  In modern radio astronomy, one of the key technologies is to widen the
frequency coverage of an instrument. The effects of higher-order modes on an
instrument associated with wider bandwidths have been reported, which may
degrade observation precision. It is important to quantify the higher-order
propagation modes, though their power is too small to measure directly. Instead
of the direct measurement of modes, we make an attempt to deduce them based on
measurable radiation patterns. Assuming a linear system, whose radiated field
is determined as a superposition of the mode coefficients in an instrument, we
obtain a coefficient matrix connecting the modes and the radiated field and
calculate the pseudo-inverse matrix. To investigate the accuracy of the
proposed method, we demonstrate two cases with numerical simulations,
axially-corrugated horn case and offset Cassegrain antenna case, and the effect
of random errors on the precision. Both cases showed the deduced mode
coefficients with a precision of 10e-6 with respect to the maximum mode
amplitude and 10e-3 degrees in phase, respectively. The calculation errors were
observed when the random errors were smaller than 0.01 percent of the maximum
radiated field amplitude, which was a much lower level compared with
measurement precision. The demonstrated method works independently of the
details of a system. The method can quantify the propagation modes inside an
instrument and will be applied to most of linear components and antennas, which
leads to various applications such as diagnosis of feed alignment and
higher-performance feed design.
