As light, or any other wave, converges into focus, the apparent wavelength of the wave increases as the phase velocity surpasses the speed of propagation in that medium. For a Gaussian beam, this causes a phase change Δϕ equal to ±π. This phenomenon, named the Gouy phase shift, can be observed when a plane wave is refracted by a lens and caused to come into focus. The location where this phase shift occurs in the axial direction is the focal length of the lens. Many biological structures are curved and thus can be modeled as lenslets. Bacterial cells have a radius of curvature that can be readily determined from high resolution images. A plane wave passing through them would be refracted and converge at some point after interacting with the bacterium. Altering the refractive index of the cells will change the effective focal length of the lenslet and thus the location of the Gouy phase shift. We have previously shown that purified gas vesicles (GVs) can be transfected into bacterial cells, altering the refractive index in large areas of the cell. In this work, we use off-axis digital holographic microscopy to measure the effect of GVs on the index of refraction of Salmonella cells and relate this to changes in the Gouy phase shift. By observing the location of this phase shift relative to the location of the bacterium, the GV concentration within the cell can be estimated, highlighting the potential of GVs as a quantitative contrast agent for QPI.
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