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.
Quantitative phase imaging (QPI) has many applications in a broad range of disciplines from astronomy to microbiology. QPI is often performed by optical interferometry, where two coherent beams of light are used to produce interference patterns at a detector plane. Many algorithms exist to calculate the phase of the incident light from these recorded interference patterns as well as enhance their quality by various de-noising methods. Many of these de-noising algorithms, however, corrupt the quantitative aspect of the measurement, resulting in phase contrast images. Among these phase calculation techniques and de-noising algorithms, none approach the optimization of phase measurements by theoretically addressing the various sources of error in its measurement, as well as how these errors propagate to the phase calculations. In this work, we investigate the various sources of error in the measurements required for QPI, as well as theoretically derive the influence of each source of error on the overall phase calculation for three common phase calculation techniques: the four bucket/step method, three bucket/step method, and the Carré method. The noise characteristics of each of these techniques are discussed and compared using error parameters of a readily available CCD sensor array. Additionally, experimental analysis is conducted on interferograms to investigate the influence of speckle noise on the phase measurements of the three algorithms discussed.
Understanding when, how, and if bacteria swim is key to understanding critical ecological and biological processes, from carbon cycling to infection. Imaging motility by traditional light microscopy is limited by focus depth, requiring cells to be constrained in z. Holographic microscopy offers an instantaneous 3D snapshot of a large sample volume, and is therefore ideal in principle for quantifying unconstrained bacterial motility. However, resolving and tracking individual cells is difficult due to the low amplitude and phase contrast of the cells; the index of refraction of typical bacteria differs from that of water only at the second decimal place. In this work we present a combination of optical and sample-handling approaches to facilitating bacterial tracking by holographic phase imaging. The first is the design of the microscope, which is an off-axis design with the optics along a common path, which minimizes alignment issues while providing all of the advantages of off-axis holography. Second, we use anti-reflective coated etalon glass in the design of sample chambers, which reduce internal reflections. Improvement seen with the antireflective coating is seen primarily in phase imaging, and its quantification is presented here. Finally, dyes may be used to increase phase contrast according to the Kramers-Kronig relations. Results using three test strains are presented, illustrating the different types of bacterial motility characterized by an enteric organism (Escherichia coli), an environmental organism (Bacillus subtilis), and a marine organism (Vibrio alginolyticus). Data processing steps to increase the quality of the phase images and facilitate tracking are also discussed.