3806 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 12, DECEMBER 2011
Optimum Two-Dimensional Uniform Spatial
Sampling for Microwave SAR-Based
NDE Imaging Systems
Joseph T. Case, Member, IEEE, Mohammad Tayeb Ghasr, Member, IEEE, and Reza Zoughi, Fellow, IEEE
Abstract—Microwave imaging systems for nondestructive eval-
uation, based on 3-D synthetic aperture radar (SAR) techniques,
utilize either a real aperture, composed of many antennas mounted
next to one another, or a synthetic aperture, generated by raster
scanning a single antenna. To obtain a quality SAR image, the
spatial sampling must be dense enough to accurately sample the
electric field reflected from a target. Conversely, the quantity of
spatial samples may be optimally reduced, resulting in reduced
system complexity and required resources for systems employing
real apertures and reduced imaging time for synthetic aperture
systems. In the literature, it has been reported that the optimum
sampling step size is equal to the theoretical resolution, as per the
Nyquist rate. It has also been reported that an image generated
using a sampling step size equal to the theoretical resolution
may not possess the same spatial resolution as predicted. Also,
as expected and reported, resolution is dependent upon the dis-
tance between the target and the aperture, aperture dimensions,
and antenna beamwidth. However, existing formulations of SAR
resolution do not account for all of the physical characteristics
of a measurement (e.g., 2-D limited-size aperture, electric field
decreasing with distance from the measuring antenna, etc.). This
paper presents a theoretical formulation of resolution and a study
into optimum uniform spatial sampling by analyzing simulated
3-D SAR images according to metrics representing image quality,
namely, half-power resolution and RMS error between practically
sampled images and an ideally sampled image. The results of this
simulation demonstrate optimum sampling given design require-
ments that fully explain resolution dependence on sampling step
size. Also, it is found that there is additional widening of the
2-D spectral estimation of the data due to the aperture-limited
nature of the measurements, which further influences the choice
of sampling step size. Subsequently, the simulated results are
compared to experimental results corroborating the efficacy of the
formulation. Finally, design curves and procedures are proposed
for selecting sampling step size as per resolution requirements.
Index Terms—Array, microwave imaging, nondestructive eval-
uation (NDE), optimum sampling, synthetic aperture radar
(SAR).
I. INTRODUCTION
M
ICROWAVE and millimeter-wave imaging techniques
for nondestructive evaluation (NDE) using 3-D synthetic
Manuscript received June 14, 2011; revised August 12, 2011; accepted
August 13, 2011. Date of publication October 17, 2011; date of current version
November 9, 2011. The work of J. T. Case was supported by the National
Science Foundation through a Graduate Research Fellowship. The Associate
Editor coordinating the review process for this paper was Dr. Matteo Pastorino.
The authors are with the Applied Microwave Nondestructive Testing Lab-
oratory, Electrical and Computer Engineering Department, Missouri Uni-
versity of Science and Technology, Rolla, MO 65409-0040 USA (e-mail:
j.t.case@mst.edu; m.t.ghasr@mst.edu; zoughi@mst.edu).
Digital Object Identifier 10.1109/TIM.2011.2169177
Fig. 1. Two-dimensional scanning system with aperture inspecting a target
below (units are in λ).
aperture radar (SAR) processing have shown great promise in a
wide range of applications, including but not limited to imaging
of composite structures [1] and low-dielectric-contrast media
[2], [3]. It is of great interest to optimize the measurement step
size on a 2-D grid for a wideband microwave 3-D SAR imaging
system, capable of producing volumetric images, for a wide
range of possible targets. This optimization reduces system
complexity, required resources, and imaging time.
Fig. 1 s hows the schematic of a typical measurement used
in NDE imaging applications where a transceiver antenna (not
shown), with a certain beamwidth (θ
b
), is raster scanned over
the target at a certain distance/range (h). This scanning region
constitutes the dimensions of the measurement aperture, here-
after referred to as the aperture. In general, the measurements
taken at coordinates (x
,y
) are constrained to a uniform rec-
tangular grid bounded by sides a
x
and a
y
with measurement
spacing of ∆x
and ∆y
in the x- and y-directions, respectively.
Alternatively, this aperture may be constructed as a collection of
small antennas constituting an imaging array. Such an aperture
is considered a real aperture, whereas an aperture formed by
raster scanning is a synthetic aperture. In either case, the
measurement consists of measuring the complex microwave
reflection coefficient (or scattered electric field distribution)
over a set of discrete frequencies (f ) in a desired bandwidth.
The use of SAR techniques for NDE applications is somewhat
unique since the aperture is relatively small and the relative
target distance/range (h) is also small as compared to typical
SAR applications in airborne or spaceborne radars.
Spatial resolution and optimum sampling requirements for
SAR images have been extensively discussed in the literature
[4]–[6]. However, spatial resolution, as described, is not neces-
sarily what is observed in practice for NDE, as will be shown
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