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Context. Understanding complex phenomena and unsolved problems in modernastronomy requires wider-bandwidth observations. The current technique fordesigning and fabricating an astronomical instrument potentially provides suchobservations with higher efficiency and precision than in the past.Higher-order modes in an instrument associated with wider bandwidths have beenreported, which may degrade observation precision. Aims. To reduce theunfavorable degradation, we need to quantify the higher-order propagationmodes, though their power is too difficult to measure directly. Instead of thedirect mode measurement, we aim at developing a method based on measurableradiation patterns from an instrument of interest. Method. Assuming a linearsystem, whose radiated field is determined as a superposition of the modecoefficients in an instrument, we obtain a coefficient matrix connecting theinside modes and the outside radiated field and calculate the pseudo-inversematrix. To understand the estimation accuracy of the proposed method, wedemonstrate two cases with numerical simulations, axially-corrugated horn caseand offset Cassegrain antenna case, and investigate the effect of random errorson the accuracy. Results. Both cases showed the estimated mode coefficientswith a precision of 10e-6 with respect to the maximum mode amplitude and 10e-3degrees in phase, respectively. The calculation errors were observed when therandom errors were smaller than 0.01 percent of the maximum radiated fieldamplitude. The demonstrated method works independently of the details of asystem. Conclusions. The method can quantify the propagation modes inside aninstrument and will be applicable to most of linear components and antennas.This method can be employed for a general purpose, such as diagnosis of feedalignment and higher-performance feed design.

Quantification of propagation modes in an astronomical instrument from its radiation pattern