We propose an ultrafast optical time-to-two-dimensional (2-D) space conversion system using a crystal of β-BaB2O4. The proposed system can optically retrieve a 2-D spatial distribution (an image signal) from an ultra-short laser pulse modulated by an image. The fundamentals are the time-to-space transform and the spatial time-frequency transform. Optical time gating using a nonlinear optical crystal is applied for the time-to-space transform. The experimental system can convert modulated temporal signals into 2-D spatial distribution at the bit rate of 8 Tbit/s.