Three-dimensional tracking using a single-spot rotating point spread function created by a multiring spiral phase plate

Abstract

Significance: Three-dimensional (3D) imaging and object tracking is critical for medical and biological research and can be achieved by multifocal imaging with diffractive optical elements (DOEs) converting depth ( $z$ ) information into a modification of the two-dimensional image. Physical insight into DOE designs will spur this expanding field.

Aim: To precisely track microscopic fluorescent objects in biological systems in 3D with a simple low-cost DOE system.

Approach: We designed a multiring spiral phase plate (SPP) generating a single-spot rotating point spread function (SS-RPSF) in a microscope. Our simple, analytically transparent design process uses Bessel beams to avoid rotational ambiguities and achieve a significant depth range. The SPP was inserted into the Nomarski prism slider of a standard microscope. Performance was evaluated using fluorescent beads and in live cells expressing a fluorescent chromatin marker.

Results: Bead localization precision was $<25\mathrm{nm}$ in the transverse dimensions and $\le 70\mathrm{nm}$ along the axial dimension over an axial range of $6\mu m$ . Higher axial precision ( $\le 50\mathrm{nm}$ ) was achieved over a shallower focal depth of $2.9\mu m$ . 3D diffusion constants of chromatin matched expected values.

Conclusions: Precise 3D localization and tracking can be achieved with a SS-RPSF SPP in a standard microscope with minor modifications.

Keywords: diffractive optical elements; fluorescence; imaging; microscopy; three dimensions; tracking.