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Data Calibration |
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All data are presented in a raw, uncalibrated format. While one of the purposes of this database is to encourage calibration research, we provide our most commonly used calibration method here.
There are two main purposes of calibration: (i) to convert the Sab values measured by the VNA into field values (u = Ez) used in the inversion algorithms, and (ii) to eliminate/compensate for modeling error and other errors. We define modeling error as arrising from any mismatch between the assumed computational model and the physical measurement system (e.g., a 2D scalar Green's function vs. physical 3D vector wave propagation).
To perform the calibration, we first measure scattered data from a known cylinder placed in the centre of the chamber. Typically, we use a metallic cylinder, but other objects are also possible. We denote these S parameters as S^sct,known_ab . Next, we consider the S parameters from the object we wish to image (e.g., the e-phantom) and we denote these S parameters as S^sct,unknown_ab . Assuming a 2D line source generated incident field, we calculate the analytic scattered fields (under the 2D TM assumption) from the known object, and label them u^sct,known. These values are easily calculated analytically for metallic or dielectric cylinders [16]. Finally, the calibrated measured fields for the unknown target are calculated by
The process is repeated independently for every transmit/receive pair. This method
of calibration will eliminate any errors which are constant over the two measurements
(S^sct_ab known and unknown). Examples of these types of `removable' errors include
cable losses and phase shifts, or mismatches at connectors. However, there are other
factors in the measurement which are not constant between the two measurements,
and thus not entirely removed via the above calibration method. For example,
the antenna factor is not guaranteed to be the same for the known and unknown
measurements (as the system is operating in the near-field). Another error which
is not entirely compensated for is the antenna coupling, as the coupling will change
when different scatterers are present in the chamber. For these reasons, we expect
that the known calibration object should be as similar as possible to the expected
class of unknown targets.