  The formation of twin images in digital inline holography (DIH) prevents the
placement of the focal plane in the center of a sample volume for DIH-based
particle tracking velocimetry (DIH-PTV) with a single camera. As a result, it
is challenging to apply DIH-PTV for flow measurements in large-scale laboratory
facilities or many field applications where it would otherwise be desirable due
to the low cost and compact setup. Here we introduce holographic astigmatic PTV
(HAPTV) by inserting a cylindrical lens in the optical setup of DIH-PTV,
generating distorted holograms. Such distortion is subsequently utilized in a
customized reconstruction algorithm to distinguish tracers positioned on
different sides of the focal plane which can in turn be placed in the middle of
a sample volume. Our HAPTV approach is calibrated under high (1 um/pixel) and
low (10 um/pixel) magnifications with an error standard deviation of 4.2 um
(one particle diameter) and 120.7 um (~5 times the particle diameter),
respectively. We compare the velocity field of a laminar jet flow obtained
using HAPTV and conventional PIV to illustrate the accuracy of the technique
when applied to practical flow measurement applications. The work demonstrates
that HAPTV improves upon the depth of field of conventional astigmatic PTV and
enables the implementation of DIH-based PTV for in situ applications.
