Using the Gouy phase anomaly to localize and track bacteria in digital holographic microscopy 4D images

Described over 100 years ago, the Gouy phase anomaly refers to the additional π phase shift that is accumulated as a wave passes through focus. It is potentially useful in analyzing any type of phase-sensitive imaging; in light microscopy, digital holographic microscopy (DHM) provides phase information in the encoded hologram. One limitation of DHM is the weak contrast generated by many biological cells, especially unpigmented bacteria. We demonstrate here that the Gouy phase anomaly may be detected directly in the phase image using the z-derivative of the phase, allowing for precise localization of unlabeled, micrometer-sized bacteria. The use of dyes that increase phase contrast does not improve detectability. This approach is less computationally intensive than other procedures such as deconvolution and is relatively insensitive to reconstruction parameters. The software is implemented in an open-source FIJI plug-in.