IEEE Aerospace and Electronic Systems Magazine - October 2020 - 47

Nanzer et al.
function at the center; the resulting response has a strong
peak at the center, and is low otherwise, indicating a
strong spatiotemporal incoherence. It is important that the
field be spatially incoherent between resolution bins, and
temporally incoherent between time bins for the Fourier
imaging process to produce reliable images.
The antenna locations define a spatial frequency sampling function given by the different antenna separations.
The sampling function for the 1-D array is shown in
Figure 6(a). An example of 1-D scene is shown in Figure 6
(b), and its corresponding visibility over normalized spatial frequency space (u) and time is shown in Figure 6(c);
it can be seen that the majority of the information is contained at low spatial frequencies (where u $ 0), however,
the higher spatial frequencies contain the information
needed for spatial resolution. The sampled visibility is the
product of the scene visibility and the sampling function,
which is shown in Figure 6(d). Almost all of the low spatial frequency content has been retained; whereas the high
spatial frequency content is reduced, there is less information at these frequencies, indicated by the lower amplitude, and thus does not contribute as much to the image
reconstruction. It is clear that appropriate design of the
sampling function is critical to successfully reconstruct
images and capture a large amount of the image spatial
frequency information. Figure 6(e) shows the reconstructed image that is integrated over the length of the
time duration. The scene reconstruction matches well with
the original scene with only 3.4% root-mean-square error,
despite the fact that the element locations were chosen
randomly and the array contained only 9% of the elements
of a filled aperture.

5.85-GHZ EXPERIMENTAL AIM MEASUREMENTS
Experimental validation of the AIM imaging approach
was conducted at two frequency bands to demonstrate the
feasibility of imaging simple scenes. The first system was
a 2-D experimental imaging system using three transmitters emitting noise signals centered at 5.85 GHz. The
transmitter locations were not moved, whereas the receive
antennas were sequentially moved to the locations in an
inverted T-array. Because AIM imaging works by crosscorrelating the collected signals pairwise, it is possible to
synthesize a larger array by sequentially collecting signals
in pairs and moving the elements to cover all baselines
desired in the full array. The 5.85 GHz experimental configuration that can be seen in Figure 7(a). The block diagram of the experimental configuration can be seen in
Figure 7(b).
The noise signals were generated using a Keysight
M8190 Arbitrary Waveform Generator. The noise was
generated at a carrier frequency of 5.85 GHz with approximately 1 GHz of bandwidth to achieve a flat frequency
OCTOBER 2020

Figure 6.
(a) Sampling function of the random array. (b) Example scene
to be imaged. (c) Spatiotemporal visibility of the example scene.
(d) Sampled visibility (product of the sampling function and the
scene visibility), which despite sampling is very close to the real visibility. (e) Reconstructed image from the 30-element random array,
with a root-mean-square error of 3.4% from the original image.

response at a receive bandwidth of 25 MHz, and because
only two independent outputs are available on the M8190,
one of the outputs was split into two using a wideband
splitter to generate two noise signals. One output of the

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