. Conventional optical measurements of neuronal activity mostly rely on calcium signals. However, calcium imaging conveys only limited information about natural signal processing in the nervous system, and it provides little or no data on the inhibitory and excitatory signals that occur continuously in most neurons. In contrast, voltage imaging allows a direct measure of neuronal electrical activity, and it has the potential to overcome the limitations inherent to calcium imaging. Particularly, the recent advances of genetically encoded voltage indicators (GEVIs) have greatly expanded the use of voltage imaging in brain research, and their successful demonstration has, in turn, motivated developing new optical instrumentation optimized for voltage imaging. Optical imaging of neuronal action potentials is challenging as it requires a millisecond temporal resolution. This requirement becomes more demanding in three-dimensional (3D) imaging, where most optical imaging technologies rely on scanning to acquire volumetric data, either pointwise like confocal microscopy or planes like light-sheet microscopy. These systems suffer from a trade-off between the imaging speed and the signal-to-noise ratio. In contrast, light field imaging captures the volumetric data simultaneously, making it an ideal strategy for 3D imaging of neuronal networks. Nonetheless, because light field imaging records both the spatial and angular information of light rays, it typically requires a large-format image sensor, which has a low frame rate due to limited electronic bandwidth. The temporal resolution enabled so far (~tens of milliseconds) is far from enough to resolve the individual neuron firing event (~one millisecond). Therefore, there is an unmet need to develop new imaging techniques to enable high-speed measurement of large-scale light-field data. The overall goal of the proposed research is to develop a light-field tomographic microscopy (LIFT microscopy) method for kilohertz volumetric imaging of neuronal action potentials in awake behaving mice. The proposed method has been only recently made possible by an emerging technique, light field tomography (LIFT), which is highly efficient in acquiring light field data for 3D imaging. Rather than measuring the entire light field datacube, LIFT captures only an en-face projection of the object in each perspective image, thereby significantly reducing the data load. Furthermore, LIFT records data using one-dimensional (1D) sensors, exploiting the fact that most fast cameras are in 1D format. In the proposed research, we will adapt LIFT for 3D fluorescence microscopy. When combined with the use of GEVI, the resultant system will provide a complete solution to high-speed voltage imaging of 3D neuronal networks. Moreover, the proposed system will be compatible with experiments in behaving animals, al...