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This article describes the theory and design of an ultra-low noise electronic readout circuit for use with room temperature video-rate terahertz imaging arrays. First, the noise characteristics of various imaging detectors, including low resistance bolometers and high resistance diodes are discussed. Theoretical approaches to white and 1/f noise mitigation are examined, and a corresponding low-noise readout circuit is designed, built, and tested. It is shown that the circuit is capable of achieving detector limited noise performance for use in room temperature terahertz imaging systems. A thorough noise analysis of the circuit provides the necessary information for applying the readout circuit to any type of imaging detector, and more generally, any measurement of small signals from various source impedances in the presence of white and 1/f noise. W-band measurements of an 8-element, high-resistance detector array, and a 32-element, low-resistance detector array demonstrate the usefulness of the readout circuit. Finally, recommended circuit configurations for various detectors in the literature are provided, with theoretical performance metrics summarized.