J. Nogueira Æ A. Lecuona Æ P. A. Rodrı
Limits on the resolution of correlation PIV iterative methods.
Received: 7 October 2004 / Revised: 16 May 2005 / Accepted: 21 May 2005 / Published online: 6 July 2005
Ó Springer-Verlag 2005
Abstract The spatial resolution of correlation particle
image velocimetry (PIV) is a frequently addressed issue
that still raises scientiﬁc interest. In conventional non-
iterative PIV, the spatial resolution limits are of com-
mon knowledge (Willert and Gharib (1991) Exp Fluids
10:181–193; Raﬀel et al. (1998) ISBN 3-540-63683-8,
Springer, Berlin Heidelberg New York, among others).
On the contrary, those advanced iterative multipass
methods that use image distortion techniques or multi-
grid techniques present a more complex scenario. One of
the concepts that raises more debate is the limiting eﬀect
of the interrogation window size. This paper focuses on
the subject, trying to clarify key points. The results
indicate that iterative algorithms using an appropriate
weighting function eliminate the window size from the
ensemble of spatial resolution limits.
The ﬁrst applications of digital particle image veloci-
metry (PIV) were mainly focused on accurate descrip-
tions of smooth ﬂow ﬁelds (Willert and Gharib 1991,
among others). This means large wavelengths and small
gradients in the spatial domain. It justiﬁes the common
tendency to evaluate PIV accuracy in ﬁelds of uniform
displacements (Westerweel et al. 1997; Huang et al.
1997). In parallel to these studies, the users of PIV on
many industrial and scientiﬁc applications progressively
request greater spatial resolution and the ability to cope
with larger gradients (Raﬀel et al. 1992; Willert et al.
1996; Cotroni et al. 2000; Di Felice et al. 2001; Lecuona
et al. 2004). In the beginning of PIV development, some
of the measurements in industrial facilities were per-
formed partially sacriﬁcing accuracy, but in favor of
overall ﬁeld description, the main strong point of PIV.
At the present moment, the development of advanced
processing algorithms with increasing capabilities is
allowing results that are progressively more accurate.
Of these two requirements (i.e., spatial resolution and
the ability to cope with large displacement gradients),
this paper focuses on the fundamentals of spatial reso-
lution for correlation-based PIV. Reasoning about par-
ticle displacement gradients can be found elsewhere, for
conventional systems (Keane and Adrian 1993; Huang
et al. 1993, among others) or for advanced systems
(Lecuona et al. 2004, among others).
In contrast with the limiting role of the window size
in the resolution of conventional correlation PIV
methods, Nogueira et al. (1999) obtained resolutions far
below the window size using an iterative multipass cor-
relation PIV with a particular weighting function. The
concept has motivated some interest and debate.
The results of this paper show that the limitation is
related to the way that the information is processed,
instead of the window size itself. In particular, Sect. 3
shows that the information of scales smaller than the size
of the interrogation window can endure the interroga-
2 Physical limits for spatial resolution in PIV
To focus on the resolution limits of an algorithm, it is
convenient to review the presence of non-recoverable
losses of information. Three processes are considered in
this section: (1) sampling; (2) a single average; and (3)
moving average, as an extension to the previous one.
According to the Nyquist sampling theorem, it is
impossible to distinguish between the output from
J. Nogueira (&) Æ A. Lecuona Æ P. A. Rodrı
Department of Thermal and Fluids Engineering,
Universidad Carlos III de Madrid, c/ Butarque 15,
s, Madrid, Spain
Experiments in Fluids (2005) 39: 305–313