Signal Processing - September 2016 - 112

also demonstrated promise in overcoming important SWaPpoints in the scene f into two regions, those that likely contain
related issues. This is particularly important at millimeter
o and those that don't.
wavelengths where high image resolution is typically
These examples represent extremes in which all processachieved with large apertures and lens-based systems that
ing is performed in the physical domain. The vast expanse of
scale volumetrically and can present challenges from a portawork in optical design speaks to the difficulty in realizing the
bility perspective.
former, and the short-lived history of optical pattern recognition in the 1960s and 1970s underscores problems with the latter. Thus, the application space of current interest is the one in
Extended depth-of-field imaging
which the processing burden is shared.
Most mmW imaging systems have a narrow DoF, the disWe delineate computational imaging into three broad applitance over which an object is considered in focus. Consider
cations: enhancing cameras, enhancing images (also known as
the application of concealed weapon detection by imaging
computational photography), and enhancthrough clothing using mmW imagers. If
ing human cognition. Reference to cameras
individuals are moving toward an imager
The goal in designing a
in the first application emphasizes the conthrough a corridor, the weapons will be
conventional imaging
ventional notion of a camera as a device that
visible only for the brief moment when
produces a recognizable representation of a
they were in the DoF. This is one reason
system is to produce a
scene. An enhanced camera uses computaindividuals are scanned in portals. Howresponse that is as close
tion to improve some aspect of the camera,
as possible to a d-function ever, extensions to scanning over a volfor example, reduce its physical depth while
ume could provide scanning without
over all expected
maintaining optical performance [17], [18],
creating bottlenecks, for example, in a
operating conditions.
increase its spatial resolution [19], or expand
public marketplace where security is
its dynamic range [20]. Others have considimportant but a visible display of security
ered computation as a hybrid element to reduce or overcome
might be counterproductive. Computational imaging methaberrations [21], [22].
ods [23], [30], [31] can be used to extend the DoF of mmW
Computation has also been used to filter or accentuate
imaging systems. One such method was developed in [5] to
information within a scene. For example, combining unique
extend the DoF of a passive mmW imaging system to allow
optics with postdetection processing allows one to extend an
for operation over a volume. In what follows, we review this
imager's depth of field (DoF) [23]. Other examples include
computational imaging method for extending the DoF of a
modulating a shutter during an exposure to reduce motion blur
passive mmW imager.
[24]. Computation in combination with new sensing modalities
In [5], a 94-GHz Stokes-vector radiometer was used to
allows humans to "see" polarimetric information [25], spectral
form images by raster scanning the system's single beam.
information [26], and three-dimensional information [27] in a
One can model the 94-GHz imaging system as a linear,
manner similar to how they "see" through a human body using
spatially incoherent, quasi-monochromatic system. The inmagnetic resonance.
tensity of the detected image can be represented as a conWith regard to enhancing cognition, some within the imagvolution between the intensity of the image predicted by the
ing community [28], [29] seek to extract information from
geometrical optics with the system point spread function
scenes directly using physical means and postdetection pro(PSF) [32]. Under these conditions, (1) is a valid representacessing but in a manner different from pure imaging processtion with H the incoherent PSF. H accounts for wave propaing, i.e., image detection followed by image processing, and
gation through the aperture and is related to the magnitude
from pure optical matched filtering. Such task-specific imagsquare of the inverse Fourier transform of the system pupil
ers require automatic feedback, dynamic elements, and adapfunction P(u, v).
tive processing to realize [29].
Displacement of an object from the nominal object plane of
the imaging system introduces a phase error in the pupil function
that increases the width of a point response and produces an outComputational mmW imaging approaches
of-focus image. For a 94-GHz imager with an aperture diameter
Many mmW imaging systems have practical considerations
that limit or preclude their use from surveillance and defenseD = 24 in and object distance d o = 180 in, DoF . 17.4 in,
related applications. In this section, we highlight several
which ranges from 175.2 to 192.6 in (see Figure 4).
examples of computational mmW imaging methods that have
The DoF of this imager was extended using a cubic phase
been used to enhance imaging capabilities and to address
element in conjunction with postdetection processing. The
some of these considerations, like size-weight-and-power
cubic phase element P(u, v) is
(SWaP), imaging speed, and limited DoF. These are important
considerations for many potential applications, like stand-off
(4)
P (u, v) = exp [ ji (u, v)] rect ` u , v j,
Wu Wv
imaging and surveillance of moving targets where high angular resolution, high image frame rates, and an extended DoF
where
are keys to mission success. Computational imagers, like the
2u 3 + 2v 3E
i (u, v) = (rc) ;c
m c
m
distributed aperture imaging system discussed below, have
Wu
Wv
112

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September 2016

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