An atmospheric imaging system based on quantum hyperentanglement has been developed. Hyper-entanglement can increase the maximum detection range of the system by more than a factor of 10, improve the signal-to-noise ratio (SNR) by more than a factor of 10,000, and decrease measurement time. Hyperentanglement refers to entanglement in more than one degree of freedom. A design for creating states hyperentangled in the degrees of freedom polarization, energy-time, orbital angular momentum (OAM), and the radial quantum number is examined. The design helps reduce propagation loss. Figures of merit related to generation and detection efficiencies, the SNR, signal to interference ratio, the measurement time, and phase estimation are provided in closed form. A formula describing how hyperentanglement greatly improves the maximum detection range of the system is derived. Hermite–Gaussian modes, Laguerre–Gaussian (LG) modes, OAM dependence of the LG modes, and mode conversion are discussed. Bell state generation and Bell state measurement, i.e., the ability to distinguish the various Bell states, is discussed. Mathematical and circuit representations of Bell state generation and the Bell state analyzer are provided. Signatures for unique detection of the various Bell states are developed. The formalism permits random noise and entangled or nonentangled sources of interference to be modeled.