Synthetic optical holography with nonlinear-phase reference.

Synthetic optical holography (SOH) provides efficient encoding of the complex optical signal, both amplitude and phase, for scanning imaging methods. Prior demonstrations have synthesized reference fields with a plane-wave-like linear variation of the phase with position. To record large images without probe-mirror synchronization, a long-travel, closed-loop reference mirror stage has been required. Here we present SOH with a synthetic reference wave with sinusoidal spatial variation of the phase. This allows the use of open loop, limited mirror travel range in SOH, and leads to a novel holographic inversion algorithm. We validate the theory with scans of graphene grain boundaries from a scanning near-field optical microscope, for which SOH has been shown to drastically increase scan speeds [Nat. Commun. 5, 3499 (2014)].