Particles 3D tracking with large axial depth by using the 2π-DH-PSF
Hangfeng Li, Famin Wang, Tongda Wei, Xin Miao, Yu Cheng, Xinpei Pang, Keming Jiang, Wei Huang, Yunhai Zhang
Abstract
We propose a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> -double-helix point spread function ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> -DH-PSF) using the Fresnel zone approach that can rotate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> rad. When 16 Fresnel zones are used, the particles can be tracked in the axial range of 10 µm in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>100</mml:mn> </mml:mrow> </mml:mrow> <mml:mo>×</mml:mo> </mml:math> microscopy imaging system ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">N</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1.4</mml:mn> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>514</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> ). We measured the diffusion coefficient of nanospheres in different concentrations of glycerol with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> -DH-PSF, and the error between the measured results and theoretical value was within 10%, indicating the superior performance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> -DH-PSF in 3D localization imaging of nanoparticles. When combined with the defocus phase, the rotation angle can reach <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:mrow> <mml:mi>π</mml:mi> </mml:math> rad, four times that of the conventional DH-PSF.