Phase of white light and its compatibility to the optical path

The phase of monochromatic light directly relates to the optical path difference (OPD), but finding this connection for spectrally broadband light is challenging. Due to a missing concept of the compatibility between the phase of randomly fluctuating fields and the OPD, demanding scanning is the only proven way for a highly accurate OPD measurement in white light. Here, we use the self-coherence function (SCF) of the spatially incoherent light to reveal the connection between the white-light phase and the OPD. Our method uses an associated field assigned to the SCF to mimic the intensity oscillation of a correlation pattern. The associated field allows restoring a cumulative OPD integrated into the SCF across all spectral constituents. The method is essential for quantitative phase microscopy, in which the SCF is available even in white light, but its processing beyond the quasi-monochromatic approach is still lacking. Improper assessment of the white-light phase may result in a loss of measurement accuracy, as we demonstrate theoretically and experimentally. Deploying our method in coherence-controlled holographic microscopy, we measured the cumulative OPD in the broadband light with a strongly asymmetric spectrum (bandwidth of 150 nm), achieving accuracy better than 5 nm in the measuring depth range of 2 µm.