Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty amplification due to density/refractive-index gradients in
  volumetric PTV and BOS experiments   We theoretically analyze the effect of density/refractive-index gradients on
the measurement precision of Volumetric Particle Tracking Velocimetry (V-PTV)
and Background Oriented Schlieren (BOS) experiments by deriving the Cramer-Rao
lower bound (CRLB) for the 2D centroid estimation process. A model is derived
for the diffraction limited image of a particle or dot viewed through a medium
containing density gradients that includes the effect of various experimental
parameters such as the particle depth, viewing direction and f-number. Using
the model we show that non-linearities in the density gradient field lead to
blurring of the particle/dot image. This blurring amplifies the effect of image
noise on the centroid estimation process, leading to an increase in the CRLB
and a decrease in the measurement precision. The ratio of position
uncertainties of a dot in the reference and gradient images is a function of
the ratio of the dot diameters and dot intensities. We term this parameter the
Amplification Ratio (AR), and we propose a methodology for estimating the
position uncertainties in tracking-based BOS measurements. The theoretical
predictions of the particle/dot position estimation variance from the CRLB are
compared to ray tracing simulations with good agreement. The uncertainty
amplification is also demonstrated on experimental BOS images of flow induced
by a spark discharge, where we show that regions of high amplification ratio
correspond to regions of density gradients. This analysis elucidates the
dependence of the position error on density and refractive-index gradient
induced distortion parameters, provides a methodology for accounting its effect
on uncertainty quantification and provides a framework for optimizing
experiment design.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom