Low-cost, open-access quantitative phase imaging of algal cells using the transport of intensity equation.

Phase microscopy allows stain-free imaging of transparent biological samples. One technique, using the transport of intensity equation (TIE), can be performed without dedicated hardware by simply processing pairs of images taken at known spacings within the sample. The resulting TIE images are quantitative phase maps of unstained biological samples. Therefore, spatially resolved optical path length (OPL) information can also be determined. Using low-cost, open-source hardware, we applied the TIE to living algal cells to measure their effect on OPL. We obtained OPL values that were repeatable within species and differed by distinct amounts depending on the species being measured. We suggest TIE imaging as a method of discrimination between different algal species and, potentially, non-biological materials, based on refractive index/OPL. Potential applications in biogeochemical modelling and climate sciences are suggested.

Adapting the 3D-printed Openflexure microscope enables computational super-resolution imaging.

We report on a 3D printed microscope, based on a design by the Openflexure project, that uses low cost components to perform fluorescence imaging. The system is sufficiently sensitive and mechanically stable to allow the use of the Super Resolution Radial Fluctuations algorithm to obtain images with resolution better than the diffraction limit. Due to the low-cost components, the entire system can be built for approximately $1200.

On the frequency-doubled conically-refracted Gaussian beam.

A Potassium Titanyl Phosphate (KTP) crystal has been used in conjunction with a 10-ps pulsed laser to produce a frequency-doubled conically-refracted Gaussian beam. The 'free' and 'forced' beams that make up the scheme for nonlinear conical refraction were readily observable in non-phase-matched conditions. The dependency of the frequency-doubled beam patterns on the incident beam polarization, which until now has remained unexplored, was examined in detail. We have also revealed the existence of two orthogonally polarized 'free' rays for particular orientations of the incident beam polarization.

Azimuthally and radially polarized light in conical diffraction.

Azimuthal and radial polarization states of light are used to produce conical diffraction (CD) from a KGd(WO4)2 crystal. The patterns produced in the ring plane in each case display marked differences than those seen when linearly polarized incident light is used, with the production of a splitting of the CD ring into two concentric rings of equal intensity. The free space evolution for each type of polarization state is also experimentally recorded and investigated. Comparison with theory shows agreement with the experimentally observed results.

Evolution of conically diffracted Gaussian beams in free space.

We present results of our observations on the free space evolution of conically diffracted beams from both single and cascade systems using various combinations of four biaxial crystals of the monoclinic double tungstate family [KGd(WO4)2]. Longitudinal shifts and radii of the Hamilton-Lloyd pair of rings were measured. In each case, the symmetric - forward and backward - evolution of the beam in free space from its focal image plane was monitored and quantified. Theoretical ring plane patterns based on a recently presented theoretical model are also compared to experimental patterns and found to be in good agreement.

Left- and right-circularly polarized light in cascade conical diffraction.

A cascade conical diffraction system consisting of three optically biaxial KGd(WO4)2 crystals is considered. The effect of left- and right-handed circularly polarized incident light on the ring patterns produced away from the focal image plane of the system, the plane in which the incident beam waist would be focused if the crystals were isotropic, is investigated. Images and intensity distributions for scaled distances (ζ values) of 2.75, 3.00, and 3.25 from the focal image plane are presented. A discrepancy between the patterns produced depending on the handedness of the incident beam is observed in agreement with the recent theoretical predictions.