29
3.3 Discussion
The THz Fourier imaging scheme in this chapter could be useful for quality control
applications, such as detection of point impurities in manufactured products, because
Fourier-domain measurements are particularly sensitive to sharp point-like features.
The CSPR reconstruction results demonstrate the applicability of our imaging
scheme not only to pulsed THz imaging systems but also to continuous-wave sys-
tems, in which phase information is typically not available. The latest research on
THz CW imaging requires high-power sources (>10 mW), such as quantum-cascade
lasers (QCLs) operating at low temperature (~30K), because the focal-plane mi-
crobolometer array used for imaging has low sensitivity at THz frequencies [3]. In
contrast, the Fourier imaging technique with CSPR can use a single-pixel THz detec-
tor with much higher sensitivity to enable imaging with a low-power CW source.
In both the CS and CSPR examples in this chapter, the reduction of measure-
ments enabled by compressive sensing can significantly reduce the image acquisition
time. Traditional THz imaging systems scan point by point in the space domain. By
application of the CSPR theorem, only O(k2 log(4∕V2∕A:2)) locations in the frequency
(modulus) domain need to be scanned if the signal is sparse in space and has к nonzero
values. Because a scanner must stop at every location to make a measurement, taking
fewer measurements will result in less scan time. In addition, the scanner does not
have to travel as far, either. The path length traveled by a scanner to k2 random
points on an N × N square lattice is, on average, .93kN [70]. For к ≪ N, this is a
significant improvement over the N2 distance required for a full raster scan. Assum-
ing a 0.1 m∕s constant scanning speed of the receiver with no signal averaging, a full
raster scan takes around 41 seconds. Scanning a random subset of 500 measurements
requires only 13 seconds, i.e., a 2/3 reduction of the total acquisition time.
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