Hyper-entanglement with an emphasis on mode type is used to extend a previously developed atmospheric imaging
system. Angular spectrum expansions combined with second quantization formalism permits many different mode types
to be considered using a common formalism. Fundamental Gaussian, standard Hermite-Gaussian, standard Laguerre-
Gaussian, and Bessel modes are developed. Hyper-entanglement refers to entanglement in more than one degree of
freedom, e.g. polarization, energy-time and orbital angular momentum. The system functions at optical or infrared
frequencies. Only the signal photon propagates in the atmosphere, the ancilla photon is retained within the detector.
This results in loss being essentially classical, giving rise to stronger forms of entanglement. A simple atomic physics
based model of the scattering target is developed. This model permits the derivation in closed form of the loss
coefficient for photons with a given mode type scattering from the target. Signal loss models for propagation,
transmission, detection, and scattering are developed and applied. The probability of detection of photonic orbital
angular momentum is considered in terms of random media theory. A model of generation and detection efficiencies for
the different degrees of freedom is also considered. The implications of loss mechanisms for signal to noise ratio (SNR),
and other quantum information theoretic quantities are discussed. Techniques for further enhancing the system’s SNR
and resolution through adaptive optics are examined. The formalism permits random noise and entangled or nonentangled
sources of interference to be modeled.