Phaseencoded

Phaseencoded, often written phase-encoded, denotes methods in which information is conveyed primarily by the phase of a waveform rather than its amplitude. The concept is applied across multiple disciplines, with phase shifts representing data symbols and phase coherence enabling reconstruction or interpretation of signals.

In communications, phase encoding is implemented through phase-shift keying and related schemes. Data are represented by distinct phases of a carrier, and differential phase-shift schemes encode information in the phase difference between successive symbols. Coherent detection is typically required to recover the phase information, which can yield high spectral efficiency but makes systems sensitive to phase noise and drift.

In magnetic resonance imaging and spectroscopy, phase encoding uses controlled magnetic-field gradients to induce position-dependent phase shifts in spins. The accumulated phase encodes spatial information, which, together with frequency encoding, allows image or spectral reconstruction. Phase information is also leveraged for motion tracking and flow measurements in MRI.

In optics and interferometry, phase-encoded techniques store or transmit information in the optical phase, enabling applications such as phase-contrast imaging, holography, interferometric sensing, and phase-sensitive tomography. In quantum information, phase encoding assigns information to the phase of quantum states, underpinning certain quantum key distribution protocols and other phase-based quantum communication schemes.

Advantages of phase encoding include robustness to certain amplitude fluctuations and compatibility with coherent detection, while limitations involve maintaining a stable phase reference, managing phase noise, and addressing phase ambiguity from 2π wrapping.